Comparison of Morphing Techniques to Develop Subject-Specific Finite Element Models of Vertebrae

Abstract

This study compared two morphing techniques (and their serial combination) to create subject-specific finite element models of 15 astronaut vertebrae. Surface deviations of the morphed models were compared against subject geometries extracted from medical images. The optimal morphing process yielded models with minimal difference in root-mean-square (RMS) deviation (C3, 0.52±0.14mm; T3, 0.34±0.04mm; L1, 0.59±0.16mm) of the subject’s vertebral geometry. <1% of model elements failed quality checks and compression simulations ran to completion. This research lays the foundation for the development of subject-specific finite element models to quantify musculoskeletal changes and injury risk from spaceflight.

Introduction

Astronauts are at increased risk for vertebral fracture due to spaceflight-induced bone loss [1,2]. Finite element (FE) models incorporating subject-specific geometry and bone density from computed tomography (CT) scans can predict fracture risk in astronaut and terrestrial populations [2,3]. There are several techniques for morphing FE meshes to a subject-specific surface geometry extracted from CT, including mesh-morphing and radial basis function interpolation algorithms [4,5]. This study aims to compare morphing methods to create subject-specific FE models of cervical, thoracic, and lumbar vertebrae using astronaut CT scans.

Materials and Methods

CT-imaging

This research focuses on pre-flight data of five astronauts enrolled in a larger study to assess vertebral strength changes following long-duration spaceflight. Institutional Review Board approval (IRB#00035882; IRB#Pro2280) and informed consent was obtained. CTs of each C3, T3, and L1 vertebra were acquired 30-180 days pre-launch (64-slice GE Lightspeed VCT: 100kVp; 100mA; pitch-1; thickness 1-mm with 0.625-mm reconstruction). Vertebral surface geometries were segmented from these scans (Mimics-v.20, Materialise, Leuven, Belgium).

Finite-element morphing

To reduce time and cost while developing subject-specific FE models, modifying element positioning and shape without altering node and element IDs is necessary [4,5]. Vertebral FE models (C3, T3, L1) from the Global Human Body Models Consortium (GHBMC) detailed 50^th-percentile male occupant model (v6.0, Elemance, LLC, Clemmons, NC) were used as the starting mesh for the morphing. Two morphing techniques (and their serial combination) were assessed to develop subject-specific models.

The first method used the open-source C++ Advanced Normalization Tools (ANTs) algorithm for image registration and transformation followed by thin-plate spline (TPS) interpolation in MATLAB (v.R2021a, MathWorks, Natick, MA) [5] (Figure 1). Source landmarks were extracted from the GHBMC model to serve as homologous points on the source and target vertebra, allowing for a one-to-one mapping that morphs the FE model towards the subject-specific geometry. Next, Neuroimaging Informatics Technology Initiative (NIfTI) images of the FE model and the subject-specific geometry were created (AMIRA-v.5.4.3, MyBioSoftware). These were input into ANTs to register the FE images to the subject-specific images, yielding an affine transform, deformation field, and inverse deformation field. The source landmarks were transformed using the affine transformation and inverse deformation field in ANTs, outputting the target landmarks. FE model nodal coordinates were then morphed to the subject-specific geometry using radial basis function interpolation with the TPS basis function and a relaxation algorithm (custom MATLAB code).

Figure 1.

Homologous landmarks between the FE model (green) and the subject target geometry (black) are used in the ANTs/TPS process to morph the original source FE model to create a subject-specific FE model. Abbreviations: finite element (FE), Global Human Body Models Consortium detailed 50^th-percentile male occupant model (GHBMC M50-O), Advanced Normalization Tools / thin-plate spline interpolation (ANTS/TPS)

The second method utilized the semi-automated Nominal2Real (N2R) function in ANSA (v.21.0.1 Beta CAE Systems, Switzerland), which takes the GHBMC FE model as the nominal input (source) and the subject-specific surface geometry as the real input (target) to output a subject-specific morphed FE model (Figure 2). Depending on the function’s success, nodes of the morphed mesh may need manual adjustment in ANSA to improve element quality.

Figure 2.

Process for the Nominal2Real morph using ANSA. Abbreviations: finite element (FE), Global Human Body Models Consortium detailed 50^th-percentile male occupant model (GHBMC M50-O)

In addition, serial combination of the morphing methods was evaluated. Both combinations were attempted for each vertebral level for two subjects (ANTS/TPS then N2R; N2R then ANTS/TPS); the optimal order was chosen from these results and used for the remaining subjects.

Effectiveness was assessed by comparing each morphed FE model to the targeted subject-specific surface geometry using surface deviation analysis in Geomagic Studio (v.2014, 3D Systems, Rock Hill, SC). Element quality for shell and solid elements was computed in ANSA for each morphed FE model using these metrics: Jacobian (minimum: 0.4 for shells; 0.3 for solids), aspect ratio (maximum: 6; 8), skew (60°; 70°), and minimum/maximum element angles (30°-150°; 25°-165°). Morphed FE models were deemed acceptable if no element failed the Jacobian criteria, and <1% of elements failed remaining quality checks. Manual plus computational time required for each morphing technique was also compared. Uniaxial compression simulations were run for the optimal morphed model for the subjects’ C3, T3, and L1 vertebrae (Appendix-A).

