Julien Henriet
email: julien.henriet@univ-fcomte.fr

Pierre-Emmanuel Leni
email: pierre-emmanuel.leni@univ-fcomte.fr

Rémy Laurent
email: remy.laurent@univ-fcomte.fr

Michel Salomon
email: michel.salomon@univ-fcomte.fr

Case-based reasoning adaptation of numerical representations of human organs by interpolation

Keywords: Case-based reasoning, adaptation, interpolation, artificial neural network, radiation protection, 3D numerical phantoms

Case-Based Reasoning (CBR) and interpolation tools can provide solutions to unknown problems by adapting solutions from other problems already solved. We propose a generic approach using an interpolation tool during the CBR-adaptation phase. The application EquiVox, which attempts to design three dimensional representations of human organs according to external measurements, was modelled. It follows the CBR-cycle with its adaptation tool based on Artificial Neural Networks and its performances are evaluated and discussed. The results show that this adaptation tool meets the requirements of radiation protection experts who use such prototypes and also what the limits are of such tools in CBR-adaptation. When adaptations are guided by experience grained through trial and error by experts, interpolation tools become well-suited methods for automatically and quickly providing adaptation strategies and knowledge through training phases.

Introduction

Case-Based Reasoning (CBR) is a problem solving method that uses similar solutions from similar past problems in order to solve new problems [START_REF] Kolodner | Case-based reasoning[END_REF]. One of the main properties of the CBR system is its ability to adapt known solutions to find unknown solutions and many adaptation strategies can be found for this in the literature. Adaptation by generalisation/specialisation requires a hierarchical organisation of the CBR source cases according to generalisation/specialisation relations. Some characteristics are hidden in the generalisation process whereas special ones are added to the general case during the specialisation process.

Adaptation through the use of rules [START_REF] Melis | Reformulation in Case-Based Reasonning[END_REF] consists of computing the solution of a target case by applying a function to it, using as parameters the solution to a source case that presents some similarities.

Differential adaptation [START_REF] Fuchs | A general strategy for adaptation in Case-Based Reasoning[END_REF] is based on the evaluation of variations found between source and target cases: an approximate solution for the target case is computed by applying the variations between the target case and the source case to the solution of the source case under consideration.

Conservative adaptation [START_REF] Lieber | Application of the Revision Theory to Adaptation in Case-Based Reasoning: the Conservative Adaptation[END_REF] is based on Revision Theory that considers knowledge modifications. This type of adaptation is based on minimising modifications applied to knowledge. A cost for the possible adaptations must be computed.

Some studies have highlighted the advantages of prototype-based classifications for CBR-systems [START_REF] Bichindaritz | Case-based reasoning in the health sciences: Whats next? In[END_REF][START_REF] Bichindaritz | Prototypical Cases for Knowledge Maintenance in Biomedical CBR[END_REF][START_REF] Little | Can Prototype-Based Classifica-tion be a good Method for Biomedical Applications? In[END_REF]. These approaches consist of choosing prototypes as representatives for each class of case. Prototypes are also interesting when solutions are not well-known. For example, if you observe someone sitting opposite you, though if it is not possible to model an accurate three-dimensional (3D) representation of his/her lung contours without 3D medical scans, you can nevertheless create a prototype of the organ contours. In such a case, interpolation tools may provide prototypes of an accurate representation of target cases.

Since rules can be discovered only through experience, interpolation tools become the best suited method for adapting solution(s) of source case(s) to target case(s). Furthermore, interpolation tools can be trained to automatically provide the required adaptation knowledge. Indeed, P. Perner and A. Attig in [START_REF] Perner | Using Prototype-Based Classification for Automatic Knowledge Acquisition[END_REF][START_REF] Attig | Incremental Learning of Model for Watershed-Based Image Segmentation[END_REF] implemented them to evaluate the accuracy and the pertinence of sets of prototypes chosen among a set of known ones. The drawback of such a method is that it is not intelligible to users since the interpolation tool functions like a black box [START_REF] Daquin | Adaptation Knowledge Acquisition: A Case Study for Case-Based Decision Support in Oncology[END_REF]. B. Pandey and R.B. Michra proposed a CBR-based system that uses a programme called Artificial Neural Network (ANN) but only during the retrieval phase [START_REF] Pandey | An integrated intelligent computing model for the interpolation of EMG based neuromuscular disease[END_REF].

We designed a generic method to use interpolation tools during the adaptation phase of a CBR-based system. This method consists in interpolating new solutions from the know prototypes of the case-base. Its applicability was also tested and evaluated through implementation in our CBR designed for Health Science (CBR-HS) called EquiVox.

In the first part of this paper we present a model of how interpolation tools can be used during the adaptation phase of CBR-based systems. In the second part we present and analyse the example of the EquiVox application in which ANNs were implemented in order to adapt 3D numerical representations of organ contours. The results are then presented and discussed.

Method

Case model and retrieval phase

In CBR approaches, a case is defined as a {problem, solution} association. The problem part can be represented using a set of n descriptors and the solution by means of a set of N elements. Thus, a source case s and a target case t are defined as follows:

s = {pb s ,sol s } = {{d s i } i∈{1,...,n} , {e s i } i∈{1,...,N} } t = {pb t ,sol t } = {{d t i } i∈{1,...,n} , {e t i } i∈{1,.
..,N} } The retrieval phase lies in sorting the source cases according to their similarity with the target case. We implemented a classical version of the k-Nearer Neighbour (kNN) algorithm [START_REF] Cover | Nearer Neighbour Pattern Classification[END_REF] which computes the distances between each descriptor of the problem parts of target and source cases.

Thus, for each source case i, a similarity index S i is computed as follows:

S i = n k=1 ∆ k -|d i k -d t k | ∆ k n (1)
where ∆ k is the difference between the maximum and the minimum known values that the descriptor d k can take. The S i value is always between 0 and 1. The greater the similarity of i to t, the closer the S i value to 1.

Adaptation phase

B. Knight and F.L. Woon [START_REF] Knight | Case Based Adaptation Using Interpolation over Nominal Values[END_REF] used the interpolation method of D. Shepard [START_REF] Shepard | A Two-Dimensional interpolation Function for irregularity Spaced Data[END_REF] to retrieve and adapt a solution to a target case over nominal values. Indeed, they have a limited number of possible solutions and the adapted solution sol t of t = {pb t ,sol t } minimises

f (sol t )= 2 i=1 (dist sol (sol t ,sol i ) 2 .dist pb (pb t ,pb i ) -1 ) i=1 2 (dist pb (pb t ,pb i ) -1 )
where dist pb (respectively dist sol ) is the distance in the problem (respectively solution) space and where cases i =1andi = 2 are the source cases most similar to t for which pb 1 ≤ pb t ≤ pb 2 .

A. Cordier et al. [START_REF] Cordier | Engineering and learning of adaptation knowledge and Case-Based Reasoning[END_REF] used Influence functions that link variations in problem descriptors to those in solution descriptors. They also used Dependencies which are relationships between problem and solution descriptors. They indicate whether each problem descriptor impacts each solution element (Dependency(e i ,d j )=TRUE if e i depends on d j , Dependency(e i ,d j )= FALSE otherwise). In fact, the Influence function of e i takes as parameters the set of d j for which Dependency(e i ,d j )=TRUE.

Our approach merges these two, considering interpolation tools as influence functions of e t i , ∀i ∈{ 1, ..., N}. Thus, we assume S = {pb S ,sol S } is the source case most similar to t,w h i c hm e a n sS S ≤ S i ∀i ∈ Ωw h e r e Ω is the set of all the source cases. For each e i ,i ∈{ 1, ..., N},w ec o nsidered the entire set of problem descriptor items Ω i dep = ∪{j} for which Dependency(e i ,d j )=TRUE. The interpolation function Interpolate i () of e i used as Influence function is then given by Equation 2:

e t i = Interpolate i (∪ j∈Ω i dep {d t j -d S j }, ∪ j∈Ω i dep {d S j },e S i ) ( 2 )
The dependency matrix is furnished by the experts in the domain. Dependency, in fact, may reflect real values. Nevertheless, interpolation tools such as ANNs only need input descriptor values in order to interpolate solution elements. During a preliminary learning phase, these interpolation tools compute, alone, the degree of dependencies between input and output values (ANN synaptic weights, in our case) during a preliminar learning phase. Thus, in our approach, the useful information is whether or not the problem descriptor has any influence on any part of the solution.

EquiVox application

In case of accidental exposure to radiation, a dosimetry evaluation must be established for each potential victim (subject) as soon as possible. This evaluation is usually based on available 3D voxel phantoms, numerical models created from medical images to represent a subject with maximum realism. Examples of voxel phantoms for dosimetric assessment following internal contamination or external exposure are found in the literature [START_REF] Farah | Examples of Mesh and NURBS modelling for in vivo lung counting studies[END_REF][START_REF] Broggio | Construction of an extended library of adult male 3D models: rationale and results[END_REF]. However, existing models are used even if their characteristics differ from the subject's biometrical data. Dosimetry assessment accuracy and the resulting decontaminating medical action are nevertheless highly dependent on the similarity between phantom and subject.

