Jean Geringer
email: geringer@emse.fr

Mathew L Taylor

Digby D Macdonald

Matthew L Taylor

Predicting the steady state thickness of passive films in order to prevent degradations of implants

Keywords: Fretting-corrosion, Proteins, Modeling, Genetic algorithm, 316L, PMMA

Predicting the steady state thickness of passive films in order to prevent degradations of implant

Introduction.

The number of hip prosthesis will increase in the future. It doubled from 2000 to 2010, in France [START_REF] Taylor | Evaluation des prothèses totales de hanche[END_REF]. In the USA, 250,000 hip prostheses annually are implanted in 2012. It is prospected that around 572,000 hip prostheses should be implanted in the USA in 2030.

It is worth noting that the number of revisions of total hip arthroplasties (THA) should follow the same trend, i.e. doubling in 2030. Every year, one in every 30 Americans has hip prosthesis. Health issues on mobility of patients are related to people aging and younger and younger patients [START_REF] Kurtz | [END_REF].

One of the big concerns related to lifetime of implants is of understanding mechanisms of wear for predicting stability and for avoiding debris production that is responsible of implants failure. When a prosthesis is implanted for the first time, the first step related to oseeointegration consists of adherence between bone tissues and the host material. After this step, due to stress shielding and the difference of mechanical properties between bone and metal alloys, debonding occurs and micro motions should appear between the femoral stem and the bone. This last factor should involve micro friction in liquid environment, called fretting corrosion [START_REF] Waterhouse | Fretting Corrosion[END_REF]. As mentioned previously, even if metallic alloy has a bigger mechanical performance as the ones of bone, under fretting corrosion degradations the wear of metallic alloy is higher than the one of bone. Before investigating some tests close to the human case some fretting corrosion tests have been investigated between 316L SS samples, material related to hip implants, and PMMA (PolyMethylMethAcrylate), material close to bone by these mechanical properties [START_REF] Geringer | [END_REF]5]. Some interesting results have been provided by these experimental tests and the authors want to develop knowledge by adding a modeling approach adapted from the Point Defect Model [6][7][8]. The point consists of adding a part related to fretting, mechanical wear, to the predicting and deterministic PDM model. It is the first time, as experimental tests of fretting corrosion with mechanical and electrochemical monitoring processes, that this kind of modeling is suggested. Many experiments were investigated under fretting corrosion at open circuit potential. The following strategy was used for getting some information in order to apply the PDM added by fretting contribution.

Many hypotheses are necessary to combine the PDM related to the fretting corrosion case. The main one is the stationary conditions required for calculating the steady state thickness. Under fretting corrosion conditions the physical reality is not the steady state. It is assumed that the Electrochemical Impedance Spectroscopy diagram took time under 3 minutes, from 10 5 Hz to 0.1 Hz on the spectral range, and the steady state conditions are supposed to be reached. The point is that the Open Circuit Potential, OCP, value did not change beyond 5 mV during the EIS acquisition i.e. the OCP value should be considered as the same.

This work aims at comparing the results coming from EIS experiments at different time and from the modeled ones for improving the parameters and the physical constants of the Point Defect Model. Thus finally, calculating the steady state thickness of the oxide layer is possible. It is worth noting that this comparison is possible because the anodic part is considered as the wear track area and the cathodic one is considered as the external part of the wear track area. This hypothesis is related to the fact that the majority of the current density is due to fretting contribution in the wear track area.

The expected steady state thickness will be considered as an indicator for knowing if the passive layer does exist or not with albumin, the thin solid film. From our opinion, knowing precisely the thickness of the oxide layer without any experimental measurement is not reasonable. However this modeling approach is a good insight for predicting the influence of experimental conditions on the passivity of materials.

Materials and methods

The experimental aspect is well described in [START_REF] Geringer | [END_REF]5]. Thus some fretting corrosion tests were succeeded in order to study the effect of chlorides concentration cumulated with the concentration of albumin. The studied contact is 316L stainless steel, parallelepiped shape, against a cylinder of PMMA. The protocol of polishing has a huge importance and it is well described in [9]. The precise protocol is defined in [10]. The test solutions are composed with NaCl solutions with increasing concentrations of 10 -3 mol.L -1 , 10 -2 mol.L -1 , 10 -1 mol.L -1 and 1 mol.L -1 . 2 solutions will be considered in this study: without albumin and with 20 g.L -1 in order to examine the effect and to model this one by the Point Defect Model. According to this experimental procedure one will pay attention on the elements required for modeling.

From experiments the expected results are the Nyquist diagrams coming from EIS measurements. During fretting corrosion tests, every 20 minutes, Nyquist diagrams, from EIS, were registered. The Figure 1 illustrated the registration process for one experiment at applied potential of -400mV/SCE and 20 g.L -1 of albumin and 1M of NaCl. The Nyquist diagrams evolve during fretting corrosion test as highlighted in the Figure 1. The imaginary part, absolute value, increases with time that it should be due to the protective effect of albumin according to the time. From that point it should possible to compare experimental EIS graphs and modeled ones coming from adapted Point Defect Model.

In this section the modeling procedure will be described based on PDM. The Figure 2 summarizes the 7 reactions-PDM model [11]. This metal dissolution takes into account of the anodic part of the equivalent electrical circuit. The relation (1) describes the steady state thickness of the oxides layer on the metal surface. Only the reactions 3 and 7 are non conservative. Thus they are involved on the steady state thickness. The added W term is related to the mechanical term related to fretting. It is issued from experimental measurements and the term is defined by the Archard's law [12]. [START_REF] Taylor | Evaluation des prothèses totales de hanche[END_REF] The fundamental model is described on [10] and in [11] concerning the contribution of fretting on the stability of the passive layer. One coefficient related to Archard's law is adapted, fitted, according to the model. This approach describes the evolution of the passive layer on the 316L SS metal.

V b L c pH a V c pH C L L L k k W W t C t t Ω Ω + -   = - -= - -      
Thus for each EIS diagram, the potential is fixed then the current (or the current density) is measured. At that point, it can be calculated by the PDM (2):

[2]
The potential is imposed and the current density is measured, thus one may suggest that an equivalent electrical circuit could be suggested. This circuit consists of an anodic part Results and discussion.

