Flow distribution in closed networks: minimal sets of measuring sites.

In microvascular research it is of great importance to know how the flow of blood is distributed to all the vessels in a capillary network. However, it is generally impossible to obtain simultaneous measurements of the flow values in all branches of a network. A method of selecting minimal subsets of branches is presented, by which the flow measurements in these branches can be used to compute the flow values in all other branches. It is sufficient to measure between half and one-third of the branch flows. The experimenter can also specify a subset of the branches as inaccessible to measurement; nevertheless the method allows him to decide whether determination of all flows is possible from the remaining branches, and in which branches the measuring devices should then be optimally placed.