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Cardiac output (CO) and stroke volume (SV) are the key hemodynamic parameters to be monitored and assessed in ambulatory and critically ill patients. The purpose of this study was to introduce and validate a new algorithm to continuously estimate, within a proportionality constant, CO and SV by means of mathematical analysis of peripheral arterial blood pressure (ABP) waveforms. The algorithm combines three variants of the Windkessel model. Input parameters to the algorithm are the end-diastolic pressure, mean arterial pressures, inter-beat interval, and the time interval from end-diastolic to peak systolic pressure. The SV estimates from the three variants of the Windkessel model were weighted and integrated to provide beat-to-beat SV estimation. In order to validate the new algorithm, the estimated CO and SV were compared to those obtained through surgically implanted Transonic™ aortic flow probes placed around the aortic roots of six Yorkshire swine. Overall, estimation errors in CO and SV derived from radial ABP were 10.1% and 14.5% respectively, and 12.7% and 16.5% from femoral ABP. The new algorithm demonstrated statistically significant improvement in SV estimation compared with previous methods.