Estimating lumbar passive stiffness behaviour from subject-specific finite element models and in vivo 6DOF kinematics

Muscle-driven forward dynamic active hybrid model of the lumbosacral spine: combined FEM and multibody simulation

Most spine models belong to either the musculoskeletal multibody (MB) or finite element (FE) method. Recently, coupling of MB and FE models has increasingly been used to combine advantages of both methods. Active hybrid FE-MB models, still rarely used in spine research, avoid the interface and convergence problems associated with model coupling. They provide the inherent ability to account for the full interplay of passive and active mechanisms for spinal stability. In this paper, we developed and validated a novel muscle-driven forward dynamic active hybrid FE-MB model of the lumbosacral spine (LSS) in ArtiSynth to simultaneously calculate muscle activation patterns, vertebral movements, and internal mechanical loads. The model consisted of the rigid vertebrae L1-S1 interconnected with hyperelastic fiber-reinforced FE intervertebral discs, ligaments, facet joints, and force actuators representing the muscles. Morphological muscle data were implemented via a semi-automated registration procedure. Four auxiliary bodies were utilized to describe non-linear muscle paths by wrapping and attaching the anterior abdominal muscles. This included an abdominal plate whose kinematics was optimized using motion capture data from upper body movements. Intra-abdominal pressure was calculated from the forces of the abdominal muscles compressing the abdominal cavity. For the muscle-driven approach, forward dynamics assisted data tracking was used to predict muscle activation patterns that generate spinal postures and balance the spine without prescribing accurate spinal kinematics. During calibration, the maximum specific muscle tension and spinal rhythms resulting from the model dynamics were evaluated. To validate the model, load cases were simulated from -10° extension to +30° flexion with weights up to 20 kg in both hands. The biomechanical model responses were compared with in vivo literature data of intradiscal pressures, intra-abdominal pressures, and muscle activities. The results demonstrated high agreement with this data and highlight the advantages of active hybrid modeling for the LSS. Overall, this new self-contained tool provides a robust and efficient estimation of LSS biomechanical responses under in vivo similar loads, for example, to improve pain treatment by spinal stabilization therapies.

A Reference Database of Standardised Continuous Lumbar Intervertebral Motion Analysis for Conducting Patient-Specific Comparisons

Lumbar instability has long been thought of as the failure of lumbar vertebrae to maintain their normal patterns of displacement. However, it is unknown what these patterns consist of. Research using quantitative fluoroscopy (QF) has shown that continuous lumbar intervertebral patterns of rotational displacement can be reliably measured during standing flexion and return motion using standardised protocols and can be used to assess patients with suspected lumbar spine motion disorders. However, normative values are needed to make individualised comparisons. One hundred and thirty-one healthy asymptomatic participants were recruited and performed guided flexion and return motion by following the rotating arm of an upright motion frame. Fluoroscopic image acquisition at 15fps was performed and individual intervertebral levels from L2-3 to L5-S1 were tracked and analysed during separate outward flexion and return phases. Results were presented as proportional intervertebral motion representing these phases using continuous means and 95%CIs, followed by verification of the differences between levels using Statistical Parametric Mapping (SPM). A secondary analysis of 8 control participants matched to 8 patients with chronic, non-specific low back pain (CNSLBP) was performed for comparison. One hundred and twenty-seven asymptomatic participants’ data were analysed. Their ages ranged from 18 to 70 years (mean 38.6) with mean body mass index 23.8 kg/m² 48.8% were female. Both the flexion and return phases for each level evidenced continuous change in mean proportional motion share, with narrow confidence intervals, highly significant differences and discrete motion paths between levels as confirmed by SPM. Patients in the secondary analysis evidenced significantly less L5-S1 motion than controls (p < 0.05). A reference database of spinal displacement patterns during lumbar (L2-S1) intersegmental flexion and return motion using a standardised motion protocol using fluoroscopy is presented. Spinal displacement patterns in asymptomatic individuals were found to be distinctive and consistent for each intervertebral level, and to continuously change during bending and return. This database may be used to allow continuous intervertebral kinematics to drive dynamic models of joint and muscular forces as well as reference values against which to make patient-specific comparisons in suspected cases of lumbar spine motion disorders.

Influence of structural and material property uncertainties on biomechanics of intervertebral discs - Implications for disc tissue engineering

This study investigated how variations of structural and material properties of human intervertebral discs (IVDs) affect the biomechanical responses of the IVDs under simulated physiological loading conditions using a stochastic finite element (SFE) model. An SFE method, which combined an anatomic FE model of human lumbar L3-4 segment and probabilistic analysis of its structural and material properties, was used to generate a dataset of 500 random disc samples with varying structural and material properties. The sensitivity of the biomechanical responses, including intervertebral displacements/rotations, intradiscal pressures (IDP), fiber stresses and matrix strains of annulus fibrosus (AF), were systematically quantified under various physiological loading conditions, including a 500N compression and 7.5Nm moments in the 3 primary rotations. Significant variations of the IDPs, IVD displacements/rotations, and stress/strain distributions were found using the dataset of 500 ramdom disc samples. Under all the loading conditions, the IDPs were positively correlated with the Poisson's ratio of the NP (r = 0.46 to 0.75, p = 0.004-0.001) and negatively with the Young's modulus of the annulus matrix (r = -0.48 to -0.65, p = 0.003-0.001). The primary intervertebral rotations were significantly affected by the Young's modulus of the annulus matrix (r = -0.44 to -0.71, p = 0.001-0.032) and the orientations of the annular fibers (r = -0.45 to -0.69, p = 0.001-0.029). The heterogeneity of structures and material properties of the IVD had distinct effects on the biomechanical performances of the IVD. These data could help improve our understanding of the intrinsic biomechanics of the IVD and provide references for optimal design of tissue engineered discs by controlling structural and material properties of the disc components.