3D phantoms provide solutions to many situations. In case of accidental exposures, the computed impacts of both the external and internal (inhaled) doses are reported. EquiVox 3D phantoms are used in this particular case, to estimate the dose due to the quantity inhaled. These representations are of precious help for dosimetric reports of inhaled substances since in this particular case, even if the radiation source is not well-known, an accurate idea of the inhaled dose can be computed and accurate representations of organ volumes are required.

Other non-ionizing imaging methods such Magnetic Resonance Imaging and ultrasound may provide accurate images as well. These methods, however, require expensive and highly specialised equipment which may not be readily available after the accident. If it is available anywhere nearby, it may already be in use by local hospitals and accessible only by appointment, which significantly increases delays before any accurate images can be obtained. In addition, radiotherapy services today treat an increasing number of cancerous lung tumours, with physicians and medical doctors using Treatment Planning Systems to treat tumours. The equipment necessary for this requires preparation and control. Its suppliers use 3D phantoms to control their calibration, though it would be reassuring to also use 3D representations from independent sources.

Finally, the use of this equipment requires additional appointments, with further and inconvenient testing, thus creating additional constraints. The already weakened subjects (elderly patients in the case of cancer treatment and patients in shock in the case of accidental exposure) are thus under greater stress and in need of quick reassurance. Consequently, 3D phantoms are useful alternatives and also comprise preliminary models in all cases of exposure to radiation. Hence, the current study aims at assisting the physician in choosing and customising the most similar phantom from among the existing and available ones.

A number of articles on CBR-HS are available [START_REF] Bichindaritz | Case-based reasoning in the health sciences: Why it matters for the health sciences and for CBR[END_REF][START_REF] Bichindaritz | Advances in case-based reasoning in the health sciences[END_REF]. Combinations with Artificial Intelligence (AI) tools are also to be found [START_REF] Diaz | Gene-CBR: A Case-Based Reason-ing Tool for Cancer Diagnosis using Microarray Datasets[END_REF][START_REF] El Balaa | FM-Ultranet: A Decision Support System Using Case-Based Reasoning Applyied to Ultrasono-graphy[END_REF][START_REF] Monati | Case-Based Reasoning for Managing Non-Compliance with Clinical Guidelines[END_REF]. E.B. Reategui et al. [START_REF] Reategui | Combining a neural network with case-based reasoning in a diagnostic system[END_REF] combined neural networks with CBR in a diagnostic system for congenital heart diseases. In their approach, the neural network is trained by means of cases stored in the library, and is used during the consultation process to both hypothesise possible diagnostic solutions and to guide the search for similar cases. EquiVox [START_REF] Henriet | Adapting numerical representations of lung contours using Case-Based Reasoning and Artificial Neural Networks[END_REF] is a CBR-HS system that also combines an AI tool with a CBR-HS system, but in the adaptation rather than in the retrieving process as in Reategui's approach. Indeed, EquiVox uses the CBR-approach to find the most similar phantom(s) within any set of phantoms and then attempts to adapt them to the characteristics of the target case (the subject) using Artificial Neural Networks (ANNs) [START_REF] Mcculloch | A logical calculus of the ideas immanent in nervous activity[END_REF]. At this point in our investigation, EquiVox can process the 3D contours of three organs: lungs, heart and oesophagus.

A large number of phantoms can be found in the literature [START_REF] Farah | Examples of Mesh and NURBS modelling for in vivo lung counting studies[END_REF][START_REF] Broggio | Construction of an extended library of adult male 3D models: rationale and results[END_REF] where radiation protection is also divided into numerous sub-domains. Indeed, some phantoms are commonly used by experts for external radiotherapy, and others are used by other physicians for evaluation of internal doses received. In fact, experts all have their own collection of 10 to 20 phantoms. When a physician's usual phantoms are all too distant from the subject, the experts must create a new one. Using iterative 3D dilations and contractions, they modify the contours of the 3D organs of their phantoms to make them correspond to those of the subject. They then assemble them to obtain the final phantom on which the computations will be based [START_REF] Farah | Examples of Mesh and NURBS modelling for in vivo lung counting studies[END_REF]. In addition, these transformations are only driven by experience, trial and error, and may take many hours or more. The delay also increases with the number of subjects, whereas the problem resolution delay may be limited. In the case of massive irradiation for example, when a disaster such as a nuclear explosion occurs, dosimetric reports are required for hundreds of people of different sizes. In fact, the creation of new organ contours requires a fast data-driven method, and since there is no physical law to govern its design, experts are not able to explicit a rule for the transformation of an organ contour. Thus, the main challenge for EquiVox is to reproduce the same transformation process automatically, without human intervention. Another requirement is that every subject increases the accuracy of dose calculations. Current implementation relies on phantoms that are usually used by a team of experts for pulmonary anthroporadiametry which consists of evaluating the internal dose inhaled [START_REF] Broggio | Construction of an extended library of adult male 3D models: rationale and results[END_REF].

Figure 1 presents the technologies that were used and the data flows over the EquiVox architecture. The whole phantoms are all stored under Rhino3D files. The corresponding biometric data are stored under an ontology scheme (data flow ♯0). The contours of the lungs, heart and oesophagus are extracted (data flow ♯1) and then transmitted to the ANN training module (data flow ♯2), which creates three ANNs (data flow ♯3): one per organ. When a new phantom is required, the target case description is transmitted to the retrieval module (data flow ♯4) which determines the similitude index by taking into account the source cases (data flow ♯5). If required by the experts, the thorax adaptation module sends the characteristics of the source cases (data flow ♯6) to the ANN interpolation module (data flow ♯7) which loads the trained ANNs (data flow ♯8) and the coordinates of the organ contour in question (data flow ♯9) in order to create interpolated contours suited to the target case (data flow ♯10), which are combined to create the interpolated organ contours (data flow ♯11).

Case modeling and retrieval phase

When radiation overexposure occurs, the expert's first task is to choose the most accurate 3D phantom according to the subject's height. Indeed, a study by I. Clairand et al. [START_REF] Clairand | Improvement of internal dose calculations using mathematical models of different adult heights[END_REF] demonstrated that the volume and shape of the lungs depend only on the subject's height. In addition, the heart and oesophagus occupy the empty spaces between the lungs. Thus, in EquiVox, the problem part of a case i is described with the subject's height pb i = {h i }. The solution part is a set of 3 3D contours of organs:

sol i = {P i } = {P i
Lungs ,P i Heart ,P i Oeso. } where ∀O ∈{ Lungs, Heart, Oeso.},P i O is a set of q O points joined by a Delauney mesh [START_REF] Christensen | Deformable shape models for anatomy[END_REF]:

P i O = {C i,O 1 , •••,C i,O q } where C i,O j
denotes the 3D coordinates of the point j of the organ O of the case i. Finally, a case i is equal to {h i , {P i Lungs ,P i Heart ,P i Oeso. }}. As before, t remains the target case.

The purpose of this phase is to sort the organ contours of the EquiVox case-base according to their similarity to t. As presented in 2.1, a classical algorithm for similarity calculation was used, namely the kNN algorithm. Considering 20 cm ≤ human height ≤ 250 cm, Equation 1 becomes S i = 230-|h i -ht| 230

. For example, considering the phantoms stored in EquiVox whose heights are reported in Figure 2, if a Physician has to compute a dosimetric report for someone whose height is 170 cm, P 4 should be retrieved as the most accurate phantom with S 4 =0.9914.

Adaptation of 3D organ contours

Once a matching case is retrieved, the expert can decide whether or not to use the organ representations of the most similar source cases, or to require the EquiVox platform to generate new ones, adapting the source cases to the target case. Indeed, assuming SIM is the source case most similar to t,i f h SIM and h t are too different, the expert may decide to adapt SIM or even to create new organ contours which may be re-used for other problems later.

For all the solutions of the source cases, the same number of points defines the 3D contours of the lungs (q Lungs = 26723), oesophagus (q oeso. = 7485), and heart (q Heart = 7895). The points were plotted in the same order and in the same Cartesian coordinate system. Thus, the task of the organ contouradaptation phase of EquiVox consists of interpolating the 3D coordinates of the points of t in the same order and in the same Cartesian coordinate system. A Delaunay mesh can then be applied so as to create the contours of the organs of t. As concluded by I. Clairand's study [START_REF] Clairand | Improvement of internal dose calculations using mathematical models of different adult heights[END_REF], organ shapes and volumes of case i depend on h i : Dependency(P i O ,h i )=TRUE ∀O ∈{Lungs, Heart, Oeso.}. Since the mesh and the number of points are not variable, the adaptation must be carried out on the point coordinates of the organ contours, point by point. Since no formal equation exists, we need a learning method to discover the rules that transform the coordinates of the points of one organ contour into other coordinates. Consequently, data-driven methods using inductive reasoning are the most suitable approaches; ANN and Fuzzy-ANN meet these requirements. We chose ANN as the tool for this step, assuming it might serve as the basis for further work with Fuzzy-ANN if the first results were not convincing. We explored the possibility of using perceptrons with one or two hidden layers trained with a back propagation-based method, but other interpolation tools may also be easily used by EquiVox: the purpose of this study was not to compare interpolation tools, but to provide and validate a general method for using a given interpolation tool.

