Hypokalaemia induces Ca²âº overload and Ca²âº waves in ventricular myocytes by reducing Na⁺,K⁺-ATPase α2 activity.

KEY POINTS: Hypokalaemia is a risk factor for development of ventricular arrhythmias. In rat ventricular myocytes, low extracellular K(+) (corresponding to clinical moderate hypokalaemia) increased Ca(2+) wave probability, Ca(2+) transient amplitude, sarcoplasmic reticulum (SR) Ca(2+) load and induced SR Ca(2+) leak. Low extracellular K(+) reduced Na(+),K(+)-ATPase (NKA) activity and hyperpolarized the resting membrane potential in ventricular myocytes. Both experimental data and modelling indicate that reduced NKA activity and subsequent Na(+) accumulation sensed by the Na(+), Ca(2+) exchanger (NCX) lead to increased Ca(2+) transient amplitude despite concomitant hyperpolarization of the resting membrane potential. Low extracellular K(+) induced Ca(2+) overload by lowering NKA α2 activity. Triggered ventricular arrhythmias in patients with hypokalaemia may therefore be attributed to reduced NCX forward mode activity linked to an effect on the NKA α2 isoform. ABSTRACT: Hypokalaemia is a risk factor for development of ventricular arrhythmias. The aim of this study was to determine the cellular mechanisms leading to triggering of arrhythmias in ventricular myocytes exposed to low Ko. Low Ko, corresponding to moderate hypokalaemia, increased Ca(2+) transient amplitude, sarcoplasmic reticulum (SR) Ca(2+) load, SR Ca(2+) leak and Ca(2+) wave probability in field stimulated rat ventricular myocytes. The mechanisms leading to Ca(2+) overload were examined. Low Ko reduced Na(+),K(+)-ATPase (NKA) currents, increased cytosolic Na(+) concentration and increased the Na(+) level sensed by the Na(+), Ca(2+) exchanger (NCX). Low Ko also hyperpolarized the resting membrane potential (RMP) without significant alterations in action potential duration. Experiments in voltage clamped and field stimulated ventricular myocytes, along with mathematical modelling, suggested that low Ko increases the Ca(2+) transient amplitude by reducing NKA activity despite hyperpolarization of the RMP. Selective inhibition of the NKA α2 isoform by low dose ouabain abolished the ability of low Ko to reduce NKA currents, to increase Na(+) levels sensed by NCX and to increase the Ca(2+) transient amplitude. We conclude that low Ko, within the range of moderate hypokalaemia, increases Ca(2+) levels in ventricular myocytes by reducing the pumping rate of the NKA α2 isoform with subsequent Na(+) accumulation sensed by the NCX. These data highlight reduced NKA α2 -mediated control of NCX activity as a possible mechanism underlying triggered ventricular arrhythmias in patients with hypokalaemia.

At the heart of computational modelling.

The link between experimental data and biophysically based mathematical models is key to computational simulation meeting its potential to provide physiological insight. However, despite the importance of this link, scrutiny and analysis of the processes by which models are parameterised from data are currently lacking. While this situation is common to many areas of physiological modelling, to provide a concrete context, we use examples drawn from detailed models of cardiac electro-mechanics. Using this biophysically detailed cohort of models we highlight the specific issues of model parameterization and propose this process can be separated into three stages: observation, fitting and validation. Finally, future research challenges and directions in this area are discussed.

Interpreting genetic effects through models of cardiac electromechanics.

Multiscale models of cardiac electromechanics are being increasingly focused on understanding how genetic variation and environment underpin multiple disease states. In this paper we review the current state of the art in both the development of specific models and the physiological insights they have produced. This growing research body includes the development of models for capturing the effects of changes in function in both single and multiple proteins in both specific expression systems and in vivo contexts. Finally, the potential for using this approach for ultimately predicting phenotypes from genetic sequence information is discussed.

Biophysical modeling to simulate the response to multisite left ventricular stimulation using a quadripolar pacing lead.

