Caveolae in ventricular myocytes are required for stretch-dependent conduction slowing.

Mechanical stretch of cardiac muscle modulates action potential propagation velocity, causing potentially arrhythmogenic conduction slowing. The mechanisms by which stretch alters cardiac conduction remain unknown, but previous studies suggest that stretch can affect the conformation of caveolae in myocytes and other cell types. We tested the hypothesis that slowing of action potential conduction due to cardiac myocyte stretch is dependent on caveolae. Cardiac action potential propagation velocities, measured by optical mapping in isolated mouse hearts and in micropatterned mouse cardiomyocyte cultures, decreased reversibly with volume loading or stretch, respectively (by 19±5% and 26±4%). Stretch-dependent conduction slowing was not altered by stretch-activated channel blockade with gadolinium or by GsMTx-4 peptide, but was inhibited when caveolae were disrupted via genetic deletion of caveolin-3 (Cav3 KO) or membrane cholesterol depletion by methyl-ß-cyclodextrin. In wild-type mouse hearts, stretch coincided with recruitment of caveolae to the sarcolemma, as observed by electron microscopy. In myocytes from wild-type but not Cav3 KO mice, stretch significantly increased cell membrane capacitance (by 98±64%), electrical time constant (by 285±149%), and lipid recruitment to the bilayer (by 84±39%). Recruitment of caveolae to the sarcolemma during physiologic cardiomyocyte stretch slows ventricular action potential propagation by increasing cell membrane capacitance.

A novel computational model of mouse myocyte electrophysiology to assess the synergy between Na+ loading and CaMKII.

Ca(2+)-calmodulin-dependent protein kinase II (CaMKII) hyperactivity in heart failure causes intracellular Na(+) ([Na(+)]i) loading (at least in part by enhancing the late Na(+) current). This [Na(+)]i gain promotes intracellular Ca(2+) ([Ca(2+)]i) overload by altering the equilibrium of the Na(+)-Ca(2+) exchanger to impair forward-mode (Ca(2+) extrusion), and favour reverse-mode (Ca(2+) influx) exchange. In turn, this Ca(2+) overload would be expected to further activate CaMKII and thereby form a pathological positive feedback loop of ever-increasing CaMKII activity, [Na(+)]i, and [Ca(2+)]i. We developed an ionic model of the mouse ventricular myocyte to interrogate this potentially arrhythmogenic positive feedback in both control conditions and when CaMKIIδC is overexpressed as in genetically engineered mice. In control conditions, simulation of increased [Na(+)]i causes the expected increases in [Ca(2+)]i, CaMKII activity, and target phosphorylation, which degenerate into unstable Ca(2+) handling and electrophysiology at high [Na(+)]i gain. Notably, clamping CaMKII activity to basal levels ameliorates but does not completely offset this outcome, suggesting that the increase in [Ca(2+)]i per se plays an important role. The effect of this CaMKII-Na(+)-Ca(2+)-CaMKII feedback is more striking in CaMKIIδC overexpression, where high [Na(+)]i causes delayed afterdepolarizations, which can be prevented by imposing low [Na(+)]i, or clamping CaMKII phosphorylation of L-type Ca(2+) channels, ryanodine receptors and phospholamban to basal levels. In this setting, Na(+) loading fuels a vicious loop whereby increased CaMKII activation perturbs Ca(2+) and membrane potential homeostasis. High [Na(+)]i is also required to produce instability when CaMKII is further activated by increased Ca(2+) loading due to ß-adrenergic activation. Our results support recent experimental findings of a synergistic interaction between perturbed Na(+) fluxes and CaMKII, and suggest that pharmacological inhibition of intracellular Na(+) loading can contribute to normalizing Ca(2+) and membrane potential dynamics in heart failure.

Improved discretisation and linearisation of active tension in strongly coupled cardiac electro-mechanics simulations.

