Musculoskeletal full-body models including a detailed thoracolumbar spine for children and adolescents aged 6-18 years

ArborSim: Articulated, branching, OpenSim routing for constructing models of multi-jointed appendages with complex muscle-tendon architecture

Computational models of musculoskeletal systems are essential tools for understanding how muscles, tendons, bones, and actuation signals generate motion. In particular, the OpenSim family of models has facilitated a wide range of studies on diverse human motions, clinical studies of gait, and even non-human locomotion. However, biological structures with many joints, such as fingers, necks, tails, and spines, have been a longstanding challenge to the OpenSim modeling community, especially because these structures comprise numerous bones and are frequently actuated by extrinsic muscles that span multiple joints-often more than three-and act through a complex network of branching tendons. Existing model building software, typically optimized for limb structures, makes it difficult to build OpenSim models that accurately reflect these intricacies. Here, we introduce ArborSim, customized software that efficiently creates musculoskeletal models of highly jointed structures and can build branched muscle-tendon architectures. We used ArborSim to construct toy models of articulated structures to determine which morphological features make a structure most sensitive to branching. By comparing the joint kinematics of models constructed with branched and parallel muscle-tendon units, we found that among various parameters-the number of tendon branches, the number of joints between branches, and the ratio of muscle fiber length to muscle tendon unit length-the number of tendon branches and the number of joints between branches are most sensitive to branching modeling method. Notably, the differences between these models showed no predictable pattern with increased complexity. As the proportion of muscle increased, the kinematic differences between branched and parallel models units also increased. Our findings suggest that stress and strain interactions between distal tendon branches and proximal tendon and muscle greatly affect the overall kinematics of a musculoskeletal system. By incorporating complex muscle-tendon branching into OpenSim models using ArborSim, we can gain deeper insight into the interactions between the axial and appendicular skeleton, model the evolution and function of diverse animal tails, and understand the mechanics of more complex motions and tasks.

Predicted vs. measured paraspinal muscle activity in adolescent idiopathic scoliosis patients: EMG validation of optimization-based musculoskeletal simulations

Musculoskeletal (MSK) models offer great potential for predicting the muscle forces required to inform more detailed simulations of vertebral endplate loading in adolescent idiopathic scoliosis (AIS). In this work, simulations based on static optimization were compared with in vivo measurements in two AIS patients to determine whether computational approaches alone are sufficient for accurate prediction of paraspinal muscle activity during functional activities. We used biplanar radiographs and marker-based motion capture, ground reaction force, and electromyography (EMG) data from two patients with mild and moderate thoracolumbar AIS (Cobb angles: 21° and 45°, respectively) during standing while holding two weights in front (reference position), walking, running, and object lifting. Using a fully automated approach, 3D spinal shape was extracted from the radiographs. Geometrically personalized OpenSim-based MSK models were created by deforming the spine of pre-scaled full-body models of children/adolescents. Simulations were performed using an experimentally controlled backward approach. Differences between model predictions and EMG measurements of paraspinal muscle activity (both expressed as a percentage of the reference position values) at three different locations around the scoliotic main curve were quantified by root mean square error (RMSE) and cross-correlation (XCorr). Predicted and measured muscle activity correlated best for mild AIS during object lifting (XCorr's ≥ 0.97), with relatively low RMSE values. For moderate AIS as well as the walking and running activities, agreement was lower, with XCorr reaching values of 0.51 and comparably high RMSE values. This study demonstrates that static optimization alone seems not appropriate for predicting muscle activity in AIS patients, particularly in those with more than mild deformations as well as when performing upright activities such as walking and running.

