Systemic venous circulation. Waves propagating on a windkessel: relation of arterial and venous windkessels to systemic vascular resistance

Abstract

. Systemic venous circulation. Waves propagating on a windkessel: relation of arterial and venous windkessels to systemic vascular resistance. Am J Physiol Heart Circ Physiol 290: H154 -H162, 2006. First published August 19, 2005 doi:10.1152/ajpheart.00494.2005.-Compared with arterial hemodynamics, there has been relatively little study of venous hemodynamics. We propose that the venous system behaves just like the arterial system: waves propagate on a time-varying reservoir, the windkessel, which functions as the reverse of the arterial windkessel. During later diastole, pressure increases exponentially to approach an asymptotic value as inflow continues in the absence of outflow. Our study in eight open-chest dogs showed that windkessel-related arterial resistance was ϳ62% of total systemic vascular resistance, whereas windkesselrelated venous resistance was only ϳ7%. Total venous compliance was found to be 21 times larger than arterial compliance (n ϭ 3). Inferior vena caval compliance (0.32 Ϯ 0.015 ml ⅐ mmHg Ϫ1 ⅐ kg Ϫ1 ; mean Ϯ SE) was ϳ14 times the aortic compliance (0.023 Ϯ 0.002 ml ⅐ mmHg Ϫ1 ⅐ kg Ϫ1 ; n ϭ 8). Despite greater venous compliance, the variation in venous windkessel volume (i.e., compliance ϫ windkessel pulse pressure; 7.8 Ϯ 1.1 ml) was only ϳ32% of the variation in aortic windkessel volume (24.3 Ϯ 2.9 ml) because of the larger arterial pressure variation. In addition, and contrary to previous understanding, waves generated by the right heart propagated upstream as far as the femoral vein, but excellent proportionality between the excess pressure and venous outflow suggests that no reflected waves returned to the right atrium. Thus the venous windkessel model not only successfully accounts for variations in the venous pressure and flow waveforms but also, in combination with the arterial windkessel, provides a coherent view of the systemic circulation. systemic circulation SIGNIFICANT EFFORTS have been devoted to the understanding of arterial hemodynamics, but much less attention has been paid to the venous systems (3, 24). The application of frequencydomain impedance analysis to venous pressure and flow seemed less successful than to arterial pressure and flow because the apparent reflection site was difficult to explain physiologically (27,32). Brecher studied venous hemodynamics, and Sjostrand suggested that the cavae constituted a "surge chamber," which Rushmer termed a "preventricular sump." Noordergraaf (24) concluded that "no analytical treatment of the pressure-flow relationship in relation to. . .cardiac activity has been proposed. As a consequence, Brecher's suggestion that the central veins constitute the functional counterpart of the arterial reservoir, transforming steady flow into pulsatile flow, has not received the scientific scrutiny that such an intuitively appealing idea deserves." Thus we have endeavored to develop a new model in an attempt to follow Brecher's suggestion and to understand venous hemodynamics better.In 1992, Tyberg (33) proposed a steady-state hydraulic mod...

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“…R circ is also equal to SVR Ϫ ¥R i , where ¥R i is the summation of the above identified resistances. These incremental resistances correspond very well (21) to measurements of pressure drop across the vascular elements in the hamster cheek pouch (5). From that comparison, we suggested that R A-Res involves arterial vessels as small as 60 m and that R V-Res also involves venous vessels as small as 60 m.…”

“…In this study, we have proposed an operational method to break up SVR into its serial resistive components, on the basis of our understanding that the systemic circulation functions as waves propagating on time-varying arterial and venous reservoirs (21,22). The measured arterial and venous pressures are respectively separated into a wave-related pressure and a reservoir pressure, both of which vary with respect to time during the cardiac cycle; each resistance is proportional to the pressure gradient across it.…”

“…The values of resistive components were by-products of the calculations of the P A-Res and PV-Res. The methods of calculation were detailed elsewhere (21,22). In brief, the arterial asymptotic pressure, P A-ϱ, is initially determined by fitting PAo during the later part of diastole by using a three-parameter exponential-decay equation.…”

“…The water level, which corresponds to P A-Res , can increase or decrease depending on the balance of inflow and outflow, and, at any level, any perturbation such as throwing a stone into the lock will produce a propagating wave. Recently, we also showed that the venous system behaves simply as an inverse of the arterial system (21): in diastole, the arterial reservoir discharges, and the venous reservoir charges. To view the systemic circulation as a whole, we observed that, during diastole, P Ao and P A-Res decrease exponentially and asymptotically approach a nonzero level (P A-ϱ ), and inferior vena caval pressure (P IVC ) and venous reservoir pressure (P V-Res ) rise exponentially to approach P V-ϱ .…”

“…By considering the arterial and venous wave-reservoir models together, systemic vascular resistance (SVR) can be viewed as a network of resistances arranged in series (21). In the absence of reflections, P A-Wave is precisely proportional to the measured aortic flow (Q Ao ), and the ratio, P A-Wave to Q Ao , is numerically equal to characteristic impedance.…”