A MICROFORCE AND NANOFORCE BIOMICROSCOPE DEVICE FOR IN VITRO MECHANOTRANSDUCTION INVE
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A MICROFORCE AND NANOFORCE BIOMICROSCOPE DEVICE FOR IN VITRO MECHANOTRANSDUCTION INVESTIGATION
College Of Engineering, Trivandrum
A MICROFORCE AND NANOFORCE BIOMICROSCOPE DEVICE FOR IN VITRO MECHANOTRANSDUCTION INVESTIGATION.ppt (Size: 3.15 MB / Downloads: 46)
Motivations of this Work
Block Diagram of the FBM Device
Description of the FBM Device
Cantilever Spring Constant Calibration
In Vitro Mechanical Characterization Experiments
Characterization of Cell Mechanical Properties
Scanning Probe Microscopy(SPM) and Advanced Robotics Approaches
Demonstration on the Epithelial Hela Cells
MOTIVATIONS OF THE WORK
SPM by Atomic Force Microscope(AFM)
Cost and Flexibility
Requires Complex Experiments and Specific Environments
Single Cell Target
Has Problems in Using Sharp tip Cantilever
Use of Tipless Cantilever and FBM System
FORCE BIO MICROSCOPE(FBM) DEVICE
Combines SPM and Advanced Robotics Approaches
Having a Tipless Catilever
Cantilever Spring Constant Calibration by Determination of Cantilever Thickness
BLOCK DIAGRAM OF THE FBM DEVICE
EXPERIMENTAL SETUP OVERVIEW
FBM is a Hybrid AFM
Has Three Units-The Mechanical Sensing Unit ,The Imaging Unit and The Clean Room In Vitro Unit
Cage Incubator is Used For Providing Suitable Condition
Force/Vision Referenced Control
Antivibration Table For Avoiding Undesired Vibrations
MECHANICAL SENSING UNIT
Performs detection , Positioning and Sensing
Sensing By Optical Technique
Four Quadrant Photodiode and Laser Diode for Measurements
Uncoated Tipless Silicon Cantilever as the Probe
3 DOF Micropositioning Stage
Use of PD Controller for Optimal Performance
CONFIGURATION OF THE MECHANICAL SENSING UNIT
For Imaging and Cell Tracking Features
Consists of an Inverted Microscope
Charged Coupled Device(CCD)Camera is Fitted with the Microscope
Automatic Mechanical Characterization Based on Image Feature Tracking
Calibration of the CCD Camera by Calibrated Glass Microarray and Calibrated Microspheres
CLEAN ROOM UNIT
Allows Experiments to be Conducted In a Biological Environment
Provide a Biological Nutritional Medium , Required Temperature of 37 ◦C , 5% CO2 Medium
A Controlled Heating Module Maintains the Temperature
Temperature Control is by a Configurable PID Controller
FBM EXPERIMENTAL SETUP
CANTILEVER SPRING CONSTANT CALIBRATION
Determination of Cantilever Thickness by a Dynamical Frequency Response Method For Spring Constant Calibration
Spring Constant Calibration According to the Dimensions of Cantilever
FREQUENCY RESPONSE METHOD FOR 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∂2v/∂t2 + EI∂4v/∂x4 = 0 (1) where v is the instantaneos deformation of beam,depends on time and position.
to solve (1),the boundary conditions required are
v(0)=0, θ(0) = 0,M(L)=0,T(L)=0;
The system of boundary equations accepts a solution only if the determinant is zero, which is equivalent to
1 + cos μ cosh μ = 0. (2)
With μ = (ω2(ρS/E’I))1/4αL, (2) gives one condition on μ to be respected, which defines the eigenfrequency of the system
from the above conditions the mean value of cantilever thickness is given by
<h>=1/N∑ ωi L2 /μi2√ 12ρ/ E’
i=1 with N being the number of the measured eigenfrequency.
