Estimating prognosis in patients with acute myocardial infarction using personalized computational heart models

Biomechanical computational models have potential prognostic utility in patients after an acute ST-segment–elevation myocardial infarction (STEMI). In a proof-of-concept study, we defined two groups (1) an acute STEMI group (n = 6, 83% male, age 54 ± 12 years) complicated by left ventricular (LV) systolic dysfunction; (2) an age- and sex- matched hyper-control group (n = 6, 83% male, age 46 ± 14 years), no prior history of cardiovascular disease and normal systolic blood pressure (SBP < 130 mmHg). Cardiac MRI was performed in the patients (2 days & 6 months post-STEMI) and the volunteers, and biomechanical heart models were synthesized for each subject. The candidate parameters included normalized active tension (ATnorm) and active tension at the resting sarcomere length (Treq, reflecting required contractility). Myocardial contractility was inversely determined from personalized heart models by matching CMR-imaged LV dynamics. Compared with controls, patients with recent STEMI exhibited increased LV wall active tension when normalized by SBP. We observed a linear relationship between Treq 2 days post-MI and global longitudinal strain 6 months later (r = 0.86; p = 0.03). Treq may be associated with changes in LV function in the longer term in STEMI patients complicated by LV dysfunction. Further studies seem warranted

Fluid-electro-mechanical model of the human heart for supercomputers

The heart is a complex system. From the transmembrane cell activity to the spatial organization in helicoidal fibers, it includes several spatial and temporal scales. The heart muscle is surrounded by two main tissues that modulate how it deforms: the pericardium and the blood. The former constrains the epicardial surface and the latter exerts a force in the endocardium. The main function of this peculiar muscle is to pump blood to the pulmonary and systemic circulations. In this way, solid dynamics of the heart is as important as the induced fluid dynamics. Despite the work done in computational research of multiphysics heart modelling, there is no reference of a tightly-coupled scheme that includes electrophysiology, solid and fluid mechanics in a whole human heart. In this work, we propose, develop and test a fluid-electro-mechanical model of the human heart. To start, the heartbeat phenomenon is disassembled in the different composing problems. The first building block is the electrical activity of the myocytes, that induces the mechanical deformation of the myocardium. The contraction of the muscle reduces the intracavitary space, that pushes out the contained blood. At the same time, the inertia, pressure and viscous stresses in this fluid exerts a force on the solid wall. In this way, we can understand the heart as a fluid-electro-mechanical problem. All the models are implemented in Alya, the Barcelona Supercomputing Center simulation software. A multi-code approach is used, splitting the problem in a solid and a fluid domain. In the former, electrophysiology coupled with solid mechanics are solved. In the later, fluid dynamics in an arbitrary Lagrangian-Eulerian domain are computed. The equations are spatially discretized using the finite element method and temporally discretized using finite differences. Facilitated by the multi-code approach, a novel high performance quasi-Newton method is developed to deal with the intrinsic issues of fluid-structure interaction problems in iomechanics. All the schemes are optimized to run in massively parallel computers. A wide range of experiments are shown to validate, test and tune the numerical model. The different hypothesis proposed — as the critical effect of the atrium or the presence of pericardium — are also tested in these experiments. Finally, a normal heartbeat is simulated and deeply analyzed. This healthy computational heart is first diseased with a left bundle branch block. After this, its function is restored simulating a cardiac resynchronization therapy. Then, a third grade atrioventricular block is simulated in the healthy heart. In this case, the pathologic model is treated with a minimally invasive leadless intracardiac pacemaker. This requires to include the device in the geometrical description of the problem, solve the structural problem with the tissue, and the fluid-structure interaction problem with the blood. As final experiment, we test the parallel performance of the coupled solver. In the cases mentioned above, the results are qualitatively compared against experimental measurements, when possible. Finally, a first glance in a coupled fluid-electro-mechanical cardiovascular system is shown. This model is build adding a one dimensional model of the arterial network created by the Laboratório Nacional de Computação Científica in Petropolis, Brasil. Despite the artificial geometries