Data-based theoretical identification of subcellular calcium compartments and estimation of calcium dynamics in cardiac myocytes.

In cardiac cells, Ca(2+) release flux (J(rel)) via ryanodine receptors (RyRs) from the sarcoplasmic reticulum (SR) has a complex effect on the action potential (AP). Coupling between J(rel) and the AP occurs via L-type Ca(2+) channels (I(Ca)) and the Na(+)/Ca(2+) exchanger (I(NCX)). We used a combined experimental and modelling approach to study interactions between J(rel), I(Ca) and I(NCX) in porcine ventricular myocytes.We tested the hypothesis that during normal uniform J(rel), the interaction between these fluxes can be represented as occurring in two myoplasmic subcompartments for Ca(2+) distribution, one (T-space) associated with RyR and enclosed by the junctional portion of the SR membrane and corresponding T-tubular portion of the sarcolemma, the other (M-space) encompassing the rest of the myoplasm. I(Ca) and I(NCX) were partitioned into subpopulations in the T-space and M-space sarcolemma. We denoted free Ca(2+) concentrations in T-space and M-space Ca(t) and Ca(m), respectively. Experiments were designed to allow separate measurements of I(Ca) and I(NCX) as a function of J(rel). Inclusion of T-space in themodel allowed us to reproduce in silico the following important experimental results: (1) hysteresis of I(NCX) dependence on Ca(m); (2) delay between peak I(NCX) and peak Ca(m) during caffeine application protocol; (3) delay between I(NCX) and Ca(m) during Ca(2+)-induced-Ca(2+)-release; (4) rapid I(Ca) inactivation (within 2 ms) due to J(rel), with magnitude graded as a function of the SR Ca(2+) content; (5) time delay between I(Ca) inactivation due to J(rel) and Ca(m). Partition of 25% NCX in T-space and 75% in M-space provided the best fit to the experimental data. Measured Ca(m) and I(Ca) or I(NCX) were used as input to the model for estimating Ca(t). The actual model-computed Ca(t), obtained by simulating specific experimental protocols, was used as a gold standard for comparison. The model predicted peak Ca(t) in the range of 6­25 µM, with time to equilibrium of Ca(t) with Ca(m) of ~350 ms. These Ca(t) values are in the range of LCC and RyR sensitivity to Ca(2+). An increase of the SR Ca(2+) load increased the time to equilibrium. The I(Ca)-based estimation method was most accurate during the ascending phase of Ca(t). The I(NCX)-based method provided a good estimate for the descending phase of Ca(t). Thus, application of both methods in combination provides the best estimate of the entire Ca(t) time course.

Microdomain [Ca²âº] near ryanodine receptors as reported by L-type Ca²âº and Na+/Ca²âº exchange currents.

During Ca²âº release from the sarcoplasmic reticulum triggered by Ca²âº influx through L-type Ca²âº channels (LTCCs), [Ca²âº] near release sites ([Ca²âº]nrs) temporarily exceeds global cytosolic [Ca²âº]. [Ca²âº]nrs can at present not be measured directly but the Na+/Ca2+ exchanger (NCX) near release sites and LTCCs also experience [Ca²âº]nrs. We have tested the hypothesis that ICaL and INCX could be calibrated to report [Ca²âº]nrs and would report different time course and values for local [Ca²âº]. Experiments were performed in pig ventricular myocytes (whole-cell voltage-clamp, Fluo-3 to monitor global cytosolic [Ca²âº], 37◦C). [Ca²âº]nrs-dependent inactivation of ICaL during a step to +10 mV peaked around 10 ms. For INCX we computationally isolateda current fraction activated by [Ca²âº]nrs; values were maximal at 10 ms into depolarization. The recovery of [Ca²âº]nrs was comparable with both reporters (>90% within 50 ms). Calibration yielded maximal values for [Ca²âº]nrs between 10 and 15 µmol l⁻¹ with both methods. When applied to a step to less positive potentials (-30 to -20 mV), the time course of [Ca²âº]nrs was slower but peak values were not very different. In conclusion, both ICaL inactivation and INCX activation, using a subcomponent analysis, can be used to report dynamic changes of [Ca²âº]nrs. Absolute values obtained by these different methods are within the same range, suggesting that they are reporting on a similar functional compartment near ryanodine receptors. Comparable [Ca²âº]nrs at +10 mV and -20 mV suggests that, although the number of activated release sites differs at these potentials, local gradients at release sites can reach similar values.