Mathematical models of cardiac electro-mechanics typically consist of three tightly coupled parts: systems of ordinary differential equations describing electro-chemical reactions and cross-bridge dynamics in the muscle cells, a system of partial differential equations modelling the propagation of the electrical activation through the tissue and a nonlinear elasticity problem describing the mechanical deformations of the heart muscle. The complexity of the mathematical model motivates numerical methods based on operator splitting, but simple explicit splitting schemes have been shown to give severe stability problems for realistic models of cardiac electro-mechanical coupling. The stability may be improved by adopting semi-implicit schemes, but these give rise to challenges in updating and linearising the active tension. In this paper we present an operator splitting framework for strongly coupled electro-mechanical simulations and discuss alternative strategies for updating and linearising the active stress component. Numerical experiments demonstrate considerable performance increases from an update method based on a generalised Rush-Larsen scheme and a consistent linearisation of active stress based on the first elasticity tensor.

A nonlinear model of passive muscle viscosity.

The material properties of passive skeletal muscle are critical to proper function and are frequently a target for therapeutic and interventional strategies. Investigations into the passive viscoelasticity of muscle have primarily focused on characterizing the elastic behavior, largely neglecting the viscous component. However, viscosity is a sizeable contributor to muscle stress and extensibility during passive stretch and thus there is a need for characterization of the viscous as well as the elastic components of muscle viscoelasticity. Single mouse muscle fibers were subjected to incremental stress relaxation tests to characterize the dependence of passive muscle stress on time, strain and strain rate. A model was then developed to describe fiber viscoelasticity incorporating the observed nonlinearities. The results of this model were compared with two commonly used linear viscoelastic models in their ability to represent fiber stress relaxation and strain rate sensitivity. The viscous component of mouse muscle fiber stress was not linear as is typically assumed, but rather a more complex function of time, strain and strain rate. The model developed here, which incorporates these nonlinearities, was better able to represent the stress relaxation behavior of fibers under the conditions tested than commonly used models with linear viscosity. It presents a new tool to investigate the changes in muscle viscous stresses with age, injury and disuse.

Minimum Information about a Cardiac Electrophysiology Experiment (MICEE): standardised reporting for model reproducibility, interoperability, and data sharing.

Cardiac experimental electrophysiology is in need of a well-defined Minimum Information Standard for recording, annotating, and reporting experimental data. As a step towards establishing this, we present a draft standard, called Minimum Information about a Cardiac Electrophysiology Experiment (MICEE). The ultimate goal is to develop a useful tool for cardiac electrophysiologists which facilitates and improves dissemination of the minimum information necessary for reproduction of cardiac electrophysiology research, allowing for easier comparison and utilisation of findings by others. It is hoped that this will enhance the integration of individual results into experimental, computational, and conceptual models. In its present form, this draft is intended for assessment and development by the research community. We invite the reader to join this effort, and, if deemed productive, implement the Minimum Information about a Cardiac Electrophysiology Experiment standard in their own work.

Cardiac resynchronization: insight from experimental and computational models.

Cardiac resynchronization therapy (CRT) is a promising therapy for heart failure patients with a conduction disturbance, such as left bundle branch block. The aim of CRT is to resynchronize contraction between and within ventricles. However, about 30% of patients do not respond to this therapy. Therefore, a better understanding is needed for the relation between electrical and mechanical activation. In this paper, we focus on to what extent animal experiments and mathematical models can help in order to understand the pathophysiology of asynchrony to further improve CRT.

Cell proliferation rates in an artificial tissue-engineered environment.

Worldwide, and particularly in Europe, Japan and the USA, cardiovascular disease is a major killer. It can be treated using tissue or organ transplant surgery, but donor organs may be scarce. Tissue engineering is the integration of engineering principles and biology to produce satisfactory synthetic replacement body parts, using viable cells in a suitable matrix, for regenerative medicine. The aim of this study was to measure and compare cell proliferation kinetics after different time intervals of myofibroblasts in a synthetic matrix, thus to be able to deduce the period that a transplanted-cell population can be expected to survive in a tissue-engineered environment. Porcine aortic wall cells were grown in a porous sponge scaffold, that later could be fashioned into aortic or heart valve substitutes. Freshly acquired cells were seeded on identical sponges and were grown under normal culture conditions for a period of 4 weeks. Seeding concentration was a million cells per sponge. Cells progressively populated the sponges, both covering the surface and infiltrating the depth of the matrix, via sponge pores. Samples were taken at 1 week and at 4 weeks, and the rate of cell proliferation was determined by the metaphase arrest technique. Specimens were also taken for light and electron microscopy to determine whether these transplanted cells were capable of synthesizing their own extracellular matrix.

