Does coronary resistance change only during systole?

This letter is intended to extend the discussion of Bellamy's (1978) intriguing analysis of diastolic coronary artery pressure-flow relations in dogs during long diastoles. In reactive hyperemia (RH), he found practically linear diastolic pressure-flow relations. These linear pressure-flow relations led him to the conclusion that coronary resistance, R, remains constant during diastole, and consequently, extrapolation of this relation to zero flow was justified. The zero-flow pressure Pf-o found in this way varies during RH such that Pro is approximately 25 mm Hg immediately after release of a 15-second occlusion and progressively increases to a steady value of approximately 45 mm Hg. In mathematical terms, Bellamy presented his model of interpretation of the experimental results by Q = (P a — Pr_o)/ R, where Q (= coronary flow) and P. (= aortic pressure) are varying during diastole, and Pf-o and R are constant during diastole but can vary from beat to beat. However, does the linear pressure-flow relation imply that coronary resistance is really constant? To examine this problem, I calculated pressure-flow relations, using a model based on assumptions contradictory to those of Bellamy. What would the pressure-flow relation look like if: (1) Pr_o remains constant during RH; (2) coronary resistance changes continuously during diastole of RH? The difference between the two models is elucidated with the aid of Figure 1. Points A and B are defined by the pressure and flow at beginning and end of the first RH diastole of Bellamy's Figure 6. Bel-lamy's model states that R is constant and, hence, a line might be drawn through A and B resulting in a Pf_o = 25 mm Hg. The present model assumes that Pro remains constant (40 mm Hg). Hence, the dotted lines through A and B represent imaginary pressure-flow relations holding at the instant of beginning and end of diastole, respectively. Would a time-varying coronary resistance lead to an apparently linear pressure-flow relation between A andB? For the present calculations, it was assumed that R during a diastole varied linearly with time between the average coronary diastolic resistance of that beat and that of the following one. The aortic pressure was assumed to decline exponentially from a value of 100 mm Hg at the beginning of diastole and with a time constant of 4.5 seconds. It was assumed that all diastoles are of 2.5 seconds duration. Coronary flow was then calculated as a function of time from …