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1、Modeling of Breast Cancer Cell Through Atomic Force Microscope Sarunyoo Leelertyuth and Teeranoot Chantasopeephan* Biological Engineering, King Mongkuts University of Technology Thonburi Bangkok, Thailand AbstractWe study the biomechanical properties of MCF7 breast cancer cell based on an experiment
2、al measurement using atomic force microscopy (AFM). This paper consists of two parts. The first part corresponds to the experimental measurement of the force and displacement of the cell during probing through atomic force microscope. The second part which is the modeling part describes the mathemat
3、ical relationship between nominal stress and nominal strain based on Neo-Hookean model. We found the material parameters of MCF7 cell in 3 experiments that C1 are 2.12x10-6 Pa, 2.72x10-6 Pa and 2.31 x10-6 Pa and D1 are 944.91 Pa, 736.08 Pa and 867.46 Pa respectively. Hence, we used these parameters
4、and displacement to create a finite element model in ABAQUS. The model is capable of determining the forces-displacement and was then compared with the experiment data of force indentation curve. The results of indentation force between AFM measurement and finite element model by ABAQUS are within t
5、he same range. Keywords- biomechanics; breast cancer cell; atomic force microscope; hyperelastic materials; Neo-Hookean model I. INTRODUCTION Cells are interconnected to the surrounding environment through extracellular matrix where the mechanical stimuli can be transferred directly to the cell. The
6、 chemical activities insides the cell can be converted into mechanical energy. During cell attachment, cell spreading, and motility of cells, mechanical energy plays an important role. Cell positively responds to mechanical stimuli by changing their own behaviors and by modifying their shape and env
7、ironment. For example, forces applied to the cell and the consequent cellular deformations induce a variety of processes, including morphological changes, growth, differentiation, secretion, gene expression and altered extracellular matrix production. This response can either lead to cell adaptation
8、 to counteract the effect of the applied stimuli or to cell damage or death when the applied stimuli exceed the adaptive capacity of the cell 1. Understanding the mechanical properties of cancer cells will help to better understand the physical mechanisms responsible for cancer metastasis 2. With th
9、e recent advances in biomechanics and nanotechnology, it has now become possible to experimentally apply mechanical influences on biological structures. A wide variety of experimental biophysical probes have been used to extract the mechanical properties of cancer cells such as Atomic Force Microsco
10、py (AFM) that great potential in biology to study cells such as cell mechanics, locomotion of cells or differentiation in cells 3. Previous studies 1, 2, 4, 5 used finite element modeling to simulate AFM indentation and determined the cellular strains induced by the indenter, or examined the effect
11、of indentation depth, tip geometry, and material nonlinearity on the finite indentation response. Finite Element Model (FEM) was introduced in several studies based on AFM nanoindentation on endothelial cells, bovine sperm cell, liver, and breast tissues. The models successfully predict the quantita
12、tive changes in the mechanical properties. The hyperelastic models, Neo-Hookean, Mooney-Rivlin and Arruda-Boyce model were used to study the tumor necrosis factor-. These models predicted the mechanical response during large deformation on AFM indentation better than Hertzs model 4. The fields of ce
13、ll biomechanics studies how cells move, deform, and interact, as well as how they sense, generate, and respond to mechanical stimuli. For example, a major issue in cell mechanics is how cells sense mechanical perturbations and convert them into biochemical signals that trigger biological responses 5
14、. Our goal is to study biomechanics of breast cancer cell by experimentally measure the force and displacement through atomic force microscope. Then, the experimental measurement was modeled based on hyperelastic property of material. The mechanical properties apply to the model was mathematically d
15、etermined. The paper consists of two parts. The first part corresponds to the experimental measurement of the force and displacement of the cell during probing through atomic force microscope. The modeling part describes the mathematical relationship between nominal stress and nominal strain which a
16、re based on Neo-Hookean model. II. MATERIALS AND METHODS A. Experimental Setup Malignant human breast epithelial cells (MCF7) were used in this study. MCF7 cell lines were obtained from National Center for Genetic Engineering and Biotechnology, Thailand. We cultured MCF7 in DMEM medium containing 10
17、% heat-inactivated FBS at 37 oC in 5% CO2. A clean glass coverslip (12x12 mm.) was immersed into 1 g/ml poly-L-lysine solution for 5 minute to create better adhesion cells to the *corresponding author978-1-4244-4713-8/10/$25.00 2010 IEEEglass substrate. The coverslip with cells was put into the liqu
