Cross-bridge Model Research Articles

Muscle short-range stiffness behaves like a maxwell element, not a spring: Implications for joint stability.

Muscles play a critical role in supporting joints during activities of daily living, owing, in part, to the phenomenon of short-range stiffness. Briefly, when an active muscle is lengthened, bound cross-bridges are stretched, yielding forces greater than what is predicted from the force length relationship. For this reason, short-range stiffness has been proposed as an attractive mechanism for providing joint stability. However, there has yet to be a forward dynamic simulation employing a cross-bridge model, that demonstrates this stabilizing role. Therefore, the purpose of this investigation was to test whether Huxley-type muscle elements, which exhibit short-range stiffness, can stabilize a joint while at constant activation. We analyzed the stability of an inverted pendulum (moment of inertia: 2.7 kg m2) supported by Huxley-type muscle models that reproduce the short-range stiffness phenomenon. We calculated the muscle forces that would provide sufficient short-range stiffness to stabilize the system based in minimizing the potential energy. Simulations consisted of a 50 ms long, 5 Nm square-wave perturbation, with numerical simulations carried out in ArtiSynth. Despite the initial analysis predicting shared activity of antagonist and agonist muscles to maintain stable equilibrium, the inverted pendulum model was not stable, and did not maintain an upright posture even with fully activated muscles. Our simulations suggested that short-range stiffness cannot be solely responsible for joint stability, even for modest perturbations. We argue that short-range stiffness cannot achieve stability because its dynamics do not behave like a typical spring. Instead, an alternative conceptual model for short-range stiffness is that of a Maxwell element (spring and damper in series), which can be obtained as a first-order approximation to the Huxley model. We postulate that the damping that results from short-range stiffness slows down the mechanical response and allows the central nervous system time to react and stabilize the joint. We speculate that other mechanisms, like reflexes or residual force enhancement/depression, may also play a role in joint stability. Joint stability is due to a combination of factors, and further research is needed to fully understand this complex system.

Analysis of metabolite and strain effects on cardiac cross-bridge dynamics using model linearisation techniques.

Multi-scale models of cardiac energetics are becoming crucial in better understanding the prevalent chronic diseases operating at the intersection of metabolic and cardiovascular dysfunction. Computationally efficient models of cardiac cross-bridge kinetics that are sensitive to changes in metabolite concentrations are necessary to simulate the effects of disease-induced changes in cellular metabolic state on cardiac mechanics across disparate spatial scales. While these models do currently exist, deeper analysis of how the modelling of metabolite effects and the assignment of strain dependence within the cross-bridge cycle affect the properties of the model is required. In this study, model linearisation techniques were used to simulate and interrogate the complex modulus of an ODE-based model of cross-bridge kinetics. Active complex moduli were measured from permeabilised rat cardiac trabeculae under five different metabolite conditions with varying ATP and Pi concentrations. Sensitivity to metabolites was incorporated into an existing three-state cross-bridge model using either a direct dependence or a rapid equilibrium approach. Combining the two metabolite binding methods with all possible locations of strain dependence within the cross-bridge cycle produced 64 permutations of the cross-bridge model. Using linear model analysis, these models were systematically explored to determine the effects of metabolite binding and their interaction with strain dependence on the frequency response of cardiac muscle. The results showed that the experimentally observed effects of ATP and Pi concentrations on the cardiac complex modulus could be attributed to their regulation of cross-bridge detachment rates. Analysis of the cross-bridge models revealed a mechanistic basis for the biochemical schemes which place Pi release following cross-bridge formation and ATP binding prior to cross-bridge detachment. In addition, placing strain dependence on the reverse rate of the cross-bridge power stroke produced the model which most closely matched the experimental data. From these analyses, a well-justified metabolite-sensitive model of rat cardiac cross-bridge kinetics is presented which is suitable for parameterisation with other data sets and integration with multi-scale cardiac models.

