Heart Muscle Model Research Articles

An Integrated Segmentation Techniques for Myocardial Ischemia

Myocardial Ischemia segmentation is a challenging task for basic and translational research on cardiovascular, as it provides ultimately “realistic” in heart muscle model. The main objective of the research work is to find an efficient segmentation technique for the myocardial ischemia based on the myocardial infarcted MRI data set for the accurate classification of scar volume. The paper will give an insight about the segmentation technique based on myocardial ischemia and discusses essential cellular components. The paper provides an integrated approach which comprises of fuzzy c-means and morphological operations along with median filtering enhancement technique help in detecting the myocardial ischemia. The developed model is tested with 2D and 3D enhanced myocardial ischemia MRI and also with normal heart. The purpose of segmentation in myocardial ischemia is to identify the scar region in the heart. The integrated model is evaluated based on statistical measures and validated based on manual segmentation done by clinical expert. The scar classification is done based on the myocardial ischemia segmentation which leads to better prediction of arrhythmia in heart patient. The integrated model is considered as one of the best model for segmenting myocardial ischemia.

Engineered Heart Muscle Models in Phenotypic Drug Screens.

Classical drug development is compromised by considerable clinical failure of promising drug candidates after decades of costly preclinical work. Failure can be because of previously unrecognized safety concerns or more commonly lack of clinical efficacy. Classical drug discovery and safety pharmacology programs rely heavily on well-established in vitro and preclinical animal models. The availability of human pluripotent stem cells and the possibility to direct them into any somatic cell type suggest that a paradigm shift in drug development may be possible and timely, with the opportunity to test safety and efficacy of candidate drugs on the human target cells and tissue. However, there is considerable uncertainty as to whether human models would only qualify as replacement for well-established tools or add substantially more information to the preclinical data package, to facilitate translation of more promising drug candidates into clinical practice. This chapter provides an overview of tissue-engineered macro-scale heart muscle models for applications in drug discovery and safety pharmacology.

Muscarinic receptors promote pacemaker fate at the expense of secondary conduction system tissue in zebrafish.

Deterioration or inborn malformations of the cardiac conduction system (CCS) interfere with proper impulse propagation in the heart and may lead to sudden cardiac death or heart failure. Patients afflicted with arrhythmia depend on antiarrhythmic medication or invasive therapy, such as pacemaker implantation. An ideal way to treat these patients would be CCS tissue restoration. This, however, requires precise knowledge regarding the molecular mechanisms underlying CCS development. Here, we aimed to identify regulators of CCS development. We performed a compound screen in zebrafish embryos and identified tolterodine, a muscarinic receptor antagonist, as a modifier of CCS development. Tolterodine provoked a lower heart rate, pericardiac edema, and arrhythmia. Blockade of muscarinic M3, but not M2, receptors induced transcriptional changes leading to amplification of sinoatrial cells and loss of atrioventricular identity. Transcriptome data from an engineered human heart muscle model provided additional evidence for the contribution of muscarinic M3 receptors during cardiac progenitor specification and differentiation. Taken together, we found that muscarinic M3 receptors control the CCS already before the heart becomes innervated. Our data indicate that muscarinic receptors maintain a delicate balance between the developing sinoatrial node and the atrioventricular canal, which is probably required to prevent the development of arrhythmia.

Optogenetic Monitoring of the Glutathione Redox State in Engineered Human Myocardium.

Redox signaling affects all aspects of cardiac function and homeostasis. With the development of genetically encoded fluorescent redox sensors, novel tools for the optogenetic investigation of redox signaling have emerged. Here, we sought to develop a human heart muscle model for in-tissue imaging of redox alterations. For this, we made use of (1) the genetically-encoded Grx1-roGFP2 sensor, which reports changes in cellular glutathione redox status (GSH/GSSG), (2) human embryonic stem cells (HES2), and (3) the engineered heart muscle (EHM) technology. We first generated HES2 lines expressing Grx1-roGFP2 in cytosol or mitochondria compartments by TALEN-guided genomic integration. Grx1-roGFP2 sensor localization and function was verified by fluorescence imaging. Grx1-roGFP2 HES2 were then subjected to directed differentiation to obtain high purity cardiomyocyte populations. Despite being able to report glutathione redox potential from cytosol and mitochondria, we observed dysfunctional sarcomerogenesis in Grx1-roGFP2 expressing cardiomyocytes. Conversely, lentiviral transduction of Grx1-roGFP2 in already differentiated HES2-cardiomyocytes and human foreskin fibroblast was possible, without compromising cell function as determined in EHM from defined Grx1-roGFP2-expressing cardiomyocyte and fibroblast populations. Finally, cell-type specific GSH/GSSG imaging was demonstrated in EHM. Collectively, our observations suggests a crucial role for redox signaling in cardiomyocyte differentiation and provide a solution as to how this apparent limitation can be overcome to enable cell-type specific GSH/GSSG imaging in a human heart muscle context.

