Venous steal blood flow simulation

This 0-D Thevenin's equivalent model simulates blood flow distribution between a compartment with external pressure P_ext (modeled as a Starling resistor) and collateral outflow pathways (1-3).

The vascular network configuration can be modified by adjusting the inflow resistance, fractional flow reserve (FFR=P_d/P_a), and the ratio of collateral to Starling conductance (G_collateral/G_starling). Loading conditions are controlled by varying arterial pressure (P_a), compartment pressure (P_ext), and venous pressure (P_v).

The model calculates the post-stenotic pressure (P_d), segmental perfusion pressure (SPP = P_d-P_ext), total inflow (Q_inflow), and its distribution between the compartment and collateral outflow (Q_Starling/Q_coll). Recruitable venous steal is quantified as the percentage reduction in Q_starling when collateral outflow pressure (P_v) drops below the compartment pressure (P_ext).

Due to the collapsibility of veins, the effective outflow pressure in the compartment is determined by P_ext rather than P_v. Similarly, because of arterial stenosis, the effective inflow pressure is governed by P_d rather than systemic arterial pressure P_a. Blood flow through the compartment is modeled using a Starling resistor equivalent:
Q_Starling=SPP × G_starling, where G_starling represents the conductance of the Starling resistor (assumed constant under maximal vasodilation).

A decrease in venous pressure below P_ext increases collateral outflow and raises the pressure drop across the arterial stenosis (P_a-P_d), which in turn lowers P_d, SPP, and flow Q_starling through the Starling resistor. This phenomenon we referred to as venous steal (1-3).

Attached is an interactive model demonstrating the venous steal phenomenon, along with a graph illustrating pressure and flow distribution between the Starling resistor and collateral outflow. For venous steal to occur, both arterial stenosis and blood flow diversion to a collateral pathway with a lower outflow pressure must be present. Increasing venous pressure to match the compartment pressure (P_ext) eliminates venous steal.

1. 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.
2. 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
3. Pranevičius, M.; Makackas, D.; Macas, A.; Petrikonis, K.; Šakalytė, G.; Pranevičius, O.; Benetis, R. The Concept of Venous Steal: The Impact of Vascular Stenosis and Outflow Pressure Gradient on Blood Flow Diversion. Medicina 2025, 61, 672. https://www.mdpi.com/3258046