Drug disposition viewed in terms of the fractal volume of distribution

Advanced pharmacokinetic models based on organ clearance, circulatory, and fractal concepts

Three advanced models of pharmacokinetics are described. In the first class are physiologically based pharmacokinetic models based on in vitro data on transport and metabolism. The information is translated as transporter and enzyme activities and their attendant heterogeneities into liver and intestine models. Second are circulatory models based on transit time distribution and plasma concentration time curves. The third are fractal models for nonhomogeneous systems and non-Fickian processes are presented. The usefulness of these pharmacokinetic models, with examples, is compared.

Morphine metabolite pharmacokinetics during venoarterial extra corporeal membrane oxygenation in neonates

OBJECTIVE

To examine morphine metabolite serum concentrations in neonates undergoing venoarterial extra corporeal membrane oxygenation (ECMO) and to quantify clearance differences between these neonates and those subjected to noncardiac major surgery.

PATIENTS AND METHODS

This was an observational study in level III referral centre. Fourteen neonates (< 7 days old) undergoing ECMO were included. Morphine and concomitant medications were given by protocol, adapted to the clinical conditions of the neonates. Pharmacokinetic findings were compared with those from a previous study in infants after noncardiac major surgery. Nonlinear mixed-effect modelling was used. Parameter estimates were standardised to a 70 kg person using allometric modeling

RESULTS

Morphine-3-glucuronide (M3G) was the predominant metabolite. Formation clearance to M3G at the start of ECMO on day 1 was lower than those in postoperative children, but matured more rapidly. After 10 days formation clearances of M3G in neonates on ECMO equalled those of postoperative children. Higher ECMO flows were associated with reduced formation clearances. Elimination clearances of M3G, but not morphine-6-glucuronide (M6G), were lower in the ECMO neonates; this was attributable to reduced renal clearance. These elimination clearances were correlated positively with ECMO flow and negatively with dopamine dose. Haemofiltration cleared M3G and M6G, but not morphine.

CONCLUSION

Formation clearance to M3G, the predominant metabolite, is reduced during the first 10 days of ECMO. Elimination clearance of M3G and M6G is related to creatinine clearance. ECMO flow had a small effect on metabolite clearance. Higher flows were associated with decreased formation clearances, possibly reflecting illness severity. Dopamine dose reflected decreased renal clearance.

Asymptotic time dependence in the fractal pharmacokinetics of a two-compartment model

We further investigate, both analytically and numerically, the properties of the fractal two-compartment model introduced by Fuite [J. Fuite, R. Marsh, and J. Tuszynski, Phys. Rev. E 66, 021904 (2002)]. Specifically, we look at the effects of the fractal exponent of the elimination rate coefficient on the long-time behavior of the pharmacokinetic clearance tail. For small exponent values, the tail exhibits exponential behavior, while for larger values, there is a transition to a power law. The theory is applied to seven data sets simulating drugs taken from the pharmacological literature.

Which in vitro Screens Guide the Prediction of Oral Absorption and Volume of Distribution?

The development of medium to high-throughput in vitro screening of ADME (Absorption, Distribution, Metabolism, Excretion) properties has been the reply to higher demands on drug metabolism scientists to cope with progress in chemistry and biology. Two areas will be discussed here, namely screens for oral absorption and for volume of distribution. The prediction of these human pharmacokinetic parameters can be based on proper combination of simple physicochemical measurements. In the future in vitro screens most likely will be combined with in silico assessments of various ADME properties leading to the concept of in combo screening in drug discovery.

Quantitative structure–pharmacokinetic relationships for disposition parameters of cephalosporins

This study explores the utility of quantitative structure-pharmacokinetic relationship models of the disposition parameters: clearance (CL), apparent volume of drug distribution (V(ap)), fractal clearance (CL(f)), and fractal volume (v(f)), for a series of 23 cephalosporins used in therapeutics. Data for CL, V(ap) and elimination half-life were obtained from literature, whereas CL(f) and v(f) were calculated from the literature data for CL and V(ap), respectively. A variety of descriptors expressing acidity/basicity, lipophilicity, molecular size and hydrogen bonding properties were estimated using computer packages. For each pharmacokinetic parameter, projection to latent structures (PLS) was applied to the total dataset. Adequate PLS models, with one principal component, were derived for CL, CL(f), V(ap) and v(f). Identical descriptors were found to be significant for the two clearance as well as for the two volume of distribution terms. CL and CL(f) expressed similar performance while the predictive performance of v(f) was much higher than that of V(ap). Multiple linear and non-linear regression models were developed. The regression results were in agreement with the PLS models. The non-linear models were superior to the relevant linear relationships. The worst models found were for V(ap) (R(2)=0.523 and R(2)=0.571 for the linear and non-linear model, respectively) and the best models found were for v(f) (R(2)=0.729 and R(2)=0.824 for the linear and non-linear model, respectively).

Multivariate statistics of disposition pharmacokinetic parameters for structurally unrelated drugs used in therapeutics

PURPOSE

To explore the quantitative structure pharmacokinetic relationships of the disposition parameters: clearance (CL), apparent volume of drug distribution (V(ap)), fractal clearance (CL(f)), and fractal volume (v(f)) for 272 structurally unrelated drugs used in therapeutics.

METHODS

Literature data were used for CL and V(ap) whereas CL(f) and v(f) were estimated as described previously (Pharm. Res. 18, 1056, 2001 and 19, 697, 2002). A variety of molecular descriptors expressing lipophilicity, ionization, molecular size and hydrogen bonding capacity were estimated using computer packages. The data were analyzed using multivariate statistics. For each disposition parameter (CL, V(ap) CL(f), v(f)) PCA (principal component analysis) and PLS (projection to latent structures) were applied to the total set of data as well as to subsets of data.

RESULTS

Drugs were divided into two classes (I and II) according to their v(f)/V(ap) ratio. Class I comprises 131 drugs with v(f)/V(ap) > 1, whereas class 11141 drugs with v(f)/V(ap) < 1. After initial PLS analysis, class I was subdivided in subclusters I(a) (30 drugs) and I(b) (101 drugs). It was found that I(a) included mostly acidic drugs with high protein binding, whereas class II comprises mainly basic, lipophilic compounds. No correlation was found between CL, V(ap), CL(f) and the used descriptors. Adequate PLS models were derived for v(f) considering subclusters I(a), I(b) and class II separately. The low v(f) values of class I(a) drugs were affected negatively from molecular size descriptors and non-polar surface area. For class I(b) drugs with intermediate v(f) values, apparent lipophilicity contributed positively, although molecular size descriptors and polarity were inhibitory factors. The high v(f) values of class II drugs were positively dependent on intrinsic lipophilicity and increased basicity, whereas polarity entered with negative contribution.

CONCLUSIONS

The parameters V(ap), CL, and CL(f) fail to reflect the physicochemical properties of drugs. The transformation of V(ap) values to v(f) is the underlying cause for the valid models for v(f). These models allow a global consideration of molecular properties (lipophilicity, ionization, molecular size, polar surface area) which govern the distribution of drugs in the human body. The present study provides additional evidence for the physiologically sound concept of v(f).