El Gemayel Charbel

Abouchi Nacer

Zaouk Doumit

Fabrice -Constantin Jumel

Joseph

Professor, Saint M Toni Sayah

Professeur Rapporteur M Richard Grisel

M Cyril Condemine

Docteur

Professor, Lebanese M Youssef Zaatar

Associate Professor, CPE M Fabrice Jumel

Maître De Conférences

Cpe Lyon

Maître Co-Directeur M Joseph Constantin

Professor, Lebanese M Doumit Zaouk

Professeur, CPE M Nacer Abouchi

Lyon Directeur

El Gemayel

Jumel Fabrice -Constantin

Joseph Membre

Professor, M Richard Grisel

Doctor, M Cyril Condemine

Lyon

Associate Professor, Lebanese M Joseph Constantin

Professor, CPE M Nacer Abouchi

2014ISAL0135 THESE EN COTUTELLE Pour obtenir le grade de Docteur délivré par

Keywords: ; application aux dispositifs médicaux embarqués modeling, simulation, medical systems, microcontroller, quality of services, architecture, mathematical model, diagnosis, control, in-silico, virtual patients, clinical case

A Biomedical research seeks good reasoning for solving medical problems, based on intensive work and great debate. It often deals with beliefs or theories that can be proven, disproven or often refined after observations or experiments. The problem is how to make tests without risks for patients, including variability and uncertainty on a number of parameters (patients, evolution of disease, treatments …). Nowadays, medical treatment uses more and more embedded devices such as sensors, actuators, and controllers. Treatment depends on the availability and well-functioning of complex electronic systems, comprising thousands of lines of codes. A mathematical representation of patient or device is presented by a number of variables which are defined to represent the inputs, the outputs and a set of equations describing the interaction of these variables.

The objective of this research is to develop tools and methodologies for the development of embedded systems for medical fields. The goal is to be able to model and jointly simulate the medical device as well the human body, at least the part of the body involved in the medical device, to analyze the performance and quality of service (QoS) of the interaction of the device with the human body. To achieve this goal our study focused on several points described below.

After starting by defining a prototype of a new global and flexible architecture of mathematical model of human body, which is able to contain required data, we begin by proposing a new global methodology for modeling and simulation human body and medical systems, in order to better understand the best way to model and simulate these systems and for detecting performance and the quality of services of all system components. We use two techniques that help to evaluate the calculated QoS value. The first one calculates an index of severity which indicates the severity of the case studied. The second one using a normalization function that represents the simulation as a point in order to construct a new error grid and use it to evaluate the accuracy of value measured by patients.

Using Keil development tools designed for ARM processors, we have declared a new framework in the objective to create a new tester model for the glucose-insulin system, and to define the basic rules for the tester which has the ability to satisfy well-established medical decision criteria. The advantage of using Keil in our work is to define a model that works with embedded C language and can be implemented in a microcontroller.

Résumé vi-1

Résumé

Les progrès des technologies de l'information et de la communication, des MEMS, des capteurs, actionneurs, etc. ont permis l'émergence de différents dispositifs biomédicaux. Ces nouveaux dispositifs, souvent embarqués, contribuent considérablement à l'amélioration du diagnostic et du traitement de certaines maladies, comme le diabète par exemple. Des dispositifs embarqués encore plus complexes sont en cours d'élaboration, leur mise en oeuvre nécessite des années de recherche et beaucoup d'expérimentation. Le coeur artificiel, encore en phase de réalisation, est un exemple concret de ces systèmes complexes. La question de la fiabilité, du test de fonctionnement et de sureté de ces dispositifs reste problématique et difficile à résoudre. Plusieurs paramètres (patient, évolution de la maladie, alimentation, activité, traitement, etc.) sont en effet à prendre en compte et la conséquence d'une erreur de fonctionnement peut être catastrophique pour le patient. L'objectif de cette thèse est de développer des outils et des approches méthodologiques permettant la validation et le test au niveau système de ce type de dispositifs. Il s'agit précisément d'étudier la possibilité de modéliser et simuler d'une manière conjointe un dispositif médical ainsi que son interaction avec le corps humain, du moins la partie du corps humain concernée par le dispositif médical, afin de mesurer les performances et la qualité de services (QoS) du dispositif considéré.

Pour atteindre cet objectif notre étude a porté sur plusieurs points. Nous avons d'abord mis en évidence une architecture simplifiée d'un modèle de corps humain permettant de représenter et de mieux comprendre les différents mécanismes du corps humain. Nous avons ensuite exploré un ensemble de métriques et une approche méthodologique générique permettant de qualifier la qualité de service d'un dispositif médical donné en interaction avec le corps humain.

Résumé vi-2

Afin de valider notre approche, nous l'avons appliquée à un dispositif destiné à la régulation du taux de sucre pour des patients atteints du diabète. La partie du corps humain concernée par cette pathologie à savoir le pancréas a été simulé par un modèle simplifié que nous avons implémenté sur un microcontrôleur. Le dispositif de régulation de l'insuline quant à lui a été simulé par un modèle informatique écrit en C. Afin de rendre les mesures de performances observées indépendantes d'un patient donné, nous avons étudiés différentes stratégies de tests sur différentes catégories de patients. Nous avons pour cette partie mis en oeuvre un générateur de modèles capable de reproduire différents états physiologiques de patients diabétiques. L'analyse et l'exploitation des résultats observés peut aider les médecins à considérablement limités les essais cliniques sur des vrai patients et les focaliser uniquement sur les cas les plus pertinent.

Mots-clés: méthodologie, modélisation, simulation, dispositifs médicaux, qualité de services, architecture, modèle mathématique, diagnostic, analyse, contrôle, microcontrôleur, essais cliniques.

Introduction

Les progrès des technologies de l'information et de la communication, des MEMS, des capteurs [START_REF] Patel Jasbir | Electroenzymatic glucose sensor using hybrid polymer fabrication process[END_REF][START_REF] David | Integrated optical glucose sensor fabricated using PDMS waveguides on a PDMS substrate[END_REF][START_REF] Chia Chee | Glucose sensors: toward closed loop insulin delivery[END_REF], des actionneurs [START_REF] Robbins | High-displacement piezoelectric actuator utilizing a meander-line geometry II[END_REF][START_REF] Ernst | Microactuators and their technologies[END_REF], des microcontrôleurs [START_REF] Harikumar R | FPGA synthesis of fuzzy (PD and PID) controller for insulin pumps in diabetes using cadence[END_REF], etc. ont permis l'émergence de différents dispositifs biomédicaux. Ces nouveaux dispositifs contribuent considérablement à l'amélioration du diagnostic et du traitement de certaines maladies, comme le diabète par exemple. Des dispositifs embarqués encore plus complexes sont en cours d'élaboration, leur mise en oeuvre nécessite des années de recherche et beaucoup d'expérimentation [START_REF] Wilinska Malgorzata | Simulation environment to evaluate closed-loop insulin delivery systems in type 1 diabetes[END_REF][START_REF] Russell Steven | Blood glucose control in type I diabetes with a bihormonal bionic endocrine pancreas[END_REF][START_REF] Dalla Man Chiara | GIM, simulation software of meal glucose insulin model[END_REF]. Le coeur artificiel, encore en phase de réalisation, est un exemple concret de ces systèmes complexes. La question du test de fonctionnement et de sureté de ces dispositifs reste problématique et difficile à résoudre. Plusieurs paramètres (patient, évolution de la maladie, traitement, etc.) sont en effet à prendre en compte et la conséquence sur le patient peut être catastrophique. L'objectif des travaux de recherche de cette thèse est de développer des outils et des méthodologies permettant la validation et le test au niveau système de dispositifs embarqués pour le domaine médical. Le but étant de pouvoir modéliser et simuler d'une manière conjointe le dispositif médical ainsi que le corps humain, du moins la partie du corps humain concernée par le dispositif médical, afin d'analyser les performances et la qualité de services (QoS) du dispositif considéré en interaction avec le corps humain. Pour atteindre cet objectif notre étude a porté sur plusieurs points. Nous avons d'abord étudié une architecture simplifiée d'un modèle de corps humain permettant de représenter et de mieux comprendre différents mécanismes du corps humain. Nous avons ensuite proposé un ensemble de métriques et une approche méthodologique générique permettant de qualifier la qualité de service d'un dispositif médical donné en interaction avec le corps humain. Deux techniques d'aide à l'évaluation de qualité de services (QoS) sont misent en évidences.

Résumé vi-4

La première technique calcule un indice de sévérité qui quantifie la gravité du cas étudié.

La seconde, basée sur une fonction de normalisation relative à une grille d'erreur construite par simulation de différents scénarios, permet d'évaluer la précision de la valeur mesurée. Afin de valider notre approche, nous l'avons appliquée sur le cas du diabète. La partie du corps humain concernée par cette pathologie à savoir le pancréas a été simulé par un modèle mathématique simplifié que nous avons implémenté sur un microcontrôleur. Le dispositif du contrôle de régulation et d'injection de l'insuline quant à lui a été simulé par un modèle informatique écrit en C. Nous avons pour cela développé, en utilisant les outils de développement Keil conçus pour les processeurs ARM, un modèle mathématique permettant le contrôle et le fonctionnement en boucle fermée du système glucose-insuline. Nous avons aussi définis les règles de base pour le dispositif à évaluer. Enfin, un nouveau modèle de contrôle a été créé afin d'analyser les performances de tous les composants du système glucose-insuline. Pour disposer de mesures fiables, nous avons étudié le cas de plusieurs patients auxquelles nous avons appliqués différentes stratégies de tests. Nous avons pour cette partie mis en oeuvre un générateur de modèles de patients capable de reproduire différents états physiologiques d'un patient atteint du diabète de type 1 et ainsi étudier les performances du dispositif face à différents scénarios. Nous avons donc créé un outil simple pour générer de nombreux patients en prenant en compte les spécificités de chaque paramètre. Une simple modification dans chacun des paramètres aide à modéliser l'état d'un patient différent. L'état de gravité d'un patient peut ainsi être modifié en changeant les valeurs des paramètres du modèle mathématique, ceci permet d'avoir des résultats cliniquement précis.

Nous avons utilisé pour la simulation globale l'approche expérimentale in-silico qui présente de nombreux avantages et qui permet des simulations précises grâce à des modèles sophistiqués. Pour la partie simulation globale, nous avons utilisé le modèle mathématique "Hovorka" qui a été testé sur un ensemble de sujets diabétiques recevant un petit déjeuner, un Résumé vi-5 déjeuner et un dîner chaque jour pendant 4 jours. Les performances de ce modèle ont été analysées par comparaison à la grille d'erreur générées par simulation de différents patients dans différents scénarios. L'analyse de chaque simulation a été effectuée en vue d'avoir une représentation graphique de l'évaluation des risques pour le patient en raison des choix des capteurs et des actionneurs. L'analyse et l'exploitation des résultats observés aidera à mieux comprendre le contrôle de l'organisme humain pour identifier et quantifier les paramètres biophysiques pertinents et à considérablement limités les essais cliniques et les focaliser uniquement sur les cas les plus pertinents.

Le résumé est structuré comme suite : après l'introduction, nous présentons dans le premier chapitre notre étude sur la modélisation du corps humain. L'architecture du modèle retenu te la représentation mathématique du corps humain. Le deuxième chapitre sera consacré à la simulation des systèmes biomédicaux et l'évaluation de leur qualité de service.

La structure du simulateur et de l'analyseur seront présentés ainsi que les schémas des indicateurs mis en oeuvre pour l'évaluation de la Qualité de Service. Le chapitre 3 présente l'étude de cas considérée et les simulations misent en place. On présente dans ce chapitre, les modèles réalisés, les algorithmes de contrôles, la génération des modèles de patients virtuels et enfin les performances de contrôle en boucle fermée obtenus en exploitant l'approche expérimentale in-silico. Le dernier chapitre est consacré à la conclusion et aux perspectives.

On reviendra sur les objectifs de la thèse et les réponses apportées.

Résumé vi-6

Chapitre 1 : modélisation du corps humain

Introduction

La modélisation et la simulation du corps humain et de l'interaction de ses variables physiologiques avec des dispositifs médicaux fait partie des sujets les plus étudiés dans le domaine de la recherche. Dans le cadre de cette thèse, un dispositif médicale représente tout instrument, appareil, outil, machine, logiciel, matériel, etc., destiné être utilisé sur le corps humain, seul ou en combinaison avec d'autres dispositifs, pour une opération de diagnostic, de prévention, de contrôle, de traitement d'une maladie, etc. Dans ce chapitre, nous présentons une méthodologie pour la modélisation et la simulation globale de dispositifs médicaux et de leurs interactions avec le corps humain, afin d'analyser leurs performances et d'évaluer leurs qualités des services.

Rappel sur le fonctionnement du corps humain

Se déplacer, réagir à son environnement, ingérer et digérer de la nourriture, avoir une activité métabolique, éliminer les déchets, se reproduire, etc. fait appel à différentes fonctions vitales interdépendantes et fait de l'humain un système d'une extrême complexité [START_REF] Tortora Gerard | Principles of Anatomy and Physiology[END_REF][START_REF] Boron Walter | [END_REF].

La figure 1 montre à titre d'illustration l'interdépendance de différentes parties du système corps humain, où le système tégumentaire protège l'ensemble du corps contre l'environnement. Une membrane forme une enveloppe et permet le passage des substances utiles, tout en empêchant le passage de substances nocives ou inutiles. Le système digestif et le système respiratoire interagissent avec l'environnement et fournissent respectivement les éléments nutritifs et l'oxygène au sang chargé de les distribuer à l'ensemble des cellules du corps. Les déchets métaboliques sont éliminés de l'organisme par l'intermédiaire du système urinaire et du système respiratoire. Aucun de ces systèmes ne travaille d'une manière totalement indépendante, ils travaillent tous ensemble, pour le bienêtre de l'organisme entier (ex.. digestif, cardio-vasculaire, musculaire et respiratoire).

Pour garantir l'équilibre du corps humain, beaucoup de variables physiologiques (que nous notons par la suite PV) doivent être contrôlées et régulées. C'est par exemple le cas de la pression artérielle, de l'acidité du sang, du taux sanguin de sucre, de la fréquence cardiaque, de la température corporelle, du rythme respiratoire, etc. Un capteur est chargé par la transmission des variations de la variable physiologique à surveiller à un contrôleur. Ce dernier connaissant la valeur de référence qui doit être maintenue, analyse les données reçût et détermine la réponse appropriée. A réception de cette réponse, un actionneur produit la contre-réaction positive ou négative nécessaire à la correction des variations du paramètre physiologique et sa stabilisation autour de la valeur considérée comme normale. La loi de commande est dans certains cas très complexe. Ces quelques rappels montrent combien la modélisation de tout ou partie du corps humain est complexe. Il s'agit comme mentionnée précédemment un des systèmes complexes. Cependant et en fonction des objectifs des études souhaitées, plusieurs niveaux de complexité peuvent être considérés et la modélisation peut être en partie simplifiée.

Représentation mathématique du corps humain

L'utilisation d'équations mathématiques pour la modélisation des systèmes biologiques, particulièrement humains, est exploitée depuis de longue date. La complexité du corps humain à même rendu cette approche incontournable pour la compréhension de certaines fonctionnalités du corps humain [START_REF] Dangelmayr Gerhard | Mathematical modeling: A Comprehensive Introduction[END_REF][START_REF] James | Mathematical models and the experimental analysis of behavior[END_REF]. Les modèles de distribution concernant l'espèce humaine ont en été et sont aujourd'hui utilisés dans de nombreux domaines [START_REF] Palumbo Pasquale | Mathematical modeling of the glucose-insulin system: A review[END_REF]. Le modèle mathématique d'un patient est souvent basé sur un ensemble d'équations mathématiques et de divers algorithmes de contrôle-commande. Les paramètres et les constantes manipulés par ces équations et algorithmes reproduisent les entrées et sorties permettant de simuler le fonctionnement du corps humain.

Si Mp définit une fonction représentant le modèle mathématique d'un patient et si :

-S représente un ensemble de systèmes du corps humain (appareil digestif, appareil respiratoire, etc.).

-Pf représente un ensemble d'informations caractéristiques du patient (poids, stress, etc.).

-Dm représente ensemble des repas (le petit-déjeuner, le déjeuner, le gouter, le diner, etc.).

-Or représente un ensemble d'organes du corps (foie, coeur, pancréas, etc.)

-
Si B représente l'ensemble des valeurs alimentaires du petit-déjeuner, comme les protéines de gras etc., L est l'ensemble de la valeur alimentaire du déjeuner, D l'ensemble des valeurs alimentaires pour le dîner et Af l'ensemble des portions supplémentaires tels que les collations. On définit l'ensemble des repas quotidiens par :

Dm = {B, L, D, Af} (2)
Si Or i représente un organe quelconque dans le corps humain. L'ensemble des organes du corps est définit par :

Or =
C = {C 1 , C 2 , C 3 … C n } (8)
Soient PV i les variables physiologiques contrôlés par le système / PV = U SPV , SPV Є S i .

On définit PV par : )

PV = {PV
) ( 1 ( ) ( ) ( ) ( ) ( ) ( ) ( 3 0 2 12 1 1 , 01 1 t x EGP t Q K t Q t x t F F t U dt t dQ R c G        ) ( )) ( ( ) ( ) ( 2 2 12 1 1 2 t Q t x K t Q x dt t dQ    S T t S t u dt t dS ) ( ) ( ) ( 1 1   S S T t S T t S dt t dS ) ( ) ( ) ( 2 1 2   dt t dD h D D ) ( * 1 1 1  
/ h est la constante de variation par rapport au temps

dt t dD h D D ) ( * 2 2 2

 

Le taux d'absorption de l'insuline, UI (t) (mU/min) peut être calculée :

S I T t S t U ) ( ) ( 2 
La concentration d'insuline, I(t) (mU/L), est trouvée en résolvant l'équation différentielle suivante:

) ( ) ( ) ( t I K V t U dt t dI e I I  
x 1 , x 2, et x 3 sont calculées en utilisant les trois équations différentielles suivantes, en fonction de la concentration de l'insuline plasmatique et des paramètres :

) ( ) ( ) ( 1 1 1 1 t I K t x K dt t dx b a    ; k b1 = S IT k a1 ) ( ) ( ) ( 2 2 2 2 t I K t x K dt t dx b a    ; k b2 = S ID k a2 ) ( ) ( ) ( 3 3 3 3 t I K t x K dt t dx b a    ; k b3 = S IE k a3 Résumé vi-12

Architecture du simulateur mis en oeuvre

Un simulateur pour le domaine médical est un dispositif qui permet de reproduire, dans des conditions donnés de test, des phénomènes susceptibles de se produire dans le monde réel [START_REF] Kratzig | From Theory to Practice: Simulation Technology as a Training Tool in Law Enforcement[END_REF]. On associe souvent à un simulateur pour le domaine médical les scénarios de tests, les patients concernés et les dispositifs médicaux utilisés. Comme le montre la figure 4, le simulateur mis en oeuvre pour notre recherche, englobe l'ensemble des éléments précédemment cités. A partir des différents et nombreux scénarios choisis, des trajectoires physiologiques sont donc générées par le simulateur (Figure 5). L'analyse de l'ensemble des trajectoires permet, par comparaison à des trajectoires connues, de savoir s'il y a anomalie ou pas et par la même occasion de déduire une indication sur la qualité du service du système considéré. L'objectif étant de vérifier si le du système est capable de garantir un niveau de qualité de service (QoS) compris dans un intervalle de valeurs considérées satisfaisantes. -PV : représente la variable que le système essaie de contrôler.

