In the model and graph above, the compartment with increased pressure (P_ext) is represented by a Starling resistor, where perfusion (Q_starling) is defined by the Segmental Perfusion Pressure (SPP):
SPP=P_d - P_outFlowStarling.
Here P_d is the common inflow pressure distal to the stenosis and P_outFlowStarling is compartment pressure P_ext, or venous pressure P_v, whichever is higher. The Fractional Flow Reserve (FFR)- defined as the ratio of the inflow pressure distal to the stenosis (P_d) to the arterial pressure (P_a) in the absence of collateral outflow: FFR=P_d/P_a. FFR reflects Thevenin equivalent of inflow resistance. The graph depicts all the pressures and flows as the functions of venous pressure P_v. In the graph, FFR=0.5 and G_collateral/G_Starling=1/1.
Control parameters can be adjusted by dragging the corresponding labels to change the vascular network configuration (inflow resistance- FFR, ratio of collateral to Starling conductance G_collateral/G_starling) and loading pressures (P_a, P_ext, P_v). The model dynamically calculates and displays: P_d, SPP, total inflow Q_inflow, and its distribution into Q_starling and collateral outflow Q_col.
Venous Steal refers to blood flow diversion away from a compartment with increased tissue pressure (1). Due to the collapsibility of the veins, effective outflow pressure is determined by the compartment pressure P_ext, rather than the venous pressure P_v. Likewise, effective inflow pressure is determined by the pressure distal to the stenosis P_d, rather than systemic arterial pressure P_a. Flow Q_starling in such a compartment is determined by the segmental perfusion pressure (SPP=P_d-P_ext): Q_starling=SPP×G_starling, where G_starling is presumed to be fixed with maximal vasodilatation (2).
Lowering venous pressure below P_ext increases collateral outflow and pressure drop P_a-P_d across the inflow stenosis, which lowers P_d and flow through the Starling resistor (Q_starling). We called this phenomenon venous steal (1-3). For venous steal to occur, both arterial stenosis and the collateral pathway with a lower outflow pressure must coexist. Raising venous pressure to the level of compartment pressure P_ext eliminates outflow pressure gradient and stops venous steal due to this gradient.
Pranevicius M, Pranevicius O. Cerebral venous steal: blood flow diversion with increased tissue pressure. Neurosurgery. 2002 Nov;51(5):1267-73; discussion 1273-4. doi: 10.1097/00006123-200211000-00023. PMID: 12383372.
Pranevicius M, Pranevicius H, Pranevicius O. Cerebral venous steal equation for intracranial segmental perfusion pressure predicts and quantifies reversible intracranial to extracranial flow diversion. Sci Rep. 2021 Apr 8;11(1):7711. doi: 10.1038/s41598-021-85931-x. PMID: 33833266; PMCID: PMC8032738. https://rdcu.be/eafZa
Pranevičius, M.; Makackas, D.; Macas, A.; Petrikonis, K.; Šakalytė, G.; Pranevičius, O.; Benetis, R. Concept of Venous Steal: The Impact of Vascular Stenosis and Outflow Pressure Gradient on Blood Flow Diversion. Preprints 2025, 2025022149. https://doi.org/10.20944/preprints202502.2149.v1