Journal of Engineering Mechanics

The transverse anisotropic poromechanics solution for the two-dimensional Mandel-type problem geometry is extended in this paper to account for the orthotropic nature of the porous media, thus mimicking the response of articular cartilage samples when subjected to load perturbation. The anisotropic solution presented takes into account the viscoelastic and anisotropic nature of the fluid-saturated cartilage specimen sandwiched between two impermeable rigid plates and subjected to quasi-static step loading conditions; thus simulating the unconfined compressive test responses of cartilage samples in biomechanics laboratory setups. The solution addresses the stress, fluid pressure, and displacement results due to load application through exact modeling of the intrinsic nature of the orthotropic viscoelastic matrix structure as well as the compressible interstitial fluid flow responses. Poromechanical parameter characterization and modeling of biological tissues, such as cartilage, will find this analytical solution to the two-dimensional anisotropic poroviscoelastic geometry very useful. This problem will not only serve as a benchmark for validating numerical schemes and simulations but also assist in calibrating laboratory results on biological tissues, including cyclic loadings.

Cyclic loading has been known to induce fluid flow and thus mechanotransduction in bones. In the past, four-point bending tests have been used exclusively in studying fluid flow in bones. In order to better understand the mechanism of deformation and fluid flow under loading, compression tests were done on trabecular bone specimens under drained and undrained conditions. In the drained tests, the volume change was observed, whereas in the undrained tests, excess pore fluid pressure was measured. Cyclic loading tests were conducted in addition to monotonic loading tests to observe the permanent volume change or excess pore fluid pressure with loading cycles. A fast loading rate gave a sharp rise in the excess fluid pressure compared to a slow loading rate. The strength and stiffness of the specimens appeared to deteriorate with an increased speed of loadings, but there was no appreciable difference between the results obtained from drained and undrained tests. The drained and undrained tests as described allowed a better understanding of bone behavior under loadings for a coupled stress-flow analysis.

We here extend the theory of microporomechanics by Dormieux et al. to multiple pore spaces. As an application, we reveal, on the basis of a recently validated multiscale elastic model for bone tissues by Fritsch and Hellmich, the effects of multiple pore pressures in various, scale-separated pore spaces, on the overall behavior of the multiporous composite material. Thereby, our focus is on the lacunar pore space, and on its interplay with the pore spaces found further below: not only those between the mineral crystals (of some $10\mathrm{nm}$ characteristic pore size) but also those of the collagen molecules building up (micro-)fibrils (with a little more than $1\mathrm{nm}$ distance between these molecules). Our results clearly show that the interplay between pore pressure and skeleton deformation depends strongly on the loading direction and on the characteristic size of the pores—hence, we can conclude that the consideration of these strongly hierarchical and anisotropic effects in whole-organ simulations including fluid mass transport, would allow for valuable new insights into the ongoing discussion on poromechanobiology of bone.

Tissue engineering (TE) is the use of a combination of biological cells, engineering and materials methods, and of suitable biochemical and physicochemical factors, in order to improve or replace biological functions. It has brought the advent of entirely new classes of hierarchically organized, multiporous materials, consisting of both chemically and biologically produced parts. Here, we aim at contributing to the unsettled question of the mechanical functioning of bone tissue-engineering scaffolds with tissue-engineered bone—from a theoretical and applied mechanics viewpoint. Therefore, we build on recently developed microelasticity models for vertebrate bone and hydroxyapatite biomaterials, respectively. Tissue engineering scaffolds with tissue-engineered bone are micromechanically represented as tissue-engineered bone-coated macropores in a matrix built up by microporous hydroxyapatite polycrystals, based on an extension toward anisotropy, of Herve–Zaoui’s $n$ -layered inclusion problem. The stiffness of macroporous hydroxyapatite-based TE scaffolds with newly ingrown bone is mainly governed by their porosities [vascular (macro) porosity defined through initial scaffold design and volume fraction of ingrown bone; and intercrystalline (micro) porosity between the hydroxyapatite crystals of the scaffold matrix material], while being less influenced by the type of bone growing inside the macropores. For a given degeneration kinetics of the scaffold, the microelastic models suggest apposition rates of bone needed to maintain the stiffness characteristics of the overall biomaterial-bone construct. This can be seen as a first step toward computer-aided engineering design of tissue-engineering scaffolds for large bone defect regeneration.