M i b L b L a V b L c pH a V c pH a V c pH m bl V a V c pH a V c pH bl ol M n a V c pH k C k k I F k k C C k C χ χ χ δ χ δ χ δ χ     + + +     = - + - +         -            
At Open Circuit Potential, OCP, the steady state thickness, Lss, should be calculated by the model. As mentioned the experiments related to Lss measurements have been not investigated. Thus the evolution of Lss has to be compared with experimental facts. The experimental evidence that could be compared with Lss evolution will be following the gaseous release from live video of the fretting contact area. Indeed this gaseous release should be reliable with an acidification of the contact area, as predicted in [10]. One will pay attention on Lss evolution according to the time during one experiment of fretting corrosion in fixed conditions. The Figure 4 shows two trends from Lss calculations issued from genetic algorithm procedure. The Figure 5 summarizes results related to the oxides layer thickness calculated thanks to the PDM. All the duration of the fretting corrosion is considered in this figure 5. The discrepancy, i.e. the confidence interval at 95%, of each experimental is so big. It is equal of 2 nm. As mentioned previously, the incubation time should be of 100 minutes. This factor should be taken into account for explaining the discrepancy that does not allow separating the influence of ionic strength and proteins. Thus it is the reason why the steady state thickness only is considered from 120 minutes of fretting corrosion experiment, Figure 6. Some tendencies can be extracted from results of Figure 6. First of all, at 10 -3 mol.L -1 , albumin has a protective effect of the 316L SS passive layer. This result is in accordance with the lowest wear volume of 316L SS with 20 g.L -1 of albumin, at this concentration of chlorides [5]. At 10 -2 mol.L -1 , the calculated steady state thickness cannot separate the effect of albumin on the stability of the passive film. At 0.1 mol.L -1 of ionic strength, i.e. 0.1 mol.L -1 of chloride ions in the solution, the trend seems reverse: albumin does not protect the metal. It is worth noting that this concentration is a threshold one and the model might be not efficient for predicting the steady state thickness. At 1 mol.L -1 , no influence of albumin can be extracted from data coming from modeling. This is the case of pure corrosion and the metal dissolution is active. The most interesting result concerns 0.156 mol.L -1 of ionic strength, i.e. the Ringer solution. Obviously albumin is protecting the 316L SS metal. This solution is close by its constitution to the physiological liquid in the human body. One may conclude that albumin protects against fretting corrosion degradations of 316L SS.

0.E+00

Conclusions

The steady state thickness has been calculated thanks to the Point Defect Model adapted to the case of fretting corrosion experiment. Two main points have been highlighted in this work. Firstly the incubation time of active dissolution can be estimated of 100 minutes of fretting corrosion test. The second point is that albumin protects 316L SS for the lowest concentration of chloride ions, i.e. 10 -3 mol.L -1 , and in the case of Ringer solution. For 1 mol.L -1 of chloride ions concentration, albumin has no effect on the steady state thickness of the passive layer of 316 SS. Finally for intermediate concentrations, i.e.

10 -2 and 10 -1 mol.L -1 , albumin cannot promote a higher protection of the passive film than the case of 10 -3 mol.L -1 of chloride ions in the medium. From these results coming from modeling, one might suggest that albumin protects 316L SS against fretting corrosion degradations for a concentration of 10 -3 mol.L -1 . It is worth noting that the chloride ions concentration is between 0.15 and 1 mol.L -1 in the physiological liquid, i.e. in the human body. Only taking into account the ions constitution of the physiological liquid, albumin has a beneficial effect on the 316L stainless steel degradation in the Ringer solution.

Concerning the modeling process, thanks to the PDM, this is the first trial to adapt in the case of fretting corrosion. The genetic algorithm process is powerful for getting some interesting results on the influence of the specific coating that is albumin. Many prospects are under progresses: the modeling approach has to be improved, adapting the Point Defect Model to the specific case of fretting corrosion; the measurements of the oxides film thickness will be a point to investigate and the constitution. Fretting corrosion experiments are in progress with Co-Cr-Mo alloy and it will be a good candidate for applying the same methodology in order to estimate if the passive layer exists or not.

List of figures

Figure 1 :

 1 Figure 1: Nyquist diagrams related to an entire experiment of fretting corrosion, applied potential of -400mV/SCE, 1 mol.L -1 of NaCl and 20 g.L -1 of albumin. Avtf: before fretting

Figure 2 :

 2 Figure 2: 7 reactions of the PDM, deterministic approach [7].

(

  an impedance related to dissolution of metal, PDM, and a Warburg one), a cathodic part (parallel association of the oxygen reduction and the protons one) and a constant phase element related to the double layer on the surface of metal. These investigations have been succeeded till now. The innovation consists of using genetic algorithm for finding the 29 parameters coming from the Point Defect Model. The usual method, as the well-known Newton-Raphson, does not allow finding easily the global minimum. Advantages of the genetic algorithm are that best intermediate solutions are selected in the entire space of parameters. Finally the Figure3shows the experimental results of a Nyquist diagram and the fitted results provided by the model. The accordance sounds good, the relative discrepancy is less than 3%.

Figure 3 :

 3 Figure 3: Nyquist diagrams related to one measurement coming from the experiment: 1 M of NaCl, 20 g.L -1 of albumin and at applied potential of -400mV/SCE; the fitted points are

Figure 4 a

 4 Figure 4 a) but the concentration of albumin is 20 g.L -1 . On this figure, Lss is a little bit

Figure 4 :

 4 Figure 4: Oxides thickness of 316L SS according to the time during one fretting corrosion experiment, 10 -2 mol.L -1 , 14,400 seconds of test; a) modeling without albumin, b)

Figure 5 : 1 2H 2 O

 512 Figure 5: Average values of oxides layer calculated by the model based on PDM; 0.156 M of ionic strength is related to the Ringer solution (NaCl: 8.5 g.L -1 , KCl: 0.25 g.L -1 , CaCl 2 ,

Figure 6 :

 6 Figure 6: Average values of oxides layer calculated by the model based on PDM; 0.156 M of ionic strength is related to the Ringer solution (NaCl: 8.5 g.L -1 , KCl: 0.25 g.L -1 , CaCl 2 , 2H 2 O: 0.22 g.L -1 , NaHCO 3 : 0.15 g.L -1 ); these values are coming from the last seven EIS

Figure 1 :

 1 Figure 1: Nyquist diagrams related to an entire experiment of fretting corrosion, applied potential of -400mV/SCE, 1 mol.L -1 of NaCl and 20 g.L -1 of albumin. Avtf: before fretting

Figure 2 :

 2 Figure 2: 7 reactions of the PDM, deterministic approach [8].

Figure 3 :

 3 Figure 3: Nyquist diagrams related to one measurement coming from the experiment: 1 M of NaCl, 20 g.L -1 of albumin and at applied potential of -400mV/SCE; the fitted points are

Figure 4 :

 4 Figure 4: Oxides thickness of 316L SS according to the time during one fretting corrosion experiment, 10 -2 mol.L -1 , 14,400 seconds of test; a) modeling without albumin, b)

Figure 5 :

 5 Figure 5: Average values of oxides layer calculated by the model based on PDM; 0.156 M of ionic strength is related to the Ringer solution (NaCl: 8.5 g.L -1 , KCl: 0.25 g.L -1 , CaCl 2 , 2H 2 O: 0.22 g.L -1 , NaHCO 3 : 0.15 g.L -1 ); these values are coming from 12 registered EIS

