Myocardial relaxation is accelerated by fast stretch, not reduced afterload

Strain rate of stretch affects crossbridge detachment during relaxation of intact cardiac trabeculae

Mechanical Control of Relaxation refers to the dependence of myocardial relaxation on the strain rate just prior to relaxation, but the mechanisms of enhanced relaxation are not well characterized. This study aimed to characterize how crossbridge kinetics varied with strain rate and time-to-stretch as the myocardium relaxed in early diastole. Ramp-stretches of varying rates (amplitude = 1% muscle length) were applied to intact rat cardiac trabeculae following a load-clamp at 50% of the maximal developed twitch force, which provides a first-order estimate of ejection and coupling to an afterload. The resultant stress-response was calculated as the difference between the time-dependent stress profile between load-clamped twitches with and without a ramp-stretch. The stress-response exhibited features of the step-stretch response of activated, permeabilized myocardium, such as distortion-dependent peak stress, rapid force decay related to crossbridge detachment, and stress recovery related to crossbridge recruitment. The peak stress was strain rate dependent, but the minimum stress and the time-to-minimum stress values were not. The initial rapid change in the stress-response indicates enhanced crossbridge detachment at higher strain rates during relaxation in intact cardiac trabeculae. Physiologic considerations, such as time-varying calcium, are discussed as potential limitations to fitting these data with traditional distortion-recruitment models of crossbridge activity.

Mechanical Control of Relaxation using Intact Cardiac Trabeculae

Diastolic dysfunction is a common phenotype across cardiovascular disease presentations. In addition to elevated cardiac stiffness (elevated left ventricular end-diastolic pressure), impaired cardiac relaxation is a key diagnostic indicator of diastolic dysfunction. While relaxation requires the removal of cytosolic calcium and deactivation of sarcomeric thin filaments, targeting such mechanisms has yet to provide effective treatments. Mechanical mechanisms, such as blood pressure (i.e., afterload), have been theorized to modify relaxation. Recently, we showed that modifying the strain rate of a stretch, not afterload, was both necessary and sufficient to modify the subsequent relaxation rate of myocardial tissue. The strain rate dependence of relaxation, called the mechanical control of relaxation (MCR), can be assessed using intact cardiac trabeculae. This protocol describes the preparation of a small animal model, experimental system and chamber, isolation of the heart and subsequent isolation of a trabecula, preparation of the experimental chamber, and experimental and analysis protocols. Evidence for lengthening strains in the intact heart suggests that MCR might provide new arenas for better characterization of pharmacological treatments, along with a method to assess myofilament kinetics in intact muscles. Therefore, studying the MCR may elucidate a path to novel approaches and new frontiers in the treatment of heart failure.

Molecular regulation of stretch activation

Stretch activation is defined as a delayed increase in force after rapid stretches. Although there is considerable evidence for stretch activation in isolated cardiac myofibrillar preparations, few studies have measured mechanisms of stretch activation in mammalian skeletal muscle fibers. We measured stretch activation following rapid step stretches [∼1%-4% sarcomere length (SL)] during submaximal Ca2+ activations of rat permeabilized slow-twitch skeletal muscle fibers before and after protein kinase A (PKA), which phosphorylates slow myosin binding protein-C. PKA significantly increased stretch activation during low (∼25%) Ca2+ activation and accelerated rates of delayed force development (kef) during both low and half-maximal Ca2+ activation. Following the step stretches and subsequent force development, fibers were rapidly shortened to original sarcomere length, which often elicited a shortening-induced transient force overshoot. After PKA, step shortening-induced transient force overshoot increased ∼10-fold following an ∼4% SL shortening during low Ca2+ activation levels. kdf following step shortening also increased after PKA during low and half-maximal Ca2+ activations. We next investigated thin filament regulation of stretch activation. We tested the interplay between cardiac troponin I (cTnI) phosphorylation at the canonical PKA and novel tyrosine kinase sites on stretch activation. Native slow-skeletal Tn complexes were exchanged with recombinant human cTn complex with different human cTnI N-terminal pseudo-phosphorylation molecules: 1) nonphosphorylated wild type (WT), 2) the canonical S22/23D PKA sites, 3) the tyrosine kinase Y26E site, and 4) the combinatorial S22/23D + Y26E cTnI. All three pseudo-phosphorylated cTnIs elicited greater stretch activation than WT. Following stretch activation, a new, elevated stretch-induced steady-state force was reached with pseudo-phosphorylated cTnI. Combinatorial S22/23D + Y26E pseudo-phosphorylated cTnI increased kdf. These results suggest that slow-skeletal myosin binding protein-C (sMyBP-C) phosphorylation modulates stretch activation by a combination of cross-bridge recruitment and faster cycling kinetics, whereas cTnI phosphorylation regulates stretch activation by both redundant and synergistic mechanisms; and, taken together, these sarcomere phosphoproteins offer precision targets for enhanced contractility.

