One surface fits all: validating the venous return model across species and scales in circulatory equilibrium

In the generalized framework of circulatory equilibrium, the cardiac output (CO), right atrial pressure (RAP), and left atrial pressure (LAP) at equilibrium are predicted from the intersection between the CO curve and venous return (VR) surface. The VR surface is represented by the following equation: VR = V/W - G_S × RAP - G_P × LAP, where V is the stressed blood volume and W, G_S, and G_P are parameters. For future clinical application of this framework, we examined whether the VR surface is valid, whether the parameters are allometrically scalable based on Kleiber's law, and whether the VR surface with allometrically scaled parameters accurately predicts hemodynamic variables across different animal species and a diverse range of body weights (BWs). Anesthetized dogs (n = 18) and pigs (n = 8) with BW ranging from 9 to 50 kg were used. In 20 animals, we characterized the VR surface under total heart bypass and examined allometric scalability of the parameters. In 19 animals, we assessed whether the allometrically scaled VR surface allows accurate predictions of CO, LAP, and RAP. VR correlated significantly with RAP and LAP as per the equation, with a median coefficient of determination (r²) of 0.95. G_S and G_P were allometrically scalable with BW^0.75, but W was not. However, if population-representative W was combined with allometrically scaled G_S and G_P, predicted CO, RAP, and LAP correlated strongly with those measured (r² = 0.99, 0.98, and 0.94, respectively). In conclusion, the VR surface is valid across species and body sizes, and the allometrically scaled VR surface allows accurate hemodynamic prediction, supporting the clinical application potential of this framework.NEW & NOTEWORTHY This study demonstrates for the first time that the venous return (VR) surface concept is valid across animal species and over a diverse range of body weights (BWs). Slopes of the VR surface are allometrically scalable with BW^0.75 based on Kleiber's law. An allometrically scaled VR surface allows accurate prediction of hemodynamics in the circulatory equilibrium framework. These results strongly support potential clinical efficacy and utility of the framework.