Figure 6 :

 6 Figure 6: Average values of oxides layer calculated by the model based on PDM; 0.156 M of ionic strength is related to the Ringer solution (NaCl: 8.5 g.L -1 , KCl: 0.25 g.L -1 , CaCl 2 , 2H 2 O: 0.22 g.L -1 , NaHCO 3 : 0.15 g.L -1 ); these values are coming from the last seven EIS

Average values of oxides thickness during fretting corrosion experiments from 120 minutes of fretting corrosion

		5.E-07
		4.E-07
					OCP, 0g.L-1
					OCP, 20g.L-1
		3.E-07
	Lss / cm	2.E-07
		1.E-07
		0.001	0.010	0.100	0.156	1.000
				Ionic strength / mol.L -1

Acknowledgements

The authors would like to acknowledge the Rhône-Alpes Region / France, for grant which financed the 2011-2012 stay at Penn State University/PA/USA and Saint-Etienne Métropole / France, for financially supporting the experimental device and ENSM-SE for granting the Ph.D of Dr. Julie Pellier.


D Prêle

D Franco

Dominique Ginhac

Khalil Jradi

F Lebrun

S Perasso

Denis Pellion

A Tonazzo

F Voisin

F L E B R U N

SiPM cryogenic operation down to 77 K

la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Silicon PhotoMultipliers (SiPMs) are being considered as possible photosensors for detectors operating at low temperatures, such as noble liquid (argon or xenon) time projection chambers for direct dark matter searches and neutrino detectors, or for Compton telescopes in space. A detailed study of their parameters in cryogenic environment are necessary to assess the expected performances.

A SiPM is composed of Geiger Mode Avalanche PhotoDiode (GM-APD). Geiger mode provides internal gain as large as 10 6 carriers per incident photon. By means of a self-sustaining avalanche process: successive impact ionizations of carriers are accelerated as long as the electric field is sufficient, above a voltage breakdown threshold (V BD ). The GM-APD current rises to the order of a milli-ampere in a few nano-secondes (rise time). This current passes through a quenching resistor [START_REF] Cova | Avalanche photodiodes and quenching circuits for single-photon detection[END_REF] (R Q in Fig. 1), placed in series with the voltage biasing, which has the effect of lowering the electric field in the GM-APD below the breakdown threshold. This causes the avalanche process to be turned out in few 10 ns (fall time). Without self-sustaining avalanche process and as long as there is no new incoming photon, the current drops below the pico-ampere level (leakages), and the GM-APD electric field is restored above the breakdown threshold. After this current pulse, the GM-APD is again ready to detect a new photon.

The main parameters of a GM-APD, and thus of a SiPM, are: the quenching resistance R Q , influencing the fall time; the junction capacitance C J , which limits the rise and fall times and the breakdown voltage V BD . Rise and fall times are represented in the Figure 2. The differential resistance of the junction R d j during the avalanche process is also an interesting parameter allowing to determine the rise time. We determined the parameters V BD ,R Q and C J as a function of temperatures for a commercial SiPM, the Hamamatsu MPPC S10362-11-100C [START_REF] Hamamatsu | MPPC (multi-pixel photon counter) -S10362-11 series[END_REF]. Most of parameters were extracted from the Current-Voltage characteristic (I(V), see Fig. 3) from 300 K to 77 K. Only, junction capacitors is obtain from dynamic measurements. This allows us to know what kind of cryogenic operation we can expect from the photosensor in cooled environements.

HV bias R Q ... R Q V out

Quenching resistance extraction from the forward bias characteristic

Using the forward bias characteristic of the SiPM, it is possible to extract the value of the quenching resistor R Q . We assume that N cells under forward bias are similar to a single diode in series with a R Q /N resistor 1 .

Following this method to extract R Q , we have measured the forward characteristic of the MPPC S10362-11-100C from 300 K to 77 K. Figure 4 shows the I(V) forward characteristics 1 SiPM ≡ Diode + RQ/N. Indeed, N diodes in parallel are equivalent to one diode with an area N times larger, where the small-signal equivalent resistance is always r d = kT qI whatever N. from room temperature to liquid nitrogen temperature. The slope of the curve is inversely proportional to the quenching resistance, so we clearly see that quenching resistance increases at low temperatures. Figure 5 shows the quenching resistance deduced from I(V) curves. It is noticeable that the quenching resistance increases more quickly as the temperature decreases and finally is 10 times larger at 77 K than at 300 K. The quenching resistance (per cell) goes from 100 kΩ at room temperature to 1 MΩ at liquid nitrogen temperature. As a consequence, for a constant junction capacitance, the fall time will increases by an order of magnitude. This R Q (T) negative temperature coefficient could inhibit the quenching process. Indeed, during the fall time, the Joule heating could reduce the R Q resistance and would lead to stay in the avalanche process. This is probably the effect that will be shown in the following section with the reverse bias characteristics (dashed line of Figure 6).

Breakdown voltage measurement from the reverse bias characteristic

Reverse bias characteristic is a common way to characterize SiPM and extract the breakdown voltage V BD . As shown in figure 3, the measurement in the dark also allows us to know the maximum voltage biasing (V Z

2 ) before SiPM self-triggering. As it is shown in figure 6, at low temperature the photo-current is too small to be measured by our equipment (Agilent B1500A source measure unit with a noise floor ≈ 100 pA). Moreover, below 250 K, a "full SiPM latching process" trigs the overall cells unexpectedly above the breakdown voltage even without photon flux ("Dark"). The arbitrary voltage where this latching occurs suggests that it is a different phenomenon than the "Zener" threshold V Z . Moreover, this phenomenon could be compatible with a positive electro-thermal feedback due to the negative temperature coefficient of the R Q .

Nevertheless, using a light source to trigger the SiPM, it is possible to clearly see the breakdown voltage, as it shown in figure 6 -solid line. The breakdown voltage is measured and plotted as a function of the temperature in Figure 7. It appears that its evolution is close to a linear function ; with a temperature coefficient equal to -50 mV/K. V BD decreases by more than 10 V (in absolute value) from room temperature to liquid nitrogen temperature.

Dynamic characteristics

SiPMs are used to detect fast pulses, therefore a dynamic characterization is mandatory to determine the SiPM behavior. A small signal analysis allows one to extract the capacitance of the junction reverse biased.

Figure 8 shows the equivalent AC electrical model of the SiPM. R d j is the differential resistance of each junction and is only considered in presence of an avalanche process ie biased below V BD (in absolute value). C J is the junction capacitance, which is due to the depleted region of the APD. The thickness of this depleted layer is proportional to the reverse biasing, therefore the junction capacitor decreases as the reverse bias increases in absolute value. However, as is shown in figure 9, this value remains constant for voltage biases larger than 30 V. Moreover, above V BD , the avalanche process prohibits the measurement of the junction capacitance due to the drop of the junction differential resistance. The junction capacitance as a function of temperature, measured with a bias voltage of 60 V, is finally reported in figure 10. We clearly notice a decrease of the junction capacitance at low temperature. However, this decrease is less than a factor of 2 between 300 K and 77 K.

