This study is aimed at providing an effective method for determining strain-load relationship and at quantifying the strain distribution within the whole tibia under axial compressive load on rats. Rat tibial models with axial compressive load were designed. Strains in three directions (0°, 45°, and 90°) at the proximal shaft of the tibia were measured by using a strain gauge rosette, which was used to calculate the maximum and minimum principal strains. Moreover, the strain at the midshaft of the tibia was measured by a single-element strain gauge. The slopes of the strain-load curves with different peak loads were calculated to assess the stability of the strain gauge measurement. Mechanical environment in the whole tibia by the axial compressive load was quantified using finite element analysis (FEA) based on microcomputed tomography images. The von Mises elastic strain distributions of the whole tibiae were evaluated. Slopes of the strain-load curves showed no significant differences among different peak loads (ANOVA;
Bone is a weight-bearing and mechanosensitive tissue. The adaptive responses to mechanical load in cortical and trabecular regions have been studied extensively. Animal studies can provide detailed data on bone response. As a valid method for controlled and repetitive load of the murine skeletons, the axial compressive load models were widely used.
Axial loading models in rodents included tibial loading models [
The animal models have been instrumental in advancing the understanding of the response of bone to mechanical stimuli. Strain is considered one of the main factors for inducing bone tissue response to load [
The mouse tibial model is usually used to investigate the strain-load relationship in other studies. However, due to the curvature of the tibiae, tissue strain distribution of the tibia under axial compression is complex. The rat models (15 samples) with axial compressive load will be used in the current study to provide an effective method to obtain the strain distribution over the whole tibiae under axial compressive load; the results will serve as reference for further exploring the mechanical response of bone to axial compressive load. Design and validation of the rat tibia loading model involved measurement of surface bone strains at the proximal shaft and the midshaft of tibia, assessment of the relationship between strains and peak loads, FEA, and the evaluation of the mechanical environment of the whole tibiae.
A total of 15 5-month-old female rats were purchased (sample information is shown in Table
Sample information (
Numbers | Body weight (g) | Tibial length (mm) |
---|---|---|
15 |
All rats were euthanized, and the intact right hindlimbs were harvested and immediately prepared for strain gauge measurements. After the knee was fixed, the tibial length was measured by using a Vernier caliper. An incision was made on the lateral aspect of the tibia, and the skin and muscle attachments were removed. After gently removing the periosteum, the bone surface was exposed and then degreased by acetone.
Strains in three directions (0°, 45°, and 90°) at the proximal shaft of the tibia were measured by using a strain gauge rosette. The maximum principal strains
Moreover, the strain at the midshaft of the tibia was measured by using a single-element strain gauge. All gauges were waterproofed for 12 h before experiment, and gauges with resistance values outside the range of
Locations of strain gauges (red line: long axis).
Cyclic dynamic axial compressive load was applied through a custom-made dynamic loading device (Figure
Custom-made dynamic loading device.
Fixed cups of rat tibia in the custom-made dynamic loading device: (a) the bottom cup and (b) the top cup.
A 4 Hz triangle waveform including 0.15 s of symmetric loading/unloading and 0.1 s rest in a cycle was applied to each tibia [
Cyclic dynamic compressive load: (a) the input waveform and (b) the process of 6-step loading regime; blue arrow: the loading waveform between the first and the second loading steps.
Finite element models based on micro-CT scanning were built. The mechanical parameters in the whole tibiae under axial compressive loads were quantified by static linear elastic FEA.
After strain gauge measurement, the samples were moved from the experimental cups to a couple of acrylonitrile butadiene styrene (ABS) cups. The ABS cups were 3D printed by a 3D-printing device in accordance with the cups used in the experimental study. The positions of the hindlimbs in the ABS and experimental cups were certified consistently. In other words, the relative positions of the hindlimbs in the ABS and experimental cups were consistent. The ABS cups were then fixed by two ABS screws. Before micro-CT scanning, the wires of gauges were cut off, followed by complete polishing of metallic explosion, and the gauge bases were maintained to confirm the gauge locations in micro-CT images, which can provide an accurate region for strains compared in FEA. Micro-CT scanning was performed by a micro-CT system operated at 79 kV and 125
Geometry of the tibia: (a) the whole tibia model and (b) the proximal tibia.
