On a Class of Admissible Constitutive Behaviors in Free-Floating Engineered Tissues

Anisotropy profoundly alters stress fields within contractile cells and cell aggregates

Many biological phenomena such as cell proliferation and death are correlated with stress fields within cells. Stress fields are quantified using computational methods which rely on fundamental assumptions about local mechanical properties. Most existing methods such as Monolayer Stress Microscopy assume isotropic properties, yet experimental observations strongly suggest anisotropy. We first model anisotropy in circular cells analytically using Eshelby's inclusion method. Our solution reveals that uniform anisotropy cannot exist in cells due to the occurrence of substantial stress concentration in the central region. A more realistic non-uniform anisotropy model is then introduced based on experimental observations and implemented numerically which interestingly clears out stress concentration. Stresses within the entire aggregate also drastically change compared to the isotropic case, resulting in better agreement with observed biomarkers. We provide a physics-based mechanism to explain the low alignment of stress fibers in the center of cells, which might explain certain biological phenomena e.g., existence of disrupted rounded cells, and higher apoptosis rate at the center of circular aggregates.

Collagen gel contraction assays: From modelling wound healing to quantifying cellular interactions with three-dimensional extracellular matrices

Cells respond to and actively remodel the extracellular matrix (ECM). The dynamic and bidirectional interaction between cells and ECM, especially their mechanical interactions, has been found to play an essential role in triggering a series of complex biochemical and biomechanical signal pathways and in regulating cellular functions and behaviours. The collagen gel contraction assay (CGCA) is a widely used method to investigate cell-ECM interactions in 3D environments and provides a mechanically associated readout reflecting 3D cellular contractility. In this review, we summarize various versions of CGCA, with an emphasis on recent high-throughput and low-consumption CGCA techniques. More importantly, we focus on the technique of force monitoring during the contraction of collagen gel, which provides a quantitative characterization of the overall forces generated by all the resident cells in the collagen hydrogel. Accordingly, we present recent biological applications of the CGCA, which have expanded from the initial wound healing model to other studies concerning cell-ECM interactions, including fibrosis, cancer, tissue repair and the preparation of biomimetic microtissues.

Constitutive modeling of compressible type-I collagen hydrogels

Collagen hydrogels have been used ubiquitously as engineering biomaterials with a biphasic network of fibrillar collagen and aqueous-filled voids that contribute to a complex, compressible, and nonlinear mechanical behavior - not well captured within the infinitesimal strain theory. In this study, type-I collagen, processed from a bovine corium, was fabricated into disks at 2, 3, and 4% (w/w) and exposed to 0, 105, 106, and 107 microjoules of ultraviolet light or enzymatic degradation via matrix metalloproteinase-2. Fully hydrated gels were subjected to unconfined, aqueous, compression testing with experimental data modeled within a continuum mechanics framework by employing the uncommon Blatz-Ko material model for porous elastic materials and a nonlinear form of the Poisson's ratio. From the Generalized form, the Special Blatz-Ko, compressible Neo-Hookean, and incompressible Mooney-Rivlin models were derived and the best-fit material parameters reported for each. The average root-mean-squared (RMS) error for the General (RMS = 0.13 ± 0.07) and Special Blatz-Ko (RMS = 0.13 ± 0.07) were lower than the Neo-Hookean (RMS = 0.23 ± 0.10) and Mooney-Rivlin (RMS = 0.18 ± 0.08) models. We conclude that, with a single fitted-parameter, the Special Blatz-Ko sufficiently captured the salient features of collagen hydrogel compression over most examined formulations and treatments.

Growth and Remodeling of Load-Bearing Biological Soft Tissues

The past two decades reveal a growing role of continuum biomechanics in understanding homeostasis, adaptation, and disease progression in soft tissues. In this paper, we briefly review the two primary theoretical approaches for describing mechano-regulated soft tissue growth and remodeling on the continuum level as well as hybrid approaches that attempt to combine the advantages of these two approaches while avoiding their disadvantages. We also discuss emerging concepts, including that of mechanobiological stability. Moreover, to motivate and put into context the different theoretical approaches, we briefly review findings from mechanobiology that show the importance of mass turnover and the prestressing of both extant and new extracellular matrix in most cases of growth and remodeling. For illustrative purposes, these concepts and findings are discussed, in large part, within the context of two load-bearing, collagen dominated soft tissues - tendons/ligaments and blood vessels. We conclude by emphasizing further examples, needs, and opportunities in this exciting field of modeling soft tissues.

