Multiscale mechanical simulations of cell compacted collagen gels

Modeling the extracellular matrix in cell migration and morphogenesis: a guide for the curious biologist

The extracellular matrix (ECM) is a highly complex structure through which biochemical and mechanical signals are transmitted. In processes of cell migration, the ECM also acts as a scaffold, providing structural support to cells as well as points of potential attachment. Although the ECM is a well-studied structure, its role in many biological processes remains difficult to investigate comprehensively due to its complexity and structural variation within an organism. In tandem with experiments, mathematical models are helpful in refining and testing hypotheses, generating predictions, and exploring conditions outside the scope of experiments. Such models can be combined and calibrated with in vivo and in vitro data to identify critical cell-ECM interactions that drive developmental and homeostatic processes, or the progression of diseases. In this review, we focus on mathematical and computational models of the ECM in processes such as cell migration including cancer metastasis, and in tissue structure and morphogenesis. By highlighting the predictive power of these models, we aim to help bridge the gap between experimental and computational approaches to studying the ECM and to provide guidance on selecting an appropriate model framework to complement corresponding experimental studies.

Polymeric reinforcements for cellularized collagen-based vascular wall models: influence of the scaffold architecture on the mechanical and biological properties

A previously developed cellularized collagen-based vascular wall model showed promising results in mimicking the biological properties of a native vessel but lacked appropriate mechanical properties. In this work, we aim to improve this collagen-based model by reinforcing it using a tubular polymeric (reinforcement) scaffold. The polymeric reinforcements were fabricated exploiting commercial poly (ε-caprolactone) (PCL), a polymer already used to fabricate other FDA-approved and commercially available devices serving medical applications, through 1) solution electrospinning (SES), 2) 3D printing (3DP) and 3) melt electrowriting (MEW). The non-reinforced cellularized collagen-based model was used as a reference (COL). The effect of the scaffold's architecture on the resulting mechanical and biological properties of the reinforced collagen-based model were evaluated. SEM imaging showed the differences in scaffolds' architecture (fiber alignment, fiber diameter and pore size) at both the micro- and the macrolevel. The polymeric scaffold led to significantly improved mechanical properties for the reinforced collagen-based model (initial elastic moduli of 382.05 ± 132.01 kPa, 100.59 ± 31.15 kPa and 245.78 ± 33.54 kPa, respectively for SES, 3DP and MEW at day 7 of maturation) compared to the non-reinforced collagen-based model (16.63 ± 5.69 kPa). Moreover, on day 7, the developed collagen gels showed stresses (for strains between 20% and 55%) in the range of [5-15] kPa for COL, [80-350] kPa for SES, [20-70] kPa for 3DP and [100-190] kPa for MEW. In addition to the effect on the resulting mechanical properties, the polymeric tubes' architecture influenced cell behavior, in terms of proliferation and attachment, along with collagen gel compaction and extracellular matrix protein expression. The MEW reinforcement resulted in a collagen gel compaction similar to the COL reference, whereas 3DP and SES led to thinner and longer collagen gels. Overall, it can be concluded that 1) the selected processing technique influences the scaffolds' architecture, which in turn influences the resulting mechanical and biological properties, and 2) the incorporation of a polymeric reinforcement leads to mechanical properties closely matching those of native arteries.

Multiscale mechanical characterization and computational modeling of fibrin gels

Fibrin is a naturally occurring protein network that forms a temporary structure to enable remodeling during wound healing. It is also a common tissue engineering scaffold because the structural properties can be controlled. However, to fully characterize the wound healing process and improve the design of regenerative scaffolds, understanding fibrin mechanics at multiple scales is necessary. Here, we present a strategy to quantify both the macroscale (1-10 mm) stress-strain response and the deformation of the mesoscale (10-1000 µm) network structure during unidirectional tensile tests. The experimental data were then used to inform a computational model to accurately capture the mechanical response of fibrin gels. Simultaneous mechanical testing and confocal microscopy imaging of fluorophore-conjugated fibrin gels revealed up to an 88% decrease in volume coupled with increase in volume fraction in deformed gels, and non-affine fiber alignment in the direction of deformation. Combination of the computational model with finite element analysis enabled us to predict the strain fields that were observed experimentally within heterogenous fibrin gels with spatial variations in material properties. These strategies can be expanded to characterize and predict the macroscale mechanics and mesoscale network organization of other heterogeneous biological tissues and matrices. STATEMENT OF SIGNIFICANCE: Fibrin is a naturally-occurring scaffold that supports cellular growth and assembly of de novo tissue and has tunable material properties. Characterization of meso- and macro-scale mechanics of fibrin gel networks can advance understanding of the wound healing process and impact future tissue engineering approaches. Using structural and mechanical characteristics of fibrin gels, a theoretical and computational model that can predict multiscale fibrin network mechanics was developed. These data and model can be used to design gels with tunable properties.