Cardiac macrotissues-on-a-plate models for phenotypic drug screens.

Facilitated by the introduction of human induced pluripotent stem cells and protocols for their efficient directed differentiation at high quantity and quality, innovative human heart muscle models are being developed for applications in drug screens. Employed models range from the microscopic cardiomyocytes-on-a-chip scale to the cardiac macrotissues-on-a-plate scale. Whilst cardiomyocyte-on-a-chip models can be readily adapted to high-throughput primary screening, they are limited as to the deep phenotyping of contractility, and here in particular contractile force development. In lower throughput cardiac macrotissue-on-a-plate platforms, organotypic function, including anisotropic electrical spread of excitation and contractility, can be recapitulated at the macroscopic scale. This review serves as an overview of cardiac macrotissue-on-a-plate technologies with a focus on their application in the investigation of drug effects on heart muscle contractility and disease modeling.

Conditioning of Cardiovascular Tissue Using a Noncontact Magnetic Stretch Bioreactor with Embedded Magnetic Nanoparticles.

Bioreactor systems, an integral component of tissue engineering, are designed to simulate complex in vivo conditions to impart functionality to artificial tissue. All standard forms of stretch bioreactors require physical contact with artificial heart muscle (AHM). However, we believe that noncontact stretch bioreactors have the potential to lead to higher functional benefit of AHM. Our work is focused on the fabrication of a noncontact magnetic stretch bioreactor (MSB) that uses magnetic nanoparticles to simulate stretch conditions to impart functionality. During our development of this system, we applied magnetically induced stretch conditioning through application of an oscillating magnetic field to a ferromagnetic heart muscle model. Fibrin scaffolds were loaded with magnetic nanoparticles prior to tissue model formation. Oscillating magnetic fields were applied by a novel bioreactor system through displacement of a neodymium magnet. The addition of commercially obtained iron(III) oxide (Fe2O3) in sufficient quantities to allow for physiologically relevant stretches (15% axial displacement) caused toxic effects after 4 days of culture. In contrast, loading scaffolds with monodispersed, high-saturation-magnetization magnetite (Fe3O4) nanoparticles specifically prepared for these experiments increased the field strength of the magnetized fibrin 10-fold over polydispersed, low-saturation magnetization, Fe2O3. Additionally, loading with Fe3O4 enabled magnetically actuated stretching with markedly reduced toxicity over 8 days of culture. Using a 20% stretch 0.5 Hz protocol, we observed a significant increase in twitch force over controls at days 4 and 6. This work provides a technology for controlled noncontact mechanical stretch to condition AHM.

P63RhoGEF regulates auto- and paracrine signaling in cardiac fibroblasts

Cardiac remodeling, a hallmark of heart disease, is associated with intense auto- and paracrine signaling leading to cardiac fibrosis. We hypothesized that the specific mediator of Gq/11-dependent RhoA activation p63RhoGEF, which is expressed in cardiac fibroblasts, plays a role in the underlying processes. We could show that p63RhoGEF is up-regulated in mouse hearts subjected to transverse aortic constriction (TAC). In an engineered heart muscle model (EHM), p63RhoGEF expression in cardiac fibroblasts increased resting and twitch tensions, and the dominant negative p63ΔN decreased both. In an engineered connective tissue model (ECT), p63RhoGEF increased tissue stiffness and its knockdown as well as p63ΔN reduced stiffness. In 2D cultures of neonatal rat cardiac fibroblasts, p63RhoGEF regulated the angiotensin II (Ang II)-dependent RhoA activation, the activation of the serum response factor, and the expression and secretion of the connective tissue growth factor (CTGF). All these processes were inhibited by the knockdown of p63RhoGEF or by p63ΔN likely based on their negative influence on the actin cytoskeleton. Moreover, we show that p63RhoGEF also regulates CTGF in engineered tissues and correlates with it in the TAC model. Finally, confocal studies revealed a closely related localization of p63RhoGEF and CTGF in the trans-Golgi network.

