Nefissa Khiari Hili

Sylvie Lelandais
email: s.lelandais@iut.univ-evry.fr

Christophe Montagne
email: cmontagne@iup.univ-evry.fr

Kamel Hamrouni²
email: kamel.hamrouni@enit.rnu.tn

BOOSTING STEERABLE FEATURES FOR 2D FACE RECOGNITION ON IV² DATABASE

Keywords: 2D face recognition, Feature extraction, Feature selection, Steerable pyramid, Adaboost

In this paper, a novel approach for 2D face recognition is proposed, based on local feature extraction through a multi-resolution multi-orientation linear method: Steerable Pyramid (SP) and on a feature selection and classification by means of a non-linear method: Adaboost. Many strategies have been elaborated and tested on IV² database including challenging variability such as pose, expression, illumination and quality. To show the robustness of the method, it was compared to five algorithms submitted to the first evaluation campaign on 2D face recognition using IV² database. Proposed algorithm is almost among the two best ones.

INTRODUCTION

In the last two decades, security concerns have deeply increased because of the incessant fraud attempts. Being considered as the ultimate solution, biometrics took part to research works to a great extent, especially, 2D-Face recognition since it is non-invasive and requires less user cooperation.

Despite the considerable efforts in 2D-face recognition, it is still difficult to achieve high accuracy under non-constrained situations. Since most of the existing databases don't offer either enough variabilies or sufficient number of subjects, relevant databases, like the IV² one, were recently developed to permit efficient evaluation of the proposed methods. Classical algorithms such as Eigenfaces, Fisherfaces, Gabor [START_REF] Li | Handbook of Face Recognition[END_REF] perform well in controlled environments; however, their performances drastically drop when variability like quality, pose and illumination occur. Therefore, new solutions are being suggested to overcome these challenges. Many of them were based on combining conventional algorithms and brought quite good results. As instance, Mellakh et al. [START_REF] Mellakh | 2D Face Recognition in the IV² Evaluation Campaign[END_REF] proposed a method based on LDA and Gabor; Zhang and Jia [START_REF] Zhang | Face Recognition Based on Steerable Feature and Random Subspace LDA[END_REF] operated an identification by means of SP and LDA and Su et al. [START_REF] Su | Hierarchical ensemble of global and local classifers for face recognition[END_REF] allied local and global features. With the persuasion of the enhancement a merging strategy could provide, the 2D face recognition system presented in this paper, was developed by combining a spacescale feature-extraction method: the Steerable Pyramid (SP) to a non-linear feature-selection and classification method: Adaboost. The idea of applying Steerable Pyramids to characterize Face images, emanates from a previous work on iris recognition by [START_REF] Khiari | Iris Recognition Using Steerable Pyramids[END_REF] where good results were reached. The Steerable Pyramid (SP) transform introduced by Simoncelli and Freeman [START_REF] Simoncelli | The Steerable Pyramid: A Flexible Architecture For Multi-scale Derivative Computation[END_REF] associates multi-scale decompositions with differential measurements, thus able to capture both frequency and orientation information, which perfectly suits this application. On the other hand, AdaBoost method, proposed by Freund and Schapire [START_REF] Freund | A decision-theoretic generalization of on-line learning and an application to boosting[END_REF], provides a simple yet effective stage-wise learning approach for feature selection and classification. Therefore, we adopt AdaBoost to select the most discriminant SP features and build a strong classifier.

Through this paper, a promising 2D-face recognition method combining SP and Adaboost is introduced. The following is divided into four sections. Section 2 explains SP and Adaboost formulations. Section 3 illustrates the collection of data and the evaluation protocol elaborated in the IV² project. Section 4 describes the proposed method and reports experimental results in comparison to five other algorithms submitted in the first IV² evaluation campaign [START_REF] Mellakh | 2D Face Recognition in the IV² Evaluation Campaign[END_REF]. Finally, section 5 ends up with conclusions and perspectives for future work.

BACKGROUND CONCEPTS

This section introduces the basical concepts of Adaboost and Steerable Pyramids (SP) as being the association that gave birth to proposed approach.

Adaboost

Boosting is a method to combine a collection of weak classification functions (weak learner) to form a stronger classifier. AdaBoost is an adaptive algorithm to boost a sequence of classifiers, in that the weights are updated dynamically according to the errors in previous learning [START_REF] Viola | Rapid Object Detection using a Boosted Cascade of Simple Features[END_REF].

AdaBoost Algorithm : Input: n training of examples (x 1 , y 1 )…(x n , y n ) with y i in {+1, -1} is the class label for the positive or negative sample x i ; where i = 1,…,n. In our case (face recognition), x i = (I 1,i ,I 2,i ) is a pair of images.

Initialize: weights D 1,i =1/n Do for t = 1,…,T: 1. For each filter Φ j , compute the best weak classifier h j , that uses Φ j . This amounts to finding the optimum threshold t j , minimizing the error e j for each possible filter.

2. Choose the classifier h t with the lowest error e t , according to weighted examples and their labels.

3. Choose α and β that define the feature f t , based on e t and the estimated labels y i,t .

4. Normalize the weights D t,i so that they are a distribution.

Output: The final Strong classifier :

ܨሺݔሻ = ݊݃݅ݏ ൭ f ୲ ሺxሻ ் ௧ୀଵ ൱ (1)
More details about Adaboost algorithm and equations are available at [????].

Steerable Pyramid (SP)

The steerable pyramid, introduced by Simoncelli & Freeman [START_REF] Simoncelli | The Steerable Pyramid: A Flexible Architecture For Multi-scale Derivative Computation[END_REF], is a linear multi-scale multi-orientation decomposition that provides a front-end to many image-processing applications particularly in texture analysis. The basis functions of a steerable pyramid are directional derivative operators that come in different sizes and orientations. The pyramid can be designed to produce any number of orientation bands. The representation is translation invariant (it is aliasing free) and rotation invariant (the sub-bands are steerable). More importantly, the transform is a tight-frame, specifically; the same filters used in the decomposition are used for the reconstruction. The block diagram of a steerable pyramid (Kasaridis, 1996) is given in figure 1 for both analysis and synthesis. In the analysis part, the image is decomposed into highpass and lowpass subbands using H 0 and L 0 filters. The lowpass band continues to break down into a collection of oriented n+1 bandpass subbands B 0 , B 1 ,…, B n and a lower lowpass subband L 1 . The lower lowpass subband is subsampled by a factor of 2 in the x and y directions. This process constitutes the first level of decomposition of a steerable pyramid. Repeating the enclosed area on the output of subsampling provides the recursive (pyramid) structure, hence the next levels. In the synthesis part, the reconstructed image is obtained by upsampling the lower lowpass subband by a factor of 2 and adding up the collection of bandpass subbands and the highpass subband. It is important to point out that only the analysis part of the steerable pyramid diagram system is applied while extracting features from the face texture.

THE IV² DATABASE AND THE EVALUATION PROTOCOL

In biometric studies, it is very crucial to have a big set of data on which the efficiency of proposed algorithms can be evaluated. Some databases are available (Petrovska, 2009) but they don't offer enough data either in number or in variability. The IV² database was designed with the aim of proposing multiple test situations to allow evaluation with regard to variability well known to be critical for the biometric systems performance, such as pose, expression, illumination and quality (Figure 3).