Conclusion

The breakdown voltage V BD , the quenching resistance R Q and the junction capacitance C J of a commercial SiPM MPPC S10362-11-100C [START_REF] Hamamatsu | MPPC (multi-pixel photon counter) -S10362-11 series[END_REF] have been measured at temperatures from 300 K to 77 K. A quasi-linear decreasing of the breakdown voltage with temperature is found, with a rate of -50 mV/K. The quenching resistance increases by a factor of 10 between 300 K to 77 K. Finally, the junction capacitance decreases by less than a factor of 2 in the same temperature range. These experimental results give a good idea of the voltage biasing required for MPPC cryogenic operation. Furthermore, they allow us to predict a fall time increase by a factor of 5 at liquid nitrogen temperature. Moreover, these tests clearly point out a phenomenon of "full triggering" of the tested SiPM at low temperature and for biasing just above the breakdown voltage. Therefore, the biasing voltage range seems to be strongly reduced at cryogenic temperatures.

Most of these results has been obtained by using "simple" I(V) measurements and are fully compatible with similar measurements using time response [START_REF] Otono | Study of MPPC at Liquid Nitrogen Temperature[END_REF].

Figure 1 .Figure 2 .

 12 Figure 1. Electrical scheme of a SiPM showing the individual GM-APD and the quenching resistors R Q . A small resistor (typically 50 Ω) in series with the SiPM and the high voltage bias (≈ 70 V in the case of the MPPC) converts the current to voltage.

Figure 3 .

 3 Figure 3. Typical SiPM I(V) characteristic at 300 K with and without incident photons. A zoom around the breakdown voltage is also shown using a log scale of the current absolute value.

Figure 4 .

 4 Figure 4.I(V) curves show that the quenching resistor increases at low temperature. Indeed, in an I(V) curve, the resistance is inversely proportional to the slope of the curve.

Figure 5 .

 5 Figure 5. Quenching resistance R Q as a function of the temperature. R Q is extract from the figure 4 and by multiplying R Q /N by the number of SiPM cells (N=100).

Figure 6 .

 6 Figure 6. Reversed biased I(V) curves of the SiPM. To see small current phenomena a log scale is used, so in absolute value.

Figure 7 .

 7 Figure 7. Breakdown voltage as a function of temperature. A linear fit gives a fluctuation of the breakdown voltage of -50 mV/K.

Figure 8 .

 8 Figure 8. Small signal electrical schematic of a SiPM for ac measurement. R d j corresponds to the differential resistance of the GM-APD junction (without R Q ). C J is the junction capacitor.

Figure 9 .

 9 Figure 9. Evolution of the junction capacitance as a function of the voltage biasing and for different temperatures from room temperature to liquid nitrogen temperature.

Figure 10 .

 10 Figure 10. Junction capacitance as a function of the temperature. The measurement has been made with a 60 V biasing.

The Zener voltage VZ corresponds to the breakdown voltage in the dark.

Acknowledgments

Measurements presented in this paper has been made with the help of B. Manceur during its master degree internship at APC. Authors are also grateful to M. Piat, who provided part of the cryogenic equipment needed for this study.


Gireg Desmeulles
email: desmeulles@enib.fr

The virtual reality applied to the biology understanding: the In Virtuo experimentation

Keywords: multi-agent system, systems biology, in virtuo, interaction reification, virtual reality

The advent of the computer and computer science, and in particular virtual reality, offers new experiment possibilities with numerical simulations and introduces a new type of investigation for the complex systems study : the in virtuo experiment.

This work lies on the framework of multi-agent systems. We propose a generic model for systems biology based on reification of the interactions, on a concept of organization and on a multi-model approach. By ``reification'' we understand that interactions are considered as autonomous agents. The aim has been to combine the systemic paradigm and the virtual reality to provide an application able to collect, simulate, experiment and understand the knowledge owned by different biologists working around an interdisciplinary subject. In that case, we have been focused on the urticaria disease understanding.

The method permits to integrate different natures of model. We have modeled biochemical reactions, molecular diffusion, cell organisations and mechanical interactions. It also permits to embed different expert system modeling methods like fuzzy cognitive maps.

Introduction

The models of systems we study become more and more complex. The diversity of organizations, of structures and of interactions is responsible for this complexity. These organizations can be structured in different levels that are initially kown. The human using his free will, plays a determinating role in this structuration. Structuration can also emerge during the evolution thanks to the various interactions between the components. These interactions can have different natures. They can work with different spatial and temporal scales. There is no theory able to formalize this complexity and no formal proof method like to those we have with the highly formalized models. Being deprived of formal proof, we have to experiment the systems during their progress. Thus, experimental a posteriori validations are provided. The conceptual, methodological and experimental framework provided by the Virtual Reality (VR) fits the modeling and the study of complex systems. The aim of CERV 1 is to use VR to study complex systems.

Within the framework of study and understanding of biological complex systems, the experimentation has been proven to be the best tool for investigation of the living, from both historical and empirical standpoints. Here, we present a new biological experimentation method based on Virtual Reality : the in virtuo experimentation.

The rest of the paper is structured as follows : the first part introduces the virtual reality and the multimodel construction aim. Section 2 defines the in silico and the in virtuo experimentations. Section 3 presents our systemic paradigm based modeling method, describing organization, Interaction and Constituent. Section 4 shows how the generic model is specialised to integrate each different biological models. We finally present the application to the study of a complex disease: the allergic urticaria.

Virtual Reality for experimentation on complex systems

The in virtuo approach takes place within the intersection between biology and virtual reality (VR). Biology being defined as the study of the living complex systems, the VR ougth to be briefly defined.

Definitions for virtual reality

Defining a scientific domain is not an easy thing to do. It is even more difficult when this domain is in constant development. Therefore any definition of VR is naturally subject to criticism. We expose here the definitions which have structured our work. The first one, a functional and theoretical definition given by Fuchs [START_REF] Fuchs | Le traité de la réalité virtuelle[END_REF] :

Virtual reality allows the user to extract himself from the physical reality, in order to experience a virtual change in time, place, and/or type of interaction : interaction with an environment simulating reality or interacting with an imaginary or symbolic world.

A technical definition can complete the previous one : Virtual reality techniques are based on real-time interaction with a virtual world, by the use of a Behavioral interface 2 allowing the pseudo natural immersion of the user in this environment.