Dependence of cardiomyocyte force, velocity, and power generation on ATP concentration

Theoretical analysis and computer modeling of myocardial energy metabolism under physiological and heart failure conditions predicts that cytoplasmic ATP and ADP levels both fall roughly in proportion to reductions in total adenine nucleotide pool observed in heart failure. Assessing sub-maximal force and velocity in loaded myocardial muscle at MgATP levels in the range of 2 to 8 mM, Beard et al. ( Biophys. J. 2022. 121: 3213–3223) observed effects of MgATP on myocardial power generation that suggest that although maximal force and velocity are not substantially sensitive to differences in [MgATP] that occur in the normal versus failing myocardium, maximal power generation, which occurs at submaximal force and velocity, is sensitive to [MgATP]. Previously developed computational models are not able to reproduce the observed dependence on MgATP. The goals of the present study are to construct and analyze a computational model of muscle dynamics to analyze data on the dependence of maximal force, velocity, and power generation on [MgATP] in order to determine a potential mechanism to explain the MgATP-dependent phenomena. Model development and identification was guided by dynamic measurements on permeabilized mouse trabecular fibers. The data include force-velocity relation and time constant of tension development. The mathematical model used to simulate cardiomyocyte crossbridge mechanics was based on the previous crossbridge and calcium models from Tewari et al. (J Mol Cell Cardiol, 2016. 96: 11-25) and Campbell et al. (Biophys J, 2018. 115: 543-553). The developed model includes strain- and metabolite-dependent transition between attachment states, and ATP-dependent destabilization of the super-relaxed (SRX) myosin state. Model-based analysis of force and velocity dyanmics is consistent with the hypothesis that ATP assocition with the myosin protein influence the kinetics and thermodynamics of transitions between the SRX and disorded (DRX) states. Funding: Department of Veterans Affairs Merit Review Award I01BX000740 (A.J.B.) and National Heart, Lung, and Blood Institute grant R01 HL154624 (A.J.B., D.A.B.) This is the full abstract presented at the American Physiology Summit 2023 meeting and is only available in HTML format. There are no additional versions or additional content available for this abstract. Physiology was not involved in the peer review process.

Numerical instability of Hill-type muscle models.

Hill-type muscle models are highly preferred as phenomenological models for musculoskeletal simulation studies despite their introduction almost a century ago. The use of simple Hill-type models in simulations, instead of more recent cross-bridge models, is well justified since computationally 'light-weight'-although less accurate-Hill-type models have great value for large-scale simulations. However, this article aims to invite discussion on numerical instability issues of Hill-type muscle models in simulation studies, which can lead to computational failures and, therefore, cannot be simply dismissed as an inevitable but acceptable consequence of simplification. We will first revisit the basic premises and assumptions on the force-length and force-velocity relationships that Hill-type models are based upon, and their often overlooked but major theoretical limitations. We will then use several simple conceptual simulation studies to discuss how these numerical instability issues can manifest as practical computational problems. Lastly, we will review how such numerical instability issues are dealt with, mostly in an ad hoc fashion, in two main areas of application: musculoskeletal biomechanics and computer animation.

A mechanistic model of cross-bridge migration in RBC aggregation and disaggregation.

Red blood cells (RBCs) clump together under low flow conditions in a process called RBC aggregation, which can alter RBC perfusion in a microvascular network. As elevated RBC aggregation is commonly associated with cardiovascular and inflammatory diseases, a better understanding of aggregation is essential. Unlike RBC aggregation in polymer solutions which can be well explained by polymer depletion theory, plasma-mediated RBC aggregation has features that best match explanations with cross-bridging mechanisms. Previous studies have demonstrated the dominant role of fibrinogen (Fg) in promoting aggregate formation and recent cell-force spectroscopy (CFS) experiments on interacting RBC doublets in plasma have reported an inverse relationship between disaggregation force and the adhesive contact area between RBCs. This has led investigators to revisit the hypothesis of inter-RBC cross-bridging which involves cross-bridge migration under interfacial tension during the forced disaggregation of RBC aggregates. In this study, we developed the cross-bridge migration model (CBMM) in plasma that mechanistically represents the migrating cross-bridge hypothesis. Transport of mobile Fg cross-bridges (mFg) was calculated using a convection-diffusion transport equation with our novel introduction of convective cross-bridge drift that arises due to intercellular friction. By parametrically transforming the diffusivity of mFg in the CBMM, we were able to match experimental observations of both RBC doublet formation kinematics and RBC doublet disaggregation forces under optical tweezers tension. We found that non-specific cross-bridging promotes spontaneous growth of adhesion area between RBC doublets whereas specific cross-bridging tends to prevent adhesion area growth. Our CBMM was also able to correlate Fg concentration shifts from healthy population blood plasma to SLE (lupus) condition blood plasma with the observed increase in doublet disaggregation forces for the RBC doublets in SLE plasma.