Database description

The publicly available IV² database allows monomodal and multimodal experiments using face data. It contains 315 subjects with one session data where 77 of them also participated to a second session. From this database, a subset of 52 subjects, distributed as a development set, constitutes also the training set.

The face and sub-face data that are present in the IV² database are: 2D audio-video talking face sequences, 2D stereoscopic data acquired with two pairs of synchronized cameras, 3D facial data acquired with a laser scanner, and iris images acquired with an portable infrared camera. This database has been collected in several locations, by many operators. From the totality of the acquired data, are available two disjoint sets for development and evaluation purposes, and also an evaluation package.

The 2D face evaluation protocol

As a closing stage of the IV² project, an evaluation campaign was performed involving iris recognition, 2D and 3D-face recognition and also multimodal recognition. In the 2D-Face evaluation [START_REF] Mellakh | 2D Face Recognition in the IV² Evaluation Campaign[END_REF], the strategy of having "one variability" at a time was adopted in order to evaluate how challenging variability -related to illumination, expression, quality or multi-session images -can be for the biometric systems.

In this evaluation campaign a set of more than 15000 images were divided into four subsets. Table 1 gives a description of the test images according to the corresponding experiment. The protocol was constructed so as to have almost the same number of client and imposters tests. This strategy allows having equivalent FAR (False Acceptance Rate) and FRR (False Rejection Rate). Each team who proposed an algorithm conducted a list of tests with no indication of their type (intraclass or interclass). Only one still image per subject was used for enrolment and one still image for the test. A set of 156 images from 52 different subjects acquired at the development stage has been as well distributed to each team for the training phase. Five appearance based methods were evaluated on the IV² database. Details about the algorithms are given in (Petrovska, 2007) and comparative results are shown in table 3.

PROPOSED METHOD AND EXPERIMENTAL RESULTS

Beforehand the recognition, normalization process is performed on gray-scale images in order to extract efficiently the region of interest. Normalization is operated so as to deal with pose variations (rotation and scale) taking place at the acquisition step, and get all the images at the same scale and size (64x64).

Characterization through Adaboost

First experiments have been conducted only with Adaboost. It has been noticed that the performance increased with the number of iterations of adaboost model. Limited by the computational time, a number of 400 iterations has been kept. It can be seen from table 3 (Test 1) that Adaboost reach very good EER: 3.7%, in Experiment 1. However, performance drastically drops in Experiments 2 to 4 that involve challenges related to illumination, quality and multisession variabilities. This is due to the fact that Adaboost is very dependent on the training set; witch has been acquired, almost under the same conditions as in Experiment 1.

Characterization through SP

Many experiments have been run on how the SP has to be performed. A first experiment constructed the feature vector from the whole information at all orientations and scales provided by the entire filtered image. Another experiment was carried out by composing the feature vector of the 49 (8x8) filtered blocs issued from the initial image. A third try was run to build the feature vector with the 49 energy values computed from the (8x8) filtered blocs. Other tests have been completed to investigate on how the recognition performance is further enhanced with the increase of the orientations and scales numbers. Specifically an exhaustive set of experimentations has been fulfilled. Optimum parameters were obtained by extracting features from the entire (64x64) filtered image by utilizing a four-level fifth derivative steerable pyramid (6 orientations). The feature vector was made of more than 10 4 intensity values. Details about EER are given in table 3 (Test 2) where it can be seen that the results obtained by the SP-based algorithm are worse than the IV² ones.

As a matter of fact, SP features are overcomplete and stand for a high dimensional representation of face images. Straightforward, implementation exhibits a lack of efficiency.

Characterization through Adaboost applied to SP

To make up for the SP and Adaboost shortcomings when operated separately, AdaBoost was adopted as a feature selector and classifier that reduces the SP feature space size in order to keep only relevant characteristics.

In the next, the influence of a non exhaustive list of parameters, related to the application strategy of Adaboost on SP-filtered images, is firstly presented. Then, a comparison with the submitted algorithms at the IV² evaluation campaign is brought. The results are reported with the Equal Error Rate percentage.

Applying Adaboost on the whole SP

A first set of tests was carried out by applying Adaboost on the whole steerable features so as to select the more discriminant ones. Increasing the number of iterations related to the Adaboost model (i.e. the number of selected features) improves the recognition rate as shown in figure 4. But, unfortunately, running tests was so time consuming that reaching more than 400 features was not practical.

Figure.4. Equal Error Rate vursus number of iterations in Adaboost model.

It is obvious from EERs in table 3 (Test3.a) that allying adaboost to SP, is much better than applying Adaboost or SP separately. The results are almost acceptable, when compared to the IV² other tests; but they are still not good enough. The aim to ameliorate the method, and at the same time, encounter the computation time restriction, led to the idea of applying Adaboost per band.

Applying Adaboost on every sub-band of SP

Many strategies of application have been tested: Using only one sub-band: A set of experiments focused on which oriented sub-band of the SP should be took into account as an input to Adaboost. Previous works [START_REF] Khiari | 2D Face recognition on IV² database by Steerable pyramid and LDA[END_REF] on SP showed that there is no favourite orientation for all tests. Each one has its own contribution. That's why; the strategy of fusing all sub-bands has been adopted, so as to take advantage of complementarities between different orientations.

Operating sub-band fusion: By adopting the alternative of fusion, several parameters had to be fixed. Among them, is the choice of the score fusion rule. Usual operators such as maximum score, scores product and scores sum were tried. Best results were achieved with Sum rule, with an augmentation reaching 4.4% compared to the best band used separately. Another question was about the number of features to keep on every sub-band. two options were tested:

Same feature number for all sub-bands : Referring to results of Test 3.b in table 3, this kind of fusion is better than applying Adaboost on the whole SP. Moreover, it is much less time consuming, making possible to increase the number of considered features.

Weighting feature number per sub-band : While conducting the test of Adaboost on the entirety of the SP, it has been noticed that the number of selected features was not the same for all sub-bands. Based on this observation, the idea of weighting the number of features for every sub-band (oriented at all scales, high-pass and low-pass) was suggested.

Once the total number of features is fixed, the weights were attributed based on feature distribution found in Test 3.a as follows: 2%; 12.75%; 13.5%; 10.25%; 18%; 15.25%; 18.5%; 9.75% respectively for High-pass, oriented band-pass 1 to 6, and lowpass sub-bands. As instance, assuming a total feature number of 800, Adaboost selects respectively: 16,102,108,82,144,122,148 and 78 features from the pre-cited sub-bands. Almost experiments were improved attaining 0.8% of enhancement (table 3, Test 3.c) when compared to taking the same feature number for all sub-bands.

Another possibility was to weight the scores of the different classifiers before the sum fusion:

Weighting scores of classifiers with same number of features : This is equivalent to a weighted sumrule at the score level while keeping the same number of features for all sub-bands. Assuming that E sb is the EER of Sub-band sb, then, the weights W sb associated to the scores of sub-band sb are calculated from Equation 2 [START_REF] Su | Hierarchical ensemble of global and local classifers for face recognition[END_REF].

An improvement reaching 0.7% was denoted (table 3, Test 3.d) when compared to taking the same feature number for all sub-bands.

ܹ ௦ = 1 ܷ ܧ ௦ , ܷ = 1 ܹ ௦ _௦ ௦ୀଵ , with ∑ ܹ ௦ = 1, 0 < ܹ ௦ < 1 _௦ ௦ୀଵ
(2)

and and nb_sb the total number of sub-bands.

