Contemporary Models of Soft Biosolids: Biological Tissues, Scaffolds, and Cells

Michael Sacks, University of Texas at Austin
Greg Rodin, University of Texas at Austin
Victor Barocas, University of Minnesota

Computational implementation of physical and physiologically realistic constitutive models is critical for numerical simulation of soft biological tissues in a variety of biomedical applications. Simulation tools such as these are imperative in the design and simulation of native and engineered tissues. This symposium will thus focus on constitutive models and their use in computational frameworks specialized for soft biological tissues, scaffolds, and cells.  It is well established that the highly nonlinear and anisotropic mechanical behaviors of soft tissues are an emergent behavior of the underlying tissue microstructure. Thus, overviews of tissue and cellular structure and function will be presented, as well as methods for detailed comparisons with experimental data to insure faithful simulations of the macro-level stress-strain, and insights into adaptations of the fiber architecture under stress, such as fiber reorientation and fiber recruitment.  In addition to insights into native tissues, many important biomaterials are composed of multiple layers of networked fibers. Elastomeric fibrous scaffolds used in engineering soft tissues are a prime example. Since soft tissues undergo large deformations, the constituent fibers must have elastomeric characteristics and undergo large macroscopic deformations as a result of large rotations and strains.  These characteristics allow the scaffolds to duplicate many of the salient characteristics of the soft tissues they are intended to replace.  To meet these multi-faceted demands, one must develop a fundamental understanding of the underlying physical processes occurring within the scaffolds across multiple scales.  In structural deterministic approaches, the constituent microstructure is typically modeled by reproducing the material geometry at the fiber level using idealized fiber networks that are stochastically generated. The mechanics can be solved at its original micro-meso scales, or can be coupled to the macroscopic scale through a multi-scale technique such as volume averaging or homogenization. These models have shown predictive capacity potential at multiple length scales.  Next, since the underlying cell populations control the remodeling processes, it is important to develop mathematical models that are capable of describing the cell mechanical responses under different external stimuli. Attempts at modeling a cell in terms of a mixture have been proposed, but represent only a start. More sophisticated models are needed to better understand the influence of cellular constituents, such as α-SMA fibers, on the overall cellular biomechanics. Thus, we will also review contemporary approaches to computational models of cells with respect to their mechanical behaviors (e.g. stiffness, contraction).  The symposium will emphasize both analytical and computational models that focus on physical realism, along with computational efficiency for practical applications such as surgical simulations.