Simulateur

Trajectoire physiologique

Scénarios

Simulateur

Trajectoire physiologique

Analyseur

Scénario

Entrée Sortie Système

-Rétroaction : aide à surveiller et à déclarer les valeurs.

-Testeur : représente notre modèle de test. Pour chaque t j / f '(t j ) = 0 et f (t j ) > α m : -C : de nature à affecter les résultats cliniques.

Ǝ t K ,t L (t K < t j < t L ) / f(t K )=f(t L )= α m et T Hyper =∑(t L -t K ) (11
-D : peut avoir un risque médical important.

-E : peut avoir des conséquences dangereuses.

Chapitre 3 : Implémentation et étude cas

Les avancées en recherche dans les domaines de l'électronique et de l'informatique embarqués ont permis une forte introduction des dispositifs de diagnostic et de suivi pour des applications biomédicales [START_REF] Abbes | A microcontroller implementation of constrained model predictive control[END_REF]. Pour le cas du diabète par exemple, il est nécessaire de comprendre l'effet de l'insuline et des hydrates de carbone sur l'évolution de la glycémie d'un patient spécifique. De nombreuses équations et modèles mathématiques ont été utilisés pour créer des simulateurs pour tester différents types de traitement et ont permis d'explorer nombreuses approches de contrôle et de régulation automatique de la glycémie [START_REF] Cobelli Claudio | Diabetes: Models, Signals, and Control[END_REF].

Dans ce chapitre, nous présentons la mise en oeuvre du modèle mathématique développé pour simuler la régulation du glucose dans le sang d'un patient. Le fonctionnement et le suivant : un patient avale plusieurs bonbons sucrés, le système digestif les transforment, ce qui provoque une augmentation rapide de la concentration sanguine. L'augmentation du niveau de glucose stimule les cellules du pancréas responsables de la fabrique de l'insuline, qui libèrent alors dans le sang. L'insuline accélère l'absorption du glucose par la plupart des cellules et favorise son stockage sous forme de glycogène dans le foie et les muscles; le corps en quelque sorte mis en glucose en réserve. Par conséquent, les rendements de glucose à la valeur de référence normale et l'événement qui a déclenché la sécrétion d'insuline diminue également. Glucagon, une autre hormone pancréatique, a un effet opposé. Il est libéré lorsque les taux de glucose sont inférieurs à la valeur de référence.

Nous commençons par le système d'insuline glucose et nous créerons un nouveau

Framework afin de pouvoir tester les performances de différents composants du système. Le Framework consiste à simuler un modèle mathématique du corps humain, de le mettre en oeuvre dans un microcontrôleur, de développer un algorithme de contrôle paramétriques du modèle afin de montrer comment les dispositifs médicaux peuvent être reliés entre eux pour former un système en boucle fermée physiologique. Ce chapitre traite de la simulation mise en place, l'explication du travail de modélisation et la présentation de l'algorithme de contrôle.

Nous présentons également les trois modèles qui sont mis en oeuvre : le modèle de corps humain, le modèle de pancréas artificiel et le modèle des capteurs et des actionneurs.

Nous proposons un nouveau modèle pour la simulation globale des équipements biomédicaux (y compris les modèles d'interaction humaine). Nous commençons par une étude in silico pour les patients diabétiques de type 1 sucré à l'aide d'un modèle mathématique, la mise en oeuvre d'un algorithme de contrôle. Ce modèle a été conçu pour fonctionner dans la boucle fermée de Résumé vi-26 l'insuline au glucose. Ensuite, le modèle de pancréas artificiel a été mis en oeuvre pour commander le modèle mathématique du corps humain.

Système de glucose-insuline

Des relations existent entre les différents organes du corps humain : le foie, les muscles, le pancréas… afin de formuler un système de glucose-insuline, et ajuster la concentration du niveau de glucose dans le sang (figure 16). Le système de glucose-insuline au sein du corps humain agit normalement comme un régulateur de la concentration du glucose dans le sang (BG), de ce fait empêchant la hausse anormale de la glycémie (hyperglycémie), ou le niveau de glucose est anormalement basse (hypoglycémie). Le système de glucose-insuline est un exemple d'un système physiologique en circuit fermé. Le règlement normal du niveau de glucose sanguin est réalisé par le système de glucose-insuline.

Une personne en bonne santé a normalement un taux de sucre entre 70-110 mg/dl. L'objectif est de formuler une co-simulation des modèles de système physiologiques et systèmes embarqués (codes, capteurs, actionneurs…), et la représentation du règlement de la glycémie sous forme de modèles mathématiques. Les modèles mathématiques de la régulation du glucose ont été étudiés au cours des années. Récemment, la modélisation d'un système insuline-glucose a été présentée [START_REF] Maira | Prediction of Postprandial Blood Glucose under Intra-Patient Variability and Uncertainly and its Use in the Design of Insulin Dosing Strategies for Type 1 Diabetic Patients[END_REF].

Tout d'abord, nous avons validé le modèle de corps humain en utilisant "Hovorka" que nous avons implémenté selon le scénario de référence définie dans [START_REF] Lassen Allan Lyngby | Modeling and Simulation of Glucose-Insulin Dynamics[END_REF][START_REF] Naerum Miriam | Model Predictive Control for Insulin Administration in People with Type 1 Diabetes[END_REF]. Nous l'avons programmé à l'aide du Keil en développement un programme de code intégré, qui a agit en tant que patient. Dans ce scénario, l'insuline est prise avant le repas. Nous avons considéré les repas prises par une personne, qui représentent le petit déjeuner, le déjeuner et le dîner dans une journée normale. Tout comme un point de référence, nous avons utilisé CHO 1 = 45g et

Implémentation d'un pancréas artificiel

La plupart des travaux proposés de la mise en oeuvre de ce modèle sont effectués sous Matlab / Simulink ou logiciel java [START_REF] Makroglou Athena | Mathematical models and software tools for the glucose-insulin regulatory system and diabetes: an overview[END_REF]. C'est souvent en raison de la complexité de l'utilisation du microcontrôleur et l'énorme quantité de temps nécessaire pour mettre en oeuvre ces méthodes lors de l'incorporation des contraintes. L'objectif supplémentaire est de vérifier si la dose calculée est autorisée à être administrée. Les différents membres de la famille de microcontrôleurs 8051 conviennent à une vaste gamme de projets [START_REF] Michael | Programming Embedded Systems using C[END_REF]. Dans cette partie, nous avons choisi de travailler avec un microcontrôleur 8051 afin de simuler notre système. Nous avons également simulé ce modèle en utilisant le programme Keil. Nous avons programmé le contrôleur en créant un programme C embarqué qui agissent comme pancréas artificiel. Son rôle principal était de réguler le niveau de sucre dans le sang par injection d'insuline (figure 19).

Patient

Etude in silico

Nous avons essayé de mettre en oeuvre la technique in silico sur un patient virtuel ayant un diabète de type I (T1DM). L'expérimentation in silico [START_REF] Moretti | In silico experiments in scientific papers on molecular biology[END_REF][START_REF] Kovatchev Boris | In silico preclinical trials: a proof of concept in closed-loop control of type 1 diabetes[END_REF][START_REF] Patek Stephen | In silico preclinical trials: methodology and engineering guide to closed-loop control in type 1 diabetes mellitus[END_REF]

Génération des patients virtuels

Le modèle utilisé Hovorka a été choisi en fonction des besoins de la recherche. Comme

List of Acronyms

The following acronyms and abbreviations are used in this thesis.

AP

I.1.1. Motivation

There is a long history of biology systems and in the concept of system theory and classical physiology [START_REF] Bertalanffy | General System Theory[END_REF][START_REF] Kitano Hiroaki | Computational systems biology[END_REF][START_REF] Kitano Hiroaki | Systems biology: a brief overview[END_REF]. The current biological systems consist of large numbers of components. Studying the components parts and also focusing on understanding its structure, help to understand the function and behavior of such systems [START_REF] Sauer | Getting closer to the whole picture[END_REF]. It is also known that these proprieties and the function of these systems emerge through the interactions of the components [START_REF]End of the interlude?[END_REF][START_REF] Dubitzky Wemer | Understanding the computational methodologies of systems biology[END_REF]. On each level of this system, this behavior depends on the proprieties of these levels, the outputs and their interaction. For this reason, we need a method for simultaneously studying the different levels of the system. An important key part of the systems biology approach is the computational and Mathematical modeling, which help to produce models for describing systems [START_REF] Sumner Thomas | Sensitivity analysis in systems biology modeling and its application to a multi-scale model of blood glucose homeostasis[END_REF].

Modeling is fundamental and there are many different ways to understand, define, and analyze the structure of the complex system and phenomena. Advances in information technologies and systems, reflect an increasing in the domain of medical devices, which leads to better diagnosis and delivery of treatment, enhancement in usability and new functionalities. The importance of simulation modeling in medical instrumentation is arriving to reduce medical errors, solve health problem and to improve patient safety. The issue of operational test and safety of these devices remains problematic and difficult to solve. Several parameters (patient, disease progression, treatment, etc.) are indeed taken into account and the impact on the patient can be catastrophic.

Recent models in the literature suggest that the simulation modeling techniques are useful tools for analyzing complex systems in critical care [START_REF] Kreke | Simulation and critical care modeling[END_REF][START_REF] Rosen Kathleen | The history of medical simulation[END_REF][START_REF]Standards of medical care in diabetes[END_REF]. For example, modeling the glucose-insulin interaction, in case of diabetes mellitus (DM), requires an understanding of the physiological and metabolic processes that determine the observable behavior [START_REF] Ibrahim Ahmmed Saadi | Advanced mathematical model of glucose-insulin concentrations in type 1 diabetes using artificial neural networks[END_REF][START_REF] Farmer Terry | Effectiveness of intravenous infusion algorithms for glucose control in diabetic patients using different simulation models[END_REF][START_REF] Sandhya | Mathematical model for glucose-insulin regulatory system of diabetes mellitus[END_REF]].

The DM is described as a metabolic disease which is characterized by high or low plasma glucose level which is a major cause of death in most countries. According to the International Diabetes Federation (IDF), for the years between 2010 and 2030, close to four million deaths group can be attributed to diabetes. There is a need to reduce, or at least contain, the health care costs.

Previously, without simulation, there was a delay in work progress and the cost was more expensive. There was a need for providing higher work productivity and minimum cost.

Simulation modeling enables to virtually investigate many prototypes and analyze all inputs and outputs, constraints and device behaviors. The simulation was defined as a technique or a method, used in health care education fields [START_REF] Passiment | Medical simulation in medical education: results of an AAMC survey[END_REF] and assessment, to replace real patient with scenarios designed to promote knowledge and experiences. Noting that, the goal of mathematical simulation is to develop an understanding of integrated physiological systems.

Biomedical simulation test [START_REF] Wilinska Malgorzata | Simulation environment to evaluate closed-loop insulin delivery systems in type 1 diabetes[END_REF][START_REF] Russell Steven | Blood glucose control in type I diabetes with a bihormonal bionic endocrine pancreas[END_REF][START_REF] Dalla Man Chiara | GIM, simulation software of meal glucose insulin model[END_REF] is a new type of medical test which is a kind of simulation medical procedure performed to detect, diagnose, analyze, or monitor biomedical equipment [START_REF] Goldsman David | Output analysis: output analysis procedures for computer simulations[END_REF][START_REF]Standards Analysis: Biomedical Technologies Sector[END_REF]. The test is used to assess scientific aptitude of biomedical equipment. The performance of simulation must be evaluated to determine whether it is optimized or not.

Hence, in measuring the quantitative performance of the simulation, mean error is implied which was to determine the error between the targets and the output. Innovations in biomedical technologies are seen as being able to provide solutions to improve the quality and the efficiency of healthcare systems [START_REF] Thomson Sarah | International Profiles of Health Care Systems[END_REF].

There is a need to improve the quality of the services (QoS) provided, by ensuring biomedical devices are fit for purpose, which give an opportunity to develop new services or new diagnosis with an objective of upgrading and improvement. In other words, a set of quality of services must be satisfied. The problem that should be solved is how to analyze embedded medical devices in order to avoid risks on patients, including variability and uncertainty on a number of parameters related to patients, evolution of disease, and treatments. Treatment depends on the availability and well functioning of complex electronic systems, including thousands lines of codes.

Today medical treatment uses more and more embedded devices including sensors [START_REF] Patel Jasbir | Electroenzymatic glucose sensor using hybrid polymer fabrication process[END_REF][START_REF] David | Integrated optical glucose sensor fabricated using PDMS waveguides on a PDMS substrate[END_REF][START_REF] Chia Chee | Glucose sensors: toward closed loop insulin delivery[END_REF], actuators [START_REF] Robbins | High-displacement piezoelectric actuator utilizing a meander-line geometry II[END_REF][START_REF] Ernst | Microactuators and their technologies[END_REF] and controllers [START_REF] Harikumar R | FPGA synthesis of fuzzy (PD and PID) controller for insulin pumps in diabetes using cadence[END_REF]. Treatment depends on the availability and the well functioning of complex electronic systems, including thousands of lines of codes.

Products of all kinds are increasingly constructed to include one or more embedded systems to improve functionality. These embedded systems often combine hardware and software that together allow a distinction. Depending on the scope, embedded systems present a wide variety of formats and technical solutions. Embedded systems, distributed real-time and manipulate streams or media critics, spread more and affect all sectors (health, recreation, avionics, telecommunications, transport ...) [START_REF] Verhoef | Modeling and Validating Distributed Embedded Real-Time Control Systems[END_REF]. These systems have strong requirements in terms of security, fault tolerance and quality of service. Issues related to QoS are not simply those of improving performance. These are mostly managing the resources of the support system to meet different QoS requirements. Testing embedded system consists of evaluating the application behavior (including its components), performance, and robustness [START_REF] Sthamer Harmen | Evolutionary testing of embedded systems[END_REF][START_REF] Yu Tingting | Testing Embedded System Applications[END_REF].

One of the reasons for the high growing in research simulations fields is the ability to have data. Various experiments grow due to faster and better methods used to obtain this amount of physiological data. This data constitute a bank of potential insight that provides us with more statistical analysis that helps to discover correlations.

First, there is a need to propose a mathematical model for body representation and a simulation tool for health management, which help to provide a new comprehensive toolset to tackle the issues of system modeling, analysis, QoS system integration and verification. Also a mathematical model is needed to represent physiological system, which describes how a system works, how organs function, and a method to deal with medical data collected.

Second, in medical fields, it's important to improve the diagnosis and treatment of patients, and analyze the performance of embedded biomedical devices; by showing its validation which helps to make safety its operation.

Third, there is a need to calculate the quality of services of such system, as well as to find a way to prove that a sensor or an actuator is more effective than another.

The method and tools developed here can be used by patients and physicians to evaluate the usage of biomedical devices and to have a complete environment for simulation and testing.

.

I.1.2. Objectives

The general objective of this research is to develop tools and methodologies for the development of embedded systems for medical fields. The goal is to be able to model and jointly simulate the medical device as well the human body, at least the part of the body involved in the medical device, to analyze the performance and quality of service (QoS) of the interaction of the device with the human body.

To achieve this objective, the study addresses the following specific aims:

-To propose a new prototype that helps to represent the human body model in order to better understand all the systems that the human body is composed of. In addition, understanding and simulating them in order to detect performance and quality of service of all system components.

-To develop a complete environment of biomedical system in order to have the ability to test testing strategies, a powerful implementation that helps to test these biomedical devices, and a bank of test can then be created. The ability to develop a model in order to analyze the performance of embedded biomedical devices can be very useful in medical research which leads to improve the diagnosis and treatment of patients.

We can generate many models and disturbed parameters to reproduce many states that might resemble to physiological cases in disease processes.

-To construct a complete realized hardware environment that has the ability to improve the modeling and analysis approaches of embedded systems in order to make them faster and less expensive.

I.1.3. Thesis structure

This thesis is divided into five chapters. Here, a detailed overview of all the chapters of the dissertation is described:

-Chapter I outlines the motivation for this research, the problems and challenges involved, and the research objectives.

-Chapter II starts by defining a prototype of a new global and flexible architecture of mathematical model of human body that is able to contain required data. Next, we

propose a new global methodology for modeling and simulation human body and medical systems, in order to understand thoroughly the best way to model and simulate these systems as well as detecting performance and the quality of services of all system components. Finally, the techniques used to help evaluate the calculated QoS value.

-Chapter III presents the implementation part of a case study where we use a mathematical model applicable in our prototype that was described in chapter II. Then, we take the glucose insulin system and create a new framework in order to test the performance of all system components. As well as, the simulation set-up, the explanation of the modeling work and the presentation of the control algorithm. Thus, we have presented the three models implementations.

-Chapter IV is for the simulations results and the QoS measurement practices. It

shows virtual patients generating part, modeling results as well as the control performances in closed-loop achieved exploiting the in-silico patient. This chapter also shows the performance of our tester model declared in chapter II for the case studied in chapter III which is the glucose level.

-Chapter V discusses the conclusions and contributions of this research, and future work.

Chapter II: Systems modeling

II.1. Introduction

With the rapid development in medical research, the study of simulating human body is moving towards more and more precise methods. Since the beginning, the scientists have been interested in the physiological system of the human body and its applications. They have tried to find the most accurate model in order to simulate the human body and all the reactions with his environment. The world health organization defines medical devices as "any instrument, apparatus, implement, machine, appliance, implant, in vitro reagent or calibrator, software, material or other similar or related article, intended by the manufacturer to be used, alone or in combination, for human beings for one or more of the specific purposes of:

diagnosis, prevention, monitoring, treatment or alleviation of disease; investigation, replacement, modification, or support of the anatomy or of a physiological process; control of conception" [START_REF] Cheng | Medical Device Regulations: Global Overview and Guiding Principles[END_REF].

The study of the structure of the human body and its parts is called anatomy while physiology is the study function of these parts. Anatomy is a broad field of study that includes many specialties; each of them would be a complete domain research. These specialized divisions of the anatomy are especially useful for scientific research and diagnosis of diseases.

