D-, L-, and 2-Deoxy-D-Glucose Uptakes in the Isolated Blood Perfused Dog Hearts

The multiple radiotracer dilution technique provides a vehicle for measuring unidirectional glucose uptake rates both in laboratory and in clinical situations. The mathematical basis for these techniques has previously been developed by BASSINGTHWAIGHTE (1974) and ROSE et al. (1977). The purpose of the study was to determine estimates of glucose uptake and transfer rate constants in canine myocardium.

In the experiments, canine hearts were removed and perfused with oxygenated saline solution to wash-out the blood, then perfused continuously through an aortic cannula with blood taken from the femoral artery of a support dog. The temperature of circulating solution was 37.5 °C. The hearts were hung on the weighing device and the arterial and perfusion pressures, sampling timing and heart rate were recorded on a photokymographic recorder. A bolus injection into the arterial inflow containing a reference substance (¹³¹I-RIHSA) and two of test substances were made. The test substances used were: 2-deoxy-D-(1-³H)-glucose, D-(6-³H)-glucose, D-(¹⁴C)-glucose and L-(1-¹⁴C)-glucose. The activities used were 40 μCi of tritium-labelled tracer, 20 μCi of carbon-labelled tracer and 10 μCi of ¹³¹I-RIHSA. The radiotracers were diluted with physiological saline to give an injectate volume of 2 ml. Venous outflow samples were collected at intervals of 1 sec for the first 30 samples and 2 sec for the last 30 samples from the right ventricular outflow; this flow and the leakage from a left ventricular vent (aortic valve leak and Thebesian drainage) were determined at the time of each injection. Samples (vol = 0.1 ml), standards, and background samples were counted using a 3-channel liquid scintillation counter, and the tracer concentrations estimated using carefully determined quench correction and background curves. 3–6 sets of dilution curves per heart were made. Injection of 9 μm sphere (⁸⁵Sr or ⁴⁶Sc) were made after the first and fourth runs to determine the heterogeneity of flow.

Three sets of dilution curves were obtained in every run, one reference and two test substances. The curves observed were normalized by the plasma flow-dose injected ratio, F_p1/D. The reference curve was terminated at 0.1% of the peak concentration and the glucose curves at 0.1% of the peak (note no recirculation). The curves had a small statistical counting noise, since the peak counting rate was usually 100,000 counts/10 min for each label.

Figure 1 shows a block diagram of the model used and the relationships between capillary, interstitial fluid space and cell. Typical sets of ¹³¹I-RIHSA and D-glucose curves are seen in figure 2.

Fig. 1.

Schematic diagram of the relationships between capillary, interstitial fluid space, and cell and permeability surface-area products in the glucose model. k₅ is the rate of irreversible sequestration per unit accessible intra-cellular space.

Fig. 2.

D-(1-³H)-glucose and ¹³¹I-RIHSA data from the experiment 4 and run 2 on the semilogarithmic/time scale.

The outflow concentration of the glucose curve (diffusible tracer) was estimated as a convolution of the reference curve shifted 1 capillary transit time, τ_cap, to left and the transfer function of the capillary system, h_diff(t):

$${\mathrm{C}}_{\mathrm{diff}}\left(\mathrm{t}\right)={\mathrm{C}}_{\mathrm{ref}}(\mathrm{t}-{\tau }_{\mathrm{cap}})\ast {\mathrm{h}}_{\mathrm{diff}}\left(\mathrm{t}\right),$$ (1)

where the reference curve was described by a sum of two gamma function integrands (KUIKKA et al., 1974) and the transfer function was given in the work of ROSE et al. (1977). Equation 1 was fitted to the observed diffusible tracer curve by adjusting parameters PS_cap, PS_cell, k₅, γ and θ. The capillary transit time was constant during the whole fitting period, and it was estimated from the mean transit time of the reference curve as follows:

$${\tau }_{\mathrm{cap}}=0.17\cdot {\stackrel{‒}{\mathrm{t}}}_{\mathrm{ref}}$$

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The apparent capillary permeability-surface product was 0.75 ± 0.29 ml/min/g (mean ± SD) and the cell permeability-surface product 0.163 ± 0.012 ml/min/g for D-glucose (n = 18). The cell consumption rate constant, k₅, was on the average 0.0072 ± 0.0032 sec⁻¹ and the mean calculated glucose consumption was 180 ± 85 mmol/min/g.

A comparison of the capillary permeability-surface product derived from the model, PS_cap/F_p1 and the permeability-surface product from the peak extraction, i.e. PS'_cap/F_p1 = −ln (1−E_peak), was made. The comparison yielded a nonlinear relationship showing that the peak extraction estimate derived directly from the outflow curves underestimates the true capillary permeability-surface product. This relationship is seen in figure 3.

Fig. 3.

Underestimation of glucose PS_cap from instantaneous extraction [i.e. PS'_cap = −F_p1 · ln (1−E_peak)] compared to capillary-ISF-cell model in dog hearts.

Conclusions

A method described gives estimates of the capillary permeability-surface area product, unidirectional myocardial cell uptake rate and cellular metabolism for tracer-labeled glucoses. These results provide a framework for the utilization of ¹⁸F-fluorodeoxyglucose over the estimation of cellular glucose using positron emission tomography to show the regional distribution.