Weighting scores of classifiers with weighted feature numbers : A final try, was to proceed by weighting at the characterization level (feature numbers) as well as at the score level (weighted sum rule). This strategy of fusion gave almost best results for the four experiments (table 3, Test 3.e).

To summarize, the method having the optimum configuration was then to filter the entire (64x64) image by a 6-orientation and 3-scale Steerable Pyramid. Then, apply Adaboost on each sub-band (oriented at all scales, high-pass and low-pass) with weighted numbers of features. Afterward, score fusion was operated on classifiers by weighted sum rule.

Table 3 illustrates also the evaluation of the proposed method put side by side with the other ones. It can be seen that combining SP to Adaboost improves considerably the performance of SP and Adaboost applied separately. On another hand, in a comparison to PCA1 (Chaari 2009) enhancements are obvious in all experiments.

Regarding PCA2, it has to be underlined that the training set on which the face space has been constructed isn't the same as indicated by the protocol. In fact, it is built using 300 images from BANCA database (30 subjects, 10 images per subject) (Petrovska, 2009) with 3 different quality images. While proposed method strictly followed the protocol using only 156 images of 52 individuals (3 images/person) acquired under quite good conditions, which is not the case of the test subsets where many variations are present. The small number of trained images besides the different acquisition conditions between training and test subsets constitutes an additional challenge, which explains the results obtained in experiment 4 that are better than ours. Despites, proposed method outperforms PCA2 in the first three experiments.

Compared to LDA, except for the first controlled scenario, proposed method achieves higher performance in the other more challenging ones. But it still remains less robust than LDA/Gabor which is a combining approach of a projection-based method (LDA) and a space-scale feature-extraction method (Gabor).

CONCLUSIONS

Through this work, a combining approach based on Steerable Pyramid and Adaboost has been introduced for 2D-face recognition. It has been proved that joining a non-linear classifier to the SP brought significant enhancements, especially when weighting both sub-bands feature numbers and classifiers scores. Future works are intended to consider Adaboost only as a feature selector, rather than a classifier, on SP outputs, and study the effectiveness of conventional projective classifiers such as PCA and LDA on the Ada-SP-features.

Figure 1 :

 1 Figure 1: First level of the diagram system of a steerable pyramid.

Figure 2 :

 2 Figure 2: Face image decomposition using a 3-level steerable pyramid with 4 orientations.

Figure 2

 2 Figure 2 illustrates a three level steerable pyramid decomposition of a face image, with 4 orientations (n=3). Shown are the four orientated bandpasss images at three scales and the final lowpass image. The initial highpass image is not shown.

  Figure.3. Examples of variability related to (1.a-c) expression, (2.a-c) illumination and (3.a-b) quality.

Table 1 :

 1 Description for the images used for the 2D-Face experiments (V. = variation and N. = number)

	Experiment	Exp1	Exp2	Exp3	Exp4
	Sessions	Mono	Mono	Mono	Multi
	Quality	High	High	Low	High
	Expression V.	Small	No	No	No
	Illumination V.	No	Yes	No	No
	N. Intraclass	2595	2503	1774	1796
	N. Interclass	2454	2364	1713	1796

Table 3 :

 3 Comparative results between proposed algorithms (blue and green) and IV² first evaluation campaign ones (black). 3.a: Adaboost on total SP. 3.a to 3.e: Adaboost on SP bands. Description: feature number; rate = weighting number of features per band; s = sum rule; ws = weighted sum rule.

	Numéro test	Description	Participants	Exp1	Exp2	Exp3	Exp4
			PCA1	6.7 (±0.8)	20.7 (±1.3)	20.1 (±1.6)	22.2 (±1.6)
			PCA2	7.3 (±0.8)	21.6 (±1.4)	13.6 (±1.4)	16.3 (±1.4)
	Previous Tests IV²	mod PCA	5.3 (±0.7)	20.7 (±1.4)	19.5 (±1.6)	20.5 (±1.5)
			LDA	3.7 (±0.6)	22.5 (±1.4)	21.7 (±1.7)	19.7 (±1.5)
			LDA/Gabor 4.2 (±0.6)	12.0 (±1.1)	8.3 (±1.1)	11.3 (±1.2)
	1		Adaboost	3.7(±0.6)	22.7(±1.4)	44.3(±2.0)	28.6(±1.8)
	2		SP	11.0 (±1.0)	23.0 (±1.4)	20.1 (±1.6)	23.9 (±1.7)
	3.a	400(total_SP)	Ada/SP	5.0(±0.7)	19.5(±1.3)	14.1(±1.4)	22.9(±1.6)
	3.b	400(8*50)s 800(8*100)s	Ada/SP Ada/SP	4.4(±0.7) 4.6(±0.7)	18.8(±1.3) 18.6(±1.3)	13.7(±1.4) 13.7(±1.4)	22.4(±1.6) 21.3(±1.6)
	3.c	400(rate)s 800(rate)s	Ada/SP Ada/SP	4.5(±0.7) 4.7(±0.7)	18.6(±1.3) 18.2(±1.3)	13.0(±1.3) 12.9(±1.3)	21.8(±1.6) 20.9(±1.6)
	3.d	400(8*50) ws 800(8*100)ws	Ada/SP Ada/SP	3.7(±0.6) 3.9(±0.6)	18.7(±1.3) 18.5(±1.3)	13.5(±1.3) 12.9(±1.3)	22.4(±1.6) 21 .0(±1.6)
	3 .e	400(rate) ws 800(rate) ws	Ada/SP Ada/SP	4.1(±0.6) 4.1(±0.7)	18.6(±1.3) 18.1(±1.3)	13.0(±1.3) 12.9(±1.3)	21.7(±1.6) 20.4(±1.6)


