Multi-scale approaches for the simulation of cardiac electrophysiology: I - Sub-cellular and stochastic calcium dynamics from cell to organ.

Computational models of the heart at multiple spatial scales, from sub-cellular nanodomains to the whole-organ, are a powerful tool for the simulation of cardiac electrophysiology. Application of these models has provided remarkable insight into the normal and pathological functioning of the heart. In these two articles, we present methods for modelling cardiac electrophysiology at all of these spatial scales. In part one, presented here, we discuss methods and approaches for modelling sub-cellular calcium dynamics at the whole-cell and organ scales, valuable for modelling excitation-contraction coupling and mechanisms of arrhythmia triggers.

Multi-scale approaches for the simulation of cardiac electrophysiology: II - Tissue-level structure and function.

Computational models of the heart, from cell-level models, through one-, two- and three-dimensional tissue-level simplifications, to biophysically-detailed three-dimensional models of the ventricles, atria or whole heart, allow the simulation of excitation and propagation of this excitation, and have provided remarkable insight into the normal and pathological functioning of the heart. In this article we present equations for modelling cellular excitation (i.e. the cell action potential) from both a phenomenological and a biophysical perspective. Hodgkin-Huxley formalism is discussed, along with the current generation of biophysically-detailed cardiac cell models. Alternative Markovian formulations for modelling ionic currents are also presented. Equations describing propagation of this cellular excitation, through one-, two- and three-dimensional idealised or realistic tissues, are then presented. For all types of model, from cell to tissue, methods for discretisation and integration of the underlying equations are discussed. The article finishes with a discussion of two tissue-level experimental imaging techniques - diffusion tensor magnetic resonance imaging and optical imaging - that can be used to provide data for parameterisation and validation of cell- and tissue-level cardiac models.

Abnormal skeletal muscle blood flow, contractile mechanics and fibre morphology in a rat model of obese-HFpEF.

KEY POINTS: Heart failure is characterised by limb and respiratory muscle impairments that limit functional capacity and quality of life. However, compared with heart failure with reduced ejection fraction (HFrEF), skeletal muscle alterations induced by heart failure with preserved ejection fraction (HFpEF) remain poorly explored. Here we report that obese-HFpEF induces multiple skeletal muscle alterations in the rat hindlimb, including impaired muscle mechanics related to shortening velocity, fibre atrophy, capillary loss, and an impaired blood flow response to contractions that implies a perfusive oxygen delivery limitation. We also demonstrate that obese-HFpEF is characterised by diaphragmatic alterations similar to those caused by denervation - atrophy in Type IIb/IIx (fast/glycolytic) fibres and hypertrophy in Type I (slow/oxidative) fibres. These findings extend current knowledge in HFpEF skeletal muscle physiology, potentially underlying exercise intolerance, which may facilitate future therapeutic approaches. ABSTRACT: Peripheral skeletal muscle and vascular alterations induced by heart failure with preserved ejection fraction (HFpEF) remain poorly identified, with limited therapeutic targets. This study used a cardiometabolic obese-HFpEF rat model to comprehensively phenotype skeletal muscle mechanics, blood flow, microvasculature and fibre atrophy. Lean (n = 8) and obese-HFpEF (n = 8) ZSF1 rats were compared. Skeletal muscles (soleus and diaphragm) were assessed for in vitro contractility (isometric and isotonic properties) alongside indices of fibre-type cross-sectional area, myosin isoform, and capillarity, and estimated muscle PO2 . In situ extensor digitorum longus (EDL) contractility and femoral blood flow were assessed. HFpEF soleus demonstrated lower absolute maximal force by 22%, fibre atrophy by 24%, a fibre-type shift from I to IIa, and a 17% lower capillary-to-fibre ratio despite increased capillary density (all P < 0.05) with preserved muscle PO2 (P = 0.115) and isometric specific force (P > 0.05). Soleus isotonic properties (shortening velocity and power) were impaired by up to 17 and 22%, respectively (P < 0.05), while the magnitude of the exercise hyperaemia was attenuated by 73% (P = 0.012) in line with higher muscle fatigue by 26% (P = 0.079). Diaphragm alterations (P < 0.05) included Type IIx fibre atrophy despite Type I/IIa fibre hypertrophy, with increased indices of capillarity alongside preserved contractile properties during isometric, isotonic, and cyclical contractions. In conclusion, obese-HFpEF rats demonstrated blunted skeletal muscle blood flow during contractions in parallel to microvascular structural remodelling, fibre atrophy, and isotonic contractile dysfunction in the locomotor muscles. In contrast, diaphragm phenotype remained well preserved. This study identifies numerous muscle-specific impairments that could exacerbate exercise intolerance in obese-HFpEF.