Inorganic phosphate accelerates cardiac myofilament relaxation in response to lengthening

Myocardial relaxation in late systole is enhanced by increasing velocities of lengthening. Given that inorganic phosphate (Pi) can rebind to the force-producing myosin enzyme prior to MgADP release and hasten crossbridge detachment, we hypothesized that myocardial relaxation in late systole would be further enhanced by lengthening in the presence of Pi. Wistar rat left ventricular papillary muscles were attached to platinum clips, placed between a force transducer and a length motor at room temperature, and bathed in Krebs solution with 1.8 mM Ca²⁺ and varying Pi of 0, 1, 2, and 5 mM. Tension transients were elicited by electrical stimulation at 1 Hz. Peak tension was significantly enhanced by Pi: 0.593 ± 0.088 mN mm⁻² at 0 mM Pi and 0.817 ± 0.159 mN mm⁻² at 5 mM Pi (mean ± SEM, p < 0.01 by ANCOVA). All temporal characteristics of the force transient were significantly shortened with increasing Pi, e.g., time-to-50% recovery was shortened from 305 ± 14 ms at 0 mM Pi to 256 ± 10 ms at 5 mM Pi (p < 0.01). A 1% lengthening stretch with varying duration of 10–200 ms was applied at time-to-50% recovery during the descending phase of the force transient. Matching lengthening stretches were also applied when the muscle was not stimulated, thus providing a control for the passive viscoelastic response. After subtracting the passive from the active force response, the resulting myofilament response demonstrated features of faster myofilament relaxation in response to the stretch. For example, time-to-70% relaxation with 100 ms lengthening duration was shortened by 8.8 ± 6.8 ms at 0 Pi, 19.6 ± 4.8* ms at 1 mM Pi, 31.0 ± 5.6* ms at 2 Pi, and 25.6 ± 5.3* ms at 5 mM Pi (*p < 0.01 compared to no change). Using skinned myocardium, half maximally calcium-activated myofilaments underwent a 1% quick stretch, and the tension response was subjected to analysis for sensitivity of myosin detachment rate to stretch, g₁, at various Pi concentrations. The parameter g₁ was enhanced from 15.39 ± 0.35 at 0 Pi to 22.74 ± 1.31 s⁻¹/nm at 8 Pi (p < 0.01). Our findings suggest that increasing Pi at the myofilaments enhances lengthening-induced relaxation by elevating the sensitivity of myosin crossbridge detachment due to lengthening and thus speed the transition from late-systole to early-diastole.

Slower shortening kinetics of cardiac muscle performing Windkessel work‑loops increases mechanical efficiency

Conventional experimental methods for studying cardiac muscle in vitro often do not expose the tissue preparations to a mechanical impedance that resembles the in vivo hemodynamic impedance dictated by the arterial system. That is, the afterload in work‑loop contraction is conventionally simplified to be constant throughout muscle shortening, and at a magnitude arbitrarily defined. This conventional afterload does not capture the time‑varying interaction between the left ventricle and the arterial system. We have developed a contraction protocol for isolated tissue experiments that allows the afterload to be described within a Windkessel framework that captures the mechanics of the large arteries. We aim to compare the energy expenditure of cardiac muscle undergoing the two contraction protocols: conventional versus Windkessel loading. Isolated rat left‑ventricular trabeculae were subjected to the two force-length work‑loop contractions. Mechanical work and heat liberation were assessed, and mechanical efficiency quantified, over wide ranges of afterloads or peripheral resistances. Both extent of shortening and heat output were unchanged between protocols, but peak shortening velocity was 39.0 % lower and peak work output was 21.8 % greater when muscles contracted against the Windkessel afterload than against the conventional isotonic afterload. The greater work led to a 25.2 % greater mechanical efficiency. Our findings demonstrate that the mechanoenergetic performance of cardiac muscles in vitro may have been previously constrained by the conventional, arbitrary, loading method. A Windkessel loading protocol, by contrast, unleashes more cardiac muscle mechanoenergetic potential, where the slower shortening increases efficiency in performing mechanical work.

