The force-frequency relationship: insights from mathematical modeling

A new method to evaluate staircase phenomenon in skeletal muscle using piezoelectric sensor

Objective

The staircase phenomenon, which refers to the increases in the force of contraction with repetitive stimulation of the muscle, has been studied for many years, but the method is difficult and not widely used. Our objective was to evaluate the staircase phenomenon in skeletal muscle using a piezoelectric sensor.

Methods

Thirty-five subjects without neuromuscular diseases (normal controls), 11 patients with Becker muscular dystrophy (BMD), and 19 patients with myotonic dystrophy type 1 (MyD) were studied. Compound muscle action potential (CMAP) and movement-related potential (MRP) waveforms were recorded using piezoelectric sensors during repetitive stimulation of the median nerve, and the amplitudes and durations were measured. Excitation-contraction (E-C) coupling time (ECCT) was calculated from the difference between onset latencies of CMAP and MRP.

Results

In normal controls, MRP amplitude ratio (relative to baseline) increased significantly with increase in stimulation duration and with increase in stimulation frequency. In BMD and MyD, however, MRP amplitude ratio did not change significantly with increase in stimulation duration. Especially, in MyD, there was no change in MRP amplitude ratio with increase in frequency.

Conclusion

Staircase phenomenon abnormalities can be evaluated easily using piezoelectric sensors, indicating their potential utility for evaluating E-C coupling impairment in myopathies.

Significance

Piezoelectric sensors may be a useful tool to evaluate staircase phenomenon in skeletal muscle.

Feed Forward Modeling: an efficient approach for mathematical modeling of the force frequency relationship in the rabbit isolated ventricular myocyte

Background and Objective. This study addresses the Force-Frequency relationship, a fundamental characteristic of cardiac muscle influenced byβ1-adrenergic stimulation. This relationship reveals that heart rate (HR) changes at the sinoatrial node lead to alterations in ventricular cell contractility, increasing the force and decreasing relaxation time for higher beat rates. Traditional models lacking this relationship offer an incomplete physiological depiction, impacting the interpretation of in silico experiment results. To improve this, we propose a new mathematical model for ventricular myocytes, named 'Feed Forward Modeling' (FFM).Methods. FFM adjusts model parameters like channel conductance and Ca2+pump affinity according to stimulation frequency, in contrast to fixed parameter values. An empirical sigmoid curve guided the adaptation of each parameter, integrated into a rabbit ventricular cell electromechanical model. Model validation was achieved by comparing simulated data with experimental current-voltage (I-V) curves for L-type Calcium and slow Potassium currents.Results. FFM-enhanced simulations align more closely with physiological behaviors, accurately reflecting inotropic and lusitropic responses. For instance, action potential duration at 90% repolarization (APD90) decreased from 206 ms at 1 Hz to 173 ms at 4 Hz using FFM, contrary to the conventional model, where APD90 increased, limiting high-frequency heartbeats. Peak force also showed an increase with FFM, from 8.5 mN mm-2at 1 Hz to 11.9 mN mm-2at 4 Hz, while it barely changed without FFM. Relaxation time at 50% of maximum force (t50) similarly improved, dropping from 114 ms at 1 Hz to 75.9 ms at 4 Hz with FFM, a change not observed without the model.Conclusion. The FFM approach offers computational efficiency, bypassing the need to model all beta-adrenergic pathways, thus facilitating large-scale simulations. The study recommends that frequency change experiments include fractional dosing of isoproterenol to better replicate heart conditionsin vivo.

The Role of Ca2+ Sparks in Force Frequency Relationships in Guinea Pig Ventricular Myocytes

Calcium sparks are the elementary Ca2+ release events in excitation-contraction coupling that underlie the Ca2+ transient. The frequency-dependent contractile force generated by cardiac myocytes depends upon the characteristics of the Ca2+ transients. A stochastic computational local control model of a guinea pig ventricular cardiomyocyte was developed, to gain insight into mechanisms of force-frequency relationship (FFR). This required the creation of a new three-state RyR2 model that reproduced the adaptive behavior of RyR2, in which the RyR2 channels transition into a different state when exposed to prolonged elevated subspace [Ca2+]. The model simulations agree with previous experimental and modeling studies on interval-force relations. Unlike previous common pool models, this local control model displayed stable action potential trains at 7 Hz. The duration and the amplitude of the [Ca2+]myo transients increase in pacing rates consistent with the experiments. The [Ca2+]myo transient reaches its peak value at 4 Hz and decreases afterward, consistent with experimental force-frequency curves. The model predicts, in agreement with previous modeling studies of Jafri and co-workers, diastolic sarcoplasmic reticulum, [Ca2+]sr, and RyR2 adaptation increase with the increased stimulation frequency, producing rising, rather than falling, amplitude of the myoplasmic [Ca2+] transients. However, the local control model also suggests that the reduction of the L-type Ca2+ current, with an increase in pacing frequency due to Ca2+-dependent inactivation, also plays a role in the negative slope of the FFR. In the simulations, the peak Ca2+ transient in the FFR correlated with the highest numbers of SR Ca2+ sparks: the larger average amplitudes of those sparks, and the longer duration of the Ca2+ sparks.