Investigation of the Role of Myocyte Orientations in Cardiac Arrhythmia Using Image-Based Models.

Cardiac electrical excitation-propagation is influenced by myocyte orientations (cellular organization). Quantitatively understanding this relationship presents a significant research challenge, especially during arrhythmias in which excitation patterns become complex. Tissue-scale simulations of cardiac electrophysiology, incorporating both dynamic action potential behavior and image-based myocardial architecture, provide an approach to investigate three-dimensional (3D) propagation of excitation waves in the heart. In this study, we aimed to assess the importance of natural variation in myocyte orientations on cardiac arrhythmogenesis using 3D tissue electrophysiology simulations. Three anatomical models (i.e., describing myocyte orientations) of healthy rat ventricles-obtained using diffusion tensor imaging at 100 µm resolution-were registered to a single biventricular geometry (i.e., a single cardiac shape), in which the myocyte orientations could be represented by each of the diffusion tensor imaging data sets or by an idealized rule-based description. The Fenton-Karma cellular excitation model was modified to reproduce rat ventricular action potential duration restitution to create reaction-diffusion cardiac electrophysiology models. Over 250 3D simulations were performed to investigate the effects of myocyte orientations on the following: 1) ventricular activation, 2) location-dependent arrhythmia induction via rapid pacing, and 3) dynamics of re-entry averaged over multiple episodes. It was shown that 1) myocyte orientation differences manifested themselves in local activation times, but the influence on total activation time was small; 2) differences in myocyte orientations could critically affect the inducibility and persistence of arrhythmias for specific stimulus-location/cycle-length combinations; and 3) myocyte orientations alone could be an important determinant of scroll wave break, although no significant differences were observed in averaged arrhythmia dynamics between the four myocyte orientation scenarios considered. Our results show that myocyte orientations are an important determinant of arrhythmia inducibility, persistence, and scroll wave break. These findings suggest that where specificity is desired (for example, when predicting location-dependent, patient-specific arrhythmia inducibility), subject-specific myocyte orientations may be important.

Dissociating external power from intramuscular exercise intensity during intermittent bilateral knee-extension in humans.

KEY POINTS: Continuous high-intensity constant-power exercise is unsustainable, with maximal oxygen uptake (V̇O2 max ) and the limit of tolerance attained after only a few minutes. Performing the same power intermittently reduces the O2 cost of exercise and increases tolerance. The extent to which this dissociation is reflected in the intramuscular bioenergetics is unknown. We used pulmonary gas exchange and 31 P magnetic resonance spectroscopy to measure whole-body V̇O2, quadriceps phosphate metabolism and pH during continuous and intermittent exercise of different work:recovery durations. Shortening the work:recovery durations (16:32 s vs. 32:64 s vs. 64:128 s vs. continuous) at a work rate estimated to require 110% peak aerobic power reduced V̇O2, muscle phosphocreatine breakdown and muscle acidification, eliminated the glycolytic-associated contribution to ATP synthesis, and increased exercise tolerance. Exercise intensity (i.e. magnitude of intramuscular metabolic perturbations) can be dissociated from the external power using intermittent exercise with short work:recovery durations. ABSTRACT: Compared with work-matched high-intensity continuous exercise, intermittent exercise dissociates pulmonary oxygen uptake (V̇O2) from the accumulated work. The extent to which this reflects differences in O2 storage fluctuations and/or contributions from oxidative and substrate-level bioenergetics is unknown. Using pulmonary gas-exchange and intramuscular 31 P magnetic resonance spectroscopy, we tested the hypotheses that, at the same power: ATP synthesis rates are similar, whereas peak V̇O2 amplitude is lower in intermittent vs. continuous exercise. Thus, we expected that: intermittent exercise relies less upon anaerobic glycolysis for ATP provision than continuous exercise; shorter intervals would require relatively greater fluctuations in intramuscular bioenergetics than in V̇O2 compared to longer intervals. Six men performed bilateral knee-extensor exercise (estimated to require 110% peak aerobic power) continuously and with three different intermittent work:recovery durations (16:32, 32:64 and 64:128 s). Target work duration (576 s) was achieved in all intermittent protocols; greater than continuous (252 ± 174 s; P < 0.05). Mean ATP turnover rate was not different between protocols (∼43 mm min-1 on average). However, the intramuscular phosphocreatine (PCr) component of ATP generation was greatest (∼30 mm min-1 ), and oxidative (∼10 mm min-1 ) and anaerobic glycolytic (∼1 mm min-1 ) components were lowest for 16:32 and 32:64 s intermittent protocols, compared to 64:128 s (18 ± 6, 21 ± 10 and 10 ± 4 mm min-1 , respectively) and continuous protocols (8 ± 6, 20 ± 9 and 16 ± 14 mm min-1 , respectively). As intermittent work duration increased towards continuous exercise, ATP production relied proportionally more upon anaerobic glycolysis and oxidative phosphorylation, and less upon PCr breakdown. However, performing the same high-intensity power intermittently vs. continuously reduced the amplitude of fluctuations in V̇O2 and intramuscular metabolism, dissociating exercise intensity from the power output and work done.

