it is possible (and commonly done) to model explicitly the correlations between parameters (for example, the non-linear relationships between age, body-mass, organ volumes and blood flows). After numerical values are assigned to each PBPK model parameter, specialized or general computer software is typically used to numerically integrate a set of ordinary differential equations like those described above, in order to calculate the numerical value of each compartment at specified values of time (see Software). However, if such equations involve only linear functions of each compartmental value, or under limiting conditions (e.g., when input values remain very small) that guarantee such linearity is closely approximated, such equations may be solved analytically to yield explicit equations (or, under those limiting conditions, very accurate approximations) for the time-weighted average (TWA) value of each compartment as a function of the TWA value of each specified input (see, e.g.,). PBPK models can rely on chemical property prediction models (QSAR models or predictive chemistry models) on one hand. For example, QSAR models can be used to estimate partition coefficients. They also extend into, but are not destined to supplant, systems biology models of metabolic pathways. They are also parallel to physiome models, but do not aim at modelling physiological functions beyond fluid circulation in detail. In fact the above four types of models can reinforce each other when integrated. References Further references: Reddy M. et al. (2005) Physiologically Based Pharmacokinetic Modeling : Science and Applications, Wiley-Interscience. Peters S.A (2012) Physiologically-Based Pharmacokinetic (PBPK) Modeling and Simulations, Wiley. Forums Ecotoxmodels is a website on mathematical models in ecotoxicology. Software Dedicated software: BioDMET GastroPlus Maxsim2 PK-Sim PKQuest PSE: gCOAS Simcyp Simulator ADME Workbench General software: ADAPT 5 Berkeley Madonna COPASI: Biochemical System Simulator Ecolego Free simulation software: GNU MCSIM GNU Octave Matlab PottersWheel ModelMaker PhysioLab R deSolve package SAAM II Phoenix WinNonlin/NLME/IVIVC/Trial Simulator Toxicology Pharmacokinetics Pharmaceutics