Comparison of distributed and compartmental models of drug disposition: assessment of tissue uptake kinetics

Abstract

The utility of a circulatory three-compartment model for the assessment of tissue uptake kinetics is tested by comparison with the respective distributed models using pharmacokinetic data of rocuronium in patients These minimal physiologically based models have a common structure consisting of two subsystems representing the lung and the lumped systemic circulation, with two regions, the vascular and tissue space. The distributed models are based on either diffusion-limited tissue distribution, permeability-limited tissue uptake or the assumption of an empirical transit time density function. With a deviation in the estimate of the permeability-surface area product (PS) of about 18 %, the compartmental approach appears as a useful alternative on condition that a priori knowledge of cardiac output is included. It is also shown that the distribution clearance calculated from the parameters of a mammillary compartment model changes proportional to PS and can be used as an indirect measure of permeability-limited tissue uptake of drugs.

Appendix

When using models D-DL or D-PL model, first the arterial ICG concentration–time curve after rapid bolus injection (dose D _iv ) is fitted to the following equation (given in the Laplace domain)

$$\hat{C}(s) = \frac{{D_{iv} }}{Q}\;\frac{{\hat{f}_{B,p} (s)}}{{1 - (1 - CL/Q)\hat{f}_{B,s} (s)\hat{f}_{B,p} (s)}}$$

(10)

where $\hat{f}_{B,p} (s)$ and $\hat{f}_{B,s} (s)$ are the Laplace transforms of pulmonary and systemic TTDs (Eq. 6); Q and CL denote cardiac output and clearance, respectively. For fitting the C(t) data rocuronium also Eq. 10 is used, but $\hat{f}_{B,s} (s)$ is replaced by f _s (s), i.e., Equation 4 in case of the D-DL model, and by Eq. 5 for the D-PL model. The same holds for f _B,p (s)(substituting V _T,s and V _B,s in Eqs. 4 and 5 by V _T,p and V _B,p , respectively. For the D-TD model, the f _i (s)are given by Eq. 6.

In model D-PL (Eq. 5) the estimated relative dispersion in the systemic circulation and cardiac output determine CL _M when the influence of the lungs is neglected [8] (Weiss, 2006)

$$CL_{M} = \frac{2Q}{{RD_{s}^{2} - 1}}$$

(11)

Calculating AUC _M defined by Eq. (8) from Eqs. 1–3 (for CL = 0), one obtains for the C-RC model C-RC:

$$CL_{M} = \frac{{QPSV_{SS} }}{{V_{B,s}^{2} PS + 2PSV_{B,s} V_{T,s} (PS + Q)}}$$

(12)

For the C-M3 model CL _M is given by [17]

$$CL_{M} = \left[ {\left( {\frac{{V_{1} }}{{V_{{ss}} }}} \right)^{2} \frac{1}{{CL_{{d1}} }} + \left[ {\left( {\frac{{V_{2} }}{{V_{{ss}} }}} \right)^{2} \frac{1}{{CL_{{d2}} }}} \right]} \right]^{{ - 1}}$$

(13)