An engineering, multiscale constitutive model for fiber-forming collagen in tension

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.

Microstructure-based biomechanics of coronary arteries in health and disease

Coronary atherosclerosis is the major cause of mortality and disability in developed nations. A deeper understanding of mechanical properties of coronary arteries and hence their mechanical response to stress is significant for clinical prevention and treatment. Microstructure-based models of blood vessels can provide predictions of arterial mechanical response at the macro- and micro-mechanical level for each constituent structure. Such models must be based on quantitative data of structural parameters (constituent content, orientation angle and dimension) and mechanical properties of individual adventitia and media layers of normal arteries as well as change of structural and mechanical properties of atherosclerotic arteries. The microstructural constitutive models of healthy coronary arteries consist of three major mechanical components: collagen, elastin, and smooth muscle cells, while the models of atherosclerotic arteries should account for additional constituents including intima, fibrous plaque, lipid, calcification, etc. This review surveys the literature on morphology, mechanical properties, and microstructural constitutive models of normal and atherosclerotic coronary arteries. It also provides an overview of current gaps in knowledge that must be filed in order to advance this important area of research for understanding initiation, progression and clinical treatment of vascular disease. Patient-specific structural models are highlighted to provide diagnosis, virtual planning of therapy and prognosis when realistic patient-specific geometries and material properties of diseased vessels can be acquired by advanced imaging techniques.

Bimodal collagen fibril diameter distributions direct age-related variations in tendon resilience and resistance to rupture

Scaling relationships have been formulated to investigate the influence of collagen fibril diameter (D) on age-related variations in the strain energy density of tendon. Transmission electron microscopy was used to quantify D in tail tendon from 1.7- to 35.3-mo-old (C57BL/6) male mice. Frequency histograms of D for all age groups were modeled as two normally distributed subpopulations with smaller (D(D1)) and larger (D(D2)) mean Ds, respectively. Both D(D1) and D(D2) increase from 1.6 to 4.0 mo but decrease thereafter. From tensile tests to rupture, two strain energy densities were calculated: 1) u(E) [from initial loading until the yield stress (σ(Y))], which contributes primarily to tendon resilience, and 2) u(F) [from σ(Y) through the maximum stress (σ(U)) until rupture], which relates primarily to resistance of the tendons to rupture. As measured by the normalized strain energy densities u(E)/σ(Y) and u(F)/σ(U), both the resilience and resistance to rupture increase with increasing age and peak at 23.0 and 4.0 mo, respectively, before decreasing thereafter. Multiple regression analysis reveals that increases in u(E)/σ(Y) (resilience energy) are associated with decreases in D(D1) and increases in D(D2), whereas u(F)/σ(U) (rupture energy) is associated with increases in D(D1) alone. These findings support a model where age-related variations in tendon resilience and resistance to rupture can be directed by subtle changes in the bimodal distribution of Ds.

Orthopaedic research in italy: state of the art

The most significant results in experimental and clinical orthopaedic research in Italy within the last three years have been primarily in major congenital diseases, bone tumors, regenerative medicine, joint replacements, spine, tendons and ligaments. The data presented in the following discussion is comparable with leading international results, highlighting Italian orthopaedic research excellemce as well as its shortcomings.

A Micromechanics Finite-Strain Constitutive Model of Fibrous Tissue

Biological tissues have unique mechanical properties due to the wavy fibrous collagen and elastin microstructure. In inflation, a vessel easily distends under low pressure but becomes stiffer when the fibers are straightened to take up the load. The current microstructural models of blood vessels assume affine deformation; i.e., the deformation of each fiber is assumed to be identical to the macroscopic deformation of the tissue. This uniform-field (UF) assumption leads to the macroscopic (or effective) strain energy of the tissue that is the volumetric sum of the contributions of the tissue components. Here, a micromechanics-based constitutive model of fibrous tissue is developed to remove the affine assumption and to take into consideration the heterogeneous interactions between the fibers and the ground substance. The development is based on the framework of a recently developed second-order homogenization theory, and takes into account the waviness, orientations, and spatial distribution of the fibers, as well as the material nonlinearity at finite-strain deformation. In an illustrative simulation, the predictions of the macroscopic stress-strain relation, and the statistical deformation of the fibers are compared to the UF model, as well as finite-element (FE) simulation. Our predictions agree well with the FE results, while the UF predictions significantly overestimate. The effects of fiber distribution and waviness on the macroscopic stress-strain relation are also investigated. The present mathematical model may serves as a foundation for native as well as for engineered tissues and biomaterials.

Modeling of fibroblast-controlled strengthening and remodeling of uniaxially constrained collagen gels

A theoretical model for the remodeling of collagen gels is proposed. The collagen fabric is modeled as a network of collagen fibers, which in turn are composed of collagen fibrils. In the model, the strengthening of collagen fabric is accomplished by fibroblasts, which continuously recruit and attach more collagen fibrils to existing collagen fibers. The fibroblasts also accomplish a reorientation of collagen fibers. Fibroblasts are assumed to reorient collagen fibers toward the direction of maximum material stiffness. The proposed model is applied to experiments in which fibroblasts were inserted into a collagen gel. The model is able to predict the force-strain curves for the experimental collagen gels, and the final distribution of collagen fibers also agrees qualitatively with the experiments.