Calibration of the finite element model of a lumbar functional spinal unit using an optimization technique based on differential evolution

Instantaneous Generation of Subject-Specific Finite Element Models of the Hip Capsule

Subject-specific hip capsule models could offer insights into impingement and dislocation risk when coupled with computer-aided surgery, but model calibration is time-consuming using traditional techniques. This study developed a framework for instantaneously generating subject-specific finite element (FE) capsule representations from regression models trained with a probabilistic approach. A validated FE model of the implanted hip capsule was evaluated probabilistically to generate a training dataset relating capsule geometry and material properties to hip laxity. Multivariate regression models were trained using 90% of trials to predict capsule properties based on hip laxity and attachment site information. The regression models were validated using the remaining 10% of the training set by comparing differences in hip laxity between the original trials and the regression-derived capsules. Root mean square errors (RMSEs) in laxity predictions ranged from 1.8° to 2.3°, depending on the type of laxity used in the training set. The RMSE, when predicting the laxity measured from five cadaveric specimens with total hip arthroplasty, was 4.5°. Model generation time was reduced from days to milliseconds. The results demonstrated the potential of regression-based training to instantaneously generate subject-specific FE models and have implications for integrating subject-specific capsule models into surgical planning software.

Biomechanical modelling of the facet joints: a review of methods and validation processes in finite element analysis

There is an increased interest in studying the biomechanics of the facet joints. For in silico studies, it is therefore important to understand the level of reliability of models for outputs of interest related to the facet joints. In this work, a systematic review of finite element models of multi-level spinal section with facet joints output of interest was performed. The review focused on the methodology used to model the facet joints and its associated validation. From the 110 papers analysed, 18 presented some validation of the facet joints outputs. Validation was done by comparing outputs to literature data, either computational or experimental values; with the major drawback that, when comparing to computational values, the baseline data was rarely validated. Analysis of the modelling methodology showed that there seems to be a compromise made between accuracy of the geometry and nonlinearity of the cartilage behaviour in compression. Most models either used a soft contact representation of the cartilage layer at the joint or included a cartilage layer which was linear elastic. Most concerning, soft contact models usually did not contain much information on the pressure-overclosure law. This review shows that to increase the reliability of in silico model of the spine for facet joints outputs, more needs to be done regarding the description of the methods used to model the facet joints, and the validation for specific outputs of interest needs to be more thorough, with recommendation to systematically share input and output data of validation studies.

Minimally invasive transforaminal and anterior lumbar interbody fusion surgery at level L5-S1

This paper presents a finite element analysis to investigate the biomechanical changes caused by transforaminal (TLIF) and anterior lumbar interbody fusion (ALIF) at the L5-S1 level, applying two different implants: T_PAL (TLIF) and SynFix (ALIF). The main objective is to determine which one is more stable for patients. Numerical simulations of segmental motion show that, in the early postoperative phase, displacements and rotation angles obtained in ALIF are greater than the corresponding ones obtained in TLIF, as well as the principal stress values on the ligaments. So, TLIF performed with T_PAL is more stable than ALIF, especially during the recovery phase.

Lumbar spinal ligament characteristics extracted from stepwise reduction experiments allow for preciser modeling than literature data

Lumbar ligaments play a key role in stabilizing the spine, particularly assisting muscles at wide-range movements. Hence, valid ligament force–strain data are required to generate physiological model predictions. These data have been obtained by experiments on single ligaments or functional units throughout the literature. However, contrary to detailed spine geometries, gained, for instance, from CT data, ligament characteristics are often inattentively transferred to multi-body system (MBS) or finite element models. In this paper, we use an elaborated MBS model of the lumbar spine to demonstrate how individualized ligament characteristics can be obtained by reversely reenacting stepwise reduction experiments, where the range of motion (ROM) was measured. We additionally validated the extracted characteristics with physiological experiments on intradiscal pressure (IDP). Our results on a total of in each case 160 ROM and 49 IDP simulations indicated superiority of our procedure (seven and eight outliers) toward the incorporation of classical literature data (on average 71 and 31 outliers).