Each C t,O j is interpolated from C SIM,O j , h i and ∆h = h SIMh t .T h u s , there are 3 ANNs (one for each organ) and Equation 2 becomes

P t O = Interpolate O (∆h, h SIM ,P SIM O
),O ∈{Lungs, Heart, Oeso.}. For example, in the adaptation of someone with a height of 170 cm, we saw in the previous section that SIM =4s i n c eP 4 was retrieved as the most accurate phantom. Each point of the contour of the lungs of the corresponding phantom representing this subject should then be computed as P P 170cm Lungs = Interpolate Lungs (1.97, 168.03,P 4 Lungs ). Indeed, the height of P 4 is 168.03 cm and 170 -168.03 = 1.97. This subject's lungs are interpolated according to the lungs of the most similar case and the distance between them. Similarly, heart and oesophagus contours are computed by the interpolation tools as follows ). ANN learning consists of determining the synaptic weights between neurons of different layers and also the optimum number of neurons in hidden layers. First, a random number of neurons per and in the hidden layer(s), along with random values for the synaptic weights are set. The synaptic weights are then computed until the mean distance d w between the interpolated and the expected phantoms is inferior to a given ε. After optimisation of these synaptic weights, the mean distance d n between interpolated and expected yet unused phantoms (those in the validation set) is computed. If d n is superior to a given ε, the number of neurons in hidden layer(s) are changed and the synaptic weights are computed again. This process is performed until d n ≤ ε. Consequently, for this preliminary phase, two sets of elements must be constituted: 1) the elements of the learning set with which the optimal synaptic weights are computed and 2) the elements of the validation set with which the optimal number of neurons and hidden layers are computed. Naturally, each element can belong to only one of these sets. Generally, 10% of the elements are used for the validation set and 90% for the learning set. Then come the other elements of a test set required to verify the ANN accuracy.

In Figure 2, the 12 heights, corresponding to P 1 through P 12 , are reported on the same axis. Since we have a limited number of 3D Organ Contours (3DOC), we studied the interpolation accuracies regarding the composition of the learning and validation sets. We thus defined two main configurations and four possibilities for each as shown in Table 1. Generally, validation sets are composed of 10% of learning sets. For each possibility the validation set was therefore composed of one phantom: P 3 for P ossibility♯1, P 4 for P ossibility♯2, P 7 for P ossibility♯3andP 9 for P ossibility♯4. Cross-validation was then performed for the other sets. We chose four phantoms for the validation sets: one of the smallest (P 3 ), one slightly smaller than average (P 4 ), one slightly taller than average (P 7 ) and one of the tallest (P 9 ). After having fixed the test and the validation sets, all the remaining phantoms were put into the learning set. For the first configuration the constraint over the ANN input ∆h>0 was added, whereas for the second ∆h<0 was required. Then, for each configuration, we explored the possibility of extracting one particular phantom from the learning set to be included it in the validation set.

Results

The Equivox platform was implemented and tested on a Personal Computer equipped with an Intel Core i3 CPU, 2.53 GHz, and 4 GiB RAM. Protégé was used to store the descriptor values. Two programming languages were used: Java and C++. All of the programmes were developed by our team. The phantoms were drawn using Rhino3D. The ANN learnings were carried out in C++ at the supercomputer facilities of the Mésocentre de calcul de Franche-Comté, containing 74 nodes based on Intel processors (4 to 6 cores) and 12 to 96 GB of RAM.

The detailed results for each of the three adapted organs are presented below prior to a presention of a global result analysis of the adaptation of 3DOC.

Tables 2 and3 show the distances obtained between interpolated and expected points for lungs (in ×10 -3 cm). Note that it is not possible to interpolate P 1 ' 3DOCs with constraint (∆h>0) or P 12 with constraint (∆h<0). With the constraint ∆h>0, the learning configuration that gave the most accurate interpolations is the one with {P 9 } as the validation set. Most of the differences were of approximately 0.02 mm. Accuracies vary from 0.015 mm (interpolation of P 4 with {P 9 } as the validation set) to 0.642 mm (interpolation of P 5 with {P 7 } as the validation set). Nevertheless, even in such a case, the adaptation is sufficiently accurate since it is inferior to spatial resolutions of phantoms used by experts (1.8mm × 1.8mm × 4.8mm). Interpolations with ∆h>0 are generally better than with ∆h<0. Contrary to what might be expected, the best adaptations of P i+1 and P i-1 are not always obtained when {P i } is the validation set. For example, the best interpolations of P 4 and P 2 are obtained when it is P 9 that is in the validation set, not P 3 . Similarly, interpolations of P 8 are better with {P 4 } as the validation set than with {P 9 } and {P 7 }. Thus, the best interpolations are not obtained when the 3D Lung contours of the phantom having the closest height are included in the validation set.

Globally, the heart interpolations are of greater accuracy than those for the lungs. As shown in Tables 4 and5, a smaller global deviation may be observed even if there is a great difference for the interpolation of P 5 with {P 4 } as the validation set (0.646 mm); all the other differences vary from 0.009 mm (interpolation of P 9 with {P 7 } as the validation set) to 0.098mm (interpolation of P 3 with {P 9 } as the validation set). Unlike the lung interpolations, the configuration ∆h<0 provides better interpolations, and, generally, the configuration with {P 3 } as the validation set produced the most accurate interpolations. As for the lungs, adaptations are accurate enough since they are inferior to spatial resolutions required by dosimetric reports, and additionally, no correlation is observed between the 3DOC used as the validation set and the best interpolated ones.

As shown in Tables 6 and7, the oesophagus interpolations were less accurate than those for the previous organs. Specifically, they are roughly only one tenth as accurate as for lungs: from 0.075 mm (interpolation of P 2 using {P 4 } as the validation set) to 14.3 mm (interpolation of P 5 using {P 3 } as the validation set). This is the only case for which the requirements of experts are not met. As for the other organs, no correlation can be found between the best interpolations of each 3DOC and the validation set used. All together, the best interpolations for all 3 organs were obtained using {P 3 } as the validation set.

Finally, one configuration did not always provide the greatest accuracy for all the 3DOCs of one phantom. For example, P 11 , with {P 4 } as the validation set and ∆h>0, produced the best lung adaptations, whereas with {P 9 } as the validation set and ∆h<0, it gave the best results for heart contours, while {P 3 } with ∆h<0 was most accurate for the oesophagus. Similar results can be observed for all the other phantoms in addition to P 6 . Indeed, the organs of P 6 are optimised with the same configuration ({P 4 } and ∆h>0).

Discussion

Figure 3 shows P 6 interpolated 3DOC and their accuracies using {P 4 } as the validation set and ∆h>0. Each point is coloured according to its interpolation error, from blue (the lowest) to red (the highest). We can observe that there is no mesh problem and no artefact is added. In addition, 3D contours show a relatively realistic representation of lungs, heart and oesophagus.

As a general remark, we observe the greatest difficulty in the interpolation of P 5 . However, in all but one of the tested cases, the requirements of the experts are satisfied. Indeed, only once are the interpolation deviations superior to the commonly used voxel dimensions used by radiation protection experts. In addition, the same configuration does not always give the best results. These observations and the deviations obtained may be explained by the fact that all the 3DOCs were designed manually and consequently contain biases.

These results emphasise the importance of the configuration and the 3DOC chosen for each set (validation and training), since the inclusion of one 3DOC in the validation set can generate an accuracy greater than any other and which is sometimes twice as high. Also, the inclusion of one 3DOC in the validation set may introduce a bias for some interpolations while simultaneously improving the accuracy of another target case. These biases may be eased by the capitalisation process: their impact will decrease as the number of source cases rises. Nevertheless, for each adaptation, choosing the training and validation sets with care may provide an additional solution for alleviating the biases introduced by source case solutions.

In addition, the interpolations take only one to three seconds, a great help to physicians who usually need many hours to adapt a single phantom. Thus, extending the use of this method to other organs may result in a useful tool in case of massive accidental radiation exposure.

More generally, we have presented a generic method for the use of interpolation tools in adapting a source-case to a target-case solution within a CBR-system. Its applicability has been confirmed through its implementation in EquiVox, a CBR-HS which responds to the requirements of the specific issue of radiation protection. The results tend to prove that the accuracy of adapted solutions mostly depends on the accuracy of the solutions furnished by the source cases. During its revision process, however (and with user help), a CBR can evaluate the accuracy of adapted solutions. A. Cordier et al. [START_REF] Cordier | Engineering and learning of adaptation knowledge and Case-Based Reasoning[END_REF] proposed that the remarks made by the users during revision processes should be used in the adaptation phase. Future study will focus on how to take revision remarks into account during CBR-adaptation phases driven by interpolation tools.

Finally, examples of adaptation of lungs, oesophagus and heart depend only on one dimension. Other measurements will be required in order to provide adaptations for other organs such as the ribs, the muscles, the skin, the fat, etc. Future investigation will test our approach in practical cases of multidimensional problem descriptions.

