An effective model of blood flow in capillary beds

Microvasc Res. 2015 Jul;100:40-7. doi: 10.1016/j.mvr.2015.04.009. Epub 2015 Apr 30.


In this article we derive applicable expressions for the macroscopic compliance and resistance of microvascular networks. This work yields a lumped-parameter model to describe the hemodynamics of capillary beds. Our derivation takes into account the multiscale nature of capillary networks, the influence of blood volume and pressure on the effective resistance and compliance, as well as, the nonlinear interdependence between these two properties. As a result, we obtain a simple and useful model to study hypotensive and hypertensive phenomena. We include two implementations of our theory: (i) pulmonary hypertension where the flow resistance is predicted as a function of pulmonary vascular tone. We derive from first-principles the inverse proportional relation between resistance and compliance of the pulmonary tree, which explains why the RC factor remains nearly constant across a population with increasing severity of pulmonary hypertension. (ii) The critical closing pressure in pulmonary hypotension where the flow rate dramatically decreases due to the partial collapse of the capillary bed. In both cases, the results from our proposed model compare accurately with experimental data.

Keywords: Compliance; Computational hemodynamics; Critical closing pressure; Hypertension; Lumped-parameter models; Microcirculation; Nonlinear Windkessel; Perfusion; Resistance.

Publication types

  • Comparative Study

MeSH terms

  • Animals
  • Blood Flow Velocity
  • Blood Pressure
  • Capillaries / pathology
  • Capillaries / physiopathology*
  • Compliance
  • Computer Simulation
  • Hemodynamics*
  • Humans
  • Hypertension, Pulmonary / pathology
  • Hypertension, Pulmonary / physiopathology*
  • Hypotension / pathology
  • Hypotension / physiopathology*
  • Lung / blood supply*
  • Microcirculation*
  • Models, Cardiovascular*
  • Nonlinear Dynamics
  • Regional Blood Flow
  • Stochastic Processes
  • Vascular Resistance