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

Stiffening mechanisms in stochastic athermal fiber networks

Stochastic athermal networks composed of fibers that deform axially and in bending strain stiffen much faster than thermal networks of axial elements, such as elastomers. Here we investigate the physical origin of stiffening in athermal network materials. To this end, we use models of stochastic networks subjected to uniaxial deformation and identify the emergence of two subnetworks, the stress path subnetwork (SPSN) and the bending support subnetwork (BSSN), which carry most of the axial and bending energies, respectively. The BSSN controls lateral contraction and modulates the organization of the SPSN during deformation. The SPSN is preferentially oriented in the loading direction, while the BSSN's preferential orientation is orthogonal to the SPSN. In nonaffine networks stiffening is exponential, while in close-to-affine networks it is quadratic. The difference is due to a much more modest lateral contraction in the approximately affine case and to a stiffer BSSN. Exponential stiffening emerges from the interplay of the axial and bending deformation modes at the scale of individual or small groups of fibers undergoing large deformations and being subjected to the constraint of rigid cross-links, and it is not necessarily a result of complex interactions involving many connected fibers. An apparent third regime of quadratic stiffening may be evidenced in nonaffinely deforming networks provided the nominal stress is observed. This occurs at large stretches, when the BSSN contribution of stiffening vanishes. However, this regime is not present if the Cauchy stress is used, in which case stiffening is exponential throughout the entire deformation. These results shed light on the physical nature of stiffening in a broad class of materials including connective tissue, the extracellular matrix, nonwovens, felt, and other athermal network materials.

Dynamical modeling reveals RNA decay mediates the effect of matrix stiffness on aged muscle stem cell fate

Loss of muscle stem cell (MuSC) self-renewal with aging reflects a combination of influences from the intracellular (e.g., post-transcriptional modifications) and extracellular (e.g., matrix stiffness) environment. Whereas conventional single cell analyses have revealed valuable insights into factors contributing to impaired self-renewal with age, most are limited by static measurements that fail to capture nonlinear dynamics. Using bioengineered matrices mimicking the stiffness of young and old muscle, we showed that while young MuSCs were unaffected by aged matrices, old MuSCs were phenotypically rejuvenated by young matrices. Dynamical modeling of RNA velocity vector fields in silico revealed that soft matrices promoted a self-renewing state in old MuSCs by attenuating RNA decay. Vector field perturbations demonstrated that the effects of matrix stiffness on MuSC self-renewal could be circumvented by fine-tuning the expression of the RNA decay machinery. These results demonstrate that post-transcriptional dynamics dictate the negative effect of aged matrices on MuSC self-renewal.

Polybutylene Succinate Processing and Evaluation as a Micro Fibrous Graft for Tissue Engineering Applications

A microfibrous tubular scaffold has been designed and fabricated by electrospinning using poly (1,4-butylene succinate) as biocompatible and biodegradable material. The scaffold morphology was optimized as a small diameter and micro-porous conduit, able to foster cell integration, adhesion, and growth while avoiding cell infiltration through the graft's wall. Scaffold morphology and mechanical properties were explored and compared to those of native conduits. Scaffolds were then seeded with adult normal human dermal fibroblasts to evaluate cytocompatibility in vitro. Haemolytic effect was evaluated upon incubation with diluted whole blood. The scaffold showed no delamination, and mechanical properties were in the physiological range for tubular conduits: elastic modulus (17.5 ± 1.6 MPa), ultimate tensile stress (3.95 ± 0.17 MPa), strain to failure (57 ± 4.5%) and suture retention force (2.65 ± 0.32 N). The shown degradation profile allows the graft to provide initial mechanical support and functionality while being colonized and then replaced by the host cells. This combination of features might represent a step toward future research on PBS as a biomaterial to produce scaffolds that provide structure and function over time and support host cell remodelling.

On modeling the multiscale mechanobiology of soft tissues: Challenges and progress

Tissues grow and remodel in response to mechanical cues, extracellular and intracellular signals experienced through various biological events, from the developing embryo to disease and aging. The macroscale response of soft tissues is typically nonlinear, viscoelastic anisotropic, and often emerges from the hierarchical structure of tissues, primarily their biopolymer fiber networks at the microscale. The adaptation to mechanical cues is likewise a multiscale phenomenon. Cell mechanobiology, the ability of cells to transform mechanical inputs into chemical signaling inside the cell, and subsequent regulation of cellular behavior through intra- and inter-cellular signaling networks, is the key coupling at the microscale between the mechanical cues and the mechanical adaptation seen macroscopically. To fully understand mechanics of tissues in growth and remodeling as observed at the tissue level, multiscale models of tissue mechanobiology are essential. In this review, we summarize the state-of-the art modeling tools of soft tissues at both scales, the tissue level response, and the cell scale mechanobiology models. To help the interested reader become more familiar with these modeling frameworks, we also show representative examples. Our aim here is to bring together scientists from different disciplines and enable the future leap in multiscale modeling of tissue mechanobiology.

Microstructure and mechanics of the bovine trachea: Layer specific investigations through SHG imaging and biaxial testing

The trachea is a complex tissue made up of hyaline cartilage, fibrous tissue, and muscle fibers. Currently, the knowledge of microscopic structural organization of these components and their role in determining the tissue's mechanical response is very limited. The purpose of this study is to provide data on the microstructure of the tracheal components and its influence on tissue's mechanical response. Five bovine tracheae were used in this study. Adventitia, cartilage, mucosa/submucosa, and trachealis muscle layers were methodically cut out from the whole tissue. Second-harmonic generation(SHG) via multi-photon microscopy (MPM) enabled imaging of collagen fibers and muscle fibers. Simultaneously, a planar biaxial test rig was used to record the mechanical behavior of each layer. In total 60 samples were tested and analyzed. Fiber architecture in the adventitia and mucosa/submucosa layer showed high degree of anisotropy with the mean fiber angle varying from sample to sample. The trachealis muscle displayed neat layers of fibers organized in the longitudinal direction. The cartilage also displayed a structure of thick mesh-work of collagen type II organized predominantly towards the circumferential direction. Further, mechanical testing demonstrated the anisotropic nature of the tissue components. The cartilage was identified as the stiffest component for strain level < 20% and hence the primary load bearing component. The other three layers displayed a non-linear mechanical response which could be explained by the structure and organization of their fibers. This study is useful in enhancing the utilization of structurally motivated material models for predicting tracheal overall mechanical response.