The influence of metabolic and circulatory heterogeneity on the expression of pulmonary oxygen uptake kinetics in humans.

We examined the relationship amongst baseline work rate (WR), phase II pulmonary oxygen uptake (V̇(O2p)) time constant (τV̇(O2p)) and functional gain (G(P)=ΔV̇(O2p)/ΔWR) during moderate-intensity exercise. Transitions were initiated from a constant or variable baseline WR. A validated circulatory model was used to examine the role of heterogeneity in muscle metabolism (V̇(O2m)) and blood flow (Q̇(m)) in determining V̇(O2p) kinetics. We hypothesized that τV̇(O2p) and G(P) would be invariant in the constant baseline condition but would increase linearly with increased baseline WR. Fourteen men completed three to five repetitions of ∆40 W step transitions initiated from 20, 40, 60, 80, 100 and 120 W on a cycle ergometer. The ∆40 W step transitions from 60, 80, 100 and 120 W were preceded by 6 min of 20 W cycling, from which the progressive ΔWR transitions (constant baseline condition) were examined. The V̇(O2p) was measured breath by breath using mass spectrometry and a volume turbine. For a given ΔWR, both τV̇(O2p) (22-35 s) and G(P) (8.7-10.5 ml min(-1) W(-1)) increased (P < 0.05) linearly as a function of baseline WR (20-120 W). The τV̇(O2p) was invariant (P < 0.05) in transitions initiated from 20 W, but G(P) increased with ΔWR (P < 0.05). Modelling the summed influence of multiple muscle compartments revealed that τV̇(O2p) could appear fast (24 s), and similar to in vivo measurements (22 ± 6 s), despite being derived from τV̇(O2p) values with a range of 15-40 s and τQ̇(m) with a range of 20-45 s, suggesting that within the moderate-intensity domain phase II V̇(O2p) kinetics are slowed dependent on the pretransition WR and are strongly influenced by muscle metabolic and circulatory heterogeneity.

Towards computational modelling of the human foetal electrocardiogram: normal sinus rhythm and congenital heart block.

AIMS: We aim to engineer a computational model of propagation during normal sinus rhythm in the foetal human heart, by modifying models for adult cardiac tissue to match foetal electrocardiogram (fECG) characteristics. The model will be partially validated by fECG data, and applied to explore possible mechanisms of arrhythmogenesis in the foetal heart. METHODS AND RESULTS: Foetal electrocardiograms have been recorded during pregnancy, with P- and T-waves, and the QRS complex, identified by averaging and signal processing. Intervals of the fECG are extracted and used to modify currently available human adult cardiomyocyte models. RR intervals inform models of the pacemaking cells by constraining their rate, the QT interval and its rate dependence constrain models of ventricular cells, and the width of the P-wave, the QR and PR intervals constrain propagation times, conduction velocities, and intercellular coupling. These cell models are coupled into a one-dimensional (1D) model of propagation during normal sinus rhythm in the human foetal heart. We constructed a modular, heterogeneous 1D model for propagation in the foetal heart, and predicted the effects of reduction in L-type Ca(++) current. These include bradycardia and atrioventricular conduction blocks. These may account quantitatively for congenital heart block produced by positive IgG antibodies. CONCLUSION: The fECG can be interpreted mechanistically and quantitatively by using a simple computational model for propagation. After further validation, by clinical recordings of the fECG and the electrophysiological experiments on foetal cardiac cells and tissues, the model may be used to predict the effects of maternally administered pharmaceuticals on the fECG.

