Jacques M. Huyghe

Estimation of the poroelastic parameters of cortical bone.

Cortical bone has two systems of interconnected channels. The largest of these is the vascular porosity consisting of Haversian and Volkmanns canals, with a diameter of about 50 microm, which contains a.o. blood vessels and nerves. The smaller is the system consisting of the canaliculi and lacunae: the canaliculi are at the submicron level and house the protrusions of the osteocytes. When bone is differentially loaded, fluids within the solid matrix sustain a pressure gradient that drives a flow. It is generally assumed that the flow of extracellular fluid around osteocytes plays an important role not only in the nutrition of these cells, but also in the bones mechanosensory system. The interaction between the deformation of the bone matrix and the flow of fluid can be modelled using Biots theory of poroelasticity. However, due to the inhomogeneity of the bone matrix and the scale of the porosities, it is not possible to experimentally determine all the parameters that are needed for numerical implementation. The purpose of this paper is to derive these parameters using composite modelling and experimental data from literature. A full set of constants is estimated for a linear isotropic description of cortical bone as a two-level porous medium. Bone, however, has a wide variety of mechanical and structural properties; with the theoretical relationships described in this note, poroelastic parameters can be derived for other bone types using their specific experimental data sets.

A case for strain-induced fluid flow as a regulator of BMU-coupling and osteonal alignment

Throughout life, human bone is renewed continuously in a tightly controlled sequence of resorption and formation. This process of bone remodeling is remarkable because it involves cells from different lineages, collaborating in so‐called basic multicellular units (BMUs) within small spatial and temporal boundaries. Moreover, the newly formed (secondary) osteons are aligned to the dominant load direction and have a density related to its magnitude, thus creating a globally optimized mechanical structure. Although the existence of BMUs is amply described, the cellular mechanisms driving bone remodeling—particularly the alignment process—are poorly understood. In this study we present a theory that explains bone remodelling as a self‐organizing process of mechanical adaptation. Osteocytes thereby act as sensors of strain‐induced fluid flow. Physiological loading produces stasis of extracellular fluid in front of the cutting cone of a tunneling osteon, which will lead to osteocytic disuse and (continued) attraction of osteoclasts. However, around the resting zone and the closing cone, enhanced extracellular fluid flow occurs, which will activate osteocytes to recruit osteoblasts. Thus, cellular activity at a bone remodeling site is well related to local fluid flow patterns, which may explain the coordinated progression of a BMU.

Influence of endocardial-epicardial crossover of muscle fibers on left ventricular wall mechanics.

The influence of variations of fiber direction on the distribution of stress and strain in the left ventricular wall was investigated using a finite element model to simulate the mechanics of the left ventricle. The commonly modelled helix fiber angle was defined as the angle between the local circumferential direction and the projection of the fiber path on the plane perpendicular to the local radial direction. In the present study, an additional angle, the transverse fiber angle, was used to model the continuous course of the muscle fibers between the inner and the outer layers of the ventricular wall. This angle was defined as the angle between the circumferential direction and the projection of the fiber path on the plane perpendicular to the local longitudinal direction. First, a reference simulation of left ventricular mechanics during a cardiac cycle was performed, in which the transverse angle was set to zero. Next, we performed two simulations in which the spatial distribution of either the transverse or the helix angle was varied with respect to the reference situation, the spatially averaged variations being about 3 and 14 degrees, respectively. The changes in fiber orientation hardly affected the pressure-volume relation of the ventricle, but significantly affected the spatial distribution of active muscle fiber stress (up to 50% change) and sarcomere length (up to 0.1 micron change). In the basal and apical region of the wall, shear deformation in the circumferential-radial plane was significantly reduced by introduction of a nonzero transverse angle. Thus, the loading of the passive tissue may be reduced by the endocardial-epicardial crossover of the muscle fibers.

