An inverse approach to determining spatially varying arterial compliance using ultrasound imaging

The mechanical properties of arteries are implicated in a wide variety of cardiovascular diseases, many of which are expected to involve a strong spatial variation in properties that can be depicted by diagnostic imaging. A pulse wave inverse problem (PWIP) is presented, which can produce spatially resolved estimates of vessel compliance from ultrasound measurements of the vessel wall displacements. The 1D equations governing pulse wave propagation in a flexible tube are parameterized by the spatially varying properties, discrete cosine transform components of the inlet pressure boundary conditions, viscous loss constant and a resistance outlet boundary condition. Gradient descent optimization is used to fit displacements from the model to the measured data by updating the model parameters. Inversion of simulated data showed that the PWIP can accurately recover the correct compliance distribution and inlet pressure under realistic conditions, even under high simulated measurement noise conditions. Silicone phantoms with known compliance contrast were imaged with a clinical ultrasound system. The PWIP produced spatially and quantitatively accurate maps of the phantom compliance compared to independent static property estimates, and the known locations of stiff inclusions (which were as small as 7 mm). The PWIP is necessary for these phantom experiments as the spatiotemporal resolution, measurement noise and compliance contrast does not allow accurate tracking of the pulse wave velocity using traditional approaches (e.g. 50% upstroke markers). Results from simulations indicate reflections generated from material interfaces may negatively affect wave velocity estimates, whereas these reflections are accounted for in the PWIP and do not cause problems.