Effect of active shortening and stretching on the rate of force re-development in rabbit psoas muscle fibres

The steady-state isometric force produced by skeletal muscle after active shortening and stretching is depressed and enhanced, respectively, compared with purely isometric force produced at corresponding final lengths and at the same level of activation. One hypothesis proposed to account for these force depression (FD) and force enhancement (FE) properties is a change in cross-bridge cycling kinetics. The rate of cross-bridge attachment (f) and/or cross-bridge detachment (g) may be altered following active shortening and active stretching, leading to FD and FE, respectively. Experiments elucidating cross-bridge kinetics in actively shortened and stretched muscle preparations and their corresponding purely isometric contractions have yet to be performed. The aim of this study was to investigate cross-bridge cycling kinetics of muscle fibres at steady-state following active shortening and stretching. This was done by determining muscle fibre stiffness and rate of active force redevelopment following a quick release-re-stretch protocol (kTR). Applying these measures to equations previously used in the literature for a two-state cross-bridge cycling model (attached/detached cross-bridges) allowed us to determine apparent f and g, the proportion of attached cross-bridges, and the force produced per cross-bridge. kTR, apparent f and g, the proportion of attached cross-bridges and the force produced per cross-bridge were significantly decreased following active shortening compared with corresponding purely isometric contractions, indicating a change in cross-bridge cycling kinetics. Additionally, we showed no change in cross-bridge cycling kinetics following active stretch compared with corresponding purely isometric contractions. These findings suggest that FD is associated with changes in cross-bridge kinetics, whereas FE is not.

Uncovering cross-bridge properties that underlie the cardiac active complex modulus using model linearisation techniques

The properties underlying cardiac cross-bridge kinetics can be characterised by a muscle’s active complex modulus. While the complex modulus can be described by a series of linear transfer functions, the biophysical mechanisms underlying these components are represented inconsistently among existing cross-bridge models. To address this, we examined the properties commonly implemented in cross-bridge models using model linearisation techniques and assessed their contributions to the complex modulus. From this analysis, we developed a biophysical model of cross-bridge kinetics that captures the three components of the active complex modulus: (1) the elastic modulus at low frequencies that arises from allowing the proportion of cross-bridges in the post-power stroke state to increase with sarcomere length, (2) the increase in elastic modulus at high frequencies that arises from the dependence of cross-bridge strain on sarcomere velocity, and (3) the negative viscous modulus which signifies the production of work by cross-bridges arises from either a sarcomere length or strain dependence, or both, on the rate of change of cross-bridge proportion in the post-power stroke state. While a model that includes all these features can theoretically reproduce the cardiac complex modulus, analysis of their transfer functions reveals that the relative contributions of these components are often not taken into account. As a result, the negative viscous component that signifies work production is not visible because the complex modulus is dominated by the effects of sarcomere velocity on cross-bridge strain.

Sensitivity of muscle force response of a two-state cross-bridge model to variations in model parameters.

Muscle models based on the cross-bridge theory (Huxley-type models) are frequently used to calculate muscle forces for different contractile conditions. Dynamic and nonlinear characteristics of muscle forces produced during isometric, concentric, and eccentric contractions can be represented to a limited extent by using cross-bridge models. Cross-bridge models use various parameters to simulate force responses. However, there remains uncertainty as to the effect of changes in model parameters on force responses in Huxley-type models. In this study, we aimed to analyze the sensitivity of force response to changes in model parameters in Huxley-type models. A two-state Huxley model was used to determine the cross-bridge attachment distributions and forces for shortening and lengthening contractions. Sensitivity of muscle force to changes in attachment rate, detachment rate, and cross-bridge binding distance was examined within a range of ±20% of the nominal value using Monte Carlo simulations. Changes in the detachment rate influenced the predicted muscle forces the most for lengthening contractions, while changes in attachment rate and binding distance affected forces the most for shortening contractions. These results show once more the asymmetry between shortening and lengthening contractions and the difficulty in using a single cross-bridge model to predict forces during shortening and elongation accurately.

A thermodynamically consistent monte carlo cross-bridge model with a trapping mechanism reveals the role of stretch activation in heart pumping.