CANTILEVER SPRING CONSTANT DETERMINATIN BY STATIC METHOD
From the dimensions of the cantilever the spring constant of the cantilever
where I=lh³/12, the moment of inertia
This Method has High Accuracy
IN VITRO MECHANICAL CHARACTERIZATION EXPERIMENTS
EpH Cells are Prepared on Petri Dishes
The Samples are of Dimension 10Цm*9Цm*6Цm
CELL’S MECHANICAL RESPONSE CHARACTERISATION
Photodiode o/p vs sample vertical displacement on EpH cell and a Hard surface
The deformation δ is the difference of Δz and Δd
The non linear elastic behaviour of EpH is
Viscoelastic behaviour of EpH cell is also investigated
IN VITRO EFFICIENCY APPROACH
To find the efficiency of the clean room unit
Perform automatic and cyclical spectroscopy operation with and without incubating system
Mechanical Characterization is temperature dependant
Presented a Microforce Sensing System for in vitro Mechanotransduction Investigation
Reliable and Effective Mechanical Characterisation and Data Acquisition Can be Achieved
Experiments on EpH Cells by FBM Demonstrated the Efficiency of the Setup
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A MICROFORCE AND NANOFORCE BIOMICROSCOPE DEVICE FOR IN VITRO MECHANOTRANSDUCTION INVESTIGATION
B.Tech, Applied Electronics and Instrumentation
A MICROFORCE AND NANOFORCE BIOMICROSCOPE DEVICE FOR IN VITRO MECHANOTRANSDUCTION INVESTIGATION.rar (Size: 5.06 MB / Downloads: 24)
This paper deals with the development of an open design platform for explorative cell mechanotransduction investigation. The produced setup combines scanning probe microscopy (SPM) techniques and advanced robotics approaches, allowing both prolonged observations and spatial measurements on biological samples. As a result, an enhanced force probing method based on scanning microscopy techniques and advanced robotics and automation approaches is integrated in this device. Visual and force feedback control is used to achieve automatic data acquisition and monitoring processes when high skills are required. Experimentation on the mechanical cell characterization under in vitro conditions on human adherent cervix epithelial Hela cells is presented to demonstrate the viability and effectiveness of the proposed setup.
Mechanotransduction is a cell process that converts mechanical stimuli into biochemical signals. Since most cells are sensitive to mechanical disturbances, the resulting response to mechanical inputs is a determinant in governing their behaviour not only in the cell culture but in the whole organism as well. It is crucial to consider how external mechanical stimuli are transmitted into the cell. Many researchers have been devoted to the understanding of the mechanotransduction mechanism. Despite these efforts, only a few studies lead to efficient models that predict force transduction to biochemical signals. Due to the complex cell behaviour as well as the complex interactions involved in such a process, mechanotransduction is subjected to many assumptions. Despite this apparent complexity, it has, however, been shown that stimulated cells are activated by similar mechanisms at the molecular level.
Understanding the mechanotransduction basis first requires accurate knowledge of the magnitude and the distribution of forces sensed by the cell in their environment. Moreover, mechanical characterization of the cell properties is also required to correlate biological and mechanical behaviours. Actually, due to the structural complexity of cells (such as the deformable cytoskeleton formed by a 3-D intercellular network of interconnected biopolymers), detecting modifications in the mechanical properties of a cell can yield additional knowledge as to the way the cell reacts to mechanical stimuli.
The development of effective tools for mechanotransduction studies at the molecular level is crucial for understanding the involved mechanisms. The design of such tools should address important issues in terms of spatial and temporal features (e.g., measurements, positioning, and monitoring). In fact, due to the complexity of the cell mechanics, as well as the requirement of life science, suitable and specific solutions are needed. Robotics and micro robotics approaches can play an important role in the exploration of mechanotransduction mechanisms by the development toward highly effective and reliable systems.
MOTIVATIONS OF THE WORK
A variety of approaches have been used to mechanically stimulate cells, sense force distribution, or determine cell mechanical properties. Among these approaches, the most promising ones involve scanning probe microscopy (SPM) techniques for nano scale. These techniques have the potential to give accurate quantitative information about local forces and
contact mechanics. The atomic force microscope (AFM) has become a commonly used tool in the field of the biosciences. A flexible cantilever with a low spring constant (0.1–0.2 N/m) and an atomic sharp tip is usually brought into the vicinity of the biological sample. The deflection of the cantilever, as a result of the mechanism interaction between the micro indenter and the sample, is monitored by a split photodiode, and the use of a laser beam is reflected on the back of the cantilever. Some commercial solutions are available for the performance of experiments on life science (e.g., Veeco, Olympus, and Andor), but only a few of them are effective for mechanotransduction studies.
The cost and the flexibility are the main drawbacks of these devices. Since these studies need complex experiments and specific environmental conditions, an open platform design is more suitable. Furthermore, studies on Mechanotransduction are usually focused on a single cell target and are seldom conducted on a large cell population. Performing mechanotransduction on large samples, based on statistical approaches, can lead to better modelling at the molecular scale.