Chang-Shing Lee

Olivier Teytaud

Mei-Hui Wang

Shi-Jim Yen

Computational Intelligence Meets Game of Go @ IEEE WCCI 2012

Since 2008, National University of Tainan (NUTN) in Taiwan and other academic organizations have hosted or organized several human vs. computer Go-related events [START_REF] Lee | The computational intelligence of MoGo revealed in Taiwan's computer Go tournaments[END_REF][START_REF] Rimmel | Current frontiers in computer Go[END_REF][START_REF] Lee | The game of Go @ IEEE WCCI 2010[END_REF][START_REF] Yen | The IEEE SSCI 2011 Human vs. Computer Go Competition[END_REF][START_REF] Yen | Human vs. Computer Go Competition in FUZZ-IEEE 2011[END_REF] in Taiwan and in IEEE CIS flag conferences, including FUZZ-IEEE 2009, IEEE WCCI 2010, IEEE SSCI 2011, and FUZZ-IEEE 2011. Chun-Hsun Chou (9P), Ping-Chiang Chou (5P), Joanne Missingham (6P), Shang-Rong Tsai (6D), Sheng-Shu Chang (6D), and Shi-Jim Yen (6D) were invited to attend the Human vs. Computer Go Competition @ IEEE WCCI 2012 (http://oase.nutn.edu.tw/wcci2012/ and http://top.twman.org/wcci2012) held in Brisbane, Australia, in June 2012. Seven computer Go programs, including MoGo/MoGoTW (France, Netherlands, and Taiwan), Many Faces of Go (USA), Zen (Japan), Erica (Taiwan), Fuego (Canada), Pachi (Czech Republic and France), and Coldmilk (Taiwan), challenged the humans in the competition. In addition to observing how many advances have been made in artificial intelligence, the competition also observed physiological measurements for testing cognitive science on the game of Go. The topic is "the Most Strategic Game" because Go is the deepest known game for the classical "depth" criterion. The planned games in the competition include: (1) 7x7 small board games to see if computers can also outperform humans when the games conditions are slightly in favor of humans, (2) 9x9, 13x13, and 19x19 board games to see how far computers are from humans now, and (3) novel activities for physiological measurements to see if physiological signals are also impacted by various conditions. It is now known that Go is specific in the sense that brain areas involved in playing Go are not exactly the same as those involved in chess, in particular, more spatial reasoning, mental verbalization, and motor control. The design of games was to investigate the current level of strong programs on various board sizes, but also to monitor the human brain and to check the player strength assessment capabilities of Go programs. Australian Broadcasting Corporation (ABC, http://www.youtube.com/watch?v=KhGvzaMFNAI) also reported this event by the topic of "AI expo underway in Brisbane" on June 15, 2012. The games' results held in the IEEE WCCI 2012 are briefly listed as follows:  7x7: We assume that the fair komi in 7x7 Go is 9, which is the usual belief on 7x7. In June 2011, MoGoTW won 20 games against 10 professional Go players with komi in favor of the computer, and each human played as Black and as White [START_REF] Chou | Towards a solution of 7×7 go with meta-MCTS[END_REF]. Komi was 9.5 when the computer was White, and 8.5 when the computer was Black. This was done in order to check the ability of the computer to reach optimal play in 7x7. In spite of a mistake in one game (followed by a mistake by the human), the computer had a perfect record of 20 wins out of 20 games [START_REF] Chou | Towards a solution of 7×7 go with meta-MCTS[END_REF]. For the competition held in IEEE WCCI 2012, we played both easy setting (Komi in favor of the computer, i.e. 9.5 when computer is White and 8.5 when computer is Black) and difficult setting (Komi in favor of the computer, i.e. 8.5 when computer is White and 9.5 when computer is Black). The game results show that MoGoTW won all games which were "easy" for it; and won 50% of "hard" games against three 6D players.

MoGoTW also won 1 out of 6 games in the hard setting against professional players. However, Joanne Missingham (6P) said that the reason she lost the game is that she is not familiar with 7x7 game, and this lost game is her first 7x7 game. MoGoTW has outperformed humans in 7x7 Go, making no mistake whereas humans, including one 6P player, did mistakes.  9x9: 9x9 is the favorite format of computers, which now win games routinely against professional players. Komi is often 7.5 in the past competitions. But komi is 7 this time so the game result may be a draw; computers must be able to deal with the draw situation. From the six 9x9 games' results, we know that (1) surprisingly, only amateurs lost games, (2) in fact, humans could perform so well in spite of playing blindfolded for two of these games, and (3) even strong bots like Pachi or Many Faces of Go can lose even games to professional players. Hence, humans are still strong in front of computers in 9x9 Go with komi 7.  13x13: 13x13 is a nice platform for Go, as it is a less immediate fight than 9x9 Go and it is less time-consuming than the standard 19x19 Go. The eleven 13x13 games' results show that humans won all games, including the four kill-all Go games. In June 2011 [START_REF] Yen | Human vs. Computer Go Competition in FUZZ-IEEE 2011[END_REF], computers won four 13x13 games out of 8 against professional players with H2 and 3.5 komi (i.e. handicap roughly 1.5), the best performance so far. For 13x13 kill-all Go, in Tainan in 2011, MoGoTW could win as White with H8 against Ping-Chiang Chou (5P), which is seemingly the best performance so far.  19x19: Humans are still stronger than computers, in particular for the big 19x19 board where strategic elements matter a lot.

19x19 Go is the main version of the game of Go. The thirteen 19x19 games' results show that the performance so far is a win with H4 when Zen was against a 9P player. The player (Chun-Hsun Chou) said that he miscounted the compensation and so he believed that the game was an easy win. When he understood his mistake, it was too late for trying to win. On the other hand, Joanne Missingham (6P) was in a very difficult situation in her H4 game against Zen; she played a move for cheating Zen (a very suboptimal move, aimed at making the situation difficult) and Zen erroneously resigned, whereas the situation was admittedly a win for Zen. There are still 4 handicap stones, giving to the program an advantage in each corner, so professional Go players mentioned that switching to handicap 3 is a huge challenge. In particular, computers still have weaknesses for combining multiple local fights. Remarkably, Many Faces of Go won as Black with komi 3.5, i.e. roughly a handicap 0.5, against a 6D player (Sheng-Shu Chang).  Level assessment in Go: Parts above were dedicated to the assessment of programs strength, and to physiological measurement. We here consider a different goal, for Go programs: to evaluate the level of the human opponents. Simple tools for level assessment in Go consist in playing several games, increasing the strength of the computer when the computer loses, and decreasing it when the computer wins. Then, the level of the human is estimated using a classical Bayes analysis using the ELO model [START_REF] Elo | The Rating of Chess Players, Past and Present[END_REF]. We performed such tests on players from kyu level to 6D, using MoGoTW playing on many computers in Taiwan in May 2012. We have then seen that in 5 games, we can estimate the strength of players somehow efficiently. This has direct applications for eLearning because evaluating Go players (by playing games) is similar to evaluating students (by proposing exercises). This time, in June 2012, each player also played only 5 games and we tried to compare three 6D players, a difficult task because they have a very similar strength. The games' results show that MoGoTW could nonetheless find out that Shang-Rong Tsai (6D) is a particularly strong 6D player. This shows that our artificial player is also able to analyze the strength of strong players. Importantly, along with this ability to evaluate the strength of humans, the computer can adaptively adjust its strength to the opponent, in order to increase entertainment, which is helpful for motivating children to learn.

 Measurement in physiological signals

Signal measurement is a good way to understand more about the difference in physiological signals between (1) normal people and Go players, (2) playing under hard and easy situation, (3) playing on small-size and big-size boards, and ( 4

  ) playing usual Go and unnatural Go (kill-all Go) or blindfolded Go. In the competition, the measured physiological signals contained brain wave (electroencephalogram, EEG), skin temperature, skin conductance, heart rate, blood volume pulse, and respiratory wave during playing the game. With the collected physiological signals, it will be feasible to analyze game-level statistics to understand the variance of strategies employed by the human and computer in each game. After a series of Human vs. Computer Go Competitions from 2008 to 2012, this event proves that artificial intelligence has improved a lot in computer Go, in particular Zen's great progress. Additionally, Prof. Nikhil R. Pal (General Chair of FUZZ-IEEE 2013) and Dr. Gary Fogel (IEEE CIS VP for Conference) also expressed their interest to continue having this kind of competition in the FUZZ-IEEE 2013 and IEEE WCCI 2014, respectively, in the future. Overall, the event in IEEE WCCI 2012 was a great success and we would like to express our heartfelt thanks to everyone who offered any help, joined, and watched the games. We would also like to sincerely thank the IEEE CIS and the organizing committee of the IEEE WCCI 2012, especially Prof. Hussein Abbass, who rendered kind support and great help. The authors would like to thank the National Science Council (NSC) of Taiwan (99-2923-E-024-003-MY3 and 101-2919-I-024-001-A1), Brisbane Marketing, and HeroIT.com for their financial support. Additionally, this work was supported by the French National Research Agency through COSINUS program (EXPLO-RA ANR-08-COSI-004) and MoGo/MoGoTW are very grateful to Grid5000 for support in parallelization and access to clusters and grids. Participatnts attending the opening ceremony, including Gary Fogel, Hisao Ishibuchi, Hussein Abbass, and Marios Polycarpou (foreground, left 1, left 5, left 7, and right 5, respectively). Hussein Abbass (background, right 2) and Chang-Shing Lee (background, left 2) with Shi-Jim Yen (foreground, left 1) measuring the physiological signals.