Preparing Excitable Cardiac Papillary Muscle and Cardiac Slices for Functional Analyses

While the reductionist approach has been fruitful in understanding the molecular basis of muscle function, intact excitable muscle preparations are still important as experimental model systems. We present here methods that are useful for preparing cardiac papillary muscle and cardiac slices, which represent macroscopic experimental model systems with fully intact intercellular and intracellular structures. The maintenance of these in vivo structures for experimentation in vitro have made these model systems especially useful for testing the functional effects of protein mutations and pharmaceutical candidates. We provide solutions recipes for dissection and recording, instructions for removing and preparing the cardiac papillary muscles, as well as instruction for preparing cardiac slices. These instructions are suitable for beginning experimentalists but may be useful for veteran muscle physiologists hoping to reacquaint themselves with macroscopic functional analyses.

Critical Evaluation of Current Hypotheses for the Pathogenesis of Hypertrophic Cardiomyopathy

Hereditary hypertrophic cardiomyopathy (HCM), due to mutations in sarcomere proteins, occurs in more than 1/500 individuals and is the leading cause of sudden cardiac death in young people. The clinical course exhibits appreciable variability. However, typically, heart morphology and function are normal at birth, with pathological remodeling developing over years to decades, leading to a phenotype characterized by asymmetric ventricular hypertrophy, scattered fibrosis and myofibrillar/cellular disarray with ultimate mechanical heart failure and/or severe arrhythmias. The identity of the primary mutation-induced changes in sarcomere function and how they trigger debilitating remodeling are poorly understood. Support for the importance of mutation-induced hypercontractility, e.g., increased calcium sensitivity and/or increased power output, has been strengthened in recent years. However, other ideas that mutation-induced hypocontractility or non-uniformities with contractile instabilities, instead, constitute primary triggers cannot yet be discarded. Here, we review evidence for and criticism against the mentioned hypotheses. In this process, we find support for previous ideas that inefficient energy usage and a blunted Frank–Starling mechanism have central roles in pathogenesis, although presumably representing effects secondary to the primary mutation-induced changes. While first trying to reconcile apparently diverging evidence for the different hypotheses in one unified model, we also identify key remaining questions and suggest how experimental systems that are built around isolated primarily expressed proteins could be useful.

Effect of Myosin Isoforms on Cardiac Muscle Twitch of Mice, Rats and Humans

To understand how pathology-induced changes in contractile protein isoforms modulate cardiac muscle function, it is necessary to quantify the temporal-mechanical properties of contractions that occur under various conditions. Pathological responses are much easier to study in animal model systems than in humans, but extrapolation between species presents numerous challenges. Employing computational approaches can help elucidate relationships that are difficult to test experimentally by translating the observations from rats and mice, as model organisms, to the human heart. Here, we use the spatially explicit MUSICO platform to model twitch contractions from rodent and human trabeculae collected in a single laboratory. This approach allowed us to identify the variations in kinetic characteristics of α- and β-myosin isoforms across species and to quantify their effect on cardiac muscle contractile responses. The simulations showed how the twitch transient varied with the ratio of the two myosin isoforms. Particularly, the rate of tension rise was proportional to the fraction of α-myosin present, while the β-isoform dominated the rate of relaxation unless α-myosin was >50%. Moreover, both the myosin isoform and the Ca2+ transient contributed to the twitch tension transient, allowing two levels of regulation of twitch contraction.

