Generation of finite wave trains in excitable media.

Spatiotemporal control of excitable media is of paramount importance in the development of new applications, ranging from biology to physics. To this end, we identify and describe a qualitative property of excitable media that enables us to generate a sequence of traveling pulses of any desired length, using a one-time initial stimulus. The wave trains are produced by a transient pacemaker generated by a one-time suitably tailored spatially localized finite amplitude stimulus, and belong to a family of fast pulse trains. A second family, of slow pulse trains, is also present. The latter are created through a clumping instability of a traveling wave state (in an excitable regime) and are inaccessible to single localized stimuli of the type we use. The results indicate that the presence of a large multiplicity of stable, accessible, multi-pulse states is a general property of simple models of excitable media.

Model of intracellular calcium cycling in ventricular myocytes.

We present a mathematical model of calcium cycling that takes into account the spatially localized nature of release events that correspond to experimentally observed calcium sparks. This model naturally incorporates graded release by making the rate at which calcium sparks are recruited proportional to the whole cell L-type calcium current, with the total release of calcium from the sarcoplasmic reticulum (SR) being just the sum of local releases. The dynamics of calcium cycling is studied by pacing the model with a clamped action potential waveform. Experimentally observed calcium alternans are obtained at high pacing rates. The results show that the underlying mechanism for this phenomenon is a steep nonlinear dependence of the calcium released from the SR on the diastolic SR calcium concentration (SR load) and/or the diastolic calcium level in the cytosol, where the dependence on diastolic calcium is due to calcium-induced inactivation of the L-type calcium current. In addition, the results reveal that the calcium dynamics can become chaotic even though the voltage pacing is periodic. We reduce the equations of the model to a two-dimensional discrete map that relates the SR and cytosolic concentrations at one beat and the previous beat. From this map, we obtain a condition for the onset of calcium alternans in terms of the slopes of the release-versus-SR load and release-versus-diastolic-calcium curves. From an analysis of this map, we also obtain an understanding of the origin of chaotic dynamics.

Patterns of wave break during ventricular fibrillation in isolated swine right ventricle.

Several different patterns of wave break have been described by mapping of the tissue surface during fibrillation. However, it is not clear whether these surface patterns are caused by multiple distinct mechanisms or by a single mechanism. To determine the mechanism by which wave breaks are generated during ventricular fibrillation, we conducted optical mapping studies and single cell transmembrane potential recording in six isolated swine right ventricles (RV). Among 763 episodes of wave break (0.75 times x s(-1) x cm(-2)), optical maps showed three patterns: 80% due to a wave front encountering the refractory wave back of another wave, 11.5% due to wave fronts passing perpendicular to each other, and 8.5% due to a new (target) wave arising just beyond the refractory tail of a previous wave. Computer simulations of scroll waves in three-dimensional tissue showed that these surface patterns could be attributed to two fundamental mechanisms: head-tail interactions and filament break. We conclude that during sustained ventricular fibrillation in swine RV, surface patterns of wave break are produced by two fundamental mechanisms: head-tail interaction between waves and filament break.

Effects of diacetyl monoxime and cytochalasin D on ventricular fibrillation in swine right ventricles.

Whether or not the excitation-contraction (E-C) uncoupler diacetyl monoxime (DAM) and cytochalacin D (Cyto D) alter the ventricular fibrillation (VF) activation patterns is unclear. We recorded single cell action potentials and performed optical mapping in isolated perfused swine right ventricles (RV) at different concentrations of DAM and Cyto D. Increasing the concentration of DAM results in progressively shortened action potential duration (APD) measured to 90% repolarization, reduced the slope of the APD restitition curve, decreased Kolmogorov-Sinai entropy, and reduced the number of VF wave fronts. In all RVs, 15-20 mmol/l DAM converted VF to ventricular tachycardia (VT). The VF could be reinduced after the DAM was washed out. In comparison, Cyto D (10-40 micromol/l) has no effects on APD restitution curve or the dynamics of VF. The effects of DAM on VF are associated with a reduced number of wave fronts and dynamic complexities in VF. These results are compatible with the restitution hypothesis of VF and suggest that DAM may be unsuitable as an E-C uncoupler for optical mapping studies of VF in the swine RVs.

Coexistence of multiple spiral waves with independent frequencies in a heterogeneous excitable medium.