A discrete fiber network finite element model of arterial elastin network considering inter-fiber crosslinking property and density

Inter-fiber crosslinks within the extracellular matrix (ECM) play important roles in determining the mechanical properties of the fibrous network. Discrete fiber network (DFN) models have been used to study fibrous biological material, however the contribution of inter-fiber crosslinks to the mechanics of the ECM network is not well understood. In this study, a DFN model of arterial elastin network was developed based on measured structural features to study the contribution of inter-fiber crosslinking properties and density to the mechanics and fiber kinematics of the network. The DFN was generated by randomly placing line segments into a given domain following a fiber orientation distribution function obtained from multiphoton microscopy until a desired fiber areal fraction was reached. Intersections between the line segments were treated as crosslinks. The generated DFN model was then incorporated into an ABAQUS finite element model to simulate the network under equi- and nonequi-biaxial deformation. The inter-fiber crosslinks were modeled using connector elements with either zero (pin joint) or infinite (weld joint) rotational stiffness. Furthermore, inter-fiber crosslinking density was systematically reduced and its effect on both network- and fiber-level mechanics was studied. The DFN model showed good fitting and predicting capabilities of the stress-strain behavior of the elastin network. While the pin and weld joints do not seem to have noticeable effect on the network stress-strain behavior, the crosslinking properties can affect the local fiber mechanics and kinematics. Overall, our study suggests that inter-fiber crosslinking properties are important to the multiscale mechanics and fiber kinematics of the ECM network.

A computational framework for biomaterials containing three-dimensional random fiber networks based on the affine kinematics

Understanding the structure-function relationship of biomaterials can provide insights into different diseases and advance numerous biomedical applications. This paper presents a finite element-based computational framework to model biomaterials containing a three-dimensional fiber network at the microscopic scale. The fiber network is synthetically generated by a random walk algorithm, which uses several random variables to control the fiber network topology such as fiber orientations and tortuosity. The geometric information of the generated fiber network is stored in an array-like data structure and incorporated into the nonlinear finite element formulation. The proposed computational framework adopts the affine fiber kinematics, based on which the fiber deformation can be expressed by the nodal displacement and the finite element interpolation functions using the isoparametric relationship. A variational approach is developed to linearize the total strain energy function and derive the nodal force residual and the stiffness matrix required by the finite element procedure. Four numerical examples are provided to demonstrate the capabilities of the proposed computational framework, including a numerical investigation about the relationship between the proposed method and a class of anisotropic material models, a set of synthetic examples to explore the influence of fiber locations on material local and global responses, a thorough mesh-sensitivity analysis about the impact of mesh size on various numerical results, and a detailed case study about the influence of material structures on the performance of eggshell-membrane-hydrogel composites. The proposed computational framework provides an efficient approach to investigate the structure-function relationship for biomaterials that follow the affine fiber kinematics.

Tailoring the multiscale architecture of electrospun membranes to promote 3D cellular infiltration

Controlling the architecture of engineered scaffolds is of outmost importance to induce a targeted cell response and ultimately achieve successful tissue regeneration upon implantation. Robust, reliable and reproducible methods to control scaffold properties at different levels are timely and highly important. However, the multiscale architectural properties of electrospun membranes are very complex, in particular the role of fiber-to-fiber interactions on mechanical properties, and their effect on cell response remain largely unexplored. The work reported here reveals that the macroscopic membrane stiffness, observed by stress-strain curves, cannot be predicted solely based on the Young's moduli of the constituting fibers but is rather influenced by interactions on the microscale, namely the number of fiber-to-fiber bonds. To specifically control the formation of these bonds, solvent systems of the electrospinning solution were fine-tuned, affecting the membrane properties at every length-scale investigated. In contrast to dichloromethane that is characterized by a high vapor pressure, the use of trifluoroacetic acid, a solvent with a lower vapor pressure, favors the generation of fiber-to-fiber bonds. This ultimately led to an overall increased Young's modulus and yield stress of the membrane despite a lower stiffness of the constituting fibers. With respect to tissue engineering applications, an experimental setup was developed to investigate the effect of architectural parameters on the ability of cells to infiltrate and migrate within the scaffold. The results reveal that differences in fiber-to-fiber bonds significantly affect the infiltration of normal human dermal fibroblasts into the membranes. Membranes of loose fibers with low numbers of fiber-to-fiber bonds, as obtained from spinning solutions using dichloromethane, promote cellular infiltration and are thus promising candidates for the formation of a 3D tissue.

A Cell-free Biodegradable Synthetic Artificial Ligament for the Reconstruction of Anterior Cruciate Ligament in a Rat Model

Traditional Anterior Cruciate Ligament (ACL) reconstruction is commonly performed using an allograft or autograft and possesses limitations such as donor site morbidity, decreased range of motion, and potential infection. However, a biodegradable synthetic graft could greatly assist in the prevention of such restrictions after ACL reconstruction. In this study, artificial grafts were generated using "wet" and "dry" electrospinning processes with a biodegradable elastomer, poly (ester urethane) urea (PEUU), and were evaluated in vitro and in vivo in a rat model. Four groups were established: (1) Wet PEUU artificial ligament, (2) Dry PEUU artificial ligament, (3) Dry polycaprolactone artificial ligament (PCL), and (4) autologous flexor digitorum longus tendon graft. Eight weeks after surgery, the in vivo tensile strength of wet PEUU ligaments had significantly increased compared to the other synthetic ligaments. These results aligned with increased infiltration of host cells and decreased inflammation within the wet PEUU grafts. In contrast, very little cellular infiltration was observed in PCL and dry PEUU grafts. Micro-computed tomography analysis performed at 4 and 8 weeks postoperatively revealed significantly smaller bone tunnels in the tendon autograft and wet PEUU groups. The Wet PEUU grafts served as an adequate functioning material and allowed for the creation of tissues that closely resembled the ACL.