We associate some problems with the use of a commercial cantilever with a sharp tip for mechanotransduction requirements. In fact, the manometer dimensions of the tip can cause important local strains that are higher than the elastic domain. Furthermore, depending on the magnitude of the force applied on the soft samples, both the cantilever tip and the samples can be easily damaged so that the local strain applied in the indented area become changed. Since mechanotransduction studies need accurate force application, a soft and non invasive approach is more suitable.
It must also be emphasized that the force measured by the cantilever is calculated by a simple analytical formula (via Hooke’s law) that expresses the force according
to both the deflection and the spring constant of the lever. Consequently, the accuracy of the force-displacement data collected by the AFM is greatly dependent on the accurate
knowledge of the spring constant since the deflection of the cantilever can be accurately detected by optical laser methods. Several authors have noted that the spring constants provided by cantilever manufacturers are incorrect.
These significant errors are mainly due to the difficulty of accurately controlling their thickness during the micro fabrication process. Much effort has been devoted to eliminating the necessity of knowing the cantilever thickness for the spring constant calibration process. As a result, various techniques have been developed and published, based on cantilever static or dynamic flexural deflection measurements. The issue of the spring constant calibration using an accurate determination of the cantilever thickness is addressed in this paper. We use the dynamical frequency response method for thickness determination. As this method is quite accurate, the spring constant calibration is done according to the dimensions of the cantilever.
Another difficulty is associated with using sharp cantilevers. Usually, the spectroscopy curves collected with the AFM are used in conjunction with an appropriate analytical model to estimate Young’s modulus, friction, wear, and other material properties. According to the literature, the Hertz model, which describes the relationship between force and indentation, is the commonly used approach for fitting the experimental data. In addition, two major assumptions are made: 1) linear elasticity and 2) infinite sample thickness.
Some authors have shown that in the case of a soft contact mechanism, models derived from linear elasticity can lead to significant errors. Moreover, due to the imperfections of the tip radius of curvature, an unknown contact region results between the probe and the sample. Consequently, uncertainties are introduced to choose the appropriate fitting analytical model. It has also been shown that depending on the applied force and the sample’s thickness, large errors may result when using infinite-thickness models. The authors compute force-displacement curves for finite sample thickness to show that for soft and thin samples, the error in the estimated elasticity modulus can be an order of magnitude. Costa and Yin have also shown, using finite-element modelling, that linear-elasticity-derived models lead to significant errors in the case of sharp pyramidal tips.
In our opinion, mechanotransduction based on a tip less cantilever seems to be a promising solution. As studies involving such cantilevers are less prone to problems associated with a sharp-tip cantilever, enhanced nondestructive cell mechanical characterization should be achieved. For this purpose, a force bio microscope (FBM) system has been developed that combines SPM techniques and advanced robotics approaches. A tip less 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. Both cell mechanical properties and the contact mechanism are modelled with appropriate models, taking into account adhesion forces. More precisely, the Johnson, Kendall, and Roberts (JKR) and Derjaguin, Muller, and Toporov (DMT) contact theories are used to estimate both Young’s modulus and the contact area that result from the mechanical characterization process. To demonstrate the accuracy of the JKR and DMT models in the case of soft contact mechanisms, the estimated force-deformation curves are compared with the one predicted by the Hertz theory.
THE FORCE BIO MICROSCOPE
The FBM device is a hybrid AFM that associates both the scanning microscopy approach and biological environment constraints. The FBM mainly consists of three units: 1) the mechanical sensing unit, which performs detection, positioning, and sensing features; 2) the imaging/grabbing unit for imaging and cell tracking features; and 3) the clean-room in vitro unit, which allows experiments to be conducted in a biological environment.
The FBM experimental setup provides suitable conditions for study in a controlled environment so that the biological cells can be kept in a living state for several hours by using a cage incubator. Therefore, the mechanical measurement process can be done on the biological sample over an extended period of time.
A master computer is used to drive the FBM in an automatic operating mode based on force/vision referenced control. The data-acquisition process between the master computer and the FBM is achieved by the use of two specialized peripheral component interconnect cards (Matrox and National Instrument). A user-definable graphical interface has been developed to make the configuration of the experiments easier. To avoid undesired mechanical vibrations during the cell characterization process, the FBM experimental setup is installed on an anti vibration table.
