Abstract
The two phase (vascular-extravascular) Sangren-Sheppard (SS) model is often used to estimate capillary permeability-surface area product (PS) from multiple indicator data. Our objective was to identify conditions where erroneous estimates of capillary PS or extravascular volume (VE) result from the application of this model to data obtained from non-homogeneous capillary units. We used a 4-phase capillary-tissue model (plasma, erythrocytes, interstitial fluid and extravascular cellular fluid) to simulate data collected from a heterogeneous capillary unit. A moment-matching technique was used to compute the parameters of the simpler SS model which would adequately describe the 4 phase tracer concentration-time (c(t)) curve. Deviations of computed values of VE and PS from the PS and extravascular volume specified in the 4-phase model were determined as functions of dimensionless red cell permeability αRC, hematocrit value, plasma-to-red cell velocity ratio, dimensionless extravascular cellular volume and permeability, capillary permeability αcap, and the fraction of indicator orginally deposited in the plasma at the capillary inlet. Our results indicate that application of the SS model to simulated low capillary permeability data produces underestimates in both VE and PS. Equations are presented which correct for this effect so long as the SS and 4-phase model c(t) curves are similar. Application of the whole blood-tissue SS model in situations where red cells are only slightly permeable or use of the plasma-tissue SS model when red cells admit tracer can lead to significant errors in VE and PS estimates. When αcap is relatively large neither SS model yields an accurate estimate of PS in the intermediate αRC range (i.e., near unity). Less than 10% error will result, regardless of αRC, if the blood-tissue SS model is used (αcap ≤ .30, Hct≤.50) and the tracer is equilibrated with a blood sample before injection.
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