Heart valve and arterial tissue engineering.

In the industrialized world, cardiovascular disease alone is responsible for almost half of all deaths. Many of the conditions can be treated successfully with surgery, often using transplantation techniques; however, autologous vessels or human-donated organs are in short supply. Tissue engineering aims to create specific, matching grafts by growing cells on appropriate matrices, but there are many steps between the research laboratory and the operating theatre. Neo-tissues must be effective, durable, non-thrombogenic and non-immunogenic. Scaffolds should be bio-compatible, porous (to allow cell/cell communication) and amenable to surgery. In the early days of cardiovascular tissue engineering, autologous or allogenic cells were grown on inert matrices, but patency and thrombogenicity of grafts were disappointing. The current ethos is toward appropriate cell types grown in (most often) a polymeric matrix that degrades at a rate compatible with the cells' production of their own extracellular matrical proteins, thus gradually replacing the graft with a living counterpart. The geometry is crucial. Computer models have been made of valves, and these are used as three-dimensional patterns for mass-production of implant scaffolds. Vessel walls have integral connective tissue architecture, and application of physiological level mechanical forces conditions bio-engineered components to align in precise orientation. This article reviews the concepts involved and successes achieved to date.

Complex distributions of residual stress and strain in the mouse left ventricle: experimental and theoretical models.

Most soft biological tissues, including ventricular myocardium, are not stress free when all external loads are removed. Residual stress has implications for mechanical performance of the heart, and may be an indicator of patterns of regional growth and remodeling. Cross-sectional rings of arrested ventricles opened up when a radial cut was made (initial mean opening angles were 64 +/- 17 degrees), but further circumferential cuts revealed the presence of additional residual stresses in the tissue with further opening of the rings. In normal mouse hearts, the inner half of a short-axis ring opened more than the outer half, and this change was dependent on apex-base location. At the apex the inner section vs. outer section opening angles were 226 +/- 47 degrees vs. 89 +/- 28 degrees, while at the base the same two angles were 160 +/- 30 degrees vs. 123 +/- 35 degrees. A simple theoretical cylindrical shell model with incompressible hyperelastic material properties was used to model the experimental deformations based on the cutting experiments. The model predicts different residual stress fields depending on the nature of the opening after the circumferential cut (which is done after the conventional radial cut). The observed opening angles were consistent with steep stress gradients near the endocardium compared with those predicted if the first cut was assumed to relieve all residual stresses. These results imply a more complex distribution of residual stress and strain in ventricular myocardium than previously thought.

In vivo finite element model-based image analysis of pacemaker lead mechanics.

BACKGROUND: Fractures of implanted pacemaker leads are currently identified by inspecting radiographic images without making full use of a priori known material and structural information. Moreover, lead designers are unable to incorporate clinical image data into analyses of lead mechanics. METHODS: A novel finite element/active contour method was developed to quantify the in vivo mechanics of implanted leads by estimating the distributions of stress, strain, and traction using biplane videoradiographic images. The nonlinear equilibrium equations governing a thin elastic beam undergoing 3-D large rotation were solved using one-dimensional isoparametric finite elements. External forces based on local image greyscale values were computed from each pair of images using a perspective transformation governing the relationship between the image planes. RESULTS: Cantilever beam forward solution results were within 0.2% of the analytic solution for a wide range of applied loads. The finite element/active contour model was able to reproduce the principal curvatures of a synthetic helix within 3% of the analytic solution and estimates of the helix's geometric torsion were within 20% of the analytic solution. Applying the method to biplane videoradiographic images of a lead acutely implanted in an anesthetized dog resulted in expected variations in curvature and bending stress between compliant and rigid segments of the lead. CONCLUSIONS: By incorporating knowledge about lead geometric and material properties, the 3-D finite element/active contour method regularizes the image reconstruction problem and allows for more quantitative and automatic assessment of implanted lead mechanics.

Oesophageal morphometry and residual strain in a mouse model of osteogenesis imperfecta.

