C F Starmer

Analysis of categorical data by linear models.

Assume there are ni., i = 1, 2, *--, s, samples from s multinomial distributions each having r categories of response. Then define any u functions of the unknown true cell probabilities {7rij: i = 1, 2, * , s; j = 1, 2, * , r, where E jrij l 1 } that have derivatives up to the second order with respect to 7rij, and for which the matrix of first derivatives is of rank u. A general noniterative procedure is described for fitting these functions to a linear model, for testing the goodness-of-fit of the model, and for testing hypotheses about the parameters in the linear model. The special cases of linear functions and logarithmic functions of the 7rin are developed in detail, and some examples of how the general approach can be used to analyze various types of categorical data are presented.

Channel specificity in antiarrhythmic drug action. Mechanism of potassium channel block and its role in suppressing and aggravating cardiac arrhythmias.

Although work on class III antiarrhythmics remains at an early stage, these agents still appear to possess greater efficacy and less proarrhythmia than conventional class I agents in those experimental arrhythmia models considered to be most representative of the clinical situation. Although prolongation of repolarization carries with its own tendency for pause-dependent arrhythmogenesis (i.e., torsade de pointes), available data suggest that this may be a function of nonspecificity in potassium channel block rather than a general characteristic of class III activity. The availability of new and more selective blockers of specific cardiac potassium channels under development as class III agents have already helped to clarify basic questions about the ionic mechanism of repolarization in the heart, and one hopes that a growing clinical data base will eventually determine the relative safety and efficacy of these agents in preventing symptomatic and life-threatening arrhythmias.

Antiarrhythmic drug action. Blockade of the inward sodium current.

THE mechanisms of action of antiarrhythmic drugs were discussed in these reviews over a decade ago (Rosen and Hoffman, 1973). Since then, important new concepts of the blocking action of drugs have been proposed and tested experimentally. Several attempts at a quantitative voltage clamp analysis of the blocking action of antiarrhythmic drugs have been made. The mechanism of the blocking action of local anesthetics has been studied in nerves to the limit of current electrical techniques—that of gating currents (Cahalan, 1980; Yeh, 1982). The volume of data dictates that we restrict the studies covered. We shall focus on the mechanism of the blockade of the sodium current. We neglect discussion of many otherwise important studies which do not have this focus. Knowledge of the number, kinetics, and relative importance of the individual pacemaker currents is sufficiently incomplete as to limit a discussion on the drug action on the individual currents. Blockade of membrane sodium conductance (GNa) is probably a major mechanism of action of antiarrhythmic drugs. To obtain a quantitative analysis of the kinetic and steady state effects of drugs on the sodium conductance, it is necessary to measure the sodium current, INa, in a stable system with the temperature and extracellular milieu that may be obtained in both normal and diseased tissues in vivo. The strategies that have been exploited for the study of INa in heart muscle include: (1) indirect estimation from Vmax of action potentials, (2) direct measurement of macroscopic sodium currents in multicellular and isolated cell preparations under voltage clamp, and (3) direct recording of unitary sodium conductance using the extracellular patch clamp technique. All these techniques use measurement of electrical properties to assess the binding kinetics of drugs to their receptor site(s). The quantitative precision of these techniques may vary. However, it is important to establish their ability to produce qualitatively similar results.

Proarrhythmic response to sodium channel blockade. Theoretical model and numerical experiments.

