Accounting for the heterogeneity of capillary transit times in modeling multiple indicator dilution data

To mathematically model multiple indicator dilution (MID) data for the purpose of estimating parameters descriptive of indicator-tissue interactions, it is necessary to account for the effects of the distribution of capillary transit times, h(c)(t). In this paper, we present an efficient approach for incorporating h(c)(t) in the mathematical modeling of MID data. In this method, the solution of the model partial differential equations obtained at different locations along the model capillary having the longest transit time provides the outflow concentrations for all capillaries. When weighted by h(c)(t), these capillary outflow concentrations provide the outflow concentration versus time curve for the capillary bed. The method is appropriate whether the available data on capillary dispersion are in terms of capillary transit time or relative flow distributions, and whether the dispersion results from convection time differences among heterogeneous parallel pathways or axial diffusion along individual pathways. Finally, we show that the knowledge of a relationship among the moments of h(c)(t), rather than h(c)(t) per se, is sufficient information to account for the effect of h(c)(t) in the mathematical modeling interpretation of MID data. This relationship can be determined by including a flow-limited indicator in the injected bolus, thus providing an efficient means for obtaining the experimental data sufficient to account for capillary flow and transit time heterogeneity in MID modeling.