Conclusion and Perspectives

In this paper our main contribution is the design of a generic method for the use of interpolation tools as influence functions for CBR-adaptation. The method's applicability has been proved since it was applied in EquiVox, a CBR-HS which can provide prototypes of 3D contours of organs based only on the subjects' height. The resulting accuracies were analysed and discussed with respect to the requirements of the field of application. These results confirm and quantify the general drawback of using interpolation as the means of adaptation in CBR systems [START_REF] Chatterjee | Interpolation as a means of fast adaptation in case-based problem solving[END_REF]: imperfections are introduced into the adapted solutions. Consequently, two improvements are now under consideration. The first consists of collecting and capitalising on phantoms so as to progressively attenuate the imperfections of the solutions; the ANN interpolations, based on ever larger learning sets, will gradually improve. However, a second and more general option must also be explored, which depends on associating vectors to the learning set so as to optimise interpolation accuracies and to determine, a priori, the best learning and validation sets for each target case. Some of the interpolation errors were related to imperfections that may be found in the source-case solutions. Thus, further investigation will need to focus on the elaboration of an adaptation algorithm capable of taking into account the reliability of a source-case solution. Our goal, in other words, is to propose a tool that creates rules for the adaptation of target cases by using confidence indices. This could be attempted through the Genetic Algorithm and/or use of metaheuristics as proposed by Z. Liao et al. [START_REF] Liao | Adaptation methodology of CBR for environmental emergency preparedness system based on an Improved Genetic Algorithm[END_REF].

Figure 1 :

 1 Figure 1: Data flows over the EquiVox architecture.

Figure 2 :

 2 Figure 2: Phantom heights of the available 3D organ contours.

Figure 3 :

 3 Figure 3: Representation of P 6 interpolated organs with {P 4 } as the validation set and ∆h>0.

  P P 170cm Heart = Interpolate Heart (1.97, 168.03,P 4 Heart )a n d P P 170cm Oeso. = Interpolate Oeso. (1.97, 168.03,P 4 Oeso.

Acknowledgements

The authors wish to thank the Institut National de la Santée td el a Recherche Médicale,t h eL i g u eC o n t r el eC a n c e r ,t h ePays de Montbéliard Agglomération and the SociétéF r a n çaise de Radioprotection for their financial aid, the National Institute of Radiological Protection and Nuclear Safety for their expertise, and John Olsen for his help with the English language.

Val.

Tested 3DOC set ∆hP 7 P 8 P 9 P 10 P 11 P 12 P 3 > 0 2.7 4.1 17.5 25.5 3.7 8.9 P 3 < 0 7.9 8.9 24.9 20.2 7.5 / P 4 > 0 2.1 2.0 1.9 31.7 1.9 8.5 P 4 < 0 6.2 6.2 4. [START_REF] Fuchs | A general strategy for adaptation in Case-Based Reasoning[END_REF]


E Chabrat
email: elodie.chabrat@ensiacet.fr

A Rouilly

P Evon

A Longieras

L Rigal

RELEVANCE OF LAB-SCALE CONICAL TWIN-SCREW EXTRUDER FOR THERMOPLASTIC STARCH/PLA BLENDS RHEOLOGY STUDY

During the last decade, thermoplastic starch (TPS) has been studied more and more, alone and in blends. One key property of TPS is its viscosity. A lab-scale conical twin-screw extruder has been used to process polymers or blends of polymers at a small scale (7 cm 3 ), and to measure their viscosity by pressure loss in a backflow channel. TPS has been tested at different temperatures (100-180°C) and for a 100-900s -1 shear rate range. One surprising result is the viscosity evolution of starch/glycerol blends (supposed to have become TPS before the rheology measurements) with temperature. An increase is observed between 120 and 140°C and then it decreases between 140 and 160°C. Therefore plasticization may happen only from 140°C. Blends of TPS with PLA and with different additives have also been studied. The additives are introduced in a second time, ten minutes after the TPS/PLA blend recirculation. Their influence on the blend viscosity is instantaneous. A viscosity increase after the additive introduction can be a clue for an improvement of the blend compatibilisation, as observed with CMC. Thanks to this micro-compounder, viscosity and behaviour of polymers can be evaluated easily even for TPS which needs shear to flow. Moreover, the solidified sample collected in the backflow channel at the end of the experiment can be used to test different properties like mechanical or thermal (DMTA, DSC) ones. Using this kind of lab-scale extruder represents then a good opportunity for preview screening studies.

Introduction

During the last decade, thermoplastic starch (TPS) has been studied more and more, alone [START_REF] Stepto | Thermoplastic Starch[END_REF] and in blends [START_REF] Ke | Effects of moisture content and heat treatment on the physical properties of starch and poly(lactic acid) blends[END_REF]. Indeed, starch is a renewable and biodegradable resource which can be transformed into a thermoplastic material by using plasticizers, shear and temperature. This product is very promising, in spite of its sensibility to water and its poor mechanical properties. It is well-known that starch plasticization can be realised in a twin screw extruder [START_REF] Martin | In-line determination of plasticized wheat starch viscoelastic behavior: impact of processing[END_REF]. Twin-screw extruders range widely from lab-scale (g/min) to industrial-scale (Tons/min). Among the smallest twin-screw extruders, one can find the Thermo-Haake Minilab (Thermo Scientific, Haake, Germany). As this instrument contains co-rotating twin screws, it can represent the performance of a corotating extruder (industrial scale) [START_REF] Moghaddam | Vibrational spectroscopic studies of laboratory scale polymer melt processing: Application to a thermoplastic polyurethane nanocomposite[END_REF]. The Minilab operates at speeds between 10 and 360 rpm, corresponding to shear rates between 35s -1 and 1248s -1 in the geometry controlled back flow channel and its heating capacity and maximum temperature are 800W and 450°C respectively. The Minilab has a maximum feed capacity of 7 cm 3 . The backflow (recirculating) channel in the Minilab allows its use as a mixing reactor with controlled recirculation rather than direct extrusion through the die. In addition to melt processing operations, the Minilab can also be used as a rheometer by using a pair of pressure transducers in the backflow channel. An approximate value for the melt viscosity is calculated automatically by the Minilab software using the pressure loss between these two sensors. This apparatus can thus be used to study new blends or new products. After a screening at small scale, the interesting blends can be processed on an industrial twin-screw extruder with new parameters like temperature profile (and not just one temperature), choice of the screw configuration… In this study, starch has first been plasticized with glycerol. Variable factors were the temperature, the screw speed (shear rate) and the glycerin rate. Then, thermoplastic starch has been blended with a biodegradable polyester, the polylactic acid (PLA). This blend already studied in several previous works is not miscible and needs to be compatibilized. The last part of this work describes a method to visualize the additive impact on the viscosity.

Experimental

Materials

Wheat starch was supplied by Gers Farine (France). Starch plasticizer was glycerol (purity 99%) supplied by Gaches Chimie (France). The PLA (Ingeo 3251D was supplied by Natureworks (USA). The three tested additives were CMC (carboxymethylcellulose), which is a Blanose 7M grade (Aqualon), succinic acid (Sigma-Aldrich) and xanthan gum (IMCD).

TPS fabrication

Starch was hand-blended with glycerol and then introduced in a lab-scale twin-screw extruder, the Minilab (Thermo Scientific Haake, Germany) (Figure 1). In our case, the experiments were performed at 120-160°C and screw speeds between 50 and 250rpm. The sample was processed in the Minilab in recirculating mode for 8 minutes (stabilization time) before measuring the viscosity for 20 minutes, i.e. 28 minutes of recirculation. To study the influence of glycerol rate, temperature and shear rate, a design of experiment (DOE) was made as described in Table 1.

Characterization

Viscosity was directly measured with the lab-scale extruder thanks to its pressure transducers. It was calculated as described in Equation 1and measured every minute for 20 minutes. Finally, these viscosities were averaged. The average is the product viscosity given in the results part. Thermal study was also performed on a Pyris 1 differential scanning calorimeter (DSC) (Perkin-Elmer). The measurement cells were purged with dry nitrogen. The temperature was calibrated by use of indium (T f = 156.6°C). The pans used for this study were airtight steel capsules with an 0-ring. They withstand high pressure (40bar) and are therefore well adapted for studying weakly hydrated biopolymers at high temperatures. The sample weighed approximately 20mg. The measurements were taken during the first scan, at 20°C/min between 40 and 200°C.

Results and Discussion

Recirculation in the Minilab

To ensure that the matter correctly recirculates in the lab-scale extruder, the following experiment was made: A starch/glycerol blend was introduced in the lab-scale extruder at 140°C with a screw speed of 150rpm. After 5 minutes, a small quantity of a dye (erythrosine) was introduced (t=0s) and the experiment was stopped after 30s, 1min, 2min and 5min.

The color of the sample in the backflow channel is representative of the circulation of the matter. On Figure 2, one can find the photographs of the 4 samples (4 different times of experiment). After 30s (top-left), the dye has only reached the middle of the channel. After one minute, the dye has colored almost all the backflow channel except for the extreme sides. After 2 minutes, the whole backflow channel is colored, the dye had circulated everywhere in the channel. After 5 minutes, the sample is darker, meaning that the dye had already circulated several times in the backflow channel. Hence, the matter does effectively recirculate in the lab-scale extruder.

