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M E Levenston

Publications and source records attributed to M E Levenston.

10 recordsLinked to original sources
PubMed1998

An energy dissipation-based model for damage stimulated bone adaptation.

Based on experimental observations, several researchers have proposed a role for damage processes in stimulating an adaptive response in bone. In the current study we propose a model for bone adaptation based on cyclic energy dissipation as a measure of bone damage creation. By reanalyzing the fatigue data of Pattin et al. (1996), we derive a uniaxial form of the damage based formulation applicable to cortical regions experiencing primarily longitudinal stresses. Because of the experimentally observed difference between damage formation under tension and compression (Pattin et al., 1996), this formulation naturally predicts a difference in the adaptive response to tensile and compressive loading. This feature distinguishes the new formulation from existing strain energy based adaptation theories which treat tensile and compressive strains identically. Thus, developmental adaptation in response to unequal generation of damage provides one possible explanation for the experimentally observed difference between peak tensile and compressive bone surface strains.

Adaptation, Physiological↗
PubMed1997

Temporal stability of node-based internal bone adaptation simulations.

Jacobs et al. (1995, J. Biomechanics 28, 449-459) introduced a new implementation of the remodeling theory developed by Beaupre et al. (1990, J. Orthop. Res. 8, 651-661) that eliminates certain spurious spatial instabilities of previous implementations. Due to the highly nonlinear, coupled nature of multi-dimensional adaptation simulations, direct stability analyses of this method are not practical. In this manuscript, a linearized stability analysis was used to derive an expression for the critical time step for the stability of a simple model problem. In addition to accurately predicting the temporal response of the single degree-of-freedom problem, the analysis provided a conservative estimate of the critical time step for a more realistic, multiple degree-of-freedom adaptation simulation.

Adaptation, Physiological↗
PubMed1996

Letter to the editor.

Explore the source record for details and available documents.

Adaptation, Physiological↗
PubMed1996

Different loads can produce similar bone density distributions.

Finite element models of a generic long bone and the proximal femur were used to identify important load characteristics and to determine whether small changes in load affect bone adaptation simulations. We also examined the effect of implants on the sensitivity of bone adaptation simulations to changes in loads. For each model, a primary load set was selected and incorporated in a bone adaptation simulation to generate a primary density distribution. A density-based load estimation method was used to determine a secondary set of loading conditions for each model. Each secondary load set was incorporated in a bone adaptation simulation and the resulting density distribution was compared to the corresponding primary density distribution. Nearly identical density distributions were produced for the natural generic long bone model (average nodal density difference 0.02 g/cm3). For the natural proximal femur model, the density distributions were very similar, but differences were apparent (average nodal density difference 0.07 g/cm3). The same primary and secondary load sets were used for bone adaptation simulations with implant models. For the proximal femur model, density distribution differences with the implant were very slightly less than those of the natural model. For the generic long bone model, the implant amplified differences between density distributions (average nodal density difference 0.14 g/cm3). Thus, variations in loading conditions may partially explain variations in long-term total joint outcome. The total equivalent stimulus load magnitudes for the two load sets for the generic long bone model were within 1%, and the stimulus-weighted average load directions were within 1 degree. The similarity of these parameters and the natural generic long bone density distributions indicate that the overall magnitude and average load direction are key factors affecting bone adaptation.

Adaptation, Physiological↗
PubMed1995

Numerical instabilities in bone remodeling simulations: the advantages of a node-based finite element approach.

Long bone structure occurs in two distinct forms. The bone mass near the joint is primarily found in a distributed, porous trabecular structure, while in the diaphyses a tubular cortical structure is formed. It seems likely that these two observed morphologies come about, at least in part, as a mechanical adaptation to the different mechanical demands in the two regions. Mathematical formulations of this dependency have been proposed, thus facilitating numerical simulations of bone adaptation. Recently two types of discontinuities have been observed in these simulations. The first type (near-field) appears in areas near distributed load application and is characterized by a 'checkerboard' pattern of density wherein adjacent remodeled elements alternate between low and high density. The second type of discontinuity (far-field) appears remote from the load application and is characterized by strut or column-like regions of elements which become fully compact bone while adjacent regions are fully resorbed. In fact, the far-field discontinuity is an accurate representation of bone physiology and morphology since it is consistent with the appearance of cortical bone in the diaphysis. On the other hand, the near-field discontinuity, appears in a region where continuous distributions of intermediate apparent densities (trabecular bone) are expected. This finding may cause some to question whether a single continuum formulation of bone remodeling can predict both discontinuous far-field behavior and continuous near-field behavior. We describe a node-based implementation of current continuum bone remodeling theories which eliminates the spurious near-field discontinuities and preserves the anatomically correct far-field discontinuities, thus indicating that a single biological process may be at work in forming and maintaining both far-field and near-field morphologies.