We studied the interactions and coexistence of stable spiral waves with independent frequencies in a heterogeneous excitable medium, using numerical simulations of a spatial system based on the FitzHugh-Nagumo cell model. When the heterogeneity of the medium exceeded a critical value, a transition took place from a single dominant spiral wave to a coexistence of multiple spiral waves with independent frequencies and n:n-1 wave conduction blocks. In this case, multiple spiral waves could coexist because they are "insulated" from each other by chaotic regions.

Effects of simulated ischemia on spiral wave stability.

Regional hyperkalemia during acute myocardial ischemia is a major factor promoting electrophysiological abnormalities leading to ventricular fibrillation (VF). However, steep action potential duration restitution, recently proposed to be a major determinant of VF, is typically decreased rather than increased by hyperkalemia and acute ischemia. To investigate this apparent contradiction, we simulated the effects of regional hyperkalemia and other ischemic components (anoxia and acidosis) on the stability of spiral wave reentry in simulated two-dimensional cardiac tissue by use of the Luo-Rudy ventricular action potential model. We found that the hyperkalemic "ischemic" area promotes wavebreak in the surrounding normal tissue by accelerating the rate of spiral wave reentry, even after the depolarized ischemic area itself has become unexcitable. Furthermore, wavebreak and fibrillation can be prevented if the dynamical instability of the normal tissue is reduced significantly by targeting electrical restitution properties, suggesting a novel therapeutic approach.

Electrophysiological heterogeneity and stability of reentry in simulated cardiac tissue.

Generation of wave break is a characteristic feature of cardiac fibrillation. In this study, we investigated how dynamic factors and fixed electrophysiological heterogeneity interact to promote wave break in simulated two-dimensional cardiac tissue, by using the Luo-Rudy (LR1) ventricular action potential model. The degree of dynamic instability of the action potential model was controlled by varying the maximal amplitude of the slow inward Ca(2+) current to produce spiral waves in homogeneous tissue that were either nearly stable, meandering, hypermeandering, or in breakup regimes. Fixed electrophysiological heterogeneity was modeled by randomly varying action potential duration over different spatial scales to create dispersion of refractoriness. We found that the degree of dispersion of refractoriness required to induce wave break decreased markedly as dynamic instability of the cardiac model increased. These findings suggest that reducing the dynamic instability of cardiac cells by interventions, such as decreasing the steepness of action potential duration restitution, may still have merit as an antifibrillatory strategy.

Role of lipids in osteoporosis.

Cardiovascular disease and osteoporosis together account for most of the morbidity and mortality in our aging population despite significant improvements in treatment. Recently, converging lines of evidence suggest that these 2 diseases share an etiologic factor--that hyperlipidemia contributes not only to atherosclerotic plaque formation, but also to osteoporosis, following a similar biologic mechanism involving lipid oxidation. In vitro studies indicate that lipid products of oxidation promote osteoblastic differentiation of vascular cells and inhibit such differentiation in bone cells. Ex vivo, in vivo, and clinical studies further suggest that lipid-lowering agents reduce both atherosclerotic calcification and osteoporosis. Whether lipid-lowering agents reduce osteoporosis directly or indirectly through lipid reduction remains controversial.

Alternans and the onset of ventricular fibrillation.

Ventricular fibrillation (VF) remains a major cause of death in the industrialized world. Alternans (a period-doubling bifurcation of cardiac electrical activity) have recently been causally linked to the progression from ventricular tachycardia (VT) to VF, a more spatiotemporally disorganized electrical activity. In this paper, we show how alternans and thus VT degenerate to chaos via multiple, specific dynamical routes, largely associated with spatial components of VF dynamics, explaining failures of many recently proposed antiarrhythmic drugs. Identification of dynamical mechanisms for the onset of VF should lead to the design of future experiments and consequently to more effective antiarrhythmic drugs.

Mechanisms of discordant alternans and induction of reentry in simulated cardiac tissue.

