Analysis program based on finite element method, MULTI(FEM), for evaluation of dose-dependent local disposition of drug in liver

AN EVALUATION METHOD FOR NONLINEAR LOCAL DISPOSITION IN RAT LIVER AND KIDNEY

A two-sampling sites method was developed to separately estimate the nonlinear local disposition in the liver and kidney by sampling blood simultaneously from the hepatic vein and an artery after intravenous administration. Using this method, it was attempted to predict the renal elimination from the systemic and hepatic elimination. Etoposide, a substrate of both P-glycoprotein and CYP3A, was used as a model drug. The blood samples from the hepatic vein and an artery were simultaneously taken from a rat after intravenous administration of etoposide at a dose of 20 or 80 mg/kg. At a dose of 20 mg/kg, the total clearance (CL), hepatic clearance (CLH), and renal clearance (CLR=CL-CLH), which were almost constant, were 2.82 +/- 0.24, 0.742 +/- 0.214, and 2.09 +/- 0.34 l/h/kg, respectively. At a dose of 80 mg/kg, CL and CLR considerably decreased with an increase in plasma concentration, whereas CLH slightly decreased. By means of the two-sampling sites method, we estimated the local drug disposition in the liver and kidney. The present local pharmacokinetic method would be applicable to assess the local disposition of other drugs that are mainly metabolized in these organs.

Analysis Methods and Recent Advances in Nonlinear Pharmacokinetics from In Vitro through In Loci to In Vivo

An attempt has been made to review the nonlinearities in the disposition in vitro, in situ, in loci and in vivo mainly from a theoretical point of view. Parallel Michaelis-Menten and linear (first-order) eliminations are often observed in the cellular uptake, metabolism and efflux of drugs. The well-stirred and parallel-tube models are mainly adopted under steady-state conditions in perfusion experiments, whereas distribution, tank-in-series and dispersion models are often used under nonsteady-state conditions with a pulse input. The analysis of the nonlinear local disposition in loci is reviewed from two points of view, namely an indirect method involving physiologically based pharmacokinetics (PBPK) and a direct (two or three samplings) method using live animals. The nonlinear global pharmacokinetics in vivo is reviewed with regard to absorption, elimination (metabolism and excretion) and distribution.

A compartmental model of hepatic disposition kinetics: 1. Model development and application to linear kinetics

The conventional convection-dispersion model is widely used to interrelate hepatic availability (F) and clearance (Cl) with the morphology and physiology of the liver and to predict effects such as changes in liver bloodflow on F and Cl. The extension of this model to include nonlinear kinetics and zonal heterogeneity of the liver is not straightforward and requires numerical solution of partial differential equation, which is not available in standard nonlinear regression analysis software. In this paper, we describe an alternative compartmental model representation of hepatic disposition (including elimination). The model allows the use of standard software for data analysis and accurately describes the outflow concentration-time profile for a vascular marker after bolus injection into the liver. In an evaluation of a number of different compartmental models, the most accurate model required eight vascular compartments, two of them with back mixing. In addition, the model includes two adjacent secondary vascular compartments to describe the tail section of the concentration-time profile for a reference marker. The model has the added flexibility of being easy to modify to model various enzyme distributions and nonlinear elimination. Model predictions of F, MTT, CV2, and concentration-time profile as well as parameter estimates for experimental data of an eliminated solute (palmitate) are comparable to those for the extended convection-dispersion model.

Quantitative evaluation of capacity-limited hepatobiliary transport based on hepatocellular diffusion model by MULTI(FEM)

The dose-dependency of hepatic uptake and hepatobiliary transport of a drug was evaluated by means of a nonlinear least square program incorporating the finite element method, MULTI(FEM). A perfusion experiment using isolated rat livers following a pulse input (i.e., under nonsteady-state conditions) was performed at three dose levels of cefpiramide as a model drug. The hepatic extraction ratio (E(H)) of cefpiramide decreased with an increase in dose, which demonstrates that the hepatic uptake is capacity-limited. The outflow time-profiles from the liver were represented by a two-compartment dispersion model with central Michaelis-Menten elimination, and the maximal elimination rate per central compartment volume (Vmax) and the Michaelis constant (Km) were estimated to be 1420 microg/ml/min and 235 microg/ml, respectively. The biliary mean transit time (t(bile)) increased slightly with an increase in dose. The hepatocellular diffusion model under non-steady-state conditions considering nonlinear transport across the bile canalicular membrane was adopted to evaluate dose-dependency in the biliary excretion of cefpiramide. The maximal penetration velocity across the bile canalicular membrane per liver (V=(bcm)max) and the affinity constant of penetration across the bile canalicular membrane (k(bcm)m = K(bcm)m A(H)L) were estimated to be 40.1 microg/min and 123 microg, respectively. Considering that the volume of a rat liver (A(H)L) is approximately 10 ml, the Michaelis constant of penetration (K(bcm)m), which is an apparent parameter, was estimated to be approximately 12.3 microg/ml. In conclusion, MULTI(FEM) is useful for evaluation of capacity-limited local disposition.

