A comprehensive and volumetric musculoskeletal model for the dynamic simulation of the shoulder function

Development of a musculoskeletal shoulder model considering anatomic joint structures and soft-tissue deformation for dynamic simulation

The shoulder joint has a high degree of freedom and an extremely complex and unstable kinematic mechanism. Coordinated contraction of the rotator cuff muscles that stop around the humeral head and the deltoid muscles and the extensibility of soft tissues, such as the joint capsule, labrum, and ligaments, contribute to shoulder-joint stability. Understanding the mechanics of shoulder-joint movement, including soft-tissue characteristics, is important for disease prevention and the development of a device for disease treatment. This study aimed to create a musculoskeletal shoulder model to represent the realistic behavior of joint movement and soft-tissue deformation as a dynamic simulation using a rigid-body model for bones and a soft-body model for soft tissues via a spring-damper-mass system. To reproduce the muscle-contraction properties of organisms, we used a muscle-expansion representation and Hill's mechanical muscle model. Shoulder motion, including the movement of the center of rotation in joints, was reproduced, and the strain in the joint capsule during dynamic shoulder movement was quantified. Furthermore, we investigated narrowing of the acromiohumeral distance in several situations to induce tissue damage due to rotator cuff impingement at the anterior-subacromial border during shoulder abduction. Given that the model can analyze exercises under disease conditions, such as muscle and tendon injuries and impingement syndrome, the proposed model is expected to help elucidate disease mechanisms and develop treatment guidelines.

Linking cortex and contraction-Integrating models along the corticomuscular pathway

Computational models of the neuromusculoskeletal system provide a deterministic approach to investigate input-output relationships in the human motor system. Neuromusculoskeletal models are typically used to estimate muscle activations and forces that are consistent with observed motion under healthy and pathological conditions. However, many movement pathologies originate in the brain, including stroke, cerebral palsy, and Parkinson's disease, while most neuromusculoskeletal models deal exclusively with the peripheral nervous system and do not incorporate models of the motor cortex, cerebellum, or spinal cord. An integrated understanding of motor control is necessary to reveal underlying neural-input and motor-output relationships. To facilitate the development of integrated corticomuscular motor pathway models, we provide an overview of the neuromusculoskeletal modelling landscape with a focus on integrating computational models of the motor cortex, spinal cord circuitry, α-motoneurons  and skeletal muscle in regard to their role in generating voluntary muscle contraction. Further, we highlight the challenges and opportunities associated with an integrated corticomuscular pathway model, such as challenges in defining neuron connectivities, modelling standardisation, and opportunities in applying models to study emergent behaviour. Integrated corticomuscular pathway models have applications in brain-machine-interaction, education, and our understanding of neurological disease.

A Shoulder Musculoskeletal Model with Three-Dimensional Complex Muscle Geometries

Muscle structure is an essential component in typical computational models of the musculoskeletal system. Almost all musculoskeletal models represent muscle geometry using a set of line segments. The straight-line approach limits models' ability to accurately predict the paths of muscles with complex geometry. This approach needs knowledge of how the muscle changes shape and interacts with fundamental structures like muscles, bones, and joints that move. Moreover, the moment arms are supposed to be equivalent to all the fibers in the muscle. This study aims to create a shoulder musculoskeletal model that includes complex muscle geometries. We reconstructed the shape of fibers in the entire volume of six muscles adjacent to the shoulder using an automated technique. This method generates many fibers from the surface geometry of the skeletal muscle and its attachment areas. Highly discretized muscle representations for all muscles were created and used to simulate different shoulder movements. The moment arms of each muscle were calculated and validated against cadaveric measurements and models of the same muscles from the literature. We found that simulations using the developed musculoskeletal models generated more realistic geometries, which expands the physical representation of muscles compared to line segments. The shoulder musculoskeletal model with complex muscle geometry is created to increase the anatomical reality of models and the lines action of muscle fibers, and to be used for finite element investigations.

