Viscoelastic finite element modeling of deformation transients of single cells

The objective of this thesis is to use computational modeling to study the deformation of single cells subjected to mechanical stresses. Our motivation stems from experimental observations that cells are subjected to mechanical stresses arising from their environment throughout their lifetime, and that such stresses can regulate many important biological processes. While the exact mechanotransduction mechanisms involved are not well understood, quantitative models for cell deformation can yield important insights. In this thesis, we developed an axisymmetric finite element model to study the deformation of suspended fibroblasts in the optical stretcher and neutrophils in tapered micropipettes. The key feature of our model is the use of a viscoelastic constitutive equation whose parameters can be varied both spatially and temporally so as to mimic the experimentally-observed spatio-temporal heterogeneity of cellular material properties. Our model suggested that cellular remodeling, in the form of an increased cellular viscosity, occurred during optical stretching of fibroblasts. The increase would have to be approximately 20-fold to explain the experimental data for different loading time-scales. We also showed that cell size is a more important factor in determining the strain response of the optically-stretched fibroblasts compared to the thickness of the actin cortical region. This result can explain the higher optical deformability observed experimentally for malignant fibroblasts. In addition, our simulations showed that maximal stress propagates into the nuclear region for malignant fibroblasts whereas for normal fibroblasts, the maximal stress does not. Finally, results from modeling the tapered micropipette experiments also suggested that cellular remodeling, in the form of a decreased cellular elasticity and viscosity, occurred during the process of neutrophil aspiration. Taken together, our simulation results on optically-stretched fibroblasts and aspirated neutrophils suggested that cells in general are able to sense mechanical stresses and respond by varying their material properties during deformation

Viscoelastic finite element modeling of deformation transients of single cells

The objective of this thesis is to use computational modeling to study the deformation of single cells subjected to mechanical stresses. Our motivation stems from experimental observations that cells are subjected to mechanical stresses arising from their environment throughout their lifetime, and that such stresses can regulate many important biological processes. While the exact mechanotransduction mechanisms involved are not well understood, quantitative models for cell deformation can yield important insights. In this thesis, we developed an axisymmetric finite element model to study the deformation of suspended fibroblasts in the optical stretcher and neutrophils in tapered micropipettes. The key feature of our model is the use of a viscoelastic constitutive equation whose parameters can be varied both spatially and temporally so as to mimic the experimentally-observed spatio-temporal heterogeneity of cellular material properties. Our model suggested that cellular remodeling, in the form of an increased cellular viscosity, occurred during optical stretching of fibroblasts. The increase would have to be approximately 20-fold to explain the experimental data for different loading time-scales. We also showed that cell size is a more important factor in determining the strain response of the optically-stretched fibroblasts compared to the thickness of the actin cortical region. This result can explain the higher optical deformability observed experimentally for malignant fibroblasts. In addition, our simulations showed that maximal stress propagates into the nuclear region for malignant fibroblasts whereas for normal fibroblasts, the maximal stress does not. Finally, results from modeling the tapered micropipette experiments also suggested that cellular remodeling, in the form of a decreased cellular elasticity and viscosity, occurred during the process of neutrophil aspiration. Taken together, our simulation results on optically-stretched fibroblasts and aspirated neutrophils suggested that cells in general are able to sense mechanical stresses and respond by varying their material properties during deformation.EThOS - Electronic Theses Online ServiceAgency of Science, Technology and Research.GBUnited Kingdo

Tracking of tumor motion in lung cancer using patient specific finite element modeling and 4D-MRI image data

This paper presents a study that demonstrates the potential of using finite element (FE) lung model constructed using 4D-MRI (3D + time) for tracking tumor motion during a respiratory cycle. A series of volumetric images of one lung cancer patient was acquired over time under free breathing and sorted into respiratory phases. A FE model of the lung with the tumor was constructed using the volume which is at full exhale phase. Displacement field from this initial volume to the subsequent 3D volumes in the respiratory phases were derived using a deformable image registration technique. This displacement field which provides displacement information of the lung surface is then used to predict the tumor motion in the lung interior using the FE model. Our results showed that the tumor motion (as represented by the trajectory of the tumor centroid) follows a highly non-linear path during the respiratory cycle from the full exhale phase to the full inhale phase. We also showed that the predicted tumor motion from our FE model is in reasonable agreement with that computed from 4D-MRI

Correlation between strain magnitudes and phosphorylation level.