3.1 Block Diagram Of FBM
3.2 Mechanical Sensing Unit
The mechanical sensing unit is based on the detection of the deflection of a cantilever by an optical technique. A four quadrant photodiode (Centro Vision) with internal amplifiers associated with a 650-nm, low-power collimated laser diode (Vector Technology) is used to perform both axial and lateral nano-Newton force measurements. The total sensing area of the photodiode is 7 mm2 with a spectral response from 400 to 1100 nm. The optical path of the Gaussian laser beam is optimized using a pair of mirrors and an aspheric condenser glass lens. Hence, the production of a sensitive and accurate detection device is 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 tip less silicon cantilever (Nano sensors) is used as a probe for the cell mechanical characterization. The lever is 450 μm long, 90 μm wide and 2 μm thick. The sample to be studied is accurately positioned below the cantilever by 3-degree-of-freedom (x-axial, y-lateral, and z-vertical) micro positioning encoded stages (Physik Instrumente) with a sub micrometer resolution (0.1 μm). The kinematic features of the micro positioning stages allow us to achieve accurate mechanical measurements in a workspace of 25 × 25 × 25 mm3 with good repeatability.
For the preliminary study, we focused on force feedback control of cantilever flexural deflection. Thus, only the vertical z motion of a micro positioning stage is served. By knowing the vertical position of the micro motors 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 control performance. The PD terms are optimized using the Ziegler–Nichols method
3.2.1 FBM and Mechanical Sensing Unit
3.2.2 Magnified View Of Mechanical Sensing Unit
Experimental results on the force feedback control approach
3.3 Imaging 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 for precise contrast operation. The inverted microscope is fitted out with a charged-coupled-device (CCD) camera (754 × 488 pixel 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 achieved by means of a calibrated glass microarray as well as calibrated microspheres
3.3.1 Calibration Of The Ccd Camera Based On
3.4 Clean Room Unit
The biological samples need specific requirements to be kept alive outside the in vitro conditions and to carry out prolonged observations. In addition to the biological nutrition medium, biological cells need a 37 ◦C temperature condition and 5% of CO2 gas. The incubating system is formed by a controlled heating module that maintains temperature at 37 ◦C using a single thermocouple probe. The desired temperature of 37 ◦C is reached in 2 h. The cage incubator ensures temperature stability within 0.1 ◦C. A mixed stream composed of 5% CO2 and humidified air is fed into a small incubating chamber that contains the biological samples, thus avoiding condensation on the cage walls that could damage the mechanical parts of the microscope and the micro positioning stages.
Temperature control is achieved by means of a configurable proportional integral differential controller that communicates with a water bath via a 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.
3.5 FBM Experimental Setup Overview
CANTILEVER SPRING CONSTANT
Since the beginning of scanning force microscopy, many methods for the spring constant calibration have been developed and studied. These methods agree to discard the use of the cantilever’s dimensions since the determination of the thickness is problematic. To overcome this problem, we use a dynamical frequency response method for thickness determination. As this method is quite accurate, the spring constant calibration is done
according to the dimensions of the cantilever.
The length and width of the cantilever are measured using an optical method by the same process used for camera calibration. The obtained values for length and width (L = 450 μm and l = 90 μm) are in good agreement with those of the manufacturer. Knowing all the dimensions of the cantilever, the spring constant is then calculated by a static method.
4.1 Frequency Response Method For
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 where v is the instantaneous deformation of the beam, depending on the time and position. The displacement can be written in two parts, i.e., one depending on the position along x-axis and another one on time: v(x, t) = f(x)g(t).
To solve (1), i.e., to calculate the solution’s constants, 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 accepts a solution only if the determinant is zero, which is equivalent to
1 + cosμ coshμ = 0 (2)
With μ = (ω² (ρS/EI))¼ αL, (2) gives one condition on μ to be respected, which defines the Eigen frequency of the system.
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 ∑_(i=1)^N▒〖ωi (L²√12ρ/E〗)/μi^2 (3)
With N being the number of the measured Eigen frequency.
In our case, the use of 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 before each experimentation. 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.
4.2 Static Approach For The Spring Constant
Knowing the dimensions of the cantilever and its material properties, the spring
constant of a rectangular cantilever is given by
Where I is the moment of inertia of the cantilever and, I=lh³/12;
4.3 Experimental Spring Constant Cantilever
These experiments aim to validate the force measurement accuracy of the mechanical sensing unit, including the cantilever and the optical laser system. Two measurements are performed. In the first one, a previously calibrated cantilever is pressed onto a rigid substrate. For the second one, 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.