Changes in intracellular calcium concentrations regulate heart beats. However, the decline in the left ventricular pressure during early diastole is much sharper than that of the Ca2+ transient, resulting in a rapid supply of blood to the left ventricle during the diastole. At the tissue level, cardiac muscles have a distinct characteristic, known as stretch activation, similar to the function of insect flight muscles. Stretch activation, which is a delayed increase in force following a rapid muscle length increase, has been thought to be related to autonomous control in these muscles. In this numerical simulation study, we introduced a molecular mechanism of stretch activation and investigated the role of this mechanism in the pumping function of the heart, using the previously developed coupling multiple-step active stiffness integration scheme for a Monte Carlo (MC) cross-bridge model and a bi-ventricular finite element model. In the MC cross-bridge model, we introduced a mechanism for trapping the myosin molecule in its post-power stroke state. We then determined the rate constants of transitions for trapping and escaping in a thermodynamically consistent manner. Based on our numerical analysis, we draw the following conclusions regarding the stretch activation mechanism: (i) the delayed force becomes larger than the original isometric force because the population of trapped myosin molecules and their average force increase after stretching; (ii) the delayed force has a duration of more than a few seconds owing to a fairly small rate constant of escape from the trapped state. For the role of stretch activation in heart pumping, we draw the following conclusions: (iii) for the regions in which the contraction force decreases earlier than the neighboring region in the end-systole phase, the trapped myosin molecules prevent further lengthening of the myocytes, which then prevents further shortening of neighboring myocytes; (iv) as a result, the contraction forces are sustained longer, resulting in a larger blood ejection, and their degeneration is synchronized.

Virgin Passive Colon Biomechanics and a Literature Review of Active Contraction Constitutive Models

The objective of this paper is to present our findings on the biomechanical aspects of the virgin passive anisotropic hyperelasticity of the porcine colon based on equibiaxial tensile experiments. Firstly, the characterization of the intestine tissues is discussed for a nearly incompressible hyperelastic fiber-reinforced Holzapfel–Gasser–Ogden constitutive model in virgin passive loading conditions. The stability of the evaluated material parameters is checked for the polyconvexity of the adopted strain energy function using positive eigenvalue constraints of the Hessian matrix with MATLAB. The constitutive material description of the intestine with two collagen fibers in the submucosal and muscular layer each has been implemented in the FORTRAN platform of the commercial finite element software LS-DYNA, and two equibiaxial tensile simulations are presented to validate the results with the optical strain images obtained from the experiments. Furthermore, this paper also reviews the existing models of the active smooth muscle cells, but these models have not been computationally studied here. The review part shows that the constitutive models originally developed for the active contraction of skeletal muscle based on Hill’s three-element model, Murphy’s four-state cross-bridge chemical kinetic model and Huxley’s sliding-filament hypothesis, which are mainly used for arteries, are appropriate for numerical contraction numerical analysis of the large intestine.

A Multiple Step Active Stiffness Integration Scheme to Couple a Stochastic Cross-Bridge Model and Continuum Mechanics for Uses in Both Basic Research and Clinical Applications of Heart Simulation.

In a multiscale simulation of a beating heart, the very large difference in the time scales between rapid stochastic conformational changes of contractile proteins and deterministic macroscopic outcomes, such as the ventricular pressure and volume, have hampered the implementation of an efficient coupling algorithm for the two scales. Furthermore, the consideration of dynamic changes of muscle stiffness caused by the cross-bridge activity of motor proteins have not been well established in continuum mechanics. To overcome these issues, we propose a multiple time step scheme called the multiple step active stiffness integration scheme (MusAsi) for the coupling of Monte Carlo (MC) multiple steps and an implicit finite element (FE) time integration step. The method focuses on the active tension stiffness matrix, where the active tension derivatives concerning the current displacements in the FE model are correctly integrated into the total stiffness matrix to avoid instability. A sensitivity analysis of the number of samples used in the MC model and the combination of time step sizes confirmed the accuracy and robustness of MusAsi, and we concluded that the combination of a 1.25 ms FE time step and 0.005 ms MC multiple steps using a few hundred motor proteins in each finite element was appropriate in the tradeoff between accuracy and computational time. Furthermore, for a biventricular FE model consisting of 45,000 tetrahedral elements, one heartbeat could be computed within 1.5 h using 320 cores of a conventional parallel computer system. These results support the practicality of MusAsi for uses in both the basic research of the relationship between molecular mechanisms and cardiac outputs, and clinical applications of perioperative prediction.

