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Biomedical subjects

B R Simon

Publications and source records attributed to B R Simon.

At least 19 recordsLinked to original sources
PubMed1998

Identification and determination of material properties for porohyperelastic analysis of large arteries.

A "porohyperelastic" (PHE) material model is described and the theoretical framework presented that allows identification of the necessary material properties functions for soft arterial tissues. A generalized Fung form is proposed for the PHE constitutive law in which the two fundamental Lagrangian material properties are the effective strain energy density function, W(e), and the hydraulic permeability, kij. The PHE model is based on isotropic forms using W(e) = Ue (phi) = 1/2C0(e phi - 1) and the radial component of permeability, kRR = kRR(phi), with phi = C1'(I1 - 3) + C2'(I2 - 3) + K'(J - 1)2. The methods for determination of these material properties are illustrated using experimental data from in situ rabbit aortas. Three experiments are described to determine parameters in Ue and kRR for the intima and media of the aortas, i.e., (1) undrained tests to determine C0, C1', and C2'; (2) drained tests to determine K'; and (3) steady-state pressurization tests of intact and de-endothelialized vessels to determine intimal and medial permeability (adventitia removed in these models). Data-reduction procedures are presented that allow determination of kRR for the intima and media and Ue for the media using experimental data. The effectiveness and accuracy of these procedures are studied using input "data" from finite element models generated with the ABAQUS program. The isotropic theory and data-reduction methods give good approximations for the PHE properties of in situ aortas. These methods can be extended to include arterial tissue remodeling and anisotropic behavior when appropriate experimental data are available.

Animals↗
PubMed1996

A poroelastic finite element formulation including transport and swelling in soft tissue structures.

A field theory is presented for the study of swelling in soft tissue structures that are modeled as poroelastic materials. As a first approximation, soft tissues are assumed to be linear isotropic materials undergoing infinitesimal strains. Material properties are identified that are necessary for the solution of initial boundary value problems where swelling and convection are significant. A finite element model is developed that includes the solid displacements, the relative fluid displacements, and a representative concentration as the primary unknowns. A numerical example is presented based on a triphasic model. The finite model simulates a typical experimental protocol for soft tissue testing and demonstrates the interaction and coupling associated with relative fluid motion and swelling in a deforming poroelastic materiaL The theory and finite element model provide a starting point for nonlinear porohyperelastic transport-swelling analyses of soft tissue structures that include finite strains in anisotropic materials.

Algorithms↗
PubMed1994

A dynamic material parameter estimation procedure for soft tissue using a poroelastic finite element model.

A three-dimensional finite element model for a poroelastic medium has been coupled with a least squares parameter estimation method for the purpose of assessing material properties based on intradiscal displacement and reactive forces. Parameter optimization may be based on either load or displacement control experiments. In this paper we present the basis of the finite element model and the parameter estimation process. The method is then applied to a test problem and the computational behavior is discussed. Sequential optimization on different parameter groups was found to have superior convergence properties. Some guidelines for choosing the starting parameter values for optimization were deduced by considering the form of the objective function. For load control experiments, in which displacement data is used for the optimization, the starting values for the elastic modulus should be lower in magnitude than an "anticipated" modulus. The permeability starting values should be higher than an anticipated permeability. For displacement control experiments, the reverse is true. The optimization scheme was also tested on data with random variations.

Anisotropy↗
PubMed1993

A poroelastic-swelling finite element model with application to the intervertebral disc.

The swelling process that occurs in soft tissue is incorporated into a poroelastic finite element model. The model is applied to a spinal segment consisting of two vertebrae and a single intervertebral disc. The theory is an extension of the poroelastic theory developed by Biot and the model is an adaptation of an axisymmetric poroelastic finite element model of the intervertebral disc by Simon. The model is completely three-dimensional although the results presented here assume symmetry about the sagittal plane. The theory is presented in two stages. First the development of the poroelastic theory. Following this, the effects of swelling caused by osmotic pressure are developed and expressed as a modification of the constitutive law and initial stresses. In the case of the disc, this pressure is produced mainly by the fixed negative charges on the proteoglycans within the disc. In this development we assume that the number of fixed charges remains constant over time and that the distribution of mobile ions has reached equilibrium. The variations over time in osmotic pressure, and thus in swelling effects are therefore only dependent on the initial state and the change in water content. Variations of the swelling effects caused by changes in mobile ion concentrations will be the subject of a future paper. The results reported in this article illustrate the dramatic effect of swelling on the load carrying mechanisms in the disc. The authors believe it is likely that this will have important useful implications for our understanding not only of normal disc function, but also of abnormal function, such as disc degeneration, herniation, and others.

