Srboljub M. Mijailovich

Derivation of a finite-element model of lingual deformation during swallowing from the mechanics of mesoscale myofiber tracts obtained by MRI

To demonstrate the relationship between lingual myoarchitecture and mechanics during swallowing, we performed a finite-element (FE) simulation of lingual deformation employing mesh aligned with the vector coordinates of myofiber tracts obtained by diffusion tensor imaging with tractography in humans. Material properties of individual elements were depicted in terms of Hills three-component phenomenological model, assuming that the FE mesh was composed of anisotropic muscle and isotropic connective tissue. Moreover, the mechanical model accounted for elastic constraints by passive and active elements from the superior and inferior directions and the effect of out-of-plane muscles and connective tissue. Passive bolus effects were negligible. Myofiber tract activation was simulated over 500 ms in 1-ms steps following lingual tip association with the hard palate and incorporated specifically the accommodative and propulsive phases of the swallow. Examining the displacement field, active and passive muscle stress, elemental stretch, and strain rate relative to changes of global shape, we demonstrate that lingual reconfiguration during these swallow phases is characterized by (in sequence) the following: 1) lingual tip elevation and shortening in the anterior-posterior direction; 2) inferior displacement related to hyoglossus contraction at its inferior-most position; and 3) dominant clockwise rotation related to regional contraction of the genioglossus and contraction of the hyoglossus following anterior displacement. These simulations demonstrate that lingual deformation during the indicated phases of swallowing requires temporally patterned activation of intrinsic and extrinsic muscles and delineate a method to ascertain the mechanics of normal and pathological swallowing.

Distributed multi-scale muscle simulation in a hybrid MPI-CUDA computational environment

We present Mexie, an extensible and scalable software solution for distributed multi-scale muscle simulations in a hybrid MPI–CUDA environment. Since muscle contraction relies on the integration of physical and biochemical properties across multiple length and time scales, these models are highly processor and memory intensive. Existing parallelization efforts for accelerating multi-scale muscle simulations imply the usage of expensive large-scale computational resources, which produces overwhelming costs for the everyday practical application of such models. In order to improve the computational speed within a reasonable budget, we introduce the concept of distributed calculations of multi-scale muscle models in a mixed CPU–GPU environment. The concept is applied to a two-scale muscle model, in which a finite element macro model is coupled with the microscopic Huxley kinetics model. Finite element calculations of a continuum macroscopic model take place strictly on the CPU, while numerical solutions of the partial differential equations of Huxley’s cross-bridge kinetics are calculated on both CPUs and GPUs. We present a modular architecture of the solution, along with an internal organization and a specific load balancer that is aware of memory boundaries in such a heterogeneous environment. Solution was verified on both benchmark and real-world examples, showing high utilization of involved processing units, ensuring high scalability. Speed-up results show a boost of two orders of magnitude over any previously reported distributed multi-scale muscle models. This major improvement in computational feasibility of multi-scale muscle models paves the way for new discoveries in the field of muscle modeling and future clinical applications.

Nebulin stiffens the thin filament and augments cross-bridge interaction in skeletal muscle

Significance Nebulin is a giant actin-binding protein in skeletal muscle which localizes along most of the length of the thin filament. Genetic alterations or reduction in the expression level of nebulin are accompanied by dramatic loss in muscle force, resulting in muscle weakness and severe skeletal muscle myopathy. Using an inducible and tissue-specific nebulin-knockout mouse model in which nebulin is not expressed in skeletal muscle, we investigated the ultrastructure of thin filaments in passive and contracting muscle under physiological conditions using X-ray diffraction. Thin filaments were found to be threefold less stiff in nebulin-knockout muscle, and thin filament regulatory protein and cross-bridge behavior was impaired. Nebulin stiffens the thin filaments and is responsible for generating physiological levels of force. Nebulin is a giant sarcomeric protein that spans along the actin filament in skeletal muscle, from the Z-disk to near the thin filament pointed end. Mutations in nebulin cause muscle weakness in nemaline myopathy patients, suggesting that nebulin plays important roles in force generation, yet little is known about nebulin’s influence on thin filament structure and function. Here, we used small-angle X-ray diffraction and compared intact muscle deficient in nebulin (using a conditional nebulin-knockout, Neb cKO) with control (Ctrl) muscle. When muscles were activated, the spacing of the actin subunit repeat (27 Å) increased in both genotypes; when converted to thin filament stiffness, the obtained value was 30 pN/nm in Ctrl muscle and 10 pN/nm in Neb cKO muscle; that is, the thin filament was approximately threefold stiffer when nebulin was present. In contrast, the thick filament stiffness was not different between the genotypes. A significantly shorter left-handed (59 Å) thin filament helical pitch was found in passive and contracting Neb cKO muscles, as well as impaired tropomyosin and troponin movement. Additionally, a reduced myosin mass transfer toward the thin filament in contracting Neb cKO muscle was found, suggesting reduced cross-bridge interaction. We conclude that nebulin is critically important for physiological force levels, as it greatly stiffens the skeletal muscle thin filament and contributes to thin filament activation and cross-bridge recruitment.

Coupling finite element and huxley models in multiscale muscle modeling

In this paper we present a novel approach in multi-scale muscle modeling based on finite element method and Huxley crossbridge kinetics model. In order to determine the mechanical response of a muscle, we implement basic mechanical principles of motion of deformable bodies using finite element method. Constitutive properties of muscle are defined by the number of molecular interconnections between the myosin and actin filaments. To account for these effects, we used Huxleys micro model based on sliding filament theory to calculate muscle active forces and instantaneous stiffnesses in FE integration points. In order to run these computationally expensive simulations we have also developed a special parallelization strategy which gives speedup of two orders of magnitude. Results obtained using presented multi-scale model are compared to those obtained by Hills phenomenological model.

Multiscale model predictions of X-ray diffraction patterns from nonuniformly stretched actin filaments

In order to explain time-resolved X-ray diffraction data from striated muscle we explored the feasibility of using dynamic 3D models of muscle contraction to predict X-ray diffraction patterns. This approach differs radically from previous attempts, which merely aimed to provide a “best fit” structure for defined quasi-static states, by providing a tool to generate families of structures that evolve in time that explains both the structural (X-ray) and the mechanical data simultaneously. Specifically, we exploit the computational platform MUSICO (Muscle Simulation Code), which was developed originally to model muscle mechanics data, by extending this framework to simulate X-ray diffraction patterns using 3D multiscale models. The platform is conceived primarily as a hypothesis-testing tool in which model predictions are tested against the best available mechanical and X-ray diffraction data on the same system. Our preliminary simulations provided dynamic X-ray diffraction patterns during force development and relaxation in skeletal muscle. The simulated patterns generally predicted well the changes in repetitive molecular spacings and were otherwise similar to the experimental data. Once fully developed, this tool will enable extraction of maximum information from the X-ray patterns, in combination with the physiological data, and therefore provide a template to test hypotheses concerning crossbridge and regulatory protein action in working muscle. Our approach can be extended to any muscle system, and it could ultimately provide an interpretive framework for studying the mechanisms of inherited or acquired diseases.