The virtual world is the model of the living system we want to experiment. It is currently our main goal to build and to make this world virtually alive, and this is the first step towards in virtuo experimentation. The experiment is possible only if the user can interact with the virtual model. This interaction is possible by recoursing to interfaces. VR interfaces have already been studied in the context of expert system an VR (Savage-Carmona, 1998). In this work, their deepened study is premature and is relegated to the background. But we must keep in mind to remain within the VR field, and therefore within the in virtuo experimentation field. Likewise, real-time 3 must not be forgotten in the simulation.

These two definitions define the domain in a broad manner. Nevertheless, we will complete them in order to situate our work more precisely within the VR field.

Autonomy in the virtual universes

To these classical definitions, we must add the notion of autonomy that presents itself to us by essence, by necessity, by ignorance and by conviction, to construct our virtual worlds (2) : Interface exploiting a human "natural" behavior and not implying any important or complex apprenticeship period before being usable.

3 By real-time, we mean that we master the instructions' execution time. For example, during an experiment, ten seconds of the real time (the one of our watch) may correspond to one virtual second (the one of the potential world).

• By essence, because we try to model systems which are made up of entities like cells. Those are autopoietic systems and are, by definition, autonomous systems (3). • By necessity, for the entities that constitute the universe can adapt their behavior, during execution, to the modifications of the conditions of the limits (due to unpredictable interactions, disruptions or modifications of the environment) . • By ignorance, because the inexistence of models for the global system behavior leads to autonomise the model of the components. In other words, we would study emerging behaviors. • By conviction, by accepting the distribution of the control of the evolution of the virtual universes between, on the one hand, the users, and, on the other hand, the numerical models that populate these universes. Thus, we decide to take as a principle the autonomy of the numerical models and also of the entities that populate the virtual worlds. These considerations apply to the study of the biological complex systems.

From autonomy to multi-model universe

If we define the models that populate our virtual universe with the principle of autonomy, we can easily make them coexist. Their autonomy allows them to adapt themselves independently, and to interact with the environment or with another entity too. Thus, we talk about multi-model universe. The models can have very different natures, as developed in this article.

Usually, the modeling of the biological mechanisms differs according to the standpoint we take. The multi-model approach allows the construction of coexisting different viewpoints that describe the living. It is then possible to construct models with different modeling levels and granularity (from molecule to cell, and then to organ) or with different modeling natures (chemical, geometrical, mechanical, etc. ..). It is why numerical multi-modeled, multi-scaled and multi-skilled models can be considered in order to combine the respective points of view of biochemists, doctors, cellular or molecular biologists.

Therefore, given the definition of the VR we gave, it seems that VR is the tool of predilection for an interdisciplinary study. Now, we will apply the VR concept to the traditional bioinformatics systems.

From in silico to in virtuo

Traditional in silico methods for the Biology

In the disciplinary field of study of the living systems, in other words in biology, the experimentation on the real system is called in vivo experimentation. These in vivo experiments may, in some cases, raise technical or ethical problems. Then, the biologist must find alternative methods to circumvent the given constraints.

A model is an artificial representation of the phenomenon or of the object of the study. The alternative method consists in testing this representation's behavior under the effect of actions that can be carried out on the model. This is the case of the in vitro experimentation where a sample or a physical model built by analogy with the real system, is experimented.

Unfortunately, the observation of a real system, of a sample or of a physical model, can sometimes interfere with the studied phenomenon. Moreover, even with in vitro experimentation, the technological means are often too limited to permit the detailed observation of the phenomenon. In that case, we use a theory that allows the possibility of the building of predictive numerical models starting from concrete data. It is then possible to simulate these numerical models thanks to the use of a computer in order to obtain in silico computations. In general, the in silico tools (4) use methods of mathematical resolution based on the ordinary [START_REF] Mendes | Gepasi, a software package for modeling the dynamics, steady states, and control of biochemical and other systems[END_REF] or partial (6) differential equations, or on stochastic tools [START_REF] Le Novere | Stochsim : Modeling of stochastic biomolecular processes[END_REF]. In other words, the biologist builds a mathematical model that he implements using a computer. In silico computations provide results that are checked against measurements on the real system. The concordance of the results allows the validation of the predictive model. If it is invalidated, the model designer can modify the model and simulate it again. Moreover, there are tools for the mathematical model analysis such as the bifurcation's analysis or as the parameters' estimation, both providing the means to deduce models' properties. Finally, there are the formal methods coming from the process algebra such as  calculus,  calculus [START_REF] Danos | Formal molecular biology[END_REF] or the brane calculus [START_REF] Cardelli | Brane calculi[END_REF]. These methods open the prospect of pointing out models' properties of the studied complex systems. The in silico computations has been providing an alternative method to the in vivo and in vitro experimentations for several years. But we can criticize those for making the user passive during the calculation. These tools only provide the ability to observe the model but not really to experiment it.

Virtual lab for the in virtuo experimentation

(Fu & Bradford, 95) have presented an hybrid modeling scheme showing the need to integrate different models in one application. Members of systems biology community have been recently working on object-oriented approaches [START_REF] Roux-Rouquié | Using the unified modelling language (uml) to guide the systemic description of biological processes and systems[END_REF]. It began with statecharts representation of biological systems [START_REF] Kam | The immune system as a reactive system: Modeling t-cell activation with statecharts[END_REF] and was followed by agent-based simulation [START_REF] González | Cellulat: an agent-based intracellular signalling model[END_REF]. Multi-agent systems avantages in dynimical environments, have been presented in (Pendharkar, 99). A recent article presented a blackboard architecture for the modeling( 13) of intra and extra cellular processes. This method provides modeling modularity, flexibility and reusabililty. Our work can be located within the framework of this agent-based method to model the biological complex systems, putting emphasis on the multi-model. We want however to improve the method by making it compatible with the definition of virtual reality and the systemic paradigm.

The advent of the computer and computer science, and in particular virtual reality, now offers new experiment possibilities with numerical simulations and introduces a new type of investigation : the in virtuo experiment. Initiated in 1997, the "in virtuo" project of the European Center for Virtual Reality (CERV), carried out in collaboration with medical institutions, proposes to apply in virtuo experimentation to biology (see figure 1). We develop a workbench for numerical simulations using multi-agent approach, in order to develop a true laboratory for in virtuo experimentation in biology. The in virtuo experimentation is more than the simple observation of the numerical models processing on a computer. The user can test the reactivity and the adaptibility of the model in progress. Thus, he can take the most of behavioral properties of the numerical models that populate the virtual universes. We need now to define how our multi-modeled universes and our autonomous entities work.

Modeling the living complex system

Autonomy principle is a major principle of the multi-agent systems (MAS). Moreover, among the agents ancestors, we find the cellular automata which have been used for complex systems study during the 40's, so that MAS provide a good candidate to study complex systems. Works on self-organization of social insects [START_REF] Bonabeau | Selforganization in social insects[END_REF] are an example of this type of recourse to the agents. In addition to the autonomy principle, notions of robustness, emergence, self-organization and adaptibility underlie the MAS.