Uniqueness and stability of action potential models during rest, pacing, and conduction using problem-solving environment.

Development and application of physiologically detailed dynamic models of the action potential (AP) and Ca2+ cycling in cardiac cells is a rapidly growing aspect of computational cardiac electrophysiology. Given the large scale of the nonlinear system involved, questions were recently raised regarding reproducibility, numerical stability, and uniqueness of model solutions, as well as ability of the model to simulate AP propagation in multicellular configurations. To address these issues, we reexamined ventricular models of myocyte AP developed in our laboratory with the following results. 1), Recognizing that the model involves a system of differential-algebraic equations, a procedure is developed for estimating consistent initial conditions that insure uniqueness and stability of the solution. 2), Model parameters that can be used to modify these initial conditions according to experimental values are identified. 3), A convergence criterion for steady-state solution is defined based on tracking the incremental contribution of each ion species to the membrane voltage. 4), Singularities in state variable formulations are removed analytically. 5), A biphasic current stimulus is implemented to completely eliminate stimulus artifact during long-term pacing over a broad range of frequencies. 6), Using the AP computed based on 1-5 above, an efficient scheme is developed for computing propagation in multicellular models.

Kinetic properties of the cardiac L-type Ca2+ channel and its role in myocyte electrophysiology: a theoretical investigation.

The L-type Ca(2+) channel (Ca(V)1.2) plays an important role in action potential (AP) generation, morphology, and duration (APD) and is the primary source of triggering Ca(2+) for the initiation of Ca(2+)-induced Ca(2+)-release in cardiac myocytes. In this article we present: 1), a detailed kinetic model of Ca(V)1.2, which is incorporated into a model of the ventricular mycoyte where it interacts with a kinetic model of the ryanodine receptor in a restricted subcellular space; 2), evaluation of the contribution of voltage-dependent inactivation (VDI) and Ca(2+)-dependent inactivation (CDI) to total inactivation of Ca(V)1.2; and 3), description of dynamic Ca(V)1.2 and ryanodine receptor channel-state occupancy during the AP. Results are: 1), the Ca(V)1.2 model reproduces experimental single-channel and macroscopic-current data; 2), the model reproduces rate dependence of APD, [Na(+)](i), and the Ca(2+)-transient (CaT), and restitution of APD and CaT during premature stimuli; 3), CDI of Ca(V)1.2 is sensitive to Ca(2+) that enters the subspace through the channel and from SR release. The relative contributions of these Ca(2+) sources to total CDI during the AP vary with time after depolarization, switching from early SR dominance to late Ca(V)1.2 dominance. 4), The relative contribution of CDI to total inactivation of Ca(V)1.2 is greater at negative potentials, when VDI is weak; and 5), loss of VDI due to the Ca(V)1.2 mutation G406R (linked to the Timothy syndrome) results in APD prolongation and increased CaT.

Application-Based Hearing Screening in the Elderly Population.

OBJECTIVES: The effects of age-related hearing loss are severe. Early detection is essential for maximum benefit. However, most hearing-impaired adults delay obtaining treatment. Diagnostic hearing testing at an appropriate facility is impractical, and new methods for screening audiometry aim to provide easy access for patients and reliable outcomes. The purpose of this study was to examine the accuracy of application-based hearing screening in an elderly population. METHODS: The uHear application was downloaded to an iPad. Application-based hearing screening was performed in a non-soundproofed quiet room, and subsequently all participants underwent full diagnostic audiometry in a soundproof booth. RESULTS: Sixty patients were recruited and completed both tests. Significant differences were observed between the hearing results obtained with the application and the standard audiogram at all frequencies and in both ears. Following subtraction of a constant factor of 25 dB from the application-based results in order to compensate for ambient noise, no significant differences in pure tone average were found between the 2 methods. CONCLUSIONS: The uHear application is inaccurate in assessing hearing thresholds for screening in the elderly. However, when site-specifically corrected, the uHear application may be used as a screening tool for hearing loss in an elderly population.

Generalized cable equation model for myelinated nerve fiber.