Dependence of trunk muscle size and position on age, height, and weight in a multi-ethnic cohort of middle-aged and older men and women

Trunk muscle size and location relative to the spine are key factors affecting their capacity to assist in trunk movement, strength, and function. There remains limited information on how age, weight and height affect these measurements across multiple spinal levels, and prior studies had limited samples in terms of size and ethnicity. In this study, we measured trunk muscles in coronal plane slices at T4 - L4 of CT scans acquired in 507 participants, aged 40-90 years, from the community-based Framingham Heart Study. Mixed-effects linear regressions, stratified by sex, determined the contributions of age, height and weight, to muscle cross-sectional area (CSA), the distance from the vertebral body centroid (CD), and the in-plane angle of the line between the vertebral body and the muscle centroids (CA). Muscle CSA decreased with higher age by an average of -0.8% per year, but weight (average 0.8% per kg) and height (average -0.05% per cm) had mixed results, with both positive and negative effects depending on muscle group and level. Muscle CD increased with weight by an average of 0.3% per kg, but had mixed effects for age (average 0.8% per year) and height (average 0.1% per cm). Muscle CA had mixed associations with age (average 0.05% per year), weight (average 0.01% per kg) and height (average -0.05% per cm). A prediction program created with these results provides a simple approach for estimating probable values for trunk muscle size and position in the absence of medical imaging.

Musculotendon Parameters in Lower Limb Models: Simplifications, Uncertainties, and Muscle Force Estimation Sensitivity

Musculotendon parameters are key factors in the Hill-type muscle contraction dynamics, determining the muscle force estimation accuracy of a musculoskeletal model. Their values are mostly derived from muscle architecture datasets, whose emergence has been a major impetus for model development. However, it is often not clear if such parameter update indeed improves simulation accuracy. Our goal is to explain to model users how these parameters are derived and how accurate they are, as well as to what extent errors in parameter values might influence force estimation. We examine in detail the derivation of musculotendon parameters in six muscle architecture datasets and four prominent OpenSim models of the lower limb, and then identify simplifications which could add uncertainties to the derived parameter values. Finally, we analyze the sensitivity of muscle force estimation to these parameters both numerically and analytically. Nine typical simplifications in parameter derivation are identified. Partial derivatives of the Hill-type contraction dynamics are derived. Tendon slack length is determined as the musculotendon parameter that muscle force estimation is most sensitive to, whereas pennation angle is the least impactful. Anatomical measurements alone are not enough to calibrate musculotendon parameters, and the improvement on muscle force estimation accuracy will be limited if the source muscle architecture datasets are the only main update. Model users may check if a dataset or model is free of concerning factors for their research or application requirements. The derived partial derivatives may be used as the gradient for musculotendon parameter calibration. For model development, we demonstrate that it is more promising to focus on other model parameters or components and seek alternative strategies to further increase simulation accuracy.

Multibody Models of the Thoracolumbar Spine: A Review on Applications, Limitations, and Challenges

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.

Evaluation of spinal force normalization techniques

Division normalization is commonly used in biomechanics studies to remove the effect of anthropometric differences (e.g., body weight) on kinetic variables, facilitating comparison across a population. In spine biomechanics, spinal forces are commonly divided by the body weight or the intervertebral load during a standing posture. However, it has been suggested that offset and power curve normalization are more appropriate than division normalization for normalizing kinetic variables such as ground reaction forces during walking and running. The present study investigated, for the first time, the effectiveness of four techniques for normalizing spinal forces to remove the effect of body weight. Spinal forces at all lumbar levels were estimated using a detailed OpenSim musculoskeletal model of the spine for 11 scaled models (50-100 kg) and during 13 trunk flexion tasks. Pearson correlations of raw and normalized forces against body weight were used to assess the effectiveness of each normalization technique. Body weight and standing division normalization could only successfully normalize L₄L₅ spinal forces in three tasks, and L₅S₁ loads in five and three tasks, respectively; however, offset and power curve normalization techniques were successful across all lumbar spine levels and all tasks. Offset normalization successfully removed the effect of body weight and maintained the influence of flexion angle on spinal forces. Thus, we recommend offset normalization to account for anthropometric differences in studies of spinal forces.