D Desmaële
email: denis.desmaele@etu.upmc.fr

M Boukallel
email: mehdi.boukallel@cea.fr

S Régnier

A resonant structure designed for probing the elastic properties of suspension and adherent cells in liquid environments ‡

Keywords: numbers: 87.85.fk, 87.17.Rt, 46.70.De, 62.40.+i

This paper presents a novel force sensitive structure exploiting a dynamic mode for probing the elastic properties of living cells. A key feature of this structure is the possibility to conduct measurements in liquid environments while keeping high dynamic performances. The structure indeed provides a steady area that can be adapted so that suspension or adherent cells can be placed in culture medium. The steady area is also connected to two adjacent beam resonators. Because these resonators never need to be immersed into the culture medium during measurements, forces applied to cells can be estimated with a high sensitivity via frequency shifts. In this paper, we conduct an extensive theoretical analysis to investigate the nonlinear effects of large static predeflections on the dynamic behavior of the structure. As a proof of concept, we also report the fabrication, characterization and calibration of a first prototype intended to deal with suspension cells with a diameter ranging from 100 to 500 µm. This prototype currently offers a quality factor of 700 and a force sensitivity of ∼2.6 Hz/mN. We also demonstrate that the prototype is capable of measuring the elastic modulus of biological samples in a rapid and sufficiently accurate manner without the need of a descriptive model.

Introduction

Measuring the elastic properties of individual living cells turns out to be of increasing interest. In particular, scientific evidences have revealed connections between alterations in the elastic modulus (i.e., Young's modulus) of single cells and pathophysiological states [1]. For instance, a dramatically reduced Young's modulus is a characteristic feature of cancerous cells [2,3,4,5,6,7]. By contrast, red blood cells infected by malaria or sickle cell disease have a significantly higher Young's modulus than their healthy counterparts [8,9].

The elastic modulus of cells hence appears as a meaningful marker to differentiate pathogenic cells and healthy cells. For diagnostic purposes, knowing the Young's modulus of cells may hence help to detect the presence of cancer as well as other cellbased degenerative diseases at earlier stages. Furthermore, elasticity measurements also have the potential to disclose the specific effects of pharmaceuticals at the cellular level [10,11,12]. Therefore, cell elasticity measurements may also prove advantageous in drug development.

Among the large variety of macro and microscale devices that have been developed to investigate various mechanical aspects of living cells (see [13,14,15,16,17] and references therein), the atomic force microscope (AFM) probably remains the most widespread tool for quantifying the Young's modulus of different types of cells. By way of example, results published in [2,3,4,5,6,7,8,9] were all derived from measures obtained with AFM cantilevers.

Notwithstanding indisputable advantages, using an AFM in order to evaluate the Young's modulus of a living cell remains a delicate, time-consuming task. Basically, the extremity of the AFM cantilever must be cautiously and precisely positioned so that it can be used to indent or compress the cell. Then, a force-deformation curve must be acquired. Conventionally, a laser that reflects off the back surface of the cantilever onto a position sensitive photodiode is used to detect the contact point with the cell and to monitor the static deflection of the cantilever. However, if the cells are maintained in a culture medium during measurements, the alignment of the laser beam may become delicate. Moreover, in the presence of aqueous solutions, capillary meniscuses arise at the air-liquid interface when the AFM cantilever is immersed and removed. The compliant cantilever must then withstand large capillary forces that may engender measurement artifacts. Alternatively, an optical microscope and a video camera can be utilized [18]. The resolution is however limited by the optical components of the microscope and measurement uncertainties can occur. Furthermore, such vision-based techniques solely prove to be suitable for suspension cells with a spherical shape (e.g., red blood cells). This paper introduces a novel force sensitive structure that has been designed with the aim to bring new solutions to these problems. In particular, the structure exploits a dynamic mode to quantify the Young's modulus of both suspension and adherent cells so that valuable information on the cell state can be obtained in a simple and sufficiently rapid manner for diagnosis applications.

Overall description of the structure

Concept

Structures exploiting resonance phenomena can outperform equivalent structures operated in a static mode [19]. Despite this potential advantage, resonant cantilevers are rarely used for determining the Young's modulus of living cells. Indeed, a major issue is that dynamic performances of AFM cantilevers are dramatically deteriorated as soon as they are surrounded by a viscous medium. Thereby, the quality factor of typical resonant AFM cantilevers immersed in liquids rarely exceeds 10-30 [20,21]. To extract the Young's modulus of a single living cell while taking full benefit of a dynamic mode, even in the presence of a liquid environment, we propose the suspended structure shown in Fig. 1(a). It consists of a planar structure clamped at its extremities. It also incorporates two rectangular apertures. Finite Element Analysis (FEA) conducted with COMSOL V.4 shows that if the structure is mechanically excited at the proper frequency, it can provide an antisymmetrical vibration mode where the two outer beams oscillate in antiphase. In the mean time, the third central beam remains immovable, as depicted in Fig. 1(b).

Sensing principle

Measuring the force applied to a cell is a prerequisite to extract its Young's modulus. Conceptually, if a static force normal to the structure's plane is applied to the half span of the central beam, the whole structure deflects. Therefore, the outer beams are forced to deflect as well. When the outer beams oscillate as illustrated in Fig. 1(b), interactions between static and dynamic behaviors occur. Thereby, the static deflection imposed by the normal force affects their initial resonance frequency. In fact, even slight static pre-deflection of beam resonators may significantly impact their dynamics [22]. Accordingly, it is possible to recover the magnitude of the normal force applied upon the central beam by monitoring frequency shifts of the outer beams, as it is demonstrated in Section 3.

Key features

The balanced mode of vibration shown in Fig. 1(b) is of particular interest for determining the Young's modulus of individual cells. Indeed, it enables high sensitivity rates offered by resonators without exposing cells to vibrations. Thereby, the area located at the half span of the central beam can be adapted to place suspension or adherent cells in liquids (see Fig. 2). A main advantage offered by such a configuration is that, unlike conventional AFM cantilevers, the oscillating outer beams do not need to be immersed in the liquid in order to measure a force applied to a cell. Therefore, major energy losses are avoided and high quality factor can be guaranteed. Because the outer beams always oscillate in air, potential difficulties related to laser alignments in liquids are eliminated and measurements based on vision techniques are not required. It is also worth noticing that since the central beam is inherently force sensitive, low-cost and commercially available microindenters can be used to apply forces on cells during experiments. Moreover, artifact measurements due to capillary effects are minimized since the microindenter is not directly used as a force sensor.

