A novel approach to calculating the kinetically derived maximum dose

Abstract

The kinetically derived maximal dose (KMD) provides a toxicologically relevant upper range for the determination of chemical safety. Here, we describe a new way of calculating the KMD that is based on sound Bayesian, theoretical, biochemical, and toxicokinetic principles, that avoids the problems of relying upon the area under the curve (AUC) approach that has often been used. Our new, mathematically rigorous approach is based on converting toxicokinetic data to the overall, or system-wide, Michaelis–Menten curve (which is the slope function for the toxicokinetic data) using Bayesian methods and using the “kneedle” algorithm to find the “knee” or “elbow”—the point at which there is diminishing returns in the velocity of the Michaelis–Menten curve (or acceleration of the toxicokinetic curve). Our work fundamentally reshapes the KMD methodology, placing it within the well-established Michaelis–Menten theoretical framework by defining the KMD as the point where the kinetic rate approximates the Michaelis–Menten asymptote at higher concentrations. By putting the KMD within the Michaelis–Menten framework, we leverage existing biochemical and pharmacological concepts such as “saturation” to establish the region where the KMD is likely to exist. The advantage of defining KMD as a region, rather than as an inflection point along the curve, is that a region reflects uncertainty and clarifies that there is no single point where the curve is expected to “break;” rather, there is a region where the curve begins to taper off as it approaches the asymptote (Vmax in the Michaelis–Menten equation).

Kinetically-derived maximal dose (KMD) indicates lack of human carcinogenicity of ethylbenzene

“…As described in “Materials and methods”, the method of Burgoon et al ( 2022 ) was used to estimate likely distributions of K m and V max representing likely Michaelis–Menten functions for ethylbenzene, and the kneedle algorithm was then used to investigate the resulting Michaelis–Menten curves to identify the likely KMD range. We used the male rat venous ethylbenzene concentration data at an external exposure of 50 ppm (Haddad et al 1999 , 2000 ) to estimate the K m and V max of the global kinetic system (Burgoon et al 2022 ). Blood measurements were taken at 4, 4.5, 5, 5.5, and 6 h post exposure.…”

“…We used a Bayesian approach to estimate the K m and V max for the system-wide Michaelis–Menten function that governs the kinetic curve (Burgoon et al 2022 ). Briefly, this involved applying Bayesian analysis with differential equations to information from published, peer-reviewed studies on ethylbenzene kinetics to build statistical distributions of plausible values of the K m and V max for ethylbenzene elimination.…”

“…From those distributions of likely K m and V max values, a set of Michaelis–Menten equations were generated that are likely to represent the slope function for the relationship between ethylbenzene exposure and blood concentration. The resulting Michaelis–Menten functions were then investigated using a change-point methodology known as the “kneedle” algorithm (Burgoon et al 2022 ; Satopaa et al 2011 ) to identify the possible KMD range, which we have defined as the range of administered concentrations at which maximum curvature has been achieved. The KMD range is thus the region of the curve that begins to approach an asymptote.…”

“…Risk assessors are tasked with characterizing and quantifying risks and identifying chemical exposure levels that are safe for humans but in doing so, are required by regulatory agencies to consider data from animals exposed up to the maximum tolerated dose (MTD). Typically, the MTD not only exceeds anticipated human exposure levels but frequently exceeds dose levels that saturate drug and chemical metabolism and elimination pathways in the test species, leading to a host of toxic effects that are irrelevant to the effects expected from lower concentrations where kinetic processes 1 are not saturated (Borgert et al 2021 ; Burgoon et al 2022 ; Bus 2017 ; Andersen 1981 ). In addition, effects seen at high dose levels provide false information on the mechanism of action by which the compound is producing the toxic effect.…”

“…We define the KMD as the maximal external dose where kinetics are unchanged relative to lower doses (Borgert et al 2021 ). In practice, we estimate the KMD as a range to represent our uncertainty about the precise location of the KMD (Burgoon et al 2022 ). The KMD has practical importance for the identification of safe exposure levels to protect against tumorigenesis and cancers.…”