BACKGROUND: Response to cardiac resynchronization therapy (CRT) is reduced in patients with posterolateral scar. Multipolar pacing leads offer the ability to select desirable pacing sites and/or stimulate from multiple pacing sites concurrently using a single lead position. Despite this potential, the clinical evaluation and identification of metrics for optimization of multisite CRT (MCRT) has not been performed. METHODS: The efficacy of MCRT via a quadripolar lead with two left ventricular (LV) pacing sites in conjunction with right ventricular pacing was compared with single-site LV pacing using a coupled electromechanical biophysical model of the human heart with no, mild, or severe scar in the LV posterolateral wall. RESULT: The maximum dP/dt(max) improvement from baseline was 21%, 23%, and 21% for standard CRT versus 22%, 24%, and 25% for MCRT for no, mild, and severe scar, respectively. In the presence of severe scar, there was an incremental benefit of multisite versus standard CRT (25% vs 21%, 19% relative improvement in response). Minimizing total activation time (analogous to QRS duration) or minimizing the activation time of short-axis slices of the heart did not correlate with CRT response. The peak electrical activation wave area in the LV corresponded with CRT response with an R(2) value between 0.42 and 0.75. CONCLUSION: Biophysical modeling predicts that in the presence of posterolateral scar MCRT offers an improved response over conventional CRT. Maximizing the activation wave area in the LV had the most consistent correlation with CRT response, independent of pacing protocol, scar size, or lead location.

Calcium dynamics in the ventricular myocytes of SERCA2 knockout mice: A modeling study.

We describe a simulation study of Ca²(+) dynamics in mice with cardiomyocyte-specific conditional excision of the sarco(endo)plasmic reticulum calcium ATPase (SERCA) gene, using an experimental data-driven biophysically-based modeling framework. Previously, we reported a moderately impaired heart function measured in mice at 4 weeks after SERCA2 gene deletion (knockout (KO)), along with a >95% reduction in the level of SERCA2 protein. We also reported enhanced Ca²(+) flux through the L-type Ca²(+) channels and the Na(+)/Ca²(+) exchanger in ventricular myocytes isolated from these mice, compared to the control Serca2(flox/flox) mice (flox-flox (FF)). In the current study, a mathematical model-based analysis was applied to enable further quantitative investigation into changes in the Ca²(+) handling mechanisms in these KO cardiomyocytes. Model parameterization based on a wide range of experimental measurements showed a 67% reduction in SERCA activity and an over threefold increase in the activity of the Na(+)/Ca²(+) exchanger. The FF and KO models were then validated against experimentally measured [Ca²(+)](i) transients and experimentally estimated sarco(endo)plasmic reticulum (SR) function. Simulation results were in quantitative agreement with experimental measurements, confirming that sustained [Ca²(+)](i) transients could be maintained in the KO cardiomyocytes despite severely impaired SERCA function. In silico analysis shows that diastolic [Ca²(+)](i) rises sharply with progressive reductions in SERCA activity at physiologically relevant pacing frequencies. Furthermore, an analysis of the roles of the compensatory mechanisms revealed that the major combined effect of the compensatory mechanisms is to lower diastolic [Ca²(+)](i). Finally, by using a comprehensive sensitivity analysis of the role of all cellular calcium handling mechanisms, we show that the combination of upregulation of the Na(+)/Ca²(+) exchanger and increased L-type Ca²(+) current is the most effective means to maintain diastolic and systolic calcium levels after loss of SERCA function.

A mathematical model of the murine ventricular myocyte: a data-driven biophysically based approach applied to mice overexpressing the canine NCX isoform.

Mathematical modeling of Ca(2+) dynamics in the heart has the potential to provide an integrated understanding of Ca(2+)-handling mechanisms. However, many previous published models used heterogeneous experimental data sources from a variety of animals and temperatures to characterize model parameters and motivate model equations. This methodology limits the direct comparison of these models with any particular experimental data set. To directly address this issue, in this study, we present a biophysically based model of Ca(2+) dynamics directly fitted to experimental data collected in left ventricular myocytes isolated from the C57BL/6 mouse, the most commonly used genetic background for genetically modified mice in studies of heart diseases. This Ca(2+) dynamics model was then integrated into an existing mouse cardiac electrophysiology model, which was reparameterized using experimental data recorded at consistent and physiological temperatures. The model was validated against the experimentally observed frequency response of Ca(2+) dynamics, action potential shape, dependence of action potential duration on cycle length, and electrical restitution. Using this framework, the implications of cardiac Na(+)/Ca(2+) exchanger (NCX) overexpression in transgenic mice were investigated. These simulations showed that heterozygous overexpression of the canine cardiac NCX increases intracellular Ca(2+) concentration transient magnitude and sarcoplasmic reticulum Ca(2+) loading, in agreement with experimental observations, whereas acute overexpression of the murine cardiac NCX results in a significant loss of Ca(2+) from the cell and, hence, depressed sarcoplasmic reticulum Ca(2+) load and intracellular Ca(2+) concentration transient magnitude. From this analysis, we conclude that these differences are primarily due to the presence of allosteric regulation in the canine cardiac NCX, which has not been observed experimentally in the wild-type mouse heart.