Rational Design of Soft-Hard Interfaces through Bioinspired Engineering

Soft-hard tissue interfaces in nature present a diversity of hierarchical transitions in composition and structure to address the challenge of stress concentrations that would otherwise arise at their interface. The translation of these into engineered materials holds promise for improved function of biomedical interfaces. Here, soft-hard tissue interfaces found in the body in health and disease, and the application of the diverse, functionally graded, and hierarchical structures that they present to bioinspired engineering materials are reviewed. A range of such bioinspired engineering materials and associated manufacturing technologies that are on the horizon in interfacial tissue engineering, hydrogel bioadhesion at the interfaces, and healthcare and medical devices are described.

Long-range mechanical signaling in biological systems

Cells can respond to signals generated by other cells that are remarkably far away. Studies from at least the 1920's showed that cells move toward each other when the distance between them is on the order of a millimeter, which is many times the cell diameter. Chemical signals generated by molecules diffusing from the cell surface would move too slowly and dissipate too fast to account for these effects, suggesting that they might be physical rather than biochemical. The non-linear elastic responses of sparsely connected networks of stiff or semiflexible filament such as those that form the extracellular matrix (ECM) and the cytoskeleton have unusual properties that suggest multiple mechanisms for long-range signaling in biological tissues. These include not only direct force transmission, but also highly non-uniform local deformations, and force-generated changes in fiber alignment and density. Defining how fibrous networks respond to cell-generated forces can help design new methods to characterize abnormal tissues and can guide development of improved biomimetic materials.

An Agent-Based Discrete Collagen Fiber Network Model of Dynamic Traction Force-Induced Remodeling

Microstructural properties of extracellular matrix (ECM) promote cell and tissue homeostasis as well as contribute to the formation and progression of disease. In order to understand how microstructural properties influence the mechanical properties and traction force-induced remodeling of ECM, we developed an agent-based model that incorporates repetitively applied traction force within a discrete fiber network. An important difference between our model and similar finite element models is that by implementing more biologically realistic dynamic traction, we can explore a greater range of matrix remodeling. Here, we validated our model by reproducing qualitative trends observed in three sets of experimental data reported by others: tensile and shear testing of cell-free collagen gels, collagen remodeling around a single isolated cell, and collagen remodeling between pairs of cells. In response to tensile and shear strain, simulated acellular networks with straight fibrils exhibited biphasic stress-strain curves indicative of strain-stiffening. When fibril curvature was introduced, stress-strain curves shifted to the right, delaying the onset of strain-stiffening. Our data support the notion that strain-stiffening might occur as individual fibrils successively align along the axis of strain and become engaged in tension. In simulations with a single, contractile cell, peak collagen displacement occurred closest to the cell and decreased with increasing distance. In simulations with two cells, compaction of collagen between cells appeared inversely related to the initial distance between cells. These results for cell-populated collagen networks match in vitro findings. A demonstrable benefit of modeling is that it allows for further analysis not feasible with experimentation. Within two-cell simulations, strain energy within the collagen network measured from the final state was relatively uniform around the outer surface of cells separated by 250 μm, but became increasingly nonuniform as the distance between cells decreased. For cells separated by 75 and 100 μm, strain energy peaked in the direction toward the other cell in the region in which fibrils become highly aligned and reached a minimum adjacent to this region, not on the opposite side of the cell as might be expected. This pattern of strain energy was partly attributable to the pattern of collagen compaction, but was still present when mapping strain energy divided by collagen density. Findings like these are of interest because fibril alignment, density, and strain energy may each contribute to contact guidance during tissue morphogenesis.

