Mechanical Models of Collagen Networks for Understanding Changes in the Failure Properties of Aging Skin

Skin undergoes mechanical alterations due to changes in the composition and structure of the collagenous dermis with aging. Previous studies have conflicting findings, with both increased and decreased stiffness reported for aging skin. The underlying structure-function relationships that drive age-related changes are complex and difficult to study individually. One potential contributor to these variations is the accumulation of nonenzymatic crosslinks within collagen fibers, which affect dermal collagen remodeling and mechanical properties. Specifically, these crosslinks make individual fibers stiffer in their plastic loading region and lead to increased fragmentation of the collagenous network. To better understand the influence of these changes, we investigated the impact of nonenzymatic crosslink changes on the dermal microstructure using discrete fiber networks representative of the dermal microstructure. Our findings suggest that stiffening the plastic region of collagen's mechanical response has minimal effects on network-level stiffness and failure stresses. Conversely, simulating fragmentation through a loss of connectivity substantially reduces network stiffness and failure stress, while increasing stretch ratios at failure.

A Systems Approach to Biomechanics, Mechanobiology, and Biotransport

The human body represents a collection of interacting systems that range in scale from nanometers to meters. Investigations from a systems perspective focus on how the parts work together to enact changes across spatial scales, and further our understanding of how systems function and fail. Here, we highlight systems approaches presented at the 2022 Summer Biomechanics, Bio-engineering, and Biotransport Conference in the areas of solid mechanics; fluid mechanics; tissue and cellular engineering; biotransport; and design, dynamics, and rehabilitation; and biomechanics education. Systems approaches are yielding new insights into human biology by leveraging state-of-the-art tools, which could ultimately lead to more informed design of therapies and medical devices for preventing and treating disease as well as rehabilitating patients using strategies that are uniquely optimized for each patient. Educational approaches can also be designed to foster a foundation of systems-level thinking.

Utilization of commercial collagens for preparing well-differentiated human beta cells for confocal microscopy

Introduction

With technical advances, confocal and super-resolution microscopy have become powerful tools to dissect cellular pathophysiology. Cell attachment to glass surfaces compatible with advanced imaging is critical prerequisite but remains a considerable challenge for human beta cells. Recently, Phelps et al. reported that human beta cells plated on type IV collagen (Col IV) and cultured in neuronal medium preserve beta cell characteristics.

Methods

We examined human islet cells plated on two commercial sources of Col IV (C6745 and C5533) and type V collagen (Col V) for differences in cell morphology by confocal microscopy and secretory function by glucose-stimulated insulin secretion (GSIS). Collagens were authenticated by mass spectrometry and fluorescent collagen-binding adhesion protein CNA35.

Results

All three preparations allowed attachment of beta cells with high nuclear localization of NKX6.1, indicating a well-differentiated status. All collagen preparations supported robust GSIS. However, the morphology of islet cells differed between the 3 preparations. C5533 showed preferable features as an imaging platform with the greatest cell spread and limited stacking of cells followed by Col V and C6745. A significant difference in attachment behavior of C6745 was attributed to the low collagen contents of this preparation indicating importance of authentication of coating material. Human islet cells plated on C5533 showed dynamic changes in mitochondria and lipid droplets (LDs) in response to an uncoupling agent 2-[2-[4-(trifluoromethoxy)phenyl]hydrazinylidene]-propanedinitrile (FCCP) or high glucose + oleic acid.

Discussion

An authenticated preparation of Col IV provides a simple platform to apply advanced imaging for studies of human islet cell function and morphology.

Native adiponectin plays a role in the adipocyte-mediated conversion of fibroblasts to myofibroblasts

Adipocytes regulate tissues through production of adipokines that can act both locally and systemically. Adipocytes also have been found to play a critical role in regulating the healing process. To better understand this role, we developed a three-dimensional human adipocyte spheroid system that has an adipokine profile similar to in vivo adipose tissues. Previously, we found that conditioned medium from these spheroids induces human dermal fibroblast conversion into highly contractile, collagen-producing myofibroblasts through a transforming growth factor beta-1 (TGF-β1) independent pathway. Here, we sought to identify how mature adipocytes signal to dermal fibroblasts through adipokines to induce myofibroblast conversion. By using molecular weight fractionation, heat inactivation and lipid depletion, we determined mature adipocytes secrete a factor that is 30-100 kDa, heat labile and lipid associated that induces myofibroblast conversion. We also show that the depletion of the adipokine adiponectin, which fits those physico-chemical parameters, eliminates the ability of adipocyte-conditioned media to induce fibroblast to myofibroblast conversion. Interestingly, native adiponectin secreted by cultured adipocytes consistently elicited a stronger level of α-smooth muscle actin expression than exogenously added adiponectin. Thus, adiponectin secreted by mature adipocytes induces fibroblast to myofibroblast conversion and may lead to a phenotype of myofibroblasts distinct from TGF-β1-induced myofibroblasts.