18、id cell placed on an Atomic Force Microscope scanner. MCF7 cell have doubling time of 54 hours. In this study, 8 day incubation was chosen for the AFM probing experiment. Before AFM indentation, we used PBS (Phosphate Buffer Saline) to clean cells on coverslip to rinse off death cells and dirt on pe
19、tri dish prior to the test. Atomic Force Microscope (AFM) XE-70 (Park System) was used to carry out the experiments. During AFM contact mode scanning, a silicon nitride Atomic Force Microscope tip was used. During AFM indentation, a modified silicon nitride Atomic Force Microscope cantilever (NSC36,
20、 Si3N4, Park Scientific Instruments) having a spring constant of 0.6 N/m with a conical tip was used to indent the cells. Indentation was carried out at the center of cell using scan rate about 0.3 Hz and an indentation depth of 1.99 m which XY scan range of 10x10 mm, at resolution of 16x16 (256 tot
21、al indentations) was applied during the tests in order to ensure that a small deformation was exerted on the cell. B. Mathematical Analysis The hyperelastic material is an ideal elastic material for which the stress-strain relationship derives from a strain energy density function. Deformable model
22、such as cell and soft tissue, linear elastic models do not accurately describe the observed material behavior. The stress-strain relationship can be defined as non-linear elastic, isotropic, incompressible and generally independent of strain rate. The most well-known stress-strain relations derived
23、from these theories is the Neo-Hookean equation that calculated from the strain energy density function on Equation (1) 6. (1) Where W is strain energy density, Jel is elastic volume ratio, C1, C2 and D1 are constants, I1 and I2 are strain invariant that in Equation (2) (2) (3) Where x, y and z are
24、stretches in x, y and z axis. And x = , y = z = -1/2. From Equation (1), expand Jel is in Equation (4) (4) (5) (6) Where J is volume ratio, Jth is thermal volume ratio, are the principal thermal expansion strains. Equation (1) is the basis of a force-indentation relationship. The uniaxial compressio
25、n and conical indentation for the elastic-plastic indentation of metals and has since been extended to other classes of materials widely accepted definitions of indentation stress (*) and strain (*). The cell was assumed incompressible and a Poissons ratio of 0.499 was used. (7) (8) (9) Where F is i
26、ndentation force, R is the radius of the spherical bead, and is indentation depth. The force-indentation relations for materials following the constitutive Equation (1) and nominal stress nominal strain in Equations (7), (8) and (9) must first be resolved prior to creating a finite element model in
27、ABAQUS. The Neo-Hookean form is the most well known and mathematically simple of all the hyperelastic models. The model of Neo-Hookean solid is usable for plastics and rubber-like substances. A general strain energy function could be obtained by an infinite series expansion in terms of the first and
28、 second strain invariants. III. RESULTS AND DISCUSSION During contact between the tip and the investigated sample, tips movement toward the sample produces the same amount of cantilever deflection. Comparison between reference calibration and cell measurements allows us to determine the cell indenta
29、tion and to construct force versus displacement plots (Fig. 1). Prior to the experimental measurement, we used non-contact mode AFM to scan for the topographical image. In contact mode, Force versus indentation depth curves of MCF7 is shown in Fig. 1. AFM indentation test was performed at scan rate
30、about 0.3 Hz with conical probe of 20 nm radius. The experiment was repeated three times with indentation depth of 1.99 m, 1.99 m, and 1.223 m at three different spots within the same cell. Figure 1 Indentation force versus displacement curve of MCF7 from three measurements. During the indentation t
31、est, the size of the cell was also observed, the thickness of MCF7 cell was approximately 2 m. We used the loading force and displacement from all three experiments to determine the nominal stress and nominal strain based on Equation (7), (8) and (9). The nominal stress and strain were presented in
32、Figure 2. 2112211(3)(3)(1)elWC ICIJD=+2222xyzI=+1/21/2aR=2*Fa=*aR=thielthJJJ=CurrentVolumeJOriginalVolume=123(1)(1)(1)ththththJ=+2221xyzI=+ Figure 2 Nominal stresses nominal strains curves from three experimental measurement. A. Modeling We determined the parameters of MCF7 cell based on Neo-Hookean
33、 model (C1, D1 in Equation (10). From the results of AFM indentation, the strain energy density (W) was calculated based on Equation (1). We assumed the MCF7 cell is incompressible and no thermal expansion and the principal thermal expansion strains = 0 from Equations (7), (8) and (9). Neo-Hookean e
34、quation is a linear combination of one invariant of finger tensor that C1 and D1. Hence, we reduced the Equation (1) to Equation (10) that (10) Equation (10), the stretches was determined based on Equations (2) by x = . Finite element analysis is performed using the commercial software ABAQUS (versi