Intra-subject stability of different expressions of spatial QRS-T angle and their relationship to heart rate

Three-dimensional angle between the QRS complex and T wave vectors is a known powerful cardiovascular risk predictor. Nevertheless, several physiological properties of the angle are unknown or poorly understood. These include, among others, intra-subject profiles and stability of the angle relationship to heart rate, characteristics of angle/heart-rate hysteresis, and the changes of these characteristics with different modes of QRS-T angle calculation. These characteristics were investigated in long-term 12-lead Holter recordings of 523 healthy volunteers (259 females). Three different algorithmic methods for the angle computation were based on maximal vector magnitude of QRS and T wave loops, areas under the QRS complex and T wave curvatures in orthogonal leads, and weighted integration of all QRS and T wave vectors moving around the respective 3-dimensional loops. These methods were applied to orthogonal leads derived either by a uniform conversion matrix or by singular value decomposition (SVD) of the original 12-lead ECG, giving 6 possible ways of expressing the angle. Heart rate hysteresis was assessed using the exponential decay models. All these methods were used to measure the angle in 659,313 representative waveforms of individual 10-s ECG samples and in 7,350,733 individual beats contained in the same 10-s samples. With all measurement methods, the measured angles fitted second-degree polynomial regressions to the underlying heart rate. Independent of the measurement method, the angles were found significantly narrower in females (p < 0.00001) with the differences to males between 10o and 20o, suggesting that in future risk-assessment studies, different angle dichotomies are needed for both sexes. The integrative method combined with SVD leads showed the highest intra-subject reproducibility (p < 0.00001). No reproducible delay between heart rate changes and QRS-T angle changes was found. This was interpreted as a suggestion that the measurement of QRS-T angle might offer direct assessment of cardiac autonomic responsiveness at the ventricular level.

Effect of a single dose of pimobendan on right ventricular and right atrial function in 11 healthy cats

OBJECTIVES

The objective of this study was to investigate the effect of pimobendan on echocardiographic parameters of right ventricular and atrial function in healthy cats.

ANIMALS

Eleven privately owned, healthy adult cats.

MATERIAL AND METHODS

Each cat underwent five echocardiographic examinations: the first and second examinations were performed 1 h apart on day 0. On day 1, the third examination served as baseline, whereas the fourth and fifth examinations were performed one and 6 h after administration of a single oral dose of pimobendan (1.25 mg/cat), respectively. Parameters of right ventricular and atrial morphology and function were collected and compared among time points.

RESULTS

Pimobendan administration produced a change in some echocardiographic variables. Specifically, heart rate, right ventricular fractional shortening and peak velocity of systolic lateral tricuspid annular motion increased (P = 0.032, P = 0.002 and P < 0.001, respectively), whereas right ventricular end-systolic internal diameter and right atrial maximum and minimum internal diameters decreased (P = 0.004, P = 0.025 and P = 0.01, respectively). Right ventricular fractional area change and tricuspid annular plane systolic excursion did not change.

CONCLUSIONS

This novel study showed that pimobendan had positive effects on right ventricular and right atrial function in healthy cats. Further studies are needed to determine whether pimobendan has similar effects in cats with cardiac diseases.