Force-Bioreactor for Assessing Pharmacological Therapies for Mechanobiological Targets

Tissue fibrosis is a major health issue that impacts millions of people and is costly to treat. However, few effective anti-fibrotic treatments are available. Due to their central role in fibrotic tissue deposition, fibroblasts and myofibroblasts are the target of many therapeutic strategies centered primarily on either inducing apoptosis or blocking mechanical or biochemical stimulation that leads to excessive collagen production. Part of the development of these drugs for clinical use involves in vitro prescreening. 2D screens, however, are not ideal for discovering mechanobiologically significant compounds that impact functions like force generation and other cell activities related to tissue remodeling that are highly dependent on the conditions of the microenvironment. Thus, higher fidelity models are needed to better simulate in vivo conditions and relate drug activity to quantifiable functional outcomes. To provide guidance on effective drug dosing strategies for mechanoresponsive drugs, we describe a custom force-bioreactor that uses a fibroblast-seeded fibrin gels as a relatively simple mimic of the provisional matrix of a healing wound. As cells generate traction forces, the volume of the gel reduces, and a calibrated and embedded Nitinol wire deflects in proportion to the generated forces over the course of 6 days while overhead images of the gel are acquired hourly. This system is a useful in vitro tool for quantifying myofibroblast dose-dependent responses to candidate biomolecules, such as blebbistatin. Administration of 50 μM blebbistatin reliably reduced fibroblast force generation approximately 40% and lasted at least 40 h, which in turn resulted in qualitatively less collagen production as determined via fluorescent labeling of collagen.

Multiscale Computational Model Predicts Mouse Skin Kinematics Under Tensile Loading

Skin is a complex tissue whose biomechanical properties are generally understood in terms of an incompressible material whose microstructure undergoes affine deformations. A growing number of experiments, however, have demonstrated that skin has a high Poisson's ratio, substantially decreases in volume during uniaxial tensile loading, and demonstrates collagen fiber kinematics that are not affine with local deformation. In order to better understand the mechanical basis for these properties, we constructed multiscale mechanical models (MSM) of mouse skin based on microstructural multiphoton microscopy imaging of the dermal microstructure acquired during mechanical testing. Three models that spanned the cases of highly aligned, moderately aligned, and nearly random fiber networks were examined and compared to the data acquired from uniaxially stretched skin. Our results demonstrate that MSMs consisting of networks of matched fiber organization can predict the biomechanical behavior of mouse skin, including the large decrease in tissue volume and nonaffine fiber kinematics observed under uniaxial tension.

Three-Dimensional Quantification of Collagen Microstructure During Tensile Mechanical Loading of Skin

Skin is a heterogeneous tissue that can undergo substantial structural and functional changes with age, disease, or following injury. Understanding how these changes impact the mechanical properties of skin requires three-dimensional (3D) quantification of the tissue microstructure and its kinematics. The goal of this study was to quantify these structure-function relationships via second harmonic generation (SHG) microscopy of mouse skin under tensile mechanical loading. Tissue deformation at the macro- and micro-scale was quantified, and a substantial decrease in tissue volume and a large Poisson’s ratio was detected with stretch, indicating the skin differs substantially from the hyperelastic material models historically used to explain its behavior. Additionally, the relative amount of measured strain did not significantly change between length scales, suggesting that the collagen fiber network is uniformly distributing applied strains. Analysis of undeformed collagen fiber organization and volume fraction revealed a length scale dependency for both metrics. 3D analysis of SHG volumes also showed that collagen fiber alignment increased in the direction of stretch, but fiber volume fraction did not change. Interestingly, 3D fiber kinematics was found to have a non-affine relationship with tissue deformation, and an affine transformation of the micro-scale fiber network overestimates the amount of fiber realignment. This result, along with the other outcomes, highlights the importance of accurate, scale-matched 3D experimental measurements when developing multi-scale models of skin mechanical function.

Magnetic tweezers with magnetic flux density feedback control

In this work, we present a single-pole magnetic tweezers (MT) device designed for integration with substrate deformation tracking microscopy and/or traction force microscopy experiments intended to explore extracellular matrix rheology and human epidermal keratinocyte mechanobiology. Assembled from commercially available off-the-shelf electronics hardware and software, the MT device is amenable to replication in the basic biology laboratory. In contrast to conventional solenoid current-controlled MT devices, operation of this instrument is based on real-time feedback control of the magnetic flux density emanating from the blunt end of the needle core using a cascade control scheme and a digital proportional-integral-derivative (PID) controller. Algorithms that compensate for a spatially non-uniform remnant magnetization of the needle core that develops during actuation are implemented into the feedback control scheme. Through optimization of PID gain scheduling, the MT device exhibits magnetization and demagnetization response times of less than 100 ms without overshoot over a wide range of magnetic flux density setpoints. Compared to current-based control, magnetic flux density-based control allows for more accurate and precise magnetic actuation forces by compensating for temperature increases within the needle core due to heat generated by the applied solenoid currents. Near field calibrations validate the ability of the MT device to actuate 4.5 μm-diameter superparamagnetic beads with forces up to 25 nN with maximum relative uncertainties of ±30% for beads positioned between 2.5 and 40 µm from the needle tip.