Elasticity↗
PubMed1993

Finite element models for arterial wall mechanics.

Arterial wall mechanics has been studied for nearly 200 years. This subject is of importance if we are to gain a fundamental understanding of this complex biological structure, as well as information needed to design prosthetics. Biomechanical arterial models continue to play an important role in the study of atherosclerosis, a disease of the arterial wall that is the chief cause of mortality and morbidity in the United States and the Western World. Over the past 20 years, the finite element model (FEM) has been used in a variety of ways to simulate the structural response of large arteries. Our purpose is to summarize the uses of FEMs in arterial mechanics. We will also indicate directions for future research in this area. A specialized FEM was described in the literature for the study of transport in the arterial wall, however the convection was not directly linked to arterial wall mechanics. In this paper special attention will be given to the development of FEMs based on the poroelastic view of arterial tissues which couple wall deformation, free tissue fluid motion, and associated transport phenomena in the arterial wall. In the future such models should provide fundamental quantitative information relating arterial wall mechanics and transport which may lead to a better understanding of both normal arterial physiology and atherogenesis.

Arteries↗
PubMed1992

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 Student's 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.

Animals↗
PubMed1992

Arterial mechanics in spontaneously hypertensive rats. Mechanical properties, hydraulic conductivity, and two-phase (solid/fluid) finite element models.

To characterize the interaction between mechanical and fluid transport properties in hypertension, we measured in vivo elastic material constants and hydraulic conductivity in intact segments of carotid arteries in normal and spontaneously hypertensive rats (SHR). With the use of a finite element model, the arterial wall was modeled as a large-deformation, two-phase (solid/fluid) medium, which accounts for the existence and motion of the tissue fluid. Measurements of internal diameter and transmural pressures were obtained during continuous increases in pressure from 0 to 200 mm Hg. Strain and stress components were calculated based on a pseudostrain exponential energy density function. To measure the hydraulic conductivity, segments of the carotid artery were isolated, filled with a 4% oxygenated albumin-Tyrode's solution, and connected to a capillary tube. The movement of the meniscus of the capillary tube represented the fluid filtration across the artery. To study the influence of transmural pressure on hydraulic conductivity, measurement of fluid filtration across the arterial wall was obtained at transmural pressures of 50 and 100 mm Hg. The material constants in the SHR (n = 9) were higher (p less than 0.05 for all variables) than in normal rats (n = 10): c = 1,343 +/- 96 versus 1,158 +/- 65 mm Hg, b1 = 1.84 +/- 0.24 versus 1.22 +/- 0.22, b2 = 0.769 +/- 0.114 versus 0.616 +/- 0.11, b3 = 0.017 +/- 0.005 versus 0.0065 +/- 0.002, b4 = 0.206 +/- 0.04 versus 0.083 +/- 0.03, b5 = 0.0594 +/- 0.007 versus 0.0217 +/- 0.006, and b6 = 0.22 +/- 0.09 versus 0.123 +/- 0.02, respectively. The hydraulic conductivity of the total wall, calculated from the filtration data, was lower (p less than 0.05) at both 50 and 100 mm Hg in the SHR (n = 6) compared with normal rats (n = 7): 1.12 +/- 0.31 x 10(-8) and 0.72 +/- 0.23 x 10(-8) versus 1.95 +/- 0.53 x 10(-8) and 1.35 +/- 0.47 x 10(-8) cm/(sec.mm Hg), respectively. The intergroup comparisons between 50 and 100 mm Hg in both SHR and normal rats were also different (p less than 0.05). The finite element model was used to predict tissue fluid pressure distribution, tissue fluid velocity distribution, and total Cauchy stress gradients developed in the arterial wall during fluid pressurization in both species.(ABSTRACT TRUNCATED AT 400 WORDS)

Animals↗
PubMed1985

Structural models for human spinal motion segments based on a poroelastic view of the intervertebral disk.

