Towards the simulation of bone-implant systems with a stratified material model

1.1Background

The whole process of the simulation of bone-implant systems has been subject to many studies in the literature over the past years [5, 6] and has even been demonstrated to be efficiently executable on cloud based computing resources [7, 8]. Furthermore, the approach of VCT is promoted by the European Commission in the final report of the Avicenna Alliance [9] and by the Food and Drug Administration (FDA) in various guidance documents [10]. With this, the baseline has been set to develop the methodology of the simulation of bone-implant systems from the stage of pure academic analyses and considerations towards productive application in clinical environments as well as in implant design and development.

Also for the three prerequisites of structural mechanics simulations, (1) the bone geometry, (2) forces acting on the bone structures and (3) a detailed modeling of the heterogeneous, anisotropic material distribution of the bony structures, significant developments were achieved. The extraction of the bone geometry from clinical Computer Tomography (CT) data is already a standard procedure implemented in various software tools and libraries [11, 12, 13, 14]. Also the determination of representative sets of muscle forces is subject to recent research on the software development and simulation side [15, 16] as well as the experimental side [17].

In the field of material modeling on the basis of CT data, the literature of the past decades shows a path leading from analytical approaches [18] and experimental methods [19] over material data determination via data-processing-based approaches directly applied to clinical CT data [20], to simulation-based approaches that use homogenisation and averaging methods to raise bone micromechanics to the level of continuum mechanics [21, 22].

Like in the case of geometry extraction, the actual continuum mechanical simulations of bone-implant systems can also be based on standard tools as was demonstrated by various studies in the recent past [23, 24]. Even for the communication of engineering type results towards medical and clinical staff approaches are developed [25].

A recent study conducted in 2023 provides compelling evidence of the surging acceptance of computer modeling and simulation within hospital settings [26]. Notably, a substantial 55.0% of respondents reported actively utilizing computational modeling and simulation for procedure planning. The degree of adoption, however, exhibited variation across different medical settings. Among those who employed modeling and simulation for procedure planning, the cardiovascular domain emerged as the most prevalent, closely followed by musculoskeletal applications. In terms of numerical tools employed, Artificial Intelligence (AI) stood out as the most frequently utilized, followed by multiscale modeling, Finite Element Analysis (FEA), and Computational Fluid Dynamics (CFD). These findings collectively underscore the increasing significance and widespread utilization of computer modeling and simulation in enhancing healthcare practices.

1.2Objective

The first objective of this paper is to present an overview of the principle approach towards the analysis of bone-implant systems by means of engineering type Finite Element Method (FEM) simulations. The second objective is to demonstrate how the nondeterministic character of biomechanical models can be captured for the part of human bone material modeling and how HPC can be used to efficiently construct nondeterministic modeling approaches suitable for VCT as well as for the uncertainty quantification of patient specific models with large parameter spaces.

Figure 1.

Anticipated workflow in simulation supported surgery.

As can be seen in Fig. 1 the principle modeling approach of bone-implant systems is not that different from the classical engineering simulation workflow comprised out of the four steps (1) model generation (i.e. preprocessing), (2) simulation (3) result evaluation (i.e post-processing) and (4) result feedback, even though considerable differences to classical deterministic modeling exist, especially in the first and last step.

Since most of the considered steps are existing pieces, put together from already developed approaches, we present their principles briefly in the Methods section. For the steps “data processing of clinical CT data” and “material modeling” a deeper dive is done. The processing of the clinical CT data is considered in more detail due to its significant difference to clinical routines and the material modeling part due to its impact on the variability of models. This leads to the results section where first findings with respect to the development of a virtual cohort as a baseline for a non deterministic modeling approach for bone-implant systems by means of HPC and its link to clinical CT data are presented.

2.1Prerequisite collection

Clinical imaging data, as recorded by CT or Magnetic Resonance Imaging (MRI), are the only data which are available from living bones and muscles which have to be represented in discretised form in order to comprise a FEM model of a bone-implant systems with all relevant load- and boundary conditions. One problem that always arises when deriving discrete simulation models from CT data is the discrepancy between clinical data collection schemes and the requirements that are posed to data once they should be used as a baseline for model extraction. In everyday clinical routine especially in the cases of CT data, x-ray exposure and other burdens to the patient have to be kept at the absolute minimum. Additionally, imaging data are collected for visual inspection by trained medical professionals which means that the in-plane resolution of the images in almost every case differs significantly from the one in normal direction of the image plane since the focus lies on the single 2D image. This means the fundamental point is to improve image resolution. This leads to clean geometry extraction and a reproducible baseline for material data generation.

2.1.1Geometry

To achieve increased image resolution we have chosen the approach to combine multiple image reconstructions in different imaging planes. In discussions with the medical staff it was found that the least disturbance of the clinical routine would result from the application of standard protocols, i.e the reconstruction of the image data normal to the three coordinate axes. To combine the three resulting data sets into one 3D data volume with isotropic resolution, the DICOM data were converted with the application 3D-Slicer into VTK-Image data and then combined by means of a VTK-pipeline realized in ParaView [27] as shown in Fig. 2. The image combination process in the ParaView Calculator Filter currently employs a simple mean calculation.

Figure 2.

Image reconstruction planes and recombination pipeline.

The geometry extraction itself is also done with ParaView by means of the ParaView Contour Filter which is based on isosurface calculation via the marching cubes algorithm. The extracted geometry is then exported as a triangulated surface mesh in a format which can afterwards be imported by the FEM preprocessor ANSA [28].

