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.Author's versio

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.Author's versio

Multiscale computer muscle model based on finite element macromodel and Huxley's micromodel : doctoral dissertation

Izučavanje ponašanja mišića na osnovu precizno definisanih računarskih modela predstavlja jedan od najvećih izazova u oblasti primenjene nauke i inženjerstva. Promene u strukturalnim i funkcionalnim karakteristikama mišića usled nekih bolesti ili poremećaja u radu mišića, zahtevaju modelovanje biofizičkih procesa na više prostornih i vremenskih skala. Višeskalni modeli mišića mogu implementirati različite fenomenološke ili biofizičke modele mišića u okviru mikroskale. Implementacija fenomenoloških mikromodela doprinosi manjoj složenosti višeskalnog modela, ali takvi modeli nisu u stanju da precizno predvide prelazna ponašanja mišića pri neizometrijskim uslovima. Da bi se poboljšali ovi nedostaci, u okviru disertacije razvijen je višeskalni model mišića zasnovan na makromodelu konačnih elemenata i Hakslijevom mikromodelu (KEHaksli). Metod konačnih elemenata (MKE) integriše aktivne i pasivne materijalne karakteristike mišića u mehaniku kontinuuma na makroskali, dok se na mikroskali koristi modifikovana verzija Hakslijevog modela poprečnih mostova kako bi se izračunao aktivni napon i trenutna krutost u mišićnim vlaknima. Sva predviđanja dobijena KE-Haksli višeskalnim modelom su verifikovana poređenjem sa eksperimentalnim rezultatima i sa rezultatima dobijenim prostorno eksplicitnim simulacijama molekularnog modela (MUSICO). Mogućnosti korišćenja KE-Haksli modela u simulacijama složenih mišića, prikazane su na 2D modelu ljudskog jezika. Takođe, prikazana je upotreba KE-Haksli modela i u simulacijama određenih bolesti mišića. Zahvaljujući Mexie platformi za paralelna izvršavanja simulacija višeskalnih modela mišića, računski zahtevne simulacije KE-Haksli modela se izvode u razumnom vremenskom okviru, što model čini upotrebljivim za razne istraživačke i kliničke primene.The study of the muscle behavior based on precisely defined computer models is one of the greatest challenges in the field of applied science and engineering. Changes in the structural and functional characteristics of muscles during some diseases or disorders, require modeling of biophysical processes on several spatial and temporal scales. Multiscale muscle models can implement different phenomenological or biophysical muscle models within a microscale. The implementation of phenomenological micromodels contributes to the lower complexity of the multiscale model, but such models are not able to accurately predict transient muscle behavior under non-isometric conditions. To improve these shortcomings, a multiscale muscle model based on the finite element macromodel and the Huxley micromodel was developed as part of the thesis. The finite element method (FEM) integrates the active and passive material characteristics of the muscles into a continuum mechanics on the macroscale, while a modified Huxley’s cross-bridge model is used to calculate active muscle tension and instantaneous stiffnessin muscle fibers on the microscale. All predictions generated by the FE-Huxley multiscale model were verified by comparison with experimental results and with simulation results obtained by spatially explicit molecular model (MUSICO). The possibilities of using the FE-Huxley model in simulations of complex muscles are presented on a 2D model of the human tongue. Also, the use of the FE-Huxley model in simulations of certain muscle diseases is presented. Thanks to the Mexie platform for parallel execution simulations of multiscale muscle models, computationally demanding simulations of the FE-Huxley model are performed in a reasonable time frame, which makes the model usable for a variety of research and clinical applications