Like anatomy, physiology includes several specialties, but physiology highlights the dynamic nature of the organization whereas anatomy gives a static image of the body.

These two complementary scientific disciplines, affect the fundamentals that allow us to understand the human body. The study of the function and the structure are inseparable.

Indeed, the function always reflects structure. That is to say that an organ can only perform the functions permitted by its structure, noting that an organ is a structure composed of at least two types of tissues that exerts a specific function in the body. Tissues are groups of cells that perform the same function. For example, the heart can pump blood only in one direction because of the structure and arrangement of the heart valves.

Each organ has a specialized functional structure that performs an essential activity that no other body can perform instead. These construct level of systems; each system consists of organs that work together to perform a single function. All systems cannot work completely independently; they all work as one organism (for example, digestive, cardiovascular, muscular and respiratory systems). Noting that, all systems work together to maintain human life, by maintaining controlled factor or what we can call physiological variables. These variables must be maintained by the system that analyzes the data it receives and then determines the appropriate response.

We can resume the variation of these variables as follow; an external event affects a physiological variable, a receptor sensor detects this modification, and sends an input signal about this detection to the system to control it. The control system sends an output signal to the effectors' actuator, the signal sent by the actuator acts on the intensity of the stimulus feedback. Simulation this procedure leads to a better understanding of the whole system.

In this chapter, we propose a global methodology for modeling and simulation medical systems and human body, in order to analyze the performance and the quality of services of all system components. We begin first by defining a new prototype of a global and flexible architecture of mathematical model of human body which is able to contain the required data.

We describe next the simulations representation, by mentioning in details the core simulator components, analyzer, and the quality of services indicators. The simulation of the mathematical models provides useful tools for the diagnosis and analysis the interactions between efficacy, therapies, side-effects, and outcomes. This will help to better understand the human organism control, to analyze experimental data, to identify and quantify relevant biophysical parameters, and to design clinical trials.

II.2. Architecture of the model

Many research centers are developing environments for developing integrative models of human physiology. Biomedical researchers can use integrative physiological models to better understand the fundamental relationships hidden in the complexity. Computational methods have been used to study and describe physiological responses [START_REF] Hester Robert | Systems biology and integrative physiological modeling[END_REF], there are few examples of integrative models of human physiology. They studied model aspects of the heart, cardiovascular, and pulmonary systems [START_REF] Ottesen Johnny | Applied Mathematical Models in Human Physiology[END_REF].

Later, they provide an analysis of the starting point for the development of multi-level systemic biological analysis, combining reduction and integration [START_REF] Kohl | Systems biology: an approach[END_REF]. Humans must keep their limits, move, react to changes in their environment, ingest and digest food, have a metabolic activity, eliminate waste, reproduce and grow. The distribution of vital functions, between different systems, leads to interdependence of all body cells [START_REF] Tortora Gerard | Principles of Anatomy and Physiology[END_REF][START_REF] Boron Walter | [END_REF]. The human body has several levels of complexity. For example using the cardiovascular system, different levels of integration complexity of the human body are illustrated. Every system appears to be the result of a combination of several levels of integration.

Figure II.1 shows the interdependence of body systems, where the integumentary system protects the whole body against the environment. There exists a membrane which forms an envelope permitting the useful substances but preventing the passage of unnecessary or harmful substances. The cardiovascular system is responsible for transporting nutrients and removing gaseous waste from the body.

The digestive system and respiratory system interact with the environment and provide respectively nutrients and oxygen to the blood which then distributes to all cells. Metabolic wastes are eliminated from the body through the urinary system and the respiratory system.

None of the systems works completely independently, they all work for the well-being of the whole organism. In the human body there are a lot of physiological variables that must be maintained or controlled. Let PV be the abbreviation concerning physiological variable. Such as: blood pressure, acidity of the blood, blood sugar level, heart rate, body temperature, and breathing rate. Any event that affects the system reflects a change in the physiological variable, and the system tends to maintain conditions that require frequent monitoring and adjustment within physiological limits.

The blood pressure is a PV controlled by the human body. When an event causes this PV to increase, pressure-sensitive nerve cells (sensors), in certain arteries, send nerve impulses (input) to brain (controller). The brain interprets the messages and responds by sending fewer nerve impulses (output) to the arterioles. This causes the arterioles (actuator) to dilate All PV needs relatively to be in stable conditions in order to live and consequently the human systems perform their functions to keep alive the whole body. Figure II.2 above shows how the human body can be interconnected to form a physiological closed-loop system. It is basically a sensor whose role is to monitor the environment and respond to changes of the PV, sending information (input) to the controller.

The controller, which sets the reference value where the variable must be maintained, analyzes the data it receives and determines the appropriate response. Then, the Actuator through which the controller produces a response (output) to the event. The response then produces a feedback action which acts on the event; it may have either a reducing or strengthening effect so that all the regulatory mechanism either ceases to operate or the reaction proceeds with increasing intensity.

Sometimes the controlling is done by changing the value of PV in the opposite direction of the initial change and returns it to a normal value.

II.3. Mathematical Representation of human body

The use of ordinary, partial, and integral differential equations to model biological systems has a long history. Mathematical modeling is becoming an increasingly important subject that helps to expand our ability to translate mathematical equations and formulations into concrete conclusions [START_REF] Dangelmayr Gerhard | Mathematical modeling: A Comprehensive Introduction[END_REF][START_REF] James | Mathematical models and the experimental analysis of behavior[END_REF]. Species distribution models have been used extensively in many fields [START_REF] Palumbo Pasquale | Mathematical modeling of the glucose-insulin system: A review[END_REF]. The mathematical model of a patient is a set of equations and various algorithms, where the use of parameters and constants to resituate the human body functioning. We define a new prototype to represent the mathematical model of the human body, described in details in the section below.

II.3.1. Prototype definition

Let Mp be a mathematical model for a patient, S is a set of system, Pf a set of personal information about the patient that may affect the system such as weight, stress, etc…, Dm a set of daily meals, Or a set of body organs, Ir a set of internal relations for the body actors, Er The set Dm is defined by:

Dm = {B, L, D, Af} (2)
Let Or i are an organ in human body. The set Or is defined as:

Or = {Or 1 , Or 2 , Or 3 … Or n } (3)
Let Ir i are an internal relation (mathematical function) for an Or i that uses values from SC Є Or i and SPar Є Or i . The set Ir is defined as:

Ir = {Ir 1 , Ir 2 , Ir 3 … Ir n } (4)
Let Er i are an external relation (mathematical function) between two or more Or i that uses values from C and Par. The set Er is defined as:

Er = {Er 1 , Er 2 , Er 3 … Er n } ( 5
)
Let SName is the name of the body system (such as Digestive system), SC and SPV are related to concerned S i . Noting that, intersections between SPV of different systems are not necessarily empty, because some physiological variables may affect several systems so they are common variables between these systems. The system S consists of one or more Or. The set S is defined by:

𝑆 = {𝑆 1 , 𝑆 2 , 𝑆 3 … 𝑆 𝑛 }/S i ( 𝑆𝑁𝑎𝑚𝑒, 𝑆𝐶, 𝑆𝑃𝑉, 𝐼𝑟, 𝐸𝑟) = ⋃ Or ij n i 𝑗=1 (6)
Let Par i are input parameters for the system, Par = U SPar , SPar Є S i . The set Par is defined as:

Par = {Par 1 , Par 2 , Par 3 … Par n } (7)
Let C i are predefined constants for the system / C = U SC , SC Є S i . The set C is defined as:

C = {C 1 , C 2 , C 3 … C n } (8)
Let PV i are physiological variables controlled by the system / PV = U SPV , SPV Є S i . The set PV is defined as:

PV = {PV 1, PV 2, PV 3… PV n } (9)
Finally Mp = (Pf, Dm, S) would be a global and flexible prototype model applicable to any analyzer for a patient and may integrate one or many body systems constituting a case of study or even all body systems.

This model can feed (input) the device model with its needed values via the results of the relations sets (Ir and Er) as well as the physiological variables set PV.

II.4. Simulation representation of the medical system

This part is described as "Core simulator components", shown in figure II.3, contains two simulations sections related with each other's by input/output hardware interface components which facilitate the communication between them. It presents the peripheral used to provide data and controlling signal between the two sections. The first section described as "Patient simulation" (PS) simulates the patient using a mathematical model; the patient model has been simulated to better understand the mechanisms of the human organic system. There are many constants and parameters involved in the model. There are usually decided upon collecting data or experimenting. These models are the best way to simulate patient physiology and pharmacology and provide responses in real time to whatever treatment has been given.

The second section named as "Device simulation" (DS) used to describe the simulation of medical devices using mathematical model equations, with the ability to simulate also sensor, actuator and controller. This mathematical model is used to mimic the function of medical device by simulating hardware and application, which helps to form a complete system simulation. The idea from simulation is to improve the design and testing of medical devices, which can be simple devices to be used in educational fields or complex devices that combine mechanical models with computer stations. We can simulate the biomedical equipment, by simulation the patient's level, sensors and actuators levels, and simulating the electronic hardware. We have successfully implemented and simulated a mathematical model of the human body (ref. chapter III), using Keil [START_REF] Elektronik | Getting Started and Create Applications[END_REF]40] development tools designed for ARM processors. Sensors and actuators were also simulated using codes that simulate their functions in chapter III.

II.4.1. μVision Keil

There is a need for a development tool of the entire system that must be reliable and crossplatform to support a diverse set of developers, for this reason, we have implemented using  Full-featured source code editor.

 Device database for configuring the development tool setting.

 Project manager for creating and maintaining your projects.

 Integrated make facility for assembling, compiling, and linking your embedded applications.

 Dialogs for all development tool settings.

 True integrated source-level Debugger with high-speed CPU and peripheral simulator.

 Advanced GDI interface for software debugging in the target hardware and for connection to Keil ULINK.

 Flash programming utility for downloading the application program into Flash ROM.

 Links to development tool manuals, device datasheets & user's guides.

The µVision3 IDE offers numerous features and advantages that help you to quickly and successfully develop embedded applications. Noting that the screen provides a menu bar for command entry, a tool bar where you can select command buttons, and windows for source files, dialog boxes, and information displays. μVision 3 can simultaneously open and view multiple source files. This version has two operating modes:

• Build Mode: It allows to translate all the application files and to generate executable programs. The features of the Build Mode are described under Creating Applications.

• Debug Mode: It provides a powerful debugger for testing your application. The Debug Mode is described in Testing Programs.

II.4.2. Simulators

The medical definition of a simulator is "a device that enables the operator to reproduce or represent under test conditions phenomena likely to occur in actual performance" [START_REF] Kratzig | From Theory to Practice: Simulation Technology as a Training Tool in Law Enforcement[END_REF]. Lack of communication and lapses human error are the most potential accidents in medicine, which leads medical simulation as a powerful technique to bridge this gap.

When talking about simulator we also talk about scenarios, patient and devices (figure II.4). The body of the simulator is composed from them. In case of patient, the simulator use a more sophisticated technique using mathematical model differential equations of a patient's physiology, with specific constants and some parameters versus time for example meals. Also in case of device, the simulator use also advanced model, constants and parameters versus time if needed. We can, for example, simulate the misuse of a particular device by either changing initial configuration or by creating a problem in utilization, will give a corruption in result. In another situation, the use of practical medical scenarios helps to illustrate effective equipment and diagnosis procedures.

S i m u l a t o r p h y s i o l o g i c a l t r a j e c t o r y S c e n a r i o s P a r a m e t e r s v e r s u s t i m e M o d e l u s e d C o n s t a n t s P a t i e n t D e v i c e

Fig. II. 4: Simulator

The simulation helps to optimizing the performance of devices avoid risks on patients and an evolution the treatment of disease. Taking many mission-critical simulations, by creating many population scenarios helps minimizing deficiency of accuracy and having a good performance and quality of service.

One of the most important uses of simulation output analysis regards the comparison of competing systems or alternative system configurations [START_REF] Law Averill | Simulation Modeling and Analysis[END_REF]. An important feature of simulation is its ability to allow the experimenter to analyze and compare scenarios quickly and efficiently.

Simulator physiological trajectory

Analyzer

Scenario qos indicator anomaly

II.5. QoS indicators

Recently, the quality of Service has received considerable scientific attention. While QoS has an important role in any system QoS has focused mainly on availability, reliability, security and cost. Most of the researches in medical applications focus on the concept of QoS and QoS requirements, measurement and management [START_REF] Engelbrecht Gerhard | Towards negotiable SLA-based QoS support for biomedical data services[END_REF][START_REF] John | A QoS data management system within a pervasive medical environment[END_REF][START_REF] Liang | A QoS-aware Routing Service Framework for Biomedical Sensor Networks[END_REF][START_REF] Curtis | Continuous Quality Improvement in Health Care: Theory, Implementation, and Applications[END_REF]. QoS issues related to data access and retrieval is rather less investigated. Maintaining QoS is equal to maintain the PV in a normal state. Each PV controlled have a maximum and minimum levels that this value must reach without arriving to the dangerous state. Estimates calculation of the range of controlled values depends on the controlled PV and on some characteristics of the human body. However, this is just an estimation; individual values vary considerably from this average value. Noting that, a normal value is the reliable value that remains constant from day to day and changes only slightly from year to year.

We are alive because important PV in our body are regulated automatically and so remained within certain levels. We can imagine what may happen without these controls by thinking about the consequences of a control failure. The human body has its main automatic control mechanisms. Feedback is a key concept. The actual values of PV are sensed, feedback and used to control the system. The behavior of these controlled variables is typically described by differential equations in the time domain.

When a change in a state of a PV is occurred upon an event, negative feedback responses are triggered to bring the PV back to its normal point. The sensor, controller, and the actuator play a role as a parts of negative feedback response.

The control specifications of the PV may refer to a static value or to a dynamic value that change by time. The study of each system helps to identify these variables, which need to be manipulated and by how much, in order to achieve given desired specifications.

Consider α i range of value that PV can reach from normal value to the maximum / α 1 is the highest value. Consider β i the range of value that PV can reach from the normal value to the minimum / β 1 is the lower value, then we can write the following:

{β 1 , β 2 , β 3 …. β n } < PV < {α n …., α 3 , α 2 , α 1 } (10)

II.5.1. QoS schema

For each scenario a quality service is recovered. After creating and simulating millions of scenarios, we can use the information of each scenario to retrieve a more comprehensive quality of service that will not depend on the scenarios.

In fact we don't generate scenarios (figure II.6), but we create a system that allows generating multiple scenarios to retrieve more relevant information. We can modify the number of device and their characteristics (N d ), the number of patients and their characteristics (N p ), or a mix of patients, devices and parameters (N s,p,d ) of different scenarios.

Creating multiple scenarios, in order to simulate and analyze data of results. To create them, we need many population and prevalence data, and with a number of generic pathways physiological trajectory to calculate the proper quality of service (QoS). The closed-loop system model chosen is based on feedback queue system, which allows describing the main characteristics of the model:

Input Output

System

-The feedback system in order to improve performance analysis.

-The system takes from the input queue, as virtual patients using generation method.

A work-conserving system means that if one flow is out of packets, the next data flow will take its place. In figure II.8, the patient generation is modeled as non-FIFO because the order of the outputs results differs from the orders of inputs, and considered as work-conserving system because of the presence of (t, Par, C) and feedback. Noting that, Non-FIFO method is used in many domain fields [START_REF] Schmitt Jens | A new service curve model to deal with non-FIFO systems[END_REF][START_REF] Bekki | Indirect cycle-time quantile estimation for non-FIFO dispatching policies[END_REF].

The meaning of the parameters mentioned in the figure II.8 is the following:

-S to represent the system to be controlled.

-PV the variable that the system tries to control.

-Feedback helps to monitor and report values.

-Tester is our tester model.

-(t, Par, C) composed from parameters, constants and t as time variable.

-Par represents the parameters given.

-Dm represents the daily meals taken by the patient. In a system there is a PV to be controlled and a tester that are interconnected to form a physiological closed-loop system. A high-level overview of the system allows creating many clinical cases that can benefit from closed-loop systems.

II.5.2. QoS evaluation

We use two techniques that help evaluate the calculated QoS value. The first one calculates an index of severity IG H (g) which indicates the severity of the case studied. It can be computed by approximating the integral of f (t) where f (t) is the function representing the state of the medical devices on a time interval [t i t f ]. The indicator has an objective; it compares the diabetic systems with the normal system.

II.5.2.1. Tester model

In the health field, an indicator is a single measure that captures a key dimension of health, such as how many people suffer from a heart attack. The international health community has come to a consensus regarding the key indicators representing health outputs and outcomes. in the minimum value case.

Result

For each t j / f'(t j )=0 and f(t j ) >α m : Ǝ t K ,t L (t K <t j <t L ) / f(t K )=f(t L )= α m and T Hyper =∑(t Lt K ) [START_REF] Ibrahim Ahmmed Saadi | Advanced mathematical model of glucose-insulin concentrations in type 1 diabetes using artificial neural networks[END_REF] For each t' j / f'(t' j )=0 et f(t' j )<β m :

Ǝ t' k ,t' L (t' K <t' j <t' L )/ f(t' K )=f(t' L )= β m and T Hypo =∑(t' L -t' K ) (12)
Then, for a given simulation, there exists a value The changing in the parameters of the control algorithm and the values of g:

-Helps to apply many scenarios in order to have many results -To deduce the best way to construct an effective tester.

II.5.2.2. Grid Analysis Representation

The error Grid can be designed to be used in diabetes screening, diagnosis, or to assess the accuracy of glucose monitoring. Trying to use a consensus error grid [START_REF] Clarke | Evaluating clinical accuracy of systems for self-monitoring of blood glucose[END_REF]50,[START_REF] Kovatchev Boris | Evaluating the accuracy of continuous glucose-monitoring sensors: continuous glucose-error grid analysis illustrated by TheraSense Freestyle Navigator data[END_REF][START_REF] Magni Lalo | Evaluating the efficacy of closed-loop glucose regulation via control-variability grid analysis[END_REF], that helps to estimate the error of the performance of devices. The best representation used for sensors is for Clarke and Parkes in order to estimate the error of the performance of sensors, actuators, and controllers.

In 1987, Clarke and al. designed the error grid analysis (EGA), taking into consideration not only the difference between the system-generated and reference blood glucose values but also the clinical significance of this difference.

There are 5 risk categories are defined as follows: A: no effect on clinical action; B: little or no effect on clinical outcome; C: likely to affect clinical outcome; D: could have significant medical risk; and E: could have dangerous consequences.

