Characterization of cellular mechanical behavior at the microscale level by a hybrid force sensing device

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1 J O U R N A L O F T H E M E C H A N I C A L B E H A V I O R O F B I O M E D I C A L M A T E R I A L S 2 ( ) available at journal homepage: Tutorial Characterization of cellular mechanical behavior at the microscale level by a hybrid force sensing device Mehdi Boukallel a, Maxime Girot b, Stéphane Régnier b, a CEA LIST, Service de Robotique Interactive, BP 6, 18 Route du Panorama, Fontenay aux Roses, France b Institut des Systèmes Intelligents et de Robotique, Université Pierre et Marie Curie, CNRS FRE 2507, BP 61, 18 Route du Panorama, Fontenay aux Roses, France A R T I C L E I N F O A B S T R A C T Article history: Received 24 January 2008 Received in revised form 12 September 2008 Accepted 18 September 2008 Published online 9 October 2008 This paper deals with the development of an open design platform for characterization of mechanical cellular behavior. The resulting setup combines Scanning Probe Microscopy (SPM) techniques and advanced robotic approaches in order to carry out both prolonged observations and spatial measurements on biological samples. Visual and force feedback is controlled to achieve automatic data acquisition and to monitor process when high skills are required. The issue of the spring constant calibration is addressed using an accurate dynamic vibration approach. Experimentation on the mechanical cell characterization under in vitro conditions on human adherent Epithelial Hela cells demonstrates the viability and effectiveness of the proposed setup. Finally, the JKR (Johnson, Kendall and Roberts), the DMT (Derjaguin, Muller and Toporov) and Hertz contact theories are used to estimate the contact area between the cantilever and the biological sample. c 2008 Elsevier Ltd. All rights reserved. 1. Introduction It is now well known that biological cells sense the mechanical disturbance from their environment. The resulting response to mechanical input is determinant in governing the cell s behavior, not only in cell culture, but also within the whole organism. The mechanical cell response is a complex phenomenon which involves different cell components ranging from the molecular to micrometer size level (nucleus, cytosqueletton, lipidic membrane,...) inducing signals from the cell surface receptors to the nucleus. Understanding the mechanical behavior of the cell, first requires an accurate knowledge of both force and stress distribution within the cell membrane. This feature is crucial since determining the force/stress of various types of load can dictate the mechanical cell response. Moreover, it requires real-time observation of cell development (growth, motility, apoptose,...) in order to correlate the molecular bio-chemical interactions with the mechanical response of the cell. Today, there is no prediction time model which can predict the morphological change of the cell due to external mechanical stimuli. Therefore, ongoing observations combined with an effective morphological tracking approach are required. Finally, mechanical cell characterization experiments need to be conducted in an in vitro environment so that the cell can be kept several hours in a living state for prolonged experiments. Therefore, reliable and automated measurements are required to reduce human involvement during the measurement process. Corresponding author. addresses: mehdi.boukallel@cea.fr (M. Boukallel), maxime.girot@robot.jussieu.fr (M. Girot), stephane.regnier@robot.jussieu.fr (S. Régnier) /$ - see front matter c 2008 Elsevier Ltd. All rights reserved. doi: /j.jmbbm

2 298 J O U R N A L O F T H E M E C H A N I C A L B E H A V I O R O F B I O M E D I C A L M A T E R I A L S 2 ( ) According to literature, much effort has been devoted to identifying the mechanism by which the cell senses the external mechanical stimuli. In fact, a variety of approaches have been developed whether to mechanically stimulate cells, sense force distributions or to determine the mechanical properties of the cells such as micropipette aspiration, atomic force microscopy, magnetocytometry or optical tweezers principles (Lukkari and Kallio, 2005). Among these approaches, the most promising ones involve Scanning Probe Microscopy (SPM) techniques for the nanoscale level. These techniques have the potential to give an accurate quantitative information relative to local forces and contact mechanics (Girot et al., 2006). The Atomic Force Microscope (AFM) has become a commonly used tool in the field of bioscience (Radmacher, 1997; Mahaffy et al., 2000). A flexible cantilever with a low spring constant ( N/m) and an atomic sharp tip is usually brought in the vicinity of the biological sample. Deflection of the cantilever as a result of the interaction between the microindenter and the sample is monitored by a split photodiode and by using a laser beam reflected on the back of the cantilever. Some commercial solutions are available for performing experiments on Life Science (Veeco, Olympus, Andor,...) but only a few of them are effective studies. The most critical component of the commercial solution is the xyz scanning device based piezotube. Of course, the piezotube can achieve high spacial positioning features with Angstrom resolution (closed loop feedback) but cells are relatively large structures, several dozen of micrometers in diameter and several micrometers in height. Thus, the scanning range must be appropriate to this size scale. Typical AFM systems for cell imaging exhibit a lateral scan range about 100 µm and a vertical scan range of about 10 µm. At these extensions, the piezotube exhibits a high nonlinear behavior including, creep and hysteresis. Reproducible positioning is only possible with effective design based on expensive electronic circuits. We associate several problems with the use of a standard commercial cantilever with a sharp tip for life science requirements. In fact, the nanometer dimensions of the tip can cause significant local strain higher than those in the elastic domain. Furthermore, depending on the magnitude of the force applied to the soft samples, both the cantilever tip and the samples can be easily damaged, consequently the local strain applied in the indented area is modified. Of course, some authors have presented a hybrid AFM tip where spheres with a few micrometers radius are fitted to the tip, but this approach requires accurate placement of the micro-sphere as well as dexterous manipulation. A sharp tip is commonly used since their precise shape can be determined using an SEM (Scanning Electron Microscope) and the contact mechanics between the tip and the cell can be analytically predicted. The Hertzian model which describes the relationship between force and indentation is the commonly used approach for a contact mechanics based prediction model. Some authors have shown that in the case of soft contact mechanics, models derived from linear elasticity can lead to significant errors. Moreover, due to imperfections of the curvature of the tip radius, an unknown contact region results between the probe and the sample. Consequently, uncertainties are introduced for choosing the appropriate fitting analytical model. The specific objective of this paper is the presentation of the development of an open platform where in vitro cell mechanical characterization can be conducted. This system, called the Force Bio-Microscope, combines SPM techniques and advanced robotic approaches. A tipless chemically inert cantilever is used in this study. The spring constant calibration using an accurate determination of the cantilever thickness is addressed in this paper. We use a dynamical frequency response method for the spring constant cantilever calibration. The contact mechanics is modeled with appropriate models taking into account the adhesion forces. More precisely, the JKR (Johnson, Kendall and Roberts), DMT (Derjaguin, Muller and Toporov) and Hertz contact theories are used to estimate the contact area between the tipless cantilever and the cell. In order to demonstrate the effectiveness of the developed system in the Life Science field, in vitro experiments have been conducted on Epithelial Hela cells (EpH). 2. Experimental setup overview The Force Bio-Microscope FBM device is an hybrid AFM microscope associating both scanning microscopy approaches and biological environment constraints. The FBM consists mainly of three units: the mechanical sensing unit which carries out detection, positioning and sensing features, the imaging/grabbing unit for imaging and cell tracking features and the clean room in vitro unit which allows experiments to be conducted in a biological environment (Fig. 1). The FBM experimental setup provides suitable conditions for the study in a controlled environment so that the biological cells can be kept several hours in a living state by using a cage incubator. Therefore, the mechanical measurement process can be done on the biological sample for an extended time period. A master computer is used to drive the FBM in an automatic operating mode based on referenced force/vision control. Data acquisition processing between the master computer and the FBM is achieved by the use of two specialized PCI cards (Matrox and National Instrument). A user-definable graphical interface has been developed in order to make configuration of the experiments easier. To avoid undesirable mechanical vibrations during the cell characterization process, the FBM experimental setup is installed on an anti-vibration table. The overall configuration of the FBM and the different working components are shown in Fig Mechanical sensing unit The mechanical sensing unit is based on detecting the deflection of a cantilever by an optical technique. A four quadrant photodiode (CentroVision) with internal amplifiers associated with a 650 nm low power collimated laser diode (Vector Technology) is used in order to perform both axial and lateral measurement of nanonewtons forces. The total sensing area of the photodiode is 7 mm 2 with a spectral response from 400 to 1100 nm. The optical path of the Gaussian laser beam is optimized using a pair of mirrors