The cantilever/substrate mechanical interaction is used to calibrate the whole system. The photodiode gives an output voltage that corresponds to the translation (tilt) of the laser beam. As the cantilever has been calibrated before, for a displacement of 1 μm, the
sensed force is 0.2 μN. This technique allows us to calculate the laser optical path as well as the accurate calibration of the photodiode. In the case of cantilever/ cantilever interaction, the mechanical system is considered to be two springs in series, with respective spring constants k1 and k2. The equivalent stiffness Keq can be expressed as a function of k1 and k2 as
follows: 1/Keq = 1/k1 + 1/k2. Fig. shows the experimental force sensed by the measuring cantilever for both the rigid subtract and the cantilever/cantilever mechanical interaction. Since the spring constant corresponds to the gradient of curves, the cantilever/cantilever curve leads to a value of Keq = 0.101 N/m on average. As the measuring cantilever is calibrated (k1 = 0.201 N/m), we found that k2 = 0.203 N/m, which is in accordance with the expected results.
4.3.1 Experimental Determination Of The Cantilever
IN VITRO MECHANICAL
The epithelial Hela (EpH) cells are prepared on petri dishes with a specific culture medium formed by Dulbecco’s modified eagle’s medium with high glucose and L-glutamine components and 10% of foetal bovine serum . The cervix (EpH) cells can be morphologically assimilated to an elliptical cell with a thin surrounding bio membrane, which has two functions: 1) ensuring the protection of the cytoplasm and 2) ensuring the adhesion feature on the substrate. In this paper, the average dimensions of the biological sample are 10 μm long, 9 μ wide, and 6 μm in height.
(a) Magnified image of the cervix EpH cells obtained with a 63× objective. (b) Cervix EpH cells morphology observed by fluorescence techniques.
5.1 Cell’s Mechanical Response Characterization
Fig1. (a).shows the experimental curves of the photodiode output as a function of the sample vertical displacement (Δz) 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. The deformation δ of the EpH cell is monitored by calculating the difference between the sample displacement Δz and the cantilever deflection Δd. The nonlinear elastic behaviour of the EpH can be seen in Fig 1. (b), which presents the sample deformation δ as a function of the load force applied by the cantilever.
The viscoelastic behaviour of the EpH cells is also investigated by the FBM device. A cyclical automatic approach and retract experimentations were conducted on the same biological sample for 2 h at 3-min intervals. In this paper, the motion amplitude and the single step of the vertical micro stage are fixed to 8 μm and 200 nm, respectively. To reduce the cantilever damping oscillations during the mechanical characterization process, the velocity of the sample positioning stage is chosen to be small (0.5 μm/s). Fig 2. (a) Shows three approach and retract curves monitored at different time intervals (t = 0, 40, and 80 min) of the cyclical experiments. A single referenced approach and retract curves performed on a hard surface are given in Fig 2.(b). According to the collected data, the EpH sample exhibits the same visco elastic behaviour during all the experimentations.
Fig 2. (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 2. (a) Experimental spectroscopy curves (approach and retract) performed on a single EpH cell at different time intervals (t = 0, 40, and 80 min).
(b) Single referenced approach and retract curves performed on a hard surface.
5.2 In Vitro Efficiency Approach For Cell Mechanical
To address either the efficiency of the in vitro clean-room unit or how mechanical cell properties can be affected by the environmental culture conditions, we have experimented with automatic and cyclical spectroscopy operation on a single EpH cell for several minutes without the use of the incubating system. As the precedent study, the sample displacement and the single step of the vertical micro positioning stage are fixed to 8 μm and 200 nm, respectively. Since the purpose of this study is to observe the difference that can occur on the mechanical behaviour of the studied biological sample, experimentation is initially conducted using the incubating system. Fig. shows the evolution of the EpH cell mechanical behaviour of cyclical spectroscopy operation with and without the use of the incubating system. More specifically, curve (A) shows the approach and retract curves using the cage incubator. Curves (B)–(D) show the mechanical behaviour of the studied EpH cell for different elapsed times t0 once the cage incubator is turned off.
Evolution of the measured force as a function of the sample displacement
for different elapsed times t0 = 0, 5, 9, and 13 min.
