Bruce R. Simon

Quasi-Linear Viscoelastic Properties of Normal Articular Cartilage

A combined experimental and analytical approach was used to determine the history-dependent viscoelastic properties of normal articular cartilage in tension. Specimens along the surface split line direction, taken from the middle zone of articular cartilage were subjected to relaxation and cyclic tests. A quasi-linear viscoelastic theory proposed by Fung was used in combination with the experimental results to determine the nonlinear viscoelastic properties and the elastic stress-strain relationship of normal articular cartilage.

Large Artery Remodeling During Aging Biaxial Passive and Active Stiffness

To examine arterial mechanical changes during aging, pressure-radius and axial force-radius curves were measured in vivo in carotid arteries from 6- and 23-month-old Brown Norway X Fischer 344 rats. Incremental passive circumferential stiffness (measured at 50, 100, and 200 mm Hg) was higher (P<0.01) in the 23- compared with the 6-month-old rats (14.02+/-1.23 versus 6.58+/-1.51; 2.68+/-0.56 versus 0.99+/-0.34; 1.10+/-0.24 versus 0.69+/-0.15 dyne/mm2x10(3), respectively). Incremental passive axial stiffness was increased (P<0.01) in the 23- compared with the 6-month-old rats (7.95+/-0.70 versus 4.24+/-0.81; 1.91+/-0.10 versus 0.61+/-0.16; 0.58+/-0.09 versus 0.36+/-0.06 dyne/mm2x10(3), respectively). Active incremental circumferential arterial stiffness at 100 and 200 mm Hg was increased (P<0.01) in the older rats. In 6-month-old rats, activation of vascular smooth muscle enhanced (P<0.01) the incremental circumferential and axial stiffness measured at 200 mm Hg. In 23-month-old rats, only active incremental stiffness was increased (P<0.01) at 200 mm Hg. Aging increased (P<0.05) media thickness, collagen content, and the collagen/elastin ratio by 12%, 21%, and 38%, respectively. Elastin density and the number of smooth muscle cell nuclei were decreased by 20% and 31%, respectively, with aging. Thus, structural alterations that occur with aging are associated with changes in both active and passive stiffness. Vascular smooth muscle tone modulates arterial wall anisotropy differently during aging.

Effect of pressure on aortic hydraulic conductance.

This study was performed to determine whether the transmural hydraulic conductance (Lp) of the rabbit aortic wall depends on its distension. In 19 rabbits, the aorta was cannulated in situ and perfused at a given pressure with a physiologically buffered solution containing 4% bovine serum albumin. The output cannula was then occluded to limit fluid flow to that traversing the artery wall. External diameter and transmural fluid flow were measured at three pressures (eight rabbits, group 1) or at four pressures (12 rabbits, group 2) in each vessel. Transmural fluid flow was determined by monitoring the velocity of an air bubble within a buffer-filled tube leading to the input cannula. From group 1 measurements, Lp values (mean +/- SD) at 50, 100, and 150 mm Hg were calculated to be 3.8 +/- 2.8, 3.5 +/- 1.3, and 4.1 +/- 1.2 x 10(-8) cm/sec/mm Hg, respectively. Group 2 measurements gave values of 4.2 +/- 1.6, 3.8 +/- 1.1, 3.8 +/- 1.1, and 4.2 +/- 1.1 x 10(-8) cm/sec/mm Hg at 75, 100, 125, and 150 mm Hg, respectively. Paired Students t tests indicated no significant change in Lp with pressure. However, linear regression analysis demonstrated a weak correlation between Lp values obtained at 50 and 100 mm Hg (r2 = 0.30) and at 75 and 100 mm Hg (r2 = 0.36). Values of Lp at 100 and 150 mm Hg and at 125 and 150 mm Hg were closely correlated in each case. These results suggest that between 50 and 100 mm Hg the structural properties of the aortic wall change so as to alter Lp but not in the same way in each vessel. Lp may increase or decrease depending on which structural change predominates in a particular vessel.

Evaluation of one-, two-, and three-dimensional finite element and experimental models of internal fixation plates.

Abstract A combined experimental and finite element model study was carried out for an internal fixation plate configuration. The experimental model was an aluminum tube (bending stiffness equal to the human femur) plated using a titanium alloy (Ti-6Al-4V) plate. The model was subjected to a four-point flexural test and strains were measured with strain gauges mounted at the midplane of the tube and plate. One-, two-, and three-dimensional finite element models were generated of the experimental model and various loads were applied including the actual flexural test values. Experimental and finite element model strain results were compared allowing evaluation of the three types of finite element models commonly used for orthopedic stress analyses. Results of this study indicated that three-dimensional models should be utilized for analysis of screw stresses or contact stresses, but one-dimensional models are equivalent to two-dimensional models in less complex areas. Screw stress analysis indicated that the outermost screws are most likely to fail between the tube (bone) and plate. Shear stress levels at the screw-tube (bone) interface were also determined. Reduction of tube (bone) stress levels on the plated side of the tube suggest that plated bone in this area could become weakened during remodeling subsequent to initial fracture healing. Results of this study indicate the validity of a combined experimental and finite element approach for biomechanical analyses of internal fixation devices.