Plasticization of starch

DOE results are represented on figures 3 to 5 (response surface). The temperature has only a small effect on the viscosity comparing to glycerol rate and screw speed. A screw speed increase (i.e. shear rate increase) leads to a decrease of the viscosity whatever the temperature and the glycerol rate, which is consistent with the shear-thinning behavior of TPS. A glycerol rate increase also leads to a viscosity decrease whatever the temperature or the screw speed. Even if the temperature has a small effect on the viscosity, at high screw speed a viscosity maximum is observed around 140°C as represented on Figure 6. This viscosity maximum could be explained by a transformation happening at 140°C. After 140°C, the viscosity decreases with the temperature which is a classical behaviour for a thermoplastic. Following this hypothesis, this means that before 140°C, the destructuration (and/or plasticization) of starch may not be complete. This idea was confirmed with thermal analysis (Figure 7). On the DSC graph, a peak is observed around 170-180°C for native starch. For a manual blend of starch and glycerol, this peak is divided into two peaks, around 175°C and around 140°C. This second peak was still observed after extrusion at 120°C, whereas it disappeared after extrusion at 140°C. This peak may be representative of the native structure and disappears totally after complete destructuration (and/or plasticization). [START_REF] Van Soest | Influence of glycerol on the melting of potato starch[END_REF] have already studied the melting of potato starch with low and high amounts of glycerol and have observed similar behavior. Blending with PLA Blends of thermoplastic starch and PLA were also made in the lab-scale extruder (Figure 8). At 140°C, TPS and PLA viscosities intersected at 500s -1 , meaning that at lower shear rates, PLA is more viscous than thermoplastic starch and reversely at higher shear rates. This is interesting because it means that at 500s -1 , the two products have the same viscosity, which is a perfect condition for blending. What is also interesting on this graph is the blend viscosities. Whatever the proportions, it is always lower than the viscosity of the two components. This result can be an indication of a bad blend compatibility where the two phases repel each other and the blend is more fluid. Opposingly, when a blend is homogeneous, the viscosity of the blend is higher than the viscosity of the components because of interactions between the two phases.

Method to study additives influence

Here is presented a simple method to study the additive influence on a blend. In each experiment, the beginning was the same. Starch, glycerol and PLA were extruded for 18min (8min of stabilization and 10min of measure). After these 18min, the additive was introduced in the extruder and the viscosity was measured for 10min (Figure 9). The continuous line is the reference curve (without mid-experiment add). Some additives lower the viscosity (succinic acid -dash and point curve), one can imagine maybe a lack of affinity between the components or a degradation of some of them (acidic degradation). Some additives have no influence on the viscosity (xanthan gum -dash curve). These additives have maybe no influence on the blend. The other additives increase the viscosity (CMC -point curve). The increase can be simply explained by a thickening effect of some products or by a compatibilisation of the blend. A viscosity increase of the blend can be a clue for a blend compatibilisation improvement.

Conclusions

Starch plasticization, starch blending with PLA and even with compatibilizers was possible in the lab-scale extruder. Moreover, instantaneous viscosity measurements provided useful information about the matter state in the extruder.

Figure 1

 1 Figure 1 Configuration of the Minilab with the twin screws and the pressure transducers

  .s) : η Shear stress (Pa) : τ and shear rate (s -1 ) : γ . Depth of the flow channel : h = 1.5mm Width of the flow channel : w = 10mm Distance between the transducers : l = 64mm Pressure drop (Pa) : P Screw speed (s -1 ) : n Extruded samples were collected from the backflow channel for analytical purposes. All experiments were performed in triplicates. These samples were 70mm long, 8mm large and 1mm thick. They were conditioned at 25°C and 60%HR for stabilization for one week prior to testing. The tensile testing was carried out at a rate of 5mm/min according to ASTM D638. Dynamic mechanical analyses (DMA) of the samples were performed with a Tritec 2000 DMA (Triton Technology, UK) over the temperature range -100 to 200°C with a scanning rate of 2°C/min. The amplitude and frequency were maintained constant at 25 m and 1 and 10Hz, respectively.

Figure 3 Figure 4 Figure 5 Figure 2

 3452 Figure 3 Viscosity as a function of the screw speed (vit) and the temperature (T), glycerol rate = 30%

Figure 6 Figure 7

 67 Figure 6 Viscosity of a starch/glycerol blend (75/25) at 622s -1 (175rpm) for different temperatures

Figure 8

 8 Figure 8 Flow curves for different TPS/PLA blends at 140°C -( : TPS, * : PLA, other curves : blends TPS/PLA from 95/5 to 50/50)

Figure 9

 9 Figure 9 Evolution of the viscosity with the introduction of an addtive at mid-experiment (continuous curve : no additive, point curve : CMC, dash curve : xanthan gum and point & dash curve : succinic acid)

Table 1 -

 1 Design of experiment for the starch plasticization

	Experiment	Temperature	Screw speed	Glycerol
	number	(°C)	(rpm)	content (%)
	1	160	150	30
	2	120	150	30
	3	150	237	30
	4	130	63	30
	5	150	63	30
	6	130	237	30
	7	150	179	34.1
	8	130	121	25.9
	9	150	121	25.9
	10	140	208	25.9
	11	130	179	34.1
	12	140	92	34.1
	13	140	150	30
	14	140	150	30
	15	140	150	30

Acknowledgements

We would like to thank Maria Konstantakopoulou for her help for the experiments and the French Environment and Energy Management Agency (ADEME) for financial help.


M Lagarrigue

S Jacquier

J Debayle

J C Pinoli

F Gruy

Multi-scale agglomerates: relationship between morphology and optical properties

1) INTRODUCTION

Multi-scale solid particle aggregates designate aggregates of clusters, which are composed of smaller clusters, themselves composed by aggregated solid particles. There are usually 3 or 4 relevant scale levels of agglomeration. The final aim of this study is to define the relationships between the geometrical and optical characteristics of different aggregates. Indeed, a previous work of Gruy and Jacquier in 2008 [START_REF] Gruy | The chord length distribution of a two-sphere aggregate[END_REF] and [START_REF] Jacquier | Anomalous diffraction approximation for light scattering cross section: Case of random clusters of non-absorbent spheres[END_REF] showed the existence of a narrow link between these two aggregate characterizations. The first step consists in modeling multi-scale aggregates with specific geometrical shape and optical properties. Thereafter, the aggregate characterization is performed. Following the Xu theory called GMM (Generalized Multiparticle Mie solution) exposed in his paper [START_REF] Xu | Electromagnetic scattering by an aggregate of spheres[END_REF], the studied optical parameter is the scattering cross section, denoted, Csca in (µm 2 ). In addition, the optical analysis is focused on aggregates with a high optical index.

Concerning the geometrical characterization, several parameters are studied: the compactness, the number of the primary particles and the volume of the aggregates, successively.

Using different 2D joint (geometrical/optical) representations, the correlation between the Csca values and the geometry of the aggregate is analyzed.

2) AGGREGATES MODELING

a. Geometrical shape Two scale levels are used for modeling the aggregates. For the first level, particles are modeled by spheres (imposed by the knowledge of the theoretical optical method). Their radius will be equal to 10, 15 and 30 nm, respectively.

On the second scale level, aggregates will have a known overall shape (Figure 1): sphere, cube, cylindrer, oblate and prolate convex hulls respectively. The sizes of these hulls are chosen so that they have the same volume of an equivalent sphere whose diameter is 300 nm. The cylindrical type depends on the size of its basis diameter and its height, k-proportional to the basis diameter, k>1. For the ellipsoidal cases, shape axes a, b and c are so that a=b, and c=a/k, with k>1 for the prolate type, and for the oblate type: 0<k<1. In this paper, we use k∈{2, 20} for the prolate case and k ∈{1/2; 1/20} for the oblate type.

We also consider four types of filling ratios of the hulls (Figure 2): filling at 100% (convex hull filled with particles with the most compact way), 75% and 50% (corresponding to the conservation of respectively 75% and 50% particles of the 100% filling, randomly and uniformly selected), and hollow filling, where only particles of the hull edge of the 100% filling case are conserved.

b. Optical properties

As previously mentioned, this study is focused on multiscale aggregates with a high optical index. For these two reasons, zinc sulfide (ZnS) aggregates are studied, because of the

3) GEOMETRICAL AND OPTICAL CHARACTERIZATION

On each graph are represented all the aggregates with different convex hulls, filling ratios and radius of primary particles. The average Csca represented corresponds to the mean Csca value for each aggregate. The markers of the legend correspond to the convex hull aggregate geometry.

a. Influence of the filling ratio

Figure 3 shows the average Csca value in the relation with the compactness for the aggregates.

We can see that the aggregates filled at 100%, 75% and 50% are grouped in relation with of their compactness (volume of the primary particles of an aggregate divided by the convex hull volume), independently of the primary particles radius. For hollow filling, it is more chaotic. But it is important to note that, for a same compactness value, several Csca can be obtained: from nearly 0 to 0.16. We can deduce that this geometrical criterion is not decisive for Csca value.

