Numerical simulation of bone remodelling is a tool applied to investigate the fracture healing and the implant integration, in order to detect and quantify the secondary stability of the endoprosthetic implant as well as bone healing time and ingrowth of bone tissue into functionalized implant surfaces. A prognosis concerning changes in bone morphology under mechanical stress can be ventured using a time-step method based on standard computer tomography (CT) datasets and finite element analysis (FEA) , , . Following this theory, the aim of our work was the development of a numerical algorithm to simulate the mechanically stimulated bone remodelling.
The basis for the simulation of bone remodelling is represented by a finite element (FE) model, whose geometry is reconstructed from a CT dataset. To create this numerical model the following software packages are used:
Segmentation: Amira 5.4.1 (FEI Company, Hillsboro, OR, USA)
CAD-Reconstruction: Geomagic Studio 2013 (3D Systems, Rock Hill, SC, USA)
Mapping of HU values: Abactmat (self-developed software, University Medicine Rostock, Germany) based on Python 2.6.2 (Python Software Foundation, Beaverton, OR, USA)
Pre-processor and Solver: Abaqus/CAE 6.12-2 (Dassault Systèmes, Providence, RI, USA)
Bone remodelling simulation software using time-step method: Remodel (self-developed software, University Medicine Rostock, Germany) based on Python 2.7.2 (Python Software Foundation, Beaverton, OR, USA)
Post-processor: Abaqus/Viewer 6.12-2 (Dassault Systèmes, Providence, RI, USA)
The software tools could be used in the described process operation without any interface problems. The process operation steps, which are shown in Figure 1, are explained in detail in the following chapters.
2.1 Reconstruction of bone morphology
The reconstruction of bone morphology is based on CT datasets containing the interesting bone structures. The CT images, which represent the attenuation of X-ray spectrum by the tissue measured in Hounsfield units (HU), are imported in Amira and the bone structures and the areas, in which bone formation is expected, are segmented layer by layer using the image segmentation editor. Once the segmentation is completed, the three-dimensional surface of the bone can be reconstructed automatically using triangular faces. The resulting surface model is committed to Geomagic via a STL interface in ASCII mode. In Geomagic the faceted polygon surface is smoothed and converted into a surface of analytical Non-Uniform Rational B-Spline surfaces (NURBS). For this purpose, the surface of the model is divided into quadrilateral patches providing that a decomposition of the bone in hexahedral bodies is conceivable. Subsequently the model is covered with a grid, which is required to generate the NURBS surface. The model is transferred to the pre-processor via an IGES interface .
2.2 Preparation of the FE-model
If the surface has no further gaps or holes, the surface model is converted into a solid model when the import in Abaqus/CAE is performed. Afterwards, the solid model is meshed automatically with tetrahedral finite elements. The mapping of the material data from the CT to the FE mesh is done node-wise. Employing the self-developed software Abactmat, each node gets an HU value from the CT data by using the corresponding node coordinates. The HU values are considered as temperatures, in order to simulate the inhomogeneous bone material properties in vivo by a linear-elastic temperature-dependent material model . Correlations between HU and Young’s modulus or bone mineral density and Young’s modulus can be found in the literature . The relationship between HU and bone mineral density can be determined through a bone mineral density phantom, which should be CT-scanned together with the interesting bone structure .
In contrast, the application of the boundary conditions (forces, pressures, and displacements) in biomechanical FEA is mostly based on assumptions. Articular force measurements with specially instrumented implants such as OrthoLoad implants  or muscle force calculations based on inverse dynamics  cannot capture the entire spectrum of the constraints in vivo. Hence, the load, which is applied on the FE model, usually reposes on an available load from the literature like the maximum load during walking, sitting down or climbing stairs. The bearing of the bone model is performed in the articular centre points, while the articular forces and the muscle forces are applied on the model surface. All boundary conditions are implemented via reference points which are linked to the volume or surface through tie constraints.
In order to avoid an excessive calculation time, the FEA can be performed with a static load and, if appropriate, carried out without nonlinearities. The interesting output parameters of the FEA have to be augmented by the node temperature and the output parameter, which should be acting as the basis of the mechanical stimulus. Through the output of the input file the FE model is made available for the bone remodelling simulation.
2.3 Bone remodelling
The simulation of bone remodelling is implemented by the adaptation of the HU values to the FE-calculated mechanical stimulus. The aim is an optimally mineralized bone structure with high HU values in high stressed areas and low HU values in low stressed areas. In consequence, the stimulus in the whole bone structure gets more uniform. To adapt the HU values of the FE nodes, the local stimuli of the nodes are determined and compared with a reference stimulus, which represents the acceptable daily strain of the bone tissue. If the current stimulus is higher than the reference stimulus, the HU value of the node needs to be increased (bone formation). If the current stimulus is smaller, the HU value has to be reduced (bone resorption). Based on a mathematical function (Figure 2) the node-individual rate of bone turnover is calculated and a new HU value for the observed FE node is determined. Assuming that the current stimulus exceeds the maximum of bone formation, the overload leads to a necrotic bone resorption. If the current stimulus of the FE node is close to the reference stimulus, no adaptation of the HU value is required (equilibrium zone). To adapt the mathematical function (Figure 2) to the desired bone model, the following parameters need to be defined:
Magnitude of the equilibrium,
Zone of necrosis stimulus,
Rate of bone turnover and
Remodelling balance between formation and degradation.