BACKGROUND: T-wave alternans, which is associated with the genesis of cardiac fibrillation, has recently been related to discordant action potential duration (APD) alternans. However, the cellular electrophysiological mechanisms responsible for discordant alternans are poorly understood. METHODS AND RESULTS: We simulated a 2D sheet of cardiac tissue using phase 1 of the Luo-Rudy cardiac action potential model. A steep (slope >1) APD restitution curve promoted concordant APD alternans and T-wave alternans without QRS alternans. When pacing was from a single site, discordant APD alternans occurred only when the pacing rate was fast enough to engage conduction velocity (CV) restitution, producing both QRS and T-wave alternans. Tissue heterogeneity was not required for this effect. Discordant alternans markedly increases dispersion of refractoriness and increases the ability of a premature stimulus to cause localized wavebreak and induce reentry. In the absence of steep APD restitution and of CV restitution, sustained discordant alternans did not occur, but reentry could be induced if there was marked electrophysiological heterogeneity. Both discordant APD alternans and preexisting APD heterogeneity facilitate reentry by causing the waveback to propagate slowly. CONCLUSION: Discordant alternans arises dynamically from APD and CV restitution properties and markedly increases dispersion of refractoriness. Preexisting and dynamically induced (via restitution) dispersion of refractoriness independently increase vulnerability to reentrant arrhythmias. Reduction of dynamically induced dispersion by appropriate alteration of electrical restitution has promise as an antiarrhythmic strategy.

Origins of spiral wave meander and breakup in a two-dimensional cardiac tissue model.

We studied the stability of spiral waves in homogeneous two-dimensional cardiac tissue using phase I of the Luo-Rudy ventricular action potential model. By changing the conductance and the relaxation time constants of the ion channels, various spiral wave phenotypes, including stable, quasiperiodically meandering, chaotically meandering, and breakup were observed. Stable and quasiperiodically meandering spiral waves occurred when the slope of action potential duration (APD) restitution was < 1 over all diastolic intervals visited during reentry; chaotic meander and spiral wave breakup occurred when the slope of APD restitution exceeded 1. Curvature of the wave changes both conduction velocity and APD, and their restitution properties, thereby modulating local stability in a spiral wave, resulting in distinct spiral wave phenotypes. In the LRI model, quasiperiodic meander is most sensitive to the Na+ current, whereas chaotic meander and breakup are more dependent on the Ca2+ and K+ currents.

From local to global spatiotemporal chaos in a cardiac tissue model.

Two kinds of chaos can occur in cardiac tissue, chaotic meander of a single intact spiral wave and chaotic spiral wave breakup. We studied these behaviors in a model of two-dimensional cardiac tissue based on the Luo-Rudy I action potential model. In the chaotic meander regime, chaos is spatially localized to the core of the spiral wave. When persistent spiral wave breakup occurs, there is a transition from local to global spatiotemporal chaos.

Mechanisms of ventricular fibrillation induction by 60-Hz alternating current in isolated swine right ventricle.

BACKGROUND: The mechanisms by which 60-Hz alternating current (AC) can induce ventricular fibrillation (VF) are unknown. METHODS AND RESULTS: We studied 7 isolated perfused swine right ventricles in vitro. The action potential duration restitution curve was determined. Optical mapping techniques were used to determine the patterns of activation on the epicardium during 5-second 60-Hz AC stimulation (10 to 999 microA). AC captured the right ventricles at 100+/-65 microA, which is significantly lower than the direct current pacing threshold (0.77+/-0.45 mA, P:<0.05). AC induced ventricular tachycardia or VF at 477+/-266 microA, when the stimulated responses to AC had (1) short activation CLs (128+/-14 ms), (2) short diastolic intervals (16+/-9 ms), and (3) short diastolic intervals associated with a steep action potential duration restitution curve. Optical mapping studies showed that during rapid ventricular stimulation by AC, a wave front might encounter the refractory tail of an earlier wave front, resulting in the formation of a wave break and VF. Computer simulations reproduced these results. CONCLUSIONS: AC at strengths less than the regular pacing threshold can capture the ventricle at fast rates. Accidental AC leak to the ventricles could precipitate VF and sudden death if AC results in a fast ventricular rate coupled with a steep restitution curve and a nonuniform recovery of excitability of the myocardium.

Scroll wave dynamics in a three-dimensional cardiac tissue model: roles of restitution, thickness, and fiber rotation.

Scroll wave (vortex) breakup is hypothesized to underlie ventricular fibrillation, the leading cause of sudden cardiac death. We simulated scroll wave behaviors in a three-dimensional cardiac tissue model, using phase I of the Luo-Rudy (LR1) action potential model. The effects of action potential duration (APD) restitution, tissue thickness, filament twist, and fiber rotation were studied. We found that APD restitution is the major determinant of scroll wave behavior and that instabilities arising from APD restitution are the main determinants of scroll wave breakup in this cardiac model. We did not see a "thickness-induced instability" in the LR1 model, but a minimum thickness is required for scroll breakup in the presence of fiber rotation. The major effect of fiber rotation is to maintain twist in a scroll wave, promoting filament bending and thus scroll breakup. In addition, fiber rotation induces curvature in the scroll wave, which weakens conduction and further facilitates wave break.