used, the outflow curves are comparable with physiological observations. The model presented in this thesis is a step towards the virtual human heart. In a near future computational models like the presented in this thesis will change how pathologies are understood and treated, and the way biomedical devices are designed.El corazón es un sistema complejo. Desde la actividad celular hasta la organización espacial en fibras helicoidales, incluye gran cantidad de escalas espaciales y temporales. El corazón está rodeado principalmente por dos tejidos que modulan su deformación: el pericardio y la sangre. El primero restringe el movimiento del epicardio, mientras el segundo ejerce fuerza sobre el endocardio. La función principal de este músculo es bombear sangre a la circulación sistémica y a la pulmonar. Así, la deformación del miocardio es tan importante como la fluidodinámica inducida. Al día de hoy, solo se han propuesto modelos parciales del corazón. Ninguno de los modelos publicados resuelve electrofisiología, mecánica del sólido, y dinámica de fluidos en una geometría completa del corazón. En esta tesis, proponemos, desarrollamos y probamos un modelo fluido -electro -mecánico del corazón. Primero, el problema del latido cardíaco es descompuesto en los distintos subproblemas. El primer bloque componente es la actividad eléctrica de los miocitos, que inducen la deformación mecánica del miocardio. La contratación de este músculo, reduce el espacio intracavitario, que empuja la sangre contenida. Al mismo tiempo, la inercia, presión y fuerzas viscosas del fluido inducen una presión sobre la pared del sólido. De esta manera, podemos entender el latido cardíaco como un problema fluido-electro-mecánico. Los modelos son implementados en Alya, el software de simulación del Barcelona Supercomputing Center. Se utiliza un diseño multi-código, separando el problema según el dominio en sólido y fluido. En el primero, se resuelve electrofisiología acoplado con mecánica del sólido. En el segundo, fluido dinámica en un dominio arbitrario Lagrangiano-Euleriano. Las ecuaciones son discretizadas espacial y temporalmente utilizando elementos finitos y diferencias finitas respectivamente. Facilitado por el diseño multi-codigo, se desarrolló un novedoso método quasi-Newton de alta performance, pensado específicamente para lidiar con los problemas intrínsecos de interacción fluido-estructura en biomecánica. Todos los esquemas fueron optimizados para correr en ordenadores masivamente paralelos.Se presenta un amplio espectro de experimentos con el fin de validar, probar y ajustar el modelo numérico. Las diferentes hipótesis propuestas tales como el efecto producido por la presencia de las aurículas o el pericardio son también demostradas en estos experimentos. Finalmente un latido normal es simulado y sus resultados son analizados con profundidad. El corazón computacional sano es, primeramente enfermado de un bloqueo de rama izquierda. Posteriormente se restaura la función normal mediante la terapia de resincronización cardíaca. Luego se afecta al corazón de un bloqueo atrioventricular de tercer grado. Esta patología es tratada mediante la implantación de un marcapasos intracardíaco. Para esto, se requiere incluir el dispositivo en la descripción geométrica, resolver el problema estructural con el tejido y la interacción fluido-estructura con la sangre. Como experimento numérico final, se prueba el desempeño paralelo del modelo acoplado.Finalmente, se muestran resultados preliminares para un modelo fluido-electro-mecánico del sistema cardiovascular. Este modelo se construye agregando un modelo unidimensional del árbol arterial. A pesar de las geometrías artificiales usadas, la curva de flujo en la raíz aórtica es comparable con observaciones experimentales. El modelo presentado aquí representa un avance hacia el humano virtual. En un futuro, modelos similares, cambiarán la forma en la que se entienden y tratan las enfermedades y la forma en la que los dispositivos biomédicos son diseñados.Postprint (published version

A multiscale model for collagen alignment in wound healing

It is thought that collagen alignment plays a significant part in scar tissue formation during dermal wound healing. We present a multiscale model for collagen deposition and alignment during this process. We consider fibroblasts as discrete units moving within an extracellular matrix of collagen and fibrin modelled as continua. Our model includes flux induced alignment of collagen by fibroblasts, and contact guidance of fibroblasts by collagen fibres. We can use the model to predict the effects of certain manipulations, such as varying fibroblast speed, or placing an aligned piece of tissue in the wound. We also simulate experiments which alter the TGF-β concentrations in a healing dermal wound and use the model to offer an explanation of the observed influence of this growth factor on scarring