In 2000, an updated version of the blood glucose error grid was proposed by Parkes [50] also present error grids as a way of specifying glucose performance needed for clinical purposes. The international Organization for Standardization (ISO) analytical accuracy standard 15197 for blood Glucose (BG) monitors specifies that 95% of data points must demonstrate acceptable, analytical accuracy but does not specify any performance targets for the remaining 5% of data points [START_REF] Klonoff David | The need for clinical accuracy guidelines for blood glucose monitors[END_REF]. Analyze each simulation in purpose to have a graphical representation of the risk assessment for the patient due to choices on sensors, actuators. A point is plotted with x-coordinate the minimum BG and y-coordinate the maximum BG for an observation period. The plot is split into zones defined by their x-and y-coordinate ranges as follows: Beginning with the index of severity tester representation and using a normalization function, we can represent the simulation as a point in order to construct a new error grid and then using it to evaluate the accuracy of glucose level measurements made by patients (figure II.14). In brief, each simulation is represented as a point in the grid; this point is calculated using normalization function. This function takes as input the array of the simulation and the percentile value, and gives as output a point in a grid using 97.5 th and 2.5 th percentile. In this work, the Grid representation will help not only to simulate the performance of sensors but also actuators and controllers (figure II.15). Analyzing the performance of the biomedical devices helps to identify the usage of such sensors, actuators or controllers.In brief, using simulation of the following components: sensors, actuator or controller, and a normalization function, we can represent this simulation using grid analysis.

II.6. Conclusion

We have provided a global flexible architecture of the human body model with mathematical representation. A full simulation representation of the simulator components, analyzer part and the QoS indicator schema and the evaluation method has been also presented. The purpose of this architecture is to have a complete environment with the ability to simulate medical equipments, and test their performance.

From these results, the tester that we are creating is a robust tool that will improve the testing in biomedical fields without having any risk on patients. The plot of each simulation as a point in a grid and then split it into zones defined by their x-and y-coordinate ranges, help to construct a new error grid and use it to evaluate the accuracy of glucose level measurements made by the patients.

Chapter III: Case study -Systems implementation

III.1. Introduction

Embedded devices used in medical research help to improve the quality of diagnostic tools available to doctors as well as the treatments offered to patients. Recently, embedded technologies have become very important for future manufacturing enterprises as well as in industrial engineering. Advanced researches in microelectronics and software engineering allow many techniques to be implemented in embedded medicals devices [START_REF] Abbes | A microcontroller implementation of constrained model predictive control[END_REF]. Biomedical research seeks all times a good reasoning for solving medical problems based on intensive work and great debate. It often deals with theories that have been proven after observations or experiments [START_REF] Pandora | Where is the evidence that animal research benefits humans?[END_REF]56].

In such system there is a necessity to understand the effect of insulin and carbohydrates on blood glucose evolution for a specific patient. In recent years, many mathematical equations or known as mathematical models have been used to create simulators to test different types of treatment and have showed many control approaches to automatic regulation of blood glucose [START_REF] Cobelli Claudio | Diabetes: Models, Signals, and Control[END_REF]. These models arrive to become a choice for control algorithm. Better understand this system via mathematical equations helping to simulate it in normal life conditions which can be useful in diabetes research. Model the system, and know how it interacts with the environment.

In last decades, simulation models of the glucose-insulin control system during meals and normal daily life has been proposed for studying the pathophysiology of diabetes [START_REF] Magni Lalo | Model predictive control of type 1 diabetes: an in silico trial[END_REF][START_REF] Dalla Man | GIM, Simulation Software of Meal Glucose-Insulin Model[END_REF].

Simulation experiments with the mathematical model of a system are valuable tools for student education and medical fields [START_REF] Okuda Yasuharu | The use of simulation in the education of emergency care providers for cardiac emergencies[END_REF].

In this chapter, we implement a mathematical model applicable in our prototype that was described in chapter II, and the PV controlled is for example the glucose level in the blood.

The event starts by eating several sweet candies. In the digestive system, they are rapidly degraded in various simple, which causes a rapid rise in blood level. The increased glucose level stimulates pancreatic cells responsible of produces the insulin, which then release it into the blood. Insulin accelerates the uptake of glucose by most cells and promotes its storage as glycogen in the liver and muscles; the body in somehow set glucose in reserve. Therefore glucose returns to normal reference value and the event that triggered insulin secretion also decreases. Glucagon, another pancreatic hormone, has an opposite effect. It is released when glucose levels fall below the reference value.

We begin by the glucose insulin system and create a new framework in order to test the performance of all system components. The framework consists of simulating a mathematical model of human body in order to implement in a microcontroller, developing a control algorithm for the model and applying parametric models of activities to show how medical devices can be interconnected to form a physiological closed-loop system. This chapter deals with the simulation set-up, the explanation of the modeling work and the presentation of the control algorithm. We also present the three models implementations which are the model of human body, the model of artificial pancreas and the model of sensors and actuators.

We propose a new model for global simulating of biomedical equipments (including human interaction models). We begins by an in-silico study for type 1 diabetes mellitus patients using a mathematical model, with implementation of a our control algorithm. This model was developed to operate in the closed loop of the glucose insulin. Next, the model of artificial pancreas has been implemented to control the mathematical model of human body.

III.2. Glucose-Insulin System

A relationship exists between the different organs of the body: liver, muscle, pancreas… in order to formulate a glucose-insulin system, and to adjust the concentration of glucose level in the blood (figure III.1). The glucose-insulin system within the human body acts normally as a regulator of the glucose concentration in the blood (BG), thus preventing what called in medical terms for high blood glucose (hyperglycemia) or low glucose level (hypoglycemia).

The glucose-insulin system is an example of a closed-loop physiological system. The normal regulation of the blood glucose level is achieved by the glucose-insulin system. A healthy person normally has a fasting sugar level in the range of 70-110 mg/dL. The blood glucose level should be maintained in a very narrow range; insulin and glucagon, secreted from the pancreas, are the hormones that regulate this level. When the control of insulin levels fails, diabetes mellitus will result. Insulin is a hormone produced by the β-cells of the islets of Langerhans in the pancreas. A high insulin level promotes storage of glucose, and a low insulin level signals the need for the release of glucose fuels, currently in storage, back into the blood stream. Glucagon and adrenaline signals the liver to release glucose. Too much glucose removal from the blood-stream can result in dangerously low blood glucose levels. Glucagon and insulin are part of a feedback system that maintains the blood glucose at the correct level. For example in case of hypoglycemia, the α-cells react by releasing glucagon, which acts on the liver cells, causing them to release glucose into the blood until the person is back in the green area again

In such system there is a need to understand the effect of insulin and carbohydrates on blood glucose evolution for a specific patient. This is done through consideration of the glucose-insulin system, its inputs, outputs and modeling it. In this case, we will use these parameters to test biomedical equipment without the use of real patients.

The integration between the human system and the electronic system to act as one system is shown in figure III.2. The glucose-insulin system with a monitoring device that take the glucose level and send signal to the controller, the controller communicate with the actuator by sending control command, the actuator send the amount of insulin regulated by the controller. In brief, this integrated system is composed from patient, sensor for monitoring, controller and an actuator. The interaction between them is described in details below in section III.2.3. The objective is to simulate the whole system of this co-simulation, in other words, build a complete system with the ability to simulate it and detect the performance of all system components. The objective is to formulate a co-simulation of physiological and embedded system models (codes, sensors, actuators ...), and schematization of the natural regulation of glucose in the form of mathematical models

III.2.1. Diabetes mellitus overview

Diabetes is often described as a chronic illness of carbohydrate metabolism, characterized by high or low blood sugar level. In other term, this disease is defined by the inability of the body to produce or properly use insulin. It can be associated with serious complications and premature death but it can be controlled by taking measures that lower the risk of complications. Diabetes results from many causes, though genetics and environmental factors such as obesity and lack of exercise appear to play a major role. Over time, the number of βcells starts to decline, and then the type 2 diabetic patient must be treated with insulin injections like the type 1 diabetic to maintain his/her blood sugar at normal levels.

Its known when a healthy patient eats a meal, the carbohydrates are broken down into glucose, galactose and fructose, with galactose and fructose transformed quickly into glucose.

During this period insulin level increases naturally to stimulate glucose uptake. Insulin increase results in increased glucose uptake by liver and peripheral tissues, keeping plasma glucose level within normal range. Unlike a diabetic person, insulin effect on glucose regulation strongly depends on the quality of insulin therapy, depending on the insulin amount administered and the time of administration. For this reason, any late in insulin administration would result in hyperglycemia at the beginning of the meal and hypoglycemia at the end of the meal or shortly after. There are three types of diabetes [START_REF] Haas Linda | Beck Joni… National Standards for Diabetes Self-Management Education and Support[END_REF]:

 Type 1 diabetes: results from the body's failure to produce insulin, and presently requires insulin injection. (IDDM for short or juvenile diabetes). Without insulin, glucose remains in the bloodstream, so blood glucose levels increase, especially after meals are consumed. The glucose is then passed out of the body in the urine. Today the treatment of this type of diabetes is done by injecting insulin into the body, by exercising and keeping a healthy diet.

 Type 2 diabetes: results from insulin resistance, a condition in which cells fail to use insulin properly, sometimes combined with an absolute insulin deficiency. Noninsulin-dependent diabetes mellitus (NIDDM for short or adult-onset diabetes). It is considered as the most common type of diabetes.

Over time, the number of β-cells starts to decline, and then the type 2 diabetic patient must be treated with insulin injections like the type 1 diabetic to maintain his/her blood sugar at normal levels.

 Gestational diabetes: is when pregnant women, who have never had diabetes before, have a high blood glucose level during pregnancy. It may precede development of type 2 DM.

All types of diabetes are treatable by different ways, such as tablets, regular insulin injections, as well as a special diet and exercise.

III.2.2. Glucose Level

The human body uses a complex metabolic system to sustain life and power its everyday actions. It converts complex forms of food into glucose, a type of sugar used in energy expenditure. A simple definition of Glucose level is the amount of glucose in the blood, this level vary before and after meals, and at various times of day.

Diabetics have to be more or less constantly aware of the current concentration of blood glucose. Daily measurement can be carried out using an electronic glucometer [START_REF] Ramchandani Neesha | New technologies for diabetes: a review of the present and the future[END_REF]. In order to prevent the complications associated with diabetes mellitus, we must maintain the blood glucose level near normal range. The following table III According to table III.1, it's clear that range between optimal state and hypoglycemia is very narrow. Since hypoglycemia is definitely the worst state to be in, it should be obvious why many diabetics prefer to "overdose" themselves with sugar. This is one of the reasons why it's so hard, especially for type 1 diabetics, to specify the right amount of insulin to be injected; even a small miscalculation could have unpleasant consequences. We can divide the level of sugar in three states (figure III.3): dangerous, normal, unwanted. The dangerous range where we have a very low level of blood sugar, the part can be considered as normal as people without diabetes and unwanted when you have a broad level of high blood sugar.

Glucose Level

Max

III.2.3. Closed-loop

The closed-loop system use the feedback from the output to completes its operating cycle within the system. A closed-loop control system, also known as a feedback control system is an open-loop with feedback, which means that the output value is returned to the input in order to improve its quality. It's important in closed-loop control system, to measure the controlled variable and calculate the control error value, in order to arrive to remove or reduce this error.

Basically, blood glucose sensors and an insulin pump help to control insulin delivery system [START_REF] Garry | Metabolic modelling and the closed-loop insulin delivery problem[END_REF][START_REF] Elleri Daniela | Closed-loop insulin delivery for treatment of type 1 diabetes[END_REF]. In brief, an implanted blood glucose sensor measure glucose level so an insulin pump, attached to a patient's body, continuously inject insulin into it. If the systems are interconnected in a cycle, we have a closed loop system. We give a high-level overview of the system, and this allows creating many clinical cases that can benefit from closed-loop systems. Figure III.4 show how a sensor detect the state of a patient, then a signal is sent to the controller, the controller upon an algorithm decide to send a controller command to the actuator, the actuator play his role to send or not the necessary insulin amount. The state of the actuator is always send to the actuator, to let him know if last command is activated or not, and the amount of insulin in the reservoir. The closed-loop system can be tested in many levels by implementation of test scenarios based on parametric models of activities, taking meals and setting of the patient (weight, pathology ...). The background squares behind zones mark these levels. These levels are detailed as follow: level Patient where different parameters can represent a set of range test, the second level of sensor and actuators in case where sensor and actuators are working fine or any problem in sensor or actuator give corruption in glucose level that should affect the system, level of controller where must of control testing can be adjusted and modified to arrive to our objective.

Patient

The closed-loop system completes its operating cycle within the system and no external interaction to diabetic patients is required. In other words, the closed-loop control uses the feedback from the output.

III.2.4. Mathematical models

Embedded systems used in medical care help more and more to improve the quality of diagnostic tools available to doctors as well as treatments offered to patients. The first step in this process resides in a better understanding of the glucose-insulin system via mathematical equations: modeling the system and knowing how it interacts with the patient's environment will help to simulate it in normal life conditions and can be thus useful in diabetes research.

Since the sixties, many mathematical models have been developed to better understand the glucose insulin regulatory system. Various models have been proposed to describe the short-term glucose-insulin dynamics. A physiological model that captures the glucose-insulin system dynamics is thus the basis for more optimally addressing the glycemic control problem. In brief, metabolic modeling of the glucose-insulin system has a very deep history in the published literature. The vast majority of these models have their roots in basic compartment modeling with differential equations (Appendix A). To date, the primary use of metabolic models has been the development of model-based measures to assess metabolic parameters, with a particular focus on measuring insulin sensitivity. Mathematical models can be used to create simulators to test different types of treatment.

a. Bergman Minimal model

Minimal model with low-order was for estimation of insulin sensitivity and glucose effectiveness. This model was developed by Richard N. Bergman and therefore is called Bergman's minimal model [START_REF] Bergman R | Nonlinear metabolic dynamics of the pancreas and liver[END_REF][START_REF] Li Jiaxu | Modeling the glucose-insulin regulatory system and ultradian insulin secretory oscillations with two explicit time delays[END_REF].

b. Hovorka model

This model was developed primarily by Roman Hovorka and is therefore being referenced as Hovorka's model [START_REF] Hovorka R | Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes[END_REF][START_REF] Lassen Allan Lyngby | Modeling and Simulation of Glucose-Insulin Dynamics[END_REF][START_REF] Naerum Miriam | Model Predictive Control for Insulin Administration in People with Type 1 Diabetes[END_REF]. It has two inputs, meal disturbances and insulin infusions and simulates a person with type 1 diabetes. It extends the original minimal model by adding three glucose and insulin sub-compartments in order to capture absorption, distribution, and disposal dynamics, respectively. The parameters of the system are defined as follows: Q 1 and Q 2 represent the masses of glucose in the accessible and non-accessible compartments; F 01 is the total non-insulindependent glucose flux corrected for the ambient glucose concentration and F R is the renal glucose clearance; G is the measurable glucose concentration; EGP represents endogenous glucose production; x 1 , x 2 , and x 3 represent three actions of insulin on glucose kinetics; S 1 and S 2 are a two-compartment chain representing absorption of subcutaneously administered short-acting; I describes the plasma insulin concentration; D 1 and D 2 are a two-compartment chain representing the amount of carbohydrates digested. BW is the weight of the patient.

The equations of the model are defined below:

)) ( 1 ( ) ( ) ( ) ( ) ( ) ( ) ( 3 0 2 12 1 1 , 01 1 t x EGP t Q K t Q t x t F F t U dt t dQ R c G        ) ( )) ( ( ) ( ) ( 2 2 12 1 1 2 t Q t x K t Q x dt t dQ    S T t S t u dt t dS ) ( ) ( ) ( 1 1   S S T t S T t S dt t dS ) ( ) ( ) ( 2 1 2   dt t dD h D D ) ( * 1 1 1   / h constant variation dt t dD h D D ) ( * 2 2 2

 

The insulin absorption rate, UI (t) (mU/min) can be calculated:

S I T t S t U ) ( ) ( 2 
The insulin concentration, I(t) (mU/L), is found by solving the following differential equation:

) ( ) ( ) ( t I K V t U dt t dI e I I  
x 1 , x 2 and x 3 are calculated using the following three differential equations, depending on only the plasma insulin concentration and parameters They proposed a nonlinear model consisting of glucose, insulin and glucagon subsystems.

) ( ) ( ) ( 1 1 1 1 t I K t x K dt t dx b a    / k b1 = S IT k a1 ) ( ) ( ) ( 2 2 2 2 t I K t x K dt t dx b a    / k b2 = S ID k a2 ) ( ) ( ) ( 3 3 3 3 t I K t x K dt t dx b a    / k b3 = S IE k a3
Picture below describes this model by giving a general overview of the glucose-insulin control system. Glucose and glucagon subsystem were modeled using a single compartment respectively, and insulin subsystem was expressed as a five-compartment model.

d. Comparison and decision

Bergman's minimal model provides a good approximation of the system, but omits several important physiological functions and features of insulin, which are included in the model of Hovorka. It includes most of the physiological parameters of the glucose and insulin action. In Hovorka, features non-insulin-dependent has been smoothed to avoid discontinuities in the system. Man-Rizza-Cobelli model is a bit more complex than Hovorka's, and is supposed to be more realistic.Like Hovorka this simulation model is based on the principle of having a system of differential equations, and we have several systems (organs), which is all modeled separately and all connected.

These models were intended for different purposes:

• Measurement of insulin sensitivity and control (Bergman)

• Simulation and control (Hovorka)

• Simulation (Man-Rizza-Cobelli)

• Control (Panunzi)

We have the choices to choose between Hovorka and Cobelli models to implement it to our system, noting that these two models have good presentation of the human system body, so as example we implement the Hovorka model. Noting that, the success in applying one of them using embedded c language, will allow us to apply any other one.

III.3. Models Implementation

A simulator is developed to make virtual experiments that show the effects of changes parameters on glucose levels in insulin-dependent diabetes mellitus. We need to perform reachability/safety analysis of the system.

In this part of this chapter we create a new framework in order to test the performance of all system components. The framework begins by simulating a mathematical model of the human body. This model was developed to operate in the closed loop of the glucose insulin.

Next, the model of artificial pancreas has been implemented to control the mathematical model of human body. Finally a new tester model was created in order to analyze the performance of all the components of the glucose-insulin system. The Keil debugger file play the role of the patient and the programmed algorithm play the role of the controller.

III.3.1. Implementation of Human body

Mathematical models of glucose regulation have been studied over years. Recently, modeling an insulin-glucose system has been presented [START_REF] Maira | Prediction of Postprandial Blood Glucose under Intra-Patient Variability and Uncertainly and its Use in the Design of Insulin Dosing Strategies for Type 1 Diabetic Patients[END_REF].

This section provides an overview of the model while references concerning the mathematical equations are defined in previously in section III.2.4.d. The model used has been selected according to the need of the research. This is a complete model for the glucoseinsulin system during a meal and it was developed using glucose tracers. The main idea of this model is to divide the compartments in specific biological processes.

