Edward A. Sander

Image-based multiscale modeling predicts tissue-level and network-level fiber reorganization in stretched cell-compacted collagen gels

The mechanical environment plays an important role in cell signaling and tissue homeostasis. Unraveling connections between externally applied loads and the cellular response is often confounded by extracellular matrix (ECM) heterogeneity. Image-based multiscale models provide a foundation for examining the fine details of tissue behavior, but they require validation at multiple scales. In this study, we developed a multiscale model that captured the anisotropy and heterogeneity of a cell-compacted collagen gel subjected to an off-axis hold mechanical test and subsequently to biaxial extension. In both the model and experiments, the ECM reorganized in a nonaffine and heterogeneous manner that depended on multiscale interactions between the fiber networks. Simulations predicted that tensile and compressive fiber forces were produced to accommodate macroscopic displacements. Fiber forces in the simulation ranged from −11.3 to 437.7 nN, with a significant fraction of fibers under compression (12.1% during off-axis stretch). The heterogeneous network restructuring predicted by the model serves as an example of how multiscale modeling techniques provide a theoretical framework for understanding relationships between ECM structure and tissue-level mechanical properties and how microscopic fiber rearrangements could lead to mechanotransductive cell signaling.

Permeability calculations in three-dimensional isotropic and oriented fiber networks

Hydraulic permeabilities of fiber networks are of interest for many applications and have been studied extensively. There is little work, however, on permeability calculations in three-dimensional random networks. Computational power is now sufficient to calculate permeabilities directly by constructing artificial fiber networks and simulating flow through them. Even with todays high-performance computers, however, such an approach would be infeasible for large simulations. It is therefore necessary to develop a correlation based on fiber volume fraction, radius, and orientation, preferably by incorporating previous studies on isotropic or structured networks. In this work, the direct calculations were performed, using the finite element method, on networks with varying degrees of orientation, and combinations of results for flows parallel and perpendicular to a single fiber or an array thereof, using a volume-averaging theory, were compared to the detailed analysis. The detailed model agreed well with existing analytical solutions for square arrays of fibers up to fiber volume fractions of 46% for parallel flow and 33% for transverse flow. Permeability calculations were then performed for isotropic and oriented fiber networks within the fiber volume fraction range of 0.3%-15%. When drag coefficients for spatially periodic arrays were used, the results of the volume-averaging method agreed well with the direct finite element calculations. On the contrary, the use of drag coefficients for isolated fibers overpredicted the permeability for the volume fraction range that was employed. We concluded that a weighted combination of drag coefficients for spatially periodic arrays of fibers could be used as a good approximation for fiber networks, which further implies that the effect of the fiber volume fraction and orientation on the permeability of fiber networks are more important than the effect of local network structure.

Nonlinear strain stiffening is not sufficient to explain how far cells can feel on fibrous protein gels.

Recent observations suggest that cells on fibrous extracellular matrix materials sense mechanical signals over much larger distances than they do on linearly elastic synthetic materials. In this work, we systematically investigate the distance fibroblasts can sense a rigid boundary through fibrous gels by quantifying the spread areas of human lung fibroblasts and 3T3 fibroblasts cultured on sloped collagen and fibrin gels. The cell areas gradually decrease as gel thickness increases from 0 to 150 μm, with characteristic sensing distances of >65 μm below fibrin and collagen gels, and spreading affected on gels as thick as 150 μm. These results demonstrate that fibroblasts sense deeper into collagen and fibrin gels than they do into polyacrylamide gels, with the latter exhibiting characteristic sensing distances of <5 μm. We apply finite-element analysis to explore the role of strain stiffening, a characteristic mechanical property of collagen and fibrin that is not observed in polyacrylamide, in facilitating mechanosensing over long distances. Our analysis shows that the effective stiffness of both linear and nonlinear materials sharply increases once the thickness is reduced below 5 μm, with only a slight enhancement in sensitivity to depth for the nonlinear material at very low thickness and high applied traction. Multiscale simulations with a simplified geometry predict changes in fiber alignment deep into the gel and a large increase in effective stiffness with a decrease in substrate thickness that is not predicted by nonlinear elasticity. These results suggest that the observed cell-spreading response to gel thickness is not explained by the nonlinear strain-stiffening behavior of the material alone and is likely due to the fibrous nature of the proteins.

