Effects of geometric individualisation of a human spine model on load sharing: neuro-musculoskeletal simulation reveals significant differences in ligament and muscle contribution

Musculoskeletal spine modeling in large patient cohorts: how morphological individualization affects lumbar load estimation

Introduction: Achieving an adequate level of detail is a crucial part of any modeling process. Thus, oversimplification of complex systems can lead to overestimation, underestimation, and general bias of effects, while elaborate models run the risk of losing validity due to the uncontrolled interaction of multiple influencing factors and error propagation. Methods: We used a validated pipeline for the automated generation of multi-body models of the trunk to create 279 models based on CT data from 93 patients to investigate how different degrees of individualization affect the observed effects of different morphological characteristics on lumbar loads. Specifically, individual parameters related to spinal morphology (thoracic kyphosis (TK), lumbar lordosis (LL), and torso height (TH)), as well as torso weight (TW) and distribution, were fully or partly considered in the respective models according to their degree of individualization, and the effect strengths of these parameters on spinal loading were compared between semi- and highly individualized models. T-distributed stochastic neighbor embedding (T-SNE) analysis was performed for overarching pattern recognition and multiple regression analyses to evaluate changes in occurring effects and significance. Results: We were able to identify significant effects (p < 0.05) of various morphological parameters on lumbar loads in models with different degrees of individualization. Torso weight and lumbar lordosis showed the strongest effects on compression (β ≈ 0.9) and anterior-posterior shear forces (β ≈ 0.7), respectively. We could further show that the effect strength of individual parameters tended to decrease if more individual characteristics were included in the models. Discussion: The induced variability due to model individualization could only partly be explained by simple morphological parameters. Our study shows that model simplification can lead to an emphasis on individual effects, which needs to be critically assessed with regard to in vivo complexity. At the same time, we demonstrated that individualized models representing a population-based cohort are still able to identify relevant influences on spinal loading while considering a variety of influencing factors and their interactions.

A new method to design energy-conserving surrogate models for the coupled, nonlinear responses of intervertebral discs

The aim of this study was to design physics-preserving and precise surrogate models of the nonlinear elastic behaviour of an intervertebral disc (IVD). Based on artificial force-displacement data sets from detailed finite element (FE) disc models, we used greedy kernel and polynomial approximations of second, third and fourth order to train surrogate models for the scalar force-torque -potential. Doing so, the resulting models of the elastic IVD responses ensured the conservation of mechanical energy through their structure. At the same time, they were capable of predicting disc forces in a physiological range of motion and for the coupling of all six degrees of freedom of an intervertebral joint. The performance of all surrogate models for a subject-specific L4 | 5 disc geometry was evaluated both on training and test data obtained from uncoupled (one-dimensional), weakly coupled (two-dimensional), and random movement trajectories in the entire six-dimensional (6d) physiological displacement range, as well as on synthetic kinematic data. We observed highest precisions for the kernel surrogate followed by the fourth-order polynomial model. Both clearly outperformed the second-order polynomial model which is equivalent to the commonly used stiffness matrix in neuro-musculoskeletal simulations. Hence, the proposed model architectures have the potential to improve the accuracy and, therewith, validity of load predictions in neuro-musculoskeletal spine models.

Invasiveness of decompression surgery affects modeled lumbar spine kinetics in patients with degenerative spondylolisthesis

Introduction: The surgical treatment of degenerative spondylolisthesis with accompanying spinal stenosis focuses mainly on decompression of the spinal canal with or without additional fusion by means of a dorsal spondylodesis. Currently, one main decision criterion for additional fusion is the presence of instability in flexion and extension X-rays. In cases of mild and stable spondylolisthesis, the optimal treatment remains a subject of ongoing debate. There exist different opinions on whether performing a fusion directly together with decompression has a potential benefit for patients or constitutes overtreatment. As X-ray images do not provide any information about internal biomechanical forces, computer simulation of individual patients might be a tool to gain a set of new decision criteria for those cases. Methods: To evaluate the biomechanical effects resulting from different decompression techniques, we developed a lumbar spine model using forward dynamic-based multibody simulation (FD_MBS). Preoperative CT data of 15 patients with degenerative spondylolisthesis at the level L4/L5 who underwent spinal decompression were identified retrospectively. Based on the segmented vertebrae, 15 individualized models were built. To establish a reference for comparison, we simulated a standardized flexion movement (intact) for each model. Subsequently, we performed virtual unilateral and bilateral interlaminar fenestration (uILF, bILF) and laminectomy (LAM) by removing the respective ligaments in each model. Afterward, the standardized flexion movement was simulated again for each case and decompression method, allowing us to compare the outcomes with the reference. This comprehensive approach enables us to assess the biomechanical implications of different surgical approaches and gain valuable insights into their effects on lumbar spine functionality. Results: Our findings reveal significant changes in the biomechanics of vertebrae and intervertebral discs (IVDs) as a result of different decompression techniques. As the invasiveness of decompression increases, the moment transmitted on the vertebrae significantly rises, following the sequence intact ➝ uILF ➝ bILF ➝ LAM. Conversely, we observed a reduction in anterior-posterior shear forces within the IVDs at the levels L3/L4 and L4/L5 following LAM. Conclusion: Our findings showed that it was feasible to forecast lumbar spine kinematics after three distinct decompression methods, which might be helpful in future clinical applications.

