Off-site control of repolarization alternans in cardiac fibers.

Repolarization alternans, a beat-to-beat alternation in action potential duration, has been putatively linked to the onset of cardiac reentry. Anti-alternans control strategies can eliminate alternans in individual cells by exploiting the rate dependence of action potential duration. The same approach, when applied to a common measuring/stimulating site at one end of a cardiac fiber, has been shown to have limited spatial efficacy. As a first step toward spatially distributed electrode control systems, we investigated "off-site" control in canine Purkinje fibers, in which the recording and control sites are different. We found experimentally that alternans can be eliminated at, or very near, the recording site, and that varying the location of the recording site along the fiber causes the node (the location with no alternans) to move along the fiber in close proximity to the recording site. Theoretical predictions based on an amplitude equation [B. Echebarria and A. Karma, Chaos 12, 923 (2002)] show that those findings follow directly from the wave nature of alternans: the most unstable mode of alternans along the fiber is a wave solution of a one-dimensional Helmholtz equation with a node position that only deviates slightly from the recording site by an amount dependent on electrotonic coupling. Computer simulations using a Purkinje fiber model confirm these theoretical and experimental results. Although off-site alternans control does not suppress alternans along the entire fiber, our results indicate that placing the node away from the stimulus site reduces alternans amplitude along the fiber, and may therefore have implications for antiarrhythmic strategies based on alternans termination.

Modeling weight-loss maintenance to help prevent body weight regain.

BACKGROUND: Lifestyle intervention can successfully induce weight loss in obese persons, at least temporarily. However, there currently is no way to quantitatively estimate the changes of diet or physical activity required to prevent weight regain. Such a tool would be helpful for goal-setting, because obese patients and their physicians could assess at the outset of an intervention whether long-term adherence to the calculated lifestyle change is realistic. OBJECTIVE: We aimed to calculate the expected change of steady-state body weight arising from a given change in dietary energy intake and, conversely, to calculate the modification of energy intake required to maintain a particular body-weight change. DESIGN: We developed a mathematical model using data from 8 longitudinal weight-loss studies representing 157 subjects with initial body weights ranging from 68 to 160 kg and stable weight losses between 7 and 54 kg. RESULTS: Model calculations closely matched the change data (R(2) = 0.83, chi(2) = 2.1, P < 0.01 for weight changes; R(2) = 0.91, chi(2) = 0.87, P < 0.0004 for energy intake changes). Our model performed significantly better than the previous models for which chi(2) values were 10-fold those of our model. The model also accurately predicted the proportion of weight change resulting from the loss of body fat (R(2) = 0.90). CONCLUSIONS: Our model provides realistic calculations of body-weight change and of the dietary modifications required for weight-loss maintenance. Because the model was implemented by using standard spreadsheet software, it can be widely used by physicians and weight-management professionals.

Dynamic coordination of macronutrient balance during infant growth: insights from a mathematical model.

BACKGROUND: Complex dynamic changes in body composition, dietary intake, energy expenditure, and macronutrient oxidation occur during infant growth. Although previous investigators have focused on energy requirements for normal growth, little is known about the dynamic coordination of macronutrient balance. OBJECTIVE: Our objective was to develop a mathematical model of the dynamic relations between diet, macronutrient oxidation, and energy expenditure during normal infant growth. DESIGN: We developed a mathematical model that integrates longitudinal data on changes of body composition and carbon dioxide production determined with the doubly labeled water method to calculate both energy intake requirements and macronutrient oxidation rates during normal infant growth. RESULTS: The calculated fat oxidation rate was initially <20 kcal x kg(-1) x d(-1), despite the consumption of >60 kcal x kg(-1) x d(-1) of dietary fat. This discrepancy was maintained until approximately 6 mo, after which fat intake was only slightly greater than fat oxidation. Nonfat oxidation closely followed nonfat dietary intake for the duration of the period studied. Model calculations of the energy intake requirements for normal growth were slightly lower than previous estimates. The calculations were robust to variations of body weight, body composition, and diet composition input data, but depended sensitively on variations of carbon dioxide production data. CONCLUSIONS: Our model presents a dynamic picture of how macronutrient oxidation adapts in concert with dietary changes and energy expenditure to give rise to normal tissue deposition. The model integrates a variety of data in a self-consistent way, simulating the complex metabolic adaptations occurring during normal growth while extracting important physiologic information from the data that would otherwise be unavailable.

