Cellular influx and efflux in the heart

Abstract

Techniques for estimating cellular uptake rates of substrates are now developed to the point where they can be used in a research setting. They are based on the use of the multiple indicator dilution technique, in which intravascular and extravascular reference tracer solutes are used simultaneously with the tracer substrate. The analysis involves fitting the dilution curves with mathematical models accounting for flow (and its regional variation), capillary permeation, dilution in the interstitial space, penetration of the sarcolemma of myocardial cells, and dilution and consumption inside the cells. The same principles and models are applicable to data in the form of externally detected residue function curves of the organ’s content of tracer as are suited to coronary sinus outflow concentration-time curves. The future developments will be in refining the external detection techniques, in making the studies less invasive and more suited to clinical studies. Multiple gamma photon imaging may be more useful than positron imaging for such studies because of the need to use simultaneous sets of tracers, including appropriate intravascular and extracellular references.

Figure 1

Model for arrangement of the vasculature in the heart. The capillary-tissue units are grouped into sets having particular flows: the flow in the ith region relative to the mean flow is f_i; the fraction of the organ mass having flow f_i is w_i; thus the fraction of the total flow going to the ith region is w_if_i. The impulse responses of the arterial and venous systems are h_A(t) and h_V(t), which are assumed to be the same for all capillary-tissue regions. Each capillary-tissue region is of the form shown in figure 1 of ref ; each has an impulse response dependent on the local flow f_i, so each differs from the others. The overall system response is the convolution of the arterial transport function, the venous transport function, and the weighted sum of the transport functions of the capillary tissue units.

Figure 2

Probability density functions of the concentrations of microspheres in pieces of the left ventricle of an awake baboon. There are six curves obtained at intervals of 20–40 min each using 15 microspheres with a different tracer label. Each curve represents the density function determined from spheres having one tracer label, and the abscissa represents the flow relative to the mean flow for the whole left ventricle. The area under each curve is unity. The microspheres were injected over several seconds into the apex of the left ventricular cavity from which they were distributed throughout the body in proportion to the regional flows. Different tracers were injected in different physiological states in this awake animal, and therefore the variance of the distribution probably represents the normal heterogeneity of flows in the heart. Similar variances have been the usual finding in isolated perfused dog and rabbit hearts in our laboratory. Data from R. B. King, J. B. Bassingthwaighte, J. R. S. Hales, and L. B. Rowell, manuscript submitted.

Figure 3

Effect of cellular uptake on the shapes of outflow dilution curves. The theoretical curves derived from the capillary-ISF cell model are denoted h_D(t), the D meaning diffusible or permeating tracer. The parameter values listed in the figure are: the flow F; the capillary wall permeability-surface area product PS_cap; the ratio of the interstitial volume of distribution V_ISF to the intracapillary volume V_C, given by γ; and the cell membrane conductance or permeability-surface area product PS_cell, here labeled PS_M, at varied values. The cell volume was set at infinity so that there was no reflux of indicator from the cell to the ISF to the outflow; the tails of the curves therefore show maximal differences at the various values of PS_cell.

Figure 4

Indicator dilution curves for D- and L-glucose from an isolated Tyrode-perfused rabbit heart. The parameters for the model fits are given in the figure. CV is the coefficient of variation; the values indicate that these fits are only moderately good. The curve of D-glucose being lower than that of L-glucose in the middle portion of the downslope gives a measure of the uptake by the cells; the return flux of D-glucose from the cells causes the D-glucose curve to become higher than the L-glucose curve during the later phase of the curves. This also indicates that the hexokinase reaction is not so fast that glucose does not leave the cell. From unpublished data obtained in collaboration with J. Kuikka and M. Levin.