Cancer modelling: Getting to the heart of the problem

Paradoxically, improvements in healthcare that have enhanced the life expectancy of humans in the Western world have, indirectly, increased the prevalence of certain types of cancer such as prostate and breast. It remains unclear whether this phenomenon should be attributed to the ageing process itself or the cumulative effect of prolonged exposure to harmful environmental stimuli such as ultraviolet light, radiation and carcinogens (Franks and Teich, 1988). Equally, there is also compelling evidence that certain genetic abnormalities can predispose individuals to specific cancers (Ilyas et al., 1999). The variety of factors that have been implicated in the development of solid tumours stems, to a large extent, from the fact that ‘cancer’ is a generic term, often used to characterize a series of disorders that share common features. At this generic level of description, cancer may be viewed as a cellular disease in which controls that usually regulate growth and maintain homeostasis are disrupted. Cancer is typically initiated by genetic mutations that lead to enhanced mitosis of a cell lineage and the formation of an avascular tumour. Since it receives nutrients by diffusion from the surrounding tissue, the size of an avascular tumour is limited to several millimeters in diameter. Further growth relies on the tumour acquiring the ability to stimulate the ingrowth of a new, circulating blood supply from the host vasculature via a process termed angiogenesis (Folkman, 1974). Once vascularised, the tumour has access to a vast nutrient source and rapid growth ensues. Further, tumour fragments that break away from the primary tumour, on entering the vasculature, may be transported to other organs in which they may establish secondary tumours or metastases that further compromise the host. Invasion is another key feature of solid tumours whereby contact with the tissue stimulates the production of enzymes that digest the tissue, liberating space into which the tumour cells migrate. Thus, cancer is a complex, multiscale process. The spatial scales of interest range from the subcellular level, to the cellular and macroscopic (or tissue) levels while the timescales may vary from seconds (or less) for signal transduction pathways to months for tumour doubling times The variety of phenomena involved, the range of spatial and temporal scales over which they act and the complex way in which they are inter-related mean that the development of realistic theoretical models of solid tumour growth is extremely challenging. While there is now a large literature focused on modelling solid tumour growth (for a review, see, for example, Preziosi, 2003), existing models typically focus on a single spatial scale and, as a result, are unable to address the fundamental problem of how phenomena at different scales are coupled or to combine, in a systematic manner, data from the various scales. In this article, a theoretical framework will be presented that is capable of integrating a hierarchy of processes occurring at different scales into a detailed model of solid tumour growth (Alarcon et al., 2004). The model is formulated as a hybrid cellular automaton and contains interlinked elements that describe processes at each spatial scale: progress through the cell cycle and the production of proteins that stimulate angiogenesis are accounted for at the subcellular level; cell-cell interactions are treated at the cellular level; and, at the tissue scale, attention focuses on the vascular network whose structure adapts in response to blood flow and angiogenic factors produced at the subcellular level. Further coupling between the different spatial scales arises from the transport of blood-borne oxygen into the tissue and its uptake at the cellular level. Model simulations will be presented to illustrate the effect that spatial heterogeneity induced by blood flow through the vascular network has on the tumour’s growth dynamics and explain how the model may be used to compare the efficacy of different anti-cancer treatment protocols

A Rapid and Computationally Inexpensive Method to Virtually Implant Current and Next-Generation Stents into Subject-Specific Computational Fluid Dynamics Models

Computational modeling is often used to quantify hemodynamic alterations induced by stenting, but frequently uses simplified device or vascular representations. Based on a series of Boolean operations, we developed an efficient and robust method for assessing the influence of current and next-generation stents on local hemodynamics and vascular biomechanics quantified by computational fluid dynamics. Stent designs were parameterized to allow easy control over design features including the number, width and circumferential or longitudinal spacing of struts, as well as the implantation diameter and overall length. The approach allowed stents to be automatically regenerated for rapid analysis of the contribution of design features to resulting hemodynamic alterations. The applicability of the method was demonstrated with patient-specific models of a stented coronary artery bifurcation and basilar trunk aneurysm constructed from medical imaging data. In the coronary bifurcation, we analyzed the hemodynamic difference between closed-cell and open-cell stent geometries. We investigated the impact of decreased strut size in stents with a constant porosity for increasing flow stasis within the stented basilar aneurysm model. These examples demonstrate the current method can be used to investigate differences in stent performance in complex vascular beds for a variety of stenting procedures and clinical scenarios