Theoretical analysis

In this section, we demonstrate that the resonant structure can act as a force sensitive cell substrate. To predict frequency shifts engendered by a normal force F applied to the central beam, static and dynamic behaviors are studied independently. We here mention that the experimental implementation of an open microchannel such as the one sketched in Fig. 2 is currently under investigation and is not addressed in this paper. Consequently, the presence of an open microchannel is not considered in the following analysis.

Static behavior: large deflection of the structure

A static analysis including nonlinear effects is first conducted in order to detail how the outer beams exactly behave during large deflections of the whole structure. Due to symmetry, and without loss of generality, our analysis can be limited to one fourth of the structure, as sketched in Fig. 3. This quarter structure, similar in shape to a tuning fork, is composed of three segments: the overhang (black), the central tine (dark gray), and the outer tine (light gray). All segments are assumed to satisfy Bernoulli's beam theory. One-dimensional coordinate functions are used to approximate the displacement field of each segment. To guarantee enough degrees of freedom, the flexural displacement w 1,2,3 (x) of each segment is modeled by third order polynomial expressions

     w 1 (x) = a 0 + a 1 x + a 2 x 2 + a 3 x 3 w 2 (x) = a 4 + a 5 x + a 6 x 2 + a 7 x 3 w 3 (x) = a 8 + a 9 x + a 10 x 2 + a 11 x 3 . (1)
The three polynomials in (1) are then used to calculate the total potential energy stored by the tuning fork during deflection

U tf = U b + U s (2)
where U b is the sum of strain energies developed by each segment during bending

U b = 3 i=1 1 2 EI i d i c i d 2 w i dx 2 2 dx. (3)
In ( 3) In addition, U s is the sum of energy contributions due to the midplane stretching of the segments that occurs during deflection

c 1 = 0, d 1 = l/2, c 2,3 = l/2,
U s = 3 j=1 EA j 4l d j c j dw j dx 2 dx 2 (4)
where 4) represents the cross section areas of the three segments with A 1 = 3bh and A 2,3 = bh. The total potential energy function can hence be written as

c 1 = 0, d 1 = l/2, c 2,3 = l/2 and d 2,3 = l. A j in (
Φ = U tf -W (5)
where W = F w 2 (l) is the work done by the punctual force F .

Applying the principle of minimum potential energy, one sets for each unknown coefficient

a i ∂ Φ ∂ a i = 0. ( 6
)
The problem is then augmented with Lagrange multipliers by considering a set of constraints. To obtain satisfactory results, mechanical constraints do not need to be considered. Enforcing geometrical constraints is enough to provide an accurate solution.

Assuming that the central tine and the outer tine are rigidly linked to the overhang at x = l/2, and that the central and outer tines are terminated by sliding conditions (see Fig. 3), the following set of conditions can be enforced

w 1 (0) = d w 1 dx (0) = 0 (7) w 1 (l/2) = w 2 (l/2) = w 3 (l/2) ( 8
)
dw 1 dx (l/2) = dw 2 dx (l/2) = dw 3 dx (l/2) ( 9
)
dw 2 dx (l) = dw 3 dx (l) = 0. ( 10
)
The augmented system can then be numerically solved for different values of F . To compute such a system, an algorithm such as the one reported in [26] was used with the following numerical values: l = 12.5 mm, b = 0.25 mm, h = 0.1 mm, E = 212 GPa.

To validate this modeling approach, FEA was used as a reference tool. COMSOL simulations were conducted in the nonlinear deflection mode with the values of l, b, h and E aforementioned. We also specified a density of 8030 kg m -3 and a Poisson's ratio of 0.29 for the structure's material. These values were selected in accordance with the material utilized for the prototype of Section 4. For a point force F = 260 mN applied at the half span of the central beam, Fig. 4 shows the deflection profile of the structure. Analytical results are in good agreement with FEA simulations and permit to predict the deflection of the structure accurately. It can also be seen that the deflection amplitude of the outer beam is smaller than the deflection of the central beam. This intuitive result is also confirmed by Fig. 5 which compares the deflection amplitude of both beams as a function of the force F applied. Analytical and FEA results are again in accordance. Figure 5 also clearly illustrates that the stretching (i.e., nonlinear) effect progressively dominates as the beams deflection increases. Thereby, for deflections above ∼50% of the structure's thickness, the structure becomes clearly stiffer.

Dynamic analysis: effects of a static predeflection on the oscillation of the outer beams

We now demonstrate that, if the force F is applied while the outer beams oscillate as shown in Fig. 1(b), the variations of deflection imposed by F actually impact the initial resonance frequency of the outer beams. To demonstrate such a coupling between static and dynamic behaviors, a symmetric structure again simplifies the analysis. Indeed, valuable insights into the structure's dynamics can be grasped by restricting the analysis to a single outer beam (see Fig. 6). To a first approximation, one can choose to model the outer beam as a hingedhinged beam terminated by two rotational springs of stiffness k r1 (see Fig. 6). The presence of rotational springs is justified by the facts that extremities of the outer beam are attached to the overhangs. Intuitively, it can be foreseen that, although the overhangs can be considered as axially immovable ends, they should not act as ideal clamping supports. In the literature, elastic rotational springs are often used to model such a flexibility [27,28,29].

Again, energy approaches can be exploited to conveniently handle the configuration of Fig. 6. Because the outer beam is terminated by rotational springs attached to pinned ends supports, it is conventional to assume a displacement function in the form of a sine

w(x) = D s sin πx l (11)
where D s is the midspan deflection of the outer beam.

D s is related to the force F applied upon the central steady beam, and can be estimated from the previous static analysis (see Fig. 3)

D s = w 3 (l) -w 1 (l/2). ( 12
)
Conceptually, it is however more convenient to consider that D s is rather due to an unknown equivalent virtual force F v (see Fig. 6). With an energy approach, a relationship between D s and F v can be derived. Considering that F v is applied at the beam midspan, the potential energy stored by the beam is the sum of the following contributions

U T = U b + U s + U rs . (13)
In ( 13) U b is the bending energy of the beam

U b = EI 2 l 0 d 2 w dx 2 2 dx (14)
U s is the energy developed during the midplane stretching of the beam

U s = EA 8 l l 0 dw dx 2 dx 2 (15)
and U rs is the energy stored by the two rotational springs of stiffness k r1

U rs = k r 1 2 θ 2 0 + k r 1 2 θ 2 l ( 16
)
where θ 0 and θ l are the slopes dw dx evaluated at x = 0 and x = l, respectively.

Considering that the work done by

F v is W 1 = F v w(l/2), the total potential energy function Φ 1 is Φ 1 = -F v D s + π 2 k r 1 l 2 + Ebh 3 π 4 48l 3 D 2 s + Ebhπ 4 32l 3 D 4 s . (17)
Minimizing (17) with respect to D s yields a cubic force-centered-deflection law

F v = k 1 D s + k 3 D 3 s ( 18
)
where

k 1 = Ebh 3 π 4 24l 3 + 2k r 1 π 2 l 2 and k 3 = Ebhπ 4 8l 3 . (19)
In (19), k 1 and k 3 are linear and nonlinear spring constants, respectively.

