J Biomech Eng. 2013;135(7):070201-070201-2. doi:10.1115/1.4024634.

The Mathematical Biosciences Institute at The Ohio State University hosted a week-long workshop on tissue engineering and regenerative medicine (TERM) from April 30 to May 4, 2012. The workshop brought together 28 speakers from an array of disciplines, with an overarching goal of contributing to the development of mathematical and computational approaches that would allow one to rigorously understand, predict, and control complex biological processes relevant to TERM. Abstracts of the presentations, along with links to videos of many of the talks, can be found at http://mbi.osu.edu/2011/terabstracts.html. One theme that was common to many of these talks was a focus on biomechanical aspects of cell-matrix interactions. This special issue includes ten articles on cell-matrix interactions that were based on these talks.

Commentary by Dr. Valentin Fuster

Research Papers

J Biomech Eng. 2013;135(7):071001-071001-9. doi:10.1115/1.4024349.

The extracellular matrix is no longer considered a static support structure for cells but a dynamic signaling network with the power to influence cell, tissue, and whole organ physiology. In the myocardium, cardiac fibroblasts are the primary cell type responsible for the synthesis, deposition, and degradation of matrix proteins, and they therefore play a critical role in the development and maintenance of functional heart tissue. This review will summarize the extensive research conducted in vivo and in vitro, demonstrating the influence of both physical and chemical stimuli on cardiac fibroblasts and how these interactions impact both the extracellular matrix and, by extension, cardiomyocytes. This work is of considerable significance, given that cardiovascular diseases are marked by extensive remodeling of the extracellular matrix, which ultimately impairs the functional capacity of the heart. We seek to summarize the unique role of cardiac fibroblasts in normal cardiac development and the most prevalent cardiac pathologies, including congenital heart defects, hypertension, hypertrophy, and the remodeled heart following myocardial infarction. We will conclude by identifying existing holes in the research that, if answered, have the potential to dramatically improve current therapeutic strategies for the repair and regeneration of damaged myocardium via mechanotransductive signaling.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(7):071002-071002-7. doi:10.1115/1.4023984.

The formation of microvascular networks (MVNs) is influenced by many aspects of the microenvironment, including soluble and insoluble biochemical factors and the biophysical properties of the surrounding matrix. It has also become clear that a dynamic and reciprocal interaction between the matrix and cells influences cell behavior. In particular, local matrix remodeling may play a role in driving cellular behaviors, such as MVN formation. In order to explore the role of matrix remodeling, an in vitro model of MVN formation involving suspending human umbilical vein endothelial cells within collagen hydrogels was used. The resulting cell and matrix morphology were microscopically observed and quantitative metrics of MVN formation and collagen gathering were applied to the resulting images. The macroscopic compaction of collagen gels correlates with the extent of MVN formation in gels of different stiffness values, with compaction preceding elongation leading to MVN formation. Furthermore, the microscopic analysis of collagen between cells at early timepoints demonstrates the alignment and gathering of collagen between individual adjacent cells. The results presented are consistent with the hypothesis that endothelial cells need to gather and align collagen between them as an early step in MVN formation.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(7):071003-071003-10. doi:10.1115/1.4024463.

Using a top-down approach, an agent-based model was developed within NetLogo where cells and extracellular matrix (ECM) fibers were composed of multiple agents to create deformable structures capable of exerting, reacting to, and transmitting mechanical force. At the beginning of the simulation, long fibers were randomly distributed and cross linked. Throughout the simulation, imposed rules allowed cells to exert traction forces by extending pseudopodia, binding to fibers and pulling them towards the cell. Simulated cells remodeled the fibrous matrix to change both the density and alignment of fibers and migrated within the matrix in ways that are consistent with previous experimental work. For example, cells compacted the matrix in their pericellular regions much more than the average compaction experienced for the entire matrix (696% versus 21%). Between pairs of cells, the matrix density increased (by 92%) and the fibers became more aligned (anisotropy index increased from 0.45 to 0.68) in the direction parallel to a line connecting the two cells, consistent with the “lines of tension” observed in experiments by others. Cells migrated towards one another at an average rate of ∼0.5 cell diameters per 10,000 arbitrary units (AU); faster migration occurred in simulations where the fiber density in the intercellular area was greater. To explore the potential contribution of matrix stiffness gradients in the observed migration (i.e., durotaxis), the model was altered to contain a regular lattice of fibers possessing a stiffness gradient and just a single cell. In these simulations cells migrated preferentially in the direction of increasing stiffness at a rate of ∼2 cell diameter per 10,000 AU. This work demonstrates that matrix remodeling and durotaxis, both complex phenomena, might be emergent behaviors based on just a few rules that control how a cell can interact with a fibrous ECM.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(7):071004-071004-9. doi:10.1115/1.4024460.