Herein, the well-known cable equation for nonmyelinated axon model is extended analytically for myelinated axon formulation. The myelinated membrane conductivity is represented via the Fourier series expansion. The classical cable equation is thereby modified into a linear second order ordinary differential equation with periodic coefficients, known as Hill's equation. The general internal source response, expressed via repeated convolutions, uniformly converges provided that the entire periodic membrane is passive. The solution can be interpreted as an extended source response in an equivalent nonmyelinated axon (i.e., the response is governed by the classical cable equation). The extended source consists of the original source and a novel activation function, replacing the periodic membrane in the myelinated axon model. Hill's equation is explicitly integrated for the specific choice of piecewise constant membrane conductivity profile, thereby resulting in an explicit closed form expression for the transmembrane potential in terms of trigonometric functions. The Floquet's modes are recognized as the nerve fiber activation modes, which are conventionally associated with the nonlinear Hodgkin-Huxley formulation. They can also be incorporated in our linear model, provided that the periodic membrane point-wise passivity constraint is properly modified. Indeed, the modified condition, enforcing the periodic membrane passivity constraint on the average conductivity only leads, for the first time, to the inclusion of the nerve fiber activation modes in our novel model. The validity of the generalized transmission-line and cable equation models for a myelinated nerve fiber, is verified herein through a rigorous Green's function formulation and numerical simulations for transmembrane potential induced in three-dimensional myelinated cylindrical cell. It is shown that the dominant pole contribution of the exact modal expansion is the transmembrane potential solution of our generalized model.

Augmentation of dilated failing left ventricular stroke work by a physiological cardiac assist device.

A novel physiological cardiac assist device (PCAD), otherwise known as the LEVRAM assist device, which is synchronized with the heartbeat, was developed to assist the left ventricle (LV) in chronic heart failure (CHF). The PCAD utilizes a single cannula, which is inserted in less than 15 s through the apex of the beating LV by means of a specially designed device. Blood is withdrawn from the LV into the PCAD in diastole and is injected back to the LV, through the same cannula, during the systolic ejection phase, thereby augmenting stroke volume (SV) and stroke work (SW). CHF with dilated LV was induced in sheep by successive intracoronary injections of 100-microm beads. The sheep (92.2 +/- 25.9 kg, n = 5) developed stable CHF with increased LV end-diastolic diameter (69.4 +/- 3.3 mm) and end-diastolic volume (LVEDV = 239 +/- 32 mL), with severely reduced ejection fraction (23.8 +/- 7.6%), as well as mild-to-moderate mitral regurgitation. The sheep were anesthetized, and the heart was exposed by left thoracotomy. Pressure was measured in the LV and aorta (Millar). The SV was measured by flow meters and the LV volume by sonocrystals. Assist was provided every 10 regular beats, and the assisted beats were compared with the preceding unassisted beats, at the same LVEDV. The PCAD displaced 13.6 +/- 3.4 mL, less than 8% of LVEDV. Added SW was calculated from the assisted and control pressure-volume loops. The efficiency, defined as an increase in SW divided by the mechanical work of the PCAD, was 85.4 +/- 16.9%. We conclude that the PCAD, working with a small displaced blood volume in synchrony with the heartbeat, efficiently augments the SW of the dilated failing LV. The PCAD is suggested for use as a permanent implantable device in CHF.

Rigorous Green's function formulation for transmembrane potential induced along a 3-D infinite cylindrical cell.

The quasi-static electromagnetic field interaction with three-dimensional infinite-cylindrical cell is investigated for both intracellular (IPS) and extracellular (EPS) current point-source excitation. The induced transmembrane potential (TMP), expressed conventionally via Green's function, may alternatively be expanded into a faster-converging representation using a complex contour integration, consisting of an infinite-discrete set of exponentially decaying oscillating modes (corresponding to complex eigenvalues) and a continuous source-mode convolution integral. The dominant contributions for both the IPS and EPS problems are obtained in simple closed-form expressions, including well documented special mathematical functions. In the IPS case, the dominant modal contribution (of order zero)--an exact solution of the well-known cable equation--is explicitly and analytically corrected by the imaginary part of its eigenvalue and the source-mode convolution contribution. However, the TMP along a fiber was shown to decay at infinity algebraically and not exponentially, as predicted by the classic cable equation solution. In the EPS case, the dominant contribution is expressed as a source-mode convolution integral. However, for a long EPS distance (e.g., >10 cable length constant) the order-one-modes involved in the convolution is not a solution of the cable equation. Only for shorter EPS distance should the cable equation solution (i.e., the order zero dominant mode) be included in addition to the modes of order one. For on-membrane EPS location, additional modes should be included as well. In view of our EPS result, we suggest that the cable equation modeling existing in the literature and related to functional electrical stimulation for EPS problems, should be critically reviewed and corrected.

