Graph theoretic analysis of compartmental models. With applications to thyroid hormone metabolic systems

A single input/single output experiment design may not provide sufficient information to quantify a model of a complex biological system, and multiple input or multiple output experiment designs are often not feasible. An alternate approach is to perform feasible studies with different combinations of input/output ports one at a time, but their simultaneous mathematical analysis can become dimensionally unwieldy. In these cases, a graphical approach can be helpful. Cut set analysis of compartmental models is presented and contrasted with more conventional analysis approaches. It is shown that the complexity of computations is reduced using cut set analysis, especially as the complexity of the model is increased. A case study is presented on quantifying parameters of the enterohepatic subsystem in thyroid hormone distribution and metabolism, based on four different sets of rat experiments performed in the Biocybernetics Laboratory at UCLA.