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The development of non-invasive medical technologies such as B-mode ultrasound has allowed direct real-time imaging of blood vessels. This enables individual patient arterial responses to be recorded and analyzed following pharmacological perturbations. By analysing intra-arterial pressure recordings together with recording of the pulse wave speed, the spatial pressure gradient can be approximated. This gradient, together with the internal vessel radius from B-mode imaging, permits the calculation of the vessel volume flow by Womersley analysis (J.R. Womersley, 1955). The Womersley solution is the only analytical solution of a time-varying flow, which is assumed to be laminar, fully developed and Newtonian in an infinitely long rigid tube. We approximated the internal arterial radius by averaging the peak-systolic arterial radius and the end-diastolic radius following their estimation using a spatial cross-correlation function of the arterial B-mode images. Womersley extended the analysis to elastic tubes, and we present illustrative calculations of both the rigid and elastic tube models; however, only the rigid tube model has been experimentally validated. |