The Dynamics of Locomotor Neuromuscular Fatigue during Ramp-Incremental Cycling to Intolerance.

INTRODUCTION: Traditional neuromuscular fatigue assessments are not task-specific and are unable to characterize neuromuscular performance decline during dynamic whole-body exercise. This study used interleaved maximal isokinetic cycling efforts to characterize the dynamics of the decline in neuromuscular performance during ramp-incremental (RI) cycle ergometry exercise to intolerance. METHODS: Eleven young healthy participants (10 male/1 female) performed two RI cycle ergometry exercise tests to intolerance: [1] RI-exercise with peak isokinetic power (Piso) at 80 rev·min-1 measured at baseline and immediately at intolerance from a maximal ~6 s effort; [2] RI-exercise where additional Piso measurements were interleaved every 90 s to characterize the decline in neuromuscular performance during the RI-test. Muscle excitation was measured using EMG during all Piso assessments, and pulmonary gas exchange was measured throughout. RESULTS: Baseline Piso was 832 ± 140 W and RI-exercise reduced Piso to 349 ± 96 W at intolerance (p = 0.001), which was not different from flywheel power at intolerance (303 ± 96 W; p = 0.292). There was no reduction in Piso between baseline cycling and gas exchange threshold (GET; baseline Piso vs. mean Piso below GET: 828 ± 146 vs. 815 ± 149 W; p = 1.00). Piso fell progressively above GET until intolerance (Piso every 90 s above GET: 759 ± 139; 684 ± 141; 535 ± 144; 374 ± 117 W; each p < 0.05 vs. baseline and mean Piso below GET). Peak muscle excitation (EMG) was also reduced only above GET (73 ± 14 % of baseline, at intolerance; p < 0.05). However, the reduction in peak Piso preceded the reduction in peak muscle excitation. CONCLUSIONS: The dynamics of the decline in neuromuscular performance (reduction in Piso and EMG) during RI-exercise are consistent with known intensity-dependent metabolic and traditional pre-post neuromuscular fatigue responses to discrete bouts of constant-power exercise.

Slowed oxygen uptake kinetics in hypoxia correlate with the transient peak and reduced spatial distribution of absolute skeletal muscle deoxygenation.

It remains unclear whether an overshoot in skeletal muscle deoxygenation (HHb; reflecting a microvascular kinetic mismatch of O2 delivery to consumption) contributes to the slowed adjustment of oxidative energy provision at the onset of exercise. We progressively reduced the fractional inspired O2 concentration (F(I,O2)) to investigate the relationship between slowed pulmonary O2 uptake (V(O2)) kinetics and the dynamics and spatial distribution of absolute[HHb]. Seven healthy men performed 8 min cycling transitions during normoxia (F(I,O2) = 0.21),moderate hypoxia (F(I,O2) = 0.16) and severe hypoxia (F(I,O2)= 0.12). V(O2) uptake was measured using a flowmeter and gas analyser system. Absolute [HHb] was quantified by multichannel,time-resolved near-infrared spectroscopy from the rectus femoris and vastus lateralis (proximal and distal regions), and corrected for adipose tissue thickness. The phase II V(O2) time constant was slowed (P <0.05) as F(I,O2) decreased (normoxia, 17 ± 3 s;moderate hypoxia, 22 ± 4 s; and severe hypoxia, 29 ± 9 s). The [HHb] overshoot was unaffected by hypoxia, but the transient peak [HHb] increased with the reduction in F(I,O2) (P <0.05). Slowed V(O2) kinetics in hypoxia were positively correlated with increased peak [HHb] in the transient (r(2) = 0.45; P <0.05), but poorly related to the [HHb] overshoot. A reduction of spatial heterogeneity in peak [HHb]was inversely correlated with slowed V(O2) kinetics (r(2) = 0.49; P <0.05). These data suggest that aerobic energy provision at the onset of exercise may be limited by the following factors: (i) the absolute ratio (i.e. peak [HHb]) rather than the kinetic ratio (i.e. [HHb] overshoot) of microvascular O2 delivery to consumption; and (ii) a reduced spatial distribution in the ratio of microvascular O2 delivery to consumption across the muscle.

A simple approach for image-based modelling of the heart that enables robust simulation of highly heterogeneous electrical excitation.

