Normalization of hemodynamic parameters: application to vascular resistance and impedance

Comparison of hemodynamic parameters among different species is complicated by the wide variety of body sizes and shapes. Although some parameters such as blood pressure and flow velocity seem to have similar absolute values among species, most other parameters such as cardiac output, pulse wave velocity, and heart rate vary greatly. Comparisons would be facilitated if one uses indices that are independent of body size and/or shape. An ideal index will bring values for individuals or species of different sizes into the same range and yet exhibit large relative changes to responses to small increments of an intervention in an individual. In this paper we demonstrate how dimensional analysis together with Buckingham's pi theorem and the assumption of biological similarity can be used to derive dimensionless hemodynamic normalization indices. Using data from the literature and from our own laboratory, we illustrate the approach by examining resistance and impedance. We compare our results with previously proposed methods of accounting for different body sizes, namely, dividing impedance by resistance or vice versa, multiplying by body weight, and using flow velocity rather than volume flow in the calculations. Both of our proposed indices bring the values for arterial and pulmonary resistance and impedance for rats, rabbits, dogs, and humans into the same range, although the variability among species using our indices is twice that of those previously proposed. On the other hand, the relative changes of our two indices induced by vasoactive agents or exercise in a dog are from two to five times greater than either the absolute values themselves or the previously used indices.