On the relationship between power mode and pressure amplitude decorrelation

Estimation of mean transit time, along with tissue blood volume, are import ant factors in determining soft tissue perfusion. Recently, power mode deco rrelation techniques have been successfully used to estimate mean transit t ime of red blood cells or contrast material through a region-of-interest (R OI) both in laminar flow phantoms and in vivo. The previously described the ory for power mode decorrelation derives from a phenomenological stochastic differential equation (Langevin equation) based on conservation of matter, relating the detected signal power to the measured rate of decorrelation. Given the experimental support for power mode decorrelation as a method to estimate mean transit time, it becomes important to determine the relations hip between the phenomenological parameters that appear in the correspondin g stochastic equation and system parameters, such as the transducer point r esponse function. With this equation as a starting point, and using the fac t that the pressure amplitude is a Gaussianly distributed random process, t he following stochastic differential equation for the pressure amplitude p( t) is derived, a necessary first step in establishing the relationship betw een the measured decorrelation rate and system parameters (i.e., point resp onse function): dp(t)/dt = - (v/2 + 2ik-v)p(t) +f(t), where v/2 represents the rate of decorrelation, 2k.v is the Doppler shift f or an insonating wave vector k and particle velocity v.f(t) is a stationary , white noise Gaussian random process.