Force-velocity and tension transient measurements from Drosophila jump muscle reveal the necessity of both weakly-bound cross-bridges and series elasticity in models of muscle contraction

Muscle contraction is a fundamental biological process where molecular interactions between the myosin molecular motor and actin filaments result in contraction of a whole muscle, a process spanning size scales differing in eight orders of magnitude. Since unique behavior is observed at every scale in between these two extremes, to fully understand muscle function it is vital to develop multi-scale models. Based on simulations of classic measurements of muscle heat generation as a function of work, and shortening rate as a function of applied force, we hypothesize that a model based on molecular measurements must be modified to include a weakly-bound interaction between myosin and actin in order to fit measurements at the muscle fiber or whole muscle scales. This hypothesis is further supported by the model's need for a weakly-bound state in order to qualitatively reproduce the force response that occurs when a muscle fiber is rapidly stretched a small distance. We tested this hypothesis by measuring steady-state force as a function of shortening velocity, and the force transient caused by a rapid length step in Drosophila jump muscle fibers. Then, by performing global parameter optimization, we quantitatively compared the predictions of two mathematical models, one lacking a weakly-bound state and one with a weakly-bound state, to these measurements. Both models could reproduce our force-velocity measurements, but only the model with a weakly-bound state could reproduce our force transient measurements. However, neither model could concurrently fit both measurements. We find that only a model that includes weakly-bound cross-bridges with force-dependent detachment and an elastic element in series with the cross-bridges is able to fit both of our measurements. This result suggests that the force response after stretch is not a reflection of distinct steps in the cross-bridge cycle, but rather arises from the interaction of cross-bridges with a series elastic element. Additionally, the model suggests that the curvature of the force-velocity relationship arises from a combination of the force-dependence of weakly- and strongly-bound cross-bridges. Overall, this work presents a minimal cross-bridge model that has predictive power at the fiber level.

Stretch-Activation in Drosophila Jump Muscle Fibers is Described by a Minimal Cross-Bridge Model that Includes Force-Dependent Weakly-Bound Cross-Bridges and Series Elasticity

Stretch-Activation in Drosophila Jump Muscle Fibers is Described by a Minimal Cross-Bridge Model that Includes Force-Dependent Weakly-Bound Cross-Bridges and Series Elasticity

MODELING AND SIMULATION OF SKELETAL MUSCLE BASED ON METABOLISM PHYSIOLOGY

Skeletal muscle energy metabolism plays a very important role in controlling movement of the whole body and has important theoretical guidance for making exercise training plans and losing weight. In this paper, we developed a mathematical model of skeletal muscle excitation–contraction pathway based on the energy metabolism that links excitation to contraction to explore the effects of different metabolic energy systems on calcium ion changes and the force during skeletal muscle contraction. In this paper, a membrane potential model, a calcium cycle model, a cross-bridge dynamics model and an energy metabolism model were established. Finally, the physiological phenomenon of calcium ion transport and calcium ion concentration change of the sarcoplasm was simulated. The results show that the phosphagen system has the fastest metabolic rate and the phosphagen system has the largest impact on the explosive power of skeletal muscle exercise. The specific characteristics of the three metabolic energy systems supporting skeletal muscle movement in vivo were also analyzed in detail.

A thermodynamic transient cross-bridge model for prediction of contractility and remodelling of the ventricle

Cardiac hypertrophy is an adaption of the heart to a change in cardiovascular loading conditions. The current understanding is that progression may be stress or strain driven, but the multi-scale nature of the cellular remodelling processes have yet to be uncovered. In this study, we develop a model of the contractile left ventricle, with the active cell tension described by a thermodynamically motivated cross-bridge cycling model. Simulation of the transient recruitment of myosin results in correct patterns of ventricular pressure predicted over a cardiac cycle. We investigate how changes in tissue loading and associated deviations in transient force generation can drive restructuring of cellular myofibrils in the heart wall. Our thermodynamic framework predicts in-series sarcomere addition (eccentric remodelling) in response to volume overload, and sarcomere addition in parallel (concentric remodelling) in response to valve and signalling disfunction. This framework provides a significant advance in the current understanding of the fundamental sub-sarcomere level biomechanisms underlying cardiac remodelling. Simulations reveal that pathological tissue loading conditions can significantly alter actin-myosin cross-bridge cycling over the course of the cardiac cycle. The resultant variation in sarcomere stress pushes an imbalance between the internal free energy of the myofibril and that of unbound contractile proteins, initiating remodelling. The link between cross-bridge thermodynamics and myofibril remodelling proposed in this study may significantly advance current understanding of cardiac disease onset.