BackgroundThe use of flecainide and encainide was terminated in the Cardiac Arrhythmia Suppression Trial because of an excess of sudden cardiac deaths in the active treatment group. Such events might arise from reentrant rhythms initiated by premature stimulation in the presence of anisotropic sodium channel availability. Drugs that bind to sodium channels increase the functional dispersion of refractoriness by slowing (a result of the drug-unbinding process) the transition from an inexcitable state to an excitable state. It is interesting that encainide and flecainide unbind slowly (15–20 seconds), whereas lidocaine and moricizine unbind rapidly (0.2–1.3 seconds). Methods and ResultsWith a computer representation of a cable with Beeler-Reuter membrane properties, we found a small (6 msec) vulnerable window that occurred 338 msec after the last drive stimulus. Premature stimuli falling within the vulnerable window resulted in unidirectional block and reentrant activation. In the presence of a slowly unbinding drug, the window was delayed an additional 341 msec, and its duration was extended to 38 msec. The delay (antiarrhythmic effect) before the onset of the vulnerable window and its duration (proarrhythmic effect) were both dependent on the sodium channel availability and the recovery process. Both effects were also prolonged when sodium channel availability was reduced by membrane depolarization. Defining the proarrhythmic potential as the duration of the vulnerable window, we found that hypothetical use-dependent class I drugs have a greater proarrhythmic potential than non-use-dependent drugs. ConclusionsThe antiarrhythmic and proarrhythmic properties of pure sodium channel antagonists are both dependent on sodium channel availability. Consequently, the price for increased antiarrhythmic efficacy (suppressed premature ventricular contractions) is an increased proarrhythmic vulnerability to unsuppressed premature ventricular contractions.

Clinical judgment and statistics. Lessons from a simulated randomized trial in coronary artery disease.

A simulated randomized clinical trial in coronary artery disease was conducted to illustrate the need for clinical judgment and modern statistical methods in assessing therapeutic claims in studies of complex diseases. Clinicians should be aware of problems that occur when a patient sample is subdivided and treatment effects are assessed within multiple prognostic categories. In this example, 1073 consecutive, medically treated coronary artery disease patients from the Duke University data bank were randomized into two groups. The groups were reasonably comparable and, as expected, there was no overall difference in survival. In a subgroup of 397 patients characterized by three–vessel disease and an abnormal left ventricular contraction, however, survival of group 1 patients was significantly different from that of group 2 patients. Multivariable adjustment procedures revealed that the difference resulted from the combined effect of small imbalances in the distribution of several prognostic factors. Another subgroup was identified in which a significant survival difference was not explained by multivariable methods.These are not unlikely examples in trials of a complex disease. Clinicians must exercise careful judgment in attributing such results to an efficacious therapy, as they may be due to chance or to inadequate baseline comparability of the groups.

Evaluation of asynergy as an indicator of myocardial fibrosis.

SUMMARYThe presence and location of asynergy within the ventriculograms of 24 patients were compared with the quantity and site of fibrosis found in the left ventricle during postmortem examination. Asynergy was detected both qualitatively, by visual inspection, and quantitatively, by tracing end-systolic and end-diastolic outlines of the left ventricle with a sonic digitizer-computer system. The perimeters of fibrotic areas were traced during postmortem study with a sonic digitizer from photos of heart slices.For the RAO view, the qualitative and quantitative methods in the 24 hearts agreed on the presence or absence of asynergy in 58 of 72 (82%) of the anterior, posterior, and apical walls. In 12 of 14 (86%) walls in which the two methods disagreed, the presence or absence of quantitatively, but not qualitatively, determined asynergy correctly indicated the presence or absence of fibrosis within the wall. Of the 44 walls containing fibrosis, 35 (76%) demonstrated asynergy qualitatively while 42 (95%) exhibited asynergy quantitatively. Mean fibrosis increased with increasing severity of quantitatively determined asynergy: normal wall motion, 0.4% fibrosis; hypokinesis, 6.3%; akinesis, 14.3%; and dyskinesis, 30.1%. For the LAO view, neither qualitatively nor quantitatively determined asynergy in the lateral and septal walls was as closely related to fibrosis as In the RAO view. The ejection fraction was linearly correlated with the percent fibrosis of the entire left ventricle (r = -0.88).This study provides evidence that quantitatively determined asynergy in the RAO ventriculogram can serve as an indicator of fibrosis within the left ventricle.