A computational method for estimating trunk muscle activations during gait using lower extremity muscle synergies

One of the surgical treatments for pelvic sarcoma is the restoration of hip function with a custom pelvic prosthesis after cancerous tumor removal. The orthopedic oncologist and orthopedic implant company must make numerous often subjective decisions regarding the design of the pelvic surgery and custom pelvic prosthesis. Using personalized musculoskeletal computer models to predict post-surgery walking function and custom pelvic prosthesis loading is an emerging method for making surgical and custom prosthesis design decisions in a more objective manner. Such predictions would necessitate the estimation of forces generated by muscles spanning the lower trunk and all joints of the lower extremities. However, estimating trunk and leg muscle forces simultaneously during walking based on electromyography (EMG) data remains challenging due to the limited number of EMG channels typically used for measurement of leg muscle activity. This study developed a computational method for estimating unmeasured trunk muscle activations during walking using lower extremity muscle synergies. To facilitate the calibration of an EMG-driven model and the estimation of leg muscle activations, EMG data were collected from each leg. Using non-negative matrix factorization, muscle synergies were extracted from activations of leg muscles. On the basis of previous studies, it was hypothesized that the time-varying synergy activations were shared between the trunk and leg muscles. The synergy weights required to reconstruct the trunk muscle activations were determined through optimization. The accuracy of the synergy-based method was dependent on the number of synergies and optimization formulation. With seven synergies and an increased level of activation minimization, the estimated activations of the erector spinae were strongly correlated with their measured activity. This study created a custom full-body model by combining two existing musculoskeletal models. The model was further modified and heavily personalized to represent various aspects of the pelvic sarcoma patient, all of which contributed to the estimation of trunk muscle activations. This proposed method can facilitate the prediction of post-surgery walking function and pelvic prosthesis loading, as well as provide objective evaluations for surgical and prosthesis design decisions.

Biomechanical Morphing for Personalized Fitting of Scoliotic Torso Skeleton Models

The use of patient-specific biomechanical models offers many opportunities in the treatment of adolescent idiopathic scoliosis, such as the design of personalized braces. The first step in the development of these patient-specific models is to fit the geometry of the torso skeleton to the patient’s anatomy. However, existing methods rely on high-quality imaging data. The exposure to radiation of these methods limits their applicability for regular monitoring of patients. We present a method to fit personalized models of the torso skeleton that takes as input biplanar low-dose radiographs. The method morphs a template to fit annotated points on visible portions of the spine, and it relies on a default biomechanical model of the torso for regularization and robust fitting of hardly visible parts of the torso skeleton, such as the rib cage. The proposed method provides an accurate and robust solution to obtain personalized models of the torso skeleton, which can be adopted as part of regular management of scoliosis patients. We have evaluated the method on ten young patients who participated in our study. We have analyzed and compared clinical metrics on the spine and the full torso skeleton, and we have found that the accuracy of the method is at least comparable to other methods that require more demanding imaging methods, while it offers superior robustness to artifacts such as interpenetration of ribs. Normal-dose X-rays were available for one of the patients, and for the other nine we acquired low-dose X-rays, allowing us to validate that the accuracy of the method persisted under less invasive imaging modalities.

Skin marker-based subject-specific spinal alignment modeling: A feasibility study

Musculoskeletal models have the potential to improve diagnosis and optimize clinical treatment by predicting accurate outcomes on an individual basis. However, the subject-specific modeling of spinal alignment is often strongly simplified or is based on radiographic assessments, exposing subjects to unnecessary radiation. We therefore developed and introduced a novel skin marker-based approach for modeling subject-specific spinal alignment and evaluated its feasibility by comparing the predicted L1/L2 spinal loads during various functional activities with the loads predicted by the generically scaled models as well as with in vivo measured data obtained from the OrthoLoad database. Spinal loading simulations resulted in considerably higher compressive forces for both scaling approaches over all simulated activities, and AP shear forces that were closer or similar to the in vivo data for the subject-specific approach during upright standing activities and for the generic approach during activities that involved large flexions. These results underline the feasibility of the proposed method and associated workflow for inter- and intra-subject investigations using musculoskeletal simulations. When implemented into standard model scaling workflows, it is expected to improve the accuracy of muscle activity and joint loading simulations, which is crucial for investigations of treatment effects or pathology-dependent deviations.