Porohyperelastic finite element modeling of abdominal aortic aneurysms.

Abdominal aortic aneurysm (AAA) is the gradual weakening and dilation of the infrarenal aorta. This disease is progressive, asymptomatic, and can eventually lead to rupture--a catastrophic event leading to massive internal bleeding and possibly death. The mechanical environment present in AAA is currently thought to be important in disease initiation, progression, and diagnosis. In this study, we utilize porohyperelastic (PHE) finite element models (FEMs) to investigate how such modeling can be used to better understand the local biomechanical environment in AAA. A 3D hypothetical AAA was constructed with a preferential anterior bulge assuming both the intraluminal thrombus (ILT) and the AAA wall act as porous materials. A parametric study was performed to investigate how physiologically meaningful variations in AAA wall and ILT hydraulic permeabilities affect luminal interstitial fluid velocities and wall stresses within an AAA. A corresponding hyperelastic (HE) simulation was also run in order to be able to compare stress values between PHE and HE simulations. The effect of AAA size on local interstitial fluid velocity was also investigated by simulating maximum diameters (5.5 cm, 4.5 cm, and 3.5 cm) at the baseline values of ILT and AAA wall permeability. Finally, a cyclic PHE simulation was utilized to study the variation in local fluid velocities as a result of a physiologic pulsatile blood pressure. While the ILT hydraulic permeability was found to have minimal affect on interstitial velocities, our simulations demonstrated a 28% increase and a 20% decrease in luminal interstitial fluid velocity as a result of a 1 standard deviation increase and decrease in AAA wall hydraulic permeability, respectively. Peak interstitial velocities in all simulations occurred on the luminal surface adjacent to the region of maximum diameter. These values increased with increasing AAA size. PHE simulations resulted in 19.4%, 40.1%, and 81.0% increases in peak maximum principal wall stresses in comparison to HE simulations for maximum diameters of 35 mm, 45 mm, and 55 mm, respectively. The pulsatile AAA PHE FEM demonstrated a complex interstitial fluid velocity field the direction of which alternated in to and out of the luminal layer of the ILT. The biomechanical environment within both the aneurysmal wall and the ILT is involved in AAA pathogenesis and rupture. Assuming these tissues to be porohyperelastic materials may provide additional insight into the complex solid and fluid forces acting on the cells responsible for aneurysmal remodeling and weakening.

Porohyperelastic–transport–swelling theory, material properties and finite element models for large arteries

Abstract A porohyperelastic–transport–swelling (PHETS) model is presented in which a soft hydrated tissue material is viewed as a continuum composed of an incompressible porous solid ( fibrous matrix) that is saturated by an incompressible fluid (water) in which a mobile species (solute) is dissolved. This PHETS theoretical model is implemented using a finite element model (FEM) including inherent nonlinearity, coupled transport processes, and complicated geometry and boundary conditions associated with soft tissue structures. The PHETS material properties are clearly identified with a physical basis describing and quantifying elasticity, permeability, diffusion, convection, and osmotic properties. The equivalence between the PHETS and the triphasic (TRI) model (Lai et al., 1991) is established using the phenomenological equations, and mathematical expressions are given to relate the PHETS and TRI material properties. A principle of virtual velocities (PVV ) links Eulerian and Lagrangian PHETS formulations and provides correspondence rules between the Eulerian and the Lagrangian field variables and material properties. The PVV is also the basis for a mixed Lagrangian PHETS FEM (Kaufmann, 1996) , which was developed for the analysis of soft hydrated tissues. Selected PHETS FEM results are presented in order to demonstrate the capability of the PHETS model to simulate coupled deformation, stress, mobile water flux, and albumin flux in the arterial wall undergoing finite straining associated with pressurization, axial stretch, and changes in albumin concentration in bath solutions surrounding a segment of rabbit thoracic aorta. Values for isotropic material parameters and specific details of the experiments and data-reduction methods were obtained from Simon et al. (1997 ; 1998) .

Drained secant modulus for human and porcine peripapillary sclera using unconfined compression testing.