FiberSim: A flexible open-source model of myofilament-level contraction

FiberSim is a flexible open-source model of myofilament-level contraction. The code uses a spatially explicit technique, meaning that it tracks the position and status of each contractile molecule within the lattice framework. This allows the model to simulate some of the mechanical effects modulated by myosin-binding protein C, as well as the dose dependence of myotropes and the effects of varying isoform expression levels. This paper provides a short introduction to FiberSim and presents simulations of tension-pCa curves with and without regulation of thick and thin filament activation by myosin-binding protein C. A myotrope dose-dependent response as well as slack/re-stretch maneuvers to assess rates of tension recovery are also presented. The software was designed to be flexible (the user can define their own model and/or protocol) and computationally efficient (simulations can be performed on a regular laptop). We hope that other investigators will use FiberSim to explore myofilament level mechanisms and to accelerate research focusing on the contractile properties of sarcomeres.

Reduced preload increases Mechanical Control (strain-rate dependence) of Relaxation by modifying myosin kinetics

Rapid myocardial relaxation is essential in maintaining cardiac output, and impaired relaxation is an early indicator of diastolic dysfunction. While the biochemical modifiers of relaxation are well known to include calcium handling, thin filament activation, and myosin kinetics, biophysical and biomechanical modifiers can also alter relaxation. We have previously shown that the relaxation rate is increased by an increasing strain rate, not a reduction in afterload. The slope of the relaxation rate to strain rate relationship defines Mechanical Control of Relaxation (MCR). To investigate MCR further, we performed in vitro experiments and computational modeling of preload-adjustment using intact rat cardiac trabeculae. Trabeculae studies are often performed using isometric (fixed-end) muscles at optimal length (Lo, length producing maximal developed force). We determined that reducing muscle length from Lo increased MCR by 20%, meaning that reducing preload could substantially increase the sensitivity of the relaxation rate to the strain rate. We subsequently used computational modeling to predict mechanisms that might underlie this preload-dependence. Computational modeling was not able to fully replicate experimental data, but suggested that thin-filament properties are not sufficient to explain preload-dependence of MCR because the model required the thin-filament to become more activated at reduced preloads. The models suggested that myosin kinetics may underlie the increase in MCR at reduced preload, an effect that can be enhanced by force-dependence. Relaxation can be modified and enhanced by reduced preload. Computational modeling implicates myosin-based targets for treatment of diastolic dysfunction, but further model refinements are needed to fully replicate experimental data.

Need for Speed: The Importance of Physiological Strain Rates in Determining Myocardial Stiffness

The heart is viscoelastic, meaning its compliance is inversely proportional to the speed at which it stretches. During diastolic filling, the left ventricle rapidly expands at rates where viscoelastic forces impact ventricular compliance. In heart disease, myocardial viscoelasticity is often increased and can directly impede diastolic filling to reduce cardiac output. Thus, treatments that reduce myocardial viscoelasticity may provide benefit in heart failure, particularly for patients with diastolic heart failure. Yet, many experimental techniques either cannot or do not characterize myocardial viscoelasticity, and our understanding of the molecular regulators of viscoelasticity and its impact on cardiac performance is lacking. Much of this may stem from a reliance on techniques that either do not interrogate viscoelasticity (i.e., use non-physiological rates of strain) or techniques that compromise elements that contribute to viscoelasticity (i.e., skinned or permeabilized muscle preparations that compromise cytoskeletal integrity). Clinically, cardiac viscoelastic characterization is challenging, requiring the addition of strain-rate modulation during invasive hemodynamics. Despite these challenges, data continues to emerge demonstrating a meaningful contribution of viscoelasticity to cardiac physiology and pathology, and thus innovative approaches to characterize viscoelasticity stand to illuminate fundamental properties of myocardial mechanics and facilitate the development of novel therapeutic strategies.

