a1 Department of Biomedical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
a2 Philips Research Laboratories, High Tech Campus 4, 5656 AE Eindhoven, The Netherlands
a3 Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
The behaviour of a miniature calorimetric sensor, which is under consideration for catheter-based coronary-artery-flow assessment, is investigated in both steady and pulsatile tube flows. The sensor is composed of a heating element operated at constant power and two thermopiles that measure flow-induced temperature differences over the sensor surface. An analytical sensor model is developed, which includes axial heat conduction in the fluid and a simple representation of the solid wall, assuming a quasi-steady sensor response to the pulsatile flow. To reduce the mathematical problem, described by a two-dimensional advection–diffusion equation, a spectral method is applied. A Fourier transform is then used to solve the resulting set of ordinary differential equations and an analytical expression for the fluid temperature is found. To validate the analytical model, experiments with the sensor mounted in a tube have been performed in steady and pulsatile water flows with various amplitudes and Strouhal numbers. Experimental results are generally in good agreement with theory and show a quasi-steady sensor response in the coronary-flow regime. The model can therefore be used to optimize the sensor design for coronary-flow assessment.
(Received November 06 2009)
(Revised August 09 2010)
(Accepted August 09 2010)
(Online publication November 10 2010)