Estimating blood flow velocity using time-resolved 3D angiography and a derived physical law of contrast media

Objective. Four-dimensional (4D) digital subtraction angiography (DSA) offers a method for evaluating hemodynamics. It is, however, unclear how the delivered contrast medium interacts with the physiological blood flow, and how hemodynamic information may be inferred from the mixture of the contrast medium and blood. In this study, we present a theoretical explanation of contrast dynamics, and an accompanying algorithm for estimating blood flow velocity. Approach. We retrospectively recruited 23 patients who underwent both 4D DSA and magnetic resonance (MR) phase-contrast imaging. The 4D DSA-reconstructed contrast dynamics were first studied for the internal carotid arteries. Using physical laws governing fluid motion within a curved tube, we showed that the reconstructed contrast dynamics obeyed a simple advection equation. We then proposed an algorithm for estimating the contrast dynamics using angiographic data, and subsequently estimated the axial blood flow velocity using an advection equation. Main results. The estimated velocities were compared using three techniques: the Fourier technique, Lin's method, and MR phase contrast. Testing with noise-corrupted artificial data showed that the proposed algorithm was noise resistant. The velocities of 23 patients computed by 4D DSA using the proposed algorithm showed a moderate correlation with the MR phase contrast (r = 0.61), and good correlations with the other two techniques (r = 0.75 and r = 0.72). Significance. The proposed algorithm and has been applied to blood vessel segments with poor signal-to-noise ratios and axial lengths of less than 3 cm, and has a physical basis for computing axial flow velocities using an advection equation. The results of the proposed algorithm are consistent with existing methods.