Modelling motor units in 3D: influence on muscle contraction and joint force via a proof of concept simulation

Functional heterogeneity is a skeletal muscle’s ability to generate diverse force vectors through localised motor unit (MU) recruitment. Existing 3D macroscopic continuum-mechanical finite element (FE) muscle models neglect MU anatomy and recruit muscle volume simultaneously, making them unsuitable for studying functional heterogeneity. Here, we develop a method to incorporate MU anatomy and information in 3D models. Virtual fibres in the muscle are grouped into MUs via a novel “virtual innervation” technique, which can control the units’ size, shape, position, and overlap. The discrete MU anatomy is then mapped to the FE mesh via statistical averaging, resulting in a volumetric MU distribution. Mesh dependency is investigated using a 2D idealised model and revealed that the amount of MU overlap is inversely proportional to mesh dependency. Simultaneous recruitment of a MU’s volume implies that action potentials (AP) propagate instantaneously. A 3D idealised model is used to verify this assumption, revealing that neglecting AP propagation results in a slightly less-steady force, advanced in time by approximately 20 ms, at the tendons. Lastly, the method is applied to a 3D, anatomically realistic model of the masticatory system to demonstrate the functional heterogeneity of masseter muscles in producing bite force. We found that the MU anatomy significantly affected bite force direction compared to bite force magnitude. MU position was much more efficacious in bringing about bite force changes than MU overlap. These results highlight the relevance of MU anatomy to muscle function and joint force, particularly for muscles with complex neuromuscular architecture.

A finite element model of the shoulder: application to the changes of biomechanical environment induced by postoperative malrotation of humeral shaft fracture

Objectives

The humerus fracture is one of the most commonly occurring fractures. In this research, we attempted to evaluate and compare the extent of malrotation and biomechanical environment after surgical treatment of humeral shaft fractures.

Methods

A finite element (FE) model of the shoulder was built based on Computed Tomography (CT) data of a patient with a humeral shaft fracture. The muscle group around the shoulder joint was simulated by spring elements. The changes of shoulder stresses under rotation were analyzed. The biomechanics of the normal shoulder and postoperative malrotation of the humeral shaft was analyzed and compared.

Results

During rotations, the maximum stress was centered in the posterosuperior part of the glenoid for the normal shoulder. The von Mises shear stresses were 4.40 MPa and 4.89 MPa at 40° of internal and external rotations, respectively. For internal rotation deformity, the shear contact forces were 7–9 times higher for the shoulder internally rotated 40° than for the normal one. For external rotation deformity, the shear contact forces were about 3–5 times higher for the shoulder with 40° external rotation than the normal one.

Conclusion

Postoperative malrotation of humeral shaft fracture induced the changes of the biomechanical environment of the shoulders. The peak degree of malrotation was correlated with increased stresses of shoulders, which could be paid attention to in humeral shaft fracture treatment. We hoped to provide information about the biomechanical environment of humeral malrotation.

Surface-based modeling of muscles: Functional simulation of the shoulder

Musculoskeletal simulations are an essential tool for studying functional implications of pathologies and of potential surgical outcomes, e.g., for the complex shoulder anatomy. Most shoulder models rely on line-segment approximation of muscles with potential limitations. Comprehensive shoulder models based on continuum-mechanics are scarce due to their complexity in both modeling and computation. In this paper, we present a surface-based modeling approach for muscles, which simplifies the modeling process and is efficient for computation. We propose to use surface geometries for modeling muscles, and devise an automatic approach to generate such models, given the locations of the origin and insertion of tendons. The surfaces are expressed as higher-order tensor B-splines, which ensure smoothness of the geometrical representation. They are simulated as membrane elements within a finite element simulation. This is demonstrated on a comprehensive model of the upper limb, where muscle activations needed to perform desired motions are obtained by using inverse dynamics. In synthetic examples, we demonstrate our proposed surface elements both to be easy to customize (e.g., with spatially varying material properties) and to be substantially (up to 12 times) faster in simulation compared to their volumetric counterpart. With our presented automatic approach of muscle wrapping around bones, the humeral head is exemplified to be wrapped physiologically consistently with surface elements. Our functional simulation is shown to successfully replicate a tracked shoulder motion during activities of daily living. We demonstrate surface-based models to be a numerically stable and computationally efficient compromise between line-segment and volumetric models, enabling anatomical correctness, subject-specific customization, and fast simulations, for a comprehensive simulation of musculoskeletal motion.