Moreover, the period of time represented by the FEA, and the weighting of different load cases (e.g. walking vs. climbing stairs) have to be clarified. By varying these input parameters, the bone remodelling rate can be changed and an increased bone formation or degradation is promoted. During the automatically proceeded optimization, FEA and HU-value adaptation are performed alternately, until a uniform strain or a previously defined termination criterion is reached.
To start the process of bone remodelling simulation, the following steps are required:
The input parameters given above are entered in a pre-formatted text file (para.txt).
The temperature table, which contains the nodes and the current HU values to be remodelled, are exported from the input file (job.inp) into a new text file that is stored as HU file (job.huf).
Instead of the temperature table a cross-reference to the HU file is supplemented in the input file.
Python code (remodel.py), parameter text file (para.txt), input file of the FE model (job.inp), HU file (job.huf) and an environment file for Abaqus (abaqus.env) are placed in a separate file folder.
Using a queue for the systematic processing of unsolved input files by the Abaqus solver, FEA and HU-value adaptation are performed automatically. After each FEA the HU-file is duplicated and edited to predetermine the new specific HU values for the following FEA. In which kind the files interact in detail is summarized in Figure 3 .
The result of the bone remodelling simulation is an output file (job.odb) for the Abaqus Viewer. This file contains the results of all FEA including the HU value distributions, which were used for the corresponding FEA cycles. In Figure 4 the results of a mechanically stimulated rat bone is shown exemplarily. The transcortical hole through the diaphysis of the femur is closed in vivo and in silico within a simulation time of 1 month postoperatively.
The relationship between morphology and mechanical stress in bones was already described in 1892 by Julius Wolff. Based on this theory, an organ-level strategy to simulate the load-driven remodelling in bones was developed. The aim was to predict the distribution of bone tissue and trabecular bone density with numerical bone models stimulated by stress or strain parameters . Since these stimulation parameters have been questioned, new strategies driven by the removal of microdamages , regulated by biological parameters  and multiscale approaches were developed , .
Our presented bone remodelling algorithm is a load-driven strategy, which is based on high-resolution CT data including the mineral density of bone. Thus, the patient-specific bone structure and the inhomogeneous material are considered. As the presented results show, the algorithm provides a realistically remodelled bone structure comparable to the result from the animal study. Nevertheless, an exact adjustment of the input parameters is necessary to obtain the correct reconstruction velocity and the desired degree of bone volume. For a reliable prediction of bone remodelling, the implementation of sensitivity analyses and experimental validations is essential. Summarized, our method represents a mechanically focused approach to analyse the macro-morphology of bone under altered mechanical conditions or in combination with different implant designs and materials.
Despite the fact that the proposed bone remodelling strategy provides a great opportunity to improve the choice of therapy in particular for complex bone defects, its use in clinical practice is not yet expedient. Besides the limitations of FE simulations related to bone structures like the complexity of the FE model creation, the lack of an assured bone material definition and the insufficient knowledge concerning the load situation of different bone types, the question how to validate the method of bone remodelling simulation impairs the targeted application . Today, validations using patient-specific data are not ethically acceptable because the patient would be exposed to an increased X-ray exposure due to frequent CT scans. Alternatively, a verification on an animal model can be performed, even if the healing process is affected through X-radiation and the transferability of the results to humans is difficult to prove because of restrictions due to different bone structures, surgical procedures and implant systems . In the future a verification of the bone remodelling algorithm on human subjects might be realized if high resolution MRI scans can be used instead of CT scans. For this purpose, the development of a sufficiently hedged material definition of the bone tissue in vivo with respect to MRI specific metrics would be required in order to offer a method for bone remodelling simulation, which could meet the challenges of patient-specific modelling in later clinical use.
We would like to thank Professor Annelie Weinberg and Ms. Elisabeth Martinelli, University Hospital Graz, for providing the animal CT scan.
Research funding: The author state no funding involved. Conflict of interest: Authors state no conflict of interest. Material and Methods: Informed consent: Informed consent is not applicable. Ethical approval: The conducted research is not related to either human or animal use.
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About the article
Published Online: 2016-09-30
Published in Print: 2016-09-01
Citation Information: Current Directions in Biomedical Engineering, Volume 2, Issue 1, Pages 643–647, ISSN (Online) 2364-5504, DOI: https://doi.org/10.1515/cdbme-2016-0141.
©2016 Josephine Mauck et al., licensee De Gruyter.. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0