Dispersion of Heterogeneous Medium in Pulsatile Blood Flow and Absolute Pulsatile Flow Velocity Quantification

Heterogeneous medium enhanced angiogr- ams are key diagnostic tools in clinical practice; the associated hemodynamic information is crucial for diagnosing cardiovascular diseases. However, the dynamics of such medium in physiological blood flow are poorly understood. Herein, we report a previously unnoticed dispersion pattern, which is a universal phenomenon, of a medium in pulsatile blood flow. We present a physical theory for studying the dispersion of a steadily injected heterogeneous medium into a thin tubular blood vessel in which the blood flow is pulsatile. In a thin tubular blood vessel, we demonstrate that variations of concentration associated with the heterogeneous medium obey a one-dimensional advection diffusion equation, and the diffusion has limited effect whenever a short vascular segment is considered. A distinct feature of the distribution of the medium in the axial distance-time plane is a "dilation-retraction" pattern. The time evolution signals at different axial positions exhibit distinct concentration waveforms. A numerical scheme is proposed for exploiting this information to estimate the pulsatile velocity. Artificial data are adopted to validate the scheme. Real X-ray angiography is also analyzed to support our theory and method. The theory is applicable whenever imaging protocols involve a heterogeneous medium in pulsatile flow.