Recently, it was demonstrated in the oesophagus that the zero-stress state is not a closed cylinder but an open circular cylindrical sector. The closed cylinder with no external loads applied is called the no-load state and residual strain is the difference in strain between the no-load state and the zero-stress state. To understand the physiology and pathology of the oesophagus, it is necessary to know the zero-stress state and the stress-strain relationships of the tissues in the oesophagus, and the changes of these states and relationships due to biological remodelling of the tissues under stress. The aim of this study was to investigate the morphological and biomechanical remodelling at the no-load and zero-stress states in mutant osteogenesis imperfecta murine (oim) mice with collagen deficiency. The oesophagi of seven oim and seven normal wild-type mice were excised, cleaned, and sectioned into rings in an organ bath containing calcium-free Krebs solution with dextran and EGTA. The rings were photographed in the no-load state and cut radially to obtain the zero-stress state. Equilibrium was awaited for 30 min and the specimens were photographed again. Circumferences, submucosa and muscle layer thicknesses and areas, and the opening angle were measured from the digitized images. The oesophagi in oim mice had smaller layer thicknesses and areas compared to the wild types. The largest reduction in layer thickness in oim mice was found in the submucosa (approximately 36%). Oim mice had significantly larger opening angles (120.2 +/- 4.5 degrees ) than wild-type mice (93.0 +/- 11.2 degrees ). The residual strain was compressive at the mucosal surface and tensile at the serosal surface in both oim and wild types. In the oim mice, the residual strains at the serosal and mucosal surfaces and the mucosa-submucosal-muscle layer interface were higher than in the wild types (P < 0.05). The gradient of residual strain per unit thickness was higher in oim mice than in wild-type mice, and was highest in submucosa (P < 0.05). The only morphometric measure that was similar in oim and wild-type mice was the inner circumference in the no-load state. In conclusion, our data show significant differences in the residual strain distribution and morphometry between oim mice and wild-type mice. The data suggest that the residual stress in oesophagus is caused by the tension in the muscle layer rather than the stiffness of the submucosa in compression and that the remodelling process in the oim oesophagus is due mainly to morphometric and biomechanical alterations in the submucosa.

Regional myocardial mechanics: integrative computational models of flow-function relations.

Many cardiac disorders result in regionally altered myocardial mechanics. Although myocardial strain distributions can be measured experimentally and clinically, regional wall stresses must be computed from computational models. Combining these approaches can provide insight into the structural basis of regional dysfunction under conditions such as acute myocardial infarction and ischemia-reperfusion. Recently, 3-dimensional computational models have helped to elucidate the structural basis of the functional border zone adjacent to acutely ischemic myocardium. They have also shown that heterogeneous dysfunction in ischemic-reperfused stunned myocardium does not necessarily imply heterogeneous myofilament injury. Now that computational models are able to reproduce many complex features of the 3-dimensional patterns of regional myocardial deformation observed experimentally, we suggest possible roles for such integrative models in clinical diagnosis.

Regional septal dysfunction in a three-dimensional computational model of focal myofiber disarray.

MLC2v/ras transgenic mice display a phenotype characteristic of hypertrophic cardiomyopathy, with septal hypertrophy and focal myocyte disarray. Experimental measurements of septal wall mechanics in ras transgenic mice have previously shown that regions of myocyte disarray have reduced principal systolic shortening, torsional systolic shear, and sarcomere length. To investigate the mechanisms of this regional dysfunction, a three-dimensional prolate spheroidal finite-element model was used to simulate filling and ejection in the hypertrophied mouse left ventricle with septal disarray. Focally disarrayed septal myocardium was modeled by randomly distributed three-dimensional regions of altered material properties based on measured statistical distributions of muscle fiber angular dispersion. Material properties in disarrayed regions were modeled by decreased systolic anisotropy derived from increased fiber angle dispersion and decreased systolic tension development associated with reduced sarcomere lengths. Compared with measurements in ras transgenic mice, the model showed similar heterogeneity of septal systolic strain with the largest reductions in principal shortening and torsional shear in regions of greatest disarray. Average systolic principal shortening on the right ventricular septal surface of the model was -0.114 for normal regions and -0.065 for disarrayed regions; for torsional shear, these values were 0.047 and 0.019, respectively. These model results suggest that regional dysfunction in ras transgenic mice may be explained in part by the observed structural defects, including myofiber dispersion and reduced sarcomere length, which contributed about equally to predicted dysfunction in the disarrayed myocardium.

Transmural distribution of three-dimensional systolic strains in stunned myocardium.