Heart-on-a-chip based on stem cell biology.

Heart diseases are one of the main causes of death around the world. The great challenge for scientists is to develop new therapeutic methods for these types of ailments. Stem cells (SCs) therapy could be one of a promising technique used for renewal of cardiac cells and treatment of heart diseases. Conventional in vitro techniques utilized for investigation of heart regeneration do not mimic natural cardiac physiology. Lab-on-a-chip systems may be the solution which could allow the creation of a heart muscle model, enabling the growth of cardiac cells in conditions similar to in vivo conditions. Microsystems can be also used for differentiation of stem cells into heart cells, successfully. It will help better understand of proliferation and regeneration ability of these cells. In this review, we present Heart-on-a-chip systems based on cardiac cell culture and stem cell biology. This review begins with the description of the physiological environment and the functions of the heart. Next, we shortly described conventional techniques of stem cells differentiation into the cardiac cells. This review is mostly focused on describing Lab-on-a-chip systems for cardiac tissue engineering. Therefore, in the next part of this article, the microsystems for both cardiac cell culture and SCs differentiation into cardiac cells are described. The section about SCs differentiation into the heart cells is divided in sections describing biochemical, physical and mechanical stimulations. Finally, we outline present challenges and future research concerning Heart-on-a-chip based on stem cell biology.

Abstract 5: Novel Tools for Identification and Purification of Cardiomyocytes, Fibroblasts and Endothelial Cells From Neonatal Mouse and Rat Hearts

Although isolation of vital cardiac cells from neonatal hearts is one of the most used experimental model in cardiac research, the manual dissociation of neonatal hearts is a laborious and difficult-to-standardize procedure. To shorten sample processing time and increase reproducibility, we developed a fully automated dissociation process followed by magnetic purification of cardiomyocytes (CMs), cardiac fibroblasts (CFs) and endothelial cells (ECs). Neonatal hearts were dissociated within 1 h resulting in high yields of single cells with excellent viability. Depending on age and species following cell ratios were recovered after dissociation: 50-70% CMs, 30-40% CFs, 10-20% ECs. In order to purify CMs from dissociated neonatal hearts, we defined antibody cocktails enabling non-myocyte removal. Our depletion strategy allowed for the enrichment of CMs from whole hearts or preparations of heart chambers with purities of up to 98%. To enable simultaneous detection of CMs and subtypes, we developed recombinant antibodies against general CM markers like alpha Actinin, Myosin Heavy Chain or cardiac Troponin T as well as CM subtype-specific antibodies against MLC2a and MLC2v distinguishing between atrial and ventricular CMs respectively. Besides, we developed magnetic enrichment strategies for the purification of CFs and ECs. Current purification strategies that are solely based on antibodies against EC surface markers do not result in sufficiently pure cardiac ECs. Therefore, we established a 2-step enrichment protocol allowing for the complete removal of contaminating fibroblasts and leukocytes. Our data indicate that this protocol significantly improves the purity of primary cardiac ECs. Functionality of ECs before and after enrichment was proven by Dil-Ac-LDL endocytosis. Similarly, our magnetic enrichment protocol for cardiac fibroblasts revealed homogenous expression of fibroblast markers like Vimentin and Prolyl-Hydroxylase, but virtually no contaminations with CMs or ECs. In summary, we established an automated protocol for dissociation of neonatal hearts enabling subsequent purification, characterization and cultivation of CMs, CFs and ECs which can readily be used for cell culture assays or to generate heart muscle models.