These mechanical characterization experiments obviously reveal that the mechanical properties of the studied sample are affected by the temperature environmental culture conditions. This difference suggests that the intracellular or extracellular matrix react to the variation of temperature
5.3 Analytical Model For Both Young’s Modulus And
Contact Area Estimation
Young’s modulus E and the contact area a that result from the EpH cell mechanical characterization process are estimated using an appropriate analytical fitted model. Since Young’s modulus can be used to predict the elongation or compression of the biological sample as long as the stress is less than the yield strength of the sample, the chosen models are fitted to sample deformations where elastic linear properties are satisfied. According to curve (B), the quasi-linear elastic behaviour is satisfied for load P less than 0.15 µn. Three analytical models are chosen to estimate Young’s modulus and the contact area. Thus, the Hertz, JKR, and DMT models, respectively, are used.
Fig. 1. Mechanical interaction scheme between the silicon tip less cantilever and the biological sample
Fig. 1 presents the mechanical interaction between the silicon tip less cantilever and the biological sample. Noting the radius of the biological sample R (R = 5 μm), the adhesion work w, and the load force applied by the cantilever P, the contact area a can be expressed, respectively, according to the Hertz, JKR, and DMT theories.
a³= RP/K (1)
a³= R/K (P+3πRω+√6πRωP+ (3πRω) ² (2)
a³= R/K (P+2πRω) (3)
Where K is the effective Young’s modulus of the two materials in contact. K is
expressed according to the Hertz, the JKR, or the DMT model as
1/K= 3/4 (1-v²/E+1-v’²/E’) (4)
Where v and v’ are, respectively, the Poisson’s coefficient of the EpH cells (v = 0.5) and the silicon cantilever. The manufacturer’s data give Young’s modulus of the silicon tip less cantilever and Poisson’s ratio as E’ = 140 GPa and v’ = 0.17.
The JKR and DMT theories suggest that adhesion work w can be expressed in two ways according to the pull-off force POFF needed to overcome adhesion forces as
POFF = 3/2πRω (JKR) (5)
POFF = 2πRω (DMT) (6)
As the pull-off force POFF is accurately measured using the FBM (POFF ≈ 20 nN), the adhesion work w is introduced in (2) and (3) to estimate the contact area a. The deformation δ of the elastic body is expressed, respectively, using the Hertz, JKR, and DMT analytical models as
δHERTZ = δDMT = a²/R (7)
δ= a²/R-√8πωa/3K (8)
Fig. (a). Estimation of the biological sample deformation δ as a function of the simulated load force P using the Hertz, JKR, and DMT theories compared to the experimental data.(b)Estimated stress σ = P/a as a function of the estimated strain ε = δ/2R using the Hertz, JKR, and DMT theories
Fig. (a) shows the estimation of the biological sample deformation δ as a function of the simulated load force P using the Hertz, JKR, and DMT theories. These analytical results are compared to the experimental measurements performed with the FBM and presented in Section V-A. The EpH cells’ Young’s modulus E is estimated using the biological sample deformation δ and the contact area a obtained by the different modelling approaches. Fig. (b) shows the estimated stress σ = P/a as a function of the estimated strain ε = δ/2R using the Hertz, JKR, and DMT theories. Since linear elastic deformation is satisfied, Young’s modulus E of the studied biological sample can be determined by calculating the slope of the obtained curves (σ = Eε). These results emphasize, in our case, that the Hertz model is not appropriate for the estimation of the contact mechanism in the case of soft materials at the micro scale. Since adhesion forces are not considered, large errors are observed between the experimental data and the predicted force deformation curves (on the order of 0.2 μm of magnitude).
We have observed a small deviation between the JKR and the DMT models to estimate the force-deformation curve. The DMT theory is applied in the case of hard solids, with a small radius of curvature and low energy of adhesion. The JKR theory is more often applied for soft solids, with a large radius and large energy of adhesion. Based on these considerations, we chose the JKR model as the model reference in our case. This model, used in conjunction with the experimental data, leads to an accurate detection of cell mechanical property modification needed in mechanotransduction studies.
This paper has presented the development of a micro force sensing system for in vitro mechanotransduction investigation. The experimental setup combines SPM techniques with advanced robotics 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. The FBM device consists of three modules with autonomous force sensing and measurement capabilities. Each module is designed, calibrated, or configured toward an effective and reliable device.
Experiments have been conducted using the FBM on human adherent cervix EpH 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 contact mechanisms that result from the cell mechanical characterization process are predicted using appropriate models, taking into account both adhesion forces and finite sample thickness.
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