Biophysically based mathematical modeling of interstitial cells of Cajal slow wave activity generated from a discrete unitary potential basis.

Spontaneously rhythmic pacemaker activity produced by interstitial cells of Cajal (ICC) is the result of the entrainment of unitary potential depolarizations generated at intracellular sites termed pacemaker units. In this study, we present a mathematical modeling framework that quantitatively represents the transmembrane ion flows and intracellular Ca2+ dynamics from a single ICC operating over the physiological membrane potential range. The mathematical model presented here extends our recently developed biophysically based pacemaker unit modeling framework by including mechanisms necessary for coordinating unitary potential events, such as a T-Type Ca2+ current, Vm-dependent K+ currents, and global Ca2+ diffusion. Model simulations produce spontaneously rhythmic slow wave depolarizations with an amplitude of 65 mV at a frequency of 17.4 cpm. Our model predicts that activity at the spatial scale of the pacemaker unit is fundamental for ICC slow wave generation, and Ca2+ influx from activation of the T-Type Ca2+ current is required for unitary potential entrainment. These results suggest that intracellular Ca2+ levels, particularly in the region local to the mitochondria and endoplasmic reticulum, significantly influence pacing frequency and synchronization of pacemaker unit discharge. Moreover, numerical investigations show that our ICC model is capable of qualitatively replicating a wide range of experimental observations.

Energetic consequences of mechanical loads.

In this brief review, we have focussed largely on the well-established, but essentially phenomenological, linear relationship between the energy expenditure of the heart (commonly assessed as the oxygen consumed per beat, oxygen consumption (VO2)) and the pressure-volume-area (PVA, the sum of pressure-volume work and a specified 'potential energy' term). We raise concerns regarding the propriety of ignoring work done during 'passive' ventricular enlargement during diastole as well as the work done against series elasticity during systole. We question the common assumption that the rate of basal metabolism is independent of ventricular volume, given the equally well-established Feng- or stretch-effect. Admittedly, each of these issues is more of conceptual than of quantitative import. We point out that the linearity of the enthalpy-PVA relation is now so well established that observed deviations from linearity are often ignored. Given that a one-dimensional equivalent of the linear VO2-PVA relation exists in papillary muscles, it seems clear that the phenomenon arises at the cellular level, rather than being a property of the intact heart. This leads us to discussion of the classes of crossbridge models that can be applied to the study of cardiac energetics. An admittedly superficial examination of the historical role played by Hooke's Law in theories of muscle contraction foreshadows deeper consideration of the thermodynamic constraints that must, in our opinion, guide the development of any mathematical model. We conclude that a satisfying understanding of the origin of the enthalpy-PVA relation awaits the development of such a model.

A meta-analysis of cardiac electrophysiology computational models.

Computational models of cardiac electrophysiology are exemplar demonstrations of the integration of multiple data sets into a consistent biophysical framework. These models encapsulate physiological understanding to provide quantitative predictions of function. The combination or extension of existing models within a common framework allows integrative phenomena in larger systems to be investigated. This methodology is now routinely applied, as demonstrated by the increasing number of studies which use or extend previously developed models. In this study, we present a meta-analysis of this model re-use for two leading models of cardiac electrophysiology in the form of parameter inheritance trees, a sensitivity analysis and a comparison of the functional significance of the sodium potassium pump for defining restitution curves. These results indicate that even though the models aim to represent the same physiological system, both the sources of parameter values and the function of equivalent components are significantly different.

Modelling and measuring electromechanical coupling in the rat heart.