Multi-cell ECM compaction is predictable via superposition of nonlinear cell dynamics linearized in augmented state space

Cells interacting through an extracellular matrix (ECM) exhibit emergent behaviors resulting from collective intercellular interaction. In wound healing and tissue development, characteristic compaction of ECM gel is induced by multiple cells that generate tensions in the ECM fibers and coordinate their actions with other cells. Computational prediction of collective cell-ECM interaction based on first principles is highly complex especially as the number of cells increase. Here, we introduce a computationally-efficient method for predicting nonlinear behaviors of multiple cells interacting mechanically through a 3-D ECM fiber network. The key enabling technique is superposition of single cell computational models to predict multicellular behaviors. While cell-ECM interactions are highly nonlinear, they can be linearized accurately with a unique method, termed Dual-Faceted Linearization. This method recasts the original nonlinear dynamics in an augmented space where the system behaves more linearly. The independent state variables are augmented by combining auxiliary variables that inform nonlinear elements involved in the system. This computational method involves a) expressing the original nonlinear state equations with two sets of linear dynamic equations b) reducing the order of the augmented linear system via principal component analysis and c) superposing individual single cell-ECM dynamics to predict collective behaviors of multiple cells. The method is computationally efficient compared to original nonlinear dynamic simulation and accurate compared to traditional Taylor expansion linearization. Furthermore, we reproduce reported experimental results of multi-cell induced ECM compaction.

Collective behaviors of multiple cells interacting through an ECM are prohibitively complex to predict with a mechanistic computational model due to its highly nonlinear dynamics and high dimensional space. We introduce a methodology where nonlinear dynamics of single cells are superposed to predict collective multi-cellular behaviors through a developed linearization method. We represent nonlinear single cell dynamics with linear state equations by augmenting the independent state variables with a set of auxiliary variables. We then transform the linear augmented state equations to a low-dimensional latent model and superpose the linear latent models of individual cells to predict collective behaviors that emerge from multi-cellular interactions. The method successfully reproduced experimental results of cell-induced ECM compaction.

Recent Advances in Engineering the Stem Cell Microniche in 3D

Conventional 2D cell culture techniques have provided fundamental insights into key biochemical and biophysical mechanisms responsible for various cellular behaviors, such as cell adhesion, spreading, division, proliferation, and differentiation. However, 2D culture in vitro does not fully capture the physical and chemical properties of the native microenvironment. There is a growing body of research that suggests that cells cultured on 2D substrates differ greatly from those grown in vivo. This article focuses on recent progress in using bioinspired 3D matrices that recapitulate as many aspects of the natural extracellular matrix as possible. A range of techniques for the engineering of 3D microenvironment with precisely controlled biophysical and chemical properties, and the impact of these environments on cellular behavior, is reviewed. Finally, an outlook on future challenges for engineering the 3D microenvironment and how such approaches would further our understanding of the influence of the microenvironment on cell function is provided.

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.

Pressure-induced microstructural changes in porcine tricuspid valve leaflets

Quantifying mechanically-induced changes in the tricuspid valve extracellular matrix (ECM) structural components, e.g. collagen fiber spread and distribution, is important as it determines the overall macro-scale tissue responses and subsequently its function/malfunction in physiological/pathophysiological states. For example, functional tricuspid regurgitation, a common tricuspid valve disorder, could be caused by elevated right ventricular pressure due to pulmonary hypertension. In such patients, the geometry and the normal function of valve leaflets alter due to chronic pressure overload, which could cause remodeling responses in the ECM and change its structural components. To understand such a relation, we developed an experimental setup and measured alteration of leaflet microstructure in response to pressure increase in porcine tricuspid valves using the small angle light scattering technique. The anisotropy index, a measure of the fiber spread and distribution, was obtained and averaged for each region of the anterior, posterior, and septal leaflet using four averaging methods. The average anisotropy indices (mean ± standard error) in the belly region of the anterior, posterior, and septal leaflets of non-pressurized valves were found to be 12 ± 2%, 21 ± 3% and 12 ± 1%, respectively. For the pressurized valve, the average values of the anisotropy index in the belly region of the anterior, posterior, and septal leaflets were 56 ± 5%, 39 ± 7% and 32 ± 5%, respectively. Overall, the average anisotropy index was found to be higher for all leaflets in the pressurized valves as compared to the non-pressurized valves, indicating that the ECM fibers became more aligned in response to an increased ventricular pressure.