In vitro evaluation of carbon-nanotube-reinforced bioprintable vascular conduits

Vascularization of thick engineered tissue and organ constructs like the heart, liver, pancreas or kidney remains a major challenge in tissue engineering. Vascularization is needed to supply oxygen and nutrients and remove waste in living tissues and organs through a network that should possess high perfusion ability and significant mechanical strength and elasticity. In this paper, we introduce a fabrication process to print vascular conduits directly, where conduits were reinforced with carbon nanotubes (CNTs) to enhance their mechanical properties and bioprintability. In vitro evaluation of printed conduits encapsulated in human coronary artery smooth muscle cells was performed to characterize the effects of CNT reinforcement on the mechanical, perfusion and biological performance of the conduits. Perfusion and permeability, cell viability, extracellular matrix formation and tissue histology were assessed and discussed, and it was concluded that CNT-reinforced vascular conduits provided a foundation for mechanically appealing constructs where CNTs could be replaced with natural protein nanofibers for further integration of these conduits in large-scale tissue fabrication.

Image-based biomechanics of collagen-based tissue equivalents

In this study, we compared experimentally measured fiber network kinematics and the macroscopic mechanical response from cell-compacted, cross-shaped collagen gels (cruciforms), with the predictions from our multiscale modeling technique. The macroscopic finite element model matched the physical dimensions and boundary conditions of the experimental cruciform to be modeled. Different microscale network models were constructed for each finite element that matched fiber microstructure described by maps of the local direction and strength of alignment obtained from polarimetric alignment imaging. The outputs of the multiscale model included the macroscopic load-deformation response and the microscopic (fiber) kinematics.

Disorganized collagen scaffold interferes with fibroblast mediated deposition of organized extracellular matrix in vitro

Many tissue engineering applications require the remodeling of a degradable scaffold either in vitro or in situ. Although inefficient remodeling or failure to fully remodel the temporary matrix can result in a poor clinical outcome, very few investigations have examined in detail, the interaction of regenerative cells with temporary scaffoldings. In a recent series of investigations, randomly oriented collagen gels were directly implanted into human corneal pockets and followed for 24 months. The resulting remodeling response exhibited a high degree of variability which likely reflects differing regenerative/synthetic capacity across patients. Given this variability, we hypothesize that a disorganized, degradable provisional scaffold could be disruptive to a uniform, organized reconstruction of stromal matrix. In this investigation, two established corneal stroma tissue engineering culture systems (collagen scaffold‐based and scaffold‐free) were compared to determine if the presence of the disorganized collagen gel influenced matrix production and organizational control exerted by primary human corneal fibroblast cells (PHCFCs). PHCFCs were cultured on thin disorganized reconstituted collagen substrate (RCS—five donors: average age 34.4) or on a bare polycarbonate membrane (five donors: average age 32.4 controls). The organization and morphology of the two culture systems were compared over the long‐term at 4, 8, and 11/12 weeks. Construct thickness and extracellular matrix organization/alignment was tracked optically with bright field and differential interference contrast (DIC) microscopy. The details of cell/matrix morphology and cell/matrix interaction were examined with standard transmission, cuprolinic blue and quick‐freeze/deep‐etch electron microscopy. Both the scaffold‐free and the collagen‐based scaffold cultures produced organized arrays of collagen fibrils. However, at all time points, the amount of organized cell‐derived matrix in the scaffold‐based constructs was significantly lower than that produced by scaffold‐free constructs (controls). We also observed significant variability in the remodeling of RCS scaffold by PHCFCs. PHCFCs which penetrated the RCS scaffold did exert robust local control over secreted collagen but did not appear to globally reorganize the scaffold effectively in the time period of the study. Consistent with our hypothesis, the results demonstrate that the presence of the scaffold appears to interfere with the global organization of the cell‐derived matrix. The production of highly organized local matrix by fibroblasts which penetrated the scaffold suggests that there is a mechanism which operates close to the cell membrane capable of controlling fibril organization. Nonetheless, the local control of the collagen alignment produced by cells within the scaffold was not continuous and did not result in overall global organization of the construct. Using a disorganized scaffold as a guide to produce highly organized tissue has the potential to delay the production of useful matrix or prevent uniform remodeling. The results of this study may shed light on the recent attempts to use disorganized collagenous matrix as a temporary corneal replacement in vivo which led to a variable remodeling response. Biotechnol. Bioeng. 2012; 109: 2683–2698.

