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The increase of arterial volume during the systole (‘pulse volume’) is essential for buffering the pulsatile ventricular output. Objectives: Deriving some mechanical properties of arteries by assuming pulse volume homeostasis. Methods: A model that includes a generalized nonlinear relationship between arterial pressure P and volume V (see figure below). Results: If the pulse volume ΔV is constant, then for a given diastolic volume VD and pressure D the systolic volume VD+ΔV and pressure S are uniquely determined. For this reason, an infinitesimal increase of the diastolic pressure by dD would result in an increase of the systolic pressure by dS with the same volume change dV for both pressures. Since the systolic and diastolic stiffness is defined by G(S)=dS/dV and G(D)=dD/dV, respectively, we find that dS/dD=G(S)/G(D) (Eq.1). As D and ΔV determine S uniquely, dS/dD is a function of D and ΔV only. However, if dS/dD is independent of D and ΔV is constant, then K=dS/dD is a constant (Eq.2) equal to the relative increase of arterial stiffness during the systole. The only solution of Eq.2 is the well-documented linear relationship between the systolic and diastolic pressures with slope K and constant A, i.e., S=A+KD (Eq.3). The solution of Eq.3, rewritten as P(V+ΔV)=A+KP(V), is the observed exponential pressure-volume relationship in arteries that is also expressed by the demonstrated linear dependence of arterial stiffness on pressure. s: Arterial stiffening at elevated pressures may reflect an arterial design principle that aims at preserving the arterial buffering function via pulse volume homeostasis. |
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