MiR-133a Enhances the Protective Capacity of Cardiac Progenitors Cells after Myocardial Infarction

SummarymiR-133a and miR-1 are known as muscle-specific microRNAs that are involved in cardiac development and pathophysiology. We have shown that both miR-1 and miR-133a are early and progressively upregulated during in vitro cardiac differentiation of adult cardiac progenitor cells (CPCs), but only miR-133a expression was enhanced under in vitro oxidative stress. miR-1 was demonstrated to favor differentiation of CPCs, whereas miR-133a overexpression protected CPCs against cell death, targeting, among others, the proapoptotic genes Bim and Bmf. miR-133a-CPCs clearly improved cardiac function in a rat myocardial infarction model by reducing fibrosis and hypertrophy and increasing vascularization and cardiomyocyte proliferation. The beneficial effects of miR-133a-CPCs seem to correlate with the upregulated expression of several relevant paracrine factors and the plausible cooperative secretion of miR-133a via exosomal transport. Finally, an in vitro heart muscle model confirmed the antiapoptotic effects of miR-133a-CPCs, favoring the structuration and contractile functionality of the artificial tissue.

Abstract 2: Automated Dissociation Of Neonatal Hearts And Immunomagnetic Purification Of Cardiomyocytes, Cardiac Fibroblasts And Endothelial Cells

Pure cardiovascular cell lineages are a requisite for an unbiased and cell-type specific investigation of (patho-) physiological mechanisms involved in heart failure. Moreover, pure heart cells are needed as building blocks for cardiac tissue engineering. Therefore, we developed a rapid and automated heart dissociation protocol followed by an immunomagnetic enrichment of the three major heart cell types, namely cardiomyocytes (CMs), cardiac fibroblasts (Fibs) and endothelial cells (Endos) from both, mouse and rat neonatal hearts. First, we developed an enzyme mix optimal for the dissociation of neonatal mouse and rat hearts by screening our enzyme library. Next, we optimized the dissociation by utilizing our gentleMACS technology resulting in a fast (1 h), robust, and fully automated heart dissociation protocol. Analysis of the dissociated heart cells prior to cell purification showed: (i) high cell vitalities (>90%), (ii) high frequencies of α-actinin-positive CMs (ca. 60%) and (iii) vimentin-positive non-CMs with a frequency of ca. 40%. In order to selectively enrich various cell-types from these heterogenous cell populations, we performed a cell-surface marker screen. We identified several candidates for the composition of antibody cocktails enabling selective enrichment of mouse and rat CMs, Fibs or Endos with purities of up to 97%. CMs grown in 2D cultures showed spontaneous beating activity and the expression of sarcomeric proteins. Additionally, heart cells were cultured on decellularized mouse heart slices. Analysis of the slice cultures after recellularization showed (i) partial restoration of synchronous contractions and (ii) orientated and elongated heart cells. Purified Fibs were highly proliferative and could be expanded 34-fold over an analyzed culture period of 15 days. Finally, functionality of the purified endothelial cells was proven by Dil-LDL endocytosis. In summary, we established an automated protocol for the dissociation of neonatal hearts, enabling the subsequent immunomagnetic enrichment of CMs, Fibs and Endos which can readily be utilized for 2D cell culture assays or to generate in vitro heart muscle models and surrogate tissue for myocardial repair.

Lights on for HIF-1α: Genetically Enhanced Mouse Cardiomyocytes for Heart Tissue Imaging

Background/Aims: The hypoxia inducible factor-1 (HIF-1) is a suitable marker for tissue oxygenation. We intended to develop cardiomyocytes (CMs) expressing the oxygen-dependent degradation domain of HIF-1α fused to the firefly luciferase (ODD-Luc) followed by proof-of-concept for its applicability in the assessment of heart muscle oxygenation. Methods and Results: We first generated embryonic stem cell (ESC) lines (ODD-Luc ESCs) from a Tg ROSA26 ODD-Luc/+ mouse. Subsequent CMs selection was facilitated by stable integration of an antibiotic resistance expressed under the control of the αMHC promoter. ODD-Luc ESCs showed a strong Luc-signal within 1 h of hypoxia (1% oxygen), which coincided with endogenous HIF-1α. Engineered heart muscle (EHM) constructed with ODD-Luc CMs confirmed the utility of the model to sense hypoxia, and monitor reoxygenation also in a multicellular heart muscle model. Pharmacologically induced inotropy/chronotropy under isoprenaline resulted in enhanced Luc-signal suggesting enhanced oxygen consumption, leading to notable myocardial hypoxia. Conclusions: ODD-Luc-CMs can be used to monitor dynamic changes of cardiomyocyte oxygenation in living heart muscle samples. We provide proof-of-concept for pharmacologically induced myocardial interventions and envision applications of the developed model in drug screens and fundamental studies of ischemia/reperfusion injury.