Commentary: using the convection-dispersion model and transit time density functions in the analysis of organ distribution kinetics

The convection-dispersion model and its extended form have been used to describe solute disposition in organs and to predict hepatic availabilities. A range of empirical transit-time density functions has also been used for a similar purpose. The use of the dispersion model with mixed boundary conditions and transit-time density functions has been queried recently by Hisaka and Sugiyama in this journal. We suggest that, consistent with soil science and chemical engineering literature, the mixed boundary conditions are appropriate providing concentrations are defined in terms of flux to ensure continuity at the boundaries and mass balance. It is suggested that the use of the inverse Gaussian or other functions as empirical transit-time densities is independent of any boundary condition consideration. The mixed boundary condition solutions of the convection-dispersion model are the easiest to use when linear kinetics applies. In contrast, the closed conditions are easier to apply in a numerical analysis of nonlinear disposition of solutes in organs. We therefore argue that the use of hepatic elimination models should be based on pragmatic considerations, giving emphasis to using the simplest or easiest solution that will give a sufficiently accurate prediction of hepatic pharmacokinetics for a particular application.

Prediction of optimal injection protocol for tumor detection in contrast-enhanced dynamic hepatic CT using simulation of lesion-to-liver contrast difference

The detection of hepatic lesions in computed tomography (CT) is improved when a contrasting material is administered intravenously, but it depends considerably on how this agent is injected. In this study, we constructed a compartment model for a liver containing a hepato-cellular carcinoma (HCC), and simulated the difference in lesion-to-liver contrast enhancement. Using this model, we simulated the effects of various injection factors on the detectability of a lesion and searched for the optimal injection protocol for detecting tumors in contrast-enhanced dynamic hepatic CTs. We found that the mass injection rate, or k-value (in mg/s), (which is the volume injection rate, in ml/s, multiplied by the contrast agent concentration, in mg/ml) plays a critical role in the injection protocol optimized for tumor detection, and has a unique value for a given body weight independent of the total injection dose.

Dose-dependency in local disposition of 5-fluorouracil under non-steady-state condition in rat liver

Dose-dependency in local disposition of 5-fluorouracil (5-FU) was evaluated using the rat liver in the once-through perfusion system under the non-steady-state condition. A curve-fitting program based on Finite Element Method, MULTI(FEM), was adopted to evaluate the capacity-limited elimination in the hepatic local disposition of 5-FU, which is described by a nonlinear dispersion model with a pulse input. The dose of 5-FU was increased from 10.4 to 208 microg for rat livers at five dose levels. Two nonlinear models, two-compartment dispersion models with Michaelis-Menten elimination from the central compartment or from the peripheral compartment, were employed for comparison. The hepatic recovery ratio, F(H), increased from 13.1% to 68.3% and the mean transit time, t(H), increased from 5.1 to 13.1 s with an increase in the dose. It was found that the hepatic local disposition of 5-FU was well represented by the peripheral elimination model. V(max) and K(m) in the model with peripheral Michaelis-Menten elimination were estimated to be 9.04 mg/h and 2.88 mg/L, respectively. V(max) estimated by the present investigation in situ was about seven times greater than that in vitro, whereas K(m) in situ was close to that in vitro. This result suggests that the elimination activity by the hepatocytes in vitro may be lowered, compared with that in situ.

Notes on the inverse Gaussian distribution and choice of boundary conditions for the dispersion model in the analysis of local pharmacokinetics

The dispersion model has been widely used to analyze local pharmacokinetics in the organs and the tissues since the 1980's. However, an ambiguity still remains in selecting the boundary conditions which are necessary to solve the basic equation of the model. In this note, theoretical considerations are given to this problem and we present here some deficiencies of the mixed boundary conditions. It seems that theoretical confusion exists in the literature for the mixed boundary conditions. It is well-known that the solution of the dispersion model with a bolus input is the inverse Gaussian distribution for the mixed boundary conditions. However, it is rarely recognized that the inverse Gaussian distribution requires an open boundary at either the inlet or the outlet. For the analysis of local pharmacokinetics, the use of the classical Danckwerts (or closed) boundary conditions is recommended.