Human Adipocyte Conditioned Medium Promotes In Vitro Fibroblast Conversion to Myofibroblasts

Adipocytes and adipose tissue derived cells have been investigated for their potential to contribute to the wound healing process. However, the details of how these cells interact with other essential cell types, such as myofibroblasts/fibroblasts, remain unclear. Using a novel in-vitro 3D human adipocyte/pre-adipocyte spheroid model, we investigated whether adipocytes and their precursors (pre-adipocytes) secrete factors that affect human dermal fibroblast behavior. We found that both adipocyte and pre-adipocyte conditioned medium induced the migration of fibroblasts, but only adipocyte conditioned medium induced fibroblast differentiation into a highly contractile, collagen producing myofibroblast phenotype. Furthermore, adipocyte mediated myofibroblast induction occurred through a TGF-β independent mechanism. Our findings contribute to a better understanding on the involvement of adipose tissue in wound healing, and may help to uncover and develop fat-related wound healing treatments.

Targeting Cell Contractile Forces: A Novel Minimally Invasive Treatment Strategy for Fibrosis

Fibrosis is a complication of tendon injury where excessive scar tissue accumulates in and around the injured tissue, leading to painful and restricted joint motion. Unfortunately, fibrosis tends to recur after surgery, creating a need for alternative approaches to disrupt scar tissue. We posited a strategy founded on mechanobiological principles that collagen under tension generated by fibroblasts is resistant to degradation by collagenases. In this study, we tested the hypothesis that blebbistatin, a drug that inhibits cellular contractile forces, would increase the susceptibility of scar tissue to collagenase degradation. Decellularized tendon scaffolds (DTS) were treated with bacterial collagenase with or without external or cell-mediated internal tension. External tension producing strains of 2-4% significantly reduced collagen degradation compared with non-tensioned controls. Internal tension exerted by human fibroblasts seeded on DTS significantly reduced the area of the scaffolds compared to acellular controls and inhibited collagen degradation compared to free-floating DTS. Treatment of cell-seeded DTS with 50 mM blebbistatin restored susceptibility to collagenase degradation, which was significantly greater than in untreated controls (p < 0.01). These findings suggest that therapies combining collagenases with drugs that reduce cell force generation should be considered in cases of tendon fibrosis that do not respond to physiotherapy.

Collective Cell Behavior in Mechanosensing of Substrate Thickness

Extracellular matrix stiffness has a profound effect on the behavior of many cell types. Adherent cells apply contractile forces to the material on which they adhere and sense the resistance of the material to deformation-its stiffness. This is dependent on both the elastic modulus and the thickness of the material, with the corollary that single cells are able to sense underlying stiff materials through soft hydrogel materials at low (<10 μm) thicknesses. Here, we hypothesized that cohesive colonies of cells exert more force and create more hydrogel deformation than single cells, therefore enabling them to mechanosense more deeply into underlying materials than single cells. To test this, we modulated the thickness of soft (1 kPa) elastic extracellular-matrix-functionalized polyacrylamide hydrogels adhered to glass substrates and allowed colonies of MG63 cells to form on their surfaces. Cell morphology and deformations of fluorescent fiducial-marker-labeled hydrogels were quantified by time-lapse fluorescence microscopy imaging. Single-cell spreading increased with respect to decreasing hydrogel thickness, with data fitting to an exponential model with half-maximal response at a thickness of 3.2 μm. By quantifying cell area within colonies of defined area, we similarly found that colony-cell spreading increased with decreasing hydrogel thickness but with a greater half-maximal response at 54 μm. Depth-sensing was dependent on Rho-associated protein kinase-mediated cellular contractility. Surface hydrogel deformations were significantly greater on thick hydrogels compared to thin hydrogels. In addition, deformations extended greater distances from the periphery of colonies on thick hydrogels compared to thin hydrogels. Our data suggest that by acting collectively, cells mechanosense rigid materials beneath elastic hydrogels at greater depths than individual cells. This raises the possibility that the collective action of cells in colonies or sheets may allow cells to sense structures of differing material properties at comparatively large distances.

Substrate deformations induce directed keratinocyte migration

Cell migration is an essential part of many (patho)physiological processes, including keratinocyte re-epithelialization of healing wounds. Physical forces and mechanical cues from the wound bed (in addition to biochemical signals) may also play an important role in the healing process. Previously, we explored this possibility and found that polyacrylamide (PA) gel stiffness affected human keratinocyte behaviour and that mechanical deformations in soft (approx. 1.2 kPa) PA gels produced by neighbouring cells appeared to influence the process of de novo epithelial sheet formation. To clearly demonstrate that keratinocytes do respond to such deformations, we conducted a series of experiments where we observed the response of single keratinocytes to a prescribed local substrate deformation that mimicked a neighbouring cell or evolving multicellular aggregate via a servo-controlled microneedle. We also examined the effect of adding either Y27632 or blebbistatin on cell response. Our results indicate that keratinocytes do sense and respond to mechanical signals comparable to those that originate from substrate deformations imposed by neighbouring cells, a finding that could have important implications for the process of keratinocyte re-epithelialization that takes place during wound healing. Furthermore, the Rho/ROCK pathway and the engagement of NM II are both essential to substrate deformation-directed keratinocyte migration.