STATEMENT OF SIGNIFICANCE

Mechanics plays a critical role in development, regeneration, and remodeling of tissues. In the current study, we have conducted experiments to examine how increasing the ventricular pressure leads to realignment of protein fibers comprising the extracellular matrix (ECM) of the tricuspid valve leaflets. Like many other tissues, in cardiac valves, cell-matrix interactions and gene expressions are heavily influenced by changes in the mechanical microenvironment at the ECM/cellular level. We believe that our study will help us better understand how abnormal increases in the right ventricular pressure (due to pulmonary hypertension) could change the structural architecture of tricuspid valve leaflets and subsequently the mechanical microenvironment at the ECM/cellular level.

Fiber Network Models Predict Enhanced Cell Mechanosensing on Fibrous Gels

The propagation of mechanical signals through nonlinear fibrous tissues is much more extensive than through continuous synthetic hydrogels. Results from recent studies indicate that increased mechanical propagation arises from the fibrous nature of the material rather than the strain-stiffening property. The relative importance of different parameters of the fibrous network structure to this propagation, however, remains unclear. In this work, we directly compared the mechanical response of substrates of varying thickness subjected to a constant cell traction force using either a nonfibrous strain-stiffening continuum-based model or a volume-averaged fiber network model consisting of two different types of fiber network structures: one with low fiber connectivity (growth networks) and one with high fiber connectivity (Delaunay networks). The growth network fiber models predicted a greater propagation of substrate displacements through the model and a greater sensitivity to gel thickness compared to the more connected Delaunay networks and the nonlinear continuum model. Detailed analysis of the results indicates that rotational freedom of the fibers in a network with low fiber connectivity is critically important for enhanced, long-range mechanosensing. Our findings demonstrate the utility of multiscale models in predicting cells mechanosensing on fibrous gels, and they provide a more complete understanding of how cell traction forces propagate through fibrous tissues, which has implications for the design of engineered tissues and the stem cell niche.

Functional and Biomimetic Materials for Engineering of the Three-Dimensional Cell Microenvironment

The cell microenvironment has emerged as a key determinant of cell behavior and function in development, physiology, and pathophysiology. The extracellular matrix (ECM) within the cell microenvironment serves not only as a structural foundation for cells but also as a source of three-dimensional (3D) biochemical and biophysical cues that trigger and regulate cell behaviors. Increasing evidence suggests that the 3D character of the microenvironment is required for development of many critical cell responses observed in vivo, fueling a surge in the development of functional and biomimetic materials for engineering the 3D cell microenvironment. Progress in the design of such materials has improved control of cell behaviors in 3D and advanced the fields of tissue regeneration, in vitro tissue models, large-scale cell differentiation, immunotherapy, and gene therapy. However, the field is still in its infancy, and discoveries about the nature of cell-microenvironment interactions continue to overturn much early progress in the field. Key challenges continue to be dissecting the roles of chemistry, structure, mechanics, and electrophysiology in the cell microenvironment, and understanding and harnessing the roles of periodicity and drift in these factors. This review encapsulates where recent advances appear to leave the ever-shifting state of the art, and it highlights areas in which substantial potential and uncertainty remain.

Toughening of fibrous scaffolds by mobile mineral deposits

Partially mineralized fibrous tissue situated between tendon and bone is believed to be tougher than either tendon or bone, possibly serving as a compliant, energy absorptive, protective barrier between the two. This tissue does not reform following surgical repair (e.g., rotator cuff tendon-to-bone re-attachment) and might be a factor in the poor outcomes following such surgeries. Towards our long-term goal of tissue engineered solutions to functional tendon-to-bone re-attachment, we tested the hypotheses that partially mineralized fibrous matrices can derive toughness from mobility of mineral along their fibers, and that in such cases toughness is maximized at levels of mineralization sufficiently low to allow substantial mobility. Nanofibrous electrospun poly(lactic-co-glycolic acid) (PLGA) scaffolds mineralized for prescribed times were fabricated as model systems to test these hypotheses. Tensile tests performed at varying angles relative to the dominant fiber direction confirmed that mineral cross-linked PLGA nanofibers without adhering to them. Peel tests revealed that fracture toughness increased with mineralization time up to a peak value, then subsequently decreased with increasing mineralization time back to the baseline toughness of unmineralized scaffolds. These experimental results were predicted by a theoretical model combining mineral growth kinetics with fracture energetics, suggesting that toughness increased with mineralization time until mineral mobility was attenuated by steric hindrance, then returned to baseline levels following the rigid percolation threshold. Results supported our hypotheses, and motivate further study of the roles of mobile mineral particles in toughening the tendon-to-bone attachment.