Advanced Computational Methods in Bio-Mechanics

A novel partnership between surgeons and machines, made possible by advances in computing and engineering technology, could overcome many of the limitations of traditional surgery. By extending surgeons’ ability to plan and carry out surgical interventions more accurately and with fewer traumas, computer-integrated surgery (CIS) systems could help to improve clinical outcomes and the efficiency of healthcare delivery. CIS systems could have a similar impact on surgery to that long since realised in computer-integrated manufacturing. Mathematical modelling and computer simulation have proved tremendously successful in engineering.Computational mechanics has enabled technological developments in virtually every area of our lives. One of the greatest challenges for mechanists is to extend the success of computational mechanics to fields outside traditional engineering, in particular to biology, the biomedical sciences, and medicine. Biomechanics has significant potential for applications in orthopaedic industry, and the performance arts since skills needed for these activities are visibly related to the human musculoskeletal and nervous systems.Although biomechanics is widely used nowadays in the orthopaedic industry to design orthopaedic implants for human joints, dental parts, external fixations and other medical purposes, numerous researches funded by billions of dollars are still running to build a new future for sports and human healthcare in what is called biomechanics era

Review of patient-specific simulations of transcatheter aortic valve implantation

International audienceTranscatheter Aortic Valve Implantation (TAVI) accounts for one of the most promising new cardiovascular procedures. This minimally invasive technique is still at its early stage and is constantly developing thanks to imaging techniques, computer science, biomechanics and technologies of prosthesis and delivery tools. As a result, patient-specific simulation can find an exciting playground in TAVI. It canexpress its potential by providing the clinicians with powerful decision support, offering great assistance in their workflow. Through a review of the current scientific field, we try to identify the challenges and future evolutions of patient-specific simulation for TAVI. This review article is an attempt to summarize and coordinate data scattered across the literature about patient-specific biomechanical simulation for TAVI

Placental mesenchymal stem cell sheets: motivation for bio-MEMS device to create patient matched myocardial patches

Congenital heart defects are the number one cause of birth defect-related deaths. Cardiovascular diseases are the most common cause of death worldwide. Layered cellular sheet constructs offer one very valuable option for cardiac patch implantation during surgical treatment of both pediatric and adult patients with cardiac defects or damage. A very exciting, relatively unexplored, autologous, available cell source for making patches are placenta-derived mesenchymal stem cells (pMSCs). In this study, pMSCs were assessed as a potential cell source for cardiac repair and regeneration by evaluating their differentiation capacity into cardiomyocytes, their effects on cardiac cell migration and proliferation, and their ability to be grown into cell sheets. It was found that pMSC cardiac protein content was enhanced by differentiation media treatment, but no beating cells were produced. Undifferentiated pMSCs improved migration and proliferation of a cardiac cell population and formed intact, aligned cell sheets. However, like many new cell sources for cardiac repair, pMSCs should still be functionally characterized to understand how compatible they will be with resident heart tissue. Implanting non-autologous, potentially pluripotent, non-myocyte (non-beating) cells presents concerns regarding electromechanical mismatch and implant rejection. The characterization of non-traditional cell sources such as pMSCs motivated the design of a bio-MEMS device that assesses contractile force and conduction velocity in response to electrical and mechanical stimulation of a cell source as it is grown and once it forms a cellular sheet. This ideally creates the ability for patient specific cell sheets to be cultured, characterized, and conditioned to be compatible with the patient’s cardiac environment in vitro, prior to implantation. In this work, the device was designed to achieve the following: cellular alignment, electrical stimulation, mechanical stimulation, conduction velocity readout, contraction force readout, and upon characterization, cell sheet release. The platform is based on a set of comb electrical contacts which are three dimensional wall contacts made of polydimethylsiloxane and coated with electrically conductive metals. Device fabrication and initial validation experiments were completed as part of this study; ultimately the device will allow for the complete functional characterization and conditioning of variable cell source cell sheet implants for myocardial implantation.2019-07-02T00:00:00