First of all, we have validated the model of human body using "Hovorka" that we have implemented using the reference scenario find in [START_REF] Lassen Allan Lyngby | Modeling and Simulation of Glucose-Insulin Dynamics[END_REF][START_REF] Naerum Miriam | Model Predictive Control for Insulin Administration in People with Type 1 Diabetes[END_REF]. We have implemented it using Keil in an embedded code program, to act as a patient. In this scenario insulin is taken before the meal. We consider meals, taken by a person, which represents breakfast, lunch and dinner in a normal day. Just as a point of reference we use CHO 1 = 45g and CHO 2 = CHO 3 = 70g, which means that we assume that the amount of carbohydrates eaten for breakfast is 45g, and so on.

The insulin doses are also exactly the same with 2U/L for breakfast and 3U/L for lunch and dinner. The Hovorka model is implemented based on algorithms defined from table III The graph below (figure III.8) represents this case, we notice that the glucose level is smooth and its range is inside the limit at all times. This scenario corresponds to the usual insulin injection made by a well educated diabetic.

III.3.2. Implementation of artificial pancreas

Most of the proposed works of the implementation of this model are done using Matlab/Simulink or java software [START_REF] Makroglou Athena | Mathematical models and software tools for the glucose-insulin regulatory system and diabetes: an overview[END_REF]. It's often due to the complexity of the use of the microcontroller and the huge amount of time needed to implement such methods when incorporating constraints. However, by proposing an optimized algorithm with a reducing size of code and by choosing a low cost microcontroller with low power consumption, one can take the advantages of such miniaturized device. The computed insulin dose required, according to the insulin dosage computation, is a complex calculation algorithm. Additional purpose is to check if the computed dose is allowed to be administered. The different members of the 8051 microcontroller family are suitable for a huge range of projects [START_REF] Michael | Programming Embedded Systems using C[END_REF]. In this part, we have choosen to work with 8051 microcontroller in order to simulate it. We have also simulated this model using Keil development. We have programmed the controller by creating an embedded C program that act as an artificial pancreas. Its main role was to regulate the blood sugar level by insulin injection (figure III.4).

After the sensor reads the level of glucose and sends the result to the controller, the later calculates the necessary dose to be delivered to maintain an existing trend in blood sugar levels between 70 mg/dl and 110 mg/dl. Using readings from the embedded sensor, the system automatically measures the level of the glucose in the sufferer's body. Consecutive readings are compared in order to provide insulin when needed. Insulin is only delivered in circumstances where it appears that the level of glucose is likely to go outside this range. The dose given as glucagon, starts to be active when the level of glucose is below 60 mg/dl .

The simulation setup is shown in figure III.9. Inputs to the virtual patient were glucose and insulin, whereas the output G(t) was blood glucose concentration. A parallel prediction algorithm was used to calculate the future plasma glucose concentration values sent to the controller. Estimated and measured blood glucose from the simulator were used by the controller to determine the doses of insulin or glucagon to be given to the virtual patient. The Artificial Pancreas Microcontroller (APM) chooses automatically the correct dose to be injected according to glucose level and basing on rules of sugar level of the control algorithm. The APM tests the glucose level many times a day, and according to its algorithm it decides whether to inject or not and if yes, the necessary computed dose to be injected. The III.1). Indeed, the human injection has been decided one hour before the meal, the APM could only detect a change in PV after the consequence on the blood glucose after having the meal, which means after the glucose level is risen.

Our goal was not to develop an ideal Artificial Pancreas which will have probably to anticipate the meal in order to regulate blood glucose in the good interval. In this Work, the controller was used only in order to test the performance of all the components of the system. We can see in figure III. [START_REF]Standards of medical care in diabetes[END_REF].b what will happen without the APM, the blood glucose reaches a very high value after lunch and dinner. As previously explained the APM is not perfect but is acceptable as a proof of concept for our tests.

In order to formulate the effective tester, we have changed some parameters. If a problem occurs in an actuator level, these produce an addition of 1 or 2 units or more on the amount of dose injected. Another case is considered, if a problem occurred on the sensor level, the glucose level measured is raised for example 10% or 20% (Figure III.11). These show how the changing in injected insulin dose or having a problem in a hardware or software level can affect the system. These results help to test the system and make a good change in performance and test the response of the system in many cases.

III.3.3. Implementation of sensors and actuators

Sensors and actuators are the essential peripherals connected. There are often used in medical technology, for example in micro-pumps, ultrasonic emitters, etc. They are broadly termed transducers and are essential devices that convert one form of energy into another.

The most widespread example of a commercial biosensor [START_REF] Webster John | Medical Instrumentation Application and Design[END_REF] is the blood glucose biosensor, which uses an enzyme to breakdown the blood glucose/sugar into its metabolites.

The GlucoWatch® G2TM Biographer (GWB) and the Continuous Glucose Monitoring System (CGMS) have both been developed to assist in closer monitoring of glucose levels [START_REF]The accuracy of the GlucoWatch G2 biographer in children with type 1 diabetes: results of the diabetes research in children network (DirecNet) accuracy study, diabetes technology and therapeutics[END_REF][START_REF] Hovorka R | Continuous glucose monitoring and closed-loop systems[END_REF]. Nano-bio sensor ASIC operates at +5V input and provides an output of 0 to 500 mV for absolute sensor output of 0 to 500 nano-amps or pico-amps.

The biosensor can be divided into three components [START_REF] Yoo Eun-Hyung | Glucose biosensors: an overview of Use in clinical practice[END_REF][START_REF] Chambers | Biosensor recognition elements[END_REF]. As shown in For the actuators, we will be interested in electromagnetic motors as they are available in small and compact versions [80]. For example Fritz Faulhaber has set a new standard within the category of DC-Micromotors with graphite commutation. The motor delivers a torque of up to 120 mN.m while measuring just 32 mm in diameter and 72 mm in length. The medical devices such as a micro-pump to extract blood through a tube have a structure which needle and pump part are mutually separated. Bio-actuators can also be implanted into a living body (in vivo) to perform special functions.

An actuator is a device that converts an electrical signal into an action. It can create a force to manipulate itself, other mechanical devices, or the surrounding environment to perform some useful function [START_REF]An Introduction to MEMS (Micro-electromechanical Systems)[END_REF]. In the case of this study, we are interested on pump insulin used for administration of insulin in case of mellitus diabetes. The blood sugar level is usually measured in either mmol/L or mg/dL. We can now find the ratio between the two units going step by step as defined by: mmol x 0, 18 = g / l g / l x 5, 56 = mmol In this model, the systems can be tested in many levels by the implementation of test scenarios based on parametric models of activities, taking meals and the setting of the patient (weight, pathology, etc.).

Sensors and actuators were simulated using mathematical functions based on many conditions states in order to simulate their functions. The purpose of this simulation is to have a complete environment with the ability to co-simulate the glucose insulin model.

For example, table III.12 below calculates the computed dose to be given by comparing the current and previous glucose level. Set Q 1 the current Glucose level, Q 2 the previous Glucose level, and "CompDose" the computed dose to be injected. We try to implement in-silico technique on a virtual type 1 diabetes mellitus (T1DM) patient. The in-silico experimentation [START_REF] Moretti | In silico experiments in scientific papers on molecular biology[END_REF][START_REF] Kovatchev Boris | In silico preclinical trials: a proof of concept in closed-loop control of type 1 diabetes[END_REF][START_REF] Patek Stephen | In silico preclinical trials: methodology and engineering guide to closed-loop control in type 1 diabetes mellitus[END_REF] presents many advantages by providing a higher work productivity, minimum cost and more accurate simulations through more sophisticated models.

Part of the control algorithm function where sugar is ok if

(Q 1 > safeMax) { // If Sugar level increasing if (Q 1 > Q 2 ) { // If

III.5. Models and methods of experimentation

III.5.1. Experimental conditions

This in-silico study, for the "Hovorka" model, considered as a nonlinear meal simulation.

Model parameters were obtained from the model in order to reproduce as faithfully as possible a T1DM patient glucose metabolism. We assume that the simulation starts at midnight with the virtual patient in a steady specific condition. Table III.13 below represents the virtual patient within 4 days in-silico visit. The performance of closed-loop glucose control is tested during these days. Every day, a certain amount of carbohydrate is being served, for example in day 2, a big lunch of 100 [g] is consumed. The amount of meal eaten and the insulin unit injected are different from one day to another. By trying, for example, to increment the portions of meals eaten in a day, while maintaining the insulin unit given. On the other hand, an increment the insulin injection and increment or maintain carbohydrate amount. This helps to determine the side effect of them in the state of the patient. Noting that meals and corresponding insulin doses calculated according to an insulin-tocarbohydrate ratio (ICR) 1:10 were administered complying with the scheme in Table III.13.

Day

Figure III

.17 shows the simulated data, the glucose level measured during 4 days must be maintained between the red lines. We have noticed that the curve in some part of this simulation is high or low due to specific parameter entry. The simulation during 4 days is so important to our tester, because the simulation in a day life cannot give a precious answer. It might be during a simulation of a day life, a part of this day for example during breakfast, the glucose level is so high and during dinner is so low, so in total the QoS is in good value.

So to have a better QoS value we try to illustrate our results from 4 days together and for each day during this simulation we compare the results to have more precision and more efficiency.

III.6. Conclusion

In this chapter, we have provided a model that represents a global view of the biomedical equipment, based on repeated simulation to minimize the error of the glucose-insulin model.

The results show the feasibility of co-simulation and therefore the ability to validate a finely embedded system without any biomedical risk taking on patients. We implement an environment allowing the co-simulation system of this model, applying in-silico technique using microcontroller system simulator.

We will try to present, a model-based analysis tool that analyze the performance of the biomedical devices and use the resulting models to identify the usage of such sensors, actuators or controllers.

Chapter IV: Simulations results & QoS measurement practices

IV.1. Introduction

Any measure, whether quantitative or a hard fault more subjective judgment of a soft fault, will not be perfect [START_REF] Tonks David | A study of the accuracy and precision of clinical chemistry determinations in 170 canadian laboratories[END_REF][START_REF] Cox Daniel | Accuracy of perceiving blood glucose in IDDM[END_REF][START_REF] Clarke William | Evaluating clinical accuracy of systems of self-monitoring of blood glucose[END_REF]. When making a decision on the conformity of an embedded system with a specification limit, any measurement uncertainty will lead to a risk that incorrect decisions will be made in compliance. This decision risk must be assessed not only in terms of relative consumer provider of respective risks, but also in terms of impact.

Innovations in biomedical technologies are seen as being able to provide solutions to improve the quality and the efficiency of healthcare systems [START_REF] Thomson Sarah | International Profiles of Health Care Systems[END_REF].

Where embedded system failure can lead to serious consequences, regulation and strict specifications of product quality are set and compliance based on testing of actual product with these requirements will need to be made both at initial type approval and subsequent verification.

Verification is a major concern for many embedded systems. Hence the importance of validation of these systems, that is to say, if to do a test, verification and certification. So there is a real and pressing need to develop methods and effective tools for the validation of embedded systems. Formal methods are developed for timed systems, but are limited to systems of low complexity.

In brief, the main objective in the domain modeling for embedded systems is to study formal models in order to describe these systems and their constraints (design, specification), to build (programming, simulation, synthesis, implementation), and analyze (validation, verification). When making a decision on compliance of an embedded system specification limit, any uncertainty measure will lead to a risk that incorrect decisions will be made of compliance.

In this chapter, the sections show virtual patients generating part, modeling results as well as the control performances in closed-loop achieved exploiting the in-silico patient. It also shows the simulations results and shows the performance of our tester model declared in chapter II for the case studied in chapter III, the glucose level.

IV.2. Clinical cases generation

Many researchers have studied the modeling of glucose-insulin regulation system in order to better understand it, and the causes of diabetes and development of advanced control algorithm to regulate glucose level concentration and investigation of the pathophysiology of diabetes. These models cannot give a meaningful prediction unless its parameters are accurately determined. Identifying virtual patient parameters is done by fitting the model to the patient data and selecting the necessary values, which give the closest fit to the data.

The Hovorka model used has been selected according to the need of the research. As discussed before, this is a complete model for the glucose-insulin system during a meal and it was developed using glucose tracers.

Eight variables were considered as the inputs data providing to each one of them different values in order to simulate the Hovorka model. The (Q 1 , Q 2 , S 1 , S 2 , I, x 1 , x 2 , x 3 , t) help to generate data while solving the Hovorka mathematical model. Indeed, solving mathematical equations inside each parameter helps to have "clinically accurate" results.

A simple modification in each parameters helps to have different patient state. The severity of a patient can be modified by changing parameters values. The objective is to have multiple scenarios in order to use them in the implementation part. We have used the suitability of Partially Observable Markov Decision Processes (POMDP) [START_REF] Finale | The infinite partially observable Markov decision process[END_REF] to formalizing the planning of clinical management (figure IV.1), where α i is the modification values when generation these virtual patients, taking into consideration the approximation range of each parameter. The modification can be done on one parameter or many parameters at the same time. This minor modification is effective to make different patients. Using POMDP it describes a stochastic control process with partially observable (hidden) states. We start from a virtual patient and after the calculation of normalization functions in order to know which zone the patient point is plotted in, we can specify a modification on parameters so to reach a second virtual patient state. is Hovorka using data input vector to have many virtual patients and later an effective tester.

To help in generating these patients automatically, we develop a simple program which generates approximately variables for each parameter that compose this model. Noting that, each element of the vector (Q 1 , Q 2 , S 1 , S 2 , I, x 1 , x 2 , x 3 , t) can be calculated (chapter II Hovorka model) using set of parameters. The F 01 , K 12 , K a1 , K a2 , K a3 , K b1 , K b2 , K b3 , K e are the effective parameters that affect all the system. value, the mean, the standard deviation, the standard error and the median. The purpose of calculating the percentile, and either calculating the standard deviation or using analysis of variance, is to determine the components of imprecision. We can use one of this attributes or the combination of one or two in our function. Table IV. 7: Standard deviation function implementation.

IV.2. Virtual patients sample

In the following two sections, we try to simulate the state of two virtual patients in one day. During this simulation, we simulate the breakfast, lunch and dinner for each one of them, and we compare the value of each meal with the value of the day. The state of a patient may differ during the meals.

IV.3.1. Virtual patient one

In Figure IV.5, we try to illustrate the state of a normal virtual patient. This patient has a glucose level between normal ranges. So if we try to plot this virtual patient during this day, by plotting the day and each meal taken.

IV.3.2. Virtual patient two

In Figure IV.7, we try to illustrate the state of a virtual patient. This patient has a different glucose level during his day. So if we try to plot this virtual patient during this day too, by plotting all the day and each meal taken.

IV.4. QoS evaluation implementation

The QoS indicator has an objective, which is the comparison of the diabetic systems with the normal system. We try to apply the tester model in this system, where the glucose level is the PV controlled and detected.

IV.4.1. Graphic representation

IV.4.2. Grid representation

We analyze each simulation in the purpose of having a graphical representation of the risk assessment for the patient due to choices on sensors, actuators. We use this grid with the percentile function to represent our implementation. The minimum BG is set at the 2.5th percentile, and the maximum BG is set at the 97.5th percentile of the BG distribution. We To simulate the 6 virtual patients from table IV.1 we use the grid analysis and we use Matlab to write the function of simulation. Table IV.9 shows the simulation process of a point in the grid, a point represents one full simulation. Noting that, points exceeding the limits of the plot are plotted on the outer border.

Function name Clarke4

Function prototype Function void clarke4 ()

Behavior description

Plotting simulation in a grid using Matlab Noting that, the virtual patient used for the simulations does not include the effect of factors that influence the blood glucose concentration for example like stress, or that person doing exercise. We notice, it's not considered as bad as an automatic injection system but it is not to have an ideal controller, but to arrive to simulate the performance of equipment. The main idea is to consider critical case on hypoglycemia and hyperglycemia, critical sensors, actuators, and controllers.

To be more precise and to have a best representation, we consider that each simulation is not considered only one point in the grid, but it's constructed from one main point and 3 other points that is the representation state of the patient during breakfast, lunch and dinner. We compare then these values in order to see if the three points are in the same Zone as the main point, which mean the main point is considered the desired value. On the other hand, if one of the three points is out of the main point zone, which means that the state of the patient has been changed during the day and more study must be done to monitor and reveal its state.

IV.5. Conclusion

Simulation results show the performance of the tester to validate glucose insulin system in order to avoid risk taking on patients. From these results the tester that we are creating is a robust tool that will improve testing in biomedical fields without having any risk on patients.

The plot of each simulation as a point in a grid and then splits it into zones defined by their xand y-coordinate ranges, helps to construct a new error grid and use it to evaluate the accuracy of glucose level measurements made by patients.

Chapter V: Conclusion

V.1. Contribution

We have declared a new comprehensive methodology for modeling and simulating the human body and medical systems, to have a better understanding of the best way to model and simulate these systems and to detect the performance and the quality of service of all system components. We have also implemented of an environment for co-simulation of a model of the human body, using Hovorka model.

We have created a programmed model that acts as an artificial pancreas. The goal is to have a complete example of a biomedical system in link with the glucose-insulin in order to be able to test testing strategies. In addition to this, we have defined simple indicators for the system-level testing. The purpose of these indicators is to have a reference to the graphical representation of a person's data in connection with the glucose.

In the implementation part, we implement these models in a comprehensive approach to associate the choices made on the biomedical system of indicators of "well-being" associated with patients. We also simulate these models using in-silico experimentation that has many advantages in providing greater labor productivity, as well as the minimum cost and more accurate simulation due to sophisticated models. The simulation of virtual patients with type I diabetes is done during 4 days, receiving breakfast, lunch and dinner every day.

By generating virtual patients, we had generalized the passage of the clinical trial in order to have several scenarios for analyzing performance. We have also created a simple tool to generate many patients taking into consideration the approximation range of each parameter.

We have used the suitability of partially observable Markov decision processes to formalize the planning of clinical management. A virtual population of subjects with type 1 diabetes comprises a simulation model of the glucose regulation accompanied by N parameter sets representing N virtual subjects.

A choice of a more sophisticated tester, by introducing different sensors and actuators scenarios appears as a promising research direction, although the extension of the algorithm to industrial applications with microcontroller having limited computational capacity requires non-trivial investigation effort.

V.2. Future work

Besides the contributions presented, several open improvements should be undertaken.

The first is aimed to the development of a software application used as a library to test embedded device. This library will contain the main global function used to test and simulate performance of these devices.

The second is related to the adjusted models using data from real patients. In this thesis, an in silico simulation was performed using virtual patient profiles, while another simulation must be performed using the profiles of real patients.

The third is oriented toward the clinical, to improve the assessment correctness of the estimation techniques.

Finally, the use of some other simulations solutions as VHDL-AMS could be a study for future development in order to improve results accuracy.