Terminal Differentiation, Advanced Organotypic Maturation, and Modeling of Hypertrophic Growth in Engineered Heart Tissue

Cardiac tissue engineering should provide "realistic" in vitro heart muscle models and surrogate tissue for myocardial repair. For either application, engineered myocardium should display features of native myocardium, including terminal differentiation, organotypic maturation, and hypertrophic growth. To test the hypothesis that 3D-engineered heart tissue (EHT) culture supports (1) terminal differentiation as well as (2) organotypic assembly and maturation of immature cardiomyocytes, and (3) constitutes a methodological platform to investigate mechanisms underlying hypertrophic growth. We generated EHTs from neonatal rat cardiomyocytes and compared morphological and molecular properties of EHT and native myocardium from fetal, neonatal, and adult rats. We made the following key observations: cardiomyocytes in EHT (1) gained a high level of binucleation in the absence of notable cytokinesis, (2) regained a rod-shape and anisotropic sarcomere organization, (3) demonstrated a fetal-to-adult gene expression pattern, and (4) responded to distinct hypertrophic stimuli with concentric or eccentric hypertrophy and reexpression of fetal genes. The process of terminal differentiation and maturation (culture days 7-12) was preceded by a tissue consolidation phase (culture days 0-7) with substantial cardiomyocyte apoptosis and dynamic extracellular matrix restructuring. This study documents the propensity of immature cardiomyocytes to terminally differentiate and mature in EHT in a remarkably organotypic manner. It moreover provides the rationale for the utility of the EHT technology as a methodological bridge between 2D cell culture and animal models.

Low‐powered and accelerative synchronization in the coupled system of nonlinear hardware oscillators

AbstractIn a diffusively coupled system using a mathematical model of heart muscle, an acceleration phenomenon has been reported in which the oscillation period after coupling becomes smaller than the intrinsic period prior to coupling. In the present research, an acceleration phenomenon is observed in a coupled system of an electronic circuit model. Also, by using an electronic circuit simulator, the conditions causing acceleration in a coupled system are studied. The power consumption of a coupled system is numerically derived. It is found that the power consumption can decrease when the acceleration phenomenon takes place. Heart muscle cells not only accelerate the oscillation (or increase the number of oscillations) by mutual coupling but also reduce the power (or energy) consumption at the same time. It is suggested that efficient information transmission may be carried out with less energy overall. © 2004 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 87(12): 1–9, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.20081

Can Tissue Engineering Mend Broken Hearts?

Cardiac tissue engineering is an emerging field that may hold great promise for advancing the treatment of heart diseases. Cardiac tissue engineering is in its infancy, and the overall field of tissue engineering, which was formalized in the late 1980s at conferences and workshops sponsored by the National Science Foundation, is still new enough to warrant some description. By broad definition, tissue engineering involves the construction of tissue equivalents through the manipulation and combination of living cells and biomaterials. It is a multidisciplinary field combining diverse aspects of the life sciences, engineering, and clinical medicine. The overall goal of tissue engineering is to develop tissue equivalents for use in the repair, replacement, maintenance, or augmentation of tissues or organs. Although some aspects of cardiac tissue engineering research have been ongoing for generations, albeit without being known as such, directed efforts in the field are only beginning. The main justification for cardiac tissue engineering initiatives is straightforward: congenital and acquired heart diseases are substantial health problems, and there is a limited amount of donor tissue for use in surgical repairs. Heart defects are the most common congenital defect and are the leading cause of death in the first year of life.1,2⇓ Congenital heart defects may occur in as many as 14 of every 1000 live births,3 and approximately 25 000 surgical procedures are performed each year to correct them. Acquired heart diseases also have a profound effect on the population, and despite tremendous advances in medical and surgical treatments, it is estimated that each year 20 000 to 40 000 Americans could benefit from a heart transplant.4 Unfortunately, fewer than 2500 heart transplants are performed each year.4,5⇓ One of the principal reasons for the disparity between patient need and procedures performed is the lack of …

Three-dimensional reconstitution of embryonic cardiomyocytes in a collagen matrix: a new heart muscle model system.

