Multiple tracer dilution estimates of D- and 2-deoxy-D-glucose uptake by the heart

Abstract

Permeability-surface area products of the capillary wall, PSc, and the myocyte sarcolemma, PSpc, for D-glucose and 2-deoxy-D-glucose were estimated via the multiple indicator-dilution technique in isolated blood-perfused dog and Tyrode-perfused rabbit hearts. Aortic bolus injections contained 131I-albumin (intravascular reference), two of three glucoses: L-glucose (an extracellular reference solute), D-glucose, and 2-deoxy-D-glucose. Outflow dilution curves were sampled for 1-2.5 min without recirculation. The long duration sampling allowed accurate evaluation of PSpc by fitting the dilution curves with a multiregional axially distributed capillary-interstitial fluid-cell model accounting for the heterogeneity of regional flows (measured using microspheres and total heart sectioning). With average blood flow of 1.3 ml . g-1 . min-1, in the dog hearts the PSc for D-glucose was 0.72 +/- 0.17 ml . g-1 . min-1 (mean +/- SD; n = 11), and PSpc was 0.57 +/- 0.15 ml . g-1 . min-1. In the rabbit hearts with perfusate flow of 2.0 ml . g-1 . min-1 (n = 6), PSc was 1.2 +/- 0.1 and PSpc was 0.4 +/- 0.1 ml . g-1 . min-1. PSc for 2-deoxy-D-glucose was about 4% higher than for D-glucose and L-glucose in both preparations. Relative to L-glucose, there was no measurable transendothelial transport of either dextroglucose, indicating that transcapillary transport was by passive diffusion, presumably via the clefts between cells. The technique allows repeated measurements of D-glucose uptake at intervals of a few minutes; it may therefore be used to assess changes in transport rates occurring over intervals of several minutes.

Fig. 1

Impulse responses and sensitivity functions (S) for a capillary interstitial fluid (ISF)-cell model solution with parameter values suitable for D-glucose in the heart. Notice that sensitivity functions are all different, indicating independence of the parameters in shaping model solutions. Note too that ${\mathrm{V}}_{\mathrm{pc}}^{\prime }$ and G_pc have little influence at early times and more later, suggesting the importance of avoiding (or accounting for) reciruculation. Parameter values used to generate model solutions were 7-path model with relative dispersion of flows = 30%; F_s = 1.5 ml·g^–1·min^–1; PS_C and PS_pc = 0.75 and 0.5 ml·g^–1·min^–1; G_pc = 0.5 ml·g^–1·min^–1; γ_pc (which is ${\mathrm{V}}_{\mathrm{pc}}^{\prime }∕{\mathrm{V}}_{\mathrm{C}}^{\prime }$) = 10, and γ_ISF (which is ${\mathrm{V}}_{\mathrm{I}}^{\prime }∕{\mathrm{V}}_{\mathrm{C}}^{\prime }$) = 5. (Input function is a gamma variate function with a mean transit time of 3 s, a relative dispersion of 0.2, and a skewness of 1.0.) Scalar multiplier of 40 S_PSpc and S_Gpc and of 100 for $S_{{\mathrm{V}}_{\mathrm{IST}}^{\prime }}$ and $S_{{\mathrm{V}}_{\mathrm{pc}}^{\prime }}$ indicate that sensitivity to PS_C is higher than to any other parameter. Units of S, s^-1/(units of parameter). See text for abbreviations.

Fig. 2

Coronary sinus outflow dilution curves for D- and L-glucose in a rabbit heart after injection of tracers into the aortic cannula at t = 0. Main peaks of impulse responses for D- and L-glucose are nearly identical. Extraction curves, E(t) in insert, provide a more critical test of their similarity and show the same result. Tail of D-glucose curve is lower than that of L-glucose, in accord with uptake by myocardial cells. (Expt no. 13078-l. Data given in numerical form in Table 3.)

Fig. 3

Multicapillary solutions for a capillary interstitial fluid (ISF)-cell-reaction model of D-glucose outflow dilution curves from same Krebs-Ringer perfused rabbit heart as in Fig. 2 (no. 13078-l). A: solutions for a reduced model for capillary permeation and cellular uptake without return flux from cell but with return flux from ISF to capillary. Heterogeneity of flows was approximated using 7 parallel pathways with a Gaussian distribution of flows with relative dispersion 30%. Five solutions are drawn for different values of the rate of cellular influx (PS_pc), all other parameters being constant. F_s = 1.68 ml·g^–1·min^–1; PS_c = 1.13 ml·g^–1·min^–1; γ_pc = 7.9; γ_pc = infinity, to prevent reflux from the cell. B: effects of cellular permeation, now with return flux from cell to ISF. Intracellular consumption, G_pc = 0.03 ml·g^–1·min^–1; other parameters same as for A. Best fit is obtained with PS_pc = 0.42 ml·g^–1·min^–1 and γ_pc = 9. C: effect of G_pc on shapes of tails of outflow dilution curves. Increasing rates of consumption reduce reflux from cell into outflow, lowering tails of curves. Best fit values were PS_c = 1.13 ml·g^–1·min^–1, γ_ISF = 7.9, PS_pc = 0.46 ml·g^–1·min^–1, γ_pc = 9, and G_pc = 0.03 ml·g^–1·min^–1. When PS_pc, is higher, sensitivity to G_pc is higher. (Numerical values of data points and of model solutions are listed in Table 3.)

Fig. 4

Outflow dilution curves for D-glucose and deoxyglucose and albumin (dog expt 4048-6) fitted with the model. Deoxyglucose curve is shifted downward by half a logarithmic decade (ordinate values divided by 10^½) to display it separately from D-glucose curve. Parameter estimates logarithmic for D- and deoxyglucose were PS_c, 0.97 and 1.0; PS_pc = 0.7 and 0.5; G_pc, = 0.01 and 0.05 ml·g^–1·min^–1; γ_ISF = 6.5 and γ_pc = 13.3 ml/g for both. Coefficients of variation were 0.19 and 0.09.

Fig. 5

Constrained fitting of a capillary interestitial-fluid (ISF)-cell-reaction model to 9 coronary outflow dilution curves for albumin, D-, L-, and 2-deoxy-D-glucose. (Expts 30284, 2, and 3.) Symbols are data points; lines give model solutions fitted to data under strong constraints. Regional flows were from microsphere deposition densities. The only free parameters were 1 value each for PS_c and ${\mathrm{V}}_{\mathrm{ISF}}^{\prime }$ and 2 for PS_pc and for D- and 2-deoxy-D-glucose (see text). Since PSC affects most strongly the first 20–30 s of the curves, result is excellent fitting of parts of curve sensitive to PS_c and poorer fitting tails at 30–80 s where ${\mathrm{V}}_{\mathrm{ISF}}^{\prime }$, PS_pc, and ${\mathrm{V}}_{\mathrm{pc}}^{\prime }$ have influences.