title: Estimation of blood flow rates in large microvascular networks.
abstract: OBJECTIVE
  Recent methods for imaging microvascular structures provide geometrical data on networks containing thousands of segments. Prediction of functional properties, such as solute transport, requires information on blood flow rates also, but experimental measurement of many individual flows is difficult. Here, a method is presented for estimating flow rates in a microvascular network based on incomplete information on the flows in the boundary segments that feed and drain the network.
  
  
  METHODS
  With incomplete boundary data, the equations governing blood flow form an underdetermined linear system. An algorithm was developed that uses independent information about the distribution of wall shear stresses and pressures in microvessels to resolve this indeterminacy, by minimizing the deviation of pressures and wall shear stresses from target values.
  
  
  RESULTS
  The algorithm was tested using previously obtained experimental flow data from four microvascular networks in the rat mesentery. With two or three prescribed boundary conditions, predicted flows showed relatively small errors in most segments and fewer than 10% incorrect flow directions on average.
  
  
  CONCLUSIONS
  The proposed method can be used to estimate flow rates in microvascular networks, based on incomplete boundary data, and provides a basis for deducing functional properties of microvessel networks.
authors.affiliation: Program in Applied Mathematics, University of Arizona, Tucson, Arizona 85724-5051, USA.
authors.forename: Brendan C
authors.initials: BC
authors.lastname: Fry
authors.forename: Jack
authors.initials: J
authors.lastname: Lee
authors.forename: Nicolas P
authors.initials: NP
authors.lastname: Smith
authors.forename: Timothy W
authors.initials: TW
authors.lastname: Secomb
mesh_terms: D000465:Algorithms; D000818:Animals; D001783:Blood Flow Velocity / Q000502:physiology; D003198:Computer Simulation; D055806:Microvessels / Q000503:physiopathology*; D008955:Models, Cardiovascular; D051381:Rats; D013152:Splanchnic Circulation / Q000502:physiology*