<p>(A) Scatterplot of ERK phosphorylation levels against applied strains, obtained from three independent experiments (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0090665#pone-0090665-g006" target="_blank">Figure 6C</a>). Pearson’s correlation coefficient (R) was calculated and found to be statistically significant (R = 0.80, <i>n</i> = 15, <i>p</i><0.01). (B) Scatterplot of tyrosine phosphorylation levels against applied strains, obtained from three independent experiments (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0090665#pone-0090665-g006" target="_blank">Figure 6D</a>). Pearson’s correlation coefficients between phosphorylation level and strain magnitude were calculated for four bands (200 kDa, 125 kDA, 33 kDa, 17 kDa) in the phosphotyrosine blot (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0090665#pone-0090665-g006" target="_blank">Figure 6D</a>). The 125 kDa and 17 kDa bands showed moderate positive correlation with applied strain magnitude (R = 0.48 and R = 0.36, respectively). However, none of the coefficients were statistically significant (<i>n</i> = 15, <i>p</i>>0.05 for all R).</p

Cell culture on collagen-coated PDMS membranes.

<p>(A) Phase-contrast images (20 X) of RPTP-α^+/+ MEFs (left) and HEK 293A cells (right), respectively. The upper row shows images of cells cultured on the PDMS membrane, while the lower row depicts cells on standard tissue-culture plastics (polystyrene). Scale bars: 50 µm. (B) Images of an RPTP-α^+/+ MEF cell before (left) and after (right) application of 10% equibiaxial strain. The diagonal lines indicate the cell length before stretching the membrane. Note the increase of the cell dimension upon membrane stretching. Scale bars: 20 µm. The images were acquired using a manually operated device (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0090665#pone.0090665.s003" target="_blank">Figure S3</a>).</p

Finite element simulations to select membrane dimensions.

<p>(A) Cross sectional sketch of proposed membrane with wall (not to scale). Red arrows indicate the region near the junction of the wall and the membrane, where strain heterogeneity can arise. To reduce this heterogeneity, values for the wall thickness (i) and the wall height (ii) were selected by varying them in finite element simulations. (B) Deformation of the PDMS membrane for Design 1 (top) and Design 2 (bottom) computed by asymmetrical finite element modeling. Colors indicate magnitude of total displacement. Wall thicknesses for Design 1 and 2 are 0.5 mm and 1 mm, respectively. For both Designs 1 and 2, the thickness of the base membrane is 0.5 mm, and the wall height is 10 mm. (C) Normalized radial strain (<i>e_r</i>/<i>e_r0</i>) profiles for both designs near the wall-membrane junction. Design 1: <i>e_r0</i> = 8.24%, Design 2: <i>e_r0</i> = 7.76%. Note the smaller variation near the wall interface in Design 2 as compared to that in Design 1.</p

Variation of strain on the membrane surface against downward displacement.

<p>(A) A snapshot of the regular grid of displacement vectors computed using the particle image velocimetry (PIV) algorithm. This set of displacement vectors tracks the motion of the marker positions as the holding plate is displaced downwards by 3.5 mm. The white circle and the red polygonal line denote the boundary of the culture surface and the boundary for strain computation presented in (E), respectively. (B – D) Mean and standard deviation of the radial (E_rr), circumferential (E_cc), and shear (E_rc) components of the strain field over the entire culture surface, respectively, plotted against corresponding downward holding plate displacement during one loading-unloading cycle. At each holding plate displacement, data points from the four membranes are horizontally staggered to allow results from individual membranes to be seen. The data points in red indicate the loading phase, during which the holding plate is being displaced downward from its initial position (0 mm) to a maximum of 11.5 mm; the data points in blue indicate the unloading phase, during which the holding plate is displaced back to its initial position. The shear strain is consistently zero regardless of the displacement of the holding plate. The curves for the radial and circumferential strains show strong overlap. Some hysteresis is seen when the membrane is unloaded; however, upon returning to the zero position, E_rr and E_cc are both consistently zero. (E) Color intensity maps of the radial and circumferential components of strain over the culture surface of membrane 4 in (B), (C), and (D) during loading phase and displaced downward by 3.5 mm (top panel), 5.5 mm (middle panel), and 9.5 mm (bottom panel). The coefficient of variation (CV), defined as the ratio of the standard deviation to the mean, is given for each intensity map.</p