Tension-dependent binding of Ca(2+) to troponin C in the cardiac myocyte has been shown to play an important role in the regulation of Ca(2+) and the activation of tension development. The significance of this regulatory mechanism is quantified experimentally by the quantity of Ca(2+) released following a rapid change in the muscle length. Using a computational, coupled, electromechanics cell model, we have confirmed that the tension dependence of Ca(2+) binding to troponin C, rather than cross-bridge kinetics or the rate of Ca(2+) uptake by the sarcoplasmic reticulum, determines the quantity of Ca(2+) released following a length step. This cell model has been successfully applied in a continuum model of the papillary muscle to analyse experimental data, suggesting the tension-dependent binding of Ca(2+) to troponin C as the likely pathway through which the effects of localized impaired tension generation alter the Ca(2+) transient. These experimental results are qualitatively reproduced using a three-dimensional coupled electromechanics model. Furthermore, the model predicts that changes in the Ca(2+) transient in the viable myocardium surrounding the impaired region are amplified in the absence of tension-dependent binding of Ca(2+) to troponin C.

A biophysically based mathematical model of unitary potential activity in interstitial cells of Cajal.

Unitary potential (UP) depolarizations are the basic intracellular events responsible for pacemaker activity in interstitial cells of Cajal (ICCs), and are generated at intracellular sites termed "pacemaker units". In this study, we present a mathematical model of the transmembrane ion flows and intracellular Ca(2+) dynamics from a single ICC pacemaker unit acting at near-resting membrane potential. This model quantitatively formalizes the framework of a novel ICC pacemaking mechanism that has recently been proposed. Model simulations produce spontaneously rhythmic UP depolarizations with an amplitude of approximately 3 mV at a frequency of 0.05 Hz. The model predicts that the main inward currents, carried by a Ca(2+)-inhibited nonselective cation conductance, are activated by depletion of sub-plasma-membrane [Ca(2+)] caused by sarcoendoplasmic reticulum calcium ATPase Ca(2+) sequestration. Furthermore, pacemaker activity predicted by our model persists under simulated voltage clamp and is independent of [IP(3)] oscillations. The model presented here provides a basis to quantitatively analyze UP depolarizations and the biophysical mechanisms underlying their production.

Measuring and modeling chloride-hydroxyl exchange in the Guinea-pig ventricular myocyte.

Protons are powerful modulators of cardiac function. Their intracellular concentration is regulated by sarcolemmal ion transporters that export or import H+-ions (or their ionic equivalent: HCO3-, OH-). One such transporter, which imports H+-equivalents, is a putative Cl-/OH- exchanger (CHE). A strong candidate for CHE is SLC26A6 protein, a product of the SLC26A gene family of anion transporters, which has been detected in murine heart. SLC26A6 protein is suggested to be an electrogenic 1Cl-/2OH-(2HCO3-) exchanger. Unfortunately, there is insufficient characterization of cardiac CHE against which the properties of heterologously expressed SLC26A6 can be matched. We therefore investigated the proton, Cl-, and voltage dependence of CHE activity in guinea-pig ventricular myocytes, using voltage-clamp, intracellular pH fluorescence, and mathematical modeling techniques. We find that CHE activity is tightly regulated by intracellular and extracellular pH, is voltage-insensitive over a wide range (+/-80 mV), and displays substrate dependence suggestive of electroneutral 1Cl-/1OH- exchange. These properties exclude electrogenic SLC26A6 as sole contributor to CHE. Either the SLC26A6 product in heart is electroneutral, or CHE comprises at least two transporters with oppositely balanced voltage sensitivity. Alternatively, CHE may comprise an H+-Cl- coinflux system, which cannot be distinguished kinetically from an exchanger. Irrespective of ionic mechanism, CHE's pH sensitivity helps to define resting intracellular pH, and hence basal function in the heart.

A novel methodology for personalized simulations of ventricular hemodynamics from noninvasive imaging data.