3 J O U R N A L O F T H E M E C H A N I C A L B E H A V I O R O F B I O M E D I C A L M A T E R I A L S 2 ( ) Fig. 1 Block diagram of the Force Bio-Microscope FBM system. Fig. 3 The mechanical sensing unit. Fig. 2 The FBM experimental setup overview. and an aspheric condenser glass lens. Hence, a sensitive and accurate detection device is produced for the aim of our study. The sensitivity of the optical detection device is 5 mv/µm. A low spring constant (0.2 N/m), uncoated, tipless, silicon cantilever (Nanosensors) is used as a probe for the mechanical cell characterization. The lever is 450 µm long, 90 µm large and 2 µm thick. The sample to be studied is accurately positioned below the cantilever by a 3 DOF s (x, y and z) micropositioning encoded stages (Physik Instrumente) with a submicrometer resolution (0.1 µm). The kinematic features of the micropositioning stages enables the achievement of accurate mechanical measurements in a workspace of mm 3 with a good repeatability. The configuration of the mechanical sensing unit including the optical detection device is presented in Fig. 3. A magnified picture of the cantilever with the focused laser beam on its reflective surface is shown in the same figure. For the preliminary study, we focused on force feedback control of cantilever flexural deflection. Thus, only the vertical motion of the micropositioning stage is servoed. By knowing the vertical position of the micromotors as well as the deflection of the cantilever using the optical detection device, an optimized Proportional and Derivative (PD) controller was designed to ensure optimal performance control. The (PD) terms are optimized using the Ziegler Nichols method Imaging/grabbing unit The imaging/grabbing unit consists of an inverted microscope (Olympus IMT-2) with Nikon 10 and 20 objectives. A phase contrast device is mounted on the microscope in order to operate precise contrast. The inverted microscope is fitted out with a CCD camera ( pixels resolution). Using a frame grabber and a specialized imaging library package (Matrox Imaging) associated with the CCD camera, automatic mechanical characterization based on image feature tracking is achieved. The pixel to real world calibration of the CCD camera is obtained by means of a calibrated glass micro-array as well as calibrated micro-spheres (cf. Fig. 4).

4 300 J O U R N A L O F T H E M E C H A N I C A L B E H A V I O R O F B I O M E D I C A L M A T E R I A L S 2 ( ) where v is the instantaneous deformation of the beam depending on time and position. The displacement can be written in two parts; one depending on the position along the x axis, the other on time: v(x, t) = f(x)g(t). In order to solve Eq. (1) i.e. to calculate the solution s constants, the boundary conditions for the cantilever are needed. The fixed end of the cantilever must have zero displacement (v(0) = 0) and zero rotation (θ(0) = 0). The free end of the cantilever cannot have a bending moment (M(L) = 0) or a shearing force (T(L) = 0). The system of boundary equations only accepts a solution only if the determinant is zero, which is equivalent to: 1 + cos µ cosh µ = 0. (2) Fig. 4 Calibration of the CCD camera based on geometrical calibration Clean room unit The biological samples need specific requirements to be kept alive outside the vivo conditions, and to carry out prolonged observations. Besides the biological nutrition medium, biological cells need a temperature condition of 37 C and 5% of CO 2 gas. The incubating system is formed with a controlled heating module which maintains the temperature at 37 C using a single thermocouple probe. The desired temperature of 37 C is reached in 2 h. The cage incubator ensures a temperature stability within the 0.1 C. A mixed stream composed of 5% CO 2 and humidified air is fed into a small incubating chamber containing the biological samples, avoiding in this way condensation on the cage walls that could damage the mechanical parts of the microscope and the micropositioning stages. Temperature control is achieved by means of a configurable PID controller communicating with a water bath via serial port to the master computer. The whole system including the FBM is placed in a positive pressure clean room to protect the biological environment. 