V.3. Publications

During the research work leading to this thesis, the following conference and journal papers have been published: -



Minimal model

The minimal model [START_REF] Ibrahim Ahmmed Saadi | Advanced mathematical model of glucose-insulin concentrations in type 1 diabetes using artificial neural networks[END_REF][START_REF] Farmer Terry | Effectiveness of intravenous infusion algorithms for glucose control in diabetic patients using different simulation models[END_REF] of the glucose-insulin system is: Noting that Insulin plasma concentration changes are considered to depend on a spontaneous constant-rate decay, due to insulin catabolism, and on pancreatic insulin secretion. The delay term refers to the pancreatic secretion of insulin: effective pancreatic secretion at time t is considered to be proportional to the average value of glucose concentration in the b 5 minutes preceding time t.

b G b t G t X b dt dG 1 1 ) ( )] ( [     ] ) ( [ ) ( dt

Fig. 1 :Fig. 2 :

 12 Fig. 1: Interdépendance des systèmes de l'organisme

- 9 -

 9 Ir un ensemble de relations internes entre les organes du corps humain (Voir l'exemple ci-dessous) Résumé viEr un ensemble des relations externes entre les organes du corps humain (Voir l'exemple ci-dessous) -C et PV un ensemble de constantes et variables physiologiques liées aux systèmes et correspondant à l'état d'un patient, C et PV ont des valeurs numériques qui peuvent être utilisées par les équations du modèle. Notons SC un jeu de constantes sousensemble de C et SPV un jeu de variables physiologiques sous-ensemble de PV, spécifiques à un patient. les variables Par et SPar paramètres d'entrée pour le système, Spar sous-ensemble de Par Si W représente le poids du patient, St un paramètre représentatif du stress du patient, Sp un paramètre indiquant si la personne fait du sport, etc. On peut définir l'ensemble d'informations personnelles sur le patient par : Pf = {W, St, Sp …}

{Or 1 , Or 2 , Or 3 … Or n } ( 3 )SoientSoit 6 ) 7 )

 123367 Soient Ir i une relation interne (fonction mathématique) pour un Or i qui utilise des valeurs de SC Є Or i et SPar Є Or i .. L'ensemble Ir est alors définit par : Er i une relation externe (fonction mathématique) entre deux ou plusieurs Or i qui utilise les valeurs de C et Par. L'ensemble Er est définit par : Er = {Er 1 , Er 2 , Er 3 … Er n SName le nom du système de corps (comme le système digestif), les variables SC et SPV sont liées à un S i concerné. Notant que, l'intersection entre SPV des différents systèmes n'est pas nécessairement vide, parce que certaines variables physiologiques peuvent affecter plusieurs systèmes, donc elles sont des variables communes entre ces systèmes. L'ensemble S est définit comme: 𝐒 = {𝐒 𝟏 , 𝐒 𝟐 , 𝐒 𝟑 … 𝐒 𝐧 }/𝐒 𝐢 ( 𝐒𝐍𝐚𝐦𝐞, 𝐒𝐂, 𝐒𝐏𝐕, 𝐈𝐫, 𝐄𝐫) = ⋃ 𝐎𝐫 𝐢𝐣 𝐧 𝐢 𝐣=𝟏 (Soient Par i les paramètres d'entrée pour le système, Par = U SPar , SPar Є S i . L'ensemble Par est définit par : Par = {Par 1 , Par 2 , Par 3 … Par n } (Soient C i des constantes prédéfinies pour le système / C = U SC , SC Є S i . L'ensemble C est définit par :

Chapitre 2 :

 2 Simulation et évaluation de la QoS des systèmes médicaux La simulation du système biomédical et de son interaction avec le corps humain repose comme indiquée sur la figure 3, sur deux parties interdépendantes : la première « Simulation des Patients », représente le comportement du patient. Celui-ci et simulé en utilisant un modèle mathématique représentant au mieux les mécanismes du système organique humain. Les nombreuses constantes et paramètres qui interviennent dans le modèle sont choisis pour simuler la physiologie et la pharmacologie du patient de façon à fournir des réponses en temps réel à tout traitement donné.

Fig. 4 :

 4 Fig. 4: Simulateur

Fig. 5 :

 5 Fig. 5: Principe de l'analyzeur

Fig. 6 :

 6 Fig. 6 : Représentation de l'indice de gravité

Fig. 8 :Fig. 9 :

 89 Fig. 8: QoS entrée et sortie

- 19 2. 4 .

 194 (t, Par, C) : représentent un ensemble de paramètres et de constantes variables spécifiques au patient en fonction du temps t. -Dm : représente les repas quotidiens pris par le patient. Résumé vi-Evaluation du QoS Nous utilisons deux techniques pour évaluer la QoS offerte par le dispositif à étudier. La première technique calcule un indice de gravité IG H (g) indiquant la gravité de la valeur mesurée sur l'état du patient. Cet indice est calculé sur un intervalle de temps [t i t f ], comme indiqué sur la figure 10, l'évolution d'une fonction f (t) représentative de l'état d'une variable physiologique à contrôlée.

Fig. 10 :

 10 Fig.10: Évolution du niveau d'un PV en fonction du temps

Fig 11 :Fig. 12 :

 1112 Fig 11 : Grilles d'analyse d'erreur de Clarke et Parkes

Fig. 15 :

 15 Fig. 15: Simulation des performances d'un équipement

Fig. 16 :Fig. 17 :

 1617 Fig. 16: Le système de glucose-insuline.

CHO 2 =Fig. 18 :

 218 Fig. 18: Insuline administrée avant le repas

Fig. 19 :

 19 Fig. 19: Représentation en boucle fermée

Fig. 20 :Tableau 2 : 32 Figure 21 :

 2023221 Fig. 20: Simulation boucle fermée

Figure 22 :

 22 Figure 22: Simulations des résultats: (a) une unité injecté (b) deux unités injectées (c) + 10% sur le taux de glucose (d) + 20% sur le niveau de glucose

Figure 23 montre

 23 Figure 23 montre les données simulées, le niveau de glucose mesurée pendant 4 jours doit être maintenue entre les lignes solides et pointillées. Les 2 lignes pointillées forment la limite que la courbe doit respectée pour que le niveau de glucose soit dans le cas normal (70 -100 mg/dL). De même pour les lignes solides (50 -180 mg/dL), forment le minimum et le maximum que le niveau de glucose doit respecter avant d'être considérer dans le cas diabétique. Nous avons remarqué que les résultats ont la courbe dans une partie de cette simulation élevé ou faible en raison de paramètres d'entrée spécifique.

Fig. 23 :

 23 Fig. 23: Simulation des données du patient pendant 4 jours

  évoqué précédemment, il s'agit d'un modèle complet du système glucose-insuline lors d'un repas, qui a été développé en utilisant des traceurs de glucose.On a choisi comme entrée huit variables et on a fournit à chacun d'eux des valeurs différentes afin de simuler le modèle Hovorka. Le (Q 1 , Q 2 , S 1 , S 2 , I, x 1 , x 2 , x 3 , t) aide à générer des données tout en résolvant le modèle mathématique Hovorka. En effet, la résolution d'équations mathématiques pour chaque paramètre est utile pour avoir des résultats "cliniquement précises".

Fig. 24 :- 36 (

 2436 Fig. 24: Patients virtuels.

Fig. 25 :

 25 Fig. 25: Présentation des méthodes utilisées

Fig. 26 :

 26 Fig. 26: Programme pour générer des patients

Fig. 27 :- 39 Conclusion

 2739 Fig. 27: Représentation graphique

Fig. II. 9 : 26 Fig. III. 1 :

 9261 Fig. II. 9: Tester implementation using closed loop ................................................................ 20

Fig. III. 15 :

 15 Fig. III. 15: Global view of biomedical equipments. ..............................................................

Fig. II. 1 :

 1 Fig. II. 1: Interdependence of body systems.

  Fig. II. 2: Physiological regulation

a

  set of external relations between the body actors, C a collection of constants related to systems actors, and Par a collection of parameters. PV is a collection of physiological variables reflecting the state of a patient. Both C and PV are numerical values that may be used by the relations (equations) in the model. SC is a set of constants and SPV is a set of physiological variables where SC is a subset of C and SPV a subset of PV. Let W is the weight, St is the symbol to indicate stress, Sp to indicate if the person do sport, etc... The set Pf is defined by: Pf = {W, St, Sp …} (1) Let B is the set of breakfast food values such as calories fat protein etc.., L is the set of lunch food value, D is the set of dinner food values, and Af is the set of additional portions values such as snacks.

Fig. II. 3 :

 3 Fig. II. 3: Core simulator components.

Fig

  Fig. II. 5: Analyzer

Fig. II. 7 :

 7 Fig. II. 7: QoS input and output.

Fig. II. 8 :

 8 Fig. II. 8: Closed loop system model.

Fig. II. 9 :Fig. II. 10 :

 910 Fig. II. 9: Tester implementation using closed loop

Figure II. 10

 10 Figure II.10 describes the closed-loop system and completes the previous one, where there is a need of a controller, sensor, actuator, an estimation function and the operation done. It's known that, we can enhance our closed-loop, for example by adding an estimation method that affects the control to be modified, and in relation with the sensor. The QoS indicator has an objective. It compares the abnormal systems with the normal system. The graph of figure II.11 describes the simple indicator in an arbitrary case that we try to propose and apply it in the tester to help us reach our objective. We propose a new tester model in order to analyze the performance of all the components of the biomedical system.

Fig. II. 11 :

 11 Fig. II. 11: Index of severity representation

  represents the surface bordered by the curve and the straight α m or β m . It exist an index of severity IG H (g) which indicates the severity of the patient's case. It can be computed by approximating the integral of f (t), using Matlab built-in functions, as follows: IG H (g) = trapz(x 1 ,f')-min(f')(max(x 1 )-min(x 1 )) (13)Where x 1 is the array of points of the formulated curve and f' is the array of values of PV level curve.

Fig. II. 12 :

 12 Fig. II. 12: Clarke and Parkes error grid for glucose.

Fig. II. 13 :

 13 Fig. II. 13: Error grid graphic representation.

The 2 .

 2 5 th and 97.5 th percentiles represents a single direction between two test boxes in the best and worst scenarios, respectively, and the median (50 th percentile) would indicate a normal value between two measurements points. If you have a set of values, then the ones in the 97.5 th percentile are the values greater than 97.5% of the others.

Fig. II. 14 :

 14 Fig. II. 14: Graphic representation using normalization function.

Fig. III. 1 :

 1 Fig. III. 1: The blood glucose-insulin system.

Fig. III. 2 :

 2 Fig. III. 2: Interaction schema of the integrated system.

Fig. III. 3 :

 3 Fig. III. 3: Blood glucose level presentation.

Fig. III. 4 :

 4 Fig. III. 4: Closed Loop system graph.

  It is commonly used to analyze the results of glucose tolerance tests in humans and laboratory animals. Bergman's minimal model describes the body as one compartment model, which mean as a compartment/tank with a basal concentration of glucose and insulin. It's a three-compartment minimal model to analyze the glucose disappearance and insulin sensitivity during an intravenous glucose tolerance test. Modifications have been made to the original minimal model to incorporate various physiological effects of glucose and insulin.

Fig. III. 5 :

 5 Fig. III. 5: Minimal glucose model.

Fig. III. 6 :

 6 Fig. III. 6: Hovorka model.

Fig. III. 7 :

 7 Fig. III. 7: Man-Rizza-Cobelli model.

Fig. III. 8 :

 8 Fig. III. 8: Insulin given before the meal.

Fig. III. 9 :

 9 Fig. III. 9: Simulation closed loop.

Fig. III. 10 :

 10 Fig. III. 10: With and without insulin injection.

Fig. III. 11 :

 11 Fig. III. 11: Simulations results: (a) +1 unit injected (b) +2 units injected (c) +10% on glucose level (d) +20% on glucose level.

Figure III. 12 ,

 12 the First component is the biological element (Bio-receptor) which is used to bind the target molecule. It must be highly specific, stable under storage conditions, and immobilized. The molecular recognition elements include receptors, enzymes, antibodies, nucleic acids, microorganisms and lectins. The second components is the physiochemical transducer that acts as an interface, measuring the physical change that occurs with the reaction at the bioreceptor then transforming that energy into a measurable electrical output. The five principal transducer classes are electrochemical, optical, thermometric, piezoelectric, and magnetic.The Third component is the detector where signals from the transducer are passed to a microprocessor where they are amplified and analyzed. The data is then converted to concentration units and transferred to a display or/and data storage device.

Fig. III. 12 :

 12 Fig. III. 12: Configuration of a biosensor.

Fig. III. 13 :

 13 Fig. III. 13: Micro-pump & micro-valve with piezoelectric actuator.

Fig. III. 14 :

 14 Fig. III. 14: Vb.net program.

Fig. III. 15 :

 15 Fig. III. 15: Global view of biomedical equipments.

Figure III. 15

 15 Figure III.15 represents the complete system that contains three components. The first component described as "Physical world" which represents the patient level. The second

  Fig. III. 16: In-silico with Hovorka model.

Fig. III. 17 :

 17 Fig. III. 17: Simulated patient data during 4 days.

Fig. IV. 1 :

 1 Fig. IV. 1: Virtual patients.

Fig. IV. 2 :

 2 Fig. IV. 2: Outline of the methods used.

Figure IV. 3

 3 Figure IV.3 below shows the set of virtual patients generated using our simple program.

Fig. IV. 3 :

 3 Fig. IV. 3: Software program to generate patients.

Fig. IV. 4 : 8 . 9 . 11 . 12 . 14 .

 489111214 Fig. IV. 4: Software program to calculate percentile, mean, std, stderr, median.

4 : 1 . 2 . 3 . 4 . 5 .

 412345 Median function definition. Algorithm : Calculation algorithm for the median function Let nbcount presents the length of the array, and halfInd be the position index in the half of the vector Let sortarray the array sorted Let pos as an element at a specified index in the sorted array. If the remainder of nbcount divided by 2 equal 0 then median = (pos(halfInd) + pos (halfInd -1) ) / 2. Otherwise Return median = pos(halfInd).

1 . 2 . 3 . 6 . 7 .

 12367 [START_REF] Sumner Thomas | Sensitivity analysis in systems biology modeling and its application to a multi-scale model of blood glucose homeostasis[END_REF] represents the standard deviation function definition and its algorithm. This function is used to calculate the value of the percentile with a standard deviation. It takes as input the simulation data array and gives as output the standard deviation value.Function name getStandardDeviationFunction prototypeFunction void getStandardDeviation (doubleList)Behavior descriptionStandarddeviation function used to calculate the value of the percentile with standard deviation Input doubleList: array.OutputStandard deviation valueTable IV. 6: Standard deviation function definition. Algorithm : Calculation algorithm for the standard deviation function Let avg be the average value of the array and n the length of the array Let sumderivation as the sum of the derivation of the array For each value in the array do 4. sumderivation  sumderivation + (value * value) 5. End For Set sqrt as the square root of a specified number. Return sqrt (sumderivation/n -(avg * avg))

Fig. IV. 5 :

 5 Fig. IV. 5: Virtual patient one.

Fig. IV. 6 :

 6 Fig. IV. 6: Normal Virtual patient (1).

Fig. IV. 7 :

 7 Fig. IV. 7: Virtual patient two.

Figure IV. 8

 8 Figure IV.8 shows the state of the patient during the morning has been in different zone, but all the day the simulation was in Zone A. All of the four points are not in the same zone, which leads us to conclude that the state of the patient during all day has been changed.

Fig. IV. 8 :

 8 Fig. IV. 8: Normal Virtual patient (2).

  determine the minimum and maximum inverted percentiles for each simulation, where for each person a point is plotted with x-coordinate the minimum BG and y-coordinate the maximum BG for an observation period. The duration of a simulation is 24 hours; and in a day study each person would get a data point on the grid. We implement our controller in order to analyze its performance.The World Health Organization (WHO) uses the percentile in their testing and measurement of health data[91]. Percentiles are position measures that are used primarily in educational and health-related fields to indicate the position of an individual in a group. It has been established to be considered as an important indicator for obtaining normalized values.

9 : 5 2. 5 3. if prct25p1<50 then prct25p1=50 end if 4 . if prct975p1<110 then prct975p1=110 end if 5 . 7 . 8 .

 9554578 Clarke4 function definition.TableIV.10 represents the algorithm for error grid implementation using Matlab. Matlab provides built-in functions which help to easy construct the grid (plot, fill, text, set, xlabel, ylabel). We have 9 zones in this grid (Upper C', 'Upper Bzone', 'A-zone', 'Upper D', 'B zone', 'Lower B-zone', 'E-zone', 'Lower D', 'Lower C') and the grid has limit values that the plotted point must respect ( more details in Appendix C). Algorithm: Error grid implementation algorithm in Matlab 1. Let prct25p1 as the percentile value for the array for a percentile 2.Let prct975p1 as the percentile value for the array for a percentile 97.Draw label axe x and axe y 6. Use to fill function to draw each zone Draw each zone 'Upper C', 'Upper Bzone', 'A-zone', 'Upper D', 'B zone', 'Lower B-zone', 'E-zone', 'Lower D', 'Lower C', in order to form the grid. Use plot function to plot the two values as a point in the grid plot(prct25p1,prct975p1)TableIV. 10: Grid function algorithm.In Figure IV.5, the plot of each simulation as a point in a grid and then splits it into zones defined by their x-and y-coordinate ranges, helps to construct a new error grid and use it to evaluate the accuracy of value measured. In the first implementation, we implement to test the controller in order to analyze its performance.

Fig. IV. 9 :

 9 Fig. IV. 9: Graphic representation.

Journal papers ( 1 )oo

 1 Ch. El-Gemayel, F.Jumel, J.Constantin, D.Zaouk, N.Abouchi, "A prototype to generalize clinical cases of the glucose-insulin system", Biomedical Engineering journal in the Walter de Gruyter (WdG), Volume 59 (s1), 2014.  International conferences (3) o Ch. El-Gemayel, F. Jumel, J. Constantin, D. Zaouk, N. Abouchi, "A global methodology for modeling and simulating medical systems", 16 th International Conference on E-health Networking, Application & Services, IEEE, pages 402-407, 2014. Ch. El-Gemayel, F. Jumel, J.Constantin, A. Tabet, D. Zaouk, N. Abouchi "A new framework for analyzing the performance of the Glucose-Insulin System", 2 nd International Conference, Advances in Biomedical Engineering (ICABME) , IEEE, pages 159-162, 2013. o Ch. El-Gemayel, F. Jumel, J. Constantin, A. Tabet, D. Zaouk, N. Abouchi "An insilico study for glucose-insulin system based on microcontroller using system simulator", 25 th international conference Microelectronics (ICM), IEEE, pages 1-4, 2013. International conferences without published proceedings (1) o Ch. El-Gemayel, F. Jumel, J. Constantin, Y. Zaatar, D. Zaouk, N. Abouchi, "A global architecture for patient simulator systems", 20th LAAS International science conference, Oral presentation, pages 23-24, Hadath-Lebanon, 2014  National Conference (1) o Ch. El-Gemayel, F. Jumel, J. Constantin, D. Zaouk, N. Abouchi, "Co-simulation of Physiological Glucose-Insulin human system and embedded system models including hardware and software components", GDR SoC-SiP, Poster ,Lyon-France, 2013 APPENDIX A This appendix contains the mathematical equations of the minimal model and the dynamic model of the glucose-insulin system.

  dX

  = 0, I (0) = b 7 + Ib, [G(t)b 5 ]+ = G(t)b 5 if G(t) > b 5 and 0 otherwise. G(t) denotes blood glucose concentration at time t [mg/dl] I (t) insulin blood concentration [pM] X(t) is an auxiliary function representing insulin-excitable tissue glucose uptake activity G b [mg/dl] is the subject's baseline glycemia I b is the subject's baseline insulinemia b 1 -b 6 are various rate constants, and b 0 , b 7 are constants. b 7 [(mg/dl) min -1 ]is the constant increase in plasma glucose concentration due to constant baseline liver glucose release.