As in [30], it can now be assumed that small deflections of the beam about a mean deflection D s can be described approximately by a single stiffness value. An effective spring constant is found by deflecting the beam from its equilibrium position by an arbitrary amount ∆ d (see Fig. 6), so that

F v = k 1 (D s + ∆ d ) + k 3 (D s + ∆ d ) 3 . ( 20
)
Considering that vibration amplitudes ∆ d are sufficiently small, terms proportional to ∆ 2 d and ∆ 3 d in ( 20) can be neglected. Then, an equivalent stiffness of the outer beam may be approximated by

k eq = dF v d∆ d ≈ k 1 + 3 k 3 D 2 s . (21)
As often in structures involving coupled beams, vibrating beams can be modeled to a first approximation as one degree of freedom oscillators (e.g., [31,32]). If the single outer beam is assumed to oscillate as an undamped lumped-parameter system, the static deflection D s affects its natural frequency as follows

f f 0 ≈ 1 + 3 k 3 k 1 D 2 s 1/2 . ( 22
)
As previously, the numerical values E = 212 GPa, b = 0.25 mm, l = 12.5 and h = 0.1 mm were used to compute (22). An order of magnitude for the rotational stiffness k r1 was also found by using [33]

k r1 = 4 E b h 3 3 l . ( 23
)
Equation ( 23) gives k r1 ≈ 5.6×10 -3 Nm/rd. Nonetheless, ( 23) is originally intended to estimate the rotational spring constant of anchors for clamped-clamped beams. In our case, the outer beams are attached to the overhangs (see Fig. 3) which do no act as ideal clamps. Therefore, the value of k r1 was slightly adapted to fit prestressed modal analyses conducted with COMSOL. For k r1 = 3.45 × 10 -3 Nm/rd, Fig. 7 proves that (22) accurately predicts the amount of frequency change engendered by a force F applied to the central beam.

Alternatively, and because displacements of the central beam can also be predicted with respect to the force F applied, the amount of frequency change can also be estimated as a function of a displacement imposed to the central beam (see Fig. 8). It is of interest to note that in both cases, quasi linear regions are predicted around points P . In particular, a force sensitivity of 2.91 Hz/mN is predicted if the force applied to the central beam exceeds 100 mN (see Fig. 7).

Experiments

To demonstrate the possibility to extract the Young's modulus of living cells with the structure, we fabricated a first prototype intended to deal with suspension cells whose diameter approximately ranges from 100 to 500 µm. This monolithic prototype was fabricated from a single sheet of biocompatible stainless steel. All dimensions are those used for the theoretical analysis. Considering the total length of the prototype (25 mm), precision wire cut electric discharge (EDM) machining was favored for rapid prototyping. Wire cut EDM, however, did not permit to implement an open microchannel.

Mechanical excitation was provided by a 3 mm long, 2 mm wide and 200 µm thick piezoelectric (PZT) element (Physik Instrumente PIC151). This PZT element was bonded onto the prototype with conductive paste and driven by an AC signal with a function generator (Agilent 33120A) connected to a laboratory power amplifier (New-tons4th LPA400).

During experiments, the prototype was suspended between two clamps. One of the clamps was fixed to a manual micropositioning stage that allowed horizontal translations along the y direction. To ensure a firm attachment of the prototype and to avoid slipping, the clamps were tightened with screws. The whole setup (see Fig. 9) was mounted on a pneumatic antivibration isolation table to minimize the presence of external disturbances. To measure small static deflection as well as beam oscillations, we do not use a laser coupled to a sensitive photodiode. Instead, we used a home made optical fiber displacement probe. This probe was constituted of two step index multimode fibers having a diameter of 50 µm at their extremity. Such dimensions offered a compact sensing head that could also be implemented in a future microfabricated version of the structure. Further details about this fiber displacement probe can be found in [START_REF] Desmaële | Proc. Int. Conf. on Intelligent Robots and Systems[END_REF].

Evaluation of static deflections

Experiments were first carried out to investigate the static deflection of the prototype. To bend the structure, an indenter terminated by a metal bead with a diameter of 500 µm was placed beneath the central beam. The stiffness of the metal bead was much higher than the stiffness of the structure. With a micropositioning stage (Physik Instrumente M112-1DG), incremental motions of 10 µm along the z direction were imposed to the central beam. Considering the prototype symmetry, deflection data were acquired only for one outer beam. Fig. 10 demonstrates that the prototype deflected as expected during experiments, even though the deflection of the outer beams tends to be 12% overestimated by theory when the deflection of the central beam is above 30 µm. Several uncertainties sources could explain this slight estimation error (e.g., values of Young's modulus and Poisson's ratio used for calculations; uncertainties related to the fabrication process, the clamping of the prototype, etc.).

Evaluation of dynamic performances

The dynamic behavior of the prototype was then explored. In a first step, the indenter was removed and no force was applied to the central beam. To actuate the prototype, the PZT element was driven with a sinusoidal voltage. The peak-peak amplitude of this sine signal after the power amplifier was 9V. The excitation frequency was then swept with the function generator in order to find the resonance modes of the prototype. As illustrated by Fig. 11(a), the antisymmetrical mode of interest was found at 3180 Hz. When the PZT element was driven with a voltage supply of 9 V, the peak-peak oscillation amplitude of the outer beams was 22 µm. During oscillations of the outer beams, a lot of attention was paid to check if potential vibrations were transferred to the central beam. As a matter of fact, they were very limited. As shown in Fig. 11(b), they never exceeded 500 nm, that is to say 2% of the oscillation amplitude of the outer beams. Droplets of water were also deposited upon the central beam with a micropipette. No particular effect on the droplets was observed. It was also confirmed that the presence of small amounts of liquids on the central beam did not alter the vibration mode.

In addition, we explored the frequency response of the antisymmetrical vibration mode. With the outer beams oscillating in air, a quality factor of 700 was obtained (see Fig. 12). This quality factor was not deteriorated when a liquid droplet was deposited on the central beam. This is a high value when compared to typical quality factors of AFM cantilevers in liquids (10-30).

Frequency variations induced by large displacements

The coupling between static and dynamic behaviors was then investigated. To that end, oscillations of the outer beams were monitored while the central beam was bent with the indenter. For a total displacement of the indenter of 250 µm, the oscillation frequency of the outer beams evolved as shown in Fig. 13. Contrary to theoretical predictions, it is experimentally observed that for small deflections of the central beam (i.e., deflections lower than 100 µm), the frequency of the outer beams actually decreases. Such a behavior has been reported for buckled and deflected beams subjected to axial loads [START_REF] Dickinson | [END_REF]36,37,38,39]. Nevertheless, this decrease finally appears as a transition period. Indeed, once the stretching effect dominates at large deflections, a behavior very similar to the one initially predicted is retrieved. In particular, it is worth noticing that the curve in Fig. 13 sensitivity of 5.75 Hz/µm around the point S. This displacement sensitivity is actually ∼17% better than the one expected initially by theory (4.8 Hz/µm).

Frequency variations induced by small forces

From the analysis of Fig. 13, it is clear that the prototype provides a much better sensitivity when the central beam is largely bent. The central beam was hence maintained permanently curved (i.e., even with the indenter removed) to exploit the region around the point S. Obviously, this axial translation compressed the whole structure. As a result, the initial resonance of the antisymmetrical vibration mode decreased from 3180 Hz to 3080 Hz. Nevertheless, no significant impact on the dynamic behavior of the prototype was noticed.

To estimate the force F applied to the central beam during small displacement intervals, the force developed by our indenter was characterized. By pressing the indenter against a precision electric scale (Kern 440-33), a linear relationship was found (see Fig. 14(a)). Then, frequency variations with respect to the force generated by the indenter were measured. With the prototype predeflected, only a linear increase of the frequency was observed, as expected (see Fig. 14(b)). This linear increase corresponded to a force sensitivity of 2.56 Hz/mN. Although a predeflection of the whole structure was not included in our theoretical analysis, the force sensitivity measured experimentally was only ∼12% lower than expected.

