Defining resistance in an autoregulating vascular bed

C. M. Quick, G. M. Drzewiecki, and J. K-J. Li
1stCardiovascular Medicine, Science, and Mechanics Conference, Washington, DC,1997
Int. J. Cardiovasc. Sci. Med. 1: 40, 1997

Abstract

The properties of an autoregulating vascular bed are commonly investigated with two experiments.  In one, average inflow, Qin,is set, and the resulting steady-state pressure, Ps(Qin), is measured.  In another, flow is stepped up or down, and the resulting instantaneous pressure, Pi(Qin), is recorded before the system has time to autoregulate (but after flow due to compliance has ceased). From these experiments, investigators have derived peripheral resistance, Rp(Qin)= Ps/Qin, and instantaneous resistance, Ri(Qin)= dPi/dQin.  In the present work, a possible misinterpretation of this data is explored.  It is assumed that Qtot=Qin+ Qc, where Qtot is the total flow through the autoregulating vessels, Qin is the observed inflow, and Qc is an unobserved collateral flow. 
 

As shown in the graph above, it is then assumed that 1) Ps(Qtot ) is sigmoidal and 2) Pi(Qtot) is linear with Ri(Qtot )=Rp(Qtot). In agreement with reported data, a nonzero Qc is predicted to cause three phenomena commonly observed in vascular beds: 1) residual pressure at Qin=0, 2) Rp(Qin) > Ri(Qin), and3) decrease in Rp(Qin) with Qin.  These phenomena have previously been ascribed to vascular waterfall.  The proposed model does not eliminate this possibility.  However, the presence of collateral flow can cause the same phenomena conventionally associated with collapsible vessels.