Mechanical Considerations of Electrospun Scaffolds for Myocardial Tissue and Regenerative Engineering

Biomaterials to facilitate the restoration of cardiac tissue is of emerging importance. While there are many aspects to consider in the design of biomaterials, mechanical properties can be of particular importance in this dynamically remodeling tissue. This review focuses on one specific processing method, electrospinning, that is employed to generate materials with a fibrous microstructure that can be combined with material properties to achieve the desired mechanical behavior. Current methods used to fabricate mechanically relevant micro-/nanofibrous scaffolds, in vivo studies using these scaffolds as therapeutics, and common techniques to characterize the mechanical properties of the scaffolds are covered. We also discuss the discrepancies in the reported elastic modulus for physiological and pathological myocardium in the literature, as well as the emerging area of in vitro mechanobiology studies to investigate the mechanical regulation in cardiac tissue engineering. Lastly, future perspectives and recommendations are offered in order to enhance the understanding of cardiac mechanobiology and foster therapeutic development in myocardial regenerative medicine.

Impact of Additives on Mechanical Properties of Supramolecular Electrospun Scaffolds

The mechanical properties of scaffolds used for mechanically challenging applications such as cardiovascular implants are unequivocally important. Here, the effect of supramolecular additive functionalization on mechanical behavior of electrospun scaffolds was investigated for one bisurea-based model additive and two previously developed antifouling additives. The model additive has no effect on the mechanical properties of the bulk material, whereas the stiffness of electrospun scaffolds was slightly decreased compared to pristine PCL-BU following the addition of the three different additives. These results show the robustness of supramolecular additives used in biomedical applications, in which mechanical properties are important, such as vascular grafts and heart valve constructs.

Contribution of nascent cohesive fiber-fiber interactions to the non-linear elasticity of fibrin networks under tensile load

Fibrin is a viscoelastic proteinaceous polymer that determines the deformability and integrity of blood clots and fibrin-based biomaterials in response to biomechanical forces. Here, a previously unnoticed structural mechanism of fibrin clots' mechanical response to external tensile loads is tested using high-resolution confocal microscopy and recently developed three-dimensional computational model. This mechanism, underlying local strain-stiffening of individual fibers as well as global stiffening of the entire network, is based on previously neglected nascent cohesive pairwise interactions between individual fibers (crisscrossing) in fibrin networks formed under tensile load. Existence of fiber-fiber crisscrossings of reoriented fibers was confirmed using 3D imaging of experimentally obtained stretched fibrin clots. The computational model enabled us to study structural details and quantify mechanical effects of the fiber-fiber cohesive crisscrossing during stretching of fibrin gels at various spatial scales. The contribution of the fiber-fiber cohesive contacts to the elasticity of stretched fibrin networks was characterized by changes in individual fiber stiffness, the length, width, and alignment of fibers, as well as connectivity and density of the entire network. The results show that the nascent cohesive crisscrossing of fibers in stretched fibrin networks comprise an underappreciated important structural mechanism underlying the mechanical response of fibrin to (patho)physiological stresses that determine the course and outcomes of thrombotic and hemostatic disorders, such as heart attack and ischemic stroke. STATEMENT OF SIGNIFICANCE: Fibrin is a viscoelastic proteinaceous polymer that determines the deformability and integrity of blood clots and fibrin-based biomaterials in response to biomechanical forces. In this paper, a novel structural mechanism of fibrin clots' mechanical response to external tensile loads is tested using high-resolution confocal microscopy and newly developed computational model. This mechanism, underlying local strain-stiffening of individual fibers as well as global stiffening of the entire network, is based on previously neglected nascent cohesive pairwise interactions between individual fibers (crisscrossing) in fibrin networks formed under tensile load. Cohesive crisscrossing is an important structural mechanism that influences the mechanical response of blood clots and which can determine the outcomes of blood coagulation disorders, such as heart attacks and strokes.

Differential outcomes of venous and arterial tissue engineered vascular grafts highlight the importance of coupling long-term implantation studies with computational modeling

Electrospinning is commonly used to generate polymeric scaffolds for tissue engineering. Using this approach, we developed a small-diameter tissue engineered vascular graft (TEVG) composed of poly-ε-caprolactone-co-l-lactic acid (PCLA) fibers and longitudinally assessed its performance within both the venous and arterial circulations of immunodeficient (SCID/bg) mice. Based on in vitro analysis demonstrating complete loss of graft strength by 12 weeks, we evaluated neovessel formation in vivo over 6-, 12- and 24-week periods. Mid-term observations indicated physiologic graft function, characterized by 100% patency and luminal matching with adjoining native vessel in both the venous and arterial circulations. An active and robust remodeling process was characterized by a confluent endothelial cell monolayer, macrophage infiltrate, and extracellular matrix deposition and remodeling. Long-term follow-up of venous TEVGs at 24 weeks revealed viable neovessel formation beyond graft degradation when implanted in this high flow, low-pressure environment. Arterial TEVGs experienced catastrophic graft failure due to aneurysmal dilatation and rupture after 14 weeks. Scaffold parameters such as porosity, fiber diameter, and degradation rate informed a previously described computational model of vascular growth and remodeling, and simulations predicted the gross differential performance of the venous and arterial TEVGs over the 24-week time course. Taken together, these results highlight the requirement for in vivo implantation studies to extend past the critical time period of polymer degradation, the importance of differential neotissue deposition relative to the mechanical (pressure) environment, and further support the utility of predictive modeling in the design, use, and evaluation of TEVGs in vivo. STATEMENT OF SIGNIFICANCE: Herein, we apply a biodegradable electrospun vascular graft to the arterial and venous circulations of the mouse and follow recipients beyond the point of polymer degradation. While venous implants formed viable neovessels, arterial grafts experienced catastrophic rupture due to aneurysmal dilation. We then inform a previously developed computational model of tissue engineered vascular graft growth and remodeling with parameters specific to the electrospun scaffolds utilized in this study. Remarkably, model simulations predict the differential performance of the venous and arterial constructs over 24 weeks. We conclude that computational simulations should inform the rational selection of scaffold parameters to fabricate tissue engineered vascular grafts that must be followed in vivo over time courses extending beyond polymer degradation.