Current state-of-the-art imaging techniques can provide quantitative information to characterize ventricular function within the limits of the spatiotemporal resolution achievable in a realistic acquisition time. These imaging data can be used to personalize computer models, which in turn can help treatment planning by quantifying biomarkers that cannot be directly imaged, such as flow energy, shear stress and pressure gradients. To date, computer models have typically relied on invasive pressure measurements to be made patient-specific. When these data are not available, the scope and validity of the models are limited. To address this problem, we propose a new methodology for modeling patient-specific hemodynamics based exclusively on noninvasive velocity and anatomical data from 3D+t echocardiography or Magnetic Resonance Imaging (MRI). Numerical simulations of the cardiac cycle are driven by the image-derived velocities prescribed at the model boundaries using a penalty method that recovers a physical solution by minimizing the energy imparted to the system. This numerical approach circumvents the mathematical challenges due to the poor conditioning that arises from the imposition of boundary conditions on velocity only. We demonstrate that through this technique we are able to reconstruct given flow fields using Dirichlet only conditions. We also perform a sensitivity analysis to investigate the accuracy of this approach for different images with varying spatiotemporal resolution. Finally, we examine the influence of noise on the computed result, showing robustness to unbiased noise with an average error in the simulated velocity approximately 7% for a typical voxel size of 2mm(3) and temporal resolution of 30ms. The methodology is eventually applied to a patient case to highlight the potential for a direct clinical translation.

Development of models of active ion transport for whole-cell modelling: cardiac sodium-potassium pump as a case study.

This study presents a method for the reduction of biophysically-based kinetic models for the active transport of ions. A lumping scheme is presented which exploits the differences in timescales associated with fast and slow transitions between model states, while maintaining the thermodynamic properties of the model. The goal of this approach is to contribute to modelling of the effects of disturbances to metabolism, associated with ischaemic heart disease, on cardiac cell function. The approach is illustrated for the sodium-potassium pump in the myocyte. The lumping scheme is applied to produce a 4-state representation from the detailed 15-state model of Läuger and Apell, Eur. Biophys. J. 13 (1986) 309, for which the principles of free energy transduction are used to link the free energy released from ATP hydrolysis (deltaGATP) to the transition rates between states of the model. An iterative minimisation algorithm is implemented to determine the transition rate parameters based on the model fit to experimental data. Finally, the relationship between deltaGATP and pump cycling direction is investigated and compared with recent experimental findings.

Immunologic differentiation of the Sézary syndrome due to cutaneous T-cell lymphoma and chronic actinic dermatitis.

Peripheral blood mononuclear cells from two well-defined groups of patients with the Sézary syndrome have been studied employing indirect immunofluorescent and indirect immunogold techniques in light and electron microscopy, using monoclonal antibodies against T-cell subpopulations. Four patients had chronic actinic dermatitis (CAD) of the actinic reticuloid variant, with erythroderma. Eight patients had cutaneous T-cell lymphoma. All patients showed the clinical features of the Sézary syndrome, including erythroderma, palmoplantar hyperkeratosis, and peripheral lymphadenopathy, and in all patients significant numbers (0.5-30.5 X 10(9) cells/liter) of circulating mononuclear cells were observed with Sézary cell morphology on light-microscopic examination of blood films. Major differences were observed in the circulating T-cell subpopulations in the two groups. In the erythrodermic CAD patients, there was a moderately elevated T-cell count (1.6 +/- 0.6 X 10(9) cells/liter; normal, 1.0 +/- 0.3 X 10(9) cells/liter) of which the majority of the cells was suppressor T cells (OKT8+) giving a very low helper:suppressor T-cell ratio of 0.1:1-0.36:1 (normal, 1.7:1-3.5:1). In cutaneous T-cell lymphoma, there was also an elevation of the T-cell count (9.5 +/- 12.9 X 10(9) cells/liter), but in these patients the predominant cell was the helper T cell (OKT4+) with a high helper:suppressor T-cell ratio of 3.7:1-98:1.

Injection-site granuloma due to aluminum.

Three patients had subcutaneous nodules at the sites of previous injections of vaccine containing tetanus toxoid. Biopsy and microscopic findings in all three cases showed foci of granulomatous inflammation, consisting of lymphoid follicles, in the deep dermis and subcutaneous tissues and a surrounding infiltrate of lymphocytes, histiocytes, plasma cells, and eosinophils. Occasional zones of eosinophilic necrosis were seen within the inflammatory foci, and surrounding dense fibrous bands were present in some areas. A solochrome-azurin stain showed aluminum crystals in the nodules from two patients. From the evidence available, we believe that these nodules are a complication of inoculations with aluminum-containing vaccines.

The a-wave of the human electroretinogram recorded with a minimally invasive technique.