Composants de simulation de base simulation des patients Modèle mathématique Constantes Paramètres Simulation des périphériques Modèle mathématique Capteur Constantes Paramètres Actionneur contrôleur Entrée/ Sortie

Fig. 3: Architecture du simulateur retenu La deuxième « Simulation des périphérique » est utilisée pour simuler les dispositifs médicaux. Les modèles mathématiques utilisés offre aussi la possibilité de simuler les capteurs, les actionneurs et les contrôleurs associés. Cette approche permet d'approcher au mieux la fonctionnalité du dispositif médical afin de permettre une simulation complète du système. La finesse du modèle peut, on fonction des objectifs recherchés, être simple ne prenant en compte que les fonctionnalités apparente du dispositif pour une analyse grossière ou complexe allant jusqu'à prendre en compte des problématiques de mécanique ou de gestion de l'énergie pour une analyse approfondie. Les modèles mathématiques des patients et des périphériques associés à savoir les capteurs, les actionneurs et les contrôleurs ont été développés est programmés en utilisant la plateforme Keil [39, 40]. La simulation conjointe de ces deux modèles : simulation des patients et simulation des périphériques, permet Résumé vi-13 d'étudier le fonctionnement et la qualité de service de différents équipements biomédicaux face à différents scénarios.

{β 1 , β 2 , β 3 …. β n } < PV < {α n …., α 3 , α 2 , α 1 } (10) Le

	propres mécanismes de contrôle automatique. Basées sur le principe de la rétroaction, ces
	mécanismes de régulations maintiennent les paramètres physiologiques à des valeurs
	normales permettant à l'individu de vivre correctement, c'est cette régulation que nous
	essayons de reproduire par notre simulateur. L'évolution dans le temps des variables
	physiologiques étant contrôlées est décrite par des équations différentielles, lorsqu'un
	événement quelconque provoque le changement de l'état d'une variable, des rétroactions sont
	déclenchées pour compenser les variations afin de ramener le paramètre physiologique à sa

2.2. La qualité de service (QoS)

La qualité de service (QoS) est un indicateur qui peut couvrir différentes performances d'un système, elle porte principalement sur la disponibilité, la fiabilité, la sécurité et le coût.

C'est une notion qui est beaucoup mis en avant pour qualifier les performances d'un système médical. Qu'il soit un service comme par exemple l'accès aux données d'un patient ou un dispositif comme par exemple un pacemaker

[START_REF] Engelbrecht Gerhard | Towards negotiable SLA-based QoS support for biomedical data services[END_REF][START_REF] John | A QoS data management system within a pervasive medical environment[END_REF][START_REF] Liang | A QoS-aware Routing Service Framework for Biomedical Sensor Networks[END_REF][START_REF] Curtis | Continuous Quality Improvement in Health Care: Theory, Implementation, and Applications[END_REF]

. Dans le cas des dispositifs embarqués biomédicaux, maintenir une qualité de service à un niveau donné, c'est maintenir un paramètre physiologique à une valeur donnée, supposée normale. [La valeur normale d'un paramètre physiologique d'un patient correspond à la valeur qui doit rester inchangée ou avec de très légères variations de jour en jour, voire d'année en année]. Comme rappelé dans Résumé vi-15 l'introduction, dans tous les cas et quel-que-soit l'individu, la valeur normal d'un paramètre physiologique, doit être contrôlée est maintenue entre un niveau maximum et un niveau minimum spécifiques à l'organisme de l'individu. Un corps humain sain dispose de ses valeur normal. La figure 2 illustre les rôles du capteur, du contrôleur et de l'actionneur dans la production de la réponse de contre-réaction. Les paramètres de contrôle de la variable physiologique peuvent se référer à des valeurs statiques ou à des valeurs dynamiques variables dans le temps. L'étude de chaque dispositif permet d'identifier les variables qui doivent être manipulées et comment elles doivent être modifiées afin d'atteindre les spécifications désirées. Si α i représente l'ensemble des valeurs qu'un paramètre physiologique PV peut prendre depuis sa valeur normale à sa valeur maximale que nous noterons α 1 . De même, si β i représente l'ensemble des valeurs que ce même paramètre physiologique peut prendre depuis sa valeur normale jusqu'à sa valeur minimale que nous noterons β 1 , on peut pour les valeurs possibles de PV écrire : suivi et l'analyse de l'évolution des valeurs prises par le paramètre physiologique PV peut être utilisé pour qualifier les performances d'un dispositif médical donné et ainsi mesurer sa qualité de service. On peut par exemple tolérer une valeur β i ou une valeur α i mais uniquement si cette dernière ne dure qu'un un laps de temps supposé autorisé. La surface de la courbe entre t 1 et t 2 doit dans ce cas rester inférieure à une certaine valeur. Résumé vi-16

k ,t' L (t' K <t' j <t' L )/ f(t' K )=f(t' L )= β m et T Hypo =∑(t' L -t' K ) (12)

  )

	Pour chaque t' j / f'(t' j )=0 et f(t' j )<β m :
	Ǝ t' Ensuite, pour une simulation donnée, il existe une valeur	g		 t t k l	f	t ( , qui représente la )
	surface délimitée par la courbe et la droite αm ou βm. Cette surface définie un indice de
	gravité IG H (g), qui indique la gravité du cas du patient. Cette surface peut être calculée par :

IG H (g) = trapz(x 1 ,f')-min(f')(max(x 1 )-min(x 1 )) (13)

	Résumé
	La deuxième, basée sur une grille d'analyse d'erreurs améliorée, relativise la dangerosité
	de la valeur mesurée en ajoutant un critère de temps. Pour le cas du diabète par exemple, nous
	avons pris comme intervalle de temps les 24 heures d'une journée et d'une nuit que nous
	avons répartis sur trois créneaux : autour du petit déjeuner, autour du déjeuner et autour du
	diner. La moyenne des valeurs du paramètre physiologique mesurées sur un créneau de temps
	représente ainsi un point de la grille d'analyse. L'objectif dans les deux cas étant de mesurer
	les différences entre les valeurs mesurées et les valeurs normales afin d'observer les réactions
	du dispositif médical et ainsi qualifier ses performances.
	vi-20

Représentation graphique de la grille d'analyse d'erreur :

	Le principe d'évaluation des performances d'un dispositif électronique par la mesure du
	paramètre à évaluer et sa comparaison à une grille d'erreur de référence connue est beaucoup
	utilisé dans le domaine des dispositifs biomédicaux [49, 50]. C'est par exemple le cas pour la
	mesure des performances des dispositifs de dépistage du diabète ou de contrôle de glycémie.
	Pour le cas du diabète, les grilles d'erreurs de mesures les plus connues pour estimer les
	performances de mesures des capteurs de contrôle de glycémie sont celles proposées par
	Clarke et Parkes [50, 51]. Clarke et Parkes ont conçu des grilles d'analyse d'erreurs (EGA :
	Error Grid Analysis) en prenant en considération non seulement la différence entre la valeur
	de glucose mesurée par le dispositif et la valeur de glucose de référence dans le sang mais en
	intégrant aussi la signification clinique de cette différence à savoir la dangerosité de la
	mesure. Comme indiqué sur la figure 11, cinq catégories de risques ont été définies :
	-A : fonctionnement normal
	-B : peu ou pas d'effet sur les résultats cliniques.

Si p >100 or p <0 alors retourner les éléments du vecteur unique sinon

	Résumé Résumé
	). En résumé, chaque simulation est représentée par La figure 13 illustre le modèle globale incluant le modèle du patient et du dispositif L'analyse de la performance des dispositifs biomédicaux aide à identifier l'utilisation des
	un point dans la grille; ce point est calculé en utilisant une fonction de normalisation. Ayant médical à évaluer retenu pour notre étude. capteurs, des actionneurs ou des contrôleurs. Dans ce travail, la représentation de la grille
	de nombreuses simulations de scénarios aident à tracer ces points dans cette grille. Le terme permettra non seulement de simuler les performances des capteurs actionneurs mais aussi et
	percentile est souvent utilisé dans la déclaration des résultats des tests, on l'a représenté sous contrôleurs (figure 15). Analyser la performance des dispositifs biomédicaux aide à identifier
	forme d'équations (Appendice C). Cette fonction de normalisation peut être percentile ou une unité de mesure qui aide à calculer un point (par exemple médiane). Le 2.5th et 97.5th percentiles représentent un sens Modèle du patient Modèle du dispositif médical Paramètres d'entrées (poids du patient, repas, activités, l'utilisation de ces capteurs, actionneurs ou contrôleurs. En résume, en utilisant la simulation évaluation Valeur estimée de la variable physiologique à du QoS des composants suivants: capteurs, actionneurs ou de contrôleur, et une fonction de à évaluer médicaments, etc.). contrôlée normalisation, nous pouvons représenter cette simulation en utilisant la grille d'analyse.
	unique entre deux boîtes de test dans le meilleur et le pire des cas, respectivement, de même
	que la médiane (50th percentile) indiquerait une valeur normale entre deux points de mesure. Retour du dispositif à évaluer
	Si vous avez un ensemble de valeurs, celles de la "percentile 97,5th" sont les valeurs Fig. 13 : Schéma de principe d'évaluation du dispositif
	supérieures à 97,5% des autres.
	La fonction prctile (vect, par) (tableau 1) prennent deux paramètres, la première est les Pour une pathologie donnée, le modèle du patient permet, à partir de paramètres d'entrées
	valeurs du vecteur de la simulation et la valeur percentile comme second paramètre, par spécifiques à un patient (poids, activités sportives, repas, etc.), d'estimer une valeur de la
	exemple 2,5. variable physiologique à surveillée. Le modèle du dispositif médical à évaluer analyse la
	valeur estimée et se charge de la correction nécessaire à apporter pour approcher au mieux prct25p1 = prctile(str,per) une valeur normale, c'est-à-dire une valeur dans les limites tolérées par l'organisme du Une partie de ces fonctions (la percentile, la moyenne, l'écart-type, l'erreur-type et la patient. Pour le cas du diabète par exemple, le retour peut être une consigne d'injection
	médiane.), de même les algorithmes sont décrits ci-dessous (l'annexe C). Tableau 1 automatique ou pas d'une dose d'insuline. La figure 14 illustre comment fonctionne le
	représente l'algorithme utilisé pour calculer la fonction de percentile. modèle du dispositif médical à évaluer. En suivant les retours du dispositif médical et leurs
	impacts sur l'évolution dans le temps de la variable physiologique à contrôlée, on peut
	Algorithme : Algorithme de calcul pour la fonction percentile quantifier la qualité de service du dispositif.
	1. Soit len la longueur du vecteur de données triées qui représentent les points de
	simulation and 0 < p <= 100 la valeur du percentile.
	Paramètres
	d'entrées (poids du patient, repas, activités, 2. 3. Calculer le percentile estimé: position / position=(len +1)*p / 100 médicaments, etc.).
	4. Poser n = p / 100 * (len-1) +1;
	5. Soit left l'élément en position floor(position) dans le vecteur et soit right
	l'élément suivant in the vecteur, où floor est le plus grand entier inférieur ou égal à la position spécifiée. Capteur Algorithme de contrôle valeur estimée de la variable physiologique Valeur mesurée de la variable physiologique à contrôlée Modèle évaluation du du QoS patient
	6. Si position >=1 alors calcule les valeurs de left et right. sinon retourner left
	comme le premier élément du vecteur et right comme le second.
	7. Si left égal right alors retourner la valeur du left. sinon retourner left + (n-Retour du dispositif à évaluer Actionneur
	floor(n)) * (right -left)
	Fig. 14 : Modèle de régulation d'une variable physiologique
	Tableau 1: percentile algorithme
	vi-23 vi-24

  présente des nombreux avantages en fournissant une plus grande productivité du travail, un coût minimal et des simulations plus précises grâce à des modèles plus sophistiqués. Dans la partie simulation, nous avons utilisé un modèle mathématique "Hovorka" qui a été testé sur un procès in-silico des sujets diabétiques type I pendant 4 jours, recevant le petit déjeuner, le déjeuner et le dîner chaque jour. De plus, l'algorithme du contrôleur a été programmé en utilisant le langage C embarqué et il a été simulé à l'aide du cycle par Keil de cycle sur le type d'architecture 8051. Tableau 4: in-silico table de données Notant que, les repas et les doses d'insuline correspondantes calculées selon un rapport insuline-glucides (ICR) 1:10, ont été administrés conforment au schéma dans le tableau 4.

						Résumé
		19:00	70	19:00	3
	4	8:00	75	8:00	4	16
		12:00	100	12:00	6
		19:00	100	19:00	6
	Jour	Temps de	CHO	Temps	Unité d'insuline	IU/Jour
		repas	(g)	d'injection	(IU)	manuelle
	1	8:00	45	8:00	2	8
		12:00	70	12:00	3
		19:00	70	19:00	3
	2	8:00	45	8:00	2	8
		12:00	100	12:00	3
		19:00	70	19:00	3
	3	8:00	45	8:00	2	10
		12:00	100	12:00	5
						vi-34

On a supposé que la simulation a été réalisée à partir de minuit avec un patient virtuel ayant un état spécifique constant. Le tableau 4 ci-dessous représente le patient virtuel dans les 4 jours de visite in-silico. La performance de boucle fermée de la glycémie est contrôlée lors de ces jours. Chaque jour, un hydrate de carbone étant servi par exemple dans le deuxième jour, un grand déjeuner de 100 [g] est consommé. La quantité de repas consommée et l'unité d'insuline injectée sont différentes d'un jour à l'autre. Nous avons essayé, par exemple, d'augmenter les portions de repas consommées en une journée, tout en maintenant l'unité de l'insuline donnée. De même, nous avons augmenté l'injection de l'insuline et tout en augmentant ou en maintenant la quantité d'hydrate de carbone. Cela aide à déterminer leurs effets indésirables sur l'état du patient.

Table of contents vii Table of contents

 ofviiof Acknowledgments .......................................................................................................................... iii Abstract .......................................................................................................................................... iv Résumé ........................................................................................................................................ vi-1Table of contents ........................................................................................................................... vii List of Acronyms ............................................................................................................................. Keil ................................................................................................... 13 II.4.2. Simulators ....................................................................................................... 15 II.5. QoS indicators .............................................................................................................. 16 Case study -Systems implementation ....................................................................... III.1. Introduction .............................................................................................................. 28 III.2. Glucose-Insulin System .............................................................................................. 30 III.2.1. Diabetes mellitus overview .................................................................................. 32 III.2.2. Glucose Level ....................................................................................................... 33 III.2.3. Closed-loop .......................................................................................................... 34 III.3. Models Implementation ............................................................................................ 41 III.3.1. Implementation of Human body .......................................................................... 41 QoS evaluation implementation ............................................................................... 69 IV.4.1. Graphic representation ......................................................................................... 70 IV.4.2. Grid representation ............................................................................................... 71 Contribution .................................................................................................................. 75 V.2. Future work .................................................................................................................. 76 V.3. Publications ............................................................................................................. 77 APPENDIX A ............................................................................................................................... APPENDIX B ............................................................................................................................... APPENDIX C ...............................................................................................................................

	Table of contents
	V.1.
	ix

x List of Tables ................................................................................................................................. xii List of Figures .............................................................................................................................. xiv Chapter I: Introduction .................................................................................................................... 1 I.1. Introduction ...................................................................................................................... 1 I.1.

1. Motivation .......................................................................................................... 1 I.1.2. Objectives ........................................................................................................... 4 I.1.3. Thesis structure .................................................................................................. 4 Chapter II: Systems modeling ......................................................................................................... 6 II.1. Introduction .................................................................................................................... 6 II.2. Architecture of the model ............................................................................................... 8 II.3. Mathematical Representation of human body .............................................................. 10 II.3.1. Prototype definition ............................................................................................... 10 II.4. Simulation representation of the medical system ......................................................... 12 II.4.1. μVision II.5.1. QoS schema ........................................................................................................... 17 II.5.2. QoS evaluation ...................................................................................................... 20 II.6. Conclusion .................................................................................................................... 27 Table of contents viii Chapter III: III.3.2. Implementation of artificial pancreas ................................................................... 47 III.3.3. Implementation of sensors and actuators ............................................................. 51 III.4. Programmed Software .............................................................................................. 54 III.5. Models and methods of experimentation ................................................................. 55 III.5.1. Experimental conditions ....................................................................................... 56 III.6. Conclusion ................................................................................................................ 59 Chapter IV: Simulations results & QoS measurement practices................................................... IV.1. Introduction .............................................................................................................. 60 IV.2. Clinical cases generation .......................................................................................... 61 IV.2. Virtual patients sample ............................................................................................. 63 IV.3. Simulation Implementations .................................................................................... 64 IV.3.1. Virtual patient one ................................................................................................ 67 IV.3.2. Virtual patient two ............................................................................................... 68 IV.4. IV.5. Conclusion .................................................................................................................. 74 Chapter V: Conclusion ..................................................................................................................

Table II .

 II 1: Error grid zones definition. ................................................................................... Table III. 1: Interpretation and approximate value of BG level. .............................................. Table III. 2: Hovorka model parameters. ................................................................................. Table III. 3: Hovorka Function definition. ............................................................................... Table III. 4: Hovorka function implementation algorithm (1). ................................................ Table IV. 3: Percentile Algorithm. ........................................................................................... Table IV. 4: Median function definition. .................................................................................