Image-based analysis and simulation of the effect of platelet storage temperature on clot mechanics under uniaxial strain

Optimal strength and stability of blood clots are keys to hemostasis and in prevention of hemorrhagic or thrombotic complications. Clots are biocomposite materials composed of fibrin network enmeshing platelets and other blood cells. We have previously shown that the storage temperature of platelets significantly impacts clot structure and stiffness. The objective of this work is to delineate the relationship between morphological characteristics and mechanical response of clot networks. We examined scanning electron microscope images of clots prepared from fresh apheresis platelets, and from apheresis platelets stored for 5 days at room temperature or at 4 °C, suspended in pooled plasma. Principal component analysis of nine different morphometric parameters revealed that a single principal component (PC1) can distinguish the effect of platelet storage on clot ultrastructure. Finite element analysis of clot response to uniaxial strain was used to map the spatially heterogeneous distribution of strain energy density for each clot. At modest deformations (25% strain), a single principal component (PC2) was able to predict these heterogeneities as quantified by variability in strain energy density distribution and in linear elastic stiffness, respectively. We have identified structural parameters that are primary regulators of stress distribution, and the observations provide insights into the importance of spatial heterogeneity on hemostasis and thrombosis.

Integrating structural heterogeneity, fiber orientation, and recruitment in multiscale ECM mechanics

Extracellular matrix (ECM) plays critical roles in establishing tissue structure-function relationships and controlling cell fate. However, the mechanisms by which ECM mechanics influence cell and tissue behavior remain to be elucidated since the events associated with this process span length scales from the tissue to molecular level. Entirely new methods are needed in order to better understand the multiscale mechanics of ECM. In this study, a multiscale experimental approach was established by integrating Optical Magnetic Twisting Cytometry (OMTC) with a biaxial tensile tester to study the microscopic (local) ECM mechanical properties under controlled tissue-level (global) loading. Adventitial layer of porcine thoracic artery was used as a collagen-based ECM. Multiphoton microscopy imaging was performed to capture the changes in ECM fiber structure during biaxial deformation. As visualized from multiphoton microscopy images, biaxial stretch induces gradual fiber straightening and the fiber families become evident at higher stretch levels. The OMTC measurements show that the local apparent storage and loss modulus increases with the global biaxial stretch, however there exists a complex interplay among local ECM mechanical properties, ECM structural heterogeneity, and fiber distribution and engagement. The phase lag does not change significantly with global biaxial stretch. Our results also show a much faster increase in global tissue tangent modulus compared to the local apparent complex modulus with biaxial stretch, indicating the scale dependency of ECM mechanics.

Meso-scale topological cues influence extracellular matrix production in a large deformation, elastomeric scaffold model

Physical cues are decisive factors in extracellular matrix (ECM) formation and elaboration. Their transduction across scale lengths is an inherently symbiotic phenomenon that while influencing ECM fate is also mediated by the ECM structure itself. This study investigates the possibility of enhancing ECM elaboration by topological cues that, while not modifying the substrate macro scale mechanics, can affect the meso-scale strain range acting on cells incorporated within the scaffold. Vascular smooth muscle cell micro-integrated, electrospun scaffolds were fabricated with comparable macroscopic biaxial mechanical response, but different meso-scale topology. Seeded scaffolds were conditioned on a stretch bioreactor and exposed to large strain deformations. Samples were processed to evaluate ECM quantity and quality via: biochemical assay, qualitative and quantitative histological assessment and multi-photon analysis. Experimental evaluation was coupled to a numerical model that elucidated the relationship between the scaffold micro-architecture and the strain acting on the cells. Results showed an higher amount of ECM formation for the scaffold type characterized by lowest fiber intersection density. The numerical model simulations associated this result with the differences found for the change in cell nuclear aspect ratio and showed that given comparable macro scale mechanics, a difference in material topology created significant differences in cell-scaffold meso-scale deformations. These findings reaffirmed the role of cell shape in ECM formation and introduced a novel notion for the engineering of cardiac tissue where biomaterial structure can be designed to both mimick the organ level mechanics of a specific tissue of interest and elicit a desirable cellular response.

Micromechanical study of the load transfer in a polycaprolactone-collagen hybrid scaffold when subjected to unconfined and confined compression

Scaffolds are used in diverse tissue engineering applications as hosts for cell proliferation and extracellular matrix formation. One of the most used tissue engineering materials is collagen, which is well known to be a natural biomaterial, also frequently used as cell substrate, given its natural abundance and intrinsic biocompatibility. This study aims to evaluate how the macroscopic biomechanical stimuli applied on a construct made of polycaprolactone scaffold embedded in a collagen substrate translate into microscopic stimuli at the cell level. Eight poro-hyperelastic finite element models of 3D printed hybrid scaffolds from the same batch were created, along with an equivalent model of the idealized geometry of that scaffold. When applying an 8% confined compression at the macroscopic level, local fluid flow of up to 20 [Formula: see text]m/s and octahedral strain levels mostly under 20% were calculated in the collagen substrate. Conversely unconfined compression induced fluid flow of up to 10 [Formula: see text]m/s and octahedral strain from 10 to 35%. No relevant differences were found amongst the scaffold-specific models. Following the mechanoregulation theory based on Prendergast et al. (J Biomech 30:539-548, 1997. https://doi.org/10.1016/S0021-9290(96)00140-6 ), those results suggest that mainly cartilage or fibrous tissue formation would be expected to occur under unconfined or confined compression, respectively. This in silico study helps to quantify the microscopic stimuli that are present within the collagen substrate and that will affect cell response under in vitro bioreactor mechanical stimulation or even after implantation.