Myocardial Contractility: Historical and Contemporary Considerations

The term myocardial contractility is thought to have originated more than 125 years ago and has remained and enigma ever since. Although the term is frequently used in textbooks, editorials and contemporary manuscripts its definition remains illusive often being conflated with cardiac performance or inotropy. The absence of a universally accepted definition has led to confusion, disagreement and misconceptions among physiologists, cardiologists and safety pharmacologists regarding its definition particularly in light of new discoveries regarding the load dependent kinetics of cardiac contraction and their translation to cardiac force-velocity and ventricular pressure-volume measurements. Importantly, the Starling interpretation of force development is length-dependent while contractility is length independent. Most historical definitions employ an operational approach and define cardiac contractility in terms of the hearts mechanical properties independent of loading conditions. Literally defined the term contract infers that something has become smaller, shrunk or shortened. The addition of the suffix “ility” implies the quality of this process. The discovery and clinical investigation of small molecules that bind to sarcomeric proteins independently altering force or velocity requires that a modern definition of the term myocardial contractility be developed if the term is to persist. This review reconsiders the historical and contemporary interpretations of the terms cardiac performance and inotropy and recommends a modern definition of myocardial contractility as the preload, afterload and length-independent intrinsic kinetically controlled, chemo-mechanical processes responsible for the development of force and velocity.

Effect of pimobendan on left atrial function: an echocardiographic pilot study in 11 healthy cats

OBJECTIVES

- To evaluate the effect of a single dose of pimobendan on left atrial (LA) function in healthy cats.

ANIMALS

- Eleven client owned healthy cats.

MATERIAL AND METHODS

- Standardized and repeated echocardiographic examinations were performed on healthy and conscious cats before and after a single dose of orally administered pimobendan (1.25 mg/cat). Left atrial systolic functional parameters were assessed.

RESULTS

- Some of the tested parameters of LA function showed significant improvement after pimobendan administration, whereas no significant effect on left ventricular function was observed. In particular, LA minimal diameters obtained from M-mode images in short (p=0.018) and long (p=0.009) axis reduced after pimobendan administration, whereas LA fractional shortening from short (p=0.027) and long (p=0.042) axis and LA appendage emptying velocity (p<0.001) significantly increased. A mild increase in heart rate (p=0.001), and a transient increase on the peak systolic wave pulmonary vein velocity (p=0.008) were also recorded as a possible effect.

CONCLUSIONS

- A single dose of pimobendan appears to impact LA function in healthy cats. However, because of the small number of cats included, and the absence of a placebo group, these results cannot be definitively separated from the effect of time. Additional studies are needed to understand if similar effects are observed in cats with cardiomyopathy and LA dilatation.

Complex Interaction Between Low-Frequency APD Oscillations and Beat-to-Beat APD Variability in Humans Is Governed by the Sympathetic Nervous System

BACKGROUND

Recent clinical, experimental and modeling studies link oscillations of ventricular repolarization in the low frequency (LF) (approx. 0.1 Hz) to arrhythmogenesis. Sympathetic provocation has been shown to enhance both LF oscillations of action potential duration (APD) and beat-to-beat variability (BVR) in humans. We hypothesized that beta-adrenergic blockade would reduce LF oscillations of APD and BVR of APD in humans and that the two processes might be linked.

METHODS AND RESULTS

Twelve patients with normal ventricles were studied during routine electrophysiological procedures. Activation-recovery intervals (ARI) as a conventional surrogate for APD were recorded from 10 left and 10 right ventricular endocardial sites before and after acute beta-adrenergic adrenergic blockade. Cycle length was maintained constant with right ventricular pacing. Oscillatory behavior of ARI was quantified by spectral analysis and BVR as the short-term variability. Beta-adrenergic blockade reduced LF ARI oscillations (8.6 ± 4.5 ms2 vs. 5.5 ± 3.5 ms2, p = 0.027). A significant correlation was present between the initial control values and reduction seen following beta-adrenergic blockade in LF ARI (r s = 0.62, p = 0.037) such that when initial values are high the effect is greater. A similar relationship was also seen in the beat-to beat variability of ARI (r s = 0.74, p = 0.008). There was a significant correlation between the beta-adrenergic blockade induced reduction in LF power of ARI and the witnessed reduction of beat-to-beat variability of ARI (r s = 0.74, p = 0.01). These clinical results accord with recent computational modeling studies which provide mechanistic insight into the interactions of LF oscillations and beat-to-beat variability of APD at the cellular level.

CONCLUSION

Beta-adrenergic blockade reduces LF oscillatory behavior of APD (ARI) in humans in vivo. Our results support the importance of LF oscillations in modulating the response of BVR to beta-adrenergic blockers, suggesting that LF oscillations may play role in modulating beta-adrenergic mechanisms underlying BVR.