STATEMENT OF SIGNIFICANCE

Effective surgical repair of interfaces between tendon and bone remains an unmet clinical need, in part due to a lack of understanding of how toughness is achieved in the healthy tissue. Using combined synthesis, experiment, and modeling approaches, the current work supported the hypothesis that toughening of a fibrous scaffold arises from brittle mineral particles that crosslink the fibers, but only if the particles are free to slide relative to the fibers. In the case of the tendon-to-bone interface, this suggests that partially mineralized tissue between tendon and bone, with mobile mineral but relatively low stiffness, may serve as a compliant, energy-absorbing barrier that guards against injury. These results suggest an opportunity for fabrication of tough and strong fibrous scaffolds for tissue engineering applications.

Cell Contractility Facilitates Alignment of Cells and Tissues to Static Uniaxial Stretch

During animal development and homeostasis, the structure of tissues, including muscles, blood vessels, and connective tissues, adapts to mechanical strains in the extracellular matrix (ECM). These strains originate from the differential growth of tissues or forces due to muscle contraction or gravity. Here we show using a computational model that by amplifying local strain cues, active cell contractility can facilitate and accelerate the reorientation of single cells to static strains. At the collective cell level, the model simulations show that active cell contractility can facilitate the formation of strings along the orientation of stretch. The computational model is based on a hybrid cellular Potts and finite-element simulation framework describing a mechanical cell-substrate feedback, where: 1) cells apply forces on the ECM, such that 2) local strains are generated in the ECM and 3) cells preferentially extend protrusions along the strain orientation. In accordance with experimental observations, simulated cells align and form stringlike structures parallel to static uniaxial stretch. Our model simulations predict that the magnitude of the uniaxial stretch and the strength of the contractile forces regulate a gradual transition between stringlike patterns and vascular networklike patterns. Our simulations also suggest that at high population densities, less cell cohesion promotes string formation.

The tendon-to-bone attachment: Unification through disarray

High-resolution imaging, composition analysis and mechanical testing reveal a disordered transitional material within the Achilles tendon-to-bone attachment, structured as a fibrous network to enable force transfer and maximize structural integrity.

Predicting cell viability within tissue scaffolds under equiaxial strain: multi-scale finite element model of collagen-cardiomyocytes constructs

Successful tissue engineering and regenerative therapy necessitate having extensive knowledge about mechanical milieu in engineered tissues and the resident cells. In this study, we have merged two powerful analysis tools, namely finite element analysis and stochastic analysis, to understand the mechanical strain within the tissue scaffold and residing cells and to predict the cell viability upon applying mechanical strains. A continuum-based multi-length scale finite element model (FEM) was created to simulate the physiologically relevant equiaxial strain exposure on cell-embedded tissue scaffold and to calculate strain transferred to the tissue scaffold (macro-scale) and residing cells (micro-scale) upon various equiaxial strains. The data from FEM were used to predict cell viability under various equiaxial strain magnitudes using stochastic damage criterion analysis. The model validation was conducted through mechanically straining the cardiomyocyte-encapsulated collagen constructs using a custom-built mechanical loading platform (EQUicycler). FEM quantified the strain gradients over the radial and longitudinal direction of the scaffolds and the cells residing in different areas of interest. With the use of the experimental viability data, stochastic damage criterion, and the average cellular strains obtained from multi-length scale models, cellular viability was predicted and successfully validated. This methodology can provide a great tool to characterize the mechanical stimulation of bioreactors used in tissue engineering applications in providing quantification of mechanical strain and predicting cellular viability variations due to applied mechanical strain.