Enhancing diastolic function by strain-dependent detachment of cardiac myosin crossbridges

The force response of cardiac muscle undergoing a quick stretch is conventionally interpreted to represent stretching of attached myosin crossbridges (phase 1) and detachment of these stretched crossbridges at an exponential rate (phase 2), followed by crossbridges reattaching in increased numbers due to an enhanced activation of the thin filament (phases 3 and 4). We propose that, at least in mammalian cardiac muscle, phase 2 instead represents an enhanced detachment rate of myosin crossbridges due to stretch, phase 3 represents the reattachment of those same crossbridges, and phase 4 is a passive-like viscoelastic response with power-law relaxation. To test this idea, we developed a two-state model of crossbridge attachment and detachment. Unitary force was assigned when a crossbridge was attached, and an elastic force was generated when an attached crossbridge was displaced. Attachment rate, f(x), was spatially distributed with a total magnitude f₀. Detachment rate was modeled as g(x) = g₀+ g₁x, where g₀ is a constant and g₁ indicates sensitivity to displacement. The analytical solution suggested that the exponential decay rate of phase 2 represents (f₀ + g₀) and the exponential rise rate of phase 3 represents g₀. The depth of the nadir between phases 2 and 3 is proportional to g₁. We prepared skinned mouse myocardium and applied a 1% stretch under varying concentrations of inorganic phosphate (Pi). The resulting force responses fitted the analytical solution well. The interpretations of phases 2 and 3 were consistent with lower f₀ and higher g₀ with increasing Pi. This novel scheme of interpreting the force response to a quick stretch does not require enhanced thin-filament activation and suggests that the myosin detachment rate is sensitive to stretch. Furthermore, the enhanced detachment rate is likely not due to the typical detachment mechanism following MgATP binding, but rather before MgADP release, and may involve reversal of the myosin power stroke.

Contraction-relaxation coupling is unaltered by exercise training and infarction in isolated canine myocardium

The two main phases of the mammalian cardiac cycle are contraction and relaxation; however, whether there is a connection between them in humans is not well understood. Routine exercise has been shown to improve cardiac function, morphology, and molecular signatures. Likewise, the acute and chronic changes that occur in the heart in response to injury, disease, and stress are well characterized, albeit not fully understood. In this study, we investigated how exercise and myocardial injury affect contraction–relaxation coupling. We retrospectively analyzed the correlation between the maximal speed of contraction and the maximal speed of relaxation of canine myocardium after receiving surgically induced myocardial infarction, followed by either sedentary recovery or exercise training for 10–12 wk. We used isolated right ventricular trabeculae, which were electrically paced at different lengths, frequencies, and with increasing β-adrenoceptor stimulation. In all conditions, contraction and relaxation were linearly correlated, irrespective of injury or training history. Based on these results and the available literature, we posit that contraction–relaxation coupling is a fundamental myocardial property that resides in the structural arrangement of proteins at the level of the sarcomere and that this may be regulated by the actions of cardiac myosin binding protein C (cMyBP-C) on actin and myosin.

Novel insights into sarcomere regulatory systems control of cardiac thin filament activation

Our review focuses on sarcomere regulatory mechanisms with a discussion of cardiac-specific modifications to the three-state model of thin filament activation from a blocked to closed to open state. We discuss modulation of these thin filament transitions by Ca²⁺, by crossbridge interactions, and by thick filament–associated proteins, cardiac myosin–binding protein C (cMyBP-C), cardiac regulatory light chain (cRLC), and titin. Emerging evidence supports the idea that the cooperative activation of the thin filaments despite a single Ca²⁺ triggering regulatory site on troponin C (cTnC) cannot be considered in isolation of other functional domains of the sarcomere. We discuss long- and short-range interactions among these domains with the regulatory units of thin filaments, including proteins at the barbed end at the Z-disc and the pointed end near the M-band. Important to these discussions is the ever-increasing understanding of the role of cMyBP-C, cRLC, and titin filaments. Detailed knowledge of these control processes is critical to the understanding of mechanisms sustaining physiological cardiac state with varying hemodynamic load, to better defining genetic and acquired cardiac disorders, and to developing targets for therapies at the level of the sarcomeres.