A minimally invasive technique is described for recording the a-wave of the human ERG and extracting the parameters of transduction in the rod and cone photoreceptors. A corneal DTL fibre electrode is used, but the pupil is not dilated and the cornea is not anaesthetized. Although the amplitude of the signal collected by the DTL electrode varies from session to session, this is not a problem, as the photoreceptor fractional circulating current is obtained by normalization of the response family. A method is described for varying the effective flash intensity over a wide range, by controlling the duration of the xenon flash. In order to fit the kinetics of the responses, an analytical equation is derived for the convolution of the previous "delayed gaussian" expression with the cell's capacitive time constant. This equation provides a good description of both the rod and the cone response families. For rods, the capacitive time constant was found to be tau rod approximately 1 msec as reported previously, but for the cones a considerably longer time constant of tau cone approximately 4-5 msec was needed. For rods, the amplification constant (Arod approximately 5 sec-2) was close to previous estimates, but for cones the sensitivity (expressed in terms of corneal illuminance) was higher than in previous work. Calculation of the amplification constant of transduction within the cones requires knowledge of their light collection properties, and the absence of hard information makes this estimate somewhat speculative. However, when account is taken of the larger diameter of the inner segments of cones in the peripheral retina, then our estimated amplification constant for the cones (Acone approximately 3-7 sec-2) is of a similar order of magnitude to that obtained for the rods.

Histologic criteria for early diagnosis of cutaneous T-cell lymphoma.

This article considers the diagnostic histopathologic criteria for the most common form of cutaneous T-cell lymphoma, that of mycosis fungoides (MF). The diagnosis of MF, as with any condition, is based on the careful taking of a history, detailed physical examination, and various investigative techniques of which a biopsy specimen of an appropriate skin lesion is undoubtedly one of the most important.

Computed tomography in the evaluation of cutaneous T-cell lymphoma.

The computed tomography (CT) scans performed in 28 patients with cutaneous T-cell lymphoma (CTCL) were reviewed. Fifteen patients had clinically advanced cutaneous mycosis fungoides, six patients Sézary syndrome and seven variant CTCL. Of the 40 scans available 12 were normal, 15 indeterminate and 13 abnormal. Indeterminate and abnormal nodes showed a predilection for inguinal and axillary sites with a relative sparing of deep nodal regions. Visceral involvement was infrequent. In six patients CT detected abnormalities not obvious clinically and upstaged the disease. CT should be performed as part of the initial staging and as a baseline for follow-up in patients with advanced mycosis fungoides, Sézary syndrome and variant CTCL.

An outbreak of methicillin-resistant Staphylococcus aureus (MRSA) infection in HIV-seropositive persons.

Staphylococcus aureus is a cause of considerable morbidity and mortality in HIV-seropositive persons. Although methicillin-resistant S. aureus (MRSA) is encountered worldwide and in many areas of medical care, little has been reported on clinical infection with MRSA in patients with HIV. We report on an outbreak of MRSA infection in HIV antibody positive patients, using case reports to describe an outbreak of MRSA infection in HIV-seropositive persons. Six cases of clinical MRSA infection were reported over a 4-week period on patients on an HIV dedicated ward. All cases had previous AIDS diagnoses and low CD4 cell counts (median 8 x 10(6)/l; range 0 to 238). Two cases had infected skin lesions and 2 cases had infected indwelling central venous catheters with septicaemia. Two cases had pneumonia, one with concurrent infection at the entry site of a percutaneous endoscopic gastrostomy (PEG) feeding tube. Isolates of MRSA from the 6 cases were compared by pulsed-field gel electrophoresis of Sma1 chromosomal digests. The resultant banding pattern showed the same strain was responsible for all the infections. A seventh inpatient, the index case, had positive carriage with the same strain of MRSA. To define ongoing MRSA carriage after the outbreak, 29 consecutive ward patients were swabbed for MRSA: all were negative. All patients identified with MRSA infection responded to treatment with intravenous teicoplanin, although carriage was unaltered. Four of the 6 cases died within 7 weeks of diagnosis of MRSA. MRSA can cause severe morbidity in patients with end-stage HIV disease. A small outbreak of MRSA was controlled by simple precautionary measures with no subsequent ongoing transmission of MRSA.