The Spectrum of Mechanism-Oriented Models and Methods for Explanations of Biological Phenomena

Developing and improving mechanism-oriented computational models to better explain biological phenomena is a dynamic and expanding frontier. As the complexity of targeted phenomena has increased, so too has the diversity in methods and terminologies, often at the expense of clarity, which can make reproduction challenging, even problematic. To encourage improved semantic and methodological clarity, we describe the spectrum of Mechanism-oriented Models being used to develop explanations of biological phenomena. We cluster explanations of phenomena into three broad groups. We then expand them into seven workflow-related model types having distinguishable features. We name each type and illustrate with examples drawn from the literature. These model types may contribute to the foundation of an ontology of mechanism-based biomedical simulation research. We show that the different model types manifest and exert their scientific usefulness by enhancing and extending different forms and degrees of explanation. The process starts with knowledge about the phenomenon and continues with explanatory and mathematical descriptions. Those descriptions are transformed into software and used to perform experimental explorations by running and examining simulation output. The credibility of inferences is thus linked to having easy access to the scientific and technical provenance from each workflow stage.

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.

Descemet membrane adhesion strength is greater in diabetics with advanced disease compared to healthy donor corneas

Descemet membrane endothelial keratoplasty (DMEK) is an increasingly popular surgical procedure for treating ocular diseases that require a corneal transplant. Previous studies have found that tissue tearing during surgical preparation is more likely elevated in eyes from donors with a history of diabetes mellitus. To quantify these potential differences, we established an experimental technique for quantifying the force required to separate the endothelium-Descemet membrane complex (EDM) from stroma in human donor corneal tissue, and we assessed differences in adhesion strength between diabetic and non-diabetic donor corneas. Transplant suitable corneas were obtained from 23 donors 50-75 years old with an average preservation to assay time of 11.5 days. Corneas were classified from a medical records review as non-diabetic (ND, n = 9), diabetic without evidence of advanced disease (NAD, n = 8), or diabetic with evidence of advanced disease (AD, n = 10). Corneas were sectioned into 3 mm wide strips and the EDM peeled from the stroma. Using the force-extension data obtained from mechanical peel testing, EDM elastic peel tension (T_E), elastic stiffness (S_E), average delamination tension (T_D), and maximum tension (T_MAX) were calculated. Mean T_E, S_E, T_D, and T_MAX values for ND corneas were 0.78 ± 0.07 mN/mm, 0.37 ± 0.05 mN/mm/mm, 0.78 ± 0.08 mN/mm, and 0.94 ± 0.17 mN/mm, respectively. NAD values did not differ significantly. However, AD values for T_E (1.01 ± 0.18 mN/mm), T_D (1.09 ± 0.21 mN/mm), and T_MAX (1.37 ± 0.24 mN/mm) were greater than ND and NAD corneas (P < 0.05). S_E did not differ significantly between groups. These findings provide proof of the concept that chronic hyperglycemia from diabetes mellitus results in a phenotypically more adhesive interface between Descemet membrane and the posterior stroma in donor corneal tissue. Results of this study provide a foundation for further investigations into the impact of diabetes on the posterior cornea, eye banking, and keratoplasty.

Vibratory stimulation enhances thyroid epithelial cell function

The tissues of the body are routinely subjected to various forms of mechanical vibration, the frequency, amplitude, and duration of which can contribute both positively and negatively to human health. The vocal cords, which are in close proximity to the thyroid, may also supply the thyroid with important mechanical signals that modulate hormone production via mechanical vibrations from phonation. In order to explore the possibility that vibrational stimulation from vocalization can enhance thyroid epithelial cell function, FRTL-5 rat thyroid cells were subjected to either chemical stimulation with thyroid stimulating hormone (TSH), mechanical stimulation with physiological vibrations, or a combination of the two, all in a well-characterized, torsional rheometer-bioreactor. The FRTL-5 cells responded to mechanical stimulation with significantly (p<0.05) increased metabolic activity, significantly (p<0.05) increased ROS production, and increased gene expression of thyroglobulin and sodium-iodide symporter compared to un-stimulated controls, and showed an equivalent or greater response than TSH only stimulated cells. Furthermore, the combination of TSH and oscillatory motion produced a greater response than mechanical or chemical stimulation alone. Taken together, these results suggest that mechanical vibrations could provide stimulatory cues that help maintain thyroid function.

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Thyroid epithelial cells responded to mechanical vibrations similar to those from vocalization.

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This response was equivalent or greater compared to chemical stimulation.

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The combination of mechanical and chemical stimulation was synergistic.

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It may be possible to influence thyroid function with mechanical vibrations.