Figure 4 shows the average Csca in relation with the primary particles number constituting the aggregates. It results that the size of the primary particles is a factor that strongly affects the Csca value. Indeed, the aggregates are arranged along curves following the primary particles radius. Besides, it appears that the aggregates are arranged along another criterion: a morphological factor which induces a different behavior above the Csca values. Indeed, for each size of primary particles, we can distinguish two curves of arrangement following the aggregate anisotropy. So, it is shown that the size of primary particles and the anisotropy of the aggregate are decisive geometrical parameters. In this graph (Figure 5), the aggregates follow two distinct curves in relation with average Csca and the particles volume. For the first one (which the highest slope), we find all aggregates whose hull is rather isotropic. For the second one: all the anisotropic aggregates. Nevertheless, this graph is not discriminative enough to correlate the anisotropy of aggregates to their average Csca.

b. Influence of the size of primary particles

4) Conclusion

Using different 2D joint (geometrical/optical) representations, it results that several geometrical parameters affect the mean Csca value of an aggregate to be studied: compactness, number of primary particles, and volume of the articles of each aggregates. A more detailed statistical analysis is needed to correlate the optical and geometrical parameters, by involving a spatial arrangement.

Figure 1 :

 1 Figure 1: Representation of aggregates with full convex hull, constituted by 750 to 854 primary particles of radius equal to 15nm: (a) spherical, (b) cubic, (c) cylindrical with k=2, (d) oblate with k=2, (e) prolate with k=2, (f) cylindrical with k=20, (g) oblate with k=20, (h) prolate with k=20.

Figure 2 :

 2 Figure 2: Representation of aggregates having a spherical convex hull with different filling ratios: (a) 100% filling, (b) 75% filling, (c) 50% filling, (d) hollow filling.

Figure 3 :

 3 Figure 3: Joint representation of compactness and average Csca for each aggregate. A color distinction is made in function of their filling ratios.

Figure 4 :Figure 5 :

 45 Figure 4: Joint representation of the number of particles and average Csca of for each aggregate. A color distinction is made in function of the size of the primary particle.


Catherine Thèves

Philippe Biagini

Eric Crubézy
email: crubezy.eric@free.fr

The discovery of major pathogens The re-discovery of smallpox

Keywords: Smallpox, Evolution, Paleomicrobiology, Ancient DNA, Yakut Population

Smallpox is an infectious disease unique to humans, caused by a poxvirus. It is one of the most lethal of diseases; the virus variant Variola major has a mortality rate of 30%. People surviving this disease have lifelong consequences, but also assured immunity. Historically, smallpox was recognised early in human populations. This led to prevention attempts: variolation, quarantine and the isolation of infected subjects, until Jenner's discovery of the first steps of vaccination in the 18 th century. After vaccination campaigns throughout the 19 th and 20 th centuries, the World Health Organization declared the eradication of smallpox in 1980. With the development of microscopy techniques, the structural characterisation of the virus began in the early 20 th century. In 1990 the genomes of different smallpox viruses were determined; viruses could be classified in order to investigate their origin, diffusion and evolution. To study the evolution and possible re-emergence of this viral pathogen, however, researchers can only use viral genomes collected during the 20 th century. Cases of smallpox in ancient periods are sometimes well-documented, so paleomicrobiology and more precisely, the study of ancient smallpox viral strains could be an exceptional opportunity. The analysis of poxvirus fragmented genomes could give new insights on the genetic evolution of the poxvirus. Recently, small fragments of the poxvirus genome were detected. With the genetic information obtained, a new phylogeny of smallpox virus was described. The interest of conducting studies on ancient strains is discussed, in order to explore the natural history of this disease.

Introduction

Smallpox (variola) is an acute infectious disease of viral origin (genus Orthopoxvirus), which has caused devastating epidemics. During the 20 th century it was responsible for 300-500 million mortalities, and in the last millennia it is estimated to have been responsible for 10% of mortalities worldwide. Thus, it is highly probably that this disease has strongly selected human populations, but there is no current evidence to validate this hypothesis. Following a global pandemic in the 18 th century, vaccination against smallpox began in the early 19 th century and the last case was reported in Somalia in 1977. In 1980, the World Health Organization (WHO) declared that smallpox had been eradicated. It is not clear what role population selection and the general improvement of hygiene conditions played in this eradication process, but the extensive vaccination programme conducted by the WHO certainly accelerated the process (www.who.int/csr/disease/smallpox/en/). In the modern era, although populations worldwide have been affected by smallpox, it is the isolated nonoccidental populations which have been impacted the most; some New World and Siberian populations have been decimated by the virus.

Today, the study of smallpox has various challenges: (i) Social and medical challenges. Many populations living in remote areas, where smallpox has become endemic only recently, will migrate to live in urban or sub-urban environments. Thus, minor cases of the disease could result in epidemics through the gradual reduction in the number of vaccinated people, and the major environmental changes that impact them. Moreover, humans are the only known reservoir of the virus, but the emergence of an animal reservoir or a very closely related animal virus that could adapt to humans is not excluded. Note, that current-day animal poxvirus strains can infect humans, but that virulence differs between strains [START_REF] Baxby | Medical Microbiology[END_REF].

Governments must therefore control live strains of the poxvirus (see below), remain informed on the hazards of the virus, its mutation potential during epidemics (which can speed up the epidemic and/or make it last longer), and the potential for competition between different strains. It is also necessary to identify these strains, and to distinguish between the natural reemergence of the disease and its genetic manipulation in the laboratory. This is also of importance since smallpox could be developed for acts of bioterrorism; and (ii) It is also a biological challenge due to co-evolution between humans and the environment. What genes were selected by smallpox epidemics during human evolution? How has the virus evolved? In human population histories what were the relationships between the major human-killers (plague, tuberculosis) and smallpox?

Recently, we demonstrated a case of smallpox through molecular analysis; an autochthonous subject who died in Yakutia, Eastern Siberia, (Figure 1), between 1628-1640 during a significant tuberculosis epidemic [START_REF] Biagini | Variola virus in a 300-year-old Siberian mummy[END_REF]. From small fragments of degraded DNA we proposed a new phylogeny of the virus. This research gave new perspectives on the genetic study of smallpox; ancient smallpox samples are now considered safe to work on due to the degraded nature of their DNA. There is no doubt that the discovery of ancient smallpox cases and the sequencing of ancient strains will give further insights into the natural history of this disease.

Clinical symptoms and epidemiology

Humans are the only known hosts or reservoirs of smallpox. Smallpox is one of the most feared diseases in the world, since its mortality rate ranges from 1% for cases of Variola minor, to more than 97% for hemorrhagic smallpox cases in unvaccinated subjects. The incubation period of 8-14 days is followed by a virus-like invasion phase (high fever, shivering, arthralgia), and then by a state phase with a maculopapular rash which produces blisters on the 3 rd day and infected pustules on the 7 th day. If the subject survives, there is a drying phase on the 10-12 th day when the scabs fall off to leave permanent scars. The patient will then be immunized, but the duration of this immunization period is still debated [START_REF] Hammarlund | Antiviral Immunity following Smallpox Virus Infection: a Case-Control Study[END_REF]. With the hemorrhagic form the subject dies after the first 24 hours of the invasion phase following bleeding of the skin and/or mucous membranes. During the 19 th century, less virulent smallpox epidemics were recorded with a death rate of 1% in South Africa and Central America, where the less virulent smallpox is known as alastrim [START_REF] Fenner | Smallpox and its eradication[END_REF]. The mode of disease transmission is usually direct contact: the virus is transmitted primarily by the exhalation of patients and then by contact with skin lesions. The virus is very stable and can survive for years in the scabs [START_REF] Sinclair | Persistence of category A select agents in the environment[END_REF]. In natural conditions, however, the virus remains pathogenic for about a couple of weeks.

The earliest and most incontestable descriptions of smallpox appeared in the 4 th century in China, and then later in India (7 th century) and in Southwest Asia and the Mediterranean (10 th century AD (Anno Domini) [START_REF] Fenner | Smallpox and its eradication[END_REF]. It was prevalent in southern Europe during the 13 th century, when it starting to spread throughout Europe causing millions of deaths over the centuries [START_REF] Albou | La variole avant Jenner (XVIIe-XVIIIe siècles)[END_REF][START_REF] Geddes | The history of smallpox[END_REF]. In the 18 th century smallpox was endemic in Europe and significant peaks in the number of mortalities were observed: 14,000 deaths in 1716, 20,000 in 1723 and 14,000 in 1796 in Paris [START_REF] Sartori | Napoléon mène l'assaut contre la variole[END_REF], killing 10% of newborns and one in three adult patients. It decimated Amerindian populations during the conquest of the New World from the beginning of the 16 th century [START_REF] Fenner | Smallpox and its eradication[END_REF], and it was the succession of smallpox epidemics and other infectious diseases imported from the Old World that destroyed what remained of the Inca culture [START_REF] Mann | New revelations of Americas before Columbus[END_REF].

Due to its distinctive clinical symptoms, smallpox has been known as a disease 'entity' for many centuries. Campaigns against smallpox began in the absence of current scientific knowledge, while the causes and mechanisms of the disease were unknown. Various protection methods against smallpox have tried to be developed. The earliest methods, reported in the 10 th century, were insufflation in China and cutaneous inoculation in India [START_REF] Fenner | Smallpox and its eradication[END_REF].

