Biomechanics and Modeling in Mechanobiology

Plasma membrane of most cells is not smooth. The surfaces of both small and large micropermeable cells are folded and corrugated which makes mammalian cells to have a larger membrane surface than the supposed ideal mode, that is, the smooth sphere of the same volume. Since cancer is an anthropic disease, cancer cells tend to have a larger membrane area than normal cells. Therefore, cancer cells have higher folding factor and larger radius than normal and healthy cells. On the other hand, the prevalence of breast cancer has prompted researchers to improve the treatment options raised for the disease in the past. In this paper, the impact of folding factor of the cell surface has been investigated. Considering that AFM is one of the most effective tools in performing the tests at micro- and nanoscales, it was used to determine the topography of MCF10 cells and then the resulting images and results were used to experimentally extract the folding factor of cells. By applying this factor in the Hertz, DMT and JKR contact models in the elastic and viscoelastic states, these models have been modified and the simulation of the three models shows that the simulation results are closer to the experimental results by considering the folding in the calculations. Additionally, the simulation of 3D manipulation has been done in both elastic and viscoelastic states with and without consideration of folding. Finally, the results were compared to investigate the effects of folding of the cell surface to the critical force and critical time of sliding and rolling in contact with the substrate and AFM tip in the 3D manipulation model.

Cell migration plays an essential role in cancer metastasis. In cancer invasion through confined spaces, cells must undergo extensive deformation, which is a capability related to their metastatic potentials. Here, we simulate the deformation of the cell and nucleus during invasion through a dense, physiological microenvironment by developing a phenomenological computational model. In our work, cells are attracted by a generic emitting source (e.g., a chemokine or stiffness signal), which is treated by using Green’s Fundamental solutions. We use an IMEX integration method where the linear parts and the nonlinear parts are treated by using an Euler backward scheme and an Euler forward method, respectively. We develop the numerical model for an obstacle-induced deformation in 2D or/and 3D. Considering the uncertainty in cell mobility, stochastic processes are incorporated and uncertainties in the input variables are evaluated using Monte Carlo simulations. This quantitative study aims at estimating the likelihood for invasion and the length of the time interval in which the cell invades the tissue through an obstacle. Subsequently, the two-dimensional cell deformation model is applied to simplified cancer metastasis processes to serve as a model for in vivo or in vitro biomedical experiments.

Articular cartilage is known to be anisotropic and inhomogeneous because of its microstructure. In particular, its elastic properties are influenced by the arrangement of the collagen fibres, which are orthogonal to the bone-cartilage interface in the deep zone, randomly oriented in the middle zone, and parallel to the surface in the superficial zone. In past studies, cartilage permeability has been related directly to the orientation of the glycosaminoglycan chains attached to the proteoglycans which constitute the tissue matrix. These studies predicted permeability to be isotropic in the undeformed configuration, and anisotropic under compression. They neglected tissue anisotropy caused by the collagen network. However, magnetic resonance studies suggest that fluid flow is “directed” by collagen fibres in biological tissues. Therefore, the aim of this study was to express the permeability of cartilage accounting for the microstructural anisotropy and inhomogeneity caused by the collagen fibres. Permeability is predicted to be anisotropic and inhomogeneous, independent of the state of strain, which is consistent with the morphology of the tissue. Looking at the local anisotropy of permeability, we may infer that the arrangement of the collagen fibre network plays an important role in directing fluid flow to optimise tissue functioning.

Optimal strength and stability of blood clots are keys to hemostasis and in prevention of hemorrhagic or thrombotic complications. Clots are biocomposite materials composed of fibrin network enmeshing platelets and other blood cells. We have previously shown that the storage temperature of platelets significantly impacts clot structure and stiffness. The objective of this work is to delineate the relationship between morphological characteristics and mechanical response of clot networks. We examined scanning electron microscope images of clots prepared from fresh apheresis platelets, and from apheresis platelets stored for 5 days at room temperature or at 4 °C, suspended in pooled plasma. Principal component analysis of nine different morphometric parameters revealed that a single principal component (PC1) can distinguish the effect of platelet storage on clot ultrastructure. Finite element analysis of clot response to uniaxial strain was used to map the spatially heterogeneous distribution of strain energy density for each clot. At modest deformations (25% strain), a single principal component (PC2) was able to predict these heterogeneities as quantified by variability in strain energy density distribution and in linear elastic stiffness, respectively. We have identified structural parameters that are primary regulators of stress distribution, and the observations provide insights into the importance of spatial heterogeneity on hemostasis and thrombosis.

