Pulse wave velocity  Pulse wave velocity (PWV) is the velocity at which the blood pressure pulse propagates through the circulatory system, usually an artery or a combined length of arteries. PWV is used clinically as a measure of arterial stiffness and can be readily measured non-invasively in humans, with measurement of carotid to femoral PWV (cfPWV) being the recommended method. cfPWV is highly reproducible, and predicts future cardiovascular events and all-cause mortality independent of conventional cardiovascular risk factors. It has been recognized by the European Society of Hypertension as an indicator of target organ damage and a useful additional test in the investigation of hypertension. The theory of the velocity of the transmission of the pulse through the circulation dates back to 1808 with the work of Thomas Young. The relationship between pulse wave velocity (PWV) and arterial wall stiffness can be derived from Newton's second law of motion (formula_1) applied to a small fluid element, where the force on the element equals the product of density (the mass per unit volume; formula_2) and the acceleration. The approach for calculating PWV is similar to the calculation of the speed of sound, formula_3, in a compressible fluid (e.g. air):  formula_4,  where "formula_5" is the bulk modulus and formula_6 is the density of the fluid. For an incompressible fluid (blood) in a compressible (elastic) tube (e.g. an artery):  formula_7,  where formula_8 is volume per unit length and formula_9is pressure. This is the equation derived by Otto Frank, and John Crighton Bramwell and Archibald Hill. Alternative forms of this equation are:  formula_10, or formula_11,  where formula_12 is the radius of the tube and formula_13 is distensibility. This equation:  characterises PWV in terms of the incremental elastic modulus formula_15of the vessel wall, the wall thickness, formula_16and the radius. It was derived independently by Adriaan Isebree Moens and Diederik Korteweg and is equivalent to the Frank / Bramwell Hill equation:  These equations assume that:   Since the wall thickness, radius and incremental elastic modulus vary from blood vessel to blood vessel, PWV will also vary between vessels. Most measurements of PWV represent an average velocity over several vessels (e.g. from the carotid to the femoral artery).