A Mathematical Model to Predict HIV Virological Failure and Elucidate the Role of Lymph Node Drug Penetration.

Preventing virological failure following HIV treatment remains a difficult task that is further complicated by the emergence of drug resistance. We have developed a mathematical model able to explain and predict HIV virological outcomes for various compounds and patients' drug intake patterns. Compared to current approaches, this model considers, altogether, drug penetration into lymph nodes, a refined adherence representation accounting for the propensity for long drug holidays, population pharmacokinetic and pharmacodynamic variability, drug interaction, and crossresistance. In silico results are consistent with clinical observations for treatment with efavirenz, efavirenz in association with tenofovir DF and emtricitabine, or boosted darunavir. Our findings indicate that limited lymph node drug penetration can account for a large proportion of cases of virological failure and drug resistance. Since a limited amount of information is required by the model, it can be of use in the process of drug discovery and to guide clinical treatment strategies.

Approaching Pharmacometrics as a Paleontologist Would: Recovering the Links Between Drugs and the Body Through Reconstruction.

Our knowledge of dinosaurs comes primarily from the fossil record. Notwithstanding the condition of these vestiges, paleontologists reconstruct early reptilian life by comparison to previously discovered specimens. When relics are missing, reasonable deductions are used to fill in the gaps.

Assessing pharmacokinetic variability directly induced by drug intake behaviour through development of a feeding behaviour-pharmacokinetic model.

Variability in drug intake is increasingly recognized as a major source of variability in drug response. The non-uniform access to medicated feed, influenced by swine individual feeding behaviour, is a determinant of antibiotic exposure, recalling the intrinsic similarity with human compliance to drug regimens. In this paper, we developed a feeding behaviour-pharmacokinetic (FBPK) model of in-feed chlortetracycline (CTC) and established, in a definite way, the effect of feeding behaviour and its induced pharmacokinetic (PK) variability. Based on reported animal behaviour, we mathematically formulated swine feeding behaviour by incorporating its main characteristics: intense feeding periods that repeat on a daily basis and random feeding periods of free access to feed, along with growth stage factors. This behaviour model was then integrated into a PK model of CTC. Moreover, we analysed the effect of each feeding behaviour component and assessed the corresponding PK variability. We have been able to delineate the impact of different feeding behaviour components and characterize the induced PK variability. We have compared different therapeutic assumptions to our model and shown that random features underlying the feeding behaviour have dramatic influence on the PK variability. A practical tool to adopt the dosing regimen in terms of dose and age has been proposed. The method developed here can be generalized to other therapeutic contexts and incorporated into medical practice, particularly to make long-term projections of drug-intake behaviour, to explain possible treatment failure and guide practitioners in adjusting the dosing regimen.

Enzymatic degradation of cross-linked high amylose starch tablets and its effect on in vitro release of sodium diclofenac.

The influence of several physicochemical parameters on enzymatic hydrolysis and the in vitro release of sodium diclofenac (SDic) from cross-linked high amylose starch (Contramid) (CLA) tablets was evaluated. These parameters included pH, ionic strength of the medium, enzyme concentration, compression force and incorporation of gel-forming polymers such as hydroxypropyl methylcellulose (HPMC), poly(ethylene oxide) (PEO) and poly(vinyl alcohol) into the tablet. Pure CLA tablets were incubated in phosphate buffer (pH 6.8) containing alpha-amylase and the extent of enzymatic erosion was determined by gravimetry. Release of SDic from CLA tablets, in the presence of alpha-amylase, was measured using a USP type III dissolution apparatus. For low alpha-amylase concentrations (<2250 IU/l), the drug release was mainly diffusion-controlled. At higher alpha-amylase concentrations (>4500 IU/l) both diffusion and erosion contributed to the release of SDic. The hydrolysis kinetics of CLA tablets by alpha-amylase was biphasic. During the first phase (2-4 h), the hydrolysis rate was hyperbolically related to the alpha-amylase concentration but was practically alpha-amylase concentration-independent during the second phase. Enzymatic erosion and drug release kinetics appear to be relatively independent of ionic strength, pre-incubation time in simulated gastric fluid, and compression force of the tablets (6-34 kN). Incorporation of HPMC or PEO into the tablet resulted in a significant decrease of both tablet erosion and drug release rates.

Peripheral link model as an alternative for pharmacokinetic-pharmacodynamic modeling of drugs having a very short elimination half-life.

Attempts to obtain estimates of pharmacokinetic-pharmacodynamic (PK-PD) parameters for mivacurium with traditional central link models were unsuccessful in many patients. We hypothesized that a link model with the peripheral compartment would be more appropriate for mivacurium in view of its extremely rapid plasma clearance and its potential elimination by tissue pseudocholinesterases. For validation purposes, the peripheral link model was applied to other neuromuscular blocking agents (NMBA), i.e., atracurium and doxacurium which have respectively an intermediate and a long elimination half-life. Assuming peripheral elimination in PK-PD modeling was investigated but found to have no impact on the estimation of PK-PD parameters. Our results indicate that, for drugs having intermediate and long elimination half-lives, EC50 values are similar with either the central or peripheral link model. For mivacurium, a peripheral link model enables PK-PD modeling in all subjects, with more precision in the PK-PD parameter estimates and a better fitting of the effect data when compared to the central link model. For these reasons, a peripheral link model should be preferred for mivacurium.

Assuming peripheral elimination: its impact on the estimation of pharmacokinetic parameters of muscle relaxants.

For anesthetic drugs undergoing nonorgan-based elimination, there is a definite trend towards using pharmacokinetic (PK) models in which elimination can occur from both central (k10) and peripheral compartments (k20). As the latter cannot be assessed directly, assumptions have to be made regarding its value. The primary purpose of this paper is to evaluate the impact of assuming various degrees of peripheral elimination on the estimation of PK parameters. For doing so, an explanatory model is presented where previously published data from our laboratory on three muscle relaxants, i.e., atracurium, doxacurium, and mivacurium, are used for simulations. The mathematical aspects for this explanatory model as well as for two specific applications are detailed. Our simulations show that muscle relaxants having a short elimination half-life are more affected by the presence of peripheral elimination as their distribution phase occupies the major proportion of their total area under the curve. Changes in the exit site dependent PK parameters (Vdss) are also mostly significant when k20 is smaller than k10. Although the physiological processes that determine drug distribution and those affecting peripheral elimination are independent, the two are mathematically tied together in the two-compartment model with both central and peripheral elimination. It follows that, as greater importance is given to k20, the rate of transfer from the central compartment (k12) increases. However, as a result of a proportional increase in the volume of the peripheral compartment, peripheral concentrations remain unchanged whether or not peripheral elimination is assumed. These findings point out the limitations of compartmental analysis when peripheral elimination cannot be measured directly.

A model of growing vascular structures.

Increasing attention is being paid to the configuration and development of vascular structures and their possible correlations with physiological events. The study of angiogenesis in normal and pathological states as well as in embryo and adult has provided new insights into the mechanism of vessel growth and organization of the vasculature. Various mathematical branching models have been developed. These constructions are mainly geometrical and only involve a branching phenomenon. We propose the use of a deterministic non-linear model based on physiological laws and hydrodynamics. Growth, branching and anastomosis, the three actual main events occurring in vascular growth, are included in this model. Space growth, including cells and vessels, is defined by a decreasing transformation. Space density and the length of new sprouts are controlled by a set of parameters. The conditions on these parameters are well established, which allows the production of realistic patterns.