The geometric models were converted to finite element in Hypermesh®. That is, 3D solid models built in Materialise Mimics® were exported to Hypermesh® and subdivided into discrete elements. The models were meshed automatically and average edge length was 150
Since the experimental strains were well correlated with the FEA results using the second-order tetrahedral finite elements [
Based on the positions of the fixed cups in the micro-CT images, the mechanical load direction was defined directly. The
Typical finite element model of the rat tibia: (a) boundary and loading conditions of the finite element model; (b) the fixed bone surface on the tibial plateau; (c) the selected surface for mechanical load on the distal tibia.
Material properties were defined as described in Razi et al. [
Based on the above equations, the maximum Young’s modulus (
The whole tibia was equally divided into 20 regions along the tibial axis. The ash mineral density of each region was calculated in Materialise Mimics®, and different Young’s moduli were derived based on the above equations. Young’s moduli were then assigned to the corresponding regions manually. Material property of the fibula was defined separately, and Young’s modulus was set as 5 GPa [
Typical material properties of the tibia model: (a) the tibia model and (b) material property distribution of the whole tibia. The meshes were hidden in order to avoid affecting the indications of the material properties.
Given the linear relationship between loads and bone strains under axial compressive load, a −40 N load was applied to the finite element models. The linear elastic FEA was performed in ANSYS®.
Node sets of the strain gauges and local coordinate system were established to obtain accurate strains in FEA (Figure
Regions of strain gauges and local coordinate system: (a) regions of strain gauges scanned by micro-CT; (b) regions of strain gauges on the samples; (c) node sets of strain gauges and local coordinate systems. Red arrow: single-element strain gauge; yellow arrow: strain gauge rosette; green arrow:
The relationship of mechanical load and strain was defined by using the slope of the strain-load curve. The average and standard deviation of the slope were then compared between the results of the experiment and FEA. One-way analysis of variance (ANOVA) followed by least significant difference (LSD) test was used to compare the means of slopes under different peak loads. Analyses of differences between the experimental and computational strains were performed using paired Student’s
Figure
Typical strain-load curves under different peak axial compressive loads: (a) −20 N peak load; (b) −30 N peak load; (c) −40 N peak load.
Table
The slopes of the strain-load curves obtained by strain gauge measurement (
−20 N ( |
−30 N ( |
−40 N ( | |
---|---|---|---|
Maximum principal strain | |||
Minimum principal strain | |||
Midshaft strain |
The relationships between the experimental and computational results (i.e., the maximum principal strain, the minimum principal strain, and the midshaft strain) were linear with
Linear regressions of the computational and experimental strains: (a) maximum principal strain; (b) minimum principal strain; (c) midshaft strain.
Comparison of the strains obtained by strain gauge measurement and FEA (
Experimental result ( |
FEA result ( |
Error (%) | ||
---|---|---|---|---|
Maximum principal strain | 5.44 | 0.984 | ||
Minimum principal strain | 12.45 | 0.546 | ||
Midshaft strain | 1.75 | 0.394 |
The von Mises elastic strain distribution of the whole tibia was evaluated (Figure
Typical von Mises elastic strain distribution of the tibial midshaft: (a) image of the tibia scanned by micro-CT; (b) von Mises elastic strain distribution of the tibial midshaft; (c) the cross section with the maximal strain; (d) the cross section with the minimal strain; red dotted box: the tibial midshaft selected for analyzing the strain distribution.
For the tibial midshaft, the von Mises elastic strain was the lowest in the middle and gradually increased to both sides along the lateral direction with the maximal von Mises elastic strain being observed on the posterior side under the distal tibiofibular synostosis. Figure
The current study combined strain gauge measurement and FEA method to obtain the relationship between loads and tibial strains. The goal was to provide a loading model to observe bone adaptation to mechanical environment and to understand the cellular and biological pathways of the cell response under mechanical stimulation.