Multiscale Mechanical Simulations of Cell Compacted Collagen Gels

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.

Multiscale model predicts tissue-level failure from collagen fiber-level damage.

Excessive tissue-level forces communicated to the microstructure and extracellular matrix of soft tissues can lead to damage and failure through poorly understood physical processes that are multiscale in nature. In this work, we propose a multiscale mechanical model for the failure of collagenous soft tissues that incorporates spatial heterogeneity in the microstructure and links the failure of discrete collagen fibers to the material response of the tissue. The model, which is based on experimental failure data derived from different collagen gel geometries, was able to predict the mechanical response and failure of type I collagen gels, and it demonstrated that a fiber-based rule (at the micrometer scale) for discrete failure can strongly shape the macroscale failure response of the gel (at the millimeter scale). The model may be a useful tool in predicting the macroscale failure conditions for soft tissues and engineered tissue analogs. In addition, the multiscale model provides a framework for the study of failure in complex fiber-based mechanical systems in general.

Collagen network strengthening following cyclic tensile loading.

The bulk mechanical properties of tissues are highly tuned to the physiological loads they experience and reflect the hierarchical structure and mechanical properties of their constituent parts. A thorough understanding of the processes involved in tissue adaptation is required to develop multi-scale computational models of tissue remodelling. While extracellular matrix (ECM) remodelling is partly due to the changing cellular metabolic activity, there may also be mechanically directed changes in ECM nano/microscale organization which lead to mechanical tuning. The thermal and enzymatic stability of collagen, which is the principal load-bearing biopolymer in vertebrates, have been shown to be enhanced by force suggesting that collagen has an active role in ECM mechanical properties. Here, we ask how changes in the mechanical properties of a collagen-based material are reflected by alterations in the micro/nanoscale collagen network following cyclic loading. Surprisingly, we observed significantly higher tensile stiffness and ultimate tensile strength, roughly analogous to the effect of work hardening, in the absence of network realignment and alterations to the fibril area fraction. The data suggest that mechanical loading induces stabilizing changes internal to the fibrils themselves or in the fibril–fibril interactions. If such a cell-independent strengthening effect is operational in vivo, then it would be an important consideration in any multiscale computational approach to ECM growth and remodelling.

Induction and quantification of collagen fiber alignment in a three-dimensional hydroxyapatite-collagen composite scaffold

Hydroxyapatite-collagen composite scaffolds are designed to serve as a regenerative load bearing replacement that mimics bone. However, the material properties of these scaffolds are at least an order of magnitude less than that of bone and subject to fail under physiological loading conditions. These scaffolds compositionally resemble bone but they do not possess important structural attributes such as an ordered arrangement of collagen fibers, which is a correlate to the mechanical properties in bone. Furthermore, it is unclear how much ordering of structure is satisfactory to mimic bone. Therefore, quantitative methods are needed to characterize collagen fiber alignment in these scaffolds for better correlation between the scaffold structure and the mechanical properties. A combination of extrusion and compaction was used to induce collagen fiber alignment in composite scaffolds. Collagen fiber alignment, due to extrusion and compaction, was quantified from polarized light microscopy images with a Fourier transform image processing algorithm. The Fourier transform method was capable of resolving the degree of collagen alignment from polarized light images. Anisotropy indices of the image planes ranged from 0.08 to 0.45. Increases in the degree of fiber alignment induced solely by extrusion (0.08-0.25) or compaction (0.25-0.44) were not as great as those by the combination of extrusion and compaction (0.35-0.45). Additional measures of randomness and fiber direction corroborate these anisotropy findings. This increased degree of collagen fiber alignment was induced in a preferred direction that is consistent with the extrusion direction and parallel with the compacted plane.