Vulnerability in an excitable medium: analytical and numerical studies of initiating unidirectional propagation

Cardiac tissue can display unusual responses to certain stimulation protocols. In the wake of a conditioning wave of excitation, spiral waves can be initiated by applying stimuli timed to occur during a period of vulnerability (VP). Although vulnerability is well known in cardiac and chemical media, the determinants of the VP and its boundaries have received little theoretical and analytical study. From numerical and analytical studies of reaction-diffusion equations, we have found that 1) vulnerability is an inherent property of Beeler-Reuter and FitzHugh-Nagumo models of excitable media; 2) the duration of the vulnerable window (VW) the one-dimensional analog of the VP, is sensitive to the medium properties and the size of the stimulus field; and 3) the amplitudes of the excitatory and recovery processes modulate the duration of the VW. The analytical results reveal macroscopic behavior (vulnerability) derived from the diffusion of excitation that is not observable at the level of isolated cells or single reaction units.

Blockade of cardiac sodium channels by amitriptyline and diphenylhydantoin. Evidence for two use-dependent binding sites.

Cardiac toxicity is a frequent manifestation in amitriptyline overdose and is felt to be due, in part, to sodium channel blockade by the drug. Another agent with sodium channel blocking properties, diphenylhydantoin, has been used clinically to reverse cardiac conduction abnormalities induced by amitriptyline. This reversal of toxicity is believed to occur secondary to competition for the sodium channel binding site. We evaluated individually and in combination the effects of amitriptyline (0.4 microM) and diphenylhydantoin (10-80 microM) on the sodium current in isolated rabbit atrial and ventricular myocytes at 17 degrees C. Using the whole-cell variant of the patch-clamp technique, we found that both amitriptyline and diphenylhydantoin reduced the sodium current in a use-dependent fashion. The time constant of recovery (tau r) from block by amitriptyline at -130 mV was very slow (13.6 +/- 3.2 seconds), whereas tau r during diphenylhydantoin exposure was fast (0.71 +/- 0.21 seconds, p less than 0.0001 compared with amitriptyline). During exposure of cells to a mixture of the two drugs, tau r was found to be 6.6 +/- 1.8 seconds, but no evidence of direct competition between amitriptyline and diphenylhydantoin was seen. Attempts to fit the recovery data of the mixture to two exponentials resulted in no significant improvement in the fit when compared with that using a single exponential. Use of the sodium channel blocking agent lidocaine (similar kinetics to diphenylhydantoin) in competition with amitriptyline resulted in findings consistent with direct competition of these two drugs for a single binding site. These observations prompted us to evaluate the possibility that diphenylhydantoin was not acting at (and therefore not competing for) the same channel binding site as amitriptyline. Experiments altering pHi and pHo revealed dramatic differences between amitriptyline and diphenylhydantoin. When pHo was increased from 7.4 to 8.0, tau r was reduced approximately threefold (from 13.6 +/- 3.2 to 4.2 +/- 0.1 seconds, p less than 0.0001) during exposure to amitriptyline, but no effect was seen on tau r after exposure to diphenylhydantoin. Conversely, when pHi was increased from 7.3 to 8.0, tau r after amitriptyline was unaffected, but tau r after diphenylhydantoin markedly increased (from 0.71 +/- 0.21 to 2.60 +/- 1.30 seconds, p less than 0.001). Additionally, diphenylhydantoin block demonstrated profound voltage dependence across the range of -130 to -90 mV, whereas amitriptyline block appeared less voltage sensitive. Single-channel studies using patch-clamp techniques in isolated ventricular myocytes supported these data.(ABSTRACT TRUNCATED AT 400 WORDS)

Proarrhythmic Response to Potassium Channel Blockade Numerical Studies of Polymorphic Tachyarrhythmias