Prediction of biomechanical responses of human lumbar discs - a stochastic finite element model analysis

BACKGROUND

Accurate biomechanical investigation of human intervertebral discs (IVDs) is difficult because of their complicated structural and material features.

AIM

To investigate probabilistic distributions of the biomechanical responses of the IVD by considering varying nonlinear structural and material properties using a stochastic finite element (FE) model.

METHODS

A FE model of a L3-4 disc was reconstructed, including the nucleus pulposus (NP), annular matrix and fibers. A Monte Carlo method was used to randomly generate 500 sets of the nonlinear material properties and fiber orientations of the disc that were implemented into the FE model. The FE model was analyzed under seven loading conditions: a 500 N compressive force, a 7.5Nm moment simulating flexion, extension, left-right lateral bending, and left-right axial rotation, respectively. The distributions of the ranges of motion (ROMs), intradiscal pressures (IDP), fiber stresses and matrix strains of the disc were analyzed.

RESULTS

Under the compressive load, the displacement varied between 0.29 mm and 0.76 mm. Under the 7.5Nm moment, the ROMs varied between 3.0° and 6.0° in primary rotations. The IDPs varied within 0.3 MPa under all the loading conditions. The maximal fiber stress (3.22 ± 0.64 MPa) and matrix strain (0.27 ± 0.12%) were observed under the flexion and extension moments, respectively.

CONCLUSION

The IVD biomechanics could be dramatically affected by the structural and material parameters used to construct the FE model. The stochastic FE model that includes the probabilistic distributions of the structural and material parameters provides a useful approach to analyze the statistical ranges of the biomechanical responses of the IVDs.

Development of a multiscale model of the human lumbar spine for investigation of tissue loads in people with and without a transtibial amputation during sit-to-stand

Quantification of lumbar spine load transfer is important for understanding low back pain, especially among persons with a lower limb amputation. Computational modeling provides a helpful solution for obtaining estimates of in vivo loads. A multiscale model was constructed by combining musculoskeletal and finite element (FE) models of the lumbar spine to determine tissue loading during daily activities. Three-dimensional kinematic and ground reaction force data were collected from participants with ([Formula: see text]) and without ([Formula: see text]) a unilateral transtibial amputation (TTA) during 5 sit-to-stand trials. We estimated tissue-level load transfer from the multiscale model by controlling the FE model with intervertebral kinematics and muscle forces predicted by the musculoskeletal model. Annulus fibrosis stress, intradiscal pressure (IDP), and facet contact forces were calculated using the FE model. Differences in whole-body kinematics, muscle forces, and tissue-level loads were found between participant groups. Notably, participants with TTA had greater axial rotation toward their intact limb ([Formula: see text]), greater abdominal muscle activity ([Formula: see text]), and greater overall tissue loading throughout sit-to-stand ([Formula: see text]) compared to able-bodied participants. Both normalized (to upright standing) and absolute estimates of L4-L5 IDP were close to in vivo values reported in the literature. The multiscale model can be used to estimate the distribution of loads within different lumbar spine tissue structures and can be adapted for use with different activities, populations, and spinal geometries.

Investigation of Alterations in the Lumbar Disc Biomechanics at the Adjacent Segments After Spinal Fusion Using a Combined In Vivo and In Silico Approach

The development of adjacent segment degeneration (ASD) is a major concern after lumbar spinal fusion surgery, but the causative mechanisms remain unclear. This study used a combined in vivo and in silico method to investigate the changes of anatomical dimensions and biomechanical responses of the adjacent segment (L3-4) after spinal fusion (L4-S1) in five patients under weight-bearing upright standing conditions. The in vivo adjacent disc height changes before and after fusion were measured using a dual fluoroscopic imaging system (DFIS), and the measured in vivo intervertebral positions and orientations were used as displacement boundary conditions of the patient-specific three-dimensional (3D) finite element (FE) disc models to simulate the biomechanical responses of adjacent discs to fusion of the diseased segments. Our data (represented by medians and 95% confidence intervals) showed that a significant decrease by - 0.8 (- 1.2, - 0.4) mm (p < 0.05) in the adjacent disc heights occurred at the posterior region after fusion. The significant increases in disc tissue strains and stresses, 0.32 (0.21, 0.43) mm/mm (p < 0.05) and 1.70 (1.07, 3.60) MPa (p < 0.05), respectively, after fusion were found in the posterolateral portions of the outermost annular lamella. The intradiscal pressure of the adjacent disc was significantly increased by 0.29 (0.13, 0.47) MPa after fusion (p < 0.05). This study demonstrated that fusion could cause alterations in adjacent disc biomechanics, and the combined in vivo and in silico method could be a valuable tool for the quantitative assessment of ASD after fusion.