Nitro-Oleic Acid (NO2-OA) Release Enhances Regional Angiogenesis in a Rat Abdominal Wall Defect Model

Ventral hernia is often addressed surgically by the placement of prosthetic materials, either synthetic or from allogeneic and xenogeneic biologic sources. Despite advances in surgical approaches and device design, a number of postsurgical limitations remain, including hernia recurrence, mesh encapsulation, and reduced vascularity of the implanted volume. The in situ controlled release of angiogenic factors from a scaffold facilitating abdominal wall repair might address some of these issues associated with suboptimal tissue reconstruction. Furthermore, a biocomposite material that combines the favorable mechanical properties achievable with synthetic materials and the bioactivity associated with xenogeneic tissue sources would be desirable. In this report, an abdominal wall repair scaffold has been designed based on a microfibrous, elastomeric poly(ester carbonate)urethane urea matrix integrated with a hydrogel derived from decellularized porcine dermis (extracellular matrix [ECM] gel) and poly(lactic-co-glycolic acid) (PLGA) microspheres loaded with nitro-oleic acid (NO₂-OA). NO₂-OA is an electrophilic fatty acid nitro-alkene derivative that, under hypoxic conditions, induces angiogenesis. This scaffold was utilized to repair a rat abdominal wall partial thickness defect, hypothesizing that the nitro-fatty acid release would facilitate increased angiogenesis at the 8-week endpoint. The quantification of neovascularization was conducted by novel methodologies to assess vessel morphology and spatial distribution. The repaired abdominal wall defects were evaluated by histopathologic methods, including quantification of the foreign body response and cellular ingrowth. The results showed that NO₂-OA release was associated with significantly improved regional angiogenesis. The combined biohybrid scaffold and NO₂-OA-controlled release strategy also reduced scaffold encapsulation, increased wall thickness, and enhanced cellular infiltration. More broadly, the three components of the composite scaffold design (ECM gel, polymeric fibers, and PLGA microparticles) enable the tuning of performance characteristics, including scaffold bioactivity, degradation, mechanics, and drug release profile, all decisive factors to better address current limitations in abdominal wall repair or other soft tissue augmentation procedures.

Longitudinal Study of the Effects of Environmental pH on the Mechanical Properties of Aspergillus niger

The regulation of environmental pH is key to the health of an ecosystem, influencing the metabolic activity, growth, and development of organisms within it. Although pH values can be measured by a wide range of readily available technologies ranging from fluorescent dyes and nanosensors, these cannot reveal the history of environmental pH from before monitoring begins. This information is sometimes crucial for piecing together what has happened to an ecosystem, and our long-term goal is therefore to develop technologies capable of obtaining it. Here, we propose monitoring environmental pH over time by tracking mechanical properties of a common fungus. As a first step toward obtaining a time history of pH, we evaluate the effect of pH upon the effective indentation modulus of spores and hyphae of Aspergillus niger. We report that the indentation modulus of this phosphorus-solubilizing fungus, obtained through atomic force microscopy and nanoindentation, correlated with environmental acidity. We observed a significant, monotonic increase in moduli over the course of incubation in an acidic environment, but no change in moduli over time for incubation in a neutral environment. Results show promise for using our scheme to detect and track environmental pH over time, and more broadly for using a microorganism's mechanical properties as a biomarker for environmental detection.

A deep learning approach to estimate chemically-treated collagenous tissue nonlinear anisotropic stress-strain responses from microscopy images

Biological collagenous tissues comprised of networks of collagen fibers are suitable for a broad spectrum of medical applications owing to their attractive mechanical properties. In this study, we developed a noninvasive approach to estimate collagenous tissue elastic properties directly from microscopy images using Machine Learning (ML) techniques. Glutaraldehyde-treated bovine pericardium (GLBP) tissue, widely used in the fabrication of bioprosthetic heart valves and vascular patches, was chosen to develop a representative application. A Deep Learning model was designed and trained to process second harmonic generation (SHG) images of collagen networks in GLBP tissue samples, and directly predict the tissue elastic mechanical properties. The trained model is capable of identifying the overall tissue stiffness with a classification accuracy of 84%, and predicting the nonlinear anisotropic stress-strain curves with average regression errors of 0.021 and 0.031. Thus, this study demonstrates the feasibility and great potential of using the Deep Learning approach for fast and noninvasive assessment of collagenous tissue elastic properties from microstructural images.

STATEMENT OF SIGNIFICANCE

In this study, we developed, to our best knowledge, the first Deep Learning-based approach to estimate the elastic properties of collagenous tissues directly from noninvasive second harmonic generation images. The success of this study holds promise for the use of Machine Learning techniques to noninvasively and efficiently estimate the mechanical properties of many structure-based biological materials, and it also enables many potential applications such as serving as a quality control tool to select tissue for the manufacturing of medical devices (e.g. bioprosthetic heart valves).

A 2.5D approach to the mechanics of electrospun fibre mats

In this paper, a discrete random network modelling approach specific to electrospun networks is presented. Owing to the manufacturing process, fibres in these materials systems have an enormous length, as compared to their diameters, and form sparse networks since fibre contact over thickness is limited to a narrow range. Representative volume elements are generated, in which fibres span the entire domain, and a technique is developed to apply computationally favourable periodic boundary conditions despite the initial non-periodicity of the networks. To capture sparsity, a physically motivated method is proposed to distinguish true fibre cross-links, in which mechanical interaction takes place, from mere fibre intersections. The model is exclusively informed by experimentally accessible parameters, demonstrates excellent agreement with the mechanical response of electrospun fibre mats, captures typical microscopic deformation patterns, and provides information on the kinematics of fibres and pores. This ability to address relevant mechanisms of deformation at both micro- and macroscopic length scales, together with the moderate computational cost, render the proposed modelling approach a highly qualified tool for the computer-based design and optimization of electrospun networks.

Microstructure based prediction of the deformation behavior of soft collagenous membranes

The response of human amnion (HA) and bovine Glisson's capsule (GC) to uniaxial and biaxial tensile loading is analyzed on tissue (∼mm) and collagen fiber (∼μm) length scales. The mechanical behavior of the membranes is rationalized based on a discrete fiber network model that relates model parameters with microstructural features of the tissues. Parameters were first determined for GC based on the quantity and organization of collagen fibers in the tissue. Next, parameters for HA were defined by comparing the microstructures of the two membranes, which differ in fiber organization in that collagen forms μm-thick fiber bundles in GC while 50 nm-thin fibrils constitute the network in HA. The flexural behavior of these structures is phenomenologically represented in the model, indicating that shear forces are transmitted through fibrils within GC bundles, but to a much lesser extent than in a corresponding solid cross section. The model provides excellent predictions of the uniaxial and biaxial mechanical response, as well as of the progressive reorientation of fibers associated with uniaxial loading. The results are particularly relevant since model parameters were not obtained through a fitting procedure of the tissue's tension-stretch curve. Furthermore, simulations of representative in vivo deformation states indicated that a large part of the fibers are expected to be un-crimped under physiological loading conditions. Thus, the crimped shape of collagen fibers in the initial test configuration, and typically observed in histological analyses, might be a consequence of the contraction occurring when membranes are extracted from their environment in the body.