Bone is a widely studied structure due to its important function in the human body and also for its unique mechanical properties, which depend upon several factors, such as, its hierarchal structure, its constituents, degree of interactions between different constituents, etc. The major constituents of bone are collagen and hydroxyapatite (HAP). In this work, the load-carrying behavior of collagen is evaluated using steered molecular dynamics simulations. It is observed that the mineral HAP influences the load-deformation behavior of collagen. The collagen molecule (tropocollagen) requires more energy to deform when it is in close proximity of HAP. The reasons for a typical load-deformation behavior are also analyzed. It is observed that with stretching of the tropocollagen, first hydrogen bonds between the tropocollagen chains break, as a result of which more water molecules start interacting with chains. HAP significantly alters the interaction between tropocollagen and water. The load-carrying behavior of tropocollagen at different loading rates is also analyzed by pulling collagen at different velocities. These simulations give important information about the molecular mechanics of collagen and are also useful for the development of novel biomimetic artificial implant materials.

Together with the globular proteins, microtubules and microfilaments, intermediate filaments are one of the three major components of the cytoskeleton in eukaryotic cells. They consist of a dimeric coiled-coil building block, assembled in a very precise, hierarchical fashion into tetramers, forming filaments with characteristic dimensions on the order of several micrometers. Here we focus on the theoretical analysis of the deformation mechanics of vimentin intermediate filaments, a type of intermediate filament expressed in leukocytes, blood vessel endothelial cells, some epithelial cells, and mesenchymal cells such as fibroblasts. The main contribution of this paper is the study of the rupture mechanics of intermediate filament tetramers, representing an assembly of two dimers, by utilizing a statistical Bell model adapted to describe the rupture dynamics of intermediate filaments. Possible deformation mechanisms, including interdimer sliding and uncoiling of the dimer, are illustrated in light of the interdimer adhesion and dimer stability. The analysis reveals that the dominating deformation mechanism depends critically on the interdimer adhesion, solvent condition, and deformation rate.

This paper is concerned with the development of a computational model of pulmonary alveoli against the background of ventilator-induced lung injuries. In order to quantify mechanical stimulation of alveolar tissue during artificial respiration, a detailed constitutive model of alveolar septa and an approach to consider interfacial phenomena is needed. For that purpose, a polyconvex hyperelastic material model formerly developed for arteries is adopted for pulmonary alveoli. Information about tissue morphology is inherently integrated into the constitutive model, therefore, establishing a connection between structure and function of the different septal constituents. Structural and interfacial dynamics are directly coupled at the alveolar surface. In order to take into account the complex behavior of surface active agents covering alveoli, a constitutive model considering dynamical changes of surface energy is employed.

Maintenance of articular cartilage’s functional mechanical properties ultimately depends on the balance between the extracellular matrix component biosynthesis, degradation, and loss. A variety of factors are known to modulate the rate of cartilage matrix synthesis (e.g., growth factors and stress/strain environment). In the present study, we develop an integrated mathematical model that quantifies biological processes within cartilage tissue modulated by insulin-like growth factors (IGFs). Specifically, the model includes IGF transport through a deforming porous media, competitive binding to binding proteins and cell receptors, and matrix macromolecule biosynthesis—particularly glycosaminoglycans (GAGs). These newly synthesized matrix molecules are then able to modify the material properties of cartilage. The model is used to investigate the effect of synovial fluid IGF-I concentration on cartilage homeostasis. The results presented here suggest that GAG production can be rapidly “switched on” when the concentration of IGF-I reaches a certain threshold, while it is predicted that high receptor concentration leads to heterogeneous matrix production. As for the combined effect of IGF-I and mechanical loading on biosynthesis, the current model predicts that a loading regime with high strain magnitude (e.g., 10%) can achieve a synergistic effect on matrix protein production. Furthermore, dynamic loading is seen to promote spatial homogeneous GAG production.

