In Doppler sonography, the physiological meaning of Gosling's pulsatility index (PI) as a measure of downstream resistance is still under dispute. We deliver the theoretical derivation of its physiological significance. We present a mathematical model based on the linked theories of critical closing pressure (CCP) and cerebrovascular impedance, verified in preterm neonates. Mathematical transformation results in a series of equations interrelating several physiological parameters. Instead of indicating cerebrovascular resistance, PI is linked to the ratio of cerebrovascular impedances at the heart rate and at zero frequency. Next to arterial blood pressure, CCP is the principal determinant of PI. PI is identical to the ratio of the alternate and the direct component of the effective driving force. Thus, PI has no distinctive physiological meaning by itself. At present, our model is confined to physiological conditions where the lowest velocity is the end diastolic, and always more than zero.