Quasiperiodicity and chaos in cardiac fibrillation.

In cardiac fibrillation, disorganized waves of electrical activity meander through the heart, and coherent contractile function is lost. We studied fibrillation in three stationary forms: in human chronic atrial fibrillation, in a stabilized form of canine ventricular fibrillation, and in fibrillation-like activity in thin sheets of canine and human ventricular tissue in vitro. We also created a computer model of fibrillation. In all four studies, evidence indicated that fibrillation arose through a quasiperiodic stage of period and amplitude modulation, thus exemplifying the "quasiperiodic transition to chaos" first suggested by Ruelle and Takens. This suggests that fibrillation is a form of spatio-temporal chaos, a finding that implies new therapeutic approaches.

Effect of heart rate on myocardial relaxation in isometric twitches.

OBJECTIVE: Increased heart rate increases the amount of calcium that triggers myofilament interaction and thereby the load of calcium to be sequestered to cause relaxation, while decreasing the time for calcium sequestration. By studying the effect of heart rate on myocardial relaxation the hypothesis was therefore tested that increased heart rate impairs myocardial relaxation. METHODS: In situ blood-perfused right ventricular papillary muscles of seven isolated Suga-Sagawa cross circulated canine hearts were studied with a servo system that clamped muscle length to produce isometric force, F(t), at one isometric length in each muscle at paced heart rates within the range 100-150. Each curve of F(t) was fitted, by Marquardt's algorithm, with the relation F(t) = C(t/A)B(e)1-(t/A)B. It was previously shown that the parameter B reflects changes in relaxation, whereas the parameters A and C reflect chronotropic and inotropic states. Changes in B reflect changes in the time course of relaxation that are not simply due to changes in total twitch duration guaranteed to be produced by altered heart rate. Linear regression analysis was performed on data from each muscle to determine whether each of the parameters A, B, and C changed significantly with heart rate. RESULTS: The mean coefficient of determination, a measure of goodness of fit of the model to observed data, was 0.996(SD 0.001). With increase in heart rate, A and C increased significantly in six of the seven muscles. On the other hand B did not show significant change with heart rate in six of the seven muscles; in the seventh muscle, B increased significantly with heart rate. Similar results were obtained when other indices of lusitropy were used. CONCLUSIONS: Increase in heart rate does not impair myocardial lusitropy as measured by the parameter B which reflects changes in the time course of relaxation independent of change in total time course of mechanical activity.

A model of the time course of myocardial dynamics: use in characterisation of relaxation and evaluation of its indices.

OBJECTIVE: Study of myocardial relaxation (lusitropy) requires a lusitropic index that should reflect changes in the time course of relaxation, and is therefore ideally based on a model that encompasses the entire time course of relaxation. Since there is no such model, investigators could not evaluate and validate current measures of relaxation. A new model is therefore proposed and analysed here: X(t) = C(t/A)B(e)1-(t/A)B. X(t) is the time course of isometric force or isotonic shortening, t is time, and A, B and C are parameters. METHODS: The model was analysed and evaluated in nine in situ canine papillary muscles studied with a servo system which produced isometric and isotonic twitches. A, B and C were determined by Marquardt's algorithm. RESULTS: The new model is analytically sufficiently tractable to ascertain, for the first time, whether previous measures of relaxation reflect the time course of relaxation. It nonetheless fits observed data closely, the coefficients of determination being 0.995(SD 0.005) and 0.990(0.004) in isometric and isotonic switches. A and B showed little or no change, with alteration of preload and afterload states averaging 0.200(0.014) s and 0.21(0.022) s for A, and 1.87(0.099) and 2.15(0.158) for B in isometric and isotonic twitches respectively. Dobutamine decreased A but the change was significant only in isotonic twitches; it increased B significantly only in isometric twitches. Thus the lusitropic and chronotropic effects of dobutamine may depend on loading conditions. CONCLUSIONS: This model is uniquely useful because it permits the evaluation and reconciliation of previously proposed measures of myocardial relaxation. It also provides a convenient model of the time course of the mechanical activity of the myocardium under isometric and isotonic conditions and is successful in assigning physiological relevance to its parameters. Moreover it permits expeditious derivation of relations for its parameters, thus providing initial parameter estimates systematically.