Understanding Key Mechanisms of Exercise-Induced Cardiac Protection to Mitigate Disease: Current Knowledge and Emerging Concepts

The benefits of exercise on the heart are well recognized, and clinical studies have demonstrated that exercise is an intervention that can improve cardiac function in heart failure patients. This has led to significant research into understanding the key mechanisms responsible for exercise-induced cardiac protection. Here, we summarize molecular mechanisms that regulate exercise-induced cardiac myocyte growth and proliferation. We discuss in detail the effects of exercise on other cardiac cells, organelles, and systems that have received less or little attention and require further investigation. This includes cardiac excitation and contraction, mitochondrial adaptations, cellular stress responses to promote survival (heat shock response, ubiquitin-proteasome system, autophagy-lysosomal system, endoplasmic reticulum unfolded protein response, DNA damage response), extracellular matrix, inflammatory response, and organ-to-organ crosstalk. We summarize therapeutic strategies targeting known regulators of exercise-induced protection and the challenges translating findings from bench to bedside. We conclude that technological advancements that allow for in-depth profiling of the genome, transcriptome, proteome and metabolome, combined with animal and human studies, provide new opportunities for comprehensively defining the signaling and regulatory aspects of cell/organelle functions that underpin the protective properties of exercise. This is likely to lead to the identification of novel biomarkers and therapeutic targets for heart disease.

Cardiophysiology Illustrated by Comparing Ventricular Volumes in Healthy Adult Males and Females

Recent advances in cardiac imaging techniques have substantially contributed to a growing interest in the analysis of global cardiac chamber dimensions and regional myocardial deformation. During the cardiac cycle, ventricular luminal volume varies due to the contraction process, which also confers a shape change including substantial alteration of long axis length, as well as rotation of the base compared to the apex. Local deformation can be assessed by strain (rate) analysis. Reviewing the present literature, it must be concluded that there is no single metric available to comprehensively characterize ventricular function. Every candidate advanced thus far has been found to incompletely reflect ventricular performance. This observation is not surprising in view of the complexity of the cardiac pump system. Additionally, sex-specific modifiers may play a role. More than three decades ago, it was shown that on average the ventricular volume is smaller in healthy women compared to matched males. Therefore, the present contribution concerns the interpretation of data derived from the healthy heart in both men and women. Starting from the classical Starling concept, we apply a simple mathematical transformation which permits an insightful representation of ventricular mechanics. Relating end-systolic volume (ESV) to end-diastolic volume creates the ventricular volume regulation graph which features the pertinent working point of an individual heart. This fundamental approach illustrates why certain proposed performance indexes cannot individually reveal the essence of ventricular systolic function. We demonstrate that particular metrics are highly interconnected and just tell us the same story in a different disguise. It is imperative to understand which associations exist and if they expectedly are (nearly) linear or frankly nonlinear. Notably, ejection fraction (EF) is primarily determined by ESV, while in turn EF is not much different from ventriculo-arterial coupling (VAC). Insight into cardiac function is promoted by identification of the paramount/essential components involved. The smaller ESV (p < 0.0001) implies that EF is higher in women and may also have consequences for VAC.

Cardiopatch platform enables maturation and scale-up of human pluripotent stem cell-derived engineered heart tissues

Despite increased use of human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) for drug development and disease modeling studies, methods to generate large, functional heart tissues for human therapy are lacking. Here we present a “Cardiopatch” platform for 3D culture and maturation of hiPSC-CMs that after 5 weeks of differentiation show robust electromechanical coupling, consistent H-zones, I-bands, and evidence for T-tubules and M-bands. Cardiopatch maturation markers and functional output increase during culture, approaching values of adult myocardium. Cardiopatches can be scaled up to clinically relevant dimensions, while preserving spatially uniform properties with high conduction velocities and contractile stresses. Within window chambers in nude mice, cardiopatches undergo vascularization by host vessels and continue to fire Ca²⁺ transients. When implanted onto rat hearts, cardiopatches robustly engraft, maintain pre-implantation electrical function, and do not increase the incidence of arrhythmias. These studies provide enabling technology for future use of hiPSC-CM tissues in human heart repair.

Cardiomyocytes derived from human induced pluripotent stem cells could be used to generate cardiac tissues for regenerative purposes. Here the authors describe a method to obtain large bioengineered heart tissues showing advanced maturation, functional features and engraftment capacity.

