How back pain is related to intervertebral disc degeneration, spinal loading or sports-related overuse remains an unanswered question of biomechanics. Coupled MBS and FEM simulations can provide a holistic view of the spine by considering both the overall kinematics and kinetics of the spine and the inner stress distribution of flexible components. We reviewed studies that included MBS and FEM co-simulations of the spine. Thereby, we classified the studies into unidirectional and bidirectional co-simulation, according to their data exchange methods. Several studies have demonstrated that using unidirectional co-simulation models provides useful insights into spinal biomechanics, although synchronizing the two distinct models remains a key challenge, often requiring extensive manual intervention. The use of a bidirectional co-simulation features an iterative, automated process with a constant data exchange between integrated subsystems. It reduces manual corrections of vertebra positions or reaction forces and enables detailed modeling of dynamic load cases. Bidirectional co-simulations are thus a promising new research approach for improved spine modeling, as a main challenge in spinal biomechanics is the nonlinear deformation of the intervertebral discs. Future studies will likely include the automated implementation of patient-specific bidirectional co-simulation models using hyper- or poroelastic intervertebral disc FEM models and muscle forces examined by an optimization algorithm in MBS. Applications range from clinical diagnosis to biomechanical analysis of overload situations in sports and injury prediction.

Numerical models of the musculoskeletal system as investigative tools are an integral part of biomechanical and clinical research. While finite element modeling is primarily suitable for the examination of deformation states and internal stresses in flexible bodies, multibody modeling is based on the assumption of rigid bodies, that are connected via joints and flexible elements. This simplification allows the consideration of biomechanical systems from a holistic perspective and thus takes into account multiple influencing factors of mechanical loads. Being the source of major health issues worldwide, the human spine is subject to a variety of studies using these models to investigate and understand healthy and pathological biomechanics of the upper body. In this review, we summarize the current state-of-the-art literature on multibody models of the thoracolumbar spine and identify limitations and challenges related to current modeling approaches.

Introduction: Biomechanical simulations can enhance our understanding of spinal disorders. Applied to large cohorts, they can reveal complex mechanisms beyond conventional imaging. Therefore, automating the patient-specific modeling process is essential.Methods: We developed an automated and robust pipeline that generates and simulates biofidelic vertebrae and intervertebral disc finite element method (FEM) models based on automated magnetic resonance imaging (MRI) segmentations. In a first step, anatomically-constrained smoothing approaches were implemented to ensure seamless contact surfaces between vertebrae and discs with shared nodes. Subsequently, surface meshes were filled isotropically with tetrahedral elements. Lastly, simulations were executed. The performance of our pipeline was evaluated using a set of 30 patients from an in-house dataset that comprised an overall of 637 vertebrae and 600 intervertebral discs. We rated mesh quality metrics and processing times.Results: With an average number of 21 vertebrae and 20 IVDs per subject, the average processing time was 4.4 min for a vertebra and 31 s for an IVD. The average percentage of poor quality elements stayed below 2% in all generated FEM models, measured by their aspect ratio. Ten vertebra and seven IVD FE simulations failed to converge.Discussion: The main goal of our work was to automate the modeling and FEM simulation of both patient-specific vertebrae and intervertebral discs with shared-node surfaces directly from MRI segmentations. The biofidelity, robustness and time-efficacy of our pipeline marks an important step towards investigating large patient cohorts for statistically relevant, biomechanical insight.

Accurate calibration of finite element (FE) models is essential across various biomechanical applications, including human intervertebral discs (IVDs), to ensure their reliability and use in diagnosing and planning treatments. However, traditional calibration methods are computationally intensive, requiring iterative, derivative-free optimization algorithms that often take days to converge. This study addresses these challenges by introducing a novel, efficient, and effective calibration method demonstrated on a human L4-L5 IVD FE model as a case study using a neural network (NN) surrogate. The NN surrogate predicts simulation outcomes with high accuracy, outperforming other machine learning models, and significantly reduces the computational cost associated with traditional FE simulations. Next, a Projected Gradient Descent (PGD) approach guided by gradients of the NN surrogate is proposed to efficiently calibrate FE models. Our method explicitly enforces feasibility with a projection step, thus maintaining material bounds throughout the optimization process. The proposed method is evaluated against state-of-the-art Genetic Algorithm (GA) and inverse model baselines on synthetic and in vitro experimental datasets. Our approach demonstrates superior performance on synthetic data, achieving a Mean Absolute Error (MAE) of 0.06 compared to the baselines' MAE of 0.18 and 0.54, respectively. On experimental specimens, our method outperforms the baseline in 5 out of 6 cases. While our approach requires initial dataset generation and surrogate training, these steps are performed only once, and the actual calibration takes under three seconds. In contrast, traditional calibration time scales linearly with the number of specimens, taking up to 8 days in the worst-case. Such efficiency paves the way for applying more complex FE models, potentially extending beyond IVDs, and enabling accurate patient-specific simulations.

The finite element (FE) method is a cornerstone of patient-specific biomechanical analysis, yet most workflows assign isotropic linear elastic behaviour, and neglect bone’s intrinsic anisotropic and non-linear response to load. We present PBMGA (Python-based Bone material grouping and anisotropy), a novel open-source tool that automates the calculation and element-specific assignment of non-linear and transversely isotropic (and, in principle, more general anisotropic) bone material parameters using user-defined equations. PBMGA integrates three customisable material grouping strategies: Percentual Thresholding, Adaptive Clustering, and Equidistant Grouping, to compress the number of unique material sets, significantly reducing computational complexity in downstream FE simulations without compromising accuracy. Its modular architecture supports seamless integration with existing preprocessing workflows and scalable analysis of large clinical datasets. By combining accurate material modelling with high‐throughput capability, PBMGA enhances biomechanical prediction and paves the way for more efficient clinical diagnostics and treatment planning.