Ventricular fibrillation: one spiral or many?

Ventricular fibrillation is the major cause of sudden cardiac death, the leading cause of death in the industrialized world; however, the mechanisms for its onset are not well understood. To further understand the dynamics of fibrillation at and near its onset, we compared spatial and temporal variability of mean interactivation intervals in a stable canine model for ventricular fibrillation. Temporal variability was very small, suggesting that the relevant physiological parameters remained constant during our experiments. Spatial variability was usually significantly larger and appeared incompatible with the dynamics of a single, meandering spiral wave. This confirmed recent results that a single spiral wave cannot generate ventricular fibrillation. Thus the onset of fibrillation is a multistage process, with spiral-wave breakdown providing a crucial step in the quasi-periodic route to fibrillation.

Effect of coronary artery size on the prevalence of atherosclerosis.

To investigate the effect of coronary artery size on the prevalence of atherosclerosis, we measured the diameters of the major coronary arteries prospectively in 884 consecutive patients referred for coronary arteriography. For each artery, we assigned patients to 3 groups: group S (small) and group L (large) with diameters >1SD smaller and larger, respectively, than the mean; and group A (average), with diameters within 1SD of the mean. As specified during study design, we compared the frequency of lesions > or = 50% diameter stenosis in groups S and L for each artery. We adjusted for relevant covariates by performing logistic regression on data from all 884 patients with coronary diameter entered as a continuous variable. In group S versus L, respectively, the frequency of > or = 50% lesion was 6.5% versus 2.4% (p = 0.13) in the left main artery; 61.3% versus 35.8% (p = 0.0001) in the right coronary artery; 58.1% versus 40.7% (p = 0.008) in the left anterior descending artery, and 47.4% versus 22.2% (p = 0.0001) in the circumflex artery. Multivariate analysis showed that coronary diameter was a significant independent predictor of lesions in the right coronary artery (p = 0.000001), left anterior descending artery (p = 0.001), and circumflex artery (p = 0.0002) and nearly significant in the left main artery (p = 0.077). Thus, small coronary artery size may be a risk factor for atherosclerosis.

Differences in left ventricular adaptation to chronic mitral and aortic regurgitation.

For comparable volume load, impedance to ejection of the regurgitant volume in AR exceeds that in MR. To determine whether this load difference results in differences in PLVH and ejection performance, we studied consecutive, untreated, asymptomatic patients (11 in each group) by echocardiography and Doppler. Mean LVID, SBP, h, and FS were, respectively, in AR vs MR: 60.3 +/- 3.1 mm vs 62.0 +/- 2.3 mm (p = NS), 152 +/- 7.1 mm Hg vs 125 +/- 6.4 mm Hg (p less than 0.005), 12.1 +/- 0.4 mm vs 10.5 +/- 0.6 mm (p less than 0.04), and 0.38 +/- 0.02 vs 0.43 +/- 0.02 (p = NS). The h/R ratio reflects the PLVH-0.41 +/- 0.02 in AR and 0.34 +/- 0.02 in MR (p less than 0.02). The FS correlates positively with h/R in either lesion, but was higher in MR for any given h/R. The difference in loading conditions imposed by both lesions is associated with a difference in the PLVH as well as in ejection performance.

Lack of association of higher insulin levels with diffuse atherosclerotic coronary artery disease in nondiabetics.

Since there is experimental evidence that insulin promotes atherosclerosis, we tested the hypothesis that insulin levels are higher in patients with diffuse atherosclerotic coronary artery disease by measuring insulin levels in 46 nondiabetic patients with angiographically defined diffuse coronary artery disease and 46 normal controls with angiographically normal coronary arteries. Fasting insulin levels were similar in both groups of patients: 7.70 +/- 5.77 microU/mL in those with diffuse coronary disease versus 7.39 +/- 5.01 microU/mL in controls. Also, insulin levels drawn 1 and 2 h after oral glucose challenge were not significantly different in patients with diffuse disease (48.78 +/- 32.46 microU/mL and 42.26 +/- 32.38 microU/mL, respectively) compared with patients with normal coronary arteries (51.03 +/- 28.01 microU/mL and 43.79 +/- 31.62 microU/mL, respectively). We conclude that insulin probably does not promote clinical atherosclerosis in nondiabetics.