Mouse models (experimental and computational models) are the most frequent models used in the previous studies. However, mouse tibiae were too small to place a gauge to confirm the numerical results [
The finite element models built from micro-CT images could provide the microarchitecture of bone accurately (include trabeculae). Finite element models which included trabeculae could better describe bone architecture and made the obtained computational results more closely to reality, which were widely used for characterizing the mechanical environment in the whole tibia [
In the current study, material property arrangements of the finite element models based on micro-CT were investigated strictly before all samples were analyzed. Heterogeneous and homogeneous bone tissue material properties were used to evaluate the whole bone strain distribution [
Five samples were randomly selected from the 15 tibiae. Then, the finite element models in Hypermesh® were subdivided into four parts including cortical bone, growing plane, trabecular bone, and fibula. The material properties of different parts were defined in Table
Different material property distribution used in the study (GPa).
Group | Abbreviation | Cortical bone | Growing plane | Trabecular bone | Fibula |
---|---|---|---|---|---|
Uniform material property distribution | UM | 15 | 15 | 15 | 15 |
Two-material property distribution | Two-M | 15 | 4 | 15 | 15 |
Three-material property distribution | Three-M | 15 | 4 | 0.5 | 15 |
Twenty-material property distribution | Twenty-M | 20 regions based on the ash mineral density | 5 |
The FEA results with different material properties were compared. The node set strains were calculated, and the differences between FEA strains and experimental strains were compared.
Strains calculated by using FEA showed that significant differences were observed between UM, Two-M, Three-M, and experimental strains (ANOVA followed by LSD,
Comparisons of FEA results from different material properties of the tibiae: (a) maximum principal strain; (b) minimum principal strain; (c) midshaft strain; UM~Twenty-M: strains of FEA under different material property distribution.
Because of the differences in strain gauge locations and the alignment errors of strain gauges, large intraindividual variability was found during strain gauge measurement [
In consideration of the larger size of bone tissue of rat than mouse, there are some differences on finite element modeling. A simplified tibial model was developed in the current study, which was convenient for meshing and cost less computational time. Although it included certain simplification, it contains most of the information about the bony tissue (including cortical bone, trabecular bone, and growing plane). The results of FEA confirmed that the computational strains matched well with the experimental results, so the simplification of model was effective.
In order to verify the accuracy of the mesh density used in the current study, a mesh sensitivity study was performed. A typical finite element model was meshed using three different element sizes (the average edge length was 75
For boundary conditions, all directions of the constrained terminal were fixed in most studies. However, the constrained terminal used in our study was the knee side and the fixed cup contacted directly with the distal femur. Given the relative location of the femur trochlear and tibial patella, a minimal slide on the Y direction can be observed. For this reason, the Y direction was not fixed in the study, whereas both X and Z directions were fixed.
Strong correlations between the experimental and computational strains were observed at the gauge locations, to indicate that the mechanical environment of the whole tibiae can be extrapolated effectively by using FEA.
Studies demonstrated that the measured strains were heavily dependent on the strain gauge location, that is, even slight difference in gauge location between specimens would induce obvious variation in the measured strains [
Octahedral shear strain can analyze the correlation between the strain and local biological response [
The maximal von Mises elastic strain was observed on the posterior side under the distal tibiofibular synostosis. Given that a maximal mechanical stimulus will generate maximal response of the tissue [
First, limited by the gauge size and bone morphology, only two regions were selected to be measured. Fortunately, the relationship of strain-load showed obvious linear relationship, and the computational strains matched well with the experimental results. Thus, the method used in this study can reflect the real mechanical environment. Second, cyclic dynamic compressive load was applied during strain gauge measurement, whereas static linear elastic FEA was performed in the study. This limitation has been pointed in a previous study [
This study combined the strain gauge measurement and FEA to obtain the strain distribution of the whole rat tibia under axial compressive load. The loading and boundary conditions and the material properties were investigated in detail. The method of strain gauge measurements and FEA used in this study can provide a feasible way to obtain the mechanical environment of the tibia under axial compressive load on the rats. The results of this study conclude that strain is directly related to mechanical stimulus. The obtained position with the highest strain could contribute to the study of cellular and biological pathways of the cell response to mechanical stimulation.
The data used to support the findings of this study are included within the article.
The authors have declared that no competing interest exists.
This work is supported by the National Natural Science Foundation of China (Nos. 11702110, 11872095, and 11432016), the Natural Science Foundation of Jilin Province (Nos. 20170519008JH and 20170520093JH), the China Postdoctoral Science Foundation (2016M591477), and the Open Fund Project of the State Key Laboratory of Automotive Simulation and Control (20171114).