Daniel Claude

Aminoglycoside Nephrotoxicity: Modeling, Simulation, and Control

ABSTRACT The main constraints on the administration of aminoglycosides are the risks of nephrotoxicity and ototoxicity, which can lead to acute, renal, vestibular, and auditory toxicities. In the present study we focused on nephrotoxicity. No reliable predictor of nephrotoxicity has been found to date. We have developed a deterministic model which describes the pharmacokinetic behavior of aminoglycosides (with a two-compartment model), the kinetics of aminoglycoside accumulation in the renal cortex, the effects of aminoglycosides on renal cells, the resulting effects on renal function by tubuloglomerular feedback, and the resulting effects on serum creatinine concentrations. The pharmacokinetic parameter values were estimated by use of the NPEM program. The estimated pharmacodynamic parameter values were obtained after minimization of the least-squares objective function between the measured and the calculated serum creatinine concentrations. A simulation program assessed the influences of the dosage regimens on the occurrence of nephrotoxicity. We have also demonstrated the relevancy of modeling of the circadian rhythm of the renal function. We have shown the ability of the model to fit with 49 observed serum creatinine concentrations for a group of eight patients treated for endocarditis by comparison with 49 calculated serum creatinine concentrations (r2 = 0.988; P < 0.001). We have found that for the same daily dose, the nephrotoxicity observed with a thrice-daily administration schedule appears more rapidly, induces a greater decrease in renal function, and is more prolonged than those that occur with less frequent administration schedules (for example, once-daily administration). Moreover, for once-daily administration, we have demonstrated that the time of day of administration can influence the incidence of aminoglycoside nephrotoxicity. The lowest level of nephrotoxicity was observed when aminoglycosides were administered at 1:30 p.m. Clinical application of this model might make it possible to adjust aminoglycoside dosage regimens by taking into account both the efficacies and toxicities of the drugs.

AMINOGLYCOSIDE DOSAGES AND NEPHROTOXICITY: QUANTITATIVE RELATIONSHIPS

ObjectiveTo develop a model that relates the probability of occurrence of nephrotoxicity to the cumulative area under the curve (AUC) of amikacin serum concentration.Design and patientsThis was a retrospective study of two groups of patients in whom nephrotoxicity was observed after administration of amikacin. The first group consisted of patients treated with once-daily administration (ODA) [n = 13]. The second group consisted of patients treated with twice-daily administration (TDA) [n = 22].Main outcome measureThe probability of nephrotoxicity occurrence.ResultsThe model is a powerful tool to represent and describe the influence of the dosage regimen on aminoglycoside nephrotoxicity. The onset of nephrotoxicity is delayed in the ODA group (p = 0.01) for the same total daily dose among the two groups. The cumulative serum AUC values at onset of nephrotoxicity were greater for the ODA group (p = 0.029). In addition, for the same probability of nephrotoxicity occurrence (50%), the cumulative AUC for the ODA dosage regimen is 2 613 mg · h/L versus only 1 521 mg · h/L for the TDA dosage regimen. The difference in nephrotoxicity between ODA and TDA is greatest for a cumulative AUC of 2 495 mg · h/L, which corresponds to standard therapy with amikacin 900 mg/day during a 7-day period, i.e. 15 mg/kg/day for a 60kg patient with normal renal function (initial creatinine clearance >80 mL/min). For an AUC above 2 495 mg · h/L, the difference in nephrotoxicity decreases slowly to zero. This result means that ODA is especially justified when the treatment is administered over a short duration, i.e. less than 7 days.ConclusionsThe utility of selecting ODA in order to obtain less nephrotoxicity in comparison with TDA is therefore not established when the treatment is prolonged. In clinical use, the choice of the dosage regimen is not clear-cut, and both expected efficacy and expected toxicity must be taken into account in order to obtain an overall optimisation of each patient’s therapy.

Time-patterned drug administration: insights from a modeling approach

The physiological effects of a drug depend not only on its molecular structure but also on the time-pattern of its administration. One of the main reasons for the importance of temporal patterns in drug action is biological rhythms—particularly those of circadian period. These rhythms affect most physiological functions as well as drug metabolism, clearance, and dynamic processes that may alter drug availability and target cell responsiveness with reference to biological time. We present an overview of the importance of time-patterned signals in physiology focused on the insights provided by a modeling approach. We first discuss examples of pulsatile intercellular communication by hormones such as gonadotropin-releasing hormone, and by cyclic adenosine monophosphate (cAMP) signals in Dictyostelium amoebae. Models based on reversible receptor desensitization account in both cases for the existence of optimal patterns of pulsatile signaling. Turning to circadian rhythms, we examine how models can be used to account for the response of 24h patterns to external stimuli such as light pulses or gene expression, and to predict how to restore the physiological characteristics of altered rhythms. Time-patterned treatments of cancer involve two distinct lines of research. The first, currently evaluated in clinical trials, relies on circadian chronomodulation of anticancer drugs, while the second, mostly based on theoretical studies, involves a resonance phenomenon with the cell-cycle length. We discuss the implications of modeling studies to improve the temporal patterning of drug administration.

PERIOD SHIFT INDUCTION BY INTERMITTENT STIMULATION IN A DROSOPHILA MODEL OF PER PROTEIN OSCILLATIONS

PER protein circadian oscillations in Drosophila have been described by Goldbeter according to a five-dimensional model that includes the possibility of genetic mutation described by changing one parameter, the maximum degradation rate of the PER protein. Assuming that, in a mutant Drosophila this parameter is unreachable, we modify another parameter, the translation rate between the mRNA and the nonphosphorylated form of PER protein, by periodic intermittent activation or inhibition. We show how such a modification, simulated in the model by a periodic, on/off, piecewise constant stimulation (which increases or decreases this parameter) allows the entrainment of oscillations exactly at, or close to, a desired period. In a different context, this suggests that some diseases may be corrected using pharmacological agents according to specific periodic delivery schedules. (Chronobiology International,17(1), 1–14, 2000)

Contribution of a mathematical modelling approach to the understanding of the ovarian function

The biological meaning of folliculogenesis is to free fertilisable oocytes at the time of ovulation. We approached the study of the control of follicular development at the level of follicular granulosa cells, on the experimental as well as mathematical modelling grounds. We built a mathematical model allowing for the processes of proliferation, differentiation and apoptosis. State variables correspond to the numbers of cells undergoing these different processes, while control variables correspond to the cellular transition rates. The model results raised the notion of proliferative resources, which leads to consider the optimal management of these resources and has motivated the settling of an experiment investigating the changes in the growth fraction within the granulosa throughout terminal development. We are now investigating the way gonadotrophins, and especially FSH, operate on granulosa cells, in order to account for the hormonal control of the divergent commitment of granulosa cells towards either proliferation, differentiation or apoptosis. We are thus focusing on the dynamics of cAMP production, which appears to be a keypoint in FSH signal transduction.