Analysis of network flow distribution: computational aid to minimize experimental expenditure

Several problems in microvascular research, e.g., total blood flow and red cell flux distribution, can only be solved by evaluating the flow distribution to all branches of microvessel networks. We present a method to obtain values of volumetric blood flow and red cell flux in individual networks by taking measurements in an adequately chosen number of the vessels (50-33%) in the network. Actual measurements are not mandatory in all vessels because in a major part of them computational quantification of flows and fluxes is possible. The proposed method consists of a procedure to document in matrix form the connections of a network found in a preparation. By appropriate mathematical manipulations of the matrix, a preselection of measuring sites within the network can be achieved. From the flow values in these sites the remaining vessel flows can be calculated by utilizing the law of mass conservation in all branching points and confluxes. The worst case error of the procedure can be calculated from the errors of the single measurements. The method can also be applied, whenever, for experimental reasons (e.g., poor microscopic focus, flow too rapid or too slow), certain branches do not lend themselves for measurement. A BASIC program can be made available upon request, which carries out all calculations necessary for an appropriate selection in such a short time (about 1 min) so that it can easily be performed before the start of data acquisition.