The constitutive behaviour of passive heart muscle tissue: a quasi-linear viscoelastic formulation

A quasi-linear viscoelastic law with a continuous relaxation spectrum describing triaxial constitutive behaviour of heart muscle tissue is presented. The elastic response of the viscoelastic law is anisotropic, while the relaxation behaviour is assumed isotropic. The law is designed for a biphasic description (fluid-solid) of the myocardial tissue. Biaxial and uniaxial stress-strain curves from the literature are used to evaluate the parameters of the model. The non-linear elastic response, the difference between fibre and cross-fibre stiffness, the phenomenon of stress relaxation, the stiffening of the stress-strain relationship with increasing strain rate and the weak frequency dependency of the dissipated energy during cyclic loading are fairly well described by the proposed law. However, it is found that the model produces realistic values for the dissipated energy during cyclic loading only when relaxation parameter values are chosen which result in an overestimation of the stress relaxation data by more than 100%. This finding may indicate non-quasi-linearity of viscoelasticity of passive heart muscle tissue.

A two-phase finite element model of the diastolic left ventricle

A porous medium finite element model of the passive left ventricle is presented. The model is axisymmetric and allows for finite deformation, including torsion about the axis of symmetry. An anisotropic quasi-linear viscoelastic constitutive relation is implemented in the model. The model accounts for changing fibre orientation across the myocardial wall. During passive filling, the apex rotates in a clockwise direction relative to the base for an observer looking from apex to base. Within an intraventricular pressure range of 0-3 kPa the rotation angle of all nodes remained below 0.1 rad. Diastolic viscoelasticity of myocardial tissue is shown to reduce transmural differences of preload-induced sarcomere stretch and to generate residual stresses in an unloaded ventricular wall, consistent with the observation of opening angles seen when the heart is slit open. It is shown that the ventricular model stiffens following an increase of the intracoronary blood volume. At a given left ventricular volume, left ventricular pressure increases from 1.5 to 2.0 kPa when raising the intracoronary blood volume from 9 to 14 ml (100 g)-1 left ventricle.

Ageing and degenerative changes of the intervertebral disc and their impact on spinal flexibility

PurposeDegeneration of the intervertebral disc is associated with various morphological changes of the disc itself and of the adjacent structures, such as reduction of the water content, collapse of the intervertebral space, disruption and tears, and osteophytes. These morphological changes of the disc are linked to alterations of the spine flexibility. This paper aims to review the literature about the ageing and degenerative changes of the intervertebral disc and their link with alterations in spinal biomechanics, with emphasis on flexibility.MethodsNarrative literature review.ResultsClinical instability of the motion segment, usually related to increased flexibility and hypothesized to be connected to early, mild disc degeneration and believed to be responsible for low back pain, was tested in numerous in vitro studies. Despite some disagreement in the findings, a trend toward spinal stiffening with the increasing degeneration was observed in most studies. Tests about tears and fissures showed inconsistent results, as well as for disc collapse and dehydration. Vertebral osteophytes were found to be effective in stabilizing the spine in bending motions.ConclusionsThe literature suggests that the degenerative changes of the intervertebral disc and surrounding structures lead to subtle alteration of the mechanical properties of the functional spinal unit. A trend toward spinal stiffening with the increasing degeneration has been observed in most studies.

Influence of osmotic pressure changes on the opening of existing cracks in 2 intervertebral disc models

Study Design. An experimental hydrogel model and a numerical mixture model were used to investigate why the disc herniates while osmotic pressure is decreasing. Objective. To investigate the influence of decreasing osmotic pressure on the opening of cracks in the disc. Summary of Background Data. In the degeneration process, the disc changes structure (i.e., cracks occur, and osmotic pressure decreases). Disc herniation typically develops when hydration declines, but, on the other hand, it is said that the anulus of a highly hydrated disc has a high risk of rupture. We hypothesized that disc herniation is preceded by the opening of cracks as a result of decreasing osmotic pressure. Methods. The osmotic pressure was changed in hydrogel samples with a crack, which was visualized with a confocal laser scanning microscope (Zeiss, Göttingen, Germany). A 2-dimensional finite element mixture model simulated a decrease in osmotic pressure around a crack in a swelling material. Results. Experiments and simulations show that a decrease in osmotic pressure results in the opening of cracks. The simulations show high effective stress concentrations around the crack tip, while the overall stress level decreases, indicating an increased risk of crack growth. Conclusions. Decreasing osmotic pressure in a degenerating intervertebral disc enhances the opening of existing cracks, despite the concomitant decrease in anular stresses.