2.2Modeling and simulation

In this section the current modeling and simulation techniques and tools utilized to evaluate bone-implant-structures are described. As explained above, the geometry extracted from clinical CT data is exported as a triangulated mesh. Since a surface mesh derived by a marching cubes algorithm is not suitable for FEM simulations, the mesh has to be restructured to regular triangulation. This is currently done with the FEM preprocessor ANSA. With this tool the necessary mesh improvements, the reassembling of fractured bones and the volume meshing of the bone structures are done. Furthermore the implant structures which in most case are provided as Computer-Aided Design (CAD) data are meshed and integrated into the bone structures. Additionally, loads and boundary conditions are applied with ANSA. To automate the application of boundary conditions a method based on template morphing is currently under development.

Figure 3.

Modelled bone and implant structures.

In Fig. 3 the typical set of bone structures modelled for the analysis of proximal femur implants is shown along with the material distribution in the model which was directly mapped from the clinical CT data with the algorithm described in [20]. Blue areas represent low material stiffness whereas red areas mark regions of high material stiffness. 432 different orthotropic material cards were used in this model combined with 48 orthotropic coordinate systems. Also shown in Fig. 3 are models of the distal humerus. They where used to analyze different external fixation methods of a distal humerus fracture. The question raised by the surgeons was, which fixation option generates the least relative movement within the fracture zone.

The FEM simulation of bone-implant systems is currently done with standard FEM software packages like Abaqus/Standard [34], code_aster [35] or in dynamic situations with LS-DYNA [36].

2.3Result analyses and metric extraction

The result analyses and metric extraction can be done with commercial software packages like the FEM post-processor META [37]. Of particular interest are the locations of plastic strains within the implant structures that can lead to locking of dynamic components inside the implant. Within the bone structures, the major principal strains are evaluated. In the case of implants for fracture stabilization, normal strains within the fracture planes are evaluated. Based on these structural mechanics results metrics are derived and evaluated my means of a scoring system that is discussed in detail in [25]. Based on this scoring system different implants can be evaluated within a single bone structure to find the best implant for a given patient or vice versa, an implant can be evaluated within a virtual cohort to evaluate its average performance score.

3.1Data sets for virtual trial testing

A total of 28 clinical CT data sets were harvested, encompassing patients aged between 49 and 90 years. The data set consists of femoral heads from 16 females and 12 males. For the scanning process, femoral heads numbered 1 to 20 were captured using the Siemens® SOMATOM Sensation 64 CT scanner, while femoral heads numbered 22 to 44 were scanned with the Siemens® SOMATOM Confidence CT scanner.11 It should be acknowledged that bone samples numbered 37 and 38 originate from the same donor. Further information regarding these data sets can be found in Table 1.

The process of explantation and imaging of the femoral heads was conducted with the approval of the Ethics Committee of the State Medical Chamber of Baden-Württemberg, under the application F-2020-118. To ensure the authenticity and accuracy of the data while safeguarding the interests and dignity of the tissue donors, the data sets were pseudonymized prior to publication. These data sets, comprising clinical CT data from all 28 cases, were collected and reconstructed in three orientations to align with the described resample combine methodology in the method section. To make these data accessible to the open public, they are published in the data repository of the University of Stuttgart called DaRUS [38, 39, 40].22

The femoral heads are presently securely stored in a locked room at the Institute of Biomaterials and Biomolecular Systems at the University of Stuttgart. Specifically, they are maintained in a freezer at a temperature of -80∘C. This storage method has been previously utilized in a study investigating the impact of storage on elastic properties over an extended period of several weeks [41]. Statistical tests conducted on the collected data indicated that the observed changes in values were not statistically significant. The storage of the femoral heads facilitates the potential for conducting destructive testing on the specimens in future studies.

3.2Data evaluation

In this section we present the initial findings of the proposed resample combine method. In Fig. 4 one can see in the upper left the outline of the data volume encompassing the three data sets along with a volume rendering of the contained femoral head no.1 and the line along which the line charts in the upper right and lower part of the figure are plotted. The line chart in the upper right presents the plot of the resampled data sets across the total volume. As can be seen, global differences are non-existent even though, taking a closer look at the data as shown in the lower, zoomed in part of the figure makes it evident that non negligible differences exist if data are reconstructed in different image planes. This is especially true for areas of local maxima and minima which are apparently equally affected.

Figure 4.

Example of the resample combine method of multiple reconstructions by simple mean calculation.

As can be read from Table 2 in which the mean, the 25% quartile and 75% quartile for the comparison of two data sets each in different imaging planes are shown, the result from the line sample presented in Fig. 4 hold true also for complete data fields. Additionally, it can be seen from Table 2 that differences also vary significantly between data sets of different femoral heads even though the same scanning and reconstructions procedures were used to record and reconstruct the different data fields. As can be seen, the maximum deviation of two different data fields reaches 3.6% within femoral head no. 1 while it shows a maximum of 14.1% within femoral head no. 5.

Another interesting results that can be observed from Table 2 is the fact that deviations between data sets are symmetric around the mean value. This leads to the conclusion that the application of the proposed resample combine methodology is not necessary for simulations in which only global strain and displacement results are of interest since local deviations between different reconstructions will be averaged out. Vice versa, however, multiple reconstruction and the application of the resample combine method are absolutely necessary once local strain patterns should be evaluated since these discrepancies subsequently will impact material modeling in which material data are directly mapped from clinical CT data.