Tissue Strain Reorganizes Collagen With a Switchlike Response That Regulates Neuronal Extracellular Signal-Regulated Kinase Phosphorylation In Vitro: Implications for Ligamentous Injury and Mechanotransduction

Excessive loading of ligaments can activate the neural afferents that innervate the collagenous tissue, leading to a host of pathologies including pain. An integrated experimental and modeling approach was used to define the responses of neurons and the surrounding collagen fibers to the ligamentous matrix loading and to begin to understand how macroscopic deformation is translated to neuronal loading and signaling. A neuron-collagen construct (NCC) developed to mimic innervation of collagenous tissue underwent tension to strains simulating nonpainful (8%) or painful ligament loading (16%). Both neuronal phosphorylation of extracellular signal-regulated kinase (ERK), which is related to neuroplasticity (R2 ≥ 0.041; p ≤ 0.0171) and neuronal aspect ratio (AR) (R2 ≥ 0.250; p < 0.0001), were significantly correlated with tissue-level strains. As NCC strains increased during a slowly applied loading (1%/s), a "switchlike" fiber realignment response was detected with collagen reorganization occurring only above a transition point of 11.3% strain. A finite-element based discrete fiber network (DFN) model predicted that at bulk strains above the transition point, heterogeneous fiber strains were both tensile and compressive and increased, with strains in some fibers along the loading direction exceeding the applied bulk strain. The transition point identified for changes in collagen fiber realignment was consistent with the measured strain threshold (11.7% with a 95% confidence interval of 10.2-13.4%) for elevating ERK phosphorylation after loading. As with collagen fiber realignment, the greatest degree of neuronal reorientation toward the loading direction was observed at the NCC distraction corresponding to painful loading. Because activation of neuronal ERK occurred only at strains that produced evident collagen fiber realignment, findings suggest that tissue strain-induced changes in the micromechanical environment, especially altered local collagen fiber kinematics, may be associated with mechanotransduction signaling in neurons.

Large strain stimulation promotes extracellular matrix production and stiffness in an elastomeric scaffold model

Mechanical conditioning of engineered tissue constructs is widely recognized as one of the most relevant methods to enhance tissue accretion and microstructure, leading to improved mechanical behaviors. The understanding of the underlying mechanisms remains rather limited, restricting the development of in silico models of these phenomena, and the translation of engineered tissues into clinical application. In the present study, we examined the role of large strip-biaxial strains (up to 50%) on ECM synthesis by vascular smooth muscle cells (VSMCs) micro-integrated into electrospun polyester urethane urea (PEUU) constructs over the course of 3 weeks. Experimental results indicated that VSMC biosynthetic behavior was quite sensitive to tissue strain maximum level, and that collagen was the primary ECM component synthesized. Moreover, we found that while a 30% peak strain level achieved maximum ECM synthesis rate, further increases in strain level lead to a reduction in ECM biosynthesis. Subsequent mechanical analysis of the formed collagen fiber network was performed by removing the scaffold mechanical responses using a strain-energy based approach, showing that the denovo collagen also demonstrated mechanical behaviors substantially better than previously obtained with small strain training and comparable to mature collagenous tissues. We conclude that the application of large deformations can play a critical role not only in the quantity of ECM synthesis (i.e. the rate of mass production), but also on the modulation of the stiffness of the newly formed ECM constituents. The improved understanding of the process of growth and development of ECM in these mechano-sensitive cell-scaffold systems will lead to more rational design and manufacturing of engineered tissues operating under highly demanding mechanical environments.

Augmenting Surgery via Multi-scale Modeling and Translational Systems Biology in the Era of Precision Medicine: A Multidisciplinary Perspective

In this era of tremendous technological capabilities and increased focus on improving clinical outcomes, decreasing costs, and increasing precision, there is a need for a more quantitative approach to the field of surgery. Multiscale computational modeling has the potential to bridge the gap to the emerging paradigms of Precision Medicine and Translational Systems Biology, in which quantitative metrics and data guide patient care through improved stratification, diagnosis, and therapy. Achievements by multiple groups have demonstrated the potential for (1) multiscale computational modeling, at a biological level, of diseases treated with surgery and the surgical procedure process at the level of the individual and the population; along with (2) patient-specific, computationally-enabled surgical planning, delivery, and guidance and robotically-augmented manipulation. In this perspective article, we discuss these concepts, and cite emerging examples from the fields of trauma, wound healing, and cardiac surgery.