Algorithms↗
PubMed1994

Improved method for analysis of whole bone torsion tests.

Structural tests, such as whole bone torsion tests, have become widely accepted methods for assessing average bone material properties. To simplify interpretation of these tests, the nonuniform bone geometry is often analyzed as a tube with a constant cross section (prismatic) and the areal properties of the smallest bone section. This approach may not adequately represent the true torsional behavior of the cross section and does not account for any lengthwise variations in bone geometry. The errors introduced by these approximations are particularly significant when comparing bones of different sizes and geometries. In this paper, we examine the effects of approximating the cross-sectional torsional behavior and of neglecting lengthwise variations in bone geometry. We then present a simple, standardized procedure utilizing a FORTRAN computer program for accurate determination of material properties. We examine first simple idealized bone geometries and then a complex three-dimensional model of the femur from a 26-day-old male Sprague-Dawley rat. For these models, the conventional methods for interpreting torsion tests introduce errors of up to 42% in the shear modulus and up to 48% in the maximum shear stress; a straightforward extension of these methods reduces the errors to within 3%.

Animals↗
PubMed1993

Computer simulations of stress-related bone remodeling around noncemented acetabular components.

The authors have used computer modeling techniques to examine stress-related bone changes in the acetabular region. Using a previously developed theory for bone development and adaptation, the authors simulated the distribution of bone density in the natural pelvis as well as changes in bone density following total hip arthroplasty. The geometry of the finite element model was based on a two-dimensional slice through the pelvis. Starting from a solid, homogeneous structure, the computer simulations predicted the distribution of bone density throughout the natural pelvis. The predicted bone density distribution in this first simulation agreed well with the actual bone density distribution only when loads representing multiple activities were incorporated. Using the predicted density distribution as a starting point the authors modified the finite element models to study two designs of noncemented, metal-backed acetabular cups. The simulations with fully fixed bone-implant interfaces predicted extensive loss of bone density medial and inferior to the prosthetic components. The simulations with loose interfaces led to more moderate losses of bone density, indicating a load transfer more similar to that which occurs in the natural joint. The differences in simulated bone remodeling between the two component designs were quite minimal. These results indicate that acetabular components with full bony ingrowth may induce significant stress-related bone remodeling due to a nonphysiologic transfer of load.

Bone Density↗
PubMedDate not supplied

Observations of convergence and uniqueness of node-based bone remodeling simulations.

Some investigators have indicated that mathematical theories and computational models of bone adaptation may not converge and that the density solutions from such simulations are dependent on the initial density distribution. In this study, two-dimensional finite element models were used to investigate the effect of initial density distribution on the final density distribution produced using a node-based bone remodeling simulation. The first model was a generic long bone, and the second was a proximal femur, For each model, we conducted time-dependent, node-based, linear rate-law bone remodeling simulations. Five initial density conditions were used with the generic long bone and three with the proximal femur. Remodeling simulations were performed, and the largest average nodal density differences at the end of the simulations were 0.000010 g/cm3 and 0.000006 g/cm3 for the generic long bone and proximal femur models, respectively. Results illustrate that, for a given set of loads and a given finite element model, the node-based bone adaptation algorithm can yield a unique density distribution. In conjunction with previous studies, this finding suggests that uniqueness of the density solution is dependent on both the mathematical theory and the computational implementation.

Algorithms↗
PubMedDate not supplied

The role of loading memory in bone adaptation simulations.

The concept that bone responds to a time-averaged value of its current mechanical loading forms the basis for many computational bone adaptation algorithms. Some mathematical formulations have incorporated a quantification of the loading experienced during a single "average" day and thus implicitly assume that bone responds abruptly to changes in its loading history. To better reflect the time delays inherent in bone cell recruitment and activation processes, we included a fading memory of past loading. Implementing an exponentially fading memory with time constants of 5, 20, and 100 days, we simulated bone adaptations to abrupt and gradual changes in mechanical loading. Both an idealized single degree-of-freedom model and a finite element model of the proximal femur were studied. A time constant of 5 days produced time-dependent density changes that were negligibly different from those of the standard approach without memory. Models with higher time constants produced significant transient time lags (up to 8.1% difference) in the predicted short-term (3 months) bone density changes. A time constant of 100 days produced overshoots (by approximately 1%) of the eventual steady-state. All models predicted comparable long-term (after several years) steady-state adaptations. Future experimental analyses will be necessary to better determine appropriate fading memory time constants for bone under various loading conditions.

Adaptation, Physiological↗