Aging of the skeletal muscle extracellular matrix drives a stem cell fibrogenic conversion

Age‐related declines in skeletal muscle regeneration have been attributed to muscle stem cell (MuSC) dysfunction. Aged MuSCs display a fibrogenic conversion, leading to fibrosis and impaired recovery after injury. Although studies have demonstrated the influence of in vitro substrate characteristics on stem cell fate, whether and how aging of the extracellular matrix (ECM) affects stem cell behavior has not been investigated. Here, we investigated the direct effect of the aged muscle ECM on MuSC lineage specification. Quantification of ECM topology and muscle mechanical properties reveals decreased collagen tortuosity and muscle stiffening with increasing age. Age‐related ECM alterations directly disrupt MuSC responses, and MuSCs seeded ex vivo onto decellularized ECM constructs derived from aged muscle display increased expression of fibrogenic markers and decreased myogenicity, compared to MuSCs seeded onto young ECM. This fibrogenic conversion is recapitulated in vitro when MuSCs are seeded directly onto matrices elaborated by aged fibroblasts. When compared to young fibroblasts, fibroblasts isolated from aged muscle display increased nuclear levels of the mechanosensors, Yes‐associated protein (YAP)/transcriptional coactivator with PDZ‐binding motif (TAZ), consistent with exposure to a stiff microenvironment in vivo. Accordingly, preconditioning of young fibroblasts by seeding them onto a substrate engineered to mimic the stiffness of aged muscle increases YAP/TAZ nuclear translocation and promotes secretion of a matrix that favors MuSC fibrogenesis. The findings here suggest that an age‐related increase in muscle stiffness drives YAP/TAZ‐mediated pathogenic expression of matricellular proteins by fibroblasts, ultimately disrupting MuSC fate.

Numerical investigation of the influence of pattern topology on the mechanical behavior of PEGDA hydrogels

Poly(ethylene glycol) diacrylate (PEGDA) hydrogels can be potentially used as scaffold material for tissue engineered heart valves (TEHVs) due to their good biocompatibility and biomechanical tunability. The photolithographic patterning technique is an effective approach to pattern PEGDA hydrogels to mimic the mechanical behavior of native biological tissues that are intrinsically anisotropic. The material properties of patterned PEGDA hydrogels largely depend on the pattern topology. In this paper, we adopt a newly proposed computational framework for fibrous biomaterials to numerically investigate the influence of pattern topology, including pattern ratio, orientation and waviness, on the mechanical behavior of patterned PEGDA hydrogels. The material parameters for the base hydrogel and the pattern stripes are directly calibrated from published experimental data. Several experimental observations reported in the literature are captured in the simulation, including the nonlinear relationship between pattern ratio and material linear modulus, and the decrease of material anisotropy when pattern ratio increases. We further numerically demonstrate that a three-region (toe-heel-linear) stress-strain relationship typically exhibited by biological tissues can be obtained by tuning the pattern waviness and the relative stiffness between the base hydrogel and pattern stripes. The numerical strategy and simulation results presented here can provide helpful guidance to optimize pattern design of PEGDA hydrogels toward the targeted material mechanical properties, therefore advance the development of TEHVs.

STATEMENT OF SIGNIFICANCE

Poly(ethylene glycol) diacrylate (PEGDA) hydrogels can be used as scaffold material for tissue engineered heart values (TEHVs) providing a promising alternative to generate suitable heart valve replacement method. The patterning of PEGDA hydrogels using photolithographic techniques creates materials that mimic the mechanical behavior of native heart valve tissues. However, targeted material properties are obtained via a trial-and-error process. Depending on experiments alone to explore the influence of pattern topology is expensive and time-consuming. We combine a newly proposed computational framework with published experimental data to numerically investigate the influence of pattern geometry on the mechanical behavior of patterned PEGDA hydrogels. The numerical strategy and simulation results presented here can provide guidance to optimize the design of PEGDA hydrogels with targeted material properties, therefore advance the development of TEHVs.

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.

Optical metrics of the extracellular matrix predict compositional and mechanical changes after myocardial infarction

Understanding the organization and mechanical function of the extracellular matrix (ECM) is critical for the development of therapeutic strategies that regulate wound healing following disease or injury. However, these relationships are challenging to elucidate during remodeling following myocardial infarction (MI) due to rapid changes in cellularity and an inability to characterize both ECM microstructure and function non-destructively. In this study, we overcome those challenges through whole organ decellularization and non-linear optical microscopy to directly relate the microstructure and mechanical properties of myocardial ECM. We non-destructively quantify collagen organization, content, and cross-linking within decellularized healthy and infarcted myocardium using second harmonic generation (SHG) and two photon excited autofluorescence. Tensile mechanical testing and compositional analysis reveal that the cumulative SHG intensity within each image volume and the average collagen autofluorescence are significantly correlated with collagen content and elastic modulus of the ECM, respectively. Compared to healthy ECM, infarcted tissues demonstrate a significant increase in collagen content and fiber alignment, and a decrease in cross-linking and elastic modulus. These findings indicate that cross-linking plays a key role in stiffness at the collagen fiber level following infarction, and highlight how this non-destructive approach to assessing remodeling can be used to understand ECM structure-function relationships.

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.

