J. H. G. M. van Beek

Lightning and the heart: fractal behavior in cardiac function

Physical systems, from galactic clusters to diffusing molecules, often show fractal behavior. Likewise, living systems might often be well described by fractal algorithms. Such fractal descriptions in space and time imply that there is order in chaos, or put the other way around, chaotic dynamical systems in biology are more constrained and orderly than seen at first glance. The vascular network, the syncytium of cells, the processes of diffusion and transmembrane transport might be fractal features of the heart. These fractal features provide a basis which enables one to understand certain aspects of more global behavior such as atrial or ventricular fibrillation and perfusion heterogeneity. The heart might be regarded as a prototypical organ from these points of view. A particular example of the use of fractal geometry is in explaining myocardial flow heterogeneity via delivery of blood through an asymmetrical fractal branching network.

The dynamic regulation of myocardial oxidative phosphorylation: Analysis of the response time of oxygen consumption

Although usually steady-state fluxes and metabolite levels are assessed for the study of metabolic regulation, much can be learned from studying the transient response during quick changes of an input to the system. To this end we study the transient response of O2 consumption in the heart during steps in heart rate. The time course is characterized by the mean response time of O2 consumption which is the first statistical moment of the impulse response function of the system (for mono-exponential responses equal to the time constant). The time course of O2 uptake during quick changes is measured with O2 electrodes in the arterial perfusate and venous effluent of the heart, but the venous signal is delayed with respect to O2 consumption in the mitochondria due to O2 diffusion and vascular transport. We correct for this transport delay by using the mass balance of O2, with all terms (e.g. O2 consumption and vascular O2 transport) taken as function of time. Integration of this mass balance over the duration of the response yields a relation between the mean transit time for O2 and changes in cardiac O2 content. Experimental data on the response times of venous [O2] during step changes in arterial [O2] or in perfusion flow are used to calculate the transport time between mitochondria and the venous O2 electrode. By subtracting the transport time from the response time measured in the venous outflow the mean response time of mitochondrial O2 consumption (tmito) to the step in heart rate is obtained.

Low- and high-blood flow regions in the normal pig heart are equally vulnerable to ischaemia during partial coronary stenosis

Abstract Myocardial perfusion is heterogeneous, even in the normal heart. It is unknown whether the resting normal blood flow level predicts the severity of mismatch between local blood flow and metabolism during acute ischaemia. In the present study local blood flow (measured with radioactively labelled microspheres) and metabolic indicators of ischaemia [tissue contents of lactate and inosine (INO), a breakdown product of adenosine triphosphate (ATP)] were determined in 84–102 simultaneously frozen samples (approximately 0.9 g) of normal (n = 7) and partially ischaemic (n = 4) porcine left ventricles. Ischaemia was induced for 20 min by partially occluding the left anterior descending artery to reduce perfusion pressure from 107 ± 17 mm Hg to 39 ± 10 mm Hg (mean ± SD). Flow reduction in the ischaemic region was strongly variable, both within the subepicardium (range 6–66%, average 34%) and the subendocardium (range 33–84%, average 57%), indicating redistribution of blood flow inside transmural layers in addition to the well-known preferential decrease in subendocardial perfusion. The relative flow reduction during stenosis was not dependent on normal local perfusion level (Spearman rank correlation coefficient –0.002, P = 0.99). Samples with low or high myocardial blood flows before stenosis showed similar increases in lactate content and INO/ATP content ratio, as long as the percentage blood flow reduction was the same. It is concluded that regions with low and high resting flows in the normally perfused heart are equally susceptible to metabolism-perfusion mismatch resulting from coronary stenosis.

Dynamic adaptation of cardiac oxidative phosphorylation is not mediated by simple feedback control.

The classic idea about regulation of cardiac oxidative phosphorylation (OxPhos) was that breakdown products of ATP (ADP and Pi) diffuse freely to the mitochondria to stimulate OxPhos. On the basis of this metabolic feedback control system, the response time of OxPhos ( t mito) is predicted to be inversely proportional to the mitochondrial aerobic capacity (MAC). We determined t mito during steps in heart rate in isolated perfused rabbit hearts ( n = 16) before and after reducing MAC with nonsaturating doses of oligomycin. The reduction of MAC was quantified in mitochondria isolated from each perfused heart, dividing oligomycin-sensitive, ADP-stimulated state 3 respiration by oligomycin-insensitive uncoupled respiration. The t mito to heart rate steps from 60 to 70 and 80 beats/min was 5.6 ± 0.6 and 7.2 ± 0.8 s (means ± SE) and increased an estimated 34 and 40% for a 50% decrease in MAC ( P < 0.05), respectively, which is much less than the 100% predicted by the feedback hypothesis. For steps to 100 or 120 beats/min, t mito was 8.3 ± 0.5 and 11.2 ± 0.6 s and was not reduced with decreases in MAC ( P > 0.05). We conclude that immediate feedback control by quickly diffusing ADP and Pi cannot explain the dynamic regulation of cardiac OxPhos. Because calcium entry into the mitochondria also cannot explain the first fast phase of OxPhos activation, we propose that delay of the energy-related signal in the cytoplasm dominates the response time of OxPhos.

Simple model analysis of 13C NMR spectra to measure oxygen consumption using frozen tissue samples.

