Modeling the chemoelectromechanical behavior of skeletal muscle using the parallel open-source software library OpenCMISS

An extensible, flexible, multiscale and multiphysics model for non-isometric skeletal muscle behavior is presented. The skeletal muscle chemoelectromechanical model is based on a bottom-up approach modeling the entire excitation-contraction pathway by strongly coupling a detailed biophysical model of a half-sarcomere to the propagation of action potentials along skeletal muscle fibers, and linking cellular parameters to a transversely isotropic continuum-mechanical constitutive equation describing the overall mechanical behavior of skeletal muscle tissue. Since the multiscale model exhibits separable time scales, a special emphasis is placed on employing computationally efficient staggered solution schemes. Further, the implementation builds on the open-source software library OpenCMISS and uses state-ofthe-art parallelization techniques taking advantage of the unique anatomical fiber architecture of skeletal muscles. OpenCMISS utilizes standardized data structures for geometrical aspects (FieldML) and cellular models (CellML). Both standards are designed to allow for a maximum on flexibility, reproducibility, and extensibility. The results demonstrate the model´s capability of simulating different aspects of non-isometric muscle contraction and to efficiently simulate the chemoelectromechanical behavior in complex skeletal muscles such as the tibialis anterior muscle

Modeling the Chemoelectromechanical Behavior of Skeletal Muscle Using the Parallel Open-Source Software Library OpenCMISS

An extensible, flexible, multiscale, and multiphysics model for nonisometric skeletal muscle behavior is presented. The skeletal muscle chemoelectromechanical model is based on a bottom-up approach modeling the entire excitation-contraction pathway by strongly coupling a detailed biophysical model of a half-sarcomere to the propagation of action potentials along skeletal muscle fibers and linking cellular parameters to a transversely isotropic continuum-mechanical constitutive equation describing the overall mechanical behavior of skeletal muscle tissue. Since the multiscale model exhibits separable time scales, a special emphasis is placed on employing computationally efficient staggered solution schemes. Further, the implementation builds on the open-source software library OpenCMISS and uses state-of-the-art parallelization techniques taking advantage of the unique anatomical fiber architecture of skeletal muscles. OpenCMISS utilizes standardized data structures for geometrical aspects (FieldML) and cellular models (CellML). Both standards are designed to allow for a maximum flexibility, reproducibility, and extensibility. The results demonstrate the model’s capability of simulating different aspects of nonisometric muscle contraction and efficiently simulating the chemoelectromechanical behavior in complex skeletal muscles such as the tibialis anterior muscle

The role of parvalbumin, sarcoplasmatic reticulum calcium pump rate, rates of cross-bridge dynamics, and ryanodine receptor calcium current on peripheral muscle fatigue: a simulation study

A biophysical model of the excitation-contraction pathway, which has previously been validated for slow-twitch and fast-twitch skeletal muscles, is employed to investigate key biophysical processes leading to peripheral muscle fatigue. Special emphasis hereby is on investigating how the model’s original parameter sets can be interpolated such that realistic behaviour with respect to contraction time and fatigue progression can be obtained for a continuous distribution of the model’s parameters across the muscle units, as found for the functional properties of muscles. The parameters are divided into 5 groups describing (i) the sarcoplasmatic reticulum calcium pump rate, (ii) the cross-bridge dynamics rates, (iii) the ryanodine receptor calcium current, (iv) the rates of binding of magnesium and calcium ions to parvalbumin and corresponding dissociations, and (v) the remaining processes. The simulations reveal that the first two parameter groups are sensitive to contraction time but not fatigue, the third parameter group affects both considered properties, and the fourth parameter group is only sensitive to fatigue progression. Hence, within the scope of the underlying model, further experimental studies should investigate parvalbumin dynamics and the ryanodine receptor calcium current to enhance the understanding of peripheral muscle fatigue

Coupled Systems of Differential-Algebraic and Kinetic Equations with Application to the Mathematical Modelling of Muscle Tissue

We consider a coupled system composed of a linear differential-algebraic equation (DAE) and a linear large-scale system of ordinary differential equations where the latter stands for the dynamics of numerous identical particles. Replacing the discrete particles by a kinetic equation for a particle density, we obtain in the mean-field limit the new class of partially kinetic systems. We investigate the influence of constraints on the kinetic theory of those systems and present necessary adjustments. We adapt the mean-field limit to the DAE model and show that index reduction and the mean-field limit commute. As a main result, we prove Dobrushin's stability estimate for linear systems. The estimate implies convergence of the mean-field limit and provides a rigorous link between the particle dynamics and their kinetic description. Our research is inspired by mathematical models for muscle tissue where the macroscopic behaviour is governed by the equations of continuum mechanics, often discretised by the finite element method, and the microscopic muscle contraction process is described by Huxley's sliding filament theory. The latter represents a kinetic equation that characterises the state of the actin-myosin bindings in the muscle filaments. Linear partially kinetic systems are a simplified version of such models, with focus on the constraints.Comment: 32 pages, 18 figure