Multiscale modeling of twitch contractions in cardiac trabeculae

Understanding the dynamics of a cardiac muscle twitch contraction is complex because it requires a detailed understanding of the kinetic processes of the Ca2+ transient, thin-filament activation, and the myosin-actin cross-bridge chemomechanical cycle. Each of these steps has been well defined individually, but understanding how all three of the processes operate in combination is a far more complex problem. Computational modeling has the potential to provide detailed insight into each of these processes, how the dynamics of each process affect the complexity of contractile behavior, and how perturbations such as mutations in sarcomere proteins affect the complex interactions of all of these processes. The mechanisms involved in relaxation of tension during a cardiac twitch have been particularly difficult to discern due to nonhomogeneous sarcomere lengthening during relaxation. Here we use the multiscale MUSICO platform to model rat trabecular twitches. Validation of computational models is dependent on being able to simulate different experimental datasets, but there has been a paucity of data that can provide all of the required parameters in a single experiment, such as simultaneous measurements of force, intracellular Ca2+ transients, and sarcomere length dynamics. In this study, we used data from different studies collected under similar experimental conditions to provide information for all the required parameters. Our simulations established that twitches either in an isometric sarcomere or in fixed-length, multiple-sarcomere trabeculae replicate the experimental observations if models incorporate a length-tension relationship for the nonlinear series elasticity of muscle preparations and a scheme for thick-filament regulation. The thick-filament regulation assumes an off state in which myosin heads are parked onto the thick-filament backbone and are unable to interact with actin, a state analogous to the super-relaxed state. Including these two mechanisms provided simulations that accurately predict twitch contractions over a range of different conditions.

Making waves: A proposed new role for myosin-binding protein C in regulating oscillatory contractions in vertebrate striated muscle

Myosin-binding protein C (MyBP-C) is a critical regulator of muscle performance that was first identified through its strong binding interactions with myosin, the force-generating protein of muscle. Almost simultaneously with its discovery, MyBP-C was soon found to bind to actin, the physiological catalyst for myosin’s activity. However, the two observations posed an apparent paradox, in part because interactions of MyBP-C with myosin were on the thick filament, whereas MyBP-C interactions with actin were on the thin filament. Despite the intervening decades since these initial discoveries, it is only recently that the dual binding modes of MyBP-C are becoming reconciled in models that place MyBP-C at a central position between actin and myosin, where MyBP-C alternately stabilizes a newly discovered super-relaxed state (SRX) of myosin on thick filaments in resting muscle and then prolongs the “on” state of actin on thin filaments in active muscle. Recognition of these dual, alternating functions of MyBP-C reveals how it is central to the regulation of both muscle contraction and relaxation. The purpose of this Viewpoint is to briefly summarize the roles of MyBP-C in binding to myosin and actin and then to highlight a possible new role for MyBP-C in inducing and damping oscillatory waves of contraction and relaxation. Because the contractile waves bear similarity to cycles of contraction and relaxation in insect flight muscles, which evolved for fast, energetically efficient contraction, the ability of MyBP-C to damp so-called spontaneous oscillatory contractions (SPOCs) has broad implications for previously unrecognized regulatory mechanisms in vertebrate striated muscle. While the molecular mechanisms by which MyBP-C can function as a wave maker or a wave breaker are just beginning to be explored, it is likely that MyBP-C dual interactions with both myosin and actin will continue to be important for understanding the new functions of this enigmatic protein.

Fast-relaxing cardiomyocytes exert a dominant role in the relaxation behavior of heterogeneous myocardium

Substantial variation in relaxation rate exists among cardiomyocytes within small volumes of myocardium; however, it is unknown how this variability affects the overall relaxation mechanics of heart muscle. In this study, we sought to modulate levels of cellular heterogeneity in a computational model, then validate those predictions using an engineered heart tissue platform. We formulated an in silico tissue model composed of half-sarcomeres with varied relaxation rates, incorporating single-cell cardiomyocyte experimental data. These model tissues randomly sampled relaxation parameters from two offset distributions of fast- and slow-relaxing populations of half-sarcomeres. Isometric muscle twitch simulations predicted a complex relationship between relaxation time and the proportion of fast-versus slow-relaxing cells in heterogeneous tissues. Specifically, a 50/50 mixture of fast and slow cells did not lead to relaxation time that was the mean of the relaxation times associated with the two pure cases. Rather, the mean relaxation time was achieved at a ratio of 70:30 slow:fast relaxing cells, suggesting a disproportionate impact of fast-relaxing cells on overall tissue relaxation. To examine whether this behavior persists in vitro, we constructed engineered heart tissues from two lines of fast- and slow-relaxing human iPSC-derived cardiomyocytes. Cell tracking via fluorescent nanocrystals confirmed the presence of both cell populations in the 50/50 mixed tissues at the time of mechanical characterization. Isometric muscle twitch relaxation times of these mixed-population engineered heart tissues showed agreement with the predictions from the model, namely that the measured relaxation rate of 50/50 mixed tissues more closely resembled that of tissues made with 100% fast-relaxing cells. Our observations suggest that cardiomyocyte diversity can play an important role in determining tissue-level relaxation.

