Basic Structure and Original Calibration of the Kirman Model

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Among PBTK models, the Kirman et al. (2003) model is unusually simple in some ways, and unusually detailed in others.  Its simplicity is that in contrast to the four or five tissue compartments that are standard in PBTK models, the Kirman model only has two tissue compartments—one for the liver, where all enzyme-mediated metabolism is assumed to occur; and one for the rest of the body.  (There are two additional compartments for blood—one for arterial blood and one for venous blood.)  On the other hand, the Kirman model is unusually detailed in accounting for a wide variety of  metabolic routes and passive tissue reactions in blood, liver and other tissues.  The basic parameter values used in the original Kirman model are shown in Table 2-1.  The model structure is illustrated in Figure 2-1.

Initial attempts to implement the Kirman model required two adaptations that are not explicitly discussed in the original paper (Kirman et al. 2003).  First, when we initially set up the model for 0.18 kg rats to match the body weight reported in one of the papers (Miller, et al., 1982) used by Kirman et al. for calibration, we found that hepatic glutathione (GSH) production and loss did not balance at the starting GSH concentration of 7 mmol/L.  Examination of the original source paper for GSH production and loss rates (D’Souza et al., 1988) revealed that the reported  GSH production rate is for rats weighing 0.25 kg; the model will only balance at the stated liver GSH concentration if its production is scaled from 0.25 kg in proportion to the body weight of the rats used in a particular experiment.  Therefore we built in to the rat model a direct dependency of GSH production rate on body weight.

Second, it can be seen in Table 2-1 that in a few places parameters are given an abbreviation with a “C” suffix, as in alveolar ventilation (QCC), the total flow of blood from the heart known as cardiac output (QPC), and the maximum velocity of major enzyme reactions governed by Michaelis-Menten enzyme kinetics (VmaxC1, and VmaxC2).  The “C” suffix in these cases signifies a parameter that has some power-law scaling to body weight, but the Kirman et al. paper does not explain this, and instead gives the units for these parameters as simple functions of body weight without mentioning the exponent used for body weight scaling.  We are grateful to these authors for providing us with the raw computer code for the published version of the model when queried about this.  This facilitated our use of  the correct body weight scaling factor to adapt Vmax and other parameters with a “C” suffix in Table 2-1.  Having access to the model code also improved confidence in our ability to reproduce the original Kirman et al. (2003) model accurately.