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Mechanical properties of the growth plate cartilage
Abstract
A method for determining the mechanical properties (including Poisson's ratio $\nu\sb{s},$ shear modulus $\mu\sb{s},$ Young's modulus $E\sb{s},$ aggregate modulus $H\sb{A},$ and permeability K) of the growth plate cartilage is presented. Indentation experiments were performed on 40 specimens of the growth plate cartilage from the proximal bovine epiphyseal plate. The experimental data of the normal displacements, u(t), that describe the creep phenomena of the growth plate cartilage under indentation in junction with the biphasic KLM-theory were used to determine these mechanical properties. For each indentation test a value for Poisson's ratio was determined which is dependent only on the steady state value of $u(\infty)$ and was used in calculating the other mechanical properties. The growth plate response in the indentation test was modeled as a biphasic KLM material overlying a rigid and perfectly permeable substrate. Using appropriate boundary conditions at the cartilage/cancellous bone junction, the cartilage was assumed to behave similar to articular cartilage. The differential equations and boundary conditions were normalized, and Laplace and Hankel transformed methods were used to solve the deferential equations. The transformed equations and boundary conditions yielded the solution of a Fredholm integral equation for $g(\gamma,s).$ Numerical computational techniques have been developed to solve the Fredholm equation to obtain the displacement $\bar u(s),$ where s is the Laplace parameter. Then, the data points of $\bar u(s)$ were curve-fitted by a nonlinear equation. This nonlinear equation contained unknown constants which were determined by the application of the Least-squares method. These constants were adjusted using Newton-Raphson/Parametric study to obtain the theoretical solution of $u(\acute t)$ that provided the normalized time-dependent displacement. Also, the experimental data of u(t) were curve-fitted following a similar procedure. The theoretical and experimental curve-fits were correlated to each other to extract the mechanical properties. In this dissertation, the mechanical properties of the growth plate cartilage at the knee joint were determined. The developed method presented in this study computes the Poisson's ratio with considerably less computer time than required for the previously proposed method of Mow et al, (88).
Subject Area
Biomedical research
Recommended Citation
Abdulshafi, Waleed Abdulkarem, "Mechanical properties of the growth plate cartilage" (1993). ETD collection for University of Nebraska-Lincoln. AAI9415948.
https://digitalcommons.unl.edu/dissertations/AAI9415948