Remodelling of cardiac tissue structure, including intercellular electrical coupling, is a major determinant of the complex and heterogeneous excitation patterns associated with cardiac arrhythmias. Evaluation of the precise mechanisms by which local tissue structure determines global arrhythmic excitation patterns is a major challenge that may be critically important for the development of effective treatment strategies. Computational modelling is a key tool in the study of cardiac arrhythmias, yet the established approaches for organ-scale modelling are unsuitable to capture the impact of local conduction heterogeneities; a novel approach is required to provide this multi-scale mechanistic insight. We present a fundamentally simple yet powerful approach to simulate electrical excitation in highly heterogeneous whole-heart models that exploits the underlying discreteness of the myocardium. Preliminary simulations demonstrate that this approach can capture lower conduction velocities and reproduce wave breakdown and the development of re-entry in a range of conditions.

Ionic current changes underlying action potential repolarization responses to physiological pacing and adrenergic stimulation in adult rat ventricular myocytes.

This study aimed to simulate ventricular responses to elevations in myocyte pacing and adrenergic stimulation using a novel electrophysiological rat model and investigate ion channel responses underlying action potential (AP) modulations. Peak ion currents and AP repolarization to 50% and 90% of full repolarization (APD50-90 ) were recorded during simulations at 1-10 Hz pacing under control and adrenergic stimulation conditions. Further simulations were performed with incremental ion current block (L-type calcium current, ICa ; transient outward current, Ito ; slow delayed rectifier potassium current, IKs ; rapid delayed rectifier potassium current, IKr ; inward rectifier potassium current, IK1 ) to identify current influence on AP response to exercise. Simulated APD50-90 closely resembled experimental findings. Rate-dependent increases in IKs (6%-101%), IKr (141%-1339%), and ICa (0%-15%) and reductions in Ito (11%-57%) and IK1 (1%-9%) were observed. Meanwhile, adrenergic stimulation triggered moderate increases in all currents (23%-67%) except IK1 . Further analyses suggest AP plateau is most sensitive to modulations in Ito and ICa while late repolarization is most sensitive to IK1 , ICa , and IKs , with alterations in IKs predominantly stimulating the greatest magnitude of influence on late repolarization (35%-846% APD90 prolongation). The modified Leeds rat model (mLR) is capable of accurately modeling APs during physiological stress. This study highlights the importance of ICa , Ito , IK1, and IKs in controlling electrophysiological responses to exercise. This work will benefit the study of cardiac dysfunction, arrythmia, and disease, though future physiologically relevant experimental studies and model development are required.

Visualization and quantification of whole rat heart laminar structure using high-spatial resolution contrast-enhanced MRI.

It has been shown by histology that cardiac myocytes are organized into laminae and this structure is important in function, both influencing the spread of electrical activation and enabling myocardial thickening in systole by laminar sliding. We have carried out high-spatial resolution three-dimensional MRI of the ventricular myolaminae of the entire volume of the isolated rat heart after contrast perfusion [dimeglumine gadopentate (Gd-DTPA)]. Four ex vivo rat hearts were perfused with Gd-DTPA and fixative and high-spatial resolution MRI was performed on a 9.4T MRI system. After MRI, cryosectioning followed by histology was performed. Images from MRI and histology were aligned, described, and quantitatively compared. In the three-dimensional MR images we directly show the presence of laminae and demonstrate that these are highly branching and are absent from much of the subepicardium. We visualized these MRI volumes to demonstrate laminar architecture and quantitatively demonstrated that the structural features observed are similar to those imaged in histology. We showed qualitatively and quantitatively that laminar architecture is similar in the four hearts. MRI can be used to image the laminar architecture of ex vivo hearts in three dimensions, and the images produced are qualitatively and quantitatively comparable with histology. We have demonstrated in the rat that: 1) laminar architecture is consistent between hearts; 2) myolaminae are absent from much of the subepicardium; and 3) although localized orthotropy is present throughout the myocardium, tracked myolaminae are branching structures and do not have a discrete identity.

Cardiac arrhythmia mechanisms in rats with heart failure induced by pulmonary hypertension.

