During contraction the energy of muscle tissue increases due to energy from the hydrolysis of ATP. This energy is distributed across the tissue as strain-energy potentials in the contractile elements, strain-energy potential from the 3D deformation of the base-material tissue (containing cellular and extracellular matrix effects), energy related to changes in the muscle's nearly incompressible volume and external work done at the muscle surface. Thus, energy is redistributed through the muscle's tissue as it contracts, with only a component of this energy being used to do mechanical work and develop forces in the muscle's longitudinal direction. Understanding how the strain-energy potentials are redistributed through the muscle tissue will help enlighten why the mechanical performance of whole muscle in its longitudinal direction does not match the performance that would be expected from the contractile elements alone. Here we demonstrate these physical effects using a 3D muscle model based on the finite element method. The tissue deformations within contracting muscle are large, and so the mechanics of contraction were explained using the principles of continuum mechanics for large deformations. We present simulations of a contracting medial gastrocnemius muscle, showing tissue deformations that mirror observations from magnetic resonance imaging. This paper tracks the redistribution of strain-energy potentials through the muscle tissue during fixed-end contractions, and shows how fibre shortening, pennation angle, transverse bulging and anisotropy in the stress and strain of the muscle tissue are all related to the interaction between the material properties of the muscle and the action of the contractile elements.

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BackgroundMost data on the architecture of the human soleus muscle have been obtained from cadaveric dissection or two-dimensional ultrasound imaging. We present the first comprehensive, quantitative study on the three-dimensional anatomy of the human soleus muscle in vivo using diffusion tensor imaging (DTI) techniques.MethodsWe report three-dimensional fascicle lengths, pennation angles, fascicle curvatures, physiological cross-sectional areas and volumes in four compartments of the soleus at ankle joint angles of 69 ± 12° (plantarflexion, short muscle length; average ± SD across subjects) and 108 ± 7° (dorsiflexion, long muscle length) of six healthy young adults. Microdissection and three-dimensional digitisation on two cadaveric muscles corroborated the compartmentalised structure of the soleus, and confirmed the validity of DTI-based muscle fascicle reconstructions.ResultsThe posterior compartments of the soleus comprised 80 ± 5% of the total muscle volume (356 ± 58 cm3). At the short muscle length, the average fascicle length, pennation angle and curvature was 37 ± 8 mm, 31 ± 3° and 17 ± 4 /m, respectively. We did not find differences in fascicle lengths between compartments. However, pennation angles were on average 12° larger (p < 0.01) in the posterior compartments than in the anterior compartments. For every centimetre that the muscle-tendon unit lengthened, fascicle lengths increased by 3.7 ± 0.8 mm, pennation angles decreased by −3.2 ± 0.9° and curvatures decreased by −2.7 ± 0.8 /m. Fascicles in the posterior compartments rotated almost twice as much as in the anterior compartments during passive lengthening.DiscussionThe homogeneity in fascicle lengths and inhomogeneity in pennation angles of the soleus may indicate a functionally different role for the anterior and posterior compartments. The data and techniques presented here demonstrate how DTI can be used to obtain detailed, quantitative measurements of the anatomy of complex skeletal muscles in living humans.

There are few comprehensive investigations of the changes in muscle architecture that accompany muscle contraction or change in muscle length in vivo. For this study, we measured changes in the three-dimensional architecture of the human medial gastrocnemius at the whole muscle level, the fascicle level and the fiber level using anatomical MRI and diffusion tensor imaging (DTI). Data were obtained from eight subjects under relaxed conditions at three muscle lengths. At the whole muscle level, a 5.1% increase in muscle belly length resulted in a reduction in both muscle width (mean change -2.5%) and depth (-4.8%). At the fascicle level, muscle architecture measurements obtained at 3,000 locations per muscle showed that for every millimeter increase in muscle-tendon length above the slack length, average fascicle length increased by 0.46 mm, pennation angle decreased by 0.27° (0.17° in the superficial part and 0.37° in the deep part), and fascicle curvature decreased by 0.18 m There was no evidence of systematic variation in architecture along the muscle's long axis at any muscle length. At the fiber level, analysis of the diffusion signal showed that passive lengthening of the muscle increased diffusion along fibers and decreased diffusion across fibers. Using these measurements across scales, we show that the complex shape changes that muscle fibers, whole muscles, and aponeuroses of the medial gastrocnemius undergo in vivo cannot be captured by simple geometrical models. This justifies the need for more complex models that link microstructural changes in muscle fibers to macroscopic changes in architecture. Novel MRI and DTI techniques revealed changes in three-dimensional architecture of the human medial gastrocnemius during passive lengthening. Whole muscle belly width and depth decreased when the muscle lengthened. Fascicle length, pennation, and curvature changed uniformly or near uniformly along the muscle during passive lengthening. Diffusion of water molecules in muscle changes in the same direction as fascicle strains.

Musculoskeletal models are intended to be used to assist in prevention and treatments of musculoskeletal disorders. To capture important aspects of shoulder dysfunction, realistic simulation of clavicular and scapular movements is crucial. The range of motion of these bones is dependent on thoracic, clavicular and scapular anatomy and therefore different for each individual. Typically, patient or subject measurements will therefore not fit on a model that uses a cadaveric morphology. Up till now, this problem was solved by adjusting measured bone rotations such that they fit on the model, but this leads to adjustments of on average 3.98° and, in some cases, even more than 8°. Two novel methods are presented that decrease this discrepancy between experimental data and simulations. For one method, the model is scaled to fit the subject, leading to a 34 % better fit compared to the existing method. In the other method, the set of possible joint rotations is increased by allowing some variation on motion constraints, resulting in a 42 % better fit. This change in kinematics also affected the kinetics: muscle forces of some important scapular stabilizing muscles, as predicted by the Delft Shoulder and Elbow Model, were altered by maximally 17 %. The effect on the glenohumeral joint contact force was however marginal (1.3 %). The methods presented in this paper might lead to more realistic shoulder simulations and can therefore be considered a step towards (clinical) application, especially for applications that involve scapular imbalance.

Cerebral palsy is a neurological condition that is known to affect muscle growth.Detailed investigations of muscle growth require segmentation of muscles from MRI scans, which is typically done manually. In this study, we evaluated the performance of 2D, 3D, and hybrid deep learning models for automatic segmentation of 11 lower leg muscles and two bones from MRI scans of children with and without cerebral palsy. All six models were trained and evaluated on manually segmented T 1 -weighted MRI scans of the lower legs of 20 children, six of whom had cerebral palsy. The segmentation results were assessed using the median Dice similarity coefficient (DSC), average symmetric surface distance (ASSD), and volume error (VError) of all 13 labels of every scan. The best performance was achieved by H-DenseUNet, a hybrid model (DSC 0.90, ASSD 0.5 mm, and VError 2.6 cm 3 ). The performance was equivalent to the inter-rater performance of manual segmentation (DSC 0.89, ASSD 0.6 mm, and VError 3.3 cm 3 ). Models trained with the Dice loss function outperformed models trained with the cross-entropy loss function. Near-optimal performance could be attained using only 11 scans for training. Segmentation performance was similar for scans of typically developing children (DSC 0.90, ASSD 0.5 mm, and VError 2.8 cm 3 ) and children with cerebral palsy (DSC 0.85, ASSD 0.6 mm, and VError 2.4 cm 3 ). These findings demonstrate the feasibility of fully automatic segmentation of individual muscles and bones from MRI scans of children with and without cerebral palsy.

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