Variolation, to avoid serious smallpox, consists of an inoculation with 'benign smallpox' from the pustules of a patient. The origin of this technique is disputed, but it is known to have been practiced in China in the 16 th century. It was imported into the West in the early 18 th century by Lady Wortley Montagu, the wife of the Ambassador of Great Britain to Turkey [START_REF] Berche | L'histoire des microbes[END_REF], but it is likely that different techniques had existed previously in the European countryside. In Scotland, farmers attached wool soaked in smallpox pus around their wrists, and in some Italian mountains children were made to wear similarly soaked shirts [START_REF] Miller | The adoption of inoculation for smallpox in England and France[END_REF][START_REF] Razzell | The conquest of smallpox[END_REF]. Results were, however, very random and many subjects still died despite these attempts of variolation. The practice was introduced into France in second half of 17 th century, where it was extensively studied and fiercely debated (due to the dangers of inoculation), with written submissions to the Academy of Sciences [START_REF] Fenner | Smallpox and its eradication[END_REF]. Before 1760, European doctors replaced the needle (used in Turkey) with the lancet, which allowed doctors to make a deeper cut [START_REF] Dreyer | Daniel Bernouilli et la variole[END_REF], but these incisions were either ineffective or catastrophic. After 1760, Sutton proposed a method involving a more superficial incision, increasing the reliability of the inoculation and hence its popularity [START_REF] Razzell | The conquest of smallpox[END_REF].

From 1769, at least six people in England and Germany successfully tested the possibility of using the cowpox vaccine against smallpox in humans [START_REF] Fenner | Smallpox and its eradication[END_REF]. At the end of the 18 th century, Edward Jenner, a country doctor in England with many farmer patients, noted that contact with livestock, particularly cows, exposed farmers to a disease transmissible to humans; cowpox or vaccinia, the smallpox of cows. From the observation that milkmaids who had contracted cowpox did not usually contract smallpox, Jenner postulated that the pus present in the cowpox vesicles protected people against smallpox. Today we know that the cowpox vaccine is a benign disease for humans, in comparison with smallpox, but at the time it seemed that a convergence of ideas led to replacing the pus of smallpox with that of cowpox.

In 1796, Jenner developed the first stages of the vaccination process: he inoculated a child with the pus from a farm worker's hand who was infected with cowpox (via contact with the infected cow's udders), causing a localized infection at the inoculation site. Three months later, he inoculated the child with smallpox; the child showed no signs of infection and so was immunized against the virus [START_REF] Fenner | Smallpox and its eradication[END_REF]. Over a period of twenty years, Jenner conducted systematic experiments which led to the establishment of the vaccination method, thus replacing inoculation. It should be noted, however, that at the same time as variolation and vaccination, procedures were taking place in Europe, the quarantine and isolation of affected individuals, which also reduced the spread of the disease [START_REF] Haygarth | Sketch of a plan to exterminate the casual small-pox from Great Britain[END_REF][START_REF] Carl | Darstellung des dritten Jahrgangs der zu Brunn gestifteten Blatternimpfanstalt[END_REF].

In the early 19 th century, vaccination against smallpox spread rapidly throughout the occidental world [START_REF] Guerin | Rapport sur la vaccination générale de l'arrondissement d'Orange[END_REF], and was largely responsible for the observed change in population demography. Before vaccination world demography is termed pre-Jenner; when considering several generations, for 1000 births, one-third of subjects died between birth and the age of one and one-third between 1 and 18 years old. After vaccination world demography is termed post-Jenner; an increase in the number of surviving subjects between birth and 18 years old is observed. If birth rates remain constant there is a population explosion, and this is what occurred in Europe in the 19 th century due to vaccination. The world population increased to about 1 billion in 1800, and to more than one and a half billion in 1900 [START_REF] Crubézy | Anthropobiologie. Évolution humaine[END_REF]. The first vaccination campaigns carried out in the first half of the 20 th century, and the WHO screening programme conducted from 1967 onwards were highly successful, and smallpox was declared eradicated in 1980 (the last reported case was in 1977 [START_REF] Fenner | Smallpox and its eradication[END_REF].

Initial isolation and characterization of the smallpox viruses

Recognition of the disease and measures for its prevention were initiated early in human history (16 th century in China), but investigations into the virus itself did not begin until the late 19 th century with the establishment of the new science of virology. Virus particles of smallpox, cowpox and vaccinia were firstly identified under the microscope, then by electron microscopy (before any other viruses had been visualised), and their chemical compositions were analysed before those of animal viruses [START_REF] Fenner | Smallpox and its eradication[END_REF]. Most studies and knowledge on orthopoxviruses were based on the vaccinia virus.

The first reports on the viral elements of vaccinia using microscopy were in 1886 by Buist [START_REF] Gordon | Virus bodies. John Buist and the elementary bodies of vaccinia[END_REF] and Calmette-Guérin in 1901 [START_REF] Calmette | Recherches sur la vaccine expérimentale[END_REF], who observed many elementary particles in the stained smears and vaccine lymph of rabbit. Prowazek in 1905 and Paschen in 1906 [START_REF] Fenner | Smallpox and its eradication[END_REF] also showed these 'elementary bodies' by using different microscopy methods. It was, however, the work of Ledingham in 1931 [START_REF] Ledingham | The aetiological importance of the elementary bodies in vaccinia and fowl-pox[END_REF] that demonstrated definitively that the elementary bodies were indeed the infectious entity in the lymph. Thereafter, the analysis of the pox virion structure was dependent on the processing powers of the electron microscopy. Between 1948 and 1970, thin sections of infected cells characterized the membrane structures, the core and the components of the vaccinia virus [START_REF] Fenner | Smallpox and its eradication[END_REF].

The detection of nucleic acids (DNA) present in the virus, but not ribonucleic acids (RNA) was demonstrated in 1940 [START_REF] Hoagland | Constituents of the elementary bodies of vaccinia. II. Propperties of nucleic acid obtained from vaccine virus[END_REF][START_REF] Smadel | Elementary bodies of vaccinia[END_REF]. In 1962, the double-stranded nature of the virus' DNA and its guanine and cytosine composition was demonstrated [START_REF] Joklik | Some properties of poxvirus deoxyribonucleic acid[END_REF]. The first genomic sequences of the smallpox virus were published in the early 1990s, with the complete DNA sequence of the vaccinia virus [START_REF] Goebel | The complete DNA sequence of vaccinia virus[END_REF][START_REF] Shchelkunov | Comparison of the genetic maps of variola and vaccinia viruses[END_REF]. Thereafter, a significant effort was made to sequence most of the isolates which had been collected during the WHO Intensified Smallpox Eradication Programme (1967)(1968)(1969)(1970)(1971)(1972)(1973)(1974)(1975)(1976)(1977)(1978)(1979)(1980). Currently, about 50 human genomes, as well as dozens of animal poxviruses, are available on the web (http://www.poxvirus.org). Thus, new insights on the origin, distribution and evolution of different human clades have been made [START_REF] Li | On the origin of smallpox: correlating variola phylogenics with historical smallpox records[END_REF][START_REF] Esposito | Genome sequence diversity and clues to the evolution of variola (smallpox) virus[END_REF].

The virus and its evolution

Viruses of the genus Orthopoxviridae are widespread in vertebrates and most of them are species specific [START_REF] Moss | Poxviridae: The viruses and their replication[END_REF][START_REF] Shchelkunov | Orthopoxviruses pathogenic for humans[END_REF]. The best studied Orthopoxviridae are the poxviruses (Poxviridae), DNA viruses that replicate in the cell cytoplasm [START_REF] Moss | Fields Virology[END_REF]. These include smallpox viruses (Variola major and Variola minor), the primate viruses (highly pathogenic to humans), and the bovine poxvirus (used as a vaccine against the three aforementioned viruses). The genome of an orthopoxvirus is a linear double-stranded DNA molecule containing approximately 200 genes. The central region of the genome has highly conserved sequences and contains the majority of genes involved in transcription, mRNA biosynthesis, DNA repair and replication, and the modification of viral structural proteins [START_REF] Shchelkunov | Orthopoxviruses pathogenic for humans[END_REF][START_REF] Moss | Fields Virology[END_REF]. The terminal regions are variable and determine the specific properties of the species, the strain of the virus, and its immunomodulatory protein genes [START_REF] Gubser | Poxvirus genomes: a phylogenetic analysis[END_REF][START_REF] Lefkowitz | Poxviruses: past, present and future[END_REF][START_REF] Upton | Poxvirus orthologous clusters: toward defining the minimum essential poxvirus genome[END_REF]. The virulence of smallpox is related to a set of genes that produce proteins that increase (compared with other viruses) the efficiency of the multiple defence mechanisms of the host organisms [START_REF] Shchelkunov | Orthopoxvirus genes that mediate disease virulence and host tropism[END_REF].

Following the eradication of smallpox in 1980, two conservatories holding the live viral strains were created: CDC in Atlanta, USA, and VECTOR in Novosibirsk, the Russian Federation. Although the purpose of these conservatories is regularly discussed [START_REF] Manuguerra | Le grand débat[END_REF], their goal is to store live strains in order to establish medical and vaccination strategies in the event of re-emergence or bioterrorism. Currently, they store live smallpox strains which were collected between 1944 and 1977 [START_REF] Li | On the origin of smallpox: correlating variola phylogenics with historical smallpox records[END_REF][START_REF] Shchelkunov | How long ago did smallpox virus emerge?[END_REF]. Their genomes have been completely sequenced and are open access (NCBI GenBank). These strains follow the global phylogeographic distribution; the first cluster groups Variola major strains from Asia, India and Africa, excluding the West, and the second cluster groups the two sub-clusters of West Africa and in South America.