In this section, we describe the multi-modeled method built on systemic paradigm and with MAS. We emphasize on the notions of interaction, constituent and organization.

In this study, an agent can be considered as an engine that is continuously following a three stroke cycle of perception, decision and action, and as belonging to the reactive agents family.

Interaction reification

The 20th century has experienced an important change of method : the emergence of the systemic paradigm complemented the reductionist and analytical paradigms. Speaking in a sketchy manner, we could say that reductionism is interested in the description of the studied system components, while the systemic paradigm leads us to focus on the relations between these components.

Interaction is the basic concept of this last paradigm. Usually, when the MAS are used for the study of complex systems, relations between the components are modeled by message mailings, components being modeled by agents.

The appeal to the systemic approach leads us to focus on the interactions rather than on components themselves. The idea to directly model the interactions by associating to each of them an autonomous agent derives from these considerations. We therefore had to modify the usual MAS modeling (figure 2), and consequently the way of modeling a complex system too. We talk about "interactions reification".

As a consequence, to each interaction a process corresponds. Processes of that kind will not allow a simultaneous execution, since it is a microprocessor that executes the computer program. This implies that we have to choose between synchronism and asynchronism scheduling. This choice will affect the state of the virtual world which is experienced by the agents during a cycle. A cycle is the time step corresponding to one, and only one activation of each agent.

• In the case of synchronism, during a cycle, each agent perceives the environment at the state of the start point of the cycle. The environment modification induced by the agents' actions are effective at the end of the cycle. In that case we consider each action are performed at the same time. • When asynchronism scheduling is considered, we made the hypothesis that events occur at different time. Each agent modify the environment when activated. The next activated agent will perceive this modification during the cycle.

Synchronism is the characteristic of the differential calculations and, more broadly, of the analytical methods. Since we wish to take distance from classical reductionist analytical methods, we have chosen asynchronism to schedule the agents. In addition to that, the complex systems are often composed of circular, unstable or oscillating mechanisms which result from the asynchronism of interactions. Futhermore, in biological systems, some interactions compete themselves for the same structural constituent. Then, if synchronism was chosen, there would be no way to assure the conservation of the amount of a constituent. For example, we can imagin two transport interactions that have to carry the same constituent to another place. If they see the state of the world at the startpoint of the cycle, the both will transport the constituent. At the end of the cycle, the constituent will be duplicated.

Finally, in order to not introduce any bias in the simulation of the systems, we use a random scheduling of the agents. In that way, we counter the prevailing of a relation on another, in the case of competition between two of them. We made the choice of considering exclusively chaotic asynchronous iterations to schedule the agents and, consequently, to schedule the interactions too.

The concept of Interaction agent being defined, the organization concept needs now to be exposed.

Organization

The organization is a central concept in systemic. This notion has already been used in MAS design(Gruer, 02). An organization is a layout of relations between constituents that form a new unity. It defines a structural and a functional aspect of a system. We need now to consider the organization as being an object containing constituents and interactions (figure 3) from a computing standpoint. Moreover, a composition relation between the organizations can exist when a system is made of sub-systems. This is the hierarchical level organization. For example, a transduction pathway is part of a system cell, which is itself a part of the system organ, which is itself part of the human system, the organism, etc... In this example, we use a composing procedure, but it is also possible to use a decomposing process : decomposition of transduction pathway into chemical chains, chemical chains into molecules, molecules into atoms, etc... The problem is that the decomposition cannot be infinite.

Organization/Constituent :

To simplify the modeling and to obtain an end to the decomposition process, a sub-system can be taken as a simple constituent if it has no autonomous action on its environment, and if it is purely reactive. In that case, the management of the interactions between the new constituent and its environment can be delegated to its root organization. The influence of the sub-system is modeled by upper level interactions.

Organization/Interaction :

When a sub-system is operationally closed (3), it can be considered as being autonomous. Its response to a stimulus will depend on its internal states. It is therefore not possible to delegate the management of its interactions on the environment to a superior organization. From the root organization standpoint, the sub-system can be considered as being the same as an interaction between its inputs and outputs (see figure 4). It is then possible to model it with an autonomous agent.

Thus, we have two ways of stopping this "infinite" regress in the decomposition process by looking at a "leaf" organization as a constituent or as an interaction. We now have to apply this generic framework of modeling to our domain of interest : biology.

Model integration for biology

In this section we present the different models implemented with this generic method. As in physics where relaxation and transport phenomena are considered, we have two interaction's types. First, we expose the time dependent interactions: the chemical reactions. And then, we present a sample of time and space dependent interaction type: the diffusion. We will discuss on the microscopic and mesoscopic chemical reactions modeling. We expose how those interactions are associated to build a cell model, how collision are managed. Finally, we present the integration of these models.

Time dependent interactions: The chemical reactions

In order to adequately model biological systems, we have to model the chemical reactions which are the basic elements of the chemical networks. These networks are the main way of communication and of regulation of the living organisms. In most chemical messengers communication cases, huge quantities of molecules are involved. A molecule cannot be individually modeled to represent systems containing billions of molecules. To overcome this problem, we appeal to the notion of molecular concentrations, and we apply the principle of interactions reification. For every reaction between molecular types, we create a Reaction agent that accomplishes the following three strokes engine :

1. Reading of the concentrations of the chemical species involved in the reaction 2. Calculation of the reaction speed and integration on the time step using a classical method (e.g. Runge-Kutta) 3. Concentrations update according to the amount of transformed species. Reaction agents accomplish three steps one after the other, in a n-long cycle, n being the number of agents. The order of interventions randomly changes from one cycle to the other. This method allows the modeling and the simulation of the kinetic of enzymatic reactions (thanks to the Henri-Michaelis-Menten equations), of dimerisation, of oxydo-reduction, of ligand-receptor associations... The approach has already been applied to works on coagulation [START_REF] Kerdélo | Multi-agent systems: A useful tool for the modelization and simulation of the blood coagulation cascade[END_REF]. The mathematical proof of the convergence of this method has been recently established 4 . The convergence has an order of 2, whatever the classical method chosen in step 2 of the engine.

The figure 5 show an example of test results obtained by simulationg a classic model of the Map Kinase transduction pathway [START_REF] Kholodenko | Negative feedback and ultrasensitivity can bring about oscillations in the mitogen-activated protein kinase cascades[END_REF]. Each reaction have been modeled by an Reaction agent The action step of an enzymatic reaction apply the law : V = (Vmax * [P]) / (Km + [S}) V is the reaction speed, Vmax is the max speed, [S] the substrate concentration, [P] the product and Km is the Michaelis-Menten constant. Naturally, this interaction-based method is slower than the traditionnal ODE solver tools. The use of this method is justified by the context of the multi-modeling. Contrary to the classical chemical calculation methods, the Reaction agents method permits to add, to modify or to destroy any reaction during the simulation. The simulation can adapt itself to any unexpected perturbation or modification.

