Lumbar model generator: a tool for the automated generation of a parametric scalable model of the lumbar spine

Abstract

Low back pain is a major cause of disability and requires the development of new devices to treat pathologies and improve prognosis following surgery. Understanding the effects of new devices on the biomechanics of the spine is crucial in the development of new effective and functional devices. The aim of this study was to develop a preliminary parametric, scalable and anatomically accurate finite-element model of the lumbar spine allowing for the evaluation of the performance of spinal devices. The principal anatomical surfaces of the lumbar spine were first identified, and then accurately fitted from a previous model supplied by S14 Implants (Bordeaux, France). Finally, the reconstructed model was defined according to 17 parameters which are used to scale the model according to patient dimensions. The developed model, available as a toolbox named the lumbar model generator, enables generating a population of models using subject-specific dimensions obtained from data scans or averaged dimensions evaluated from the correlation analysis. This toolbox allows patient-specific assessment, taking into account individual morphological variation. The models have applications in the design process of new devices, evaluating the biomechanics of the spine and helping clinicians when deciding on treatment strategies.

Keywords: biomechanics; finite-element analysis; lumbar spine; morphing; parametric model; spine.

Figure 1.

Workflow of the lumbar model generator (LMG), from the generation of the geometrical model to the solution of the FE simulation. The FE model is shown for the purpose of description and will be described in details in a future publication. (a) The inputs of the LMG are the baseline model previously generated and the dimensions, measured on subject-specific scans or average dimensions based on the height, age and gender of a patient. (b) Parametrization of the geometrical model. The anatomical dimensions have been identified in each region of the vertebrae and IVD and then independently scaled. Accordingly with the input, the output of this step can be a population of geometrical models or a subject-specific model. (c) Generation of a triangulated surface model and output of STL files. (d) Solid meshing of the vertebrae (tetrahedral elements) and the IVD (hexahedral elements). The output of this step can be exported to commercial software. (e) Pre-processing of the meshed model, defining the material properties, boundary conditions, contact properties and then run the simulations in FEBio.

Figure 2.

The picture shows the input requested in the toolbox, in the first and simplest case only body height, age and gender are requested. In the second case, the dimensions identified have to be added as input.

Figure 3.

Lumbar spine model (a) lateral, (b) anteriorposterior views generated from subject-specific measurements obtained from the VHP and listed in tables 5 and 6. (Online version in colour.)

Figure 4.

The vertebral body was divided into cancellous and cortical bone. The thickness of the cortical bone can be defined by the user in the toolbox.

Figure 5.

IVD mesh. (a) Representation of the surface, meshed by quadrangular elements, where in the AF they follow the external perimeter, arranged in nl layers. (b) Division between NP and AF, and the volumetric ratio (VP) is an input of the toolbox. (c) The number of elements nz can be defined to obtain a finer mesh.

Figure 6.

Accuracy evaluation. Qualitative evaluation of the accuracy between the VHP model in black and the generated model in orange. (a) IVD, (b) vertebrae and (c) quantitative evaluation of the accuracy through the RMS error values for the vertebrae.

Figure 7.

Accuracy on the whole model. The VH model (black) has been overlapped on the model generated (orange), using the best fit registration in Cloudcompare. Owing to the supine position of the cadaveric specimen, the lumbar curvature is lost in the VH model.

Figure 8.

Accuracy on the whole model. The VH model (black) has been overlapped on the model generated (orange), using the best fit registration in Cloudcompare. Owing to the supine position of the cadaveric specimen, the lumbar curvature is lost in the VH model.

Figure 9.

QQ-plots between (a) the L1 vertebrae and the other vertebrae at mesh size of 1.6 mm (b) and between the geometrical model based on a person 1.75 m height and those ones at 1.80 m and 1.82 m. The three different criteria are shown: (i) aspect ratio, (ii) face angle and (iii) dihedral angle. (Online version in colour.)

Figure 10.

Qualitative analyses of the dihedral angles for the tetrahedral elements of the vertebral bodies. The minimum (a) and maximum (b) dihedral angles are shown and the colourmaps refer to the histograms below. The figure shows the unloaded geometry of the spine, in a non-physiological status, where the bodies were only placed in their locations and no loads are applied.