Bi-layered polyurethane - Extracellular matrix cardiac patch improves ischemic ventricular wall remodeling in a rat model

As an intervention to abrogate ischemic cardiomyopathy, the concept of applying a temporary, local patch to the surface of the recently infarcted ventricle has been explored from a number of design perspectives. Two important features considered for such a cardiac patch include the provision of appropriate mechanical support and the capacity to influence the remodeling pathway by providing cellular or biomolecule delivery. The objective of this report was to focus on these two features by first evaluating the incorporation of a cardiac extracellular matrix (ECM) component, and second by evaluating the impact of patch anisotropy on the pathological remodeling process initiated by myocardial infarction. The functional outcomes of microfibrous, elastomeric, biodegradable cardiac patches have been evaluated in a rat chronic infarction model. Ten weeks after infarction and 8 wk after patch epicardial placement, echocardiographic function, tissue-level structural remodeling (e.g., biaxial mechanical response and microstructural analysis), and cellular level remodeling were assessed. The results showed that the incorporation of a cardiac ECM altered the progression of several keys aspects of maladaptive remodeling following myocardial infarction. This included decreasing LV global mechanical compliance, inhibiting echocardiographically-measured functional deterioration, mitigating scar formation and LV wall thinning, and promoting angiogenesis. In evaluating the impact of patch anisotropy, no effects from the altered patch mechanics were detected after 8 wk, possibly due to patch fibrous encapsulation. Overall, this study demonstrates the benefit of a cardiac patch design that combines both ventricle mechanical support, through a biodegradable, fibrillary elastomeric component, and the incorporation of ECM-based hydrogel components.

A structural finite element model for lamellar unit of aortic media indicates heterogeneous stress field after collagen recruitment

Incorporation of collagen structural information into the study of biomechanical behavior of ascending thoracic aortic (ATA) wall tissue should provide better insight into the pathophysiology of ATA. Structurally motivated constitutive models that include fiber dispersion and recruitment can successfully capture overall mechanical response of the arterial wall tissue. However, these models cannot examine local microarchitectural features of the collagen network, such as the effect of fiber disruptions and interaction between fibrous and non-fibrous components, which may influence emergent biomechanical properties of the tissue. Motivated by this need, we developed a finite element based three-dimensional structural model of the lamellar units of the ATA media that directly incorporates the collagen fiber microarchitecture. The fiber architecture was computer generated utilizing network features, namely fiber orientation distribution, intersection density and areal concentration, obtained from image analysis of multiphoton microscopy images taken from human aneurysmal ascending thoracic aortic media specimens with bicuspid aortic valve (BAV) phenotype. Our model reproduces the typical J-shaped constitutive response of the aortic wall tissue. We found that the stress state in the non-fibrous matrix was homogeneous until the collagen fibers were recruited, but became highly heterogeneous after that event. The degree of heterogeneity was dependent upon local network architecture with high stresses observed near disrupted fibers. The magnitude of non-fibrous matrix stress at higher stretch levels was negatively correlated with local fiber density. The localized stress concentrations, elucidated by this model, may be a factor in the degenerative changes in aneurysmal ATA tissue.

Cell structure, stiffness and permeability of freeze-dried collagen scaffolds in dry and hydrated states

Scaffolds for tissue engineering applications should be highly permeable to support mass transfer requirements while providing a 3-D template for the encapsulated biological cells. High porosity and cell interconnectivity result in highly compliant scaffolds. Overstraining occurs easily with such compliant materials and can produce misleading results. In this paper, the cell structure of freeze-dried collagen scaffolds, in both dry and hydrated states, was characterised using X-ray tomography and 2-photon confocal microscopy respectively. Measurements have been made of the scaffold's Young's modulus using conventional mechanical testing and a customised see-saw testing configuration. Specific permeability was measured under constant pressure gradient and compared with predictions. The collagen scaffolds investigated here have a coarse cell size (∼100-150 μm) and extensive connectivity between adjacent cells (∼10-30 μm) in both dry and hydrated states. The Young's modulus is very low, of the order of 10 kPa when dry and 1 kPa when hydrated. There is only a single previous study concerning the specific permeability of (hydrated) collagen scaffolds, despite its importance in nutrient diffusion, waste removal and cell migration. The experimentally measured value reported here (5 × 10(-)(10)m(2)) is in good agreement with predictions based on Computational Fluid Dynamics simulation and broadly consistent with the Carman-Kozeny empirical estimate. It is however about three orders of magnitude higher than the single previously-reported value and this discrepancy is attributed at least partly to the high pressure gradient imposed in the previous study.

STATEMENT OF SIGNIFICANCE

The high porosity and interconnectivity of tissue engineering scaffolds result in highly compliant structures (ie large deflections under low applied loads). Characterisation is essential if these scaffolds are to be systematically optimised. Scaffold overstraining during characterisation can lead to misleading results. In this study, the stiffness (in dry and hydrated states) and specific permeability of freeze-dried collagen scaffolds have been measured using techniques customised for low stiffness structures. The scaffold cell structure is investigated using X-ray computed tomography, which has been applied previously to visualise such materials, without extracting any structural parameters or simulating fluid flow. These are carried out in this work. 2-photon confocal microscopy is used for the first time to study the structure in hydrated state.

Arsenic Promotes NF-Κb-Mediated Fibroblast Dysfunction and Matrix Remodeling to Impair Muscle Stem Cell Function

Arsenic is a global health hazard that impacts over 140 million individuals worldwide. Epidemiological studies reveal prominent muscle dysfunction and mobility declines following arsenic exposure; yet, mechanisms underlying such declines are unknown. The objective of this study was to test the novel hypothesis that arsenic drives a maladaptive fibroblast phenotype to promote pathogenic myomatrix remodeling and compromise the muscle stem (satellite) cell (MuSC) niche. Mice were exposed to environmentally relevant levels of arsenic in drinking water before receiving a local muscle injury. Arsenic-exposed muscles displayed pathogenic matrix remodeling, defective myofiber regeneration and impaired functional recovery, relative to controls. When naïve human MuSCs were seeded onto three-dimensional decellularized muscle constructs derived from arsenic-exposed muscles, cells displayed an increased fibrogenic conversion and decreased myogenicity, compared with cells seeded onto control constructs. Consistent with myomatrix alterations, fibroblasts isolated from arsenic-exposed muscle displayed sustained expression of matrix remodeling genes, the majority of which were mediated by NF-κB. Inhibition of NF-κB during arsenic exposure preserved normal myofiber structure and functional recovery after injury, suggesting that NF-κB signaling serves as an important mechanism of action for the deleterious effects of arsenic on tissue healing. Taken together, the results from this study implicate myomatrix biophysical and/or biochemical characteristics as culprits in arsenic-induced MuSC dysfunction and impaired muscle regeneration. It is anticipated that these findings may aid in the development of strategies to prevent or revert the effects of arsenic on tissue healing and, more broadly, provide insight into the influence of the native myomatrix on stem cell behavior.