Multi-scale computer models of lymphatic pumping

The lymphatic system maintains fluid homeostasis by returning interstitial fluid to the veins. Lymphatics pump fluid locally with contracting segments of the vessel (lymphangions) bounded by valves. Contractions are generated by specialized muscle exhibiting phasic and tonic contractions. Deficient pumping can result in accumulation of interstitial fluid, called lymphoedema. Lymphoedema treatments have limited effectiveness, partially attributable to a lack of understanding of contractions. A lumped parameter computational model of lymphangion pumping has previously been developed in the group. In this thesis I detail development of two multiscale models of lymphatic pumping to facilitate improved treatments for lymphoedema. The first model captures subcellular mechanisms of lymphatic muscle contraction. This model is based on the sliding filament model and its smooth muscle adaptation. Contractile elements are combined with passive viscoelastic elements to model a cell. Many arrangements were trialled but only one behaved physiologically. The muscle model was then combined with the lymphangion model for comparison with experiments. This model captures mechanical and energetic aspects of both contraction types. I show that the model provides results similar to published experiments from rat mesenteric lymphatics. The model predicted a peak efficiency of 35%, in the upper range from other muscle types. In the range of frequencies and amplitudes simulated, the direct effect of calcium oscillations can increase lymphangion outflow by up to 40% of the flow in their absence. The second model aims to improve our understanding of lymphangion interaction in large networks through computational homogenisation. In this model we do not directly simulate all lymphangions but sample lymphangions at evenly spaced intervals to reduce the computational intensity. We show through this model that increased external pressure at the network inlet collapses lymphangions and that this disruption of pumping for a few lymphangions reduces the outflow from the entire network.Open Acces

Surrogate muscle models based on artificial neural networks with applications in finite element analysis

Biofizički modeli mišića, zasnovani na fiziološkim principima funkcionisanja mišića, se mogu koristiti da odrede mehanički odziv mišića preciznije nego fenomenološki modeli, koji su zasnovani na eksperimentalnim merenjima. Međutim, za razliku od fenomenoloških, biofizički modeli mišića su računski veoma zahtevni, što otežava njihovu upotrebu u višeskalnim simulacijama. Tipičan primer biofizičkog modela mišića je Hakslijev model. U ovoj disertaciji, da bi se omogućila efikasnija upotreba biofizičkih modela, kreirani su surogat modeli zasnovani na veštačkim neuronskim mrežama takvi da oni imitiraju originalni Hakslijev model, ali koriste manju količinu memorije i drugih računarskih resursa. Najbolji rezultati su postignuti zatvorenim rekurentnim jedinicama, koje su dale najtačnije napone u mišiću od svih konstruisanih mreža. U različitim numeričkim eksperimentima je pokazano da su predviđeni naponi i trenutna krutost skoro potpuno isti kao originalni. Pokazano je da je konstruisani surogat model za red veličine brži od Hakslijevog modela rešavanog klasičnim numeričkim postupkom i da troši manju količinu memorije. Pored toga, u ovoj disertaciji su prikazane neuronske mreže podržane fizičkim zakonima, koje su obučavane tako da aproksimiraju rešenje Hakslijeve jednačine za mišićnu kontrakciju. Pokazano je da višeslojni perceptron, podržan fizičkim zakonima, bolje generalizuje ponašanje mišića nego standardni višeslojni perceptron. U ovoj disertaciji su predstavljene procedure za kreiranje surogat modela mišića, zajedno sa procedurama za integraciju surogat modela u softverski okvir za analizu metodom konačnih elemenata. Da bi potencijal surogat modela za korišćenje u zahtevnim višeskalnim simulacijama bio demonstriran u punom obimu, simuliran je srčani ciklus leve komore, što bi bilo značajno teže uraditi sa originalnim Hakslijevim modelom.Biophysical muscle models, which are based on the underlying physiology of the muscles, can evaluate the mechanical response of the muscles more accurately than phenomenological muscle models, which are based on experimental measurements. On the other hand, biophysical muscle models are much more computationally intensive. Biophysical muscle models are often called Huxley-type muscle models. In this dissertation, to enable the efficient use of Huxley-type muscle models in multi-scale simulations of the cardiac cycle, surrogate models were created such that they mimic the original Huxley muscle model but use less memory and processing power. The best results were achieved with the gated recurrent units, which produced the most accurate stresses. Stresses and instantaneous stiffnesses produced by the surrogate model were almost indistinguishable from the original values. The constructed surrogate model was an order of magnitude faster than Huxley’s muscle model and used less memory. Additionally, in this dissertation, physics-informed neural networks were trained to approximately solve Huxley’s muscle contraction equation. It was shown that the generalization of the physics-informed multilayer perceptron is greater than that of the ordinary multilayer perceptron. The procedures for the creation of the surrogate muscle models were introduced in this dissertation, along with the procedures for the integration of the surrogate models into a finite element analysis framework. To show the potential of the surrogate models in larger-scale simulations, the cardiac cycle of the left ventricle model was simulated, which would be much higher to do with the original Huxley’s muscle model