Experimental and model determination of human intervertebral disc osmoviscoelasticity

Finite element (FE) models have become an important tool to study load distribution in the healthy and degenerated disc. However, model predictions require accurate constitutive laws and material properties. As the mechanical properties of the intervertebral disc are regulated by its biochemical composition and fiber‐reinforced structure, the relationship between the constitutive behavior of the tissue and its composition requires careful consideration. While numerous studies have investigated the annulus fibrosus compressive and tensile properties, specific conditions required to determine model parameters for the osmoviscoelastic model are unavailable. Therefore, the objectives of this study were (1) to complement the existing material testing in the literature with confined compression and tensile tests on human annulus fibrosus and (2) to use these data, together with existing nucleus pulposus compression data to tune a composition‐based, osmoviscoelastic material constitutive law. The osmoviscoelastic material constitutive law and the experimental data were used to describe the fiber and nonfiber properties of the human disc. The compressive material properties of normal disc tissue were Gm = 1.23 MPa, M = 1.57, and α = 1.964 × 10−16 m4/Ns; the tensile fiber material parameters were E0 = 77.0 MPa; Eε = 500 MPa, and η = 1.8 × 103 MPa−s. The goodness of fit ranged from 0.88 to 0.96 for the four experimental conditions evaluated. The constitutive law emphasized the interdependency of the strong swelling ability of the tissue and the viscoelastic nature of the collagen fibers. This is especially important for numerical models to further study the load sharing behavior with regard to disc degeneration and regeneration.

A biochemical/biophysical 3D FE intervertebral disc model

Present research focuses on different strategies to preserve the degenerated disc. To assure long-term success of novel approaches, favorable mechanical conditions in the disc tissue are essential. To evaluate these, a model is required that can determine internal mechanical conditions which cannot be directly measured as a function of assessable biophysical characteristics. Therefore, the objective is to evaluate if constitutive and material laws acquired on isolated samples of nucleus and annulus tissue can be used directly in a whole-organ 3D FE model to describe intervertebral disc behavior. The 3D osmo-poro-visco-hyper-elastic disc (OVED) model describes disc behavior as a function of annulus and nucleus tissue biochemical composition, organization and specific constituent properties. The description of the 3D collagen network was enhanced to account for smaller fibril structures. Tissue mechanical behavior tests on isolated nucleus and annulus samples were simulated with models incorporating tissue composition to calculate the constituent parameter values. The obtained constitutive laws were incorporated into the whole-organ model. The overall behavior and disc properties of the model were corroborated against in vitro creep experiments of human L4/L5 discs. The OVED model simulated isolated tissue experiments on confined compression and uniaxial tensile test and whole-organ disc behavior. This was possible, provided that secondary fiber structures were accounted for. The fair agreement (radial bulge, axial creep deformation and intradiscal pressure) between model and experiment was obtained using constitutive properties that are the same for annulus and nucleus. Both tissue models differed in the 3D OVED model only by composition. The composition-based modeling presents the advantage of reducing the numbers of material parameters to a minimum and to use tissue composition directly as input. Hence, this approach provides the possibility to describe internal mechanical conditions of the disc as a function of assessable biophysical characteristics.

Mechanical blood-tissue interaction in contracting muscles: a model study

A finite element (FE) model of blood perfused biological tissue has been developed. Blood perfusion is described by fluid flow through a series of 5 intercommunicating vascular compartments that are embedded in the tissue. Each compartment is characterized by a blood flow permeability tensor, blood volume fraction and vessel compliance. Local non-linear relationships between intra-extra vascular pressure difference and blood volume fraction, and between blood volume fraction and the permeability tensor, are included in the FE model. To test the implementation of these non-linear relations, FE results of blood perfusion in a piece of tissue that is subject to increased intramuscular pressure, are compared to results that are calculated with a lumped parameter (LP) model of blood perfusion. FE simulation of blood flow through a contracting rat calf muscle is performed. The FE model used in this simulation contains a transversely isotropic, non-linearly elastic description of deforming muscle tissue, in which local contraction stress is prescribed as a function of time. FE results of muscle tension, total arterial inflow and total venous outflow of the muscle during contraction, correspond to experimental results of an isometrically and tetanically contracting rat calf muscle.