Microstructure-dependent mechanical properties of electrospun core-shell scaffolds at multi-scale levels

Mechanical factors among many physiochemical properties of scaffolds for stem cell-based tissue engineering significantly affect tissue morphogenesis by controlling stem cell behaviors including proliferation and phenotype-specific differentiation. Core-shell electrospinning provides a unique opportunity to control mechanical properties of scaffolds independent of surface chemistry, rendering a greater freedom to tailor design for specific applications. In this study, we synthesized electrospun core-shell scaffolds having different core composition and/or core-to-shell dimensional ratios. Two independent biocompatible polymer systems, polyetherketoneketone (PEKK) and gelatin as the core materials while maintaining the shell polymer with polycaprolactone (PCL), were utilized. The mechanics of such scaffolds was analyzed at the microscale and macroscales to determine the potential implications it may hold for cell-material and tissue-material interactions. The mechanical properties of individual core-shell fibers were controlled by core-shell composition and structure. The individual fiber modulus correlated with the increase in percent core size ranging from 0.55±0.10GPa to 1.74±0.22GPa and 0.48±0.12GPa to 1.53±0.12GPa for the PEKK-PCL and gelatin-PCL fibers, respectively. More importantly, it was demonstrated that mechanical properties of the scaffolds at the macroscale were dominantly determined by porosity under compression. The increase of scaffold porosity from 70.2%±1.0% to 93.2%±0.5% by increasing the core size in the PEKK-PCL scaffold resulted in the decrease of the compressive elastic modulus from 227.67±20.39kPa to 14.55±1.43kPa while a greater changes in the porosity of gelatin-PCL scaffold from 54.5%±4.2% to 89.6%±0.4% resulted in the compressive elastic modulus change from 484.01±30.18kPa to 17.57±1.40kPa. On the other hand, the biphasic behaviors under tensile mechanical loading result in a range from a minimum of 5.42±1.05MPa to a maximum of 12.00±1.96MPa for the PEKK-PCL scaffolds, and 10.19±4.49MPa to 22.60±2.44MPa for the gelatin-PCL scaffolds. These results suggest a feasible approach for precisely controlling the local and global mechanical characteristics, in addition to independent control over surface chemistry, to achieve a desired tissue morphogenesis using the core-shell electrospinning.

Constitutive modeling of ascending thoracic aortic aneurysms using microstructural parameters

Ascending thoracic aortic aneurysm (ATAA) has been associated with diminished biomechanical strength and disruption in the collagen fiber microarchitecture. Additionally, the congenital bicuspid aortic valve (BAV) leads to a distinct extracellular matrix structure that may be related to ATAA development at an earlier age than degenerative aneurysms arising in patients with the morphological normal tricuspid aortic valve (TAV). The purpose of this study was to model the fiber-reinforced mechanical response of ATAA specimens from patients with either BAV or TAV. This was achieved by combining image-analysis derived parameters of collagen fiber dispersion and alignment with tensile testing data. Then, numerical simulations were performed to assess the role of anisotropic constitutive formulation on the wall stress distribution of aneurysmal aorta. Results indicate that both BAV ATAA and TAV ATAA have altered collagen fiber architecture in the medial plane of experimentally-dissected aortic tissues when compared to normal ascending aortic specimens. The study findings highlight that differences in the collagen fiber distribution mostly influences the resulting wall stress distribution rather than the peak stress. We conclude that fiber-reinforced constitutive modeling that takes into account the collagen fiber defect inherent to the aneurysmal ascending aorta is paramount for accurate finite element predictions and ultimately for biomechanical-based indicators to reliably distinguish the more from the less 'malignant' ATAAs.

The anisotropic mechanical behaviour of electro-spun biodegradable polymer scaffolds: Experimental characterisation and constitutive formulation

Electro-spun biodegradable polymer fibrous structures exhibit anisotropic mechanical properties dependent on the degree of fibre alignment. Degradation and mechanical anisotropy need to be captured in a constitutive formulation when computational modelling is used in the development and design optimisation of such scaffolds. Biodegradable polyester-urethane scaffolds were electro-spun and underwent uniaxial tensile testing in and transverse to the direction of predominant fibre alignment before and after in vitro degradation of up to 28 days. A microstructurally-based transversely isotropic hyperelastic continuum constitutive formulation was developed and its parameters were identified from the experimental stress-strain data of the scaffolds at various stages of degradation. During scaffold degradation, maximum stress and strain in circumferential direction decreased from 1.02 ± 0.23 MPa to 0.38 ± 0.004 MPa and from 46 ± 11 % to 12 ± 2 %, respectively. In longitudinal direction, maximum stress and strain decreased from 0.071 ± 0.016 MPa to 0.010 ± 0.007 MPa and from 69 ± 24 % to 8 ± 2 %, respectively. The constitutive parameters were identified for both directions of the non-degraded and degraded scaffold for strain range varying between 0% and 16% with coefficients of determination r(2)>0.871. The six-parameter constitutive formulation proved versatile enough to capture the varying non-linear transversely isotropic behaviour of the fibrous scaffold throughout various stages of degradation.

Finite element implementation of a multiscale model of the human lens capsule

An axisymmetric finite element implementation of a previously described structural constitutive model for the human lens capsule (Burd in Biomech Model Mechanobiol 8(3):217-231, 2009) is presented. This constitutive model is based on a hyperelastic approach in which the network of collagen IV within the capsule is represented by an irregular hexagonal planar network of hyperelastic bars, embedded in a hyperelastic matrix. The paper gives a detailed specification of the model and the periodic boundary conditions adopted for the network component. Momentum balance equations for the network are derived in variational form. These balance equations are used to develop a nonlinear solution scheme to enable the equilibrium configuration of the network to be computed. The constitutive model is implemented within a macroscopic finite element framework to give a multiscale model of the lens capsule. The possibility of capsule wrinkling is included in the formulation. To achieve this implementation, values of the first and second derivatives of the strain energy density with respect to the in-plane stretch ratios need to be computed at the local, constitutive model, level. Procedures to determine these strain energy derivatives at equilibrium configurations of the network are described. The multiscale model is calibrated against previously published experimental data on isolated inflation and uniaxial stretching of ex vivo human capsule samples. Two independent example lens capsule inflation analyses are presented.