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Accurate noninvasive average flow and differential pressure estimation of implantable rotary blood pumps (IRBPs) is an important practical element for their physiological control. While most attempts at developing flow and differential pressure estimate models have involved purely empirical techniques, dimensional analysis utilizes theoretical principles of fluid mechanics that provides valuable insights into parameter relationships. Based on data obtained from a steady flow mock loop under a wide range of pump operating points and fluid viscosities, flow and differential pressure estimate models were thus obtained using dimensional analysis. The algorithm was then validated using data from two other VentrAssist IRBPs. Linear correlations between estimated and measured pump flow over a flow range of 0.5 to 8.0 L/min resulted in a slope of 0.98 (R 2 = 0.9848). The average flow error was 0.20 plusmn 0.14 L/min (mean plusmn standard deviation) and the average percentage error was 5.79%. Similarly, linear correlations between estimated and measured pump differential pressure resulted in a slope of 1.027 (R 2 = 0.997) over a pressure range of 60 to 180 mmHg. The average differential pressure error was 1.84 plusmn 1.54 mmHg and the average percentage error was 1.51%.