Similarities and differences in the time course of mechanical activity of the canine myocardium and isovolumic left ventricle.

BACKGROUND: The isovolumic non-ejecting left ventricle (LV) is functionally analogous to the isometric myocardium and the curve of the time course of left ventricular isovolumic pressure, P(t), resembles the curve of the time course of myocardial isometric force, F(t). In this study therefore, we first tested the hypothesis that the same general empirical model that fit F(t) and L(t), the isotonic shortening curve, will also fit P(t) by evaluating the model P(t) = P0 + C(t/A)B exp[1-(t/A)]B in 8 Suga-Sagawa isolated cross-circulated canine left ventricles. P0 is the end-diastolic pressure; A, B, and C are parameters. We went further to compare the time course of P(t) to those of F(t) and L(t) exploiting their common basic analytical models not only to characterize similarities but also to highlight differences between them. METHODS: To obtain curves of P(t), we inserted a latex balloon in the LV and injected water into it and recorded the isovolumic pressure curve, P(t), in each of 8 ventricles. Eight in situ right ventricular papillary muscles of the isolated canine heart were also studied with a servo system that clamped length or force to produce F(t) or L(t). Each curve, P(t), F(t), or L(t) was fit with the above model by Marquardt's algorithm and A, B, and C determined. RESULTS: The model fit the curves closely, the coefficient of determination being 0.995 +/- 0.003 for P(t); 0.994 +/- 0.003 for F(t), and 0.990 +/- 0.004 for L(t). The common model allowed direct quantitative comparison of the time course of either myocardial isometric or isotonic dynamics with the time course of left ventricular isovolumic dynamics by comparing the ventricular parameters A and B, which determine details of time course, with their corresponding myocardial counterparts. Under basal (i.e. control) conditions, A and B averaged 0.194 +/- 0.015 and 2.09 +/- 0.065 respectively for P(t). Mean A for isotonic shortening was 0.219 +/- 0.022 (p < 0.02 compared to mean A for P(t)). Mean B for F(t) was 1.87 +/- 0.100 (p < 0.001 compared to mean B for P(t)). The values of A for P(t) and F(t) were not different and the values of B for P(t) and L(t) were closely similar. CONCLUSION: The same empirical model that fits F(t) and L(t) also fits P(t). Comparison of myocardial to ventricular curves showed that during contraction, P(t) corresponded closely to F(t) and L(t). However during relaxation, P(t) led both F(t) and L(t) both of which pursued a similar time course. This suggests that myocardial contraction may be isometric during LV isovolumic contraction and it may be valid to extrapolate information about myocardial isometric contraction directly to left ventricular isovolumic contraction and vice versa. On the other hand during left ventricular isovolumic relaxation, myocardial dynamics may well involve some length changes. It is difficult, however, to reconcile such presumed length changes to the putative isometricity of myocardial function during contraction.

Dynamics of cardiac muscle: analysis of isotonic, isometric, and isochronal curves.