Modeling and simulation of excitation- contraction coupling of fast-twitch skeletal muscle fibers.

BACKGROUND: The current excitation-contraction coupling model of fast-twitch skeletal muscle fibers cannot completely simulate the excitation-contraction process.OBJECTIVE: To solve this problem, this study proposes an excitation-contraction model of fast-twitch skeletal muscle fibers based on the physiological structure and contractile properties of half-sarcomeres.METHODS: The model includes the action potential model of fast-twitch fiber membranes and transverse tubule membranes, the cycle model of in myofibril, the cross-bridge cycle model, and the fatigue model of metabolism.RESULTS: Finally, detailed analyses of the results from the simulation are conducted using the Simulink toolbox in MATLAB. Two conditions, non-coincidence and coincidence, are analyzed for both the thick and thin myofilaments.CONCLUSIONS: The simulation results of two groups of models are the same as the previous research results, which validates the accuracy of models.

A Coupled Electromechanical Myocyte Model to Assess the Effects of 2‐deoxy‐ATP on Contractile Function in the Heart

IntroductionHeart failure (HF) remains a significant cause of morbidity, mortality, and medical costs. HF is characterized by reduced contractile function and inability of the heart to pump sufficient blood to meet the body’s demands. Existing treatments for HF do not permanently restore cardiac function and can lead to side effects such as impaired ventricular relaxation. 2‐deoxy‐ATP (dATP), a novel heart failure therapeutic, has been shown to increase contractile function while enhancing relaxation [1]. Previous studies have shown that dATP increases the rate of crossbridge cycling [2]. It has also been shown that dATP acts on the sarcoplasmic reticulum ATPase (SERCA), the pump responsible for removing calcium (Ca2+) from the cytosol, which could explain the enhanced relaxation kinetics seen experimentally [3]. However, the mechanism of dATP is still not fully understood. Further, it is not clear whether the increased rate of crossbridge cycling with dATP treatment could aggravate energy starvation in HF.MethodsTo assess the full mechanism of dATP at the cellular level, we utilized a myocyte model containing several ion channels, including SERCA [4]. We coupled this model to a mitochondria model to investigate whether dATP treatment aggravates energy starvation by tracking ATP, ADP, Pi, and oxygen concentrations over time [5]. We also coupled the myocyte model to a previously developed 5 state Markov model of crossbridge cycling, which captures regulation of contraction via Ca2+ binding to troponin [2]. The crossbridge cycling model was modified to capture the effects of sarcomere length on Ca2+ sensitivity. dATP treatment was simulated by adjusting the ATP and Ca2+ binding rates in the SERCA model and the rate of crossbridge cycling in the sarcomere model based on previous studies [2, 3].Results and ConclusionsWe found that the combined effects of dATP on both SERCA and the sarcomere within the coupled myocyte model could explain the increase in fractional shortening and time to 50% and 90% relaxation of the Ca2+ transient seen experimentally more accurately than either model alone. Additionally, we found no evidence that dATP aggravates energy starvation, affirming dATP as a promising therapeutic for HF.Support or Funding InformationNIH HLT32 TG

Ratchet-integrated pneumatic actuator (RIPA): a large-stroke soft linear actuator inspired by sarcomere muscle contraction