Finally, in order to describe chemical networks, we define an organization Reactor that contains the constituent Species and the relations between these constituents : the Reaction agents. This organization does not contain any space dimension, since the species concentrations are supposed to be homogenous in the chemical reactor. As a consequence, Reaction agents only represent time-dependent relations.

We now have to model the molecular species diffusion in space. This is an essential mechanism of the chemical messages transmission.

Diffusion reactions

The adopted solution to translate the diffusion phenomenon and to add a spatial dimension to the chemical reactions models consists in the partitioning of space. Each piece of space becomes a Compartment organization and contains a Reactor sub-organization. Diffusion agents are transportation relations between these organizations (figure 6). Diffusion agent are close to the Reaction agents in their way of proceeding. They use the laws of Ficks and represent the diffusion through a 2D surface. This method allows the modeling of the transportation of molecules through a cell membrane. The three times engine of the agent will be as follow:

1. Reading of the concentrations of the chemical species in two adjacent compartment. 2. Calculation of the diffusion speed and integration on the time step.

3. Concentrations update according to the amount of transported species. Finally, the diffusion through a membrane and the method of the Reaction agents give us access to the describing of the chemical model of a cell.

Microscopic molecule simulation

There, the chemical reactions have been described at a macroscopic level. But in the case of intracellular biochemical reactions, the number of involved molecules is not enough. Then, the deterministic methods cannot be used [START_REF] Takahashi | Space in systems biology of signaling pathways -towards intracellular molecular crowding in silico[END_REF]. By using the method we present, it is possible to model the chemical phenomenon at a mesoscopic and microscopic level. We are working at the introduction of the Gillespie algorithm (18) in our model. The Reaction and Diffusion agents will have to adapt themselves and to choose between a differential method or between the Gillespie algorithm. This to perform the interactions in and between the chemical reactors.

Cell models

The Compartment organization contains at least one Reactor sub-organization representing the chemical environment in the tissue. It can also contain some more complex sub-organizations : cells. These cells can be modeled in different ways (figure 7), thanks to our multi-model approach. From a biochemist standpoint, a cell can be defined as an organization composed of sub-organizations (i.e. chemical reactors), of constituents (i.e. the molecular species), and of interactions (i.e the Reaction and Diffusion agents) [START_REF] Querrec | Uses of multiagents systems for simulation of mapk pathway[END_REF].

The cell is an autonomous system. When the cell's behavior, which needs to be modeled, is simple enough, the cell can be modeled by an autonomous agent. Consequently, the sub-organization modeling the cell can be replaced by an autonomous agent producing the same behaviour. From the root organization viewpoint, this system is equivalent to an interaction between species which are normally in relation to the cell (see 3.2.2).

Finally, it is possible to replace an autonomous sub-system in the cell by agents to create an hybrid model containing predictive parts (reactors and Reaction/Diffusion agents ) and other parts that are either predictive or explicative, which fill in the "holes" of the chemical model. The behavior of these subsystems can be produced by any artificial intelligence tool (neuronal networks, cognitive Maps, states machines,...). The fuzzy cognitive maps have already been apply to in virtuo modeling (Querrec,05) The hybrid solution is the most often used. The chains of chemical reactions defining the behavior of a cell cannot be completly described.

This section only defines a cell's chemical's modeling method. It seems desirable to give the cells spatial dimensions. Giving the cell a shape would allow the cell to move in space and eventually to interact with other cells.

Collision managment

In order to give the cell a shape, a Shape3d constituent has been added to the Cell organization. This constituent is defined with a position, a mass, a 3D shape, a color... Giving spatial dimensions to the simulation raises a major problem well known in the VR domain : the problem of collisions. We have solved this problem while still remaining within the described multi-model reasoning. When two Shape3D constituents are in collision, a Collision agent simulates the interaction between the two shapes, by applying a given pressure on them. The Compartment organization which contains the cells creates a Collision agent when two shapes are at a certain distance from another one. Next, the Collision agent has an autonomous life : it destroys itself when the two components are too far away from each other. To create collisions, the Compartment organization has a collisions detection unit. This unit verifies whether relations between the constituents of the organization or of the sub-organizations should emerge or not. Consequently, the management of the collisions is partitioned within each compartment (figure 8). The number of compartments is chosen proportionnal to n, the number of simulated entities (i.e. when the simulation size grows, the number of compartments increases). Thus, on average, the number of entities in a compartment is constant and the simulation's complexity remains 5 in O(n).

Integration of the whole

All the models mentionned here were integrated into the same software architecture. Programs were developed thanks to the AReVi (20) library. AReVi is an autonomous entities simulation library, as well as a 3D rendering library. It is a C++ written library. The UML diagram of the figure 9 shows this architecture. The application includes three levels.

• At the top level, the AReVi library instanciates a scheduler. This scheduler randomly initiates activities (chaotic asynchronous iterations). An activity is the active part of an agent. • The generic model defines generic objects : interaction, component and organization.

• Last, the different models inherit from the generic model. The Shape3D and the Species inherit from the class Component. The chemical Reactions, the Diffusion reactions, the Collisions and the simplifications of autonomous systems (3.2.2) inherit from Interaction. The chemical Reactors, the Compartments, the Cells and the Universe inherit from organization. This is the generic model that allows all these models to cohabitate and to interact in the same virtual universe.

Application

We already have implemented this multi-model method in the context of a complex disease study : the allergic urticaria. We have modeled a 600m cube of skin (figure 10). In this model, sub-models were included : cell's models (mast cells, macrophages, keratinocytes), a macroscopic model of the capillary 5

The complexity in O(n) has been proven and will be presented in a manuscript in preparation. vessels, a membrane's model (a basal membrane separating the epidermis of the dermis). These entities are located in a partitioned environment that allows the molecular species' diffusion. The cell's models have been implemented using Reaction agents between the cells' receptors and the diffusing molecules. The simulation led to the observation of the effects produced by allergen on the tissue (histamin liberation, capillary vasodilatation...). Previous study on the histamin effect on its receptor H1(21) have been insert in the model too.

In the current state, we can now affirm that two important things have been shown. The first one is the validity of the generic model on an application example. The other one is the basis for the establishment of a biological model improving disease comprehension. We wish to show the retroaction and the amplification function of the nervous fibers in the pathology. This type of model renders possible the testing of a priori influences of a drug on the system [START_REF] Ballet | Simulation of thrombin generation during plasmatic coagulation and primary hemostasis[END_REF].

