Arterial transfer functions: background, applications and reservations.

Use of arterial transfer functions in modern medicine stems from the pioneering work of McDonald, Taylor and Womersley in London’s St Bartholomew’s Hospital in the 1950s. Womersley [1], an applied mathematician, showed that the nonlinearities in the equations of motion for fluid in elastic tubes were sufficiently small to be neglected to a first approximation. McDonald and Taylor [2], with the benefit of this background, expressed pressure and flow waves in the frequency domain, and related corresponding frequency components (harmonics) of pressure and flow waves to describe transfer functions – of pressure and flow at the same site (vascular impedance) – and to describe pressure relationships at different sites (pressure propagation). This concept expanded resistance of a vascular bed (as the ratio of mean pressure/mean flow) and of a mean pressure gradient along a segment or network of arteries, so that other arterial properties including elasticity, momentum and wave reflection could be embraced together with vascular resistance [3–6].

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