Ultrasonography is becoming the favored hemodynamic monitoring utensil of emergentologists, anesthesiologists and intensivists. While the roles of ultrasound grow and evolve, many clinical applications of ultrasound stem from qualitative, image-based protocols, especially for diagnosing and managing circulatory failure. Often, these algorithms imply or suggest treatment. For example, intravenous fluids are opted for or against based upon ultrasonographic signs of preload and estimation of the left ventricular ejection fraction. Though appealing, image-based algorithms skirt some foundational tenets of cardiac physiology; namely, (1) the relationship between cardiac filling and stroke volume varies considerably in the critically ill, (2) the correlation between cardiac filling and total vascular volume is poor and (3) the ejection fraction is not purely an appraisal of cardiac function but rather a measure of coupling between the ventricle and the arterial load. Therefore, management decisions could be enhanced by quantitative approaches, enabled by Doppler ultrasonography. Both fluid ‘responsiveness’ and ‘tolerance’ are evaluated by Doppler ultrasound, but the physiological relationship between these constructs is nebulous. Accordingly, it is argued that the link between them is founded upon the Frank–Starling–Sarnoff relationship and that this framework helps direct future ultrasound protocols, explains seemingly discordant findings and steers new routes of enquiry.