Several studies on the strains are being conducted by the WHO and authorized laboratories: tests for the diagnosis of smallpox in the laboratory, smallpox genomic studies, the establishment of animal models and of pathogenesis, and the development of antivirals for the treatment of smallpox [37]. Independent advisory experts consequently assess all smallpox research programmes [38]. With technological advances in high-throughput sequencing and the generation of whole genomes for modern strain, the origin and variability in virulence factors for these poxviruses are well-studied by phylogeny [START_REF] Li | On the origin of smallpox: correlating variola phylogenics with historical smallpox records[END_REF][START_REF] Shchelkunov | How long ago did smallpox virus emerge?[END_REF]. The evolution of different smallpox viruses are studied using data on sequence diversity, genome structure and variation in coding regions [START_REF] Esposito | Genome sequence diversity and clues to the evolution of variola (smallpox) virus[END_REF]. The evolution and phylogeny of poxviruses specific to vertebrates are also studied for a better understanding of the hypotheses related to the dispersion and the date of the origin of these strains [START_REF] Babkin | Molecular dating in the evolution of vertebrate poxviruses[END_REF][START_REF] Babkin | A retrospective study of the orthopoxvirus molecular evolution[END_REF].

The published phylogenetic tree found a root/tMRCA calculation for the sequences of 120 AD (maximum) (Figure 2 in [START_REF] Biagini | Variola virus in a 300-year-old Siberian mummy[END_REF]; mean estimate of 928 AD for the tMRCA of all smallpox sequences; 5%-95% confidence range = 120 AD -1714 AD; median = 1585 AD). This date is consistent with that reported in early documents on smallpox (before 1000 AD [START_REF] Fenner | Smallpox and its eradication[END_REF]), but it is certainly very recent considering when the disease first appeared (between 1500-1100 BC in China and India [START_REF] Fenner | Smallpox and its eradication[END_REF]). Indeed, apart from the traditional descriptions of the disease, interpretations of certain texts and/or archaeological discoveries suggest a much earlier existence of the disease, especially in its cutaneous form. Observations of typical rashes have been identified in Egyptian mummies dating from 1100-1580 BC [START_REF] Fenner | Smallpox and its eradication[END_REF][START_REF] Dixon | Smallpox. Churchill[END_REF][START_REF] Hopkins | The Greatest Killer -Smallpox in History[END_REF], and the disease could have struck China in 1122 BC and India in 1500 BC [START_REF] Fenner | Smallpox and its eradication[END_REF][START_REF] Hopkins | The Greatest Killer -Smallpox in History[END_REF]. The divergence between current phylogenies archaeological evidence is related to the fact that current strains only represent a small part of smallpox genetic variability in the 20 th century. This has several implications: (i) as more strains are discovered variability increases, so it probable that the most recent common ancestor is older than present estimations; and (ii) a large number of strains have disappeared during human history, or they are not detected today as they are no longer virulent. Strains affecting European and American human populations between the 13 th and 18 th centuries have been eradicated since the 19 th century following the first vaccination campaigns [START_REF] Geddes | The history of smallpox[END_REF].

Paleogenetic studies

Paleomicrobiology is a field of research based on the detection of infectious diseases in the past [START_REF] Drancourt | Palaeomicrobiology: current issues and perspectives[END_REF]. Fragments of bacterial or viral DNA are searched for in possibly infected tissues, or in the teeth of subjects, who died during a bacteremia or viremia, taking into account the specific characteristics of the ancient DNA sample (Figure 3). Regarding smallpox, our work in Central Yakutia (Eastern Siberia) in 2004 led to the discovery of an elite burial (wealthy and organized) dating from between 1730 and 1740, with five remarkably well-preserved subjects (Figure 4). The anatomical study revealed no trauma, and the burial of subjects at the same time during winter suggested that they had died during a disease epidemic [START_REF] Crubézy | Chamane: Kyys, jeune fille des glaces[END_REF]. The search for pathogens was initially focused on bacterial pathogens, but since none were found a viral origin was hypothesized. This was reinforced by the presence of iron in the lung alveoli of the subject, suggesting death due to a haemorrhage. Smallpox was not the first virus to be tested for, because none of the four subjects, for whose skin could be examined, showed any traces of blisters or pustules. Only in the best preserved subject were we able to identify three DNA fragments of the ancient human poxvirus by PCR [START_REF] Biagini | Variola virus in a 300-year-old Siberian mummy[END_REF]. To assess the persistence of large DNA fragments, we conducted long range PCRs on the E9l gene (encoding for polymerase) following [START_REF] Babkin | Molecular dating in the evolution of vertebrate poxviruses[END_REF]. The amplifications expected were about 1000 and 2043 bp: no positive results were obtained, suggesting a fragmented viral genome [START_REF] Biagini | Variola virus in a 300-year-old Siberian mummy[END_REF]. The absence of pustules, the presence of a pulmonary hemorrhage and the detection of the virus could indicate that the subject presented hemorrhagic smallpox. It would be interesting to look for the presence of smallpox in the other subjects in the grave (Figure 4). The first phylogenetic study conducted on these fragments showed, as expected (see above), that this ancient strain is distinct from the modern strains described previously (Figure 2). This study was the first of its kindit opens up interesting avenues for phylogenic and natural history approaches to studying smallpox. The virus is considered resistant to environmental conditions, but the subject was buried in Central Yakutia where temperatures can drop below 50°C in winter (see conservation of burials and bodies in Figure 5), and a burial of two and a half centuries has destroyed the virus, fragmenting and degrading its DNA. It is hoped that research on archaeological samples will be facilitated in the future.

According to current legislation and risk assessments, the theoretically level of containment required in a laboratory, due to the classification of a parental strain, does not necessarily need to be implemented. Smallpox and archaeological samples which are significantly degraded are not pathogenic. Thus, we can assume that a biosafety level of two would be required in a laboratory, corresponding to the minimum level required by the regulations for handling of samples of human origin (e.g., teeth). The scientific community can then use the 'smallpox model' to assess the co-evolution of virulence and resistance genes (if they exist in humans) in subjects buried before, during and after an epidemic. The future of smallpox natural history remains to be written; it will not be dangerous, so the interest in keeping live strains of the virus is brought into question again. [START_REF] Thèves | Molecular identification of bacteria by total sequence screening: determining the cause of death in ancient human subjects[END_REF][START_REF] Crubézy | Human evolution in Siberia: from frozen bodies to ancient DNA[END_REF]. It is important to note that such archaeological samples consist of many DNA molecules, not only originating from the subject (human nuclear and mitochondrial DNA) and the pathogen potentially responsible for the death of the subject (bacterial or viral DNA), but also environmental bacteria from this complex environment: soil, water, plants. Metagenomic or bacterial genome analyzes show that the majority of bacteria in this kind of sample are environmental [START_REF] Thèves | Molecular identification of bacteria by total sequence screening: determining the cause of death in ancient human subjects[END_REF]. well-organized, which shows that the population and the related subjects had not all been eradicated. It is interesting to note that the golden age in Yakutia ends after 1728/1740 [44, 20 46]. Originally we discussed a major economic change [START_REF] Crubézy | Chamane: Kyys, jeune fille des glaces[END_REF], it would be interesting to determine how a hemorrhagic smallpox epidemic could have participated in this decline. Eletcheï 1 (2009) © Nicolas Senegas. The main ethnic group from this region, the Yakuts, used inhumation as a common funerary practice ever since they discovered the region in the Middle Ages [START_REF] Crubézy | Chamane: Kyys, jeune fille des glaces[END_REF]. This is unique to Yakuts in Siberia and the Arctic, and provides a unique opportunity to access a continuous temporal sampling from the Middle Ages onwards.

Figure 1 :

 1 Figure 1:

Figure 5 :Figure 1 :

 51 Figure 5:

Figure 2 :

 2 Figure 2: Phylogenetic analysis of concatenated sequences of an ancient Siberian smallpox

Figure 3 :

 3 Figure 3: Composition of environmental, undetermined and potential pathogenic 16S rDNA

Figure 4 :

 4 Figure 4: Evocation of the shamanic tree grave © Nicolas Senegas; watercolour of different

Figure 5 :

 5 Figure 5: The frozen graves of Yakutia: an exceptional conservation. From left to right:

Acknowledgments:

The French archaeological Mission in Oriental Siberia (Ministère des Affaires Etrangères et Européennes, France), the North-Eastern Federal University (Yakutsk, Sakha Republic), the HUMAD programme in IPEV (Institut Polaire français Paul Emile Victor) funded the study. The project's administration and research were permitted through the programme of the France-Russia Associated International Laboratory (LIA COSIE number 1029), associating the North-Eastern Federal University (Yakutsk, Sakha Republic), the State Medical University of Krasnoyask, the Russia Foundation for the Fundamental Research (Moscow, Russia), the University of Paul Sabatier Toulouse III (France), the University of Strasbourg I (France) and the National Centre of Scientific Research (Paris, France).