Results

Surface deviations between the morphed model and subject geometry for the different morphing techniques are in Figure 3 and Appendix-B. For C3, N2R alone and N2R combined with ANTs/TPS yielded similar results, however the combination provided a slightly closer fit to the subject, with mean±SD 0.52±0.14mm of the root-mean-square (RMS) of the deviations between the morphed model and the subject geometry. ANTs/TPS followed by N2R morphing produced the smallest deviations for T3 (0.34±0.04mm), while N2R followed by ANTs/TPS was optimal for L1 (0.59±0.16mm).

Figure 3.

Average ± SD of the root-mean-square of the surface deviations between the FE model and the subject-specific geometry before morphing (left-most bar), and after each morphing method. Abbreviations: Nominal2Real (N2R), Advanced Normalization Tools / thin-plate spline interpolation (ANTS/TPS); root-mean-square (RMS)

Across all morphs, each model had <1% of elements failing quality checks and no Jacobian element failures. Time to complete each morph on average was ~20-30 minutes (ANTs/TPS) versus ~5-15 minutes (N2R). Simulations ran to completion with no error terminations (Appendix-A).

Discussion

Exploring morphing methods that can accurately map unique geometric variations extracted from medical images enables quicker production of subject-specific FE models [4]. This study examined two FE morphing techniques and their serial combination to determine the optimal subject-specific morphing pipeline for cervical, thoracic, and lumbar vertebrae. From the resulting morphed models, the optimal morphing method for each vertebral level was identified, yielding 15 optimal models used in simulations. The subject-specific FE model product of the optimal morphing procedure for each of the three vertebral levels showed marked improvement when compared with the average surface deviation between the original GHBMC model and the subject-specific surface geometry. The average surface deviation between the optimal subject-specific morphed models and surface geometries fell well below the image resolution of the CT scans, indicating that the morphed models accurately capture the unique geometrical features of the astronauts’ vertebrae. While this study focused on spaceflight applications, the methods are broadly applicable to other populations at risk for vertebral fracture, including motor vehicle crash occupants, military service members, and older adults. The GHBMC model and software used in the morphing pipeline are either open source or commercially licensable, enabling uptake by other researchers.

Although this study is limited by the number of subjects studied (common for astronaut flight studies), the models of the pre-flight vertebrae of the five astronauts serve as a good foundation for creating the remaining pre-flight and post-flight subject-specific FE models for all nine astronauts enrolled in the study. Results from this study highlight the optimal morphing pipeline to use for the remaining astronauts’ C3, T3, and L1 vertebrae. These subject-specific models will be used to investigate the injury risk astronauts face under different loading conditions described by the FE simulations. Future analyses will create subject-specific models for the post-flight scans to compare the change in injury risk between astronaut’s pre-flight versus post-flight vertebrae. Additionally, the subject-specific cortical thickness and bone mineral density will be mapped to the vertebral models to further increase the accuracy of the FE simulations to estimate bone strength. Results from the computational analyses will assist space agencies in determining injury risk and appropriate musculoskeletal countermeasures for astronauts.

Appendix-A

Finite element model simulation methodology

Uniaxial compression testing of the most optimal morphed model for each of the five subjects’ C3, T3, and L1 vertebrae was simulated using nonlinear implicit analysis with LS-DYNA (v.12.0 ANSYS, Canonsburg, PA). The boundary conditions of the simulation were set such that they accurately represented the experimental data, against which they were compared [6]. A 3mm layer of polymethylmethacrylate (PMMA) was fixed to the inferior end of the vertebral body specifically matched to the geometry of each vertebra. Similarly, a subject-specific, 3mm PMMA impactor plate moving at a rate of 0.15mm/s directly compressing the superior end of the vertebral body was simulated (Figure A1). The vertebrae were modeled as an isotropic elastic-plastic material. Although vertebrae are composed of both cortical and trabecular bone, most prior research on vertebral material properties only lists data for trabecular bone and has shown that cortical bone holds an insignificant role [6–11]. The trabecular bone in the vertebrae was modeled to fracture upon exceeding an effective plastic strain value of 0.0061 [9]. When this strain failure parameter was exceeded, the element was deleted, indicating a fracture occurred. During the simulations, the force of the impactor on the vertebral body was recorded, and the peak force achieved during the compression test was defined as the peak fracture force.

Figure A1.

Uniaxial compression simulation setup.

Simulation results

Uniaxial compression simulations of each subject’s C3, T3, and L1 vertebrae all ran to desired completion with no error terminations (Figure A2). The trabecular bone elements that exceeded the effective plastic strain value deleted, as expected. These simulations will serve as the foundation for the completion of the larger, ongoing study. However, the astronauts’ risk for vertebral fracture cannot be accurately extracted from these simulations until the subject-specific cortical thickness and bone mineral density is incorporated in the models.

Figure A2.

Effective plastic strain during simulation run.

Appendix-B

Color maps of surface deviations between the morphed FE model vs. subject-specific geometry, and morphed, subject-specific FE mesh (in gray) for the C3, T3, and L1 vertebrae of the 5 subjects.