BACKGROUND Prompted by the results of CAST results, attention has shifted from class I agents that primarily block sodium channels to class III agents that primarily block potassium channels for pharmacological management of certain cardiac arrhythmias. Recent studies demonstrated that sodium channel blockade, while antiarrhythmic at the cellular level, was inherently proarrhythmic in the setting of a propagating wave front as a result of prolongation of the vulnerable period during which premature stimulation can initiate reentrant activation. From a theoretical perspective, sodium (depolarizing) and potassium (repolarizing) currents are complementary so that if antiarrhythmic and proarrhythmic properties are coupled to modulation of sodium currents, then antiarrhythmic and proarrhythmic properties might similarly be coupled to modulation of potassium currents. The purpose of the present study was to explore the role of repolarization currents during reentrant excitation. METHODS AND RESULTS To assess the generic role of repolarizing currents during reentry, we studied the responses of a two-dimensional array of identical excitable cells based on the FitzHugh-Nagumo model, consisting of a single excitation (sodium-like) current and a single recovery (potassium-like) current. Spiral wave reentry was initiated by use of S1S2 stimulation, with the delay timed to occur within the vulnerable period (VP). While holding the sodium conductance constant, the potassium conductance (gK) was reduced from 1.13 to 0.70 (arbitrary units), producing a prolongation of the action potential duration (APD). When gK was 1.13, the tip of the spiral wave rotated around a small, stationary, unexcited region and the computed ECG was monomorphic. As gK was reduced, the APD was prolonged and the unexcited region became mobile (nonstationary), such that the tip of the spiral wave inscribed an outline similar to a multipetaled flower; concomitantly, the computed ECG became progressively more polymorphic. The degree of polymorphism was related to the APD and the configuration of the nonstationary spiral core. CONCLUSIONS Torsadelike (polymorphic) ECGs can be derived from spiral wave reentry in a medium of identical cells. Under normal conditions, the spiral core around which a reentrant wave front rotates is stationary. As the balance of repolarizing currents becomes less outward (eg, secondary to potassium channel blockade), the APD is prolonged. When the wavelength (APD.velocity) exceeds the perimeter of the stationary unexcited core, the core will become unstable, causing spiral core drift. Large repolarizing currents shorten the APD and result in a monomorphic reentrant process (stationary core), whereas smaller currents prolong the APD and amplify spiral core instability, resulting in a polymorphic process. We conclude that, similar to sodium channel blockade, the proarrhythmic potential of potassium channel blockade in the setting of propagation may be directly linked to its cellular antiarrhythmic potential, ie, arrhythmia suppression resulting from a prolonged APD may, on initiation of a reentrant wave front, destabilize the core of a rotating spiral, resulting in complex motion (precession) of the spiral tip around a nonstationary region of unexcited cells. In tissue with inhomogeneities, core instability alters the activation sequence from one reentry cycle to the next and can lead to spiral wave fractination as the wave front collides with inhomogeneous regions. Depending on the nature of the inhomogeneities, wave front fragments may annihilate one another, producing a nonsustained arrhythmia, or may spawn new spirals (multiple wavelets), producing fibrillation and sudden cardiac death.

The relationship between enzymatic and histologic estimates of the extent of myocardial infarction in conscious dogs with permanent coronary occlusion.

Relationships between enzyme estimates (EE) and histologic measurements of infarct size (HIS) were analyzed in 14 conscious dogs with permanent occlusion of the circumflex coronary artery. EE were derived from serial CPK, CPK-MM, CPK-MB, and CPK-BB. Estimates were obtained using methods of Shell et al.,1 Norris et al.,1 and Roberts et al.4 HIS was determined from muldple histologic sections 5–6 days after infarction. In 14 animals, HIS ranged from 0.1–26.6 grams. Regression analysis demonstrated poor correlation (r2 < 0.06) between EE by each method and HIS. Using the Shell method and restricting the analysis to HIS of < 13 grams, improved the correlation (r1 = 0.42). Correlation in this subgroup could be further improved by using CPK-MM and MB data, elimination of animals with high background values, or limiting analysis to the portion of the curve where LDH isoenzymes indicated a cardiac zone. When the analysis was restricted to animals with HIS of < 13 grams, Norris and Roberts modifications as compared to Shells method improved correlation with CPK-MB but reduced correlation using CPK and CPKMM data. In this subgroup, each method overestimated extent of HIS; Shell > Norris > Roberts. In this study it was not possible to distinguish small from large HIS by serum enzyme measurements.