Characterising the mechanical properties of flowing microcapsules is important from both fundamental and applied points of view. In the present study, we develop a novel multilayer perceptron (MLP)-based machine learning (ML) approach, for real-time simultaneous predictions of the membrane mechanical law type, shear and area-dilatation moduli of microcapsules, from their camera-recorded steady profiles in tube flow. By MLP, we mean a neural network where many perceptrons are organised into layers. A perceptron is a basic element that conducts input–output mapping operation. We test the performance of the present approach using both simulation and experimental data. We find that with a reasonably high prediction accuracy, our method can reach an unprecedented low prediction latency of less than 1 millisecond on a personal computer. That is the overall computational time, without using parallel computing, from a single experimental image to multiple capsule mechanical parameters. It is faster than a recently proposed convolutional neural network-based approach by two orders of magnitude, for it only deals with the one-dimensional capsule boundary instead of the entire two-dimensional capsule image. Our new approach may serve as the foundation of a promising tool for real-time mechanical characterisation and online active sorting of deformable microcapsules and biological cells in microfluidic devices.

In this work, a nonlinear strain rate dependent plugin developed for the OpenSim® platform was used to estimate the instantaneous strain rate (ISR) and the forces on the ACL’s anteromedial (aACL) and posterolateral (pACL) bundles during walking and sudden change of direction of running termed as ‘plant-and-cut’ (PC). The authors obtained the kinematics data for walking via optical motion capture. PC movements, along with running kinematics, were obtained from the literature. A nonlinear plugin developed for ligaments was interfaced with OpenSim® platform to simulate walking and PC motions with a flexed knee and an extended knee. PC phase is sandwiched between an approach phase and take-off phase and was studied at various event velocities (1.8, 3, and 4.2 m s−1), and angles of PC (23°, 34°, and 45°) as encountered in adult ball games. In both cases of PC-with-extended knee and PC-with-flexed-knee, the maximum forces on both the ACL bundles were observed after the take-off phase. A maximum force of ~ 35 N kg−1 of body weight (BW) was observed on aACL after the take-off phase for an event velocity of 4.2 m s−1. In the posterolateral bundle (pACL), the maximum forces (~ 40 N kg−1 of BW) were observed towards the end of the mid-swing phase (after the take-off phase) for the various combinations of the parameters studied. The forces observed in the simulation of PC-with-flexed-knee and PC-with-extended-knee has resulted in magnitude higher than sustainable by the adults. This study is novel in attempting to incorporate differing rates-of-strain that have been shown to alter soft tissue properties into the OpenSim® musculoskeletal model. The proposed model can be used by researchers to predict the forces during various kinematic activities for other soft tissues.

It is well argued that osteocytes are mechanosensory cells and are involved in the regulation of bone remodeling. In previous works, the predictions from a simulation model have suggested that both the influencing distance of osteocytes and the magnitude of the mechanical loads determine the thickness of trabeculae whereas the number of osteocytes primarily affects the rate of bone remodeling. The question that remains not completely answered is: for the same number of osteocytes, what is the effect of different distributions on the remodeling process? Based on a particular regulatory bone remodeling model, the question is addressed, in part, by performing a stability analysis in connection with numerical simulations. The results allow us to demonstrate that, on one hand, we cannot reach a conclusion about the stability of the model for a nonuniform osteocyte distribution. This implies that there is no relationship between the different parameters conveying the stability of the model. On the other hand, we show that the osteocyte cell distribution has a significant influence on the bone morphology, which seems to be confirmed by simulations with real data obtained from rat tibia.