A physiologically enhanced muscle spindle model: using a Hill-type model for extrafusal fibers as template for intrafusal fibers

The muscle spindle is an essential proprioceptor, significantly involved in sensing limb position and movement. Although biological spindle models exist for years, the gold-standard for motor control in biomechanics are still sensors built of homogenized spindle output models due to their simpler combination with neuro-musculoskeletal models. Aiming to improve biomechanical simulations, this work establishes a more physiological model of the muscle spindle, aligned to the advantage of easy integration into large-scale musculoskeletal models. We implemented four variations of a spindle model in Matlab/Simulink®: the Mileusnic et al. (2006) model, Mileusnic model without mass, our enhanced Hill-type model, and our enhanced Hill-type model with parallel damping element (PDE). Different stretches in the intrafusal fibers were simulated in all model variations following the spindle afferent recorded in previous experiments in feline soleus muscle. Additionally, the enhanced Hill-type models had their parameters extensively optimized to match the experimental conditions, and the resulting model was validated against data from rats' triceps surae muscle. As result, the Mileusnic models present a better overall performance generating the afferent firings compared to the common data evaluated. However, the enhanced Hill-type model with PDE exhibits a more stable performance than the original Mileusnic model, at the same time that presents a well-tuned Hill-type model as muscle spindle fibers, and also accounts for real sarcomere force-length and force-velocity aspects. Finally, our activation dynamics is similar to the one applied to Hill-type model for extrafusal fibers, making our proposed model more easily integrated in multi-body simulations.

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.

Effect of neglecting passive spinal structures: a quantitative investigation using the forward-dynamics and inverse-dynamics musculoskeletal approach

Purpose: Inverse-dynamics (ID) analysis is an approach widely used for studying spine biomechanics and the estimation of muscle forces. Despite the increasing structural complexity of spine models, ID analysis results substantially rely on accurate kinematic data that most of the current technologies are not capable to provide. For this reason, the model complexity is drastically reduced by assuming three degrees of freedom spherical joints and generic kinematic coupling constraints. Moreover, the majority of current ID spine models neglect the contribution of passive structures. The aim of this ID analysis study was to determine the impact of modelled passive structures (i.e., ligaments and intervertebral discs) on remaining joint forces and torques that muscles must balance in the functional spinal unit. Methods: For this purpose, an existing generic spine model developed for the use in the demoa software environment was transferred into the musculoskeletal modelling platform OpenSim. The thoracolumbar spine model previously used in forward-dynamics (FD) simulations provided a full kinematic description of a flexion-extension movement. By using the obtained in silico kinematics, ID analysis was performed. The individual contribution of passive elements to the generalised net joint forces and torques was evaluated in a step-wise approach increasing the model complexity by adding individual biological structures of the spine. Results: The implementation of intervertebral discs and ligaments has significantly reduced compressive loading and anterior torque that is attributed to the acting net muscle forces by -200% and -75%, respectively. The ID model kinematics and kinetics were cross-validated against the FD simulation results. Conclusion: This study clearly shows the importance of incorporating passive spinal structures on the accurate computation of remaining joint loads. Furthermore, for the first time, a generic spine model was used and cross-validated in two different musculoskeletal modelling platforms, i.e., demoa and OpenSim, respectively. In future, a comparison of neuromuscular control strategies for spinal movement can be investigated using both approaches.