Canine papillary muscle force-length-time relation (F-L-t) was investigated under pentobarbital sodium anesthesia. The time intervals taken from end diastole to any point (P) on the force-length plane was determined for isometric (t1) and isotonic (t2) systole and corrected for excitation contraction coupling duration. The ratio t1/t2, designated km, was approximately constant for widely scattered positions of P chosen systematically. The km in the 10 dogs ranged from 0.36 to 0.94 with means +/- SD of 0.66 +/- 0.16; km correlated negatively with muscle average cross-sectional area (r = -0.82; P less than 0.005). Assuming constancy of km, a general relationship was derived between (delta F/delta t)t1L, the rate of isometric force development at P; (delta L/delta t)t2F, the velocity of isotonic shortening at P; (delta F/delta L)(t1,t2)t, the stiffness; and (delta L/delta F)(t1,t2)t, the compliance of the myocardium (all taken at P) as follows (delta F/delta L)t1,t2t = -km(delta F/delta t)t1L/(delta L/delta t)t2F and (delta L/delta F)t1,t2t = -km-1(delta L/delta t)t2F/(delta F/delta t)t1t. The ratio of (delta F/delta t)t1L to (delta L/delta t)t2F defines functional proclivity and measures the differential propensity to force development relative to shortening. Thus myocardial stiffness or compliance determines functional proclivity by acting as an impedance-matching transformer that steps up or steps down force development of shortening as warranted by the loading conditions.

Mechanism of mechanical alternans in ischemia-reperfusion: role of deficient relaxation of the strong twitch.

We tested the hypothesis that impaired and incomplete relaxation of the strong twitch of mechanical alternans causes the peak force deficit (PFD) of the weak twitch and that, by decreasing the relaxation deficit (RD) of the strong twitch, dobutamine would diminish the PFD. We studied isometric twitches of the in situ blood-perfused canine papillary muscle (n = 8). To produce mechanical alternans, we paced the heart at 110-155 beats/min and decreased mean coronary perfusion pressure (MCPP) stepwise to produce ischemia and then increased it to produce reperfusion. We measured the RD and PFD and fit each curve of isometric force [F(t)] with the relation F(t) = F0 + C(t/A)Be1-(t/A)B, where F0 is force at twitch onset, to obtain the parameters A, B, and C. B is a dimensionless index of myocardial relaxation; it decreases with impaired (delayed) relaxation. At each MCPP, we averaged B for the strong and weak twitches. The PFD showed a positive correlation with the RD. At each MCPP, mean B was lower for the strong twitch than for the weak twitch, indicating impaired relaxation of the strong twitch. Dobutamine increased B from 1.83 +/- 0.14 to 2.12 +/- 0.16 (P = 0.00002) in the strong twitch and decreased B from 4.15 +/- 2.42 to 2.19 +/- 0.18 (P = 0.05) in the weak twitch. Dobutamine thus equalized the relaxation of the strong and weak twitches. Consequently it decreased the RD from 2.57 +/- 2.14 to 0.16 +/- 0.24 g (P = 0.01) and the PFD from 5.50 +/- 3.67 to 1.04 +/- 1.15 g (P = 0.01).(ABSTRACT TRUNCATED AT 250 WORDS)

Coronary artery bypass graft disease.

PURPOSE: To review saphenous vein graft disease and its prevention and management. DATA SOURCES: A MEDLINE search of articles published on saphenous vein and arterial bypass grafts. STUDY SELECTION: The reference sections of articles focused the selection of key studies. DATA EXTRACTION: Relevant data representing key findings were noted. DATA SYNTHESIS: The outcome of coronary artery bypass grafting with the saphenous vein graft is unsatisfactory because vein grafts are prone to occlusive disease. By 10 years after surgery, 50% have closed, mainly because of atherosclerosis. With vein graft disease and graft closure, symptoms return. The best way to prevent vein graft disease is to use the internal mammary artery graft. This has become the preferred graft because it is not affected by atherosclerosis. Consequently, it has a much higher patency rate: 90% after more than 10 years. This provides such clinical benefits as decreased occurrence of symptoms, better left ventricular performance, decreased need for reoperation, and prolongation of life. The limited supply of mammary arteries has stimulated interest in identifying alternative arterial grafts. CONCLUSIONS: To prevent vein graft disease, surgeons should bypass diseased coronary arteries with at least one arterial graft and take measures during the surgery to avoid endothelial injury to vein grafts. Treatment with antiplatelet agents decreases the vein graft occlusion rate. When graft atherosclerosis causes symptoms, reoperation will probably prolong life if an old graft to the left anterior descending coronary artery is diseased. Reoperation increases a patient's chance for survival if the surgeon uses at least one arterial graft.