Pulmonary hypertension provokes right heart failure and arrhythmias. Better understanding of the mechanisms underlying these arrhythmias is needed to facilitate new therapeutic approaches for the hypertensive, failing right ventricle (RV). The aim of our study was to identify the mechanisms generating arrhythmias in a model of RV failure induced by pulmonary hypertension. Rats were injected with monocrotaline to induce either RV hypertrophy or failure or with saline (control). ECGs were measured in conscious, unrestrained animals by telemetry. In isolated hearts, electrical activity was measured by optical mapping and myofiber orientation by diffusion tensor-MRI. Sarcoplasmic reticular Ca(2+) handling was studied in single myocytes. Compared with control animals, the T-wave of the ECG was prolonged and in three of seven heart failure animals, prominent T-wave alternans occurred. Discordant action potential (AP) alternans occurred in isolated failing hearts and Ca(2+) transient alternans in failing myocytes. In failing hearts, AP duration and dispersion were increased; conduction velocity and AP restitution were steeper. The latter was intrinsic to failing single myocytes. Failing hearts had greater fiber angle disarray; this correlated with AP duration. Failing myocytes had reduced sarco(endo)plasmic reticular Ca(2+)-ATPase activity, increased sarcoplasmic reticular Ca(2+)-release fraction, and increased Ca(2+) spark leak. In hypertrophied hearts and myocytes, dysfunctional adaptation had begun, but alternans did not develop. We conclude that increased electrical and structural heterogeneity and dysfunctional sarcoplasmic reticular Ca(2+) handling increased the probability of alternans, a proarrhythmic predictor of sudden cardiac death. These mechanisms are potential therapeutic targets for the correction of arrhythmias in hypertensive, failing RVs.

A raised metabolic rate slows pulmonary O(2) uptake kinetics on transition to moderate-intensity exercise in humans independently of work rate.

During exercise below the lactate threshold (LT), the rate of adjustment (τ) of pulmonary VO(2) uptake (τ) is slowed when initiated from a raised work rate. Whether this is consequent to the intrinsic properties of newly recruited muscle fibres, slowed circulatory dynamics or the effects of a raised metabolism is not clear. We aimed to determine the influence of these factors on τV(O(2)) using combined in vivo and in silico approaches. Fifteen healthy men performed repeated 6 min bouts on a cycle ergometer with work rates residing between 20 W and 90% LT, consisting of the following: (1) two step increments in work rate (S1 and S2), one followed immediately by the other, equally bisecting 20 W to 90% LT; (2) two 20 W to 90% LT bouts separated by 30 s at 20 W to raise muscle oxygenation and pretransition metabolism (R1 and R2); and (3) two 20 W to 90% LT bouts separated by 12 min at 20 W allowing full recovery (F1 and F2). Pulmonary O(2) uptake was measured breath by breath by mass spectrometry and turbinometry, and quadriceps oxygenation using near-infrared spectroscopy. The influence of circulatory dynamics on the coupling of muscle and τV(O(2)) lung was assessed by computer simulations. The τV(O(2)) in R2 (32 ± 9 s) was not different (P > 0.05) from S2 (30 ± 10 s), but both were greater (P < 0.05) than S1 (20 ± 10 s) and the F control bouts (26 ± 10 s). The slowed V(O(2)) kinetics in R2 occurred despite muscle oxygenation being raised throughout, and could not be explained by slowed circulatory dynamics (τV(O(2)) predicted by simulations: S1 = R2 < S2). These data therefore suggest that the dynamics of muscle O(2) consumption are slowed when exercise is initiated from a less favourable energetic state.

Quantitative prediction of the arrhythmogenic effects of de novo hERG mutations in computational models of human ventricular tissues.

Mutations to hERG which result in changes to the rapid delayed rectifier current I(Kr) can cause long and short QT syndromes and are associated with an increased risk of cardiac arrhythmias. Experimental recordings of I(Kr) reveal the effects of mutations at the channel level, but how these changes translate to the cell and tissue levels remains unclear. We used computational models of human ventricular myocytes and tissues to predict and quantify the effects that de novo hERG mutations would have on cell and tissue electrophysiology. Mutations that decreased I(Kr) maximum conductance resulted in an increased cell and tissue action potential duration (APD) and a long QT interval on the electrocardiogram (ECG), whereas those that caused a positive shift in the inactivation curve resulted in a decreased APD and a short QT. Tissue vulnerability to re-entrant arrhythmias was correlated with transmural dispersion of repolarisation, and any change to this vulnerability could be inferred from the ECG QT interval or T wave peak-to-end time. Faster I(Kr) activation kinetics caused cell APD alternans to appear over a wider range of pacing rates and with a larger magnitude, and spatial heterogeneity in these cellular alternans resulted in discordant alternans at the tissue level. Thus, from channel kinetic data, we can predict the tissue-level electrophysiological effects of any hERG mutations and identify how the mutation would manifest clinically, as either a long or short QT syndrome with or without an increased risk of alternans and re-entrant arrhythmias.