Experimental and computational biomedicine : Russian Conference with International Participation in memory of Professor Vladimir S. Markhasin : abstract book

Toward 100 Anniversary of I. P. Pavlov's Physiological Society.The volume contains the presentations that were made during Russian conference with international participation "Experimental and Computational Biomedicine" dedicated to corresponding member of RAS V.S. Markhasin (Ekaterinburg, April 10‒12, 2016). The main purpose of the conference is the discussion of the current state of experimental and theoretical research in biomedicine. For a wide range of scientists, as well as for lecturers, students of the biological and medical high schools.Сборник содержит тезисы докладов, представленных на российской конференции с международным участием «Экспериментальная и компьютерная биомедицина», посвященной памяти члена‐корреспондента РАН В. С. Мархасина (г. Екатеринбург, 10‒12 апреля 2016 г.). Основной целью конференции является обсуждение современного состояния экспериментальных и теоретических исследований в области биомедицины. Сборник предназначен для ученых, преподавателей, студентов и аспирантов биологического и медицинского профиля.МАРХАСИН ВЛАДИМИР СЕМЕНОВИЧ (1941-2015)/ MARKHASIN VLADIMIR SEMENOVICH (1941-2015). [3] PROGRAMM COMMITTEE. [5] ORGANIZING COMMITTEE. [6] KEYNOTE SPEAKERS. [7] CONTENTS. [9] PLENARY LECTURES. [10] Fedotov S. Non-Markovian random walks and anomalous transport in biology. [10] Hoekstra A. Multiscale modelling in vascular disease. [10] Kohl P. Systems biology of the heart: why bother? [10] Meyerhans A. On the regulation of virus infection fates. [11] Panfilov A.V., Dierckx H., Kazbanov I., Vandersickel N. Systems approach to studying mechanisms of ventricular fibrillationusing anatomically accurate modeling. [11] Revishvili A.S. Atrial fibrillation. Noninvasive diagnostic and treatment:from fundamental studies to clinical practice. [12] Rice J. Life sciences research at IBM. [12] Roshchevskaya I.M., Smirnova S., Roshchevsky M.P. Regularities of the depolarization of an atria:an experimental comparative-physiological study. [12] Rusinov V.L., Chupahin O.N., Charushin V.N Scientific basis for development of antiviral drugs. [13] Solovyova O.E. Tribute Lecture. Mechano-electric heterogeneity of the myocardiumas a paradigm of its function. [13] Veksler V. Myocardial energy starvation in chronic heart failure:perspectives for metabolic therapy. [13] Wladimiroff J.W. Fetal cardiac assessment using new methodsof ultrasound examination. [14] Yushkov B.G., Chereshnev V.A. The important questions of regeneration theory. [14] EXPERIMENTAL AND COMPUTATIONAL MODELS IN CARDIOVASCULARPHYSIOLOGY AND CARDIOLOGY. [15] EXPERIMENTAL AND COMPUTATIONAL MODELS IN CARDIOVASCULARPHYSIOLOGY AND CARDIOLOGY. [15] Arteyeva N. T-wave area along with Tpeak-Tend interval is the most accurateindex of the dispersion of repolarization. [15] Borodin N., Iaparov B.Y., Moskvin A. Mathematical modeling of the calmodulin effect on the RyR2 gating. [15] Dokuchaev A., Katsnelson L.B., Sulman T.B., Shikhaleva E.V., Vikulova N.A. Contribution of cooperativity to the mechano-calcium feedbacksin myocardium. Experimental discrepancy and mathematicalapproach to overcome it. [16] Elman K.A., Filatova D.Y., Bashkatova Y.V., Beloschenko D.V. The stochastic and chaotic estimation of parametersof cardiorespiratory system of students of Ugra. [16] Erkudov V.O., Pugovkin A.P., Verlov N.A., Sergeev I.V., Ievkov S.A., Mashood S., Bagrina J.V. Characteristics of the accuracy of calculation of values of systemic blood pressure