Global analysis of myocardial isotonic shortening: comparison with isometric dynamics.

Although potentially analytically useful, a global empirical model of the myocardial isotonic curve, L(t), has not been described. We propose the following relation: L(t) = C(t/A)B-1e-(t/A)B, where A, B, and C are global parameters, L is length, and t is time. We evaluated this model in nine in situ canine papillary muscles studied with a servo-system to produce isotonic twitches at different isotonic forces (F). For each twitch, the parameters were determined by nonlinear curve fitting. The model fit the observed curves of L(t) closely, with the coefficient of determination being 0.995 +/- 0.002. C changed with F, but A and B varied little with F, averaging 0.262 +/- 0.021 s and 2.76 +/- 0.17, respectively. Our predictions that A reflects chronotropic, B reflects lusitropic, and C reflects heterotonic (different afterloads) and inotropic states were supported. Comparison done in five muscles showed that A was the same but B was higher for isotonic than for isometric twitches: 0.270 +/- 0.020 vs. 0.264 +/- 0.038 s (P = not significant) for A and 2.79 +/- 0.18 vs. 2.39 +/- 0.05 (P less than 0.008) for B. Dobutamine increased A but not B in isotonic twitches. Thus shortening is lusitropic but leaves no lusitropic reserve to be mobilized by dobutamine. The relation L(t) = C(t/A)B-1e-(t/A)B provides a framework that undergirds global analysis of myocardial shortening and enables comparison with isometric dynamics.

Analysis of myocardial isometric dynamics using parameters of a global model.

Despite previous efforts, a global empirical relation has not been described for the myocardial isometric curve, F(t). We propose here that a useful relation is F(t) = CtB-1e-AtB. A, B, and C are global parameters. We evaluated this model and the effect of change in muscle length (L) and dobutamine on the parameters in nine in situ canine papillary muscles. A servo-system clamped muscle length to produce isometric twitches. For each twitch, the parameters were determined by curve fitting. The model fit the observed curves of F(t) closely; the correlation coefficient was 0.997 +/- 0.001. Whereas C changed with L, A and especially B varied little with L averaging 28.6 +/- 5.2 and 2.42 +/- 0.08, respectively. Our predictions that A reflects chronotropic state, B lusitropic, and C heterometric and inotropic states, were verified with dobutamine. We also derived relations for various attributes of the F(t) curve in terms of A, B, and C only. An excellent correlation was noted between the calculated and the observed values of these attributes. The empirical relation F(t) = CtB-1e-AtB therefore provides a valid cohesive reference frame for analysis of myocardial dynamics.

Short-term memory in the in situ canine myocardium.

We studied the effect of intracycle (short-term) mechanical history on canine myocardial performance. Intracycle muscle force and/or length history was varied, and the resultant changes in end-systolic force-length relationship were analyzed. Antecedent isotonic shortening impaired, whereas isometric force development enhanced end-systolic myocardial performance. A history of shortening concurrent with force development produced an intermediate effect. We conclude that decreasing force or length impairs whereas increasing length or force enhances performance in the same cycle. Different combinations of antecedent force and length changes affect end-systolic performance by algebraic summation (superposition) of their disparate effects. Time measurements established that 1) total systolic time varied little with altered history, 2) isotonic shortening took longer than isometric contraction in reaching a point P in the force-length plane, and 3) less time was therefore available for contraction after P with antecedent isotonic shortening than with antecedent isometric force development. This history-dependent time differential accounts for the corresponding differential in performance.

Nonlinear dynamics in ventricular fibrillation.

Electrogram recordings of ventricular fibrillation appear complex and possibly chaotic. However, sequences of beat-to-beat intervals obtained from these recordings are generally short, making it difficult to explicitly demonstrate nonlinear dynamics. Motivated by the work of Sugihara on atmospheric dynamics and the Durbin-Watson test for nonlinearity, we introduce a new statistical test that recovers significant dynamical patterns from smoothed lag plots. This test is used to show highly significant nonlinear dynamics in a stable canine model of ventricular fibrillation.

