Numerical modeling of cortical bone adaptation due to mechanical loading using the finite element method

Bone adaptation;Cortical bone;poroelasticity;rat ulna;finite element methods;Biomechanics

Chennimalai Kumar, Natarajan

关键词: Bone adaptation;    Cortical bone;    poroelasticity;    rat ulna;    finite element methods;    Biomechanics;   

Others  :  https://www.ideals.illinois.edu/bitstream/handle/2142/16700/1_ChennimalaiKumar_Natarajan.pdf?sequence=2&isAllowed=y

美国|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 摘 要 】

It is well known that bone tissue adapts its shape and structure according to its mechanical environment. Bone adaptation occurs on the dense cortical bone and porous trabecularbone. The process of bone adaptation is shown to be dependent on a number of mechanicalloading parameters such as magnitude, frequency, number of bouts etc. of applied loadingthrough experimental studies. We propose to develop a numerical framework, which cansimulate and predict cortical bone adaptation due to diff erent parameters of loading. Inpursuit of the development of the framework, we develop a method to generate fi nite element (FE) models of actual rat ulna from micro computed tomography (micro-CT) images. Theexternal adaptation process is implemented in the model by moving the surface nodes of theFE mesh along the normal direction based on an evolution law characterized by two parameters: one that captures the rate of the adaptation process (referred to as gain); and theother characterizing the threshold value of the mechanical stimulus required for adaptation(referred to as threshold-sensitivity).Cortical bone isfirstly modeled as an elastic material. Loading from experiments ofRobling et al is applied on the FE model and the elastic boundary value problem issolved. Based on the results of the FE solution, the surface nodes are displaced according tothe local strain energy density as the growth stimulus. Using this stimulus, we show that themodel can simulate the e ffect of the magnitude of applied loading on the growth response.We calibrate the growth law parameters by comparing the results from our model to theexperimental results. A parametric study is carried out to evaluate the e ffect of these twoparameters on the adaptation response. We show, following comparison of results from thesimulations to the experimental observations, that splitting the loading cycles into di fferentnumber of bouts a ffects the threshold-sensitivity but not the rate of adaptation. We alsoshow that the threshold-sensitivity parameter can quantify the mechanosensitivity of theosteocytes. The use of strain energy density stimulus and elastic material model cannotsimulate the e ect of frequency of applied loading on the cortical bone adaptation response.We model cortical bone as a poroelastic material to account for the interstitial fluid flow.We aim to develop a growth stimulus similar to strain energy density for the poroelasticmaterial model. In order to achieve this goal, we develop the FE model of a rectangular beamsubjected to pure bending. This geometric model is chosen for simplicity, as an idealizedrepresentation of cortical bone. We then propose the use of the dissipation energy of theporoelastic ow as a mechanical stimulus for bone adaptation, and show that it can predict the eff ect of frequency of the applied load. Surface adaptation in the model depends on theweighted average of the mechanical stimulus in a "zone of influence" near each surface point,in order to incorporate the non-locality in the mechanotransduction of osteocytes present in the lacunae. We show that the dissipation energy stimulus and the resulting increasein second moment of inertia of the cross section increase linearly with frequency in the lowfrequency range (less than 10 Hz) and saturate at the higher frequency range (greater than 10Hz). Similar non-linear adaptation frequency response also has been observed in numerousexperiments. We extend the poroelastic material model, dissipation energy stimulus, and the zone of infuence to the actual rat ulna FE model. We implement orthotropic permeabilityon the rat ulna model in order to be anatomically consistent. We calibrate the growthlaw parameters (gain and threshold-sensitivity) using experimental results. We analyze thegrowth response of cortical bone for a range of frequencies (from 2 Hz to 25 Hz) and showthat the adaptation response is non-linear with respect to the frequency of loading.