Wishing to remain within the VR domain, user interfaces were implemented so that the user could have an interaction at any time during the simulation's course :

• An viewer which is provided by AReVi, enabled the observation of and the moving through the model and to interact with the constituents Shape3D. • A virtual syringe allowed the injection of any quantity of molecules anywhere in the model. • An inspector plots on a graph the species quantities we want to observe in a given place of the model. Consequently, in order to study and to understand the urticaria, the researcher can experiment the principle of the disease by virtually injecting in the skin a certain amount of allergen which diffuses and activates the urticaria mechanism.

In addition to that, we have added the possibility of interfacing our application with the norm SBML [START_REF] Hucka | The systems biology markup language (sbml): a medium for representation and exchange of biochemical network models[END_REF]. SBML allows the simplification of the model definition and provides the possibility to exchange data with the systems biology community.

Conclusion

We can now affirm that we have developed improvements in the design of a virtual laboratory for experimentation in biology, in the context of in virtuo the experimentation. We are able to provide a generic modeling method for a multi-model approach which is the heart of this virtual laboratory. We deliberately put a stress on the interaction's reification, for it is intrinsically related to the systemic paradigm. Once again, by "reification" we understand that interactions are taken as autonomous agents. This was achieved in works concerned with the modeling of social organization [START_REF] Buche | MASCARET : A pedagogical multi-agent system for virtual environment for training. Special issue[END_REF]. The model here exposed differs from these works, for interactions are taken as the "only" active objects in the simulation. We introduce this vision into the systems biology field, using multi-agent systems according to both the concept of organization and the chaotic asynchronous iterations.

Nowadays a large amount of articles in the scientific litterature talk about the necessity of an interdisciplinary research, the framework here proposed allows interdisciplinary modeling. Thanks to systemics way of thinking, it provides an interface able to collect the knowledge of experts in biology. These experts are researchers who may work in very different fields of biology and may not be used to communicate together. Thus, the application appears to be a great tool to centralize the data that have been collected by different biologists' teams to understand a phenomenon. Each biologist can complete the global model according to its speciality and its knowledge. It is an efficient communication vector between researcher, providing different viewpoint on the case of study. Furthermore, it was pleasant to realize the application great interest for teaching in order to understand complex phenomena.

From our standpoint, the in virtuo experimentation is design for the study of biological complex systems. The main reasons are:  Environment and disturbances caused by it, on the system, is modeled.  Random which is essential to reproduce biological processes, is simulated.  Different modeling level are considered depending on the knowledge we have in the part of the system we are focused on (molecule, cell, organe, organism, ..., biotope).  Different nature of model coexist in the same application. Chemistry causes mecanics and mecanics modifiy chemistry.  Thanks to the autonomy principle: fuzzy expert system, neural network, rules-based system... can be embedded by the agents. This is interesting according to the suggestion of the expert system methodologies review (Liao, 05) : different methodologies can be integrated into the same VR application.  As a consequence we can mix qualitative and quantitative approach, depending on our knowledge and on the objective we have set.  Hypothesis driven experiments can be performed at cellular or molecular level. Those experiments permit understand and to increase the model. We don't build a model of understood systems but we build model to understand systems.

We have design a toolbox to perform alternative experimentation on complex biological system. At the time where in vivo and in vitro research are more and more difficult to perform, owing to the statutory constraints, the simulations allowed by the in virtuo or in silico research, represents an interesting alternative. The construction of the model and the experimentations by using this toolbox may be quick and remain in very low cost in front of in vivo and in vitro experimentations.

Limitations/Perspectives Computational :

The simulation size is currently limited by the power of computer. The multi-agent systems properties should make the application easily distributed. We are working on the distribution on several computers taking into account the generic model of interaction, organization and constituent. Some optimizations and improvements of the model are naturally planed such using adaptative grid for the molecular diffusion.

Biological :

As to the biological aspect, we keep working on the development of the urticaria model which needs to be completed in order to give significant results. We work on the addition of a nervous fiber model to observe its influence on the allergic reaction. The objective is to test hypothesis concerning the mechanisms of amplification, retro action, and inhibition... which all are characteristic mechanisms of complex systems. We currently plan to test the effect of drugs such as anti-antihistamines which reduce the allergic response.

The model construction may be limited be the range of knowledge. But the lack of information is a part of the biologist everyday life. The experiment and modeling task being led together, the knowledge "holes" may be filled by producing new hypothesis. We are completing our urticaria model, producing new hypothesis and going to meet with another experts in different biology fields. Those meetings have given rise to new starting application: the modeling of the endothelium and the study of cardio-vascular risks; the modeling in toxicology and the study combinated effects of different molecular substances.

531.

@article{ea3883-2005-4, title = "Computer simulation of multiple myeloma in the context of systems biology", author = "G. Querrec, R. Bataille, V. Rodin, J-F. Abgrall et J. Tisseau", journal = "Haematologica / The hematology journal", number = "Supplem 1", pages = "92-93", month = Apr, year = "2005" } The three means of cell's modeling. On the left, chemical and transport interactions constitute a predictive model. On the middle, cell is taken as an autonomous agent. On the right, the hybrid method using autonomous "black box" interactions allows the modeling of the cell.

Figure 1 :

 1 Figure 1: The diagram represents the various means of experimentation. From the left to the right : traditional in vivo and in vitro experimentations, computations in silico and finally the experimentation in virtuo. In the four cases, experiments are carried out accordingly to the model. The results obtained give space for the evolution of the theorical model.

Figure 2 :

 2 Figure 2: Reification of interactions changes our vision of a system. This two dual graphs symbolize the reductionnist (left) and the systemic (right) modeling. Vertex/constituents are turned into links/constituents, and links/interactions into vertex/interactions.

Figure 3 :

 3 Figure 3:The class Organization can be composed of passive objects i.e. the components, of active objects i.e. the interaction agents, and of sub-organizations. An interaction can take place on a single constituent or between several constituents.

Figure 4 :

 4 Figure4: An autonomous sub-system (on the left) can be replaced by an interaction with the environment (on the right) that will have an equivalent behavior.

Figure 6 :

 6 Figure 6:The virtual 3D universe is partitioned in compartments. A chemical reactor without spatial dimension is associated to each compartment. Diffusion agents achieve the transportation of the chemical species from a compartment to another.

Figure 7 :

 7 Figure 7:The three means of cell's modeling. On the left, chemical and transport interactions constitute a predictive model. On the middle, cell is taken as an autonomous agent. On the right, the hybrid method using autonomous "black box" interactions allows the modeling of the cell.

Figure 8 :

 8 Figure 8: CollisionDetector modules of the organization detect collisions between the Shape3D constituents and create Collision agents.

Figure 9 :

 9 Figure 9: This classes diagram shows the integration of the described models which inherits from the generic model.

Figure 10 :

 10 Figure 10: A screenshot of the in virtuo experimentation of urticaria.

P. Redou, S. Kerdélo, J. Tisseau, manuscript in preparation

Acknowledgment

This project benefits from the financial supports of the "Région Bretagne", France