Kinetic conversion of hazard characterisations¶
When the hazard characerisation level is internal and points of departure are available for external exposures (e.g., NOAELs from in-vivo animal studies) or when the hazard characterisation level is external and benchmark doses are available at the internal level, then kinetic conversion models are needed to translate the external doses to equivalent internal doses at the target compartment/organ of interest or vice-versa.
In the toolbox, this alignment from internal to external or from external to internal is generally termed kinetic conversion, associated with a kinetic conversion factor. The kinetic conversion factor is a multiplication factor needed to obtain a hazard characterisation on the target level from a hazard characterisation of the point of departure or benchmark dose. Depending on the chosen kinetic modelling tier, this kinetic conversion factor may be 1) assumed to be one, 2) derived from absorption factors, or 3) derived using PBPK models.
An important detail in the use of kinetic conversion factors for computing hazard characterisations is the order between kinetic conversion and inter-species extrapolation. Notice that when points of departure are determined for animals, a choice should be made regarding the order of inter-species extrapolation and kinetic modelling. That is, one may first choose to convert animal external point of departure to an internal hazard characterisation for that animal, using the available animal kinetic model. Alternatively, one may first extrapolate the animal external point of departure to a human external hazard characterisation, and thereafter apply the human kinetic model to obtain internal hazard characterisations. In the toolbox, only the latter approach is currently implemented.
Extrapolation from external to internal hazard characterisations¶
The calculation of internal hazard characterisations based on external hazard characterisations is similar to the procedure for computing internal exposures. In the simplest tier, equivalence can be assumed between internal and external hazard characterisations, and in higher tiers absorption factors, respectively PBPK models can be used.
Calculation of internal doses using absorption factors¶
In the simplest form, internal doses are obtained from external exposure concentrations using multiplication factors (or, absorption factors) that can be specified by substance and by route. That is, for a given substance, the internal hazard characterisation \(\mathit{HC}_{\mathtt{int}}\) can be derived from an external hazard characterisation \(\mathit{HC}_{\mathtt{ext}}\) as
Here, \(\mathit{r}\) denotes the route of the external exposure \(\mathit{HC}_{\mathtt{ext}}\), and \(\mathit{f}_{\mathtt{abs}, r}\) denotes the absorption factor of route \(r\) for the specified compartment. Note that this model assumes that the external hazard characterisations are specified as concentrations (i.e., substance amount divided by the body weight).
Calculation of internal doses using human PBPK models¶
A more detailed alternative to using absorption factors is to use one of the advanced PBPK models available in MCRA. In this approach, for each substance independently, an external exposure equivalent to the dose of the external hazard characterisation is presented to a representative simulated individual for a number of simulated days to the PBPK model of the individual. This representative individual should represent the “average” individual of the population, with nominal physiological properties (e.g., an average bodyweight of 70kg). This yields a time course of the internal substance amount at the specified target compartment/organ from which a long term average substance amount (chronic) or peak substance amount (acute) can be obtained. By dividing this substance amount by the weight of the compartment, an internal concentration is obtained, which then represents the internal hazard characterisation.
More details on computing internal doses from external doses can be found in the description of the calculation of internal exposures from external exposures. For both tasks, the procedure for computing internal exposures/doses is exactly and the same kinetic model settings, such as dosing patterns and non-stationary period period apply for calculation of internal hazard characterisations as well.
Calculation of internal doses using animal PBPK models¶
In the above methods, the assumption is that the external points of departure (often obtained from experiments on animals) are first converted to external hazard characterisations for humans, and a human kinetic model is used for obtaining the internal hazard characterisations. As mentioned, an alternative approach is to use first the animal PBPK models to derive an internal hazard characterisation specific for the tested animal species and thereafter extrapolate to humans. When there are more precise kinetic models available for the animal used in the experiments for obtaining the point of departure, this could be a prefered path.
Note
Notice that this procedure is not yet implemented.
Extrapolation from internal to external hazard characterisations¶
In some cases, hazard characterisations are available at the internal level whereas the specified hazard characerisation level is external. This situation may occur, for instance, in in-vitro in-vivo extrapolation (IVIVE). In this case, conversion is needed from the internal level to the external level, where the external level is implicitly defined as comming from the dietary/oral route of exposure.
When using absorption factors, the external (dietary) hazard characterisation of a substance is simply computed by dividing the internal hazard characterisation by the dietary absorption factor. I.e.,
When using PBPK models, reverse dosimetry is needed to find for the available internal hazard characterisation, the corresponsing external (dietary) doses that yield the internal concentrations specified by the internal hazard characterisation. In MCRA, this is done using a bisection method, in which external doses are systematically fed to the PBPK model in order to converge to an external dose that yields the specified internal hazard characterisation with some level of precision.