An Inverse Method for Predicting Tissue-Level Mechanics from Cellular Mechanical Input

Extracellular matrix (ECM) provides a dynamic three-dimensional structure which translates mechanical stimuli to cells. This local mechanical stimulation may direct biological function including tissue development. Theories describing the role of mechanical regulators hypothesize the cellular response to variations in the external mechanical forces on the ECM. The exact ECM mechanical stimulation required to generate a specific pattern of localized cellular displacement is still unknown. The cell to tissue inverse problem offers an alternative approach to clarify this relationship. Developed for structural dynamics, the inverse dynamics problem translates measurements of local state variables (at the cell level) into an unknown or desired forcing function (at the tissue or ECM level). This paper describes the use of eigenvalues (resonant frequencies), eigenvectors (mode shapes), and dynamic programming to reduce the mathematical order of a simplified cell–tissue system and estimate the ECM mechanical stimulation required for a specified cellular mechanical environment. Finite element and inverse numerical analyses were performed on a simple two-dimensional model to ascertain the effects of weighting parameters and a reduction of analytical modes leading toward a solution. Simulation results indicate that the reduced number of mechanical modes (from 30 to 14 to 7) can adequately reproduce an unknown force time history on an ECM boundary. A representative comparison between cell to tissue (inverse) and tissue to cell (boundary value) modeling illustrates the multiscale applicability of the inverse model

Manipulation of Suspended Single Cells by Microfluidics and Optical Tweezers

Chondrocytes and osteoblasts experience multiple stresses in vivo. The optimum mechanical conditions for cell health are not fully understood. This paper describes the optical and microfluidic mechanical manipulation of single suspended cells enabled by the μPIVOT, an integrated micron resolution particle image velocimeter (μPIV) and dual optical tweezers instrument (OT). In this study, we examine the viability and trap stiffness of cartilage cells, identify the maximum fluid-induced stresses possible in uniform and extensional flows, and compare the deformation characteristics of bone and muscle cells. These results indicate cell photodamage of chondrocytes is negligible for at least 20 min for laser powers below 30 mW, a dead cell presents less resistance to internal organelle rearrangement and deforms globally more than a viable cell, the maximum fluid-induced shear stresses are limited to ~15 mPa for uniform flows but may exceed 1 Pa for extensional flows, and osteoblasts show no deformation for shear stresses up to 250 mPa while myoblasts are more easily deformed and exhibit a modulated response to increasing stress. This suggests that global and/or local stresses can be applied to single cells without physical contact. Coupled with microfluidic sensors, these manipulations may provide unique methods to explore single cell biomechanics

Examination of the Slip Boundary Condition by μ-PIV and Lattice Boltzmann Simulations

This work examines the slip boundary condition by Lattice Boltzmann simulations, addresses the validity of the Navier's hypothesis that the slip velocity is proportional to the shear rate and compares the Lattice Boltzmann simulations to the experimental results of Tretheway and Meinhart (Phys. of Fluids, 14, L9-L12). The numerical simulation models the boundary condition as the probability, P, of a particle to bounce-back relative to the probability of specular reflection, 1- P. For channel flow, the numerically calculated velocity profiles are consistent with the experimental profiles for both the no-slip and slip cases. No-slip is obtained for a probability of 100% bounce-back, while a probability of 0.03 is required to generate a slip length and slip velocity consistent with the experimental results of Tretheway and Meinhart for a hydrophobic surface. The simulations indicate that for microchannel flow the slip length is nearly constant along the channel walls, while the slip velocity varies with wall position as a results of variations in shear rate. Thus, the resulting velocity profile in a channel flow is more complex than a simple combination of the no-slip solution and slip velocity as is the case for flow between two infinite parallel plates