In silico assessment of biomedical products: the conundrum of rare but not so rare events in two case studies

In silico clinical trials, defined as “The use of individualized computer simulation in the development or regulatory evaluation of a medicinal product, medical device, or medical intervention,” have been proposed as a possible strategy to reduce the regulatory costs of innovation and the time to market for biomedical products. We review some of the the literature on this topic, focusing in particular on those applications where the current practice is recognized as inadequate, as for example, the detection of unexpected severe adverse events too rare to be detected in a clinical trial, but still likely enough to be of concern. We then describe with more details two case studies, two successful applications of in silico clinical trial approaches, one relative to the University of Virginia/Padova simulator that the Food and Drug Administration has accepted as possible replacement for animal testing in the preclinical assessment of artificial pancreas technologies, and the second, an investigation of the probability of cardiac lead fracture, where a Bayesian network was used to combine in vivo and in silico observations, suggesting a whole new strategy of in silico-augmented clinical trials, to be used to increase the numerosity where recruitment is impossible, or to explore patients’ phenotypes that are unlikely to appear in the trial cohort, but are still frequent enough to be of concern

Chemo-elektro-mechanische Modellierung des neuromuskulären Systems

Body movement is the result of cascades of complex chemical, electrical, and mechanical processes taking place at different length and time scales. This thesis deals with the biophysical modelling of these processes. In detail, the generation of electrical signals in spinal motor neurons is investigated based on the Hodgkin-Huxley formalism. Next, the complex signaling pathway leading from electrical excitation to contraction and force generation of the muscle fibres is modelled. Based on a structural model of the muscle and the bidomain equations, a method is proposed to predict electromyographic signals, which are frequently recorded in the clinic and result from the propagation of electrical signals along the muscle fibres to induce the contraction. Extending this model by a continuum-mechanical approach, a multiscale model of the neuromuscular system is obtained that considers chemical, electrical, and mechanical properties and allows to predict force generation, muscle deformation, and the EMG signal during fixed-length and non-isometric contractions. The proposed framework can potentially be used as an in-silico laboratory to investigate changes in the behaviour resulting from pathological conditions or drug treatment.Bewegungen des Körpers sind das Ergebnis von komplexen chemischen, elektrischen und mechanischen Prozessen, die auf verschiedenen Zeit- und Längenskalen ablaufen. Die vorliegende Arbeit beschäftigt sich mit der biophysikalischen Modellierung dieser Prozesse. Im Einzelnen wird die Erzeugung von elektrischen Signalen in Motorneuronen des Rückenmarks basierend auf dem Hodgkin-Huxley-Formalismus untersucht. Danach wird der komplexe Signalweg von der elektrischen Erregung zur Kontraktion und Krafterzeugung in den Skelettmuskelfasern modelliert. Basierend auf einem strukturellen Modell des Muskels und den Bidomain-Gleichungen wird eine Methode vorgeschlagen, um elektromyographische Signale zu berechnen, die häufig in klinischen Anwendungen gemessen werden und aus der Ausbreitung von elektrischen Signalen entlang der Muskelfasern resultieren. Die Erweiterung dieses Modells um einen kontinuumsmechanischen Ansatz führt zu einem Modell des neuromuskulären Systems, das chemische, elektrische und mechanische Größen beinhaltet, und es erlaubt die Krafterzeugung, die Muskeldeformation und das EMG Signal während Kontraktionen bei festgehaltener Länge und nichtisometrischen Kontraktionen vorherzusagen. Das vorgeschlagene Modell könnte als virtuelles Labor verwendet werden, um Verhaltensänderungen zu untersuchen, die von Krankheiten oder einer medikamentösen Behandlung resultieren

Clinical Prognosis of Left Main Stenting ist Associated with Individual Response to Clopidogrel