		List of Acronyms List of Tables List of Tables
	IVGTT	Intravenous Glucose Tolerance Test
	NIDDM	Non-insulin-dependent diabetes mellitus List of Tables
	POMDP	Partially Observable Markov Decision Processes
	PS	Patient simulation
	QoS	Quality of service
	SMA	Artificial Pancreas Shape Memory Alloy
	ADA Std	American Diabetes Association Standard deviation
	APM Stderr	Artificial Pancreas Microcontroller Standard error
	BG T1DM	Blood Glucose Type 1 diabetes mellitus
	CGM WHO	Continuous Glucose Monitor World Health Organization
	CGMS	Continuous Glucose Monitoring System
	CHO	Carbohydrates
	CG-EGA	Continuous Glucose-Error Grid Analysis
	DM	Diabetes Mellitus
	DS	Device simulation
	EGP	Endogenous Glucose Production
	EGA	Error Grid Analysis
	FDA	Food and Drug Administration
	GOx	Glucose oxidase
	GDH	Glucose dehydrogenase
	GWB	GlucoWatch® G2TM Biographer
	IDDM	Insulin-dependent diabetes mellitus
	IU	Insulin Unit
	IDF	International Diabetes Federation
	ICR	Insulin-to-carbohydrate ratio
	ISO	International Organization for Standardization
		xi xii xiii

Table III. 5: TestGB function definition. ................................................................................. Table III. 6: Hovorka function implementation algorithm (2) ................................................. Table III. 7: Testins function definition. .................................................................................. Table III.

8: Hovorka scenario implementation algoritm. ........................................................ Table III. 9: Control algorithm main rules. .............................................................................. Table III. 10: Specific parameters. ...........................................................................................

Table III. 11: Glucose test before and after meal. .................................................................... Table III. 12: Function that Calculate the computed dose. ...................................................... Table III. 13: In-silico table data. ............................................................................................. Table IV. 1: 6 virtual patients' data…………………………………………………………..64 Table IV.

2: Percentile function definition. .............................................................................. Table IV. 5: Median algorithm. ................................................................................................ Table IV. 6: Standard deviation function definition. ...............................................................

Table IV .

 IV 7: Standard deviation function implementation. ...................................................... Table IV. 8: IG H (g) with α, β predefined constant values. ...................................................... Table IV. 9: Clarke4 function definition. ................................................................................. Table IV. 10: Grid function algorithm. .................................................................................... Interdependence of body systems. ............................................................................. 9 Fig. II. 2: Physiological regulation ............................................................................................. 9 Fig. II. 3: Core simulator components. ..................................................................................... 13 Fig. II. 4: Simulator ................................................................................................................. 15 Fig. II. 5: Analyzer .................................................................................................................. 16

	List of Figures
	Fig. II. 1:

Fig. II. 6: QoS indicator schema. ............................................................................................ 18 Fig. II. 7: QoS input and output. ............................................................................................. 18 Fig. II. 8: Closed loop system model. ...................................................................................... 19

  3: Blood glucose level presentation. .......................................................................... 34 Hovorka model. ..................................................................................................... Fig. III. 7: Man-Rizza-Cobelli model. ..................................................................................... Fig. III. 8: Insulin given before the meal. ............................................................................... Fig. III. 9: Simulation closed loop. .......................................................................................... Fig. III. 10: With and without insulin injection. ....................................................................... Fig. III. 11: Simulations results: (a) +1 unit injected (b) +2 units injected ............................ Fig. III. 12: Configuration of a biosensor. ...............................................................................

Fig. III. 4: Closed Loop system graph. .................................................................................... 35 Fig. III. 5: Minimal glucose model. ........................................................................................ 37 Fig. III. 6: Fig. III. 13: Micro-pump & micro-valve with piezoelectric actuator. ..................................... Fig. III. 14: Vb.net program. ....................................................................................................

  that combines project management, source code editing, and program debugging in one single, powerful environment. The main advantage of using Keil in our work is to define an optimal model that works with embedded C language and can

	be implemented in a microcontroller. And because it allows us to debug programs using only
	my PC and device simulation drivers provided by Keil and various third-party developers. it
	simulates our entire target system including interrupts, startup code, on-chip peripherals,
	external signals, and I/O.
	µVision3 helps to expedite the development process of embedded applications by
	providing the following:
	Keil μVision 3 development tools designed for ARM an processor-based microcontroller
	device; that works with embedded C language. Keil is used as software development tools for
	embedded microcontroller applications. It has a simulator part that simulates most features of
	a microcontroller without the need for target hardware. By using it, we can test, debug and
	simulates codes and a wide variety of peripherals. It has a powerful compiler and tools used to

write the C-code for the programmable core. In this software editor, we are writing the program in Embedded C that helps to generate embedded applications for virtually every 8051 derivative. In brief, it compiles C code, assembles assembly source files, link and locate object modules and libraries, creates HEX files, and debugs the target program. Vision is an integrated development environment

  Consider f (t) the function representing the PV controlled level on a time interval [t i t f ]. The parameters α m and β m are predefined constants / α m = {α 1, α 2, α 3… α n } and β m = {β 1 , β 2 , β 3… β n }. Set T Hyper the duration in [t i t f ] in the maximum value case and T Hypo the duration in [t i t f ]

  .1 gives an approximate interpretation of the major blood glucose recorded levels.

	400	Max mg/dl for some meters and strips
	600	High danger of severe electrolyte imbalance
	Table III. 1: Interpretation and approximate value of BG level.
	mg/dl	Interpretation
	35	Extremely low
	55	Low
	75	Slightly low
	100	Normal
	90-110	Normal pre-prandial in non-diabetics
	150	Normal postprandial in non-diabetics
	180	Maximum postprandial in non-diabetics
	200	A little high
	270	A little high to very high depending on patient
	300	Arrive to a sensitive state
	360	Getting up there

  This model was developed by Chiara Dalla Man, Robert A. Rizza and Claudio Cobelli, therefore, called Man-Rizza Cobelli model[START_REF] Dalla Man Chiara | Meal simulation model of the glucose-insulin system[END_REF] (figure III.7). They provided a revised minimal model in order to separate the effects of glucose production from utilization.

	Symbol	Value /Unit	Description
	K 12	0.066 min -1	Transfer rate
	K a1	0.006 min -1	Deactivation rate
	K a2	0.06	min -1	Deactivation rate
	K a3	0.03	min -1	Deactivation rate
	K e	0.138 min -1	Insulin elimination rate
	T D	40	min	CHO absorption constant
	T S	55	min	Insulin absorption constant
	A G	0.8		CHO to glucose utilization
	EGP 0 /BW	0.0161 mmol.Kg -1 min -1 Liver glucose production at zero insulin
	F 01 /BW	0.00097 mmol.Kg -1 min -1 Insulin independent CNS consumption
	S IT	51.2e -4 L/mU	Insulin sensitivity of transport/ distribution
	S ID	8.2e -4	L/mU	Insulin sensitivity of disposal
	S IE	520e -4 L/mU	Insulin sensitivity of EGP
			Table III. 2: Hovorka model parameters.
	c. Man-Rizza-Cobelli's Model

Table III .

 III .3 to table III.8. Table III.3 and table III.4 represents the definition and implementation of the function Hovorka in keil. This function takes three inputs (the weight, the insulin absorption rate and the meal input, and describes how we implement the mathematical equations of Hovorka. Hovorka model applied in Keil debugger file 5 and table III.6 describes the definition and the implementation algorithm of the function used to calculate the values of parameters related to patient by the weight. It's called the function of metabolic processes and takes as input the weight.Table III.7 and table III.8 describes the definition and the implementation algorithm of the simulation of the Hovorka model in keil. We have simulated a whole day (more details in Appendix B). We simulate a day life of a patient using Hovorka model, where the patient takes insulin before each meal. The simulation progress is for a diabetic person that tries to maintain his glucose level within limit. Before each meal (breakfast, lunch and dinner), the system call a function to get necessary insulin shot needed, and during it, the system call a function to calculate the meal input. A function named ReleventMoments is used to specify the time of each meal, for example at 8.00 breakfast, at 12.00 lunch, and at 19.00 dinner. Day life scenario algorithm for function Testins.

	Call function testGB with weight as parameter Input bwi: weight If countspan is after dinner then
	dD1 ←A_G*dbas -D1/tau_G Output Call function Hovorka with parameters Weight , insulin shot None
	dD2 ←D1/tau_G -D2/tau_G Table III. 5: TestGB function definition. End if
	dS1 ←uins -S1/tau_I Step 12: 24 hours passed
	dS2 ←S1/tau_I -S2/tau_I Algorithm: Hovorka model applied in Keil debugger file If hours =24 then
	Exit dQ1 ←-(F_01c + F_R )-x1*Q1+ k_12*Q2 + U_G + EGP_0*(1-x3) Variables: Declare all variables as decimal values End if
	dQ2 ←x1*Q1 -(k_12 + x2)*Q2 Input : one decimal variable represent the weight : Function name Testins End
	dI ←U_I/V_I -k_e*I ; bwi decimal Function prototype	Func void Testins ()
	dx1 ←k_b1*I -k_a1*x1 Begin : Behavior description	This function is a day life scenario for a
	dx2 ←k_b2*I -k_a2*x2 BW←bwi	patient. The simulation started at 7.00, for
	dx3 ←k_b3*I -k_a3*x3 U_G ←D2/tau_G	example, then these times would simulate
	D1←D1 + h*dD1 U_I ←S2/tau_I	at 8.00 breakfast, 12.00 lunch, and 19.00
	D2←D2 + h*dD2 V_I ←0.12*BW	dinner.
	S1←S1 + h*dS1 V_G ← 0.16*BW Input	bwi: weight
	Output F_01 ← 0.0097*BW S2←S2 + h*dS2 Q1←Q1 + h*dQ1 EGP_0 ←0.0161*BW	None Table III. 7: Testins function definition.
	Q2←Q2 + h*dQ2 uins←0.0954119*BW
	Function name I←I + h*dI Gb ← Q1/V_G	Hovorka
	Function prototype x1←x1 + h*dx1 If Gb >=4.5 then Variables: Declare all variables as decimal values Function void Hovorka(float we,float uI, float dbas)
	Behavior description x2←x2 + h*dx2 F_01c ← F_01 bCHO, lCHO, dCHO are quantities eaten during each meal Hovorka model simulation
	Input else x3←x3 + h*dx3 eatingTime represent the time needed for eating a meal we: weight uI: the insulin absorption rate End F_01c ←F_01*Gb/4.5 Begin :
	dbas: the meal input in mmol/min None Call the function RELEVENTMOMENTS to specify the time of each meal Output End if Table III. 4: Hovorka function implementation algorithm (1). If Gb >=9 then Declare countspan as time during simulation
	Table III. 3: Hovorka Function definition. F_R ←0.003*(Gb -9)*V_G Step 1 : initialize the value of Hovorka models
	else Step 2: Midnight
	F_R ←0 If countspan is during midnight then
	Input : Three decimal variables : weight decimal Function name Call function Hovorka with parameters Weight , insulin shot End if End if End Step 3: Before breakfast testGB Function prototype Table III. 6: Hovorka function implementation algorithm (2) If countspan is before breakfast then Function void testGB (long bwi) insulin absorption rate decimal Behavior description Call function to get insulin shot needed before meal Hovorka model simulation, called by Hovorka meal input decimal Call function Hovorka with parameters Weight , insulin shot function to calculate specific parameters related to Variables: Declare all variables as decimal values End if weight. It's the function of metabolic processes. Begin Step 4: Breakfast start

Algorithm:

Algorithm:

Table III .

 III 8: Hovorka scenario implementation algorithm.

table below (

 below table III.9) describes the mainly basic rule that was taken into consideration to build our control algorithm.We define the basic rules for the quality of service with the ability of the system to satisfy well-established medical decision criteria. This QoS must respect the value in table III.10 part of the result is shown in the graph below (figure III.10a) (with the same scenario for the meal as in the first model). It shows the result after applying the control algorithm with the same scenario for meal as in the first model. The results are of course worse than the previous case with human decision. We can see that after breakfast and dinner the blood glucose was too high (cf table

	Rule #		Description
	1	Low sugar level
	2	Medium sugar level
	3	High sugar level
	4	Increasing in sugar level
	5	Stable sugar level
	6	Falling sugar level
	7	Rate of increase is falling
	8	Rate of increase is increasing
	9	Rate of decrease increasing
	10	Rate of decrease decreasing
	11	Administer computed dose
	12	Manage maximum daily dose
		Table III. 9: Control algorithm main rules.
	below:
	Parameters	Value	Description
	SafeMin	70 mg/dL	Safe minimum level of blood sugar
	SafeMax	110 mg/dL Safe maximum level of blood sugar
	MaxDailyDose	25 IU	The maximum dose of insulin in 24 h
	MaxSingleDose	5 IU	Maximum dose in a single injection
	MinDose	1 IU	The min dose to maintain an existing trend in blood sugar
	MaxDose	4 IU	The max dose to maintain an existing trend in blood sugar
		Table III. 10: Specific parameters.

A

Table III .

 III [START_REF] Ibrahim Ahmmed Saadi | Advanced mathematical model of glucose-insulin concentrations in type 1 diabetes using artificial neural networks[END_REF] shows the range value of glucose-insulin level measured before a meal or two hours after meal, for non-diabetics and diabetic persons. This table shows that the normal value of glucose level for non-diabetics person is 70-110mg/dL and greater than 140 mg/dL for diabetics.

	Glucose test	non-diabetics	Diabetic person
	before meal	70-110mg/dL	> 140mg/dL
	2 hours after meal....	<110mg/dL	> 200mg/dL

Table III. 11: Glucose test before and after meal.

  Table IV. 3: Percentile Algorithm. Table IV.4 and tableIV.5 represents the definition of the function median and its algorithm. Noting that, the median is the middle number of a set of numbers. If there is an even number of entries, it is the average of the two middle numbers.

Table IV .

 IV 5: Median algorithm. Table IV.6 and table IV.

  Consider f (t) the function representing the glucose level (blood sugar level) on a time interval [t i t f ], already defined in chapter II in paragraph tester model. The parameters α m and β m are predefined constants: α m = {600, 400,360, 300, 270, 200, 180, 150} β m = {75, 55, 35}.Set T Hyper the duration in [t i t f ] in the hyperglycemia case and T Hypo the duration in [t i t f ] in the hypoglycemia case.TableIV.8 shows IG H (g) which represents the severity of the patient's case. We implement it in some results done before which would help to formulate an indicator that will be a good step to build the tester. This tester is the first step in building a more comprehensive tester; it will also open a gate to develop a language or equivalent system to facilitate testing of biomedical devices.The values in table IV.8 showed many severe cases when compared them to normal injection and it will be considered as a reference to graphical representation of the data of a person via glucose and risk traces and plots, and at a group level via Control Variability Grid Analysis. These help to facilitate the extraction of information, and the interpretation of complex and voluminous CGM time series . Table IV. 8: IG H (g) with α, β predefined constant values.

	α = 360	-	848,700	-		-		-		-
	α =400	-	155,490	-		-		-		-
	α =600	-	-	-		-		-		-
	β = 35	-	-	35,124		41,413		-		97,599
	β = 55	7,145	-	613,850		111,190		266,360		675,650
	β = 75	484,470	-	949,010		248,310		609,530		902,820
	Graph	Normal	Without	+1	to	+2	to	+10%	to	+20%	to
	State	Algorithm	insulin	injected		injected		measured		measured
		Injection	injection	insulin		insulin		glucose		glucose
	IG H (g)			dose		dose		level		level
	α = 150	1,381,200	9,476,600	895,690		632,250		1,224,500		1,073,600
	α = 180	682,470	7,849,200	469,810		285,640		615,380		619,350
	α = 200	398,620	6,782,200	245,530		124,940		367,490		372,140
	α = 270	-	3,501,700	-		-		44.1		4.8
	α = 300	-	2,480,600	-		-		-		49.5341

Cette thèse est accessible à l'adresse : http://theses.insa-lyon.fr/publication/2014ISAL0135/these.pdf © [C. El Gemayel], [2015], INSA de Lyon, tous droits réservés

Acknowledgements iii

Acknowledgments

There are many people who helped me during my studies and this work would not end without their contributions.

allowing me to do a thesis under their direction. Their advice and assistance have been most helpful to the success of this work. 1 have the honor to do a Ph.D. under joint supervision between the National lnstitute of Applied Sciences (INSA) in Lyon and the Lebanese University in collaboration with the INL Laboratory (CPE Lyon) and LPA laboratory Fanar. , and the director of the Lebanese university-faculty of sciences II Fanar-Dr. Georges Rahbani for his support.

End if

Step 11:

Table III. 12: Function that Calculate the computed dose.

III.4. Programmed Software

When setting the output of result of keil experimentation as a file, the values of glucose are joined together without space but in a specific format. So we need to find a way to take these values that are on most scenarios around 80 935 values in each simulation, and represented as an array. This array will look like this one: Str = [90.374962 90.381195 90.387421 90.393639 …..] We have programmed a vb.net program (figure III.14) that helps to take the output of the Keil and plot it in Matlab as a graph. This program reads as input the source file generated by keil as output that contains the glucose level values, and generates a vector of all the values organized in a way that Matlab accept it. We also use a function to calculate the percentile with the Mean, the standard deviation (std), the standard error (stderr) and the median, a part of this method of values calculated is used in the grid representation section described in this thesis.

K b1

2.56e-4 5.12e-5 Each virtual patient can be used as a part of our simulation model, where the system performance of each component will be simulated and tested.

IV.3. Simulation Implementations

In this part, we will try to use this bank of virtual patients and our Vb.net program to calculate percentile values in order to specify each one belongs to which Grid zone (A, Upper B,….) when we apply a day life simulation with normal manual injection. This classification helps to know the state of patient in many cases.

The calculation of total analytical errors, of relative is usually more appropriate for intervals containing high values and calculation of differences is for low intervals. It should identify the 2.5th and 97.5th percentiles used in the calculation of the total error for 95% differences [START_REF]Draft Guidance for Industry and FDA Staff: Recommendations for Clinical Laboratory Improvement Amendments of 1988 (CLIA) Waiver Applications[END_REF][START_REF] Krouwer | A Review of Standards and Statistics Used to Describe Blood Glucose Monitor Performance[END_REF]. This 95 % are percentiles, which means that the requirement is for the 95 th percentile of the distribution of the differences to be less than the limit stated.

The function prctile (vect, per) (table IV.2 that take two parameters the first one is the array values of the simulation and the percentile value as the second parameter for example 2.5. prct25p1 = prctile(str1,per)

Function name prctile

Function prototype

Func void prctile (str1,per)

Behavior description

Percentile function to calculate the percentile of a simulation The model describes glucose concentration changes in blood as depending on spontaneous, insulin-independent net glucose tissue uptake, on insulin-dependent net glucose tissue uptake and on constant baseline liver glucose production.

The dynamic mode [START_REF] Ibrahim Ahmmed Saadi | Advanced mathematical model of glucose-insulin concentrations in type 1 diabetes using artificial neural networks[END_REF] of the glucose-insulin system to be studied is:

Error grid implementation