A hierarchy of mathematical model can be defined according to the degree of detail (or mechanism) in their description of physiological processes (Aarons BJCP 60, 2005). As the mechanistic detail of a mathematical model increases, the data it can be applied to (or required to develop it in the first place) and its potential uses change. Broadly, the **“Top-down” **and**“bottom up” **approaches to PK modelling summarise the different ways of examining a given dataset.

A **Top-down**approach will usually use empirical models with less physiological/mechanistic detail, applied in a fitting paradigm to simple data (e.g. plasma observations only). The model will describe and summarise the data, allow for objective comparison of one drug’s PK vs. another and define the dose to exposure relationship and potentially covariates that can explain variation in exposure. The model will have less rationale for prediction/extrapolation .

A **Bottom up **approach will often use more mechanistic models applied in a prediction/simulation paradigm. The more mechanistic model applied will require prior information not intrinsic to the data being described, and may be more challenging to fit to the data in question. Once developed however the model has greater biological rationale for prediction and extrapolation.

PKPD modelling is a similar exercise to PK modelling in that the aim is to describe, summarise and interpret quantitiative exposure and response data through use of a mathematical model.

An enormous variety of PKPD models exist however three core recurring concepts for PKPD modelling are:

– The need often to model a time delay between the concentration timecourse and effect timecourse. This reflects both PK distributional delays (i.e. it takes time for drug to get where it needs to go to elicit an effect) and also pharmacological delays in eliciting an effect (an effect might require e.g. signal transduction, protein synthesis, or a cascade chain of prior effects before being manifested). The effect compartment PKPD model is an example of an empirical PKPD model incorporating a delay between concentration and effect.

– The need to account for saturation effect. Pharmacological effects often saturate to a maximum value which can often be attributed to biological effects being manifested by receptor binding, which is a saturable process. Mathematical models describing PD data must often be able to account for this (e.g. the “Emax model” is a PD model commonly used to describe saturable processes).

– The need to account for endogenous baseline in effect. Often a drug’s effect manifests as a perturbation of an underlying physiological measure and this baseline effect needs to be accounted for.