Analytical and finite element models (FEMs) were used to quantify poroelastic material properties for a human intervertebral disk. An axisymmetric FEM based on a poroelastic view of disk constituents was developed for a representative human spinal motion segment (SMS). Creep and steady-state response predicted by FEMs agreed with experimental observations, i.e., long-time creep occurs with flow in the SMS, whereas for rapid steady-state loading an "undrained," nearly incompressible response is evident. A relatively low value was determined for discal permeability. Transient and long-term creep FE analyses included the study of deformation, pore fluid flow, stress, and pore fluid pressure. Relative fluid motion associated with transient creep is related to nuclear nutrition and the overall mechanical response in the normal disk. Degeneration of the disk may be associated with an increase in permeability.

Biomechanical Phenomena↗
PubMed1984

Less rigid internal fixation plates: historical perspectives and new concepts.

In the application of "rigid" plates for diaphyseal fractures, lack of callus healing and overprotection of the underlying bone are viewed by many investigators as undesirable consequences. Potential solutions offered to overcome these deficiencies include modification of the timing of plate removal, use of biologically degradable materials for plates so that stress-shielding can be minimized, and use of less rigid plate fixation systems. This study emphasizes the selection of appropriate design criteria for less rigid plate-fixation systems. To accomplish this goal, the axial, bending, and torsional stiffness parameters are considered in place of the oversimplified terms such as "flexible plate" or "elastic fixation." With the aid of finite element modeling and simplified bench experiments, we performed parametric studies and singled out the plate axial stiffness as the dominant factor in altering the bone stresses. As a result, we designed two experimental plates, one a thin Ti-6Al-4V (titanium with 6% aluminum and 4% vanadium) alloy plate with low stiffness in axial and bending directions, and the other a tubular stainless steel plate with low stiffness in the axial direction but moderate stiffness in bending and torsional directions. The low-stiffness Ti-6Al-4V alloy plate was first tested in a demanding bilateral canine midshaft osteotomy, and proved to be inadequate. Both experimental plates were successful in the unilateral osteotomies, with the tubular plate yielding the best results. After 6 months of plating, the bones beneath the tubular plate had superior mechanical and structural properties as compared to those of the control "rigid" stainless steel and the Ti-6Al-4V alloy plates. Application of this plate prolonged for 9 months did not cause reduction in bone properties and strength. The success of the tubular plate is due to its moderate bending and torsional stiffnesses, which provide adequate fixation to achieve callus union, while its low axial stiffness permits the underlying bone to share the physiological stresses needed for bone remodeling. These drastic changes in mechanical demands on the internal fixation plate during the early healing phase and the postunion remodeling phase are discussed.

Alloys↗
PubMed1984

Relaxation and creep quasilinear viscoelastic models for normal articular cartilage.

A quasilinear viscoelastic model was used to develop relaxation and creep forms for a constitutive law for soft tissues. Combined relaxation and cyclic test data as well as preconditioned and nonpreconditioned creep data were used to demonstrate the approach for normal bovine articular cartilage. Values for mechanical parameters in the analytical models were determined using a generalized least squares method.

Animals↗
PubMed1983

A new approach to the design of internal fixation plates.

Mathematical analysis by finite element modeling methods was used in conjunction with laboratory bench experiments in selecting appropriate stiffness parameters for internal fixation plate designs. Bench experiments performed included tests of an idealized plated magnesium tube and of a plated canine femur. Finite element modeling of the plate-tube and plate-bone structures was also performed, and the computed results were compared with those obtained experimentally. Three types of internal fixation plates--one "rigid" control plate and two less rigid experimental plates--were examined using both the finite element and experimental models. These plates were further examined by finite element modeling of a plated human femur during single stance loading. In all cases, the "rigid" control plate was found to shield the underlying bone from stress, while both experimental plates were found to have significantly less bone stress shielding. Our findings suggest that an improved plate design should have a low axial stiffness but moderate bending and torsional stiffnesses to facilitate fracture healing and bone remodeling without causing osteopenia.

Animals↗
PubMed1980

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.

Animals↗