# Estimation of the pulmonary capillary volume and endothelium barrier function using the multiple indicator dilution method

#### Abstract

Let h(t) be the probability density function of transit times. The following equations relate the moments (mean transit time, t, variance, $\sigma\sp2,$ and skewness, m$\sp3)$ of the capillary function, h$\sb{\rm c}$(t); of the extravascular function, h$\sb{\rm e}$(t), and of the noncapillary function, h$\sb{\rm n}$(t), to the moments of the venous concentration versus time curves for a vascular reference indicator, C$\sb{\rm R}$(t), and a flow-limited diffusible indicator, C$\sb{\rm D}$(t), following a bolus injection of the indicators upstream from the lung: \eqalign{\rm\bar{t}\sb{R} &= \rm\bar{t}\sb{n} + \bar{t}\sb{c};\ \sigma\sbsp{R}{2} = \sigma\sbsp{n}{2} + \sigma\sbsp{c}{2};\ m\sbsp{R}{3} = m\sbsp{n}{3} + m\sbsp{c}{3}\cr \rm\bar{t}\sb{D} &= \rm\bar{t}\sb{n} + \left(1 + {\bar{t}\sb{e}\over\bar{t}\sb{c}}\right)\bar{t}\sb{c};\ \sigma\sbsp{D}{2} = \sigma\sbsp{n}{2} + \left(1 + {\bar{t}\sb{e}\over\bar{t}\sb{c}}\right)\sp2\sigma\sbsp{c}{2};\cr &\sk{60}\rm m\sbsp{D}{3} = m\sbsp{n}{3} + \left(1 + {\bar{t}\sb{e}\over\bar{t}\sb{c}}\right)\sp3 m\sbsp{c}{3}\cr}The moments of h$\sb{\rm c}$(t) can be estimated if the injected bolus includes, along with vascular reference indicator, at least two flow-limited diffusible indicators each with different $\rm\bar{t}\sb{e}.$ A least squares optimization procedure can then be used to specify the moments of h$\sb{\rm c}$(t). This approach was applied to isolated dog lung lobes with ($\sp{14}$C) diazepam as the diffusible indicator. The tissue-to-perfusate partition coefficient for ($\sp{14}$C) diazepam could be adjusted to any desired value by altering the perfusate albumin concentration. Thus, by making two injections at different perfusate albumin concentrations, data were obtained in a manner equivalent to making one injection with two flow-limited diffusible indicators each with a different $\rm\bar{t}\sb{e}.$ The estimated capillary mean transit time (blood volume) was about 48% of the total lobar mean transit time (blood volume), and the relative dispersion of the h$\sb{\rm c}$(t) was about 75%. Using the estimated moments of the capillary transit time distribution, an optimization procedure for estimating the permeability-surface area product (PS) for barrier-limited indicators exchanged via linear uptake processes is suggested.

#### Recommended Citation

Audi, Said Halim, "Estimation of the pulmonary capillary volume and endothelium barrier function using the multiple indicator dilution method" (1993). Dissertations (1962 - 2010) Access via Proquest Digital Dissertations. AAI9411496.
https://epublications.marquette.edu/dissertations/AAI9411496

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