Force, sarcomere shortening velocity and ATPase activity.

UNLABELLED: We have tested the hypothesis that the transition rate (G) of the cardiac XB from the strong force generating state to the weak state is a linear function V of the sarcomere (VSL); furthermore, we tested whether the ATPase rate of the two isoforms of myosin can be held responsible for the difference between V0 of rat cardiac trabeculae containing V1 isomyosin versus those containing V3 isomyosin. METHODS: V1 isomyosin was induced by thyroid hormone treatment of the rats for 2 weeks, V3 isomyosin by PTU treatment for 1 month. Force was measured with a strain gauge in trabeculae from the rat right ventricle in K-H solution ([Ca]o=1.5 mM, 25 degrees C). Sarcomere length (SL) was measured with laser diffraction techniques. Twitch force at constant SL, and the force response to shortening at constant VSL (0-8 microm/s; deltaSL 50-100 nm) were measured at varied time during the twitch. RESULTS: The force response to shortening consisted of a fast initial exponential decline (tau = 2 ms) followed by a slow decrease of F. The instantaneous difference (deltaF) between isometric force (FM) and the declining force depended on shortening duration (deltat), VSL and instantaneous FM: deltaF = G1 x FM x deltat x VSL x (1-VSL/VMAX), where VMAX is the unloaded VSL and G1 was 6.15 +/- 2.12 microm(-1) (mean +/- s.d.; n=6). deltaF/FM was independent of the time onset of shortening. G1 of V1 and V3 trabeculae did not differ. V0 of V1 and V3 trabeculae differed 2-2.5 fold, as did both the ATPase rate and the velocity of actin sliding in a motility assay of the myosin purified from V1 or V3 hearts. The temperature dependence of the ATPase rate (Q10: 4.03 and 4.33, respectively; n.s.) was similar to that of V0 that has previously been reported for predominantly V1 trabeculae. Cross-linking of actin to myosin with the short chain cross linker EDC increased the ATPase rate of the two isomyosins (200-fold and 600-fold respectively) to exactly the same final level and reduced their Q10 by 50%. CONCLUSION: The linear interrelation between deltaF and VSL is consistent with feedback, whereby XB kinetics depends on VSL. This feedback provides an integrated description of cardiac muscle mechanics and energetics. The results, also, suggests that it is unlikely that the hydrolytic domain of the cross bridge determines V0 and warrant ongoing experiments to investigate the role of the actin binding domain of the XB in cardiac sarcomere kinetics. In order to further investigate the role of the actin binding domain, we have expressed chimeric cardiac myosin, co-assembled with MLC, by mutual substitution of actin binding loop on alpha MHC and beta MHC.

Regulation of Ca2+ and electrical alternans in cardiac myocytes: role of CAMKII and repolarizing currents.

Alternans of cardiac repolarization is associated with arrhythmias and sudden death. At the cellular level, alternans involves beat-to-beat oscillation of the action potential (AP) and possibly Ca(2+) transient (CaT). Because of experimental difficulty in independently controlling the Ca(2+) and electrical subsystems, mathematical modeling provides additional insights into mechanisms and causality. Pacing protocols were conducted in a canine ventricular myocyte model with the following results: 1) CaT alternans results from refractoriness of the sarcoplasmic reticulum Ca(2+) release system; alternation of the L-type calcium current has a negligible effect; 2) CaT-AP coupling during late AP occurs through the sodium-calcium exchanger and underlies AP duration (APD) alternans; 3) increased Ca(2+)/calmodulin-dependent protein kinase II (CaMKII) activity extends the range of CaT and APD alternans to slower frequencies and increases alternans magnitude; its decrease suppresses CaT and APD alternans, exerting an antiarrhythmic effect; and 4) increase of the rapid delayed rectifier current (I(Kr)) also suppresses APD alternans but without suppressing CaT alternans. Thus CaMKII inhibition eliminates APD alternans by eliminating its cause (CaT alternans) while I(Kr) enhancement does so by weakening CaT-APD coupling. The simulations identify combined CaMKII inhibition and I(Kr) enhancement as a possible antiarrhythmic intervention.