Toxicodynamics and toxicokinetics of amikacin in the guinea pig cochlea

Abstract

An extensive overview of the relationship between cochlear toxicity and amikacin blood concentrations in teh guinea pig is provided which should assist in the clinical application of this class of antibiotic. A data set previously used to relate the incidence of amikacin ototoxicity to dosing rates and blood concentrations was re-examined to assess the toxicodynamics of amikacin in terms of decibels of hearing loss across dosing rate, hearing frequency and time following drug exposure. Animals in this data set had received continuously i.v. infused amikacin over an 8-fold range of dosing rates. Preliminary analysis indicated that the data were consistent with a sigmoid relationship between hearing loss (decibels) and area under the amikacin plasma concentration vs time curve cumulated over the entire course of drug administration (cAUC). The sigmoid model was therefore used as the backbone of a far more comprehensive toxicodynamic model which described all the data with a single equation. Testing with this model showed that the cAUC required to produce half-maximum hearing loss (cAUC-1/2) was related to dosing rate ( P < 0.01), to hearing frequency ( P < 0.00001), and to post-drug interval ( P < 0.00001). Maximum hearing loss (difference between upper and lower sigmoid asymptotes) was less than total and was significantly related to frequency ( P < 0.00001). No effects could be detected on the sigmoid slope. Further modelling of the significant effects detected by the comprehensive toxicodynamic model was doen to determine if they could be described by simple relationships or by biologically relevant sub-models. Modelling of maximum hearing loss (postulated to represent loss of mainly outer hair cell function) indicated that this parameter was constant at about 61 decibels or 2–12 kHz and linearly decreased with log frequency for frequencies > 12 kHz. Modelling of cAUC-1/2 on frequency indicated that there was a strong inverse linear relationship to log frequency. Modelling of cAUC-1/2 on post-drug interval indicated that delayed ototoxicity continued at progressively slower rates for at least 56 days after drug administration had ceased. Modelling of cAUC-1/2 on dosing rate showed an increased requirement for drug as the dosing rate decreased. However, cAUC-1/2 changed no more than 20% across the range of dosing rates compared to the 8-fold difference in mean steady-state plasma concentrations, suggesting that plasma concentration is not a primary determinant of ototoxicity. A toxicokinetic model was developed which explained the dosing rate effect on cAUC-1/2 very successfully. This model postulated (1) zero order accumulation of drug in the ototoxic pool at a rate directly proportional to steady-state amikacin plasma concentration, (2) first order disappearance kinetics from the ototoxic pool, and (3) that the level of drug accumulation in the ototoxic pool required to produce a given severity of hearing loss is the same for all dosing rates or plasma concentrations. The disappearance half-life from the ototoxic pool calculated from the fit of this toxicokinetic model to the data was about 80 days. Since the sloping portion of the sigmoid relationship for any one frequency covered several octaves of differential sensitivity to drug, it would appear that the slope results principally from row-to-row and to within row differences in drug sensitivity rather than to longitudinal differences. Cluster analysis of standardized hearing loss values (obtained by removing the influence of all significant effects from the residuals to the final toxicodynamic model) about a common sigmoid curve indicated that the hearing loss data falls into 4 main clusters whose means are about 20 dB apart, presumably corresponding to the loss of 0, 1, 2, or 3 rows of outer hair cells. These results show that, for a limited range of dosing exposures, amikacin-induced hearing loss in the guinea pig cochlea is well described as a sigmoid function of cAUC (R 2 = 0.71 with statistically significant parameters modelled in), and that sensitivity to drug can be expressed as a complex mathematical function of hearing frequency, dosing rate and post exposure time within an expanded sigmoid model. The estimate of a very long disappearance half-life of drug at the ototoxic pool has important clinical implications.