Engineered tissues are commonly stretched or compressed (i.e., conditioned) during culture to stimulate extracellular matrix (ECM) production and to improve the mechanical properties of the growing construct. The relationships between mechanical stimulation and ECM remodeling, however, are complex, interdependent, and dynamic. Thus, theoretical models are required for understanding the underlying phenomena so that the conditioning process can be optimized to produce functional engineered tissues. Here, we continue our development of multiscale mechanical models by simulating the effect of cell tractions on developing isometric tension and redistributing forces in the surrounding fibers of a collagen gel embedded with explants. The model predicted patterns of fiber reorganization that were similar to those observed experimentally. Furthermore, the inclusion of cell compaction also changed the distribution of fiber strains in the gel compared to the acellular case, particularly in the regions around the cells where the highest strains were found.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(7):071005-071005-9. doi:10.1115/1.4024139.

We present a modeling and computational approach to study fusion of multicellular aggregates during tissue and organ fabrication, which forms the foundation for the scaffold-less biofabrication of tissues and organs known as bioprinting. It is known as the phase field method, where multicellular aggregates are modeled as mixtures of multiphase complex fluids whose phase mixing or separation is governed by interphase force interactions, mimicking the cell-cell interaction in the multicellular aggregates, and intermediate range interaction mediated by the surrounding hydrogel. The material transport in the mixture is dictated by hydrodynamics as well as forces due to the interphase interactions. In a multicellular aggregate system with fixed number of cells and fixed amount of the hydrogel medium, the effect of cell differentiation, proliferation, and death are neglected in the current model, which can be readily included in the model, and the interaction between different components is dictated by the interaction energy between cell and cell as well as between cell and medium particles, respectively. The modeling approach is applicable to transient simulations of fusion of cellular aggregate systems at the time and length scale appropriate to biofabrication. Numerical experiments are presented to demonstrate fusion and cell sorting during tissue and organ maturation processes in biofabrication.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(7):071006-071006-5. doi:10.1115/1.4024199.

Cells imbedded in biopolymer gels are important components of tissue engineering models and cancer tumor microenvironments. In both these cases, contraction of cells attached to the gel is an important phenomenon, and the nonlinear nature of most biopolymers (such as collagen) makes understanding the mechanics of the contraction a challenging problem. Here, we investigate a unique feature of such systems: a point source of contraction leads to substantial deformation of the environment, but large strains and large alignment of the fibers of the gel are confined to a small region surrounding the source. For fibroblasts in collagen-I, we estimate that the radius of this region is of order 90 μ. We investigate this idea using continuum estimates and a finite element code, and we point out experimental manifestations of the effect.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(7):071007-071007-9. doi:10.1115/1.4024350.

In addition to their obvious biological roles in tissue function, cells often play a significant mechanical role through a combination of passive and active behaviors. This study focused on the passive mechanical contribution of cells in tissues by improving our multiscale model via the addition of cells, which were treated as dilute spherical inclusions. The first set of simulations considered a rigid cell, with the surrounding ECM modeled as (1) linear elastic, (2) Neo-Hookean, and (3) a fiber network. Comparison with the classical composite theory for rigid inclusions showed close agreement at low cell volume fraction. The fiber network case exhibited nonlinear stress–strain behavior and Poisson's ratios larger than the elastic limit of 0.5, characteristics similar to those of biological tissues. The second set of simulations used a fiber network for both the cell (simulating cytoskeletal filaments) and matrix, and investigated the effect of varying relative stiffness between the cell and matrix, as well as the effect of a cytoplasmic pressure to enforce incompressibility of the cell. Results showed that the ECM network exerted negligible compression on the cell, even when the stiffness of fibers in the network was increased relative to the cell. Introduction of a cytoplasmic pressure significantly increased the stresses in the cell filament network, and altered how the cell changed its shape under tension. Findings from this study have implications on understanding how cells interact with their surrounding ECM, as well as in the context of mechanosensation.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(7):071008-071008-10. doi:10.1115/1.4023987.

