Validating the Venous Return Surface in Circulatory Equilibrium: Experimental Insights Across Species and Diverse Body Sizes

Study Objective:In the generalized framework of circulatory equilibrium (GCE), venous return (VR, ml/min) for a given stressed volume (V, ml) is characterized by a flat surface as a function of right (P RA , mmHg) and left (P LA , mmHg) atrial pressures as follows: VR =V/W – G S x P RA – G P x P LA , where W, G S , and G P denote linear parameters. In experimental dogs with body weight (BW, kg) of 20 to 30 kg range, the VR surface equation was validated with standard values for W, Gs, and Gp defined as 0.129 (min), 19.61 x BW (ml/min/mmHg), and 3.49 x BW (ml/min/mmHg), respectively. For potential future clinical application of GCE, we aim to experimentally investigate whether the VR surface is valid across species and diverse BW range, and whether an allometric scaling of G S , G P , and W based on Kleiber’s law can improve the hemodynamic predictability of GCE. Hypothesis: Kleiber’s allometric law suggests that an animal's VR scales to the 3⁄4 power of the animal's BW. Based on this, we hypothesized that G S and G P may be proportionate to BW 3/4 , and W may be proportionate to BW 1/4 . METHODOLOGY: Twelve dogs (BW of 9 to 28 kg) and 8 pigs (BW of 20 to 50 kg) were anesthetized, and their left and right hearts were replaced by dual mechanical pumps. By controlling the pump speeds and changing V strategically, VR, P LA and P RA were changed variably over a wide range to obtain 12 sets of VR, P LA and P RA . Using the 12 datasets, we computed G S , G P , and W using regression analysis in each animal. We analyzed relations between BW and the 3 parameters (G S , G P , and W) using regression analysis for the 20 animals to evaluate applicability of the Kleiber’s allometric law. We further examined whether equilibrium cardiac output (CO), P RA , and P LA are accurately predicted from the intersection between the known CO curve and the VR surface characterized with the original standard or the allometrically scaled G S , G P , and W in 19 animals (11 dogs and 8 pigs). Results: In the 20 animals, VR was significantly and tightly correlated with P RA and P LA with a coefficient of determination (r 2 ) of 0.93 ± 0.02. G S (r 2 =0.72, p value for independent variable, p iv <0.001; p value for intercept, p i =0.36) and G P (r 2 =0.21, p iv =0.042, p i =0.075) were proportionate to BW 3/4 . However, W was not associated with BW 1/4 (r 2 =0.12, p iv =0.13, p i =0.72). Based on the linear regression analysis above, we defined allometrically scaled G S and G P as 44.2 x BW 3/4 (ml/min/mmHg) and 5.6 x BW 3/4 (ml/min/mmHg), respectively. W was defined as the average of all animals with 0.161 (min). In the 19 animals, both the original standard or the newly scaled G S , G P , and W allowed accurate prediction of CO, P RA , and P LA . Absolute prediction error of P RA by the newly scaled parameters was significantly smaller than that by the original standard parameters (0.5 ± 0.4 vs 0.4 ± 0.4 mmHg, p=0.003). There was no significant difference in absolute prediction error in CO or P LA between the two sets of the 3 parameters. Irrespective of which sets of the 3 parameters used, measured and predicted CO were strongly correlated (r 2 > 0.98) with percentage prediction error lower than 12% over a wide range of CO of 1000 to 5000 ml/min. Measured and predicted P RA were tightly correlated (r 2 > 0.97) over a wide range of P RA of 1 to 18 mmHg. Measured and predicted P LA were tightly correlated (r 2 > 0.92) over a wide range of P LA of 2 to 25 mmHg. Conclusions: Across species and diverse BW ranges, VR surface was indeed flat, and the Kleiber’s allometric law was applicable to G S and G P . W did not show a significant association with BW 1/4 , potentially due to reduction of variance in BW by the 1/4 power calculation. Both sets of G S , G P , and W are highly efficacious in hemodynamic prediction, suggesting the potential clinical utility of GCE. NTT Research, Inc. This abstract was presented at the American Physiology Summit 2025 and is only available in HTML format. There is no downloadable file or PDF version. The Physiology editorial board was not involved in the peer review process.