BACKGROUND: Regional function in stunned myocardium is usually thought to be more depressed in the endocardium than the epicardium. This has been attributed to the greater loss of blood flow at the endocardium during ischemia. METHODS AND RESULTS: We measured transmural distributions of 3D systolic strains relative to local myofiber axes in open-chest anesthetized dogs before 15 minutes of left anterior descending coronary artery occlusion and during 2 hours of reperfusion. During ischemia, regional myocardial blood flow was reduced 84% at the endocardium and 32% at the epicardium (P<0.005, n=7), but changes in end-systolic fiber length from baseline were transmurally uniform. Relative to baseline, radial segments in stunned tissue were significantly thinner at the endocardium than the epicardium at end systole (24+/-5% versus 16+/-3%; P<0.05, n=8), consistent with previous reports. Unlike radial and cross-fiber segments, however, the increase of end-systolic fiber lengths in stunned myocardium had no significant transmural gradient (23+/-8% epicardium versus 21+/-4% endocardium). We also observed significant 3D diastolic dysfunction in the ischemic-reperfused region transmurally. CONCLUSIONS: Myocardial ischemia/reperfusion in the dog results in a significant transmural gradient of dysfunction between epicardial and endocardial layers in radial and cross-fiber segments, but not for fiber segments, despite a gradient in blood flow reduction during ischemia. Perhaps systolic fiber dysfunction rather than the degree of perfusion deficit during the preceding ischemic period may be the main determinant of myocardial dysfunction during reperfusion.

Mechanoelectric feedback in a model of the passively inflated left ventricle.

Mechanoelectric feedback has been described in isolated cells and intact ventricular myocardium, but the mechanical stimulus that governs mechanosensitive channel activity in intact tissue is unknown. To study the interaction of myocardial mechanics and electrophysiology in multiple dimensions, we used a finite element model of the rabbit ventricles to simulate electrical propagation through passively loaded myocardium. Electrical propagation was simulated using the collocation-Galerkin finite element method. A stretch-dependent current was added in parallel to the ionic currents in the Beeler-Reuter ventricular action potential model. We investigated different mechanical coupling parameters to simulate stretch-dependent conductance modulated by either fiber strain, cross-fiber strain, or a combination of the two. In response to pressure loading, the conductance model governed by fiber strain alone reproduced the epicardial decrease in action potential amplitude as observed in experimental preparations of the passively loaded rabbit heart. The model governed by only cross-fiber strain reproduced the transmural gradient in action potential amplitude as observed in working canine heart experiments, but failed to predict a sufficient decrease in amplitude at the epicardium. Only the model governed by both fiber and cross-fiber strain reproduced the epicardial and transmural changes in action potential amplitude similar to experimental observations. In addition, dispersion of action potential duration nearly doubled with the same model. These results suggest that changes in action potential characteristics may be due not only to length changes along the long axis direction of the myofiber, but also due to deformation in the plane transverse to the fiber axis. The model provides a framework for investigating how cellular biophysics affect the function of the intact ventricles.

Age-associated cardiac dysfunction in Drosophila melanogaster.

The fruit fly, Drosophila melanogaster, has served as a valuable model/organism for the study of aging and was the first organism possessing a circulatory system to have its genome completely sequenced. However, little is known about the function of the heartlike organ of flies during the aging process. We have developed methods for studying cardiac function in vivo in adult flies. Using 2 different cardiovascular stress methods (elevated ambient temperature and external electrical pacing), we found that maximal heart rate is significantly and reproducibly reduced with aging in Drosophila, analogous to observations in elderly humans. We also describe for the first time several other aspects of the cardiac physiology of young adult and aging Drosophila, including an age-associated increase in rhythm disturbances. These observations suggest that the study of declining cardiac function in aging flies may serve as a genetically tractable model for genome-wide mutational screening for genes that participate in or protect against cardiac aging and disease.

Relating myocardial laminar architecture to shear strain and muscle fiber orientation.