Glaucoma is an ocular disease characterized by damage of the optic nerve head (ONH) resulting in blindness. Recent research has identified the material properties of the sclera as being an important factor in the biomechanics of major load bearing tissues near the ONH. Most mechanical investigations performed on sclera have focused on the tensile behavior of this tissue, neglecting its compressive stiffness. The present study characterized the compressive moduli of peripapillary sclera using an unconfined compression (UCC) technique, for both human and porcine sources. UCC stress-relaxation tests were performed on human and porcine peripapillary scleral samples at 5%, 10% and 15% sequential compressive strain. Our results indicate a linearly decreasing drained equilibrium stress (at 5%) with age in male human samples, ranging from 79.4 Pa at 78 yrs to 40.1 Pa at 89 yrs of age. The drained secant modulus (E(5)) of human and porcine sclera was found to be 1.1 +/- 0.08 kPa and 3.9 +/- 0.57 kPa, respectively. Our experimental results also reveal a non-linear increase in drained equilibrium stress with increasing compressive strain. The compressive stiffness of sclera, as reported here, provides important information on the mechanical response of peripapillary ocular tissues. This information will be useful in future computational simulations of the sclera, especially as they relate to understanding mechanical damage near the ONH. Furthermore, our results indicate that age-related changes in the biomechanical response of the sclera occur, suggesting that these factors may be playing a role in the increasing prevalence of glaucoma with age.

Coupled porohyperelastic mass transport (PHEXPT) finite element models for soft tissues using ABAQUS.

Finite element models (FEMs) including characteristic large deformations in highly nonlinear materials (hyperelasticity and coupled diffusive/convective transport of neutral mobile species) will allow quantitative study of in vivo tissues. Such FEMs will provide basic understanding of normal and pathological tissue responses and lead to optimization of local drug delivery strategies. We present a coupled porohyperelastic mass transport (PHEXPT) finite element approach developed using a commercially available ABAQUS finite element software. The PHEXPT transient simulations are based on sequential solution of the porohyperelastic (PHE) and mass transport (XPT) problems where an Eulerian PHE FEM is coupled to a Lagrangian XPT FEM using a custom-written FORTRAN program. The PHEXPT theoretical background is derived in the context of porous media transport theory and extended to ABAQUS finite element formulations. The essential assumptions needed in order to use ABAQUS are clearly identified in the derivation. Representative benchmark finite element simulations are provided along with analytical solutions (when appropriate). These simulations demonstrate the differences in transient and steady state responses including finite deformations, total stress, fluid pressure, relative fluid, and mobile species flux. A detailed description of important model considerations (e.g., material property functions and jump discontinuities at material interfaces) is also presented in the context of finite deformations. The ABAQUS-based PHEXPT approach enables the use of the available ABAQUS capabilities (interactive FEM mesh generation, finite element libraries, nonlinear material laws, pre- and postprocessing, etc.). PHEXPT FEMs can be used to simulate the transport of a relatively large neutral species (negligible osmotic fluid flux) in highly deformable hydrated soft tissues and tissue-engineered materials.

Deformationally dependent fluid transport properties of porcine coronary arteries based on location in the coronary vasculature.

OBJECTIVE Understanding coronary artery mass transport allows researchers to better comprehend how drugs or proteins move through, and deposit into, the arterial wall. Characterizing how the convective component of transport changes based on arterial location could be useful to better understand how molecules distribute in different locations in the coronary vasculature. METHODS AND RESULTS We measured the mechanical properties and wall fluid flux transport properties of de-endothelialized (similar to post-stenting or angioplasty) left anterior descending (LADC) and right (RC) porcine coronary arteries along their arterial lengths. Multiphoton microscopy was used to determine microstructural differences. Proximal LADC regions had a higher circumferential stiffness than all other regions. Permeability decreased by 198% in the LADC distal region compared to other LADC regions. The RC artery showed a decrease of 46.9% from the proximal to middle region, and 51.7% from the middle to distal regions. The porosity increased in the intima between pressure states, without differences through the remainder of the arterial thickness. CONCLUSIONS We showed that the permeabilities and mechanical properties do vary in the coronary vasculature. With variations in mechanical properties, overexpansion of stents can occur more easily while variations in permeability may lead to altered transport based on location.

DEFORMATION OF THE ARTERIAL VASA VASORUM AT NORMAL AND HYPERTENSIVE ARTERIAL PRESSURE

Abstract In a previous paper, a numerical procedure (the finite element method) was presented for the structural analysis of soft biological structures possessing complex geometry and mechanical properties and undergoing large deformations. This method was used here to model a vas vasorum in an arterial cross-section subjected to physiological and hypertensive mean arterial pressure levels. The deformation of the lumen of the model vas vasorum was determined for two cases: an arteriole and a venule. Estimates of hydraulic resistance and flow rate for these model vasa vasorum were calculated and compared with experimental total flow rates in the vasa vasorum reported in the literature. The results indicate that prolonged abnormally elevated arterial pressure could constrict venules of the vasa vasorum thereby impairing arterial wall tissue nourishment. If no compensatory mechanisms exist, tissue degeneration and/or atherogenesis could occur.