Left ventricular vortex and intraventricular pressure difference in dogs under various loading conditions

Restrictions on the conventional evaluation of diastolic function have been recognized, especially under various loading conditions. Recently, new noninvasive ventricular vortex indexes have been introduced and are expected to reflect the cardiac function. Physiologically, there is a hypothesis that the intraventricular pressure difference (IVPD) is related to the formation of vortexes. IVPD and vortex indexes were simultaneously measured, and the relationship between the two was investigated. To verify the possibility of diastolic vorticity as an index of diastolic relaxation, a correlation between diastolic vorticity and the load dependency of vorticity [time constant (τ)] was examined. Six healthy dogs were studied using transthoracic echocardiography, pressure, and a conductance catheter. Vorticity was analyzed using vector flow mapping (VFM). IVPD was determined using Euler's equation with color M-mode Doppler images. Data were obtained at baseline, at balloon dilatation in the thoracic aorta to alter afterload, at hydroxyethyl starch infusion to alter preload, and at milrinone administration to alter ventricular relaxation. Peak vorticity at early diastole (E-Vor) and IVPD of the midventricle (MIVPD) decreased under pressure loading, were unchanged under volume loading, and increased during milrinone administration. In multivariate analysis, the independent predictors of τ were global longitudinal strain, strain rate at early diastole, and E-Vor. MIVPD was strongly correlated with E-Vor ( r = 0.84). VFM-derived peak E vorticity was strongly related to IVPD, especially MIVPD, under various loading conditions. Both of these novel indexes are promising as reliable indexes of ventricular relaxation, independent from preload. NEW & NOTEWORTHY We showed the close relationship of vortex and intraventricular pressure difference and showed that both of them can become new markers of the left ventricular relaxation property. Our present study creates a paradigm for future studies in the field of intraventircular flow physiology and clinical diastology.

A short history of the development of mathematical models of cardiac mechanics

Cardiac mechanics plays a crucial role in atrial and ventricular function, in the regulation of growth and remodelling, in the progression of disease, and the response to treatment. The spatial scale of the critical mechanisms ranges from nm (molecules) to cm (hearts) with the fastest events occurring in milliseconds (molecular events) and the slowest requiring months (growth and remodelling). Due to its complexity and importance, cardiac mechanics has been studied extensively both experimentally and through mathematical models and simulation. Models of cardiac mechanics evolved from seminal studies in skeletal muscle, and developed into cardiac specific, species specific, human specific and finally patient specific calculations. These models provide a formal framework to link multiple experimental assays recorded over nearly 100 years into a single unified representation of cardiac function. This review first provides a summary of the proteins, physiology and anatomy involved in the generation of cardiac pump function. We then describe the evolution of models of cardiac mechanics starting with the early theoretical frameworks describing the link between sarcomeres and muscle contraction, transitioning through myosin-level models to calcium-driven systems, and ending with whole heart patient-specific models.

How myofilament strain and strain rate lead the dance of the cardiac cycle

Movement of the myocardium can modify organ-level cardiac function and its molecular (crossbridge) mechanisms. This motion, which is defined by myocardial strain and strain rate (muscle shortening, lengthening, and the speed of these movements), occurs throughout the cardiac cycle, including during isovolumic periods. This review highlights how the left ventricular myocardium moves throughout the cardiac cycle, how muscle mechanics experiments provide insight into the regulation of forces used to move blood in and out of the left ventricle, and its impact on (and regulation by) crossbridge and sarcomere kinetics. We specifically highlight how muscle mechanics experiments explain how myocardial relaxation is accelerated by lengthening (strain rate) during late systole and isovolumic relaxation, a lengthening which has been measured in human hearts. Advancing and refining both in vivo measurement and ex vivo protocols with physiologic strain and strain rates could reveal important insights into molecular (crossbridge) kinetics. These advances could provide an improvement in both diagnosis and precise treatment of cardiac dysfunction.

