Two-port analysis of microcirculation: an extension of windkessel

H. F. Frasch, J. Y. Kresh and A. Noordergraaf Center for Anesthesia Research, University of Pennsylvania, Philadelphia 19104, USA. We examined the suitability of the three-element windkessel as a reduced model of pulsatile pressure-flow relations at arteriolar and venular ends of a microcirculatory bed. Frequency domain (two-port) analysis of a distributed model of an idealized (single input, single output) microvascular network in skeletal muscle, consisting of 391 discrete vessel segments from a 20-microns-diameter arteriole to a 28-microns-diameter venule, demonstrated that the three-element windkessel is a good representation of arterial input impedance when pressure pulsations are absent at the venous end. The same model with different parameter values accounts well for venous pressure-flow relations if no pulsations occur at the arterial end. We showed that a five-element model (2 compliances, 3 resistors) provided a superior representation of pulsatile pressure-flow relations at both arterial and venous ends. Relating parameter values to known properties of the network revealed the physiological significance of the five elements. This model may prove a useful component in circulatory models incorporating both arteries and veins. While parameter values obtained herein were strictly valid for the particular microvascular network described, guidelines are provided based on physiological properties so that values may be estimated for different microvascular beds.