A Combined In Vitro Imaging and Multi-Scale Modeling System for Studying the Role of Cell Matrix Interactions in Cutaneous Wound Healing

Many cell types remodel the extracellular matrix of the tissues they inhabit in response to a wide range of environmental stimuli, including mechanical cues. Such is the case in dermal wound healing, where fibroblast migrate into and remodel the provisional fibrin matrix in a complex manner that depends in part on the local mechanical environment and the evolving multi-scale mechanical interactions of the system. In this study, we report on the development of an image-based multi-scale mechanical model that predicts the short-term (24 hours), structural reorganization of a fibrin gel by fibroblasts. These predictive models are based on an in vitro experimental system where clusters of fibroblasts (i.e., explants) were spatially arranged into a triangular geometry onto the surface of fibrin gels that were subjected to either Fixed or Free in-plane mechanical constraints. Experimentally, regional differences in short-term structural remodeling and cell migration were observed for the two gel boundary conditions. A pilot experiment indicated that these small differences in the short-term remodeling of the fibrin gel translate into substantial differences in long-term (4 weeks) remodeling, particularly in terms of collagen production. The multi-scale models were able to predict some regional differences in remodeling and qualitatively similar reorganization patterns for the two boundary conditions. However, other aspects of the model, such as the magnitudes and rates of deformation of gel, did not match the experiments. These discrepancies between model and experiment provide fertile ground for challenging model assumptions and devising new experiments to enhance our understanding of how this multi-scale system functions. These efforts will ultimately improve the predictions of the remodeling process, particularly as it relates to dermal wound healing and the reduction of patient scarring. Such models could be used to recommend patient-specific mechanical-based treatment dependent on parameters such as wound geometry, location, age, and health.

Remodeling of fibrous extracellular matrices by contractile cells: predictions from discrete fiber network simulations

Contractile forces exerted on the surrounding extracellular matrix (ECM) lead to the alignment and stretching of constituent fibers within the vicinity of cells. As a consequence, the matrix reorganizes to form thick bundles of aligned fibers that enable force transmission over distances larger than the size of the cells. Contractile force-mediated remodeling of ECM fibers has bearing on a number of physiologic and pathophysiologic phenomena. In this work, we present a computational model to capture cell-mediated remodeling within fibrous matrices using finite element-based discrete fiber network simulations. The model is shown to accurately capture collagen alignment, heterogeneous deformations, and long-range force transmission observed experimentally. The zone of mechanical influence surrounding a single contractile cell and the interaction between two cells are predicted from the strain-induced alignment of fibers. Through parametric studies, the effect of cell contractility and cell shape anisotropy on matrix remodeling and force transmission are quantified and summarized in a phase diagram. For highly contractile and elongated cells, we find a sensing distance that is ten times the cell size, in agreement with experimental observations.

On the presence of affine fibril and fiber kinematics in the mitral valve anterior leaflet

In this study, we evaluated the hypothesis that the constituent fibers follow an affine deformation kinematic model for planar collagenous tissues. Results from two experimental datasets were utilized, taken at two scales (nanometer and micrometer), using mitral valve anterior leaflet (MVAL) tissues as the representative tissue. We simulated MVAL collagen fiber network as an ensemble of undulated fibers under a generalized two-dimensional deformation state, by representing the collagen fibrils based on a planar sinusoidally shaped geometric model. The proposed approach accounted for collagen fibril amplitude, crimp period, and rotation with applied macroscopic tissue-level deformation. When compared to the small angle x-ray scattering measurements, the model fit the data well, with an r(2) = 0.976. This important finding suggests that, at the homogenized tissue-level scale of ∼1 mm, the collagen fiber network in the MVAL deforms according to an affine kinematics model. Moreover, with respect to understanding its function, affine kinematics suggests that the constituent fibers are largely noninteracting and deform in accordance with the bulk tissue. It also suggests that the collagen fibrils are tightly bounded and deform as a single fiber-level unit. This greatly simplifies the modeling efforts at the tissue and organ levels, because affine kinematics allows a straightforward connection between the macroscopic and local fiber strains. It also suggests that the collagen and elastin fiber networks act independently of each other, with the collagen and elastin forming long fiber networks that allow for free rotations. Such freedom of rotation can greatly facilitate the observed high degree of mechanical anisotropy in the MVAL and other heart valves, which is essential to heart valve function. These apparently novel findings support modeling efforts directed toward improving our fundamental understanding of tissue biomechanics in healthy and diseased conditions.