Deterministic and Stochastic Cellular Mechanisms Contributing to Carbon Monoxide Induced Ventricular Arrhythmias.

Chronic exposure to low levels of Carbon Monoxide is associated with an increased risk of cardiac arrhythmia. Microelectrode recordings from rat and guinea pig single isolated ventricular myocytes exposed to CO releasing molecule CORM-2 and excited at 0.2/s show repolarisation changes that develop over hundreds of seconds: action potential prolongation by delayed repolarisation, EADs, multiple EADs and oscillations around the plateau, leading to irreversible repolarisation failure. The measured direct effects of CO on currents in these cells, and ion channels expressed in mammalian systems showed an increase in prolonged late Na+, and a decrease in the maximal T- and L-type Ca++. peak and late Na+, ultra-rapid delayed, delayed rectifier, and the inward rectifier K+ currents. Incorporation of these CO induced changes in maximal currents in ventricular cell models; (Gattoni et al., J. Physiol., 2016, 594, 4193-4224) (rat) and (Luo and Rudy, Circ. Res., 1994, 74, 1071-1096) (guinea-pig) and human endo-, mid-myo- and epi-cardial (O'Hara et al., PLoS Comput. Biol., 2011, 7, e1002061) models, by changes in maximal ionic conductance reproduces these repolarisation abnormalities. Simulations of cell populations with Gaussian distributions of maximal conductance parameters predict a CO induced increase in APD and its variability. Incorporation of these predicted CO induced conductance changes in human ventricular cell electrophysiology into ventricular tissue and wall models give changes in indices for the probability of the initiation of re-entrant arrhythmia.

Power Reserve at Intolerance in Ramp-Incremental Exercise Is Dependent on Incrementation Rate.

INTRODUCTION: The mechanism(s) of exercise intolerance at V˙O2max remain poorly understood. In health, standard ramp-incremental (RI) exercise is limited by fatigue-induced reductions in maximum voluntary cycling power. Whether neuromuscular fatigue also limits exercise when the RI rate is slow and RI peak power at intolerance is lower than standard RI exercise, is unknown. METHODS: In twelve healthy participants, maximal voluntary cycling power was measured during a short (~6 s) isokinetic effort at 80 rpm (Piso) at baseline and, using an instantaneous switch from cadence-independent to isokinetic cycling, immediately at the limit of RI exercise with RI rates of 50, 25, and 10 W·min-1 (RI-50, RI-25, and RI-10). Breath-by-breath pulmonary gas exchange was measured throughout. RESULTS: Baseline Piso was not different among RI rates (analysis of variance; P > 0.05). Tolerable duration increased with decreasing RI rate (RI-50, 411 ± 58 s vs RI-25, 732 ± 93 s vs RI-10, 1531 ± 288 s; P < 0.05). At intolerance, V˙O2peak was not different among RI rates (analysis of variance; P > 0.05), but RI peak power decreased with RI rate (RI-50, 361 ± 48 W vs RI-25, 323 ± 39 W vs RI-10, 275 ± 38 W; P < 0.05). Piso at intolerance was 346 ± 43 W, 353 ± 45 W, and 392 ± 69 W for RI-50, RI-25, and RI-10, respectively (P < 0.05 for RI-10 vs RI-50 and RI-25). At intolerance, in RI-50 and RI-25, Piso was not different from RI peak power (P > 0.05), thus there was no "power reserve." In RI-10, Piso was greater than RI peak power at intolerance (P < 0.001), that is, there was a "power reserve." CONCLUSIONS: In RI-50 and RI-25, the absence of a power reserve suggests the neuromuscular fatigue-induced reduction in Piso coincided with V˙O2max and limited the exercise. In RI-10, the power reserve suggests neuromuscular fatigue was insufficient to limit the exercise, and additional mechanisms contributed to intolerance at V˙O2max.

The canine virtual ventricular wall: a platform for dissecting pharmacological effects on propagation and arrhythmogenesis.