3. Cantilever spring constant calibration The length and width of the cantilever are measured by an optical method using the same process as for the camera calibration. The values obtained for length and width (L = 450 µm and l = 90 µm) correctly correspond to those of the manufacturer. Knowing all the dimensions of the cantilever, the spring constant is then calculated using a static method Frequency response method for the determination of cantilever s thickness Let us consider a cantilever of uniform section S, density ρ, Young s modulus E, and inertial moment I. Each point of the cantilever should validate the classic wave equation for a beam in vibration, under the hypothesis of an undamped system: ρs 2 v t 2 + E I 4 v x 4 = 0 (1) With µ = (ω 2 ρs E I ) 1 4 L, Eq. (2) gives one condition on µ to be respected, which defines the eigen frequency of the system. The first four solutions of this transcendent equation, determined numerically, are listed below: µ 1 µ 2 µ 3 µ Given these solutions, if the length, and the experimental eigen frequency of the cantilever are known, the mean value of the thickness can easily be calculated by the following equation: h = 1 N L 2 12ρ ω N i i=1 µ 2 E (3) i with N the number of the measured eigen frequency. In our case, using the eigen frequency to determine the last dimension of the cantilever improves the accuracy, in comparison to the optical method, by a factor of 100. Moreover, this method can be achieved prior to each experiment. Actually, the useful life of the cantilevers is very short (they can only be used once because of biological environment constraints), and the calibration process is repeated at every cantilever exchange Static approach for the determination of the spring constant cantilever Knowing the dimensions of the cantilever and its material properties, the spring constant of a rectangular cantilever is given by k = 3E I/L 3, with the inertia momentum I = lh 3 /12. All the results for different modes (experimental results of mode 3 are unexploitable, because some mechanical parts of the microscope start resonating) are summarized in the following table: Modes number µ Theory f (khz) Measured h (µm) Estimated k (N/m) Estimated The difference on the value of k can be explained by the error on the measured eigen frequency, but also because the estimated thickness is a mean value. Actually, the variation

5 J O U R N A L O F T H E M E C H A N I C A L B E H A V I O R O F B I O M E D I C A L M A T E R I A L S 2 ( ) Fig. 5 Cantilever/sphere/cantilever contact. Fig. 6 Experimental determination of the cantilever spring constant. of the thickness all along the cantilever affects the eigen frequency of each mode differently. The variations from the mean value of k are weak and acceptable, the logarithmic error is about 3.7%, with a contribution of the thickness for this error of 1.9%. Compared with the spring constant announced by the manufacturer, the mean value is close for this batch, but the uncertainty is greatly reduced (3.7% instead of 90%) Validation of the experimental spring constant cantilever These experiments aim to validate the accuracy of the force measurements of the mechanical sensing unit, including the cantilever and the optical laser system. Two measurements are carried out. For the first, a cantilever that has been previously calibrated is pressed onto a rigid substratum. For the second, another calibrated cantilever (from the same batch) is pressed against the other one. A silicon sphere is placed between the two cantilevers to avoid adhesion effects and to guarantee punctual contacts on both sides (cf. Fig. 5). The cantilever/substratum mechanical interaction is used to calibrate the whole system. The photodiode gives an output voltage corresponding to the translation (tilt) of the laser beam. As the cantilever has been previously calibrated, for a displacement of 1 µm, the sensed force is 0.2 µm. This technique allows one to avoid to calculate the laser optical path as well as the accurate calibration of the photodiode. In the case of the cantilever/cantilever interaction, the mechanical system is considered as two springs in sequence, with a respective spring constant of k 1 and k 2. The equivalent stiffness K eq can be expressed as a function of k 1 and k 2 as: 1/K eq = 1/k 1 + 1/k 2. Fig. 6 shows the experimental force sensed by the measuring cantilever for both the rigid substratum and the cantilever/cantilever mechanical interaction. Since the spring constant corresponds to the gradient (slope) of the curves, the cantilever/cantilever curve leads to a value of K eq = N/m on average. As the measuring cantilever is calibrated (k 1 = N/m), we found k 2 = N/m which is in keeping with the expected results. 4. In vitro mechanical characterization experiments The Epithelial Hela cells (EpH) are prepared on Petri dishes with a specific culture medium formed by Dulbecco s Modified Eagle s Medium (DMEM) with high glucose and L- glutamine components and 10% of foetal bovine serum. The (EpH) cells can be assimilated morphologically to an elliptical cells with a thin surrounding biomembrane which has two functions: to ensure both the protection of the cytoplasm and the adhesion features on the subtractum. In the present study, the average dimensions of the biological sample are 10 µm long, 9 µm large and 6 µm height Cell s mechanical response characterization Fig. 7(A) shows the experimental curves of the photodiode output as a function of the sample displacement ( z) performed on both a single EpH cell and a hard surface. The single step of the sample displacement is 200 nm and the total displacement is 8 µm. Deformation δ of the EpH cell is monitored by calculating the difference between the sample displacement z and the cantilever deflection d. The nonlinear