Model structure of the physiology-based toxicokinetic model

The PBTK model accounts for Al kinetics in plasma (pla), blood (blo), liver (liv), spleen (spl), muscle (mus), bone (bon), brain (bra), kidney (kid), and urine (uri). A ‘rest of body’ compartment (rob) describes the sum of the remaining body spaces like carcass, adipose tissue, and lung, as well as sites escaping quantification in before-mentioned tissue homogenates. The term tissue refers to the sum of interstitial and cellular space, thus excluding the vascular space, i.e., peripheral blood. The organs are in exchange via a central blood compartment that includes the arterio-venous space as well as the vascular space of the tissues. An overview of the detailed model structure is given in Fig. 1 (with black and grey parts).

Detailed (black and grey) and simplified (black) PBTK model structure. Amount of Al in body tissues and fluids denoted by A. Mass transfer indicated by black arrows with corresponding substance-dependent and -independent (i.e., species-specific) parameters (the latter being stated in brackets). In the blood compartment, different Al species are considered: added, i.e., iv-administered, citrate (addCit), and chloride (addChl) salts as well as a ‘mixed’ state, where all Al species—including transferrin bound Al—are assumed to be in quasi-steady state (Mix). Routes of administration are indicated by red arrows, and comprise intravenous (iv) and per oral (po) administration with bioavailability F. Parameters Ktis, Vtis, Qtis, and Itis represent retention coefficients, tissue volumes, organ blood flows, and tissue uptake coefficients, respectively (see Eqs.(5)–(6), Table 3 and text below)

The amount of Al in the different tissues and blood was denoted by Acmt, where ‘cmt’ denoted the corresponding compartment. Time was denoted by t. For associated units, see Table 3.

Fixed parameter values and parameter estimates, complementing the fixed species-specific parameters of the reference individuals tabulated in Table 1

Reported values refer to the population estimate of the fixed effects on the original (non-transformed) scale, including relative standard error (R.S.E.) of the estimated parameter values

Where appropriate, inter-individual variability was quantified as standard deviation of the random effects on the transformed scale and was denoted by ω. We scaled the GFR fixed-effect parameter as described in the “Methods” section, while the related variability parameter ω was estimated. Since the transition from Chl to Mix was assumed instantaneous, values for the parameters kChl2Mix and fuChl from Eqs. (8) and (13) are not required. The assumed values for Hct can be found in Table 1