On the pressure and flow-rate distributions in tree-like and arterial-venous networks.
A solution algorithm yielding the pressure and flow-rate distributions for steady flow in an arbitrary, tree-like network is provided. Given the tree topology, the conductance of each segment and the pressure distribution at the boundary nodes, the solution is obtained from a simple recursion based on perfect Gauss elimination. An iterative solution method using this algorithm is suggested to solve for the pressure and flow-rate distributions in an arbitrary diverging-converging (arterial-venous) network consisting of two tree-like networks which are connected to each other at the capillary nodes. A number of special solutions for tree-like networks are obtained for which the general algorithm is either simplified or can be replaced by closed form solutions of the pressure and flow-rate distributions. These special solutions can also be obtained for each tree of diverging-converging networks having particular topologies and conductance distributions. Sample numerical results are provided.
Mayer
S
S
Department of Theoretical and Applied Mechanics, University of Illinois at Urbana-Champaign 61801, USA. smayer@m.tam.uiuc.edu
D000465:Algorithms; D000818:Animals; D001158:Arteries / Q000033:anatomy & histology / Q000502:physiology*; D001783:Blood Flow Velocity; D001794:Blood Pressure; D017709:Fractals; D008433:Mathematics; D008955:Models, Cardiovascular; D014680:Veins / Q000033:anatomy & histology / Q000502:physiology*