elastic behavior of the EpH can be seen in the Fig. 7(B) which presents the sample deformation δ as a function of the load force applied by the cantilever. The elastic behavior of the EpH cells is also investigated by the FBM device. Cyclical and automatic approaches and retract experiments were conducted on the same biological sample during 2 h with 3 min intervals (scan rate 0.05 µm s 1 ). For this given study, the motion amplitude and the single step of the vertical microstage are fixed to 8 µm and 200 nm, respectively. In order to reduce the cantilever damping oscillations during the mechanical characterization process, velocity of the sample positioning stage is chosen small (0.5 µm/s). Fig. 8(A) shows 3 approach and retract curves monitored at different time intervals (t = 0 min, 40 min and 80 min) during the experiments. A single referenced approach/retract curves performed on a hard surface is given in Fig. 8(B). According to the data collected, the EpH

6 302 J O U R N A L O F T H E M E C H A N I C A L B E H A V I O R O F B I O M E D I C A L M A T E R I A L S 2 ( ) Fig. 7 (A) Experimental data of the photodiode output as a function of the sample displacement performed on both a single EpH cell and a hard surface. (B) Experimental curve of the sample deformation δ as a function of the applied load by the cantilever. Fig. 9 Evolution of the measured force as a function of the sample displacement for different time intervals t 0 = 0, 5, 9 and 13 min. respectively. Since the purpose of this study is to observe the differences which can occur in the mechanical behavior of the biological sample under study, experimentation is initially conducted using the incubating system. Fig. 9 shows th evolution of the EpH cell s mechanical behavior under cyclical spectroscopy operation with and without the use of the incubating system. More specifically, curve (A) shows the approach and retract curves using the incubating system. Curves (B), (C) and (D) show the mechanical behavior of the studied EpH cell under study for different time intervals t 0 once the cage incubator is turned off. These mechanical characterization experiments obviously reveal that the mechanical properties of the sample are affected by the temperature conditions of the culture s environment. These differences suggest that the intra or extra-cellular matrix reacts to a variation of temperature. Fig. 8 (A) Experimental spectroscopy curves (approach and retract) performed on a single EpH cell at different time intervals (t = 0 min, 40 min and 80 min). (B) Single referenced approach and retract curves performed on a hard surface. sample exhibits the same elastic behavior during the whole experiment In vitro efficiency approach for cell mechanical characterization In order to address either the efficiency of the in vitro clean room unit or how mechanical cell properties can be affected by the culture s environmental conditions, we have experimented automatic and cyclical spectroscopy operations on a single EpH cell during several minutes without the use of the incubating system. As in the previous study, the sample displacement and the single step of the vertical micropositioning stage are fixed at 8 µm and 200 nm 4.3. Analytical model for sample deformation and contact area estimation The sample deformation δ as well as the contact area radius a resulting from the EpH cells mechanical characterization process is estimated using an appropriate analytical fitted model. Three analytical models are chosen based on the Hertz, the JKR (Johnson, Kendall and Roberts) and the DMT (Derjaguin, Muller and Toporov) theories. The chosen models are fitted to sample deformations where elastic linear properties are satisfied. According to Fig. 6(B) the quasi linear elastic behavior is satisfied for load P less than 0.15 µn. Fig. 10 presents the mechanical interaction between the silicon tipless cantilever and the biological sample. Noting R the radius of the biological sample (R = 5 µm), w the adhesion work and P the load force applied by the cantilever, the contact area a can be expressed according to the Hertz, the JKR and the DMT theories respectively (Maugis, 2000; Derjaguin et al., 1975): a 3 = RP K (4)

7 J O U R N A L O F T H E M E C H A N I C A L B E H A V I O R O F B I O M E D I C A L M A T E R I A L S 2 ( ) Fig. 10 Mechanical interaction scheme between the silicon tipless cantilever and the biological sample. a 3 = R K (P + 3πRw + 6πRwP + (3πRw) 2 ) (5) a 3 = R (P + 2πRw) (6) K where K is the effective Young s modulus of the two materials in contact. K is expressed according to either the Hertz, the JKR or the DMT models as: 1 K = 3 4 ( 1 ν 2 E + 1 ν 2 E ) ν and ν are respectively the Poisson s coefficients of the EpH cells (ν = 0.5) and the silicon cantilever. The manufacture s data gives the Young s modulus of the silicon tipless cantilever and the Poisson s ratio as E = 140 GPa and ν = The JKR and the DMT theories suggest that adhesion work w can be expressed in two ways according to the pull-off force P off needed to overcome adhesion forces as (Maugis, 