Blebbistatin-Loaded Poly(d,l-lactide-co-glycolide) Particles For Treating Arthrofibrosis

Joint immobility is a debilitating complication of articular trauma that is characterized by thickening and stiffening of the joint capsule and the formation of fibrotic lesions inside joints. Capsule release surgery can temporarily restore mobility, but contraction often recurs due to the contractile activities of fibroblasts, which exert tension on the capsule ECM via nonmuscle myosin II. Based on these findings we hypothesized that blebbistatin, a drug that reversibly inhibits the activity of this protein, would relax ECM tension imposed by fibroblasts and reduce fibrosis. In this study, we characterized the effectiveness of blebbistatin as an anticontractile treatment. Given that sustained suppression of contractile activity may be required to achieve capsule release and reduce fibrosis, we compared the effects on fibroblast-mediated collagen ECM displacement of blebbistatin-loaded poly(lactide-co-gylcolide) (PLGA) particles versus bolus blebbistatin dosing. Time-lapse imaging of fluorescent microspheres embedded in collagen gels confirmed that PLGA/blebbistatin inhibited force generation and reduced both gel displacement and rate of displacement. In addition, collagen production at 10 days was significantly reduced. Taken together, these data indicate that blebbistatin-loaded PLGA particles can be used to inhibit fibroblast force-generation and reduce collagen production and lay the foundation for optimization of drug delivery technology for treating arthrofibrosis.

Correction to 'Collagen network strengthening following cyclic tensile loading'

[This corrects the article DOI: 10.1098/rsfs.2015.0088.].

Synthesis, Optimization, and Performance Demonstration of Electrospun Carbon Nanofiber-Carbon Nanotube Composite Sorbents for Point-of-Use Water Treatment

We developed an electrospun carbon nanofiber-carbon nanotube (CNF-CNT) composite with optimal sorption capacity and material strength for point-of-use (POU) water treatment. Synthesis variables including integration of multiwalled carbon nanotubes (CNTs) and macroporosity (via sublimation of phthalic acid), relative humidity (20 and 40%), and stabilization temperature (250 and 280 °C) were used to control nanofiber diameter and surface area (from electron microscopy and BET isotherms, respectively), surface composition (from XPS), and strength (from AFM nanoindentation and tensile strength tests). Composites were then evaluated using kinetic, isotherm, and pH-edge sorption experiments with sulfamethoxazole (log Kow = 0.89) and atrazine (log Kow = 2.61), representative micropollutants chosen for their different polarities. Although CNFs alone were poor sorbents, integration of CNTs and macroporosity achieved uptake comparable to granular activated carbon. Through reactivity comparisons with CNT dispersions, we propose that increasing macroporosity exposes the embedded CNTs, thereby enabling their role as the primary sorbent in nanofiber composites. Because the highest capacity sorbents lacked sufficient strength, our optimal formulation (polyacrylonitrile 8 wt %, CNT 2 wt %, phthalic acid 2.4 wt %; 40% relative humidity; 280 °C stabilization) represents a compromise between strength and performance. This optimized sorbent was tested with a mixture of ten organic micropollutants at environmentally relevant concentrations in a gravity-fed, flow-through filtration system, where removal trends suggest that both hydrophobic and specific binding interactions contribute to micropollutant uptake. Collectively, this work highlights the promise of CNF-CNT filters (e.g., mechanical strength, ability to harness CNT sorption capacity), while also prioritizing areas for future research and development (e.g., improved removal of highly polar micropollutants, sensitivity to interfering cosolutes).

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.

Collagen network strengthening following cyclic tensile loading

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

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.

Development of the mechanical properties of engineered skin substitutes after grafting to full-thickness wounds

Engineered skin substitutes (ESSs) have been reported to close full-thickness burn wounds but are subject to loss from mechanical shear due to their deficiencies in tensile strength and elasticity. Hypothetically, if the mechanical properties of ESS matched those of native skin, losses due to shear or fracture could be reduced. To consider modifications of the composition of ESS to improve homology with native skin, biomechanical analyses of the current composition of ESS were performed. ESSs consist of a degradable biopolymer scaffold of type I collagen and chondroitin-sulfate (CGS) that is populated sequentially with cultured human dermal fibroblasts (hF) and epidermal keratinocytes (hK). In the current study, the hydrated biopolymer scaffold (CGS), the scaffold populated with hF dermal skin substitute (DSS), or the complete ESS were evaluated mechanically for linear stiffness (N/mm), ultimate tensile load at failure (N), maximum extension at failure (mm), and energy absorbed up to the point of failure (N-mm). These biomechanical end points were also used to evaluate ESS at six weeks after grafting to full-thickness skin wounds in athymic mice and compared to murine autograft or excised murine skin. The data showed statistically significant differences (p <0.05) between ESS in vitro and after grafting for all four structural properties. Grafted ESS differed statistically from murine autograft with respect to maximum extension at failure, and from intact murine skin with respect to linear stiffness and maximum extension. These results demonstrate rapid changes in mechanical properties of ESS after grafting that are comparable to murine autograft. These values provide instruction for improvement of the biomechanical properties of ESS in vitro that may reduce clinical morbidity from graft loss.

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

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

Multiscale mechanical simulations of cell compacted collagen gels

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

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.

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

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

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

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

Identification of regional mechanical anisotropy in soft tissue analogs

In a previous work (Raghupathy and Barocas, 2010, "Generalized Anisotropic Inverse Mechanics for Soft Tissues,"J. Biomech. Eng., 132(8), pp. 081006), a generalized anisotropic inverse mechanics method applicable to soft tissues was presented and tested against simulated data. Here we demonstrate the ability of the method to identify regional differences in anisotropy from full-field displacements and boundary forces obtained from biaxial extension tests on soft tissue analogs. Tissue heterogeneity was evaluated by partitioning the domain into homogeneous subdomains. Tests on elastomer samples demonstrated the performance of the method on isotropic materials with uniform and nonuniform properties. Tests on fibroblast-remodeled collagen cruciforms indicated a strong correlation between local structural anisotropy (measured by polarized light microscopy) and the evaluated local mechanical anisotropy. The results demonstrate the potential to quantify regional anisotropic material behavior on an intact tissue sample.