Characterizing the contribution of voltage- and calcium-dependent coupling to action potential stability: implications for repolarization alternans.

Experiments have provided suggestive but inconclusive insights into the relative contributions of transmembrane voltage and intracellular calcium handling to the development of cardiac electrical instabilities such as repolarization alternans. In this study, we applied a novel combination of techniques (action potential voltage clamping, calcium-transient clamping, and stability analysis) to cardiac cell models to more clearly determine the roles that voltage- and calcium-dependent coupling play in regulating action potential stability and the development of alternans subsequent to the loss of stability. Using these techniques, we are able to demonstrate that voltage- and calcium-dependent coupling exhibit varying degrees of influence on action potential stability across models. Our results indicate that cellular dynamic instabilities such as alternans may be initiated by either voltage- or calcium-dependent mechanisms or by some combination of the two. Based on these modeling results, we propose novel single-cell experiments that incorporate action-potential voltage clamping, calcium imaging, and real-time measurement of action potential stability. These experiments will make it possible to experimentally determine the relative contribution of voltage coupling to the regulation of action potential stability in real cardiac myocytes, thereby providing further insights into the mechanism of alternans.

Action potential morphology influences intracellular calcium handling stability and the occurrence of alternans.

Instability in the intracellular Ca2+ handling system leading to Ca2+ alternans is hypothesized to be an underlying cause of electrical alternans. The highly coupled nature of membrane voltage and Ca2+ regulation suggests that there should be reciprocal effects of membrane voltage on the stability of the Ca2+ handling system. We investigated such effects using a mathematical model of the cardiac intracellular Ca2+ handling system. We found that the morphology of the action potential has a significant effect on the stability of the Ca2+ handling system at any given pacing rate, with small changes in action potential morphology resulting in a transition from stable nonalternating Ca2+ transients to stable alternating Ca2+ transients. This bifurcation occurs as the alternans eigen value of the system changes from absolute value <1 to absolute value >1. These results suggest that the stability of the intracellular Ca2+ handling system and the occurrence of Ca2+ alternans are not dictated solely by the Ca2+ handling system itself, but are also modulated to a significant degree by membrane voltage (through its influence on sarcolemmal Ca2+ currents) and, therefore, by all ionic currents that affect membrane voltage.

Therapies for ventricular cardiac arrhythmias.

During recent years, engineers and physicists have become increasingly interested in studying the electrical activity of the heart. Despite the fact that the heart is a complex and highly nonlinear system, its electrical behavior can be studied using a variety of experimental and clinical techniques, and can be modeled mathematically using relatively simple systems of differential equations, allowing scientists to perform both real and virtual (in silico) experiments to gain insights into its physiology and pathophysiology. Although these approaches have in recent years allowed great headway to be made into understanding the dynamic behavior of the heart, cardiac arrhythmias such as ventricular fibrillation still claim the lives of hundreds of thousands of people each year in the United States alone. Bridging the gap between understanding the mechanistic bases of arrhythmias and applying such knowledge to improving therapy presents one of the greatest challenges in the field of cardiac electrophysiology. In this review, we describe the basic electrical properties and dynamic behavior of the heart and review the current state of the art in ventricular arrhythmia therapy. We also discuss some possibilities for future therapies, with the hope that such informed speculation will promote new investigations in these areas.

Adaptive diastolic interval control of cardiac action potential duration alternans.

INTRODUCTION: Recent experimental and computational studies have shown that beat-to-beat alternation in action potential duration can trigger cardiac reentry, suggesting that such "alternans" is a mechanistic precursor to arrhythmias. Given such a link, termination of alternans may help prevent the onset of arrhythmias. To this end, recent efforts have shown that chaos control methods can modulate the timing of electrical stimulation to eliminate alternans. METHODS AND RESULTS: We have developed an alternative control method founded entirely in cardiac electrophysiology (rather than borrowing techniques from the control of physical systems as with existing control techniques). Using computer simulations, we show that this method, which exploits the rate-dependent behavior of cardiac tissue, can be used to control alternans (and higher-order) rhythms, and is robust to drift and noise. When applied to individual model cells exhibiting alternans, the algorithm converges to the period-1 rhythm over as wide, and in some cases a wider, range of feedback proportionality constant values relative to existing methods. Control success comparable to existing methods is achieved when the algorithm is applied to a simulated one-dimensional Purkinje fiber exhibiting alternans. CONCLUSION: We have developed a method that adaptively controls the timing of electrical stimulation to rapidly eliminate action potential duration alternans in cardiac tissue. This control method may prove valuable in future arrhythmia prevention therapies.