Agent-based modeling traction force mediated compaction of cell-populated collagen gels using physically realistic fibril mechanics

Agent-based modeling was used to model collagen fibrils, composed of a string of nodes serially connected by links that act as Hookean springs. Bending mechanics are implemented as torsional springs that act upon each set of three serially connected nodes as a linear function of angular deflection about the central node. These fibrils were evaluated under conditions that simulated axial extension, simple three-point bending and an end-loaded cantilever. The deformation of fibrils under axial loading varied &lt;0.001% from the analytical solution for linearly elastic fibrils. For fibrils between 100 μm and 200 μm in length experiencing small deflections, differences between simulated deflections and their analytical solutions were &lt;1% for fibrils experiencing three-point bending and &lt;7% for fibrils experiencing cantilever bending. When these new rules for fibril mechanics were introduced into a model that allowed for cross-linking of fibrils to form a network and the application of cell traction force, the fibrous network underwent macroscopic compaction and aligned between cells. Further, fibril density increased between cells to a greater extent than that observed macroscopically and appeared similar to matrical tracks that have been observed experimentally in cell-populated collagen gels. This behavior is consistent with observations in previous versions of the model that did not allow for the physically realistic simulation of fibril mechanics. The significance of the torsional spring constant value was then explored to determine its impact on remodeling of the simulated fibrous network. Although a stronger torsional spring constant reduced the degree of quantitative remodeling that occurred, the inclusion of torsional springs in the model was not necessary for the model to reproduce key qualitative aspects of remodeling, indicating that the presence of Hookean springs is essential for this behavior. These results suggest that traction force mediated matrix remodeling may be a robust phenomenon not limited to fibrils with a precise set of material properties.

From single fiber to macro-level mechanics: A structural finite-element model for elastomeric fibrous biomaterials

In the present work, we demonstrate that the mesoscopic in-plane mechanical behavior of membrane elastomeric scaffolds can be simulated by replication of actual quantified fibrous geometries. Elastomeric electrospun polyurethane (ES-PEUU) scaffolds, with and without particulate inclusions, were utilized. Simulations were developed from experimentally-derived fiber network geometries, based on a range of scaffold isotropic and anisotropic behaviors. These were chosen to evaluate the effects on macro-mechanics based on measurable geometric parameters such as fiber intersections, connectivity, orientation, and diameter. Simulations were conducted with only the fiber material model parameters adjusted to match the macro-level mechanical test data. Fiber model validation was performed at the microscopic level by individual fiber mechanical tests using AFM. Results demonstrated very good agreement to the experimental data, and revealed the formation of extended preferential fiber orientations spanning the entire model space. We speculate that these emergent structures may be responsible for the tissue-like macroscale behaviors observed in electrospun scaffolds. To conclude, the modeling approach has implications for (1) gaining insight on the intricate relationship between fabrication variables, structure, and mechanics to manufacture more functional devices/materials, (2) elucidating the effects of cell or particulate inclusions on global construct mechanics, and (3) fabricating better performing tissue surrogates that could recapitulate native tissue mechanics.

Observing and quantifying fibroblast-mediated fibrin gel compaction

Cells embedded in collagen and fibrin gels attach and exert traction forces on the fibers of the gel. These forces can lead to local and global reorganization and realignment of the gel microstructure. This process proceeds in a complex manner that is dependent in part on the interplay between the location of the cells, the geometry of the gel, and the mechanical constraints on the gel. To better understand how these variables produce global fiber alignment patterns, we use time-lapse differential interference contrast (DIC) microscopy coupled with an environmentally controlled bioreactor to observe the compaction process between geometrically spaced explants (clusters of fibroblasts). The images are then analyzed with a custom image processing algorithm to obtain maps of the strain. The information obtained from this technique can be used to probe the mechanobiology of various cell-matrix interactions, which has important implications for understanding processes in wound healing, disease development, and tissue engineering applications.