Cardiac myofibers are organized into laminar sheets about four cells thick. Recently, it has been suggested that these layers coincide with the plane of maximum shear during systole. In general, there are two such planes, which are oriented at +/-45 degrees to the main principal strain axes. These planes do not necessarily contain the fiber axis. In the present study, we explicitly added the constraint that the sheet planes should also contain the muscle fiber axis. In a mathematical analysis of previously measured three-dimensional transmural systolic strain distributions in six dogs, we computed the planes of maximum shear, adding the latter constraint by using the also-measured muscle fiber axis. Generally, for such planes two solutions were found, suggesting that two populations of sheet orientation may exist. The angles at which the predicted sheets intersected transmural tissue slices, cut along left ventricular short- or long-axis planes, were strikingly similar to experimentally measured values. In conclusion, sheets coincide with planes of maximum systolic shear subject to the constraint that the muscle fiber axis is contained in this plane. Sheet orientation is not a unique function of the transmural location but occurs in two distinct populations.

Regional heterogeneity of function in nonischemic dilated cardiomyopathy.

OBJECTIVE: To quantify regional three-dimensional (3D) motion and myocardial strain using magnetic resonance (MR) tissue tagging in patients with non-ischemic dilated cardiomyopathy (DCM). METHODS: MR grid tagged images were obtained in multiple short- and long-axis planes in thirteen DCM patients. Regional 3D displacements and strains were calculated with the aid of a finite element model. Five of the patients were also imaged after LV volume reduction by partial left ventriculectomy (PLV), combined with mitral and tricuspid valve repair. RESULTS: DCM patients showed consistent, marked regional heterogeneity. Systolic lengthening occurred in the septum in both circumferential (%S(C) -5+/-7%) and longitudinal (%S(L) -2+/-5%) shortening components (negative values indicating lengthening). In contrast, the lateral wall showed relatively normal systolic shortening (%S(C) 12+/-6% and %S(L) 6+/-5%, P<0.001 lateral vs. septal walls). A geometric estimate of regional stress was correlated with shortening on a regional basis, but could not account for the differences in shortening between regions. In the five patients imaged post-PLV, septal function recovered (%S(C) 9+/-5%,%S(L) 6+/-5%, P<0.02 pre vs. post) with normalization of wall stress, whereas lateral wall shortening was reduced (%S(C) 7+/-6%,%S(L) 3+/-3%, P<0.02 pre vs. post) around the site of surgical resection. CONCLUSIONS: A consistent pattern of regional heterogeneity of myocardial strain was seen in all patients. Reduced function may be related to increased wall stress, since recovery of septal function is possible after PLV. However, simple geometric stress determinants are not sufficient to explain the functional heterogeneity observed.

Phase shifting prior to spatial filtering enhances optical recordings of cardiac action potential propagation.

Optical imaging of cardiac electrical activity using a voltage-sensitive dye provides high spatial resolution maps of action potential propagation and repolarization. Charge-coupled-device (CCD) camera-based imaging systems, however, are limited by their low signal-to-noise ratio. We have developed an image processing method to enhance the quality of optical signals recorded using a CCD camera. The method is based on the observation that within a small neighborhood of adjacent pixels, the morphology of the optical action potential varies little except for a phase shift in time resulting from the propagation of the wavefront. The method uses a phase-correlation technique to first correct for this time shift before spatially filtering with a 5 x 5 Gaussian convolution kernel (sigma = 1.179). A length 5 median filter is then applied to further reduce noise by filtering in the temporal domain. The image-processing scheme allows for more accurate extraction of maps of electrical activation, repolarization, and action potential duration.

Model-based analysis of optically mapped epicardial activation patterns and conduction velocity.

A novel parametric model-based method was developed to quantify epicardial conduction patterns and velocity in an isolated Langendorff-perfused rabbit heart. The method incorporated geometric and anatomical features of the left and right ventricles into the analysis. Optical images of propagation were obtained using the voltage-sensitive dye DI-4-ANEPPS, and a high-speed digital camera. Activation maps were extracted from these images and interpolated onto a three-dimensional finite-element model of epicardial geometry and fiber structure. Activation time was expressed as a function of local parametric coordinates, and a conduction velocity vector field was computed from the gradient of the scalar field. Activation times measured using bipolar electrodes did not differ significantly from times measured using the optical mapping technique. The method was able to detect a 34% decrease in average fiber velocity and a 28% decrease in average cross-fiber velocity following the addition of 0.5 mM heptanol into the perfusate. The combination of optical mapping with a three-dimensional geometric model of the ventricles provides a new tool to quantify wave-front propagation relative to anatomy at a relatively high spatial resolution.