A method has been developed for culturing cardiac myocytes in a collagen matrix to produce a coherently contracting 3-dimensional model heart tissue that allows direct measurement of isometric contractile force. Embryonic chick cardiomyocytes were mixed with collagen solution and allowed to gel between two Velcro-coated glass tubes. During culture, the cardiomyocytes formed spontaneously beating cardiac myocyte-populated matrices (CMPMs) anchored at opposite ends to the Velcro-covered tubes through which they could be attached to a force measuring system. Immunohistochemistry and electron microscopy revealed a highly organized tissue-like structure of alpha-actin and alpha-tropomyosin-positive cardiac myocytes exhibiting typical cross-striation, sarcomeric myofilaments, intercalated discs, desmosomes, and tight junctions. Force measurements of paced or unpaced CMPMs were performed in organ baths after 6-11 days of cultivation and were stable for up to 24 h. Force increased with frequency between 0.8 and 2.0 Hz (positive "staircase"), increasing rest length (Starling mechanism), and increasing extracellular calcium. The utility of this system as a test bed for genetic manipulation was demonstrated by infecting the CMPMs with a recombinant beta-galactosidase-carrying adenovirus. Transduction efficiency increased from about 5% (MOI 0.1) to about 50% (MOI 100). CMPMs display more physiological characteristics of intact heart tissue than monolayer cultures. This approach, simpler and faster than generation of transgenic animals, should allow functional consequences of genetic or pharmacological manipulation of cardiomyocytes in vitro to be studied under highly controlled conditions.

On the theory of the electrocardiogram

The biophysical basis for understanding the electrocardiogram is set forth. Bioelectric sources arise from electrical activity in the heart at the cellular level. The relation of these sources, which can be formally represented as impressed currents, to potentials involves solution of the volume conductor problem. This solution is based on Green's theorem. Sources are related to the transmembrane action potential through a bidomain model of heart muscle. Microscopic and macroscopic aspects of the bidomain model are developed. Various transformations of the source are considered, including multipoles, multiple dipoles, and replacement of the volume distribution with distributions on the heart surface. Time integrals of the waveform are related to excitation time and action potential duration. The theoretical results form the basis of a computer model of the electrocardiogram that relates skin potentials to the spatial and temporal distribution of action potentials in the heart. >

Contractile Filament Stress in the Left Ventricle and its Relationship to Wall Stress

A three-dimensional composite model of heart muscle is proposed, consisting of one-dimensional (uniaxial) active contractile filaments embedded in a passive elastic binder. Equations are developed which relate the force developed by the filaments to the local tissue stress. An approximate analysis is employed to determine the time variation of the contractile filament stress throughout the cardiac cycle from catheterization data. Results from 15 patients with normal left ventricles demonstrate that the stress developed by the contractile filaments is up to 25 percent more tensile than the wall stress, and that the binder stress is compressive during most of systole. In contrast, the one-dimensional lumped parameter muscle models previously employed predict active (CE) stresses less tensile than the wall stress and binder (PE) stresses that are tensile. We conclude that the use of a one-dimensional muscle model results in a significant underestimation of the active force generation required for pressure development and the power requirements for ejection. Prior studies relating muscle work and power to ventricular oxygen consumption should be re-examined in this light.

A one-dimensional viscoelastic model of cat heart muscle studied by small length perturbations during isometric contraction.

To develop a model of heart muscle, we studied cat papillary muscle contracting in a quasi-isometric condition under a fixed inotropic state. The properties of resting muscle were determined by using a step stretch of less than 1.2% of Lmax for initial lengths from 85 to 100% Lmax. The passive force response suggested the model of the passive branch (Fig. 1). All five parameters were small at muscle lengths below 95% of Lmax but increased markedly at longer lengths. The properties of contracting muscle were studied with a sinusoidal length change (amplitude less than 0.15% of Lmax, frequency 0.1-35.0 Hz). The frequency response of active (total minus passive) stiffness suggested the model of the active branch (Fig. 1). We determined the dependency of the elastic elements (K, Ks) and the viscous element (C) on length and time by recording the frequency response at various combinations of length and time Ks varied linearly with active force (FA). K and C exhibited time courses that paralleled FA up to 0.6tmax, and they maintained their values until 1.4tmax. K then fell toward zero, whereas C exhibited a secondary rise before it fell toward zero. K was dependent of length up to 95% of Lmax and then began to decline, but C varied in proportion to muscle length.