Tissue Transglutaminase, Not Lysyl Oxidase, Dominates Early Calcium-Dependent Remodeling of Fibroblast-Populated Collagen Lattices

Cell-populated collagen gels have provided significant insight into the cellular contractile mechanisms and cell-matrix interactions that are necessary for compacting and remodeling extant matrix. Nevertheless, little research has been devoted towards determining how cells entrench these deformations that contribute to establishing a preferred mechanical state. To this end, we examined the roles of two covalent matrix cross-linkers, i.e. tissue transglutaminase and lysyl oxidase, during global remodeling of the free-floating fibroblast-populated collagen lattice. Inhibition of tissue transglutaminase resulted in a reduced rate of compaction compared to controls during early remodeling (up to 2 days). In contrast, inhibition of lysyl oxidase did not alter the early compaction of these lattices, but it reduced the compaction after 2 days of culture. Acute inhibition of different contractile mechanisms suggested further that calcium-dependent contractility may have dominated during the initial remodeling of the collagen lattice before giving way to calcium-independent contractility at later times. In summary, these findings suggest that early remodeling of the free-floating collagen lattice is facilitated by calcium-dependent cell contraction while entrenchment is dominated by a tissue transglutaminase-mediated cross-linking of the extant matrix. As remodeling continues, however, lysyl oxidase increases its contribution, perhaps by consolidating de novo collagen fibrils into fibers to continue the remodeling while the cells transition to a more sustained, calcium-independent contractility. These results promise to influence future tissue engineering studies as well as computational simulations aimed at understanding matrix remodeling in complex in vivo situations.

Computational model of matrix remodeling and entrenchment in the free-floating fibroblast-populated collagen lattice

Tissue equivalents represent excellent model systems for elucidating principles of mechanobiology and for exploring methods to improve the functionality of tissue-engineered constructs. The simplest tissue equivalent is the free-floating fibroblast-populated collagen lattice. Although introduced over 30 years ago, the associated mechanics of the cell-mediated compaction of this lattice was only recently analyzed in detail. The goal of this paper was to build on this recent stress analysis by developing a computational model of the evolving geometry, regionally varying material properties and cell stresses, and overall residual stress fields during the first two days of compaction. Baseline results were found to agree well with most experimental observations, namely evolving changes in radius, thickness, and material symmetry, yet hypothesis testing revealed aspects of the mechanobiology that require more experimental attention. Given the generality of the proposed framework, we submit that modifications and refinements can be used to study many similar systems and thereby help guide future experiments.

Regulating tension in three-dimensional culture environments

The processes of development, repair, and remodeling of virtually all tissues and organs, are dependent upon mechanical signals including external loading, cell-generated tension, and tissue stiffness. Over the past few decades, much has been learned about mechanotransduction pathways in specialized two-dimensional culture systems; however, it has also become clear that cells behave very differently in two- and three-dimensional (3D) environments. Three-dimensional in vitro models bring the ability to simulate the in vivo matrix environment and the complexity of cell-matrix interactions together. In this review, we describe the role of tension in regulating cell behavior in three-dimensional collagen and fibrin matrices with a focus on the effective use of global boundary conditions to modulate the tension generated by populations of cells acting in concert. The ability to control and measure the tension in these 3D culture systems has the potential to increase our understanding of mechanobiology and facilitate development of new ways to treat diseased tissues and to direct cell fate in regenerative medicine and tissue engineering applications.

Mechanical restrictions on biological responses by adherent cells within collagen gels

Cell-seeded collagen and fibrin gels represent excellent assays for studying interactions between adherent interstitial cells and the three-dimensional extracellular matrix in which they reside. Over one hundred papers have employed the free-floating collagen gel assay alone since its introduction in 1979 and much has been learned about mechanobiological responses of diverse types of cells. Yet, given that mechanobiology is the study of biological responses by cells to mechanical stimuli that must respect the basic laws of mechanics, we must quantify better the mechanical conditions that are imposed on or arise in cell-seeded gels. In this paper, we suggest that cell responses and associated changes in matrix organization within the classical free-floating gel assay are highly restricted by the mechanics. In particular, many salient but heretofore unexplained or misinterpreted observations in free-floating gels can be understood in terms of apparent cell-mediated residual stress fields that satisfy quasi-static equilibria and continuity of tractions. There is a continuing need, therefore, to bring together the allied fields of mechanobiology and biomechanics as we continue to elucidate cellular function within both native connective tissues and tissue equivalents that are used in basic scientific investigations or regenerative medicine.