A simplified finite-element model for tissue regeneration is proposed. The model takes into account the sequential steps of angiogenesis (neo-vascularization) and wound closure (the actual healing of a wound). An innovation in the present study is the combination of both partially overlapping processes, yielding novel insights into the process of wound healing, such as geometry related influences, and could be used to investigate the influence of local injection of hormones that stimulate partial processes occurring during wound healing. These insights can be used to improve wound healing treatments. The models consist of nonlinearly coupled diffusion-reaction equations, in which transport of oxygen, growth factors, and epidermal cells and mitosis are taken into account.

In this paper, we study a model layered structure mimicking nacre. We start from an elastic energy appropriate for the model. We formulate how to obtain stress and strain distributions for this special elastic theory and explicitly derive a solution to a certain boundary condition. This solution predicts a reduction of the stress concentration around the crack tip, which proves the strength of the model structure.

Hydroxyapatite is an important constituent of natural bone, and possesses excellent biocompatibility and bioactivity, but its brittle nature limits its use for bone tissue engineering. Nanohydroxyapatite (nanoHAP) has been used in synthesis of biomimetic composites for more than a decade, yet the mechanics of nanoHAP particles is not fully understood. The present work attempts to advance the current understanding of mechanics of hydroxyapatite at nanoscale, by carrying out systematic nanoindentation experiments on nanoHAP and surface modified nanoHAP [prepared by in situ mineralization in presence of polyacrylic acid (PAAc)]. Quantitative nanomodulus maps of both modified and unmodified HAP nanoparticles indicate that various surface features of HAP nanoparticles can be probed. Dips in values of elastic moduli across the nanoparticle surfaces in modified nanohydroxyapatite are indicative of composite responses from both polymer and mineral phases (PAAc-HAP) on the surface. Nanoindentation experiments were performed at 100, 1,000, 3,000, 5,000, and $\mathrm{8,000}\mu \mathrm{N}$ loads, respectively, to obtain the indentation response from both shallow and deep penetration depths. Nanoindentation results at shallow penetration depths are influenced by nanoscale surface roughness of irregular-shaped HAP nanoparticles and nonuniform distribution of PAAc in the microstructure. Significant nonbonded interactions between HAP and PAAc, as well as the mechanical properties of individual constituents (HAP and PAAc) lead to superior nanomechanical properties of surface-modified nanoHAP as compared to unmodified HAP. The overall inelastic nanomechanical response (including damage leading to reduced overall elastic modulus) is strongly influenced by the nature of the interfaces between the nanoparticles, especially when indent size is much larger than the particle size.

Reported here are the diaphyseal cross-sectional geometrical properties of two fossilized femora from Kenya dated at $6\mathrm{Ma}$ (million years ago), designated as the taxon Orrorin tugenensis. These femora are sampled at a temporal level near the divergence of ape and human lineages. The geometric properties of the bones are compared with previous findings from SK 82 and SK 97, hominid fossils from 2 million years later, and a sample of extant humans from Pecos Pueblo, N. M. The Orrorin femoral specimens BAR 1002’00 and BAR 1003’00 are notably robust, exhibiting cross-sectional areas with relatively high percentages of cortical bone in comparison to a contemporary sample. Total cross-sectional area is markedly smaller for BAR 1002’00 and BAR 1003’00 than for either of the Swartkrans early hominid proximal femora or the Pecos Pueblo sample, but %CA of the two Kenyan fossil femurs are comparable to those from Swartkrans and one third higher than the modern sample. Despite their relatively thicker cortical areas BAR 1002’00 and BAR 1003’00 do not exhibit higher bending resistance ( $I_{\max }$ and $I_{\min }$ ) or torsional rigidity $\left(J\right)$ in compared to a modern human sample. These findings extend our knowledge of internal femoral structure related to the origins of human locomotion.