using transfer functions in experimental blood loss and its compensation. [16] Ermolaev P., Khramykh T.Mechanisms of cardiodepression after 80% liver resection in rats. [17] Filatova O.E., Rusak S.N., Maystrenko E.V., Dobrynina I.Y. Aging dynamics of cardio-vascular parameters аboriginal systemand alien population of the Russian North. [17] Frolova S., Agladze K.I., Tsvelaya V., Gaiko O. Photocontrol of voltage-gated ion channel activity by azobenzenetrimethylammonium bromide in neonatal rat cardiomyocytes. [18] Gorbunov V.S., Agladze K.I., Erofeev I.S. The application of C-TAB for excitation propagation photocontrolin cardiac tissue. [18] Iribe G. Localization of TRPC3 channels estimated by in-silicoand cellular functional experiments. [19] Kachalov V.N., Tsvelaya V., Agladze K.I. Conditions of the spiral wave unpinning from the heterogeneitywith different boundary conditions in a model of cardiac tissue. [19] Kalita I., Nizamieva A.A., Tsvelaya V., Kudryashova N., Agladze K.I. The influence of anisotropy on excitation wave propagationin neonatal rat cardiomyocytes monolayer. [19] Kamalova Y. The designing of vectorcardiograph prototype. [20] Kapelko V., Shirinsky V.P., Lakomkin V., Lukoshkova E., Gramovich V.,Vyborov O., Abramov A., Undrovinas N., Ermishkin V. Models of chronic heart failure with acute and gradual onset. [20] Khassanov I., Lomidze N.N., Revishvili A.S. Remote Patient Monitoring and Integration of Medical Data. [20] Kislukhin V. Markov chain for an indicator passing throughoutcardio-vascular system (CVS). [21] Konovalov P.V., Pravdin S., Solovyova O.E., Panfilov A.V. Influence of myocardial heterogeneity on scroll wave dynamicsin an axisymmetrical anatomical model of the left ventricle of thehuman heart. [21] Koshelev A., Pravdin S., Ushenin K.S., Bazhutina A.E. An improved analytical model of the cardiac left ventricle. [22] Lookin O., Protsenko Y.L. Sex-related effects of stretch on isometric twitch and Ca2+ transientin healthy and failing right ventricular myocardiumof adult and impuberal rats. [22] Moskvin A. Electron-conformational model of the ligand-activated ion channels. [22] Nezlobinsky T., Pravdin S., Katsnelson L.B. In silico comparison of the electrical propagation wave alongmyocardium fibers in the left ventricle wall vs. isolation. [23] Nigmatullina R.R., Zemskova S.N., Bilalova D.F., Mustafin A.A., Kuzmina O.I., Chibireva M.D., Nedorezova R.S. Valid method for estimation of pulmonary hypertention degreein children. [23] Parfenov A. Mathematical modeling of the cardiovascular systemunder the influence of environmental factors. [24] Pimenov V.G., Hendy A. Adaptivity of the alternating direction method for fractional reactiondiffusion equation with delay effects in electrocardiology. [24] Podgurskaya A.D., Krasheninnikova A., Tsvelaya V., Kudryashova N., Agladze K.I. Influence of alcohols on excitation wave propagationin neonatal rat ventricular cardiomyocyte monolayer. [24] Pravdin S. A mathematical model of the cardiac left ventricle anatomy and morphology. [24] Seemann G. Cause and effects of cardiac heterogeneity:insights from experimental and computational models. [25] Seryapina A.A., Shevelev O.B. Basic metabolomic patterns in early hypertensive rats: MRI study. [25] Shestakov A.P., Vasserman I.N., Shardakov I.N. Modeling of cardiac arrhythmia generation caused bypathological distribution of myocardial conductivity. [26] Shutko A.V., Gorbunov V.S., Nizamieva A.A., Guriya K.G., Agladze K.I. Contractile micro-constructs from cardiac tissue culturefor the research of autowave propagation in excitable