Pneumatic artificial muscles (PAMs) have a wide range of robotics applications, especially in soft robots, for their ability to generate linear force and displacement with the soft, lightweight, compact, and safe characteristics as well as high power densities. However, the compressibility of the air causes a spring-like behavior of PAMs, resulting in several common issues of limited stroke, load-dependent stroke lengths, difficulty in maintaining their length against disturbance, and necessity of accurate pressure control system. To address these issues, this study borrows inspiration from a biological soft linear actuator, a muscle, and proposes a ratchet-integrated pneumatic actuator (RIPA). Utilizing two pawls integrated at both ends of a McKibben muscle and a flexible rack inserted in the middle of the muscle, the RIPA achieves a large stroke length by accumulating displacements from multiple small strokes of the McKibben muscle by repeating the cycle of pressurization and depressurization. This cycle mimics the cross-bridge model of a sarcomere, a basic unit of a skeletal muscle, in which a muscle accumulates nanoscale strokes of myosin head motors to generate large strokes. The synergy between a PAM and the inspiration from a sarcomere enabled a large-stroke soft linear actuator that can generate independent strokes from loads. The proposed actuator is not only capable of maintaining its length against unexpected mechanical disturbances but also controllable with a relatively simple system. In this paper, we describe the design of the RIPA and provide analytical models to predict the stroke length and the period per cycle for actuation. We also present experimental results for characterization and comparison with model predictions.

Computational prediction of the effect of D172N KCNJ2 mutation on ventricular pumping during sinus rhythm and reentry.

The understanding of cardiac arrhythmia under genetic mutations has grown in interest among researchers. Previous studies focused on the effect of the D172N mutation on electrophysiological behavior. In this study, we analyzed not only the electrophysiological activity but also the mechanical responses during normal sinus rhythm and reentry conditions by using computational modeling. We simulated four different ventricular conditions including normal case of ten Tusscher model 2006 (TTM), wild-type (WT), heterozygous (WT/D172N), and homozygous D172N mutation. The 2D simulation result (in wire-shaped mesh) showed the WT/D172N and D172N mutation shortened the action potential duration by 14%, and by 23%, respectively. The 3D electrophysiological simulation results showed that the electrical wavelength between TTM and WT conditions were identical. Under sinus rhythm condition, the WT/D172N and D172N reduced the pumping efficacy with a lower left ventricle (LV) and aortic pressures, stroke volume, ejection fraction, and cardiac output. Under the reentry conditions, the WT condition has a small probability of reentry. However, in the event of reentry, WT has shown the most severe condition. Furthermore, we found that the position of the rotor or the scroll wave substantially influenced the ventricular pumping efficacy during arrhythmia. If the rotor stays in the LV, it will cause very poor pumping performance. Graphical Abstract A model of a ventricular electromechanical system. This whole model was established to observe the effect of D172N KCNJ2 mutation on ventricular pumping behavior during sinus rhythm and reentry conditions. The model consists of two components; electrical component and mechanical component. The electrophysiological model based on ten Tusscher et al. with the IK1 D172N KCNJ2 mutation, and the myofilament dynamic (cross-bridge) model based on Rice et al. study. The 3D electrical component is a ventricular geometry based on MRI which composed of nodes representing single-cell with electrophysiological activation. The 3D ventricular mechanic is a finite element mesh composed of single-cells myofilament dynamic model. Both components were coupled with Ca2+ concentration. We used Gaussian points for the calcium interpolation from the electrical mesh to the mechanical mesh.

The Huxley crossbridge model as the basic mechanism for airway smooth muscle contraction.

The cyclic interaction between myosin crossbridges and actin filaments underlies smooth muscle contraction. Phosphorylation of the 20-kDa myosin light chain (MLC20) is a crucial step in activating the crossbridge cycle. Our current understanding of smooth muscle contraction is based on observed correlations among MLC20 phosphorylation, maximal shortening velocity (Vmax), and isometric force over the time course of contraction. However, during contraction there are changes in the extent of phosphorylation of many additional proteins as well as changes in activation of enzymes associated with the signaling pathways. As a consequence, the mechanical manifestation of muscle contraction is likely to change with time. To simplify the study of these relationships, we measured the mechanical properties of airway smooth muscle at different levels of MLC20 phosphorylation at a fixed time during contraction. A simple correlation emerged when time-dependent variables were fixed. MLC20 phosphorylation was found to be directly and linearly correlated with the active stress, stiffness, and power of the muscle; the observed weak dependence of Vmax on MLC20 phosphorylation could be explained by the presence of an internal load in the muscle preparation. These results can be entirely explained by the Huxley crossbridge model. We conclude that when the influence of time-dependent events during contraction is held constant, the basic crossbridge mechanism in smooth muscle is the same as that in striated muscle.