Higher prevalence and greater severity of coronary disease in short versus tall men referred for coronary arteriography.

The incidence of myocardial infarction is higher in short individuals than in tall ones. To test whether the prevalence and severity of coronary disease is greater in short than in tall individuals, we compared a group of short men (height < [mean height - one SD]) to a group of tall men (height > [mean height + one SD]) drawn from a sample of 1046 consecutive men referred for coronary arteriography. Short men had a higher frequency of > or = 50% diameter stenosis; more diseased vessels (1.61 +/- 1.09 vs 1.15 +/- 1.11, p = 0.0004); a higher frequency of three-vessel disease (26.8% vs 16.1%, p = 0.04); and more total occlusions (40.1% vs 27.3%, p = 0.03). By multivariate analysis, height independently predicted > or = 50% lesions in the right coronary artery (p = 0.01) and left anterior descending artery (p = 0.06); three-vessel disease (p = 0.04); total occlusion (p = 0.04); and the number of diseased vessels (p = 0.005). This higher prevalence and greater severity of coronary disease may explain the higher incidence of and deaths caused by myocardial infarction previously reported in short men.

Bypass surgery for chronic stable angina: predictors of survival benefit and strategy for patient selection.

The variable mortality risk associated with chronic stable angina calls for careful selection of patients for coronary artery bypass grafting (CABG) if the aim of management is to prolong life. The randomized and observational studies done in the last 20 years have identified the variables relevant to patient selection and thus have provided a rational basis for such clinical decisions. These studies showed that the sicker the patient, as gauged by relevant measures of coronary disease and cardiovascular morbidity, the more likely it is that CABG will prolong life. A CABG-related improvement in survival is therefore more likely to occur the worse the left ventricular function; the greater the number of diseased vessels; the more proximal the location of coronary lesions (more muscle is threatened by such lesions); the greater the severity of the lesions as determined by angiography; the more severe the angina; the more easily provocable the ischemia or the more extreme the measures of ischemia; and, within limits, the older the patient. Greater survival gain after CABG also occurs in patients with peripheral vascular disease, in patients with baseline electrocardiographic ST-segment and T-wave changes, and probably in women. Thus, patients are likely to live longer after CABG if they have left main disease; three-vessel disease with left ventricular dysfunction (ejection fraction less than 50%), class III or IV angina, provocable ischemia, or disease in the proximal left anterior descending coronary artery; two-vessel disease with proximal left anterior descending artery involvement; and two-vessel disease with class III or IV angina as well as either severe left ventricular dysfunction alone or moderate left ventricular dysfunction together with at least one proximal lesion. When the decision of whether to do CABG is less clear-cut, the presence of peripheral vascular disease, female sex, baseline electrocardiographic ST-segment and T-wave changes, or older age (over 60 but under 80 years) should weigh in favor of doing CABG. In general, patients with single-vessel disease do not seem to derive survival benefit from CABG.

Cardiovascular changes during laparoscopic cholecystectomy.

Although the technique of laparoscopic cholecystectomy has increasing appeal, physiologic data to support the safety of this procedure are lacking. We studied the cardiovascular changes in 16 patients undergoing laparoscopic cholecystectomy, using impedance cardiography as a noninvasive means of continuous monitoring of cardiac output. Serial measurements of mean arterial pressure (MAP), heart rate (HR), intraperitoneal pressure and expired carbon dioxide tension (PECO2) were also recorded. Results revealed a decrease of 30 percent (p < 0.001) in cardiac index and 5 percent (p = 0.089) in HR, along with increases of 15 percent (p < 0.001) in MAP and of 79 percent (p < 0.001) in the calculated total peripheral resistance index. This elevation in afterload could lead to both an increase in myocardial oxygen consumption and to the potential risk of myocardial ischemia and possibly infarction or congestive heart failure, or both, in patients who are susceptible. The data suggest that patients with a history of cardiac disease should have preoperative cardiac evaluation and be closely monitored during laparoscopic cholecystectomy, as in any other extensive operation.