Production of highly aligned collagen lamellae by combining shear force and thin film confinement

Load-bearing tissues owe their mechanical strength to their highly anisotropic collagenous structure. To date attempts to engineer mechanically strong connective tissue have failed, mainly due to a lack of ability to reproduce the native collagen organization in constructs synthesized by cultured cells in vitro. The ability to influence the orientation of self-assembling collagen molecules to produce highly anisotropic structures has applications ranging from de novo engineering of complex tissues to the production of organized scaffolds for cell culture contact guidance. In this investigation we have used the simple technique of spin-coating to produce highly aligned arrays of collagen fibrils. By a simple modification of the method we have also successfully produced orthogonal collagen lamellae. Alternating collagen lamellae are frequently seen in load-bearing tissues such as cornea, annulus fibrosus, and cortical bone. Culturing of corneal fibroblasts on aligned collagen shows that the cells adopt the organization of fibrils. In this investigation we observed the reversal of fibrillar growth direction or "hook" formation similar to that seen previously in a microfluidic shear flow chamber. Although the results of this investigation clearly show that it is possible to produce small areas (1cm(2)) of collagen fibrils with enough alignment to guide fibroblasts, there is evidence that thin film instabilities are likely to be a significant barrier to producing organized collagen fibrils over larger areas. Successful application of this method to produce highly controlled and organized collagenous structures will require the development of techniques to control thin film instability and will be the subject of future work.

Initial fiber alignment pattern alters extracellular matrix synthesis in fibroblast-populated fibrin gel cruciforms and correlates with predicted tension

Human dermal fibroblasts entrapped in fibrin gels cast in cross-shaped (cruciform) geometries with 1:1 and 1:0.5 ratios of arm widths were studied to assess whether tension and alignment of the cells and fibrils affected ECM deposition. The cruciforms of contrasting geometry (symmetric vs. asymmetric), which developed different fiber alignment patterns, were harvested at 2, 5, and 10 weeks of culture. Cruciforms were subjected to planar biaxial testing, polarimetric imaging, DNA and biochemical analyses, histological staining, and SEM imaging. As the cruciforms compacted and developed fiber alignment, fibrin was degraded, and elastin and collagen were produced in a geometry-dependent manner. Using a continuum mechanical model that accounts for direction-dependent stress due to cell traction forces and cell contact guidance with aligned fibers that occurs in the cruciforms, the mechanical stress environment was concluded to influence collagen deposition, with deposition being the greatest in the narrow arms of the asymmetric cruciform where stress was predicted to be the largest.

Image-based multiscale structural models of fibrous engineered tissues

While it is firmly established that the mechanical behavior of most biological tissues, including bioengineered tissues, is governed by an underlying network of protein fibers, it is still not clear how best to obtain and utilize structural information to predict mechanical response. In this paper, methods are presented to (1) quantify the fiber arrangement in a tissue from different imaging tools, (2) incorporate that structure into a multiscale model, and (3) solve the model equations to predict both the microscopic and the macroscopic tissue response. In principle these concepts could be applied to any tissue (incorporating the specific tissue components as needed), but for demonstration purposes, the focus of the current work is on cell-compacted collagen gel, a model engineered tissue.

Dynamic shear-influenced collagen self-assembly

The ability to influence the direction of polymerization of a self-assembling biomolecular system has the potential to generate materials with extremely high anisotropy. In biological systems where highly-oriented cellular populations give rise to aligned and often load-bearing tissue such organized molecular scaffolds could aid in the contact guidance of cells for engineered tissue constructs (e.g. cornea and tendon). In this investigation we examine the detailed dynamics of pepsin-extracted type I bovine collagen assembly on a glass surface under the influence of flow between two plates. Differential Interference Contrast (DIC) imaging (60x-1.4NA) with focal plane stabilization was used to resolve and track the growth of collagen aggregates on borosilicate glass for 4 different shear rates (500, 80, 20, and 9s(-1)). The detailed morphology of the collagen fibrils/aggregates was examined using Quick Freeze Deep Etch (QFDE) electron microscopy. Nucleation of fibrils on the glass was observed to occur rapidly (approximately 2 min) followed by continued growth of the fibrils. The growth rates were dependent on flow in a complex manner with the highest rate of axial growth (0.1 micro/s) occurring at a shear rate of 9s(-1). The lowest growth rate occurred at the highest shear. Fibrils were observed to both branch and join during the experiments. The best alignment of fibrils was observed at intermediate shear rates of 20 and 80s(-1). However, the investigation revealed that fibril directional growth was not stable. At high shear rates, fibrils would often turn downstream forming what we term "hooks" which are likely the combined result of monomer interaction with the initial collagen layer or "mat" and the high shear rate. Further, QFDE examination of fibril morphology demonstrated that the assembled fibrillar structure did not possess native D-periodicity. Instead, fibrils comprised a collection of generally aligned, monomers which were self-assembled to form a fibril-like aggregate. In conclusion, though constant shear-rate clearly influences collagen fibrillar alignment, the formation of highly-organized collagenous arrays of native-like D-banded fibrils remains a challenge. Modulation of shear in combination with surface energy patterning to produce a highly-aligned initial mat may provide significant improvement of both the fibril morphology and alignment.