Myocardial relaxation in human heart failure: Why sarcomere kinetics should be center-stage

Myocardial relaxation is critical for the heart to allow for adequate filling of the ventricles prior to the next contraction. In human heart failure, impairment of myocardial relaxation is a major problem, and impacts most patients suffering from end-stage failure. Furthering our understanding of myocardial relaxation is critical in developing future treatment strategies. This review highlights processes involved in myocardial relaxation, as well as governing processes that modulate myocardial relaxation, with a focus on impairment of myocardium-level relaxation in human end-stage heart failure.

Force-Dependent Recruitment from the Myosin Off State Contributes to Length-Dependent Activation

Cardiac muscle develops more force when it is activated at longer lengths. The concentration of Ca²⁺ required to develop half-maximal force also decreases. These effects are known as length-dependent activation and are thought to play critical roles in the Frank-Starling relationship and cardiovascular homeostasis. The molecular mechanisms underpinning length-dependent activation remain unclear, but recent experiments suggest that they may include recruitment of myosin heads from the off (sometimes called super-relaxed) state. This manuscript presents a mathematical model of muscle contraction that was developed to investigate this hypothesis. Myosin heads in the model transitioned between an off state (that could not interact with actin), an on state (that could bind to actin), and a single attached state. Simulations were fitted to experimental data using multidimensional parameter optimization. Statistical analysis showed that a model in which the rate of the off-to-on transition increased linearly with force reproduced the length-dependent behavior of chemically permeabilized myocardium better than a model with a constant off-to-on transition rate (F-test, p < 0.001). This result suggests that the thick-filament transitions are modulated by force. Additional calculations showed that the model incorporating a mechanosensitive thick filament could also reproduce twitch responses measured in a trabecula stretched to different lengths. A final set of simulations was then used to test the model. These calculations predicted how reducing passive stiffness would impact the length dependence of the calcium sensitivity of contractile force. The prediction (a 60% reduction in ΔpCa₅₀) mimicked the 58% reduction in ΔpCa₅₀ in myocardium from rats that expressed a giant isoform of titin and had low resting tension. Together, these computational results suggest that force-dependent recruitment of myosin heads from the thick-filament off state contributes to length-dependent activation and the Frank-Starling relationship.

The link between exercise and titin passive stiffness

NEW FINDINGS

What is the topic of this review? This review focuses on how in vivo and molecular measurements of cardiac passive stiffness can predict exercise tolerance and how exercise training can reduce cardiac passive stiffness. What advances does it highlight? This review highlights advances in understanding the relationship between molecular (titin-based) and in vivo (left ventricular) passive stiffness, how passive stiffness modifies exercise tolerance, and how exercise training may be therapeutic for cardiac diseases with increased passive stiffness. Exercise can help alleviate the negative effects of cardiovascular disease and cardiovascular co-morbidities associated with sedentary behaviour; this may be especially true in diseases that are associated with increased left ventricular passive stiffness. In this review, we discuss the inverse relationship between exercise tolerance and cardiac passive stiffness. Passive stiffness is the physical property of cardiac muscle to produce a resistive force when stretched, which, in vivo, is measured using the left ventricular end diastolic pressure-volume relationship or is estimated using echocardiography. The giant elastic protein titin is the major contributor to passive stiffness at physiological muscle (sarcomere) lengths. Passive stiffness can be modified by altering titin isoform size or by post-translational modifications. In both human and animal models, increased left ventricular passive stiffness is associated with reduced exercise tolerance due to impaired diastolic filling, suggesting that increased passive stiffness predicts reduced exercise tolerance. At the same time, exercise training itself may induce both short- and long-term changes in titin-based passive stiffness, suggesting that exercise may be a treatment for diseases associated with increased passive stiffness. Direct modification of passive stiffness to improve exercise tolerance is a potential therapeutic approach. Titin passive stiffness itself may be a treatment target based on the recent discovery of RNA binding motif 20, which modifies titin isoform size and passive stiffness. Translating these discoveries that link exercise and left ventricular passive stiffness may provide new methods to enhance exercise tolerance and treat patients with cardiovascular disease.