Zusammenfassung Hintergrund: Die zweifache antithrombozytäre Therapie mit Aspirin und Clopidogrel ist zur Standardtherapie nach koronarer Stentimplantation geworden. Neuere Daten zeigen, dass im Ansprechen auf die antithrombozytäre Therapie eine hohe Variabilität besteht. Ziel dieser retrospektiven Studie war es den klinischen Verlauf von Patienten nach Hauptstammstenting zu untersuchen, unter Berücksichtigung des individuellen Ansprechens auf die antithrombozytäre Therapie. Material und Methoden: 30 Patienten (24 Männer, 6 Frauen, Altersdurchschnitt 67±11 Jahre, durchschnittliche linksventrikuläre Funktion 46±13 %) mit kritischer Hauptstammstenose, die als Risikopatienten für die operative Therapie durch ACVB angesehen wurden, wurden einem Hauptstammstenting unterzogen (geschützter Hauptstamm n=14, 47%). Alle Patienten erhielten eine Aufsättigungsdosis von 600mg Clopidogrel und 500mg Aspirin vor der Stentimplantation, gefolgt von einer Erhaltungsdosis von 150mg/d Clopidogrel für einen Monat und 75mg/d für weitere mindestens 11 Monate und zusätzlich 100mg/d Aspirin. Das Ansprechen auf Clopidogrel wurde mittels ADP (20µmol/l)-induzierter Aggregation beurteilt. Ergebnisse: Trotz zweifacher antithrombozytärer Therapie, wurde bei 40 % der Patienten eine erhöhte residuelle Thrombozytenaggregation gemessen. Vier Patienten (13,3%) starben 30±10 Monate nach der Intervention. Drei dieser Patienten (75%) wiesen eine erhöhte residuelle Thrombozytenaggregation auf, die über dem Median einer großen konsekutiv untersuchten Patientenkohorte lag. Eine erhöhte residuelle Thrombozytenaggregation wurde bei 28 % der Patienten gefunden, die nach der Intervention ereignisfrei blieben. Diskussion: Die Ergebnisse dieser retrospektiven Studie lassen darauf schließen, dass eine erhöhte residuelle Thrombozytenaggregation nach Hauptstammstenting mit schlechter klinischer Prognose assoziiert ist. Deswegen sollte bei Patienten die eine Stentimplantation in den Hauptstamm erhalten das Ansprechen auf die antithrombozytäre Therapie vor der perkutanen transluminalen Koronarintervention untersucht und individuell optimiert werden.Abstract Background: An efficient, combined antithrombotic treatment with clopidogrel and ASA is essential for the clinical prognosis of patients after coronary stent implantation. Recent data show that there is a high variability of response to antiplatelet therapy. Aim of this retrospective study was to evaluate the clinical course of patients after left main (LM) stenting with special regard to the individual response to antiplatelet treatment. Methods and Results: Thirty patients (24 men, 6 women, mean age 67±11 years, average left ventricular ejection fraction: 46±13%) with critical left main stenosis (LMS) who were considered as poor surgical candidates for CABG were treated with left main stenting (protected LM n=14, 47%). Indications for interventional therapy were cardiogenic shock (n=7), acute myocardial infarction (n=3), inoperability (n=13) or refusal of CABG (n=7). All patients received a loading dose of 600mg clopidogrel and 500mg ASA before stenting, followed by a maintenance dose of 150mg/day for 1 month and further 75mg/day for at least 11 months plus 100mg/day of aspirin. Response to clopidogrel was assessed by ADP (20µmol/L)-induced platelet aggregation. Patients were followed by telephone interview for at least 6 months. Despite combined antiplatelet therapy 40% of patients presented with enhanced residual platelet aggregation (>70% maximal aggregation response). In two of the patients presenting with cardiogenic shock, significant in-stent-restenosis occurred after intervention, leading to elective CABG surgery. Repeat coronary angiography revealed in stent-restenosis in 2 other patients with protected left main stenosis, leading to repeat left main stenting with drug eluting stent. Four patients (10%) died 30±10 months after intervention. Three of these 4 patients (75%) were classified as „low responder“ to clopidogrel. In all patients, who stayed event-free after intervention, the percentage of clopidogrel-„low-responder“ was 28%. Conclusions: The results of this retrospective study indicate that enhanced residual platelet aggregation after left main stenting is associated with poor clinical prognosis. Therefore the response to antiplatelet therapy should be evaluated before PCI and individually optimized in all patients that undergo stent implantation of the left main stem

Controlling Chaos—Forced van der Pol Equation

Nonlinear systems are typically linearized to permit linear feedback control design, but, in some systems, the nonlinearities are so strong that their performance is called chaotic, and linear control designs can be rendered ineffective. One famous example is the van der Pol equation of oscillatory circuits. This study investigates the control design for the forced van der Pol equation using simulations of various control designs for iterated initial conditions. The results of the study highlight that even optimal linear, time-invariant (LTI) control is unable to control the nonlinear van der Pol equation, but idealized nonlinear feedforward control performs quite well after an initial transient effect of the initial conditions. Perhaps the greatest strength of ideal nonlinear control is shown to be the simplicity of analysis. Merely equate coefficients order-of-differentiation insures trajectory tracking in steady-state (following dissipation of transient effects of initial conditions), meanwhile the solution of the time-invariant linear-quadratic optimal control problem with infinite time horizon is needed to reveal constant control gains for a linear-quadratic regulator. Since analytical development is so easy for ideal nonlinear control, this article focuses on numerical demonstrations of trajectory tracking error

Nonlinear Feed Forward Control of a Perturbed Satellite using ExtendedLeast Squares Adaptation and a Luenberger Observer

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