The measurement of oxygen consumption in small tissue regions has been problematic. The perfusion of myocardium is very heterogeneous,1 and it was desirable to measure whether aerobic metabolic rate paralleled the blood flow heterogeneity. However, no method was available to measure local oxygen consumption in tissue regions of a similar size as used for measurement of local blood flow with labeled microspheres. Our goal was to develop a method to measure local O2 consumption (VO2) in many tissue samples simultaneously. VO2 is proportional to the rate in the tricarboxylic acid (TCA) cycle. Methods to determine the flux in the TCA cycle by measuring the gradual enrichment of glutamate with 13C isotopes with NMR spectroscopy exist.2–6 NMR spectra are measured every few minutes until a steady state has been reached, and the time course of enrichment is analyzed with a model for the isotope distribution in the TCA cycle.2 Local blood flow is measured in many small regions simultaneously, and VO2 too must be assessed in many regions simultaneously, which is not yet feasible with NMR coils in vivo. Our strategy is to freeze tissue sam ples quickly at a prescribed time briefly after starting infusion of 13C-enriched substrate for the TCA cycle (e.g. acetate, pyruvate, lactate) and to analyze the 13C NMR multiplets of glutamate in extracts of the samples. We will show below that measurement of O2 consumption is feasible in this way, and test the method in isolated perfused rabbit hearts.

The microvascular unit size for fractal flow heterogeneity relevant for oxygen transport.

In this study we used a computer model for oxygen transport in heterogeneously perfused tissue to define the microvascular unit size of relevance to oxygen transport. Flow within this unit is presumably heterogeneous, but this internal heterogeneity is by definition of negligible importance for the oxygen tension distribution. In saline-perfused heart the linear dimension of the thus defined unit is 500 microns, in blood-perfused heart it is 100 microns.

Is Local Metabolism the Basis of the Fractal Vascular Structure in the Heart

The distribution of blood flow in the heart muscle is very heterogeneous and shows a self-similar fractal pattern, extending to small spatial scales. It is very likely that local oxygen consumption is more or less proportional to local blood flow and that local aerobic metabolism also is very heterogeneous. It is not yet clear whether local metabolism is heterogeneous in origin and the distribution of flow has secondarily adapted to metabolism, or, the other way around, whether flow is primarily heterogeneous because of the irregular structure of the coronary tree and flow has adapted to metabolism. Little is known yet about the developmental and adaptive mechanisms which bring about mutual adjustment between vascular growth and local metabolic demand, and genes and growth factors involved in shaping the structure of the coronary tree have only begun to be identified. Fractal and nonlinear dynamic mathematical models generate complex heterogeneous structures from simple nonlinear deterministic rules which are recursively applied. Such nonlinear models may thus help to explain the generation of large vascular trees regulated by synergy of a limited number of genes and signaling molecules. This may explain the relative regularity of space filling of the vascular tree and the asymmetry of branching and flow distribution in the tree.

Diffusion barriers for ADP in the cardiac cell

The regulation of mitochondrial respiration in the intact heart may differ from that of isolated mitochondria if intracellular diffusion is restricted. Here we consider which factors may hinder diffusion in vivo and, based on computational analysis, design a reverse engineering approach to estimate the role of diffusional resistance in mitochondrial regulation from an experiment on the intact heart. Computational analysis of respiration measurements on skinned heart fibers shows that the outer mitochondrial membrane does not hinder diffusion enough to cause ADP gradients of tens of micromolars. A diffusion model further shows that the mesoscale structure of the myofibrillar space also does not hinder diffusion appreciably. However, ADP gradients are suggested by the measured activation time of oxidative phosphorylation and may be caused by diffusion restriction of other intracellular structures or the in vivo microstructure of networks of physically interacting proteins. Based on computational modeling we propose an experiment on the intact heart that allows to estimate the effective diffusion restriction between ATP producing and consuming sites in the cardiac cell.

Function of Isolated Rabbit Hearts Perfused with Erythrocyte Suspension is not Stable but Improvement may be Feasible with Hemoglobin Solution

In the present study isolated rabbit hearts were perfused with erythrocyte suspensions (hematocrit 21.5 +/- 0.5%) or hemoglobin solutions according to Langendorff with a constant flow at 37 degrees C. In preliminary experiments three types of stroma-free hemoglobin were used: unmodified, but carefully purified, stroma-free hemoglobin (SFHb), HbNFPLP which is a chemically modified Hb molecule and polyHbNFPLP which is a polymer of HbNFPLP. In hearts perfused with erythrocyte suspensions left ventricular developed pressure and oxygen consumption decreased and perfusion pressure increased steadily from the beginning of the perfusion. Dark spots appeared on the surfaces of these hearts, which were the result of extravasation of erythrocytes. As a consequence capillaries probably became obstructed, leading to reduced cardiac function. Hearts perfused with stroma-free hemoglobin solutions showed an initial increase in left ventricular developed pressure after switching from Tyrode perfusion to perfusion with hemoglobin solutions. Left ventricular developed pressure and perfusion pressure were stable for about 2 hours in hearts perfused with SFHb and were reasonable for 2 hours when the heart was perfused with HbNFPLP or more than 4 hours with polyHbNFPLP. More extensive experiments with stroma-free hemoglobin solutions when these become available in sufficient quantities have, according to the results from preliminary experiments, the potential of showing good oxygen supply resulting in reasonable cardiac function.

Response Time of Mitochondrial Oxygen Consumption Following Stepwise Changes in Cardiac Energy Demand

We determined the speed with which mitochondrial oxygen consumption and therefore the mitochondrial ATP-synthesis adapted to changes in metabolic demand in the rabbit heart. This was done by measuring the oxygen uptake of the whole heart during a stepwise change in heart rate and correcting for the time taken by diffusion and by convective transport in the blood vessels. Data for the correction for transport time were obtained from the response of venous oxygen concentration to a stepwise change of arterial oxygen concentration. The time constant of the response of mitochondrial oxygen consumption to a step change in heart rate was found to be 4-8 s.