Preventing ventricular fibrillation by flattening cardiac restitution.

Ventricular fibrillation is the leading cause of sudden cardiac death. In fibrillation, fragmented electrical waves meander erratically through the heart muscle, creating disordered and ineffective contraction. Theoretical and computer studies, as well as recent experimental evidence, have suggested that fibrillation is created and sustained by the property of restitution of the cardiac action potential duration (that is, its dependence on the previous diastolic interval). The restitution hypothesis states that steeply sloped restitution curves create unstable wave propagation that results in wave break, the event that is necessary for fibrillation. Here we present experimental evidence supporting this idea. In particular, we identify the action of the drug bretylium as a prototype for the future development of effective restitution-based antifibrillatory agents. We show that bretylium acts in accord with the restitution hypothesis: by flattening restitution curves, it prevents wave break and thus prevents fibrillation. It even converts existing fibrillation, either to a periodic state (ventricular tachycardia, which is much more easily controlled) or to quiescent healthy tissue.

Systolic blood pressure and mortality.

BACKGROUND: The current systolic blood-pressure threshold for hypertension treatment is 140 mm Hg for all adults. WHO and the International Society of Hypertension have proposed that normal pressure be lower than 130 mm Hg, with an optimum pressure of less than 120 mm Hg. These recommendations are based largely on the assumption that cardiovascular and overall mortality depend in a strictly increasing manner on systolic blood pressure. The Framingham study was instrumental in establishing this viewpoint. We reassessed data from that study to find out whether the relation is strictly increasing or whether there is a threshold in this relation. METHODS: We used logistic splines to model the relation of risk of cardiovascular and all-cause death with systolic blood pressure, using age-specific and sex-specific rates. We tested for the independence of the slope parameters from age and sex, and the reduced model with common slopes was used to produce a model different from the conventional linear logistic model. FINDINGS: Against the predictions of the linear logistic model, neither all-cause nor cardiovascular deaths depended on systolic blood pressure in a strictly increasing manner. The linear logistic model was rejected by the Framingham data. Instead, risk was independent of systolic blood pressure for all pressures lower than a threshold at the 70th percentile for a person of a given age and sex. Risk sharply increased with pressure higher than the 80th percentile. Since systolic blood pressure steadily increases with age, the threshold increases with age, but more rapidly in women than in men. INTERPRETATION: The Framingham data contradict the concept that lower pressures imply lower risk and the idea that 140 mm Hg is a useful cut-off value for hypertension for all adults. There is an age-dependent and sex-dependent threshold for hypertension. A substantial proportion of the population who would currently be thought to be at increased risk are, therefore, at no increased risk.

Ventricular fibrillation: how do we stop the waves from breaking?

Combined experimental and theoretical developments have demonstrated that in addition to preexisting electrophysiological heterogeneities, cardiac electrical restitution properties contribute to breakup of reentrant wavefronts during cardiac fibrillation. Developing therapies that favorably alter electrical restitution properties have promise as a new paradigm for preventing fibrillation.

How the science and engineering of spaceflight contribute to understanding the plasticity of spinal cord injury.

Space programs support experimental investigations related to the unique environment of space and to the technological developments from many disciplines of both science and engineering that contribute to space studies. Furthermore, interactions between scientists, engineers and administrators, that are necessary for the success of any science mission in space, promote interdiscipline communication, understanding and interests which extend well beyond a specific mission. NASA-catalyzed collaborations have benefited the spinal cord rehabilitation program at UCLA in fundamental science and in the application of expertise and technologies originally developed for the space program. Examples of these benefits include: (1) better understanding of the role of load in maintaining healthy muscle and motor function, resulting in a spinal cord injury (SCI) rehabilitation program based on muscle/limb loading; (2) investigation of a potentially novel growth factor affected by spaceflight which may help regulate muscle mass; (3) development of implantable sensors, electronics and software to monitor and analyze long-term muscle activity in unrestrained subjects; (4) development of hardware to assist therapies applied to SCI patients; and (5) development of computer models to simulate stepping which will be used to investigate the effects of neurological deficits (muscle weakness or inappropriate activation) and to evaluate therapies to correct these deficiencies.