Effects of reduced oxygen and glucose levels on ocular cells in vitro: implications for tissue models

An important goal of tissue engineering is the development of better in vitro tissue models for the study and treatment of diseases, especially those that are difficult to model in animals, such as glaucoma. In order to properly interpret experimental results designed to mimic in vivo conditions, it is necessary to characterize the metabolic state of the in vitro culture. The goal of this study was to determine how porcine lamina cribrosa cells (PLC), porcine scleral fibroblasts (PSC) and rat astrocytes (RAS) respond metabolically to reduced glucose and oxygen levels compared to normal in vitro culture conditions. Throughout the culture period, cell number and the levels of glucose, lactate, pyruvate and glutamate were characterized. Cell number in the PLC and PSC was more sensitive to glucose level than oxygen, while the RAS exhibited sensitivities to both variables. While the pyruvate and glutamate levels did not vary substantially between groups, glucose consumption and lactate production were dependent on culture condition. In addition, the DeltaL/DeltaG ratio was dependent on glucose and oxygen levels, but not cell type at early time points. By day 7, however, the RAS exhibited ratios consistently lower than the other cell types. The results of this study serve as a basis for future studies into the degenerative matrix remodeling in the glaucomatous optic nerve head, and may prove insightful for other tissue engineering applications.

Comparison of 2D fiber network orientation measurement methods

The mechanical properties of tissues, tissue analogs, and biomaterials are dependent on their underlying microstructure. As such, many mechanical models incorporate some aspect of microstructure, but a robust protocol for characterizing fiber architecture remains a challenge. A number of image-based methods, including mean intercept length (MIL), line fraction deviation (LFD), and Fourier transform methods (FTM), have been applied to microstructural images to describe material heterogeneity and orientation, but a performance comparison, particularly for fiber networks, has not been conducted. In this study, we constructed 40 two-dimensional test images composed of simulated fiber networks varying in fiber number, orientation, and anisotropy index. We assessed the accuracy of each method in measuring principal direction (theta) and anisotropy index (alpha). FTM proved to be the superior method because it was more reliable in measurement accuracy (Deltatheta = 2.95 degrees +/- 6.72 degrees , Deltaalpha = 0.03 +/- 0.02), faster in execution time, and flexible in its application. MIL (Deltatheta = 6.23 degrees +/- 10.68 degrees , Deltaalpha = 0.08 +/- 0.06) was not significantly less accurate than FTM but was much slower. LFD (Deltatheta = 9.97 degrees +/- 11.82 degrees , Deltaalpha = 0.24 +/- 0.13) consistently underperformed. FTM results agreed qualitatively with fibrin gel SEM micrographs, suggesting that FTM can be used to obtain image-based statistical measurements of microstructure.

Permeability calculations in three-dimensional isotropic and oriented fiber networks

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

Modeling the mechanical consequences of vibratory loading in the vertebral body: microscale effects

Osteoporosis affects nearly 10 million individuals in the United States. Conventional treatments include anti-resorptive drug therapies, but recently, it has been demonstrated that delivering a low magnitude, dynamic stimulus via whole body vibration can have an osteogenic effect without the need for large magnitude strain stimulus. Vibration of the vertebral body induces a range of stimuli that may account for the anabolic response including low magnitude strains, interfacial shear stress due to marrow movement, and blood transport. In order to evaluate the relative importance of these stimuli, we integrated a microstructural model of vertebral cancellous bone with a mixture theory model of the vertebral body. The predicted shear stresses on the surfaces of the trabeculae during vibratory loading are in the range of values considered to be stimulatory and increase with increasing solid volume fraction. Peak volumetric blood flow rates also varied with strain amplitude and frequency, but exhibited little dependence on solid volume fraction. These results suggest that fluid shear stress governs the response of the vertebrae to whole body vibration and that the marrow viscosity is a critical parameter which modulates the shear stress.

A cellular solid model of the lamina cribrosa: mechanical dependence on morphology

The biomechanics of the optic nerve head (ONH) may underlie many of the potential mechanisms that initiate the characteristic vision loss associated with primary open angle glaucoma. Therefore, it is important to characterize the physiological levels of stress and strain in the ONH and how they may change in relation to material properties, geometry, and microstructure of the tissue. An idealized, analytical microstructural model of the ONH load bearing tissues was developed based on an octagonal cellular solid that matched the porosity and pore area of morphological data from the lamina cribrosa (LC). A complex variable method for plane stress was applied to relate the geometrically dependent macroscale loads in the sclera to the microstructure of the LC, and the effect of different geometric parameters, including scleral canal eccentricity and laminar and scleral thickness, was examined. The transmission of macroscale load in the LC to the laminar microstructure resulted in stress amplifications between 2.8 and 24.5xIOP. The most important determinants of the LC strain were those properties pertaining to the sclera and included Young's modulus, thickness, and scleral canal eccentricity. Much larger strains were developed perpendicular to the major axis of an elliptical canal than in a circular canal. Average strain levels as high as 5% were obtained for an increase in IOP from 15 to 50 mm Hg.