2000): P off = 3 πrw (JKR) (8) 2 P off = 2πRw (DMT). (9) As the pull-off force P off is accurately measured using the FBM (P off 20 nn), the adhesion work w is introduced in Eq. (6). This equation is then used to estimate the contact area a. The deformation δ of the elastic body is expressed respectively using the Hertz, the JKR and the DMT analytical models as Maugis (2000): δ Hertz = δ DMT = a2 (10) R δ JKR = a2 8πwa R 3K. (11) Fig. 11 (A) shows the estimation of the deformation of the biological sample δ as a function of the simulated load force P using Hertz, JKR and DMT theories. These analytical results are compared with the experimental measurements performed with the FBM and presented in Section 4.1. Fig. 11(B) shows the estimated contact area radius as a function of the load force P. These results emphasize, in our case, that the Hertz model is not appropriate for the estimation of contact mechanisms in the case of soft materials at the microscale level. Since adhesion forces are not considered, large errors are observed (7) Fig. 11 (A) Estimation of the deformation of the biological sample δ as a function of the simulated load force P using Hertz, JKR and DMT theories compared with the experimental data. (B) Estimation of the contact area radius a using the Hertz, JKR and DMT theories. between the experimental data and the predicated forcedeformation curve (in the order of 0.2 µm of magnitude). Even, the contact area radius a in the latter case is approximately two times greater than predicted by the JKR and the DMT models. We have observed small deviation between the JKR and the DMT models for force-deformation prediction. In the case of the contact area radius estimation with large deformations, deviations have been observed in the order of 0.3 µm of magnitude. According to the literature, the JKR theory in opposition to DMT theory is applied for soft materials, high energy adhesion and a large radius (Maugis, 2000), which is the case in this study. 5. Conclusion This paper has presented the development of a micro-force sensing platform for the investigation of in vitro cell mechanical behavior. The experimental setup combines Scanning Probe Microscopy (SPM) techniques with advanced robotic approaches. As the developed system operates in a fully automatic mode based on visual and force tracking control, effective mechanical characterization and reliable data acquisition are achieved. Each module is designed, calibrated or configured towards an effective and reliable device. Experiments have been conducted using the platform on adherent human Epithelial Hela cells. The experiments demonstrate the efficiency of the experimental setup developed to explore the mechanical response in in vitro conditions of adherent biological samples. The study shows the complex mechanical response of the cells which exhibits elastic response combining hysteric behavior. The contact mechanisms resulting from the cell mechanical characterization process are predicted using appropriate models taking into account both adhesion forces and finite sample thickness. The results emphasize that the Hertz

8 304 J O U R N A L O F T H E M E C H A N I C A L B E H A V I O R O F B I O M E D I C A L M A T E R I A L S 2 ( ) model is not appropriate for the estimation of contact mechanisms in the case of soft materials at the microscale level. Since adhesion forces are not considered, large errors are observed between the experimental data and the predicted force-deformation curve. 6. Future work Current work involves modeling the contact mechanics resulting from the cell mechanical characterization process using a tipless cantilever. Some important issues will be addressed such as friction, osmotic influence, non-linear elastic behavior and adhesion forces. Future work will be focused on exploring the mechanical transduction of living cells in in vitro environment conditions. One of the most promising results of this study will be the description of both mechanosensitivity and mechanical transduction mechanisms at the microscale for biological cells or tissue configuration. R E F E R E N C E S Derjaguin, B.V., Muller, V., Toporov, Y.P., Effect of contact deformations on the adhesion of particles. Journal of Colloid and interface science 53 (2), Girot, M., Boukallel, M., Régnier, S., An hybrid micro-force sensing device for mechanical cell characterization. In: Proc. of the Int. Conference on Instrumentation and Measurement Technology. pp Lukkari, M., Kallio, P., Multi-purpose impedance-based measurement system to automate microinjection of adherent cells. In: Proc. of the Int. Sympos. on Computational Intelligence in Robotics and Automation. pp Mahaffy, R., Shih, C.K., Mackintosh, F.C., Kas, J., Scanning probe-based frequency-dependent microrheology of polymer gels and biological cell. Physical Review Letters 85, Maugis, D., Contact, Adhesion and Rupture of Elastic Solids. Springer-Verlag. Radmacher, M., Measuring the elastic properties of biological samples with afm. In: Proc. of the IEEE Conference on Engineering in Medicine and Biology. pp