Computational modelling of the scoliotic spine: A literature review

Scoliosis is a deformity of the spine that in severe cases requires surgical treatment. There is still disagreement among clinicians as to what the aim of such treatment is as well as the optimal surgical technique. Numerical models can aid clinical decision-making by estimating the outcome of a given surgical intervention. This paper provided some background information on the modelling of the healthy spine and a review of the literature on scoliotic spine models, their validation, and their application. An overview of the methods and techniques used to construct scoliotic finite element and multibody models was given as well as the boundary conditions used in the simulations. The current limitations of the models were discussed as well as how such limitations are addressed in non-scoliotic spine models. Finally, future directions for the numerical modelling of scoliosis were addressed.

An energy approach describes spine equilibrium in adolescent idiopathic scoliosis

The adolescent idiopathic scoliosis (AIS) is a 3D deformity of the spine whose origin is unknown and clinical evolution unpredictable. In this work, a mixed theoretical and numerical approach based on energetic considerations is proposed to study the global spine deformations. The introduced mechanical model aims at overcoming the limitations of computational cost and high variability in physical parameters. The model is constituted of rigid vertebral bodies associated with 3D effective stiffness tensors. The spine equilibrium is found using minimization methods of the mechanical total energy which circumvents forces and loading calculation. The values of the model parameters exhibited in the stiffness tensor are retrieved using a combination of clinical images post-processing and inverse algorithms implementation. Energy distribution patterns can then be evaluated at the global spine scale to investigate given time patient-specific features. To verify the reliability of the numerical methods, a simplified model of spine was implemented. The methodology was then applied to a clinical case of AIS (13-year-old girl, Lenke 1A). Comparisons of the numerical spine geometry with clinical data equilibria showed numerical calculations were performed with great accuracy. The patient follow-up allowed us to highlight the energetic role of the apical and junctional zones of the deformed spine, the repercussion of sagittal bending in sacro-illiac junctions and the significant role of torsion with scoliosis aggravation. Tangible comparisons of output measures with clinical pathology knowledge provided a reliable basis for further use of those numerical developments in AIS classification, scoliosis evolution prediction and potentially surgical planning.

Spinal Compressive Forces in Adolescent Idiopathic Scoliosis With and Without Carrying Loads: A Musculoskeletal Modeling Study

The pathomechanisms of curve progression in adolescent idiopathic scoliosis (AIS) remain poorly understood and biomechanical data are limited. A deeper insight into spinal loading could provide valuable information toward the improvement of current treatment strategies. This work therefore aimed at using subject-specific musculoskeletal full-body models of patients with AIS to predict segmental compressive forces around the curve apex and to investigate how these forces are affected by simulated load carrying. Models were created based on spatially calibrated biplanar radiographic images from 24 patients with mild to moderate AIS and validated by comparing predictions of paravertebral muscle activity with reported values from in vivo studies. Spinal compressive forces were predicted during unloaded upright standing as well as standing with external loads of 10, 15, and 20% of body weight (BW) applied to the scapulae to simulate carrying a backpack in the regular way on the back as well as in front of the body and over the shoulder on the concave and convex sides of the scoliotic curve. The predicted muscle activities around the curve apex were higher on the convex side for the erector spinae (ES) and multifidi (MF) muscles, which was comparable to the EMG-based in vivo measurements from the literature. In terms of spinal loading, the implementation of spinal deformity resulted in a 10% increase of compressive force at the curve apex during unloaded upright standing. Apical compressive forces further increased by 50–62% for a simulated 10% BW load and by 77–94% and 103–128% for 15% and 20% BW loads, respectively. Moreover, load-dependent compressive force increases were the lowest in the regular backpack and the highest in the frontpack and convex conditions, with concave side-carrying forces in between. The predictions indicated increased segmental compressive forces during unloaded upright standing, which could be ascribed to the scoliotic deformation. When carrying loads, compressive forces further increased depending on the carrying mode and the weight of the load. These results can be used as a basis for further studies investigating segmental loading in AIS patients during functional activities. Models can thereby be created using the same approach as proposed in this study.