Solvent effects on the microstructure and properties of 75/25 poly(D,L-lactide-co-glycolide) tissue scaffolds

Poly(lactide-co-glycolide) (PLGA) is used in many biomedical applications because it is biodegradable, biocompatible, and FDA approved. PLGA can also be processed into porous tissue scaffolds, often through the use of organic solvents. A static light scattering experiment showed that 75/25 PLGA is well solvated in acetone and methylene chloride, but forms aggregates in chloroform. This led to an investigation of whether the mechanical properties of the scaffolds were affected by solvent choice. Porous 75/25 PLGA scaffolds were created with the use of the solvent casting/particulate leaching technique with three different solvents: acetone, chloroform, and methylene chloride. Compression testing resulted in stiffness values of 21.7 +/- 4.8 N/mm for acetone, 18.9 +/- 4.2 N/mm for chloroform, and 30.2 +/- 9.6 N/mm for methylene chloride. Permeability testing found values of 3.9 +/- 1.9 x 10(-12) m2 for acetone, 3.6 +/- 1.3 x 10(-12) m2 for chloroform, and 2.4 +/- 1.0 x 10(-12) m2 for methylene chloride. Additional work was conducted to uncouple polymer/solvent interactions from evaporation dynamics, both of which may affect the scaffold properties. The results suggest that solvent choice creates small but significant differences in scaffold properties, and that the rate of evaporation is more important in affecting scaffold microstructure than polymer/solvent interactions.

Effect of porosity on the fluid flow characteristics and mechanical properties of tantalum scaffolds

In many cases of traumatic bone injury, bone grafting is required. The primary source of graft material is either autograft or allograft. The use of both material sources are well established, however, both suffer limitations. In response, many grafting alternatives are being explored. This article specifically focuses on a porous tantalum metal grafting material (Trabecular Metaltrade mark) marketed by Zimmer. Twenty-one cylindrical scaffolds were manufactured (66% to 88% porous) and tested for porosity, intrinsic permeability, tangent elastic modulus, and for yield stress and strain behavior. Scaffold microstructural geometries were also measured. Tantalum scaffold intrinsic permeability ranged from 2.1 x 10(-10) to 4.8 x 10(-10) m(2) and tangent elastic modulus ranged from 373 MPa to 2.2 GPa. Both intrinsic permeability and tangent elastic modulus closely matched porosity-matched cancellous bone specimens from a variety of species and anatomic locations. Scaffold yield stress ranged from 4 to 12.7 MPa and was comparable to bovine and human cancellous bone. Yield strain was unaffected by scaffold porosity (average = 0.010 mm/mm). Understanding these structure-function relationships will help complete the basic physical characterization of this new material and will aid in the development of realistic mathematical models, ultimately enhancing future implant designs utilizing this material.

Permeability of musculoskeletal tissues and scaffolding materials: experimental results and theoretical predictions

Fluid movement produces a wide range of phenomena in musculoskeletal tissues, including streaming potentials, hydrodynamic lubrication, nutrient transport, and mechanical signaling, all of which are governed by tissue permeability. Permeability is a measurement of the ease with which a fluid passes through a material and is described by Darcy's law. An appreciation of the flow-related structure-function relationships that have been found for musculoskeletal tissues as well as the materials used to engineer substitutes is important for clinicians and engineers alike. In addition, fluid transport phenomena is one of the most often neglected, but important, aspects of developing functional musculoskeletal tissue replacements. Mathematical models provide the means to relate permeability to microstructure and enable one to span multiple hierarchical length scales. In this article, we have summarized the experimentally determined permeability for a range of musculoskeletal tissues. In addition, we have included a summary of the microstructural models that are available to relate bulk permeability to microstructural flow profiles. These models have the potential to predict cellular level fluid shear stresses, nutrient and drug transport, degradation kinetics, and the fluid-solid interactions that govern mechanical response.

Examination of continuum and micro-structural properties of human vertebral cancellous bone using combined cellular solid models

Two- and three-dimensional structural models of the vertebral body have been used to estimate the mechanical importance of parameters that are difficult to quantify experimentally such as lattice disorder, trabecular thickness, trabecular spacing, connectivity, and fabric. Many of the models that investigate structure-function relationships of the vertebral body focus only on the trabecular architecture and neglect solid-fluid interactions. We developed a cellular solid model composed of two idealized unit cell geometries to investigate the continuum and micro-structural properties of human vertebral cancellous bone in a mathematically tractable model. Using existing histomorphological data we developed structure-function relationships for the mechanical properties of the solid phase, estimated the micro-structural strains, and predicted the fluid flow characteristics. We found that the micro-structural strains may be 1.7 to 2.2 times higher than the continuum level strains between the ages of 40 and 80. In addition, the predicted permeability agrees well with the experimental data.