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The flow through a curved tube whose radius of curvature varies with time was studied in order to better understand flow patterns in coronary arteries. A computational flow model was constructed using commercially available software. The artery model featured a uniform circular cross section, and the curvature was assumed to be constant along the tube, and in one plane. The computational model was verified with the use of a dynamically similar in vitro apparatus. A steady uniform velocity was prescribed at the entrance at a Reynolds number of 300. Two sets of results were obtained: one in which the curvature was held constant at the mean, maximum and minimum radii of curvature (quasistatic), and another in which the curvature was varied sinusoidally in time at a frequency of 1 Hz (dynamic). The results of the dynamic analysis showed that the wall shear rates varied as much as 52% of the static mean wall shear rate within a region of 10 tube diameters from the inlet. The results of the dynamic analysis were within 6% of the quasistatic predictions. Realistic modeling of the deforming geometry is important in determining which locations in the coronary arteries are subjected to low and oscillating wall shear stresses, flow patterns that have been associated with atherogenesis.