A role for membrane shape and information processing in cardiac physiology

While the heart is a dynamic organ and one of its major functions is to provide the organism with sufficient blood supply, the regulatory feedback systems, which allow adaptation to hemodynamic changes, remain not well understood. Our current description of mechanosensation focuses on stretch-sensitive ion channels, cytoskeletal components, structures such as the sarcomeric Z-disc, costameres, caveolae, or the concept of tensegrity, but these models appear incomplete as the remarkable plasticity of the myocardium in response to biomechanical stress and heart rate variations remains unexplained. Signaling activity at membranes depends on their geometric parameters such as surface area and curvature, which links shape to information processing. In the heart, continuous cycles of contraction and relaxation reshape membrane morphology and hence affect cardio-mechanic signaling. This article provides a brief review on current models of mechanosensation and focuses on how signaling, cardiac myocyte dynamics, and membrane shape interact and potentially give rise to a self-organized system that uses shape to sense the extra- and intracellular environment. This novel concept may help to explain how changes in frequency, and thus membrane shape, affect cardiac plasticity. One of the conclusions is that hypertrophy and associated fibrosis, which have been considered as necessary to cope with increased wall stress, can also be seen as part of complex feedback systems which use local membrane inhomogeneity in different cardiac cell types to influence whole organphysiology and which are predicted to fine-tune and thus regulate membrane-mediated signaling.

Sodium-calcium exchangers (NCX): molecular hallmarks underlying the tissue-specific and systemic functions

NCX proteins explore the electrochemical gradient of Na(+) to mediate Ca(2+)-fluxes in exchange with Na(+) either in the Ca(2+)-efflux (forward) or Ca(2+)-influx (reverse) mode, whereas the directionality depends on ionic concentrations and membrane potential. Mammalian NCX variants (NCX1-3) and their splice variants are expressed in a tissue-specific manner to modulate the heartbeat rate and contractile force, the brain's long-term potentiation and learning, blood pressure, renal Ca(2+) reabsorption, the immune response, neurotransmitter and insulin secretion, apoptosis and proliferation, mitochondrial bioenergetics, etc. Although the forward mode of NCX represents a major physiological module, a transient reversal of NCX may contribute to EC-coupling, vascular constriction, and synaptic transmission. Notably, the reverse mode of NCX becomes predominant in pathological settings. Since the expression levels of NCX variants are disease-related, the selective pharmacological targeting of tissue-specific NCX variants could be beneficial, thereby representing a challenge. Recent structural and biophysical studies revealed a common module for decoding the Ca(2+)-induced allosteric signal in eukaryotic NCX variants, although the phenotype variances in response to regulatory Ca(2+) remain unclear. The breakthrough discovery of the archaebacterial NCX structure may serve as a template for eukaryotic NCX, although the turnover rates of the transport cycle may differ ~10(3)-fold among NCX variants to fulfill the physiological demands for the Ca(2+) flux rates. Further elucidation of ion-transport and regulatory mechanisms may lead to selective pharmacological targeting of NCX variants under disease conditions.

In silico investigation of the short QT syndrome, using human ventricle models incorporating electromechanical coupling

INTRODUCTION

Genetic forms of the Short QT Syndrome (SQTS) arise due to cardiac ion channel mutations leading to accelerated ventricular repolarization, arrhythmias and sudden cardiac death. Results from experimental and simulation studies suggest that changes to refractoriness and tissue vulnerability produce a substrate favorable to re-entry. Potential electromechanical consequences of the SQTS are less well-understood. The aim of this study was to utilize electromechanically coupled human ventricle models to explore electromechanical consequences of the SQTS.

METHODS AND RESULTS

The Rice et al. mechanical model was coupled to the ten Tusscher et al. ventricular cell model. Previously validated K(+) channel formulations for SQT variants 1 and 3 were incorporated. Functional effects of the SQTS mutations on [Ca(2+)] i transients, sarcomere length shortening and contractile force at the single cell level were evaluated with and without the consideration of stretch-activated channel current (I sac). Without I sac, at a stimulation frequency of 1Hz, the SQTS mutations produced dramatic reductions in the amplitude of [Ca(2+)] i transients, sarcomere length shortening and contractile force. When I sac was incorporated, there was a considerable attenuation of the effects of SQTS-associated action potential shortening on Ca(2+) transients, sarcomere shortening and contractile force. Single cell models were then incorporated into 3D human ventricular tissue models. The timing of maximum deformation was delayed in the SQTS setting compared to control.

CONCLUSION

The incorporation of I sac appears to be an important consideration in modeling functional effects of SQT 1 and 3 mutations on cardiac electro-mechanical coupling. Whilst there is little evidence of profoundly impaired cardiac contractile function in SQTS patients, our 3D simulations correlate qualitatively with reported evidence for dissociation between ventricular repolarization and the end of mechanical systole.