A force based model of cell migration is presented which gives new insight into the importance of the dynamics of cell binding to the substrate. The main features of the model are the focus on discrete attachment dynamics, the treatment of the cellular forces as springs, and an incorporation of the stochastic nature of the attachment sites. One goal of the model is to capture the effect of the random binding and unbinding of cell attachments on global cell motion. Simulations reveal one of the most important factor influencing cell speed is the duration of the attachment to the substrate. The model captures the correct velocity and force relationships for several cell types.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(7):071009-071009-9. doi:10.1115/1.4024467.

The interactions between adherent cells and their extracellular matrix (ECM) have been shown to play an important role in many biological processes, such as wound healing, morphogenesis, differentiation, and cell migration. Cells attach to the ECM at focal adhesion sites and transmit contractile forces to the substrate via cytoskeletal actin stress fibers. This contraction results in traction stresses within the substrate/ECM. Traction force microscopy (TFM) is an experimental technique used to quantify the contractile forces generated by adherent cells. In TFM, cells are seeded on a flexible substrate and displacements of the substrate caused by cell contraction are tracked and converted to a traction stress field. The magnitude of these traction stresses are normally used as a surrogate measure of internal cell contractile force or contractility. We hypothesize that in addition to contractile force, other biomechanical properties including cell stiffness, adhesion energy density, and cell morphology may affect the traction stresses measured by TFM. In this study, we developed finite element models of the 2D and 3D TFM techniques to investigate how changes in several biomechanical properties alter the traction stresses measured by TFM. We independently varied cell stiffness, cell-ECM adhesion energy density, cell aspect ratio, and contractility and performed a sensitivity analysis to determine which parameters significantly contribute to the measured maximum traction stress and net contractile moment. Results suggest that changes in cell stiffness and adhesion energy density can significantly alter measured tractions, independent of contractility. Based on a sensitivity analysis, we developed a correction factor to account for changes in cell stiffness and adhesion and successfully applied this correction factor algorithm to experimental TFM measurements in invasive and noninvasive cancer cells. Therefore, application of these types of corrections to TFM measurements can yield more accurate estimates of cell contractility.

Commentary by Dr. Valentin Fuster
J Biomech Eng. 2013;135(7):071010-071010-12. doi:10.1115/1.4024619.

Delineating the normal postnatal development of the pulmonary artery (PA) and ascending aorta (AA) can inform our understanding of congenital abnormalities, as well as pulmonary and systolic hypertension. We thus conducted the following study to delineate the PA and AA postnatal growth deformation characteristics in an ovine model. MR images were obtained from endoluminal surfaces of 11 animals whose ages ranged from 1.5 months/15.3 kg mass (very young) to 12 months/56.6 kg mass (adult). A bicubic Hermite finite element surface representation was developed for the each artery from each animal. Under the assumption that the relative locations of surface points were retained during growth, the individual animal surface fits were subsequently used to develop a method to estimate the time-evolving local effective surface growth (relative to the youngest measured animal) in the end-diastolic state. Results indicated that the spatial and temporal surface growth deformation patterns of both arteries, especially in the circumferential direction, were heterogeneous, leading to an increase in taper and increase in cross-sectional ellipticity of the PA. The longitudinal PA growth stretch of a large segment on the posterior wall reached 2.57 ± 0.078 (mean ± SD) at the adult stage. In contrast, the longitudinal growth of the AA was smaller and more uniform (1.80 ± 0.047). Interestingly, a region of the medial wall of both arteries where both arteries are in contact showed smaller circumferential growth stretches—specifically 1.12 ± 0.012 in the PA and 1.43 ± 0.071 in the AA at the adult stage. Overall, our results indicated that contact between the PA and AA resulted in increasing spatial heterogeneity in postnatal growth, with the PA demonstrating the greatest changes. Parametric studies using simplified geometric models of curved arteries during growth suggest that heterogeneous effective surface growth deformations must occur to account for the changes in measured arterial shapes during the postnatal growth period. This result suggests that these first results are a reasonable first-approximation to the actual effective growth patterns. Moreover, this study clearly underscores how functional growth of the PA and AA during postnatal maturation involves complex, local adaptations in tissue formation. Moreover, the present results will help to lay the basis for functional replacement by defining critical geometric metrics.

Commentary by Dr. Valentin Fuster

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