Obstruction to blood flow is accompanied by a pressure gradient across the obstructed site. In certain clinical settings, magnitude of pressure gradient has been used to judge severity of obstruction, and gradient reduction to judge success of an interventional procedure. In percutaneous transluminal coronary angioplasty (PTCA) the relationships between transstenotic pressure gradient, diameter stenosis, and lesion length are imprecisely known. We therefore examined 4263 sets of measurements in patients who underwent PTCA on single, discrete coronary arterial lesions. Multivariate regression analysis demonstrated that pressure gradient was artifactually elevated by about 12 mm Hg at low values of diameter stenosis but increased by the 4th power of stenosis as expected from fluid dynamics models. Pressure gradient was dampened and relatively constant at values of diameter stenosis of 60% or higher, probably because of total or near-total occlusion of the artery. Lesion length was not found to influence pressure gradient. Reductions in diameter stenosis (delta D) and pressure gradient (delta G) were related nonlinearly, with delta D proportional to the square root of delta G, suggesting that a reduction in gradient is directly proportional to an increase in cross-sectional area of the stenosis. The predictive value of final post-PTCA pressure gradients was found: a final gradient of 15 mm Hg or less predicted a final post-PTCA diameter stenosis of 30% or less, with 75% sensitivity and 29% specificity (p less than .01). The results of this study suggest that (1) pressure gradient as currently measured during PTCA is related to diameter stenosis but not to lesion length (2) reductions in pressure gradient and diameter stenosis are nonlinearly related.(ABSTRACT TRUNCATED AT 250 WORDS)