We have constructed computational models of canine ventricular cells and tissues, ultimately combining detailed tissue architecture and heterogeneous transmural electrophysiology. The heterogeneity is introduced by modifying the Hund-Rudy canine cell model in order to reproduce experimentally reported electrophysiological properties of endocardial, midmyocardial (M) and epicardial cells. These models are validated against experimental data for individual ionic current and action potential characteristics, and their rate dependencies. 1D and 3D heterogeneous virtual tissues are constructed, with detailed tissue architecture (anisotropy and orthotropy, due to fibre orientation and sheet structure) of the left ventricular wall wedge extracted from a diffusion tensor imaging data set. The models are used to study the effects of tissue heterogeneity and class III drugs on transmural propagation and tissue vulnerability to re-entry. We have determined relationships between the transmural dispersion of action potential duration (APD) and the vulnerable window in the 1D virtual ventricular wall, and demonstrated how changes in the transmural heterogeneity, and hence tissue vulnerability, can lead to generation of re-entry in the 3D ventricular wedge. Two class III drugs with opposite qualitative effects on transmural APD heterogeneity are considered: d-sotalol that increases transmural APD dispersion, and amiodarone that decreases it. Simulations with the 1D virtual ventricular wall show that under d-sotalol conditions the vulnerable window is substantially wider compared to amiodarone conditions, primarily in the epicardial region where unidirectional conduction block persists until the adjacent M cells are fully repolarised. Further simulations with the 3D ventricular wedge have shown that ectopic stimulation of the epicardial region results in generation of sustained re-entry under d-sotalol conditions, but not under amiodarone conditions or in control. Again, APD increase in M cells was identified as the major contributor to tissue vulnerability--re-entry was initiated primarily due to ectopic excitation propagating around the unidirectional conduction block in the M cell region. This suggests an electrophysiological mechanism for the anti- and proarrhythmic effects of the class III drugs: the relative safety of amiodarone in comparison to d-sotalol can be explained by relatively low transmural APD dispersion, and hence, a narrow vulnerable window and low probability of re-entry in the tissue.

Effects of Heart Rate and Ventricular Wall Thickness on Non-invasive Mapping: An in silico Study.

Background: Non-invasive cardiac mapping-also known as Electrocardiographic imaging (ECGi)-is a novel, painless and relatively economic method to map the electrical activation and repolarization patterns of the heart, providing a valuable tool for early identification and diagnosis of conduction abnormalities and arrhythmias. Moreover, the ability to obtain information on cardiac electrical activity non-invasively using ECGi provides the potential for a priori information to guide invasive surgical procedures, improving success rates, and reducing procedure time. Previous studies have shown the influence of clinical variables, such as heart rate, heart size, endocardial wall, and body composition on surface electrocardiogram (ECG) measurements. The influence of clinical variables on the ECG variability has provided information on cardiovascular control and its abnormalities in various pathologies. However, the effects of such clinical variables on the Body Surface Potential (BSP) and ECGi maps have yet to be systematically investigated. Methods: In this study we investigated the effects of heart size, intracardiac thickness, and heart rate on BSP and ECGi maps using a previously-developed 3D electrophysiologically-detailed ventricles-torso model. The inverse solution was solved using the three different Tikhonov regularization methods. Results: Through comparison of multiple measures of error/accuracy on the ECGi reconstructions, our results showed that using different heart geometries to solve the forward and inverse problems produced a larger estimated focal excitation location. An increase of ~2 mm in the Euclidean distance error was observed for an increase in the heart size. However, the estimation of the location of focal activity was still able to be obtained. Similarly, a Euclidean distance increase was observed when the order of regularization was reduced. For the case of activation maps reconstructed at the same ectopic focus location but different heart rates, an increase in the errors and Euclidean distance was observed when the heart rate was increased. Conclusions: Non-invasive cardiac mapping can still provide useful information about cardiac activation patterns for the cases when a different geometry is used for the inverse problem compared to the one used for the forward solution; rapid pacing rates can induce order-dependent errors in the accuracy of reconstruction.

Regional localisation of left ventricular sheet structure: integration with current models of cardiac fibre, sheet and band structure.

The architecture of the heart remains controversial despite extensive effort and recent advances in imaging techniques. Several opposing and non-mutually compatible models have been proposed to explain cardiac structure, and these models, although limited, have advanced the study and understanding of heart structure, function and development. We describe key areas of similarity and difference, highlight areas of contention and point to the important limitations of these models. Recent research in animal models on the nature, geometry and interaction of cardiac sheet structure allows unification of some seemingly conflicting features of the structural models. Intriguingly, evidence points to significant inter-individual structural variability (within constrained limits) in the canine, leading to the concept of a continuum (or distribution) of cardiac structures. This variability in heart structure partly explains the ongoing debate on myocardial architecture. These developments are used to construct an integrated description of cardiac structure unifying features of fibre, sheet and band architecture that provides a basis for (i) explaining cardiac electromechanics, (ii) computational simulations of cardiac physiology and (iii) designing interventions.