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 inte ractions, it is necessary to account for the effects of the distributi on of capillary transit times, h(c)(t). In this paper, we present an e fficient approach for incorporating h(c)(t) in the mathematical modeli ng of MID data. In this method, the solution of the model partial diff erential equations obtained at different locations along the model cap illary having the longest transit time provides the outflow concentrat ions for ail capillaries. When weighted by h(c)(t), these capillary ou tflow concentrations provide the outflow concentration versus time cur ve for the capillary bed. The method is appropriate whether the availa ble data on capillary dispersion are in terms of capillary transit tim e or relative flow distributions, and whether the dispersion results f rom convection time differences among heterogeneous parallel pathways or axial diffusion along individual pathways. Finally, we show that th e knowledge of a relationship among the moments of h(c)(t), rather tha n 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. Th is relationship can be determined by including a flow-limited indicato r in the injected bolus, thus providing an efficient means for obtaini ng the experimental data sufficient to account for capillary flow and transit time heterogeneity in MID modeling. (C) 1998 Biomedical Engine ering Society. [S0090-6964(98)01806-2].