systems. [26] Simakov S., Gamilov T., Kopylov Ph. Computational study of the haemodynamic significanceof the stenosis during multivessel coronary disease. [27] Syomin F., Zberiya M.V. A numerical simulation of changes in the performance of the leftventricle of the heart under various hemodynamic conditions. [27] Tsaturyan A. A simple model of cardiac muscle:mechanics, actin-myosin interaction and Ca-activation. [27] Tsvelaya V., Krasheninnikova A., Kudryashova N., Agladze K.I. Calcium-current dominated upstroke in severe hyperkalemia. [28] Ushenin K.S., Pravdin S., Chumarnaya T.V., Alueva Y.S., Solovyova O.E. Dynamics of scroll wave filaments in personalized modelsof the left ventricle of the human heart. [28] Vasserman I.N., Shardakov I.N., Shestakov A.P. Deriving of macroscopic intracellular conductivity of deformedmyocardium based on its microstructure. [28] Vassilevski Y.V., Pryamonosov R., Gamilov T. Personalized 3D models and applications. [29] Zun P.S., Hoekstra A., Anikina T.S. First results of fully coupled 3D models of in-stent restenosis. [29] BIOMECHANICS. EXPERIMENTAL AND MATHEMATICAL MODELSSBIOMECHANICS. EXPERIMENTAL AND MATHEMATICAL MODELS. EXPERIMENTAL AND MATHEMATICAL MODELS. [30] Balakin A., Kuznetsov D., Protsenko Y.L. The ‘length-tension’ loop in isolated myocardial preparations of theright ventricle of normal and hypertrophied hearts of male rats. [30] Belousova M.D., Kruchinina A.P., Chertopolokhov V.A. Automatic control model of the three-tier arm type manipulatorin the aimed-movement task. [30] Berestin D.K., Bazhenova A.E., Chernikov N.A., Vokhmina Y.V. Mathematical modeling of dynamics of development of Parkinson'sdisease on the tremor parameters. [31] Dubinin A.L., Nyashin Y.I., Osipenko M.A. Development of the biomechanical approach to tooth movementunder the orthodontic treatment. [31] Galochkina T., Volpert V. Reaction-diffusion waves in mathematical model of bloodcoagulation. [31] Golov A.V., Simakov S., Timme E.A. Mathematical modeling of alveolar ventilationand gas exchange during treadmill stress tests. [32] Gurev V., Rice J. Strain prediction in 3D finite element models of cardiac mechanics. [32] Kamaltdinov M.R. Simulation of digestion processes in antroduodenum:food particles dissolution in consideration of functional disorders. [33] Khamzin S., Kursanov A., Solovyova O.E. Load-dependence of the electromechanical function of myocardiumin a 1D tissue model. [33] Khokhlova A., Iribe G., Solovyova O.E Transmural gradient in mechanical properties of isolatedsubendocardial and subepicardial cardiomyocytes. [33] Kruchinin P.A. Optimal control problem and indexesof stabilometric "test with the visual step input". [34] Kruchinina A.P., Yakushev A.G. A study of the edge segments of saccadic eye trajectory. [34] Kursanov A., Khamzin S., Solovyova O.E. Load-dependence of intramyocardial slow force responsein heterogeneous myocardium. [35] Lisin R.V., Balakin A., Protsenko Y.L. Experimental study of the intramyocardial slow force response. [35] Melnikova N.B., Hoekstra A. The mechanics of a discrete multi-cellular model of arterial in‐stent restenosis. [35] Murashova D.S., Murashov S.A., Bogdan O.P., Muravieva O.V., Yugova S.O. Modelling of soft tissue deformation for static elastometry. [36] Nikitin V.N., Tverier V.M., Krotkikh A.A. Occlusion correction based on biomechanical modelling. [36] Nyashin Y.I., Lokhov V.A. Development of the “Virtual physiological human” concept. [37] Shulyatev A.F., Akulich Y.V., Akulich A.Y., Denisov A.S. 3D FEA simulation of the proximal human femur. 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