35、on 6.8-1) to calculate the parameters in Neo-Hookean model of MCF7. The model was a 2D deformable cell with cell geometry of 10 m wide and 2 m high. The cell was constrained on the bottom surface in the y-direction. The conical tip is given a vertical displacement and was model as cell displacement
36、at the top part. The symmetric cell model is discretized using an axisymmetric finite element with a finer mesh towards the top of the cell (Figure 3). A symmetric loading and boundary condition is assumed. The finite elements model consists of quad-dominated shape with 108 elements of MCF7 model. W
37、e used nominal stress and nominal strain from AFM measurement as an input into our 2D finite element model which section of cell is assumed isotropic and homogeneous. The parameters of MCF7 cell was determined by Neo-Hookean model. The displacement was set in y-axis at various displacements of 1.223
38、 m and 1.99 m. The result from graph fitting of the model showed the parameters of MCF7 cell that C1 and D1 was shown on Table 1. TABLE I. THE MATERAIL PARAMETER OF NEO-HOOKEAN MODEL (C1, D1) FROM THREE EXPERIMENTS DATA Experiment Data Material Parameter of Neo Hookean Model C1 D1 Experiment Data 1
39、2.12x10-6 944.91 Experiment Data Material Parameter of Neo Hookean Model C1 D1 Experiment Data 2 2.72x10-6 736.08 Experiment Data 3 2.31x10-6 867.46 3a 3b Figure 3 a) The spatial displacement of MCF7 model at displacement of 1.223 m. b) The spatial displacement of MCF7 model at displacement of 1.99
40、m. 4a 4b 4c 21111(3)(1)elWCIJD=+Figure 4 The comparison between force and displacement between Atomic Force Microscope experiment (-*-) and Hookean model of MCF7 cell from ABAQUS (-o-) from three experiments. 5a 5b 5c Figure 5 The comparison between nominal stress and nominal strain from Atomic Forc
41、e Microscope experiment (-*-) and Neo-Hookean model of MCF7 cell from ABAQUS (-o-) from all three measurements. To verify our model, the determined parameters were applied to the finite element model as part of material property. We then simulated the inverse problem to obtain the relationship betwe
42、en force and displacement as showed in Figure 4. Figure 4 shows the force-displacement curve of three AFM experiments compared with ABAQUS model. The result shows good approximation of force and displacement in Figure 4 a) and b), while in Figure 4c), the model and the experimental results are diffe
43、rent. In addition to the force and displacement, it is crucial to understand the stress and strain within the cell once external force is applied to deform the cell. Through that, the nominal stress nominal strain curve from experiment compared with FEM model were presented in Figure 5. Figure 5a) a
44、nd b) present the experimental results and the FEM results based on Neo-Hookean model. These graphs show a promising model for future prediction in term of stress and strain within the cell once it under gone deformation stage. Further investigations are required in our future work, since cells are
45、different from time to time and the properties are varying within a cell. It is important to perform additional experiments in order to validate our finite element model. IV. CONCLUSION The Neo-Hookean model, the sample nominal stress and strain behavior of MCF7 from experiment were used to determin
46、e the parameters of MCF7 through representative dataset fit with the uniaxial Neo-Hookean equation. The material parameter of three experiments in AFM that C1 and D1 was shown in Table 1. Since the experiment was performed on deformable cell, the large standard deviation of result is expected. The r
47、epresented parameter can be a good prediction, for large deformation as show in the results from experiment data 1 and 2. However, the model can be developed for better fit through more experimental measurements to cover the variation of cells in different area. The more experimental measurement wil
48、l give us a better parameter to cover the input in the material property for any MCF7 cell. Nonetheless, this model of MCF7 could be a good representation for further alteration system of cancer cell such as stress, strain and external force of MCF7 for predicting how mechanical stimuli are transfer
49、red from the external environment to the cell and distributed throughout the cell. REFERENCES 1 Peeters, Emiel A.G., Biomechanics of single cells under compression, University of Technology, Eindhoven, 2004 2 Q.S. Li, G. h. Y. L., C.N. Ong and C.T. Lim, AFM indentation study of breast cancer cells,
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51、astic properties of endothelial cells induced by Tumor Necrosis Factor-, Biophysical Journal, Vol. 94, pp. 32733285, 2008. 5 C. Zhu, G. Bao and N. Wang, Cell mechanics: mechanical response, cell adhesion, and molecular deformation, Annu. Rev. Biomed. Eng., Vol. 2, pp. 189-226, 2002 6 D. C. Lin, D. I. S., E. K. Dimitriadis and F. Horkay, Spherical indentation of soft matter beyond the Hertzian regime: Numerical and Experimental Validation of Hyperelastic Models, Biomech Model Mechanobiology, Vol. 8, pp. 345-358, 2008.
