Micro-finite Element Modeling And Simulating Investigation On The Mechanical Loading Experiment Of Rat Tibia

When subjected to changes of the external load,bone can sense and respond to mechanical signals,then adjusts its mass and architecture.During the transmission of mechanical signals,dynamic stimulus rather than static stimulus,induces the interstitial fluid flow in canaliculi,leading to the activation of bone cells.New bone formation occurs once the mechanical strain generated by the dynamic load amplitude exceeds a threshold value.The compressive loading models of long bone have been widely used to study bone formation in response to mechanical loading,in which the combination of mechanical test and finite element analysis is the most typical method used.Until now,there have been many studies on the dynamic loading model of mouse tibia and rat ulna,but few of rat tibia is reported.In the in vitro rat tibial loading experiment in this dissertation,the periosteal strain on the loaded bone was measured using strain gauges attached to the bone surface.To better understand the mechanisms of anabolic response in dynamic loading,finite element models based on the images of samples were established for the characterization of strain distribution in the whole bones.These models were routinely calibrated using the strain data acquired from strain gauges placed on the tibia.In this dissertation,first,the right lower limbs of fifteen 5-month-old female Wistar rats were used.Two strain gauges were attached to the medial surface of every tibia,subsequently the limbs were placed on the dynamic cyclic loading equipment.There were three different amplitudes(20N,30 N,40N)of the load.Then,experimental strain values were measured by the strain gauges.Second,tibia samples were scanned by Micro-CT scanner,and a series of softwares including Mimics,Magics,Geomagic Studio and HyperMesh were used to create geometric models of rat tibia,whereby the models were meshed by second order tetrahedral elements(Element size = 0.15mm),applied loads and boundary conditions,given the properties of isotropic linear elastic materials(The model was assigned one material,two materials,three materials,and twenty materials,i.e.there were totally four different methods.In view of the fact that the four kinds of finite element models had the same structures but different materials,the effects of different material-giving methods on strains of the tibia were analyzed).All models with twenty materials were used to calculate the stiffness.Third,the models were imported into ANSYS software,for each sample four finite element models were calculated and simulation of tibia loading was achieved.In addition,a typical finite element model was selected to refine the mesh(Element size = 0.075mm),and it was calculated.Finally,the results of computational models were analyzed involving the stability of calculation results,the match for experimental strain and numerical strain,the relationship between finite element stiffness and Young's modulus,the distribution of principal strain in the volumes of interest,the overall displacement distribution,and the variation of the principal strain along the longitudinal direction.Results showed that,before and after the mesh refinement the calculated results of the finite element models were similar at the similar position,including displacement,stress and strain;the experimental strain was consistent with the calculated strain;the linear relationship between calculated stiffness and elastic modulus was very strong.These results demonstrate that a combination of mechanical test and finite element analysis in this dissertation can simulate rat tibia under axial loading conditions accurately.For models from the same sample,four kinds of material-giving methods were adopted,and the calculation results all reflected the "down-up-down"("up-down-up")variation pattern of the maximum(minimum)principal strain of the tibia along the longitudinal axis;besides,the more the material was subdivided,the more effectively the strain of the tibia could be described.For different samples,the simulated results of the same material models were significantly different,indicating that the bone structure has a greater impact on the strain results,but the lowest value of the minimum principal strain appears at the same position of 40%-length from the proximal end.The dynamic loading experiment in this study provides an effective method for determining the load and load-strain relationship of rat tibia,providing a solid foundation for further exploration of the effect of local strain distribution on bone formation.The finite element modeling investigation in this study quantified the strain distribution of bone during dynamic loading,and it may serve as a reference for further exploring mechanism of response of bone tissue to the mechanical environment.