Direct extraction of the elastic modulus of a suspension cell

With the suspended structure, the force applied to a cell can be measured. In addition, the cell deformation must also be determined. Conventionally, force-deformation information are then used in conjunction with Hertz theory to retrieve the Young's modulus of the cell. Hertz theory, however, is subjected to a number of important assumptions. In particular, when dealing with a living cell, the condition of negligible force adhesion is not always fulfilled. Furthermore, for suspension cells, Hertz theory requires to know the radius of curvature of the cell to be probed. As an alternative, we preferred to calibrate our structure so that a sufficient estimation of the Young's modulus of the cell could be rapidly obtained without the use of a descriptive model. For calibration, two gel samples T7 and T5 were bought from the company Gelmec. They had a Young's modulus of 37.5 kPa and 119 kPa, respectively. The gel samples were manually prepared so that their size was as similar as possible to the size of the cells targeted. Thereby, efforts were made to obtain small cubic pieces whose edges measured approximately 500 µm. The gel samples were then cautiously placed on a flat indenter and compressed upon the central beam of the structure. To probe only the elastic properties of the gels, the amount of compression applied did not exceed 10% of their thickness [40]. Moreover, the velocity of the translation steps was kept very slow (4 µm/s) to minimize the occurrence of viscoelastic effects [18,41]. The same protocol was repeated with a biological entity. Because embryos or oocytes could not be obtained easily, we used a lobster egg with a diameter of 500 µm as a viable alternative (see Fig. 15). Linear frequency variations induced during the compression of the gel samples and the lobster egg are compared in Fig. 16(a).

To determine more precisely the elastic modulus of the lobster egg, slopes S T 5 and S T 7 indicated in Fig. 16(a) were used as single values plotted against the Young's modulus of the gels (see Fig. 16(b)). Since only the elastic properties of the materials were probed, a linear regression equation linking these two values could be determined [42] S egg = 0.02914 × E egg -0.2329 (24) where S egg is the slope of frequency variations measured for the lobster egg and E egg is its Young's modulus. For S egg = 2.03 Hz/mN, (24) yields a Young's modulus of 78 kPa for the lobster egg. Although no reference value has been found for lobster eggs in the literature by the authors, the Young's modulus obtained is in accordance with orders of magnitude usually reported for most living cells [43,44,45].

Conclusion

This paper has presented a new force sensitive structure exploiting a dynamic mode for probing the elastic modulus of living cells. A key feature of the triple beam configuration reported is the possibility to conduct measurements in liquids while keeping high dynamic performances. Another potential advantage is the possibility to adapt the structure's design for addressing both suspension and adherent cells. A first mesocale prototype has been characterized and calibrated with commercial gel samples. The Young's modulus of a lobster egg has also been experimentally measured without the need of a descriptive model. Such an indirect technique might prove to be useful for diagnosis applications since relative changes or observation of tendencies may be sufficient to bring valuable information on the cell state.

Although performance characteristics of the prototype are encouraging, several challenges still need to be addressed. In particular, it remains presently difficult to obtain repeatable results due to our current clamping system. Likewise, maintaining the structure in a slightly curved position turns out to be a delicate task. A microfabricated version of the structure aimed at solving these problems is presently under investigation. The implementation of an open fluidic channel coupled to a simple positioning and/or trapping system is also ongoing. In the near future, tests with a larger number of cells will also be conducted to validate the possibility to implement the suspended structure in a workable platform.

Figure 1 .

 1 Figure 1. (a) Three dimensional schematic of the structure illustrated with a suspension cell (trapping system not represented). (b) FEA showing the antisymmetrical vibration mode exploited to extract the elastic properties of a biological sample: the two outer beams oscillate in antiphase whereas the third central beam remains immovable.

Figure 2 .

 2 Figure 2. Top: Illustration of an open microfluidic channel for cell studies, as reported by Ryu et al. (adapted from [23, 24, 25]). Bottom: Conceptual view showing the structure equipped with a similar open microfluidic channel (fluid inlet and outlet not represented).

Figure 3 .

 3 Figure 3. Top: for predicting the quasi-static deflection of the structure engendered by a normal force F , only the darker "tuning fork" (top view) is considered. Bottom: equivalent one-dimensional model (side view) of the colored beams (proportions exaggerated for illustration purposes).

d 2 , 3 =

 23 l. I i are the moments of inertia of the three segments with I 1 = bh 3 /4 and I 2 = I 3 = bh 3 /12, E represents the Young's modulus of the structure's material, the width b and the length l are defined in Fig.3and h is the structure's thickness.

Figure 4 .

 4 Figure 4. Deflection profile and deflection amplitude when a normal force F = 260 mN is applied at the half span of the central beam.

Figure 5 .

 5 Figure 5. Half span deflections of the central beam and one outer beam as a function of the force F applied to the central beam. Due to symmetry, the second outer beam deflects exactly in the same manner.

Figure 6 .

 6 Figure 6. For predicting frequency shifts, only one outer beam is considered. Vibrations (dashed green lines) take place around an equilibrium position (thick green line). The curved shape is indirectly engendered by static deflections (proportions not to scale)

Figure 7 .

 7 Figure 7. Evolution of the resonance frequency of the outer beams when a vertical force F is applied upon the half span of the central beam.

Figure 8 .

 8 Figure 8. Evolution of the resonance frequency of the outer beams when a vertical displacement is imposed upon the half span of the central beam.

Figure 9 .

 9 Figure 9. Top view of the prototype and experimental arrangement. The inset provides a microscope view of the area indicated by dashed lines. CB and OB stand for central beam and outer beams, respectively. Scale bar equals 1.5 mm.

Figure 10 .

 10 Figure 10. Difference of static deflection ∆ d between the central and the outer beams. Solid line is plotted thanks to the curves from Fig. 5. Circles represent experimental data. Dashed line is a fitting curve.

Figure 11 .

 11 Figure 11. Oscilloscope screenshots showing: (a) The two outer beams oscillating in antiphase when the structure is driven at 3180 Hz; (b) Vibrations measured at the half span of the central beam with no force applied.

Figure 12 .

 12 Figure 12. Experimental frequency response for the prototype of Fig. 9 driven around 3180 Hz.

Figure 13 .

 13 Figure 13. Frequency variations measured for a normal displacement applied to the half span of the central beam. Circles and solid line correspond to experimental data. Dashed line represents variations predicted by Fig. 8 for the same initial frequency.

Figure 14 .

 14 Figure 14. (a) Experimental force-displacement relationship obtained for small displacements of the indenter. (b) Lin ear frequency shift measured for the structure maintained slightly curved. Circles correspond to experimental data. Solid lines are fitting curves.

Figure 15 .

 15 Figure 15. Side view of the slightly curved prototype for measuring the Young's modulus of a lobster egg. The optical fiber probe used for monitoring frequency shifts of the outer beams is visible in the upper right corner. Scale bar represents 500 µm.

Figure 16 .

 16 Figure 16. (a) Frequency variations measured during the compression of the commercial gel samples and the lobster egg; (b) Interpolation curve for extracting the Young's modulus of the lobster egg.