Biophysical validity of reduced soft tissue modelling in neuro-musculoskeletal simulations

Abstract

In the past decades, neuro-musculoskeletal simulations have become a key technology in biomechanical research, and are increasingly utilised to support clinical decision-making processes, evaluate occupational safety, and facilitate the design of assistive devices. The importance of precise and physiologically valid simulations cannot be emphasised enough across all application fields. However, achieving this accuracy becomes particularly challenging when developing reduced descriptions of soft tissue compartments, where the degrees of freedom and structural complexity are condensed into predominantly phenomenological or homogenised sub-models. Furthermore, it necessitates a deep understanding of the dynamic interplay among different soft tissue elements in the body, which, in turn, requires a high level of reliability and confidence in the employed underlying model. In order to ensure the usefulness of the models, it is crucial to strike a balance between the level of detail and the limitations arising from simplifications. This involves considering various possibilities to validate the mechanical behaviour of each sub-model individually and the overall model as a whole. The scientific aim of this dissertation is to investigate the load sharing of soft tissue compartments at the example of the human lumbar spine during active motions by using predictive simulations. To set the basis for this kind of research, the main objective is to create, calibrate, verify and validate a detailed neuro-musculoskeletal model, which gives rise to three research questions that guide this thesis: (1) How can (and should) common approaches for reduced single tissue models be improved to increase the level of biomechanical validity and physical verification of both the sub-models themselves, and the multibody models composed of them? (2) Which sub-structures are of biomechanical relevance for estimating internal forces and torques on a full-body scale? (3) Which validation methods need to be considered during the development of a physiological spine model, and how can the corresponding simulation results be assessed? This thesis encompasses five journal articles studies, contributing to the different aspects of the three research questions. More precisely, Contribution I addresses research questions (1) and (3) regarding how to enhance biomechanical validity of muscle routing in multibody models by introducing a novel algorithm for redirecting muscle paths. With this method, the physiological accuracy of muscle length and moment arm representations within Hill-type models can be refined, particularly for muscles spanning multiple joints with multiple degrees of freedom. Contribution II focuses on the intuitive assessment of the relative motion between two vertebral bodies. Using a newly developed method for graphical representation of finite helical axes, which fully encapsulates the information about rotation and translation of the relative motion between two vertebral bodies, extensive data sets were effectively presented through clustering methods. This work, thereby, contributes to research question (3) since the finite helical axis can serve as measure for model validation. Contribution III presents a comprehensive simulation study and introduces a detailed generic model of the human thoracolumbar spine. This generic model includes several hundred muscle and ligament strands, along with intervertebral joints modelled as free joints constrained only by intervertebral discs. Notably, the model is able to balance gravity in an upright position without additional constraints and with only a physiologically low level of muscle stimulation. The description of model development and validation significantly contributes to research question (3). Moreover, the analysis of load sharing among the three soft tissue sub-structures, namely ligaments, muscles, and intervertebral discs, revealed an almost equal distribution of bending moment during forward flexion, offering insights for research question (2). Additionally, this paper introduces a workflow for geometric individualisation of the generic model based on landmark data obtained from computed-tomography scans. The investigation of subject-specific forces and torques exhibits significant inter- and intrapersonal differences in the lumbar load distribution. These findings deepen the biomechanical understanding of complex interactions within the spine. Contribution IV explores the influence of neglecting entire passive tissue groups, precisely intervertebral discs and ligaments, which is common practice in many spine models. Using an inverse dynamic approach, this study contributes to research questions (2) and (3) by providing cross-platform validation. The examination of kinematic models that exclude ligament and intervertebral disc tissues reveals a tendency for highly overestimated muscle forces. These findings highlight the importance of considering all relevant soft tissue structures in computational models to ensure accurate muscle force estimations. Lastly, the Contribution V directly addresses research question (1) by tackling the challenge of incorporating energy conservation in surrogate models representing the elastic mechanical responses of intervertebral discs. It introduces a novel approach that surpasses currently used elastic models in terms of precision, coupling of different degrees of freedom, and nonlinear behaviour. This advancement increases the accuracy and physical validity while also enabling the individualisation of the mechanical behaviour of subject- and level-specific intervertebral disc geometry. In order to achieve the aforementioned aims and answer the research questions, a multibody simulation framework has been extended by the novel algorithms developed within the scope of this thesis. These algorithms improve the geometric quality of soft tissue representations and refine accuracy of predicted internal forces and torques while preserving basic physical principles. Furthermore, a pre-processor typically used to scale population-based models has been modified to serve two additional purposes. On the one hand, the existing code was advanced to create geometrically individualised models based on landmark positions derived from computed-tomography scans. On the other hand, the functionality to generate models compatible with another widely used multibody simulation tool was included. Having identical models facilitates cross-platform validation, and allows to test muscle, ligament and intervertebral disc sub-models, and whole thoracolumbar spine models in different scenarios. In summary, this thesis enhances existing methods and provides new approaches to create more accurate neuro-musculoskeletal models capable of predicting internal forces and kinematics. The detailed spine model developed during this thesis serves as a valuable foundation for future investigations, including subject-specific, non-invasive implant testing, and exploration of the rotation axes in complex movements and post-surgical scenarios.