Determining the effects of memory and action potential duration alternans on cardiac restitution using a constant-memory restitution protocol.

Restitution, the dependence of action potential duration (APD) on diastolic interval, may be causally linked to the vulnerability of cardiac tissue to certain types of arrhythmias. While a number of pacing protocols are commonly used to quantify the restitution relation, one of these, the dynamic protocol, may result in the occurrence of APD alternans. However, the effects of APD alternans, and the concomitant alternation in cardiac memory, on the restitution curve are currently not well understood. Alternans preceding a given action potential may cause that action potential to have a different duration from one preceded by action potentials of identical duration. This interaction of alternans and memory can result in a dynamic restitution curve that is not unique. To address this, we have developed a constant-memory restitution protocol that enables the experimenter or modeller to obtain unique, constant-memory restitution curves at all diastolic intervals. Using this protocol, we obtained unique restitution curves for two ionic models of the cardiac action potential in the absence of alternans at all diastolic intervals. A comparison of the unique constant-memory and non-unique dynamic restitution curves for the two models shows that the presence of alternans can significantly alter the shape of the restitution curve compared to when alternans is absent.

Effect of beta-adrenergic blockade on dynamic electrical restitution in vivo.

The slope of the action potential duration (APD) restitution curve may be a significant determinant of the propensity to develop ventricular fibrillation, with steeper slopes associated with a more arrhythmogenic substrate. We hypothesized that one mechanism by which beta-blockers reduce sudden cardiac death is by flattening the APD restitution curve. Therefore, we investigated whether infusion of esmolol modulates the APD restitution curve in vivo. In 10 Yorkshire pigs, dynamic APD restitution curves were determined from measurements of APD at 90% repolarization with a monophasic action potential catheter positioned against the right ventricular septum during right ventricular apical pacing in the basal state and during infusion of esmolol. APD restitution curves were fitted to the three-parameter (a, b, c) exponential equation, APD = a.[1 - e((-b.DI))] + c, where DI is the diastolic interval. Esmolol decreased the maximal APD slope, 0.68 +/- 0.14 vs. 0.94 +/- 0.24 (baseline), P = 0.002, and flattened the APD restitution curve at shorter DIs, 75 and 100 ms (P < 0.05). To compare the slopes of the APD restitution curves at similar steady states, slopes were also computed at points of intersection between the restitution curve and the lines representing pacing at a fixed cycle length (CL) of 200, 225, 250, 275, and 300 ms using the relationship CL = APD + DI. Esmolol decreased APD restitution slopes at CLs 200-275 ms (P < 0.05). Esmolol flattens the cardiac APD restitution curve in vivo, particularly at shorter CLs and DIs. This may represent a novel mechanism by which beta-blockers prevent sudden cardiac death.

MinK-related peptide 2 modulates Kv2.1 and Kv3.1 potassium channels in mammalian brain.

Delayed rectifier potassium current diversity and regulation are essential for signal processing and integration in neuronal circuits. Here, we investigated a neuronal role for MinK-related peptides (MiRPs), membrane-spanning modulatory subunits that generate phenotypic diversity in cardiac potassium channels. Native coimmunoprecipitation from rat brain membranes identified two novel potassium channel complexes, MiRP2-Kv2.1 and MiRP2-Kv3.1b. MiRP2 reduces the current density of both channels, slows Kv3.1b activation, and slows both activation and deactivation of Kv2.1. Altering native MiRP2 expression levels by RNAi gene silencing or cDNA transfection toggles the magnitude and kinetics of endogenous delayed rectifier currents in PC12 cells and hippocampal neurons. Computer simulations predict that the slower gating of Kv3.1b in complexes with MiRP2 will broaden action potentials and lower sustainable firing frequency. Thus, MiRP2, unlike other known neuronal beta subunits, provides a mechanism for influence over multiple delayed rectifier potassium currents in mammalian CNS via modulation of alpha subunits from structurally and kinetically distinct subfamilies.