Improving the Process of Adjusting the Parameters of Finite Element Models of Healthy Human Intervertebral Discs by the Multi-Response Surface Method

The kinematic behavior of models that are based on the finite element method (FEM) for modeling the human body depends greatly on an accurate estimate of the parameters that define such models. This task is complex, and any small difference between the actual biomaterial model and the simulation model based on FEM can be amplified enormously in the presence of nonlinearities. The current paper attempts to demonstrate how a combination of the FEM and the MRS methods with desirability functions can be used to obtain the material parameters that are most appropriate for use in defining the behavior of Finite Element (FE) models of the healthy human lumbar intervertebral disc (IVD). The FE model parameters were adjusted on the basis of experimental data from selected standard tests (compression, flexion, extension, shear, lateral bending, and torsion) and were developed as follows: First, three-dimensional parameterized FE models were generated on the basis of the mentioned standard tests. Then, 11 parameters were selected to define the proposed parameterized FE models. For each of the standard tests, regression models were generated using MRS to model the six stiffness and nine bulges of the healthy IVD models that were created by changing the parameters of the FE models. The optimal combination of the 11 parameters was based on three different adjustment criteria. The latter, in turn, were based on the combination of stiffness and bulges that were obtained from the standard test FE simulations. The first adjustment criteria considered stiffness and bulges to be equally important in the adjustment of FE model parameters. The second adjustment criteria considered stiffness as most important, whereas the third considered the bulges to be most important. The proposed adjustment methods were applied to a medium-sized human IVD that corresponded to the L3–L4 lumbar level with standard dimensions of width = 50 mm, depth = 35 mm, and height = 10 mm. Agreement between the kinematic behavior that was obtained with the optimized parameters and that obtained from the literature demonstrated that the proposed method is a powerful tool with which to adjust healthy IVD FE models when there are many parameters, stiffnesses, and bulges to which the models must adjust.

Anisotropic Multishell Analytical Modeling of an Intervertebral Disk Subjected to Axial Compression

Studies on intervertebral disk (IVD) response to various loads and postures are essential to understand disk's mechanical functions and to suggest preventive and corrective actions in the workplace. The experimental and finite-element (FE) approaches are well-suited for these studies, but validating their findings is difficult, partly due to the lack of alternative methods. Analytical modeling could allow methodological triangulation and help validation of FE models. This paper presents an analytical method based on thin-shell, beam-on-elastic-foundation and composite materials theories to evaluate the stresses in the anulus fibrosus (AF) of an axisymmetric disk composed of multiple thin lamellae. Large deformations of the soft tissues are accounted for using an iterative method and the anisotropic material properties are derived from a published biaxial experiment. The results are compared to those obtained by FE modeling. The results demonstrate the capability of the analytical model to evaluate the stresses at any location of the simplified AF. It also demonstrates that anisotropy reduces stresses in the lamellae. This novel model is a preliminary step in developing valuable analytical models of IVDs, and represents a distinctive groundwork that is able to sustain future refinements. This paper suggests important features that may be included to improve model realism.

Specimen specific parameter identification of ovine lumbar intervertebral discs: On the influence of fibre-matrix and fibre-fibre shear interactions

Numerical models of the intervertebral disc, which address mechanical questions commonly make use of the difference in water content between annulus and nucleus, and thus fluid and solid parts are separated. Despite this simplification, models remain complex due to the anisotropy and nonlinearity of the annulus and regional variations of the collagen fibre density. Additionally, it has been shown that cross-links make a large contribution to the stiffness of the annulus. Because of this complex composite structure, it is difficult to reproduce several sets of experimental data with one single set of material parameters. This study addresses the question to which extent the ultrastructure of the intervertebral disc should be modelled so that its moment-angle behaviour can be adequately described. Therefore, a hyperelastic constitutive law, based on continuum mechanical principles was derived, which does not only consider the anisotropy from the collagen fibres, but also interactions among the fibres and between the fibres and the ground substance. Eight ovine lumbar intervertebral discs were tested on a custom made spinal loading simulator in flexion/extension, lateral bending and axial rotation. Specimen-specific geometrical models were generated using CT images and T2 maps to distinguish between annulus fibrosus and nucleus pulposus. For the identification of the material parameters the annulus fibrosus was described with two scenarios: with and without fibre-matrix and fibre-fibre interactions. Both scenarios showed a similar behaviour on a load displacement level. Comparing model predictions to the experimental data, the mean RMS of all specimens and all load cases was 0.54±0.15° without the interaction and 0.54±0.19° when the fibre-matrix and fibre-fibre interactions were included. However, due to the increased stiffness when cross-links effects were included, this scenario showed more physiological stress-strain relations in uniaxial and biaxial stress states. Thus, the present study suggests that fibre-matrix and fibre-fibre interactions should be considered in the constitutive law when the model addresses questions concerning the stress field of the annulus fibrosus.