Specialized Compartments

Lung

The inclusion of a lung compartment in a physiologic model is an important consideration because inhalation is a common route of exposure to many toxic chemicals. The assumptions inherent in lung compartment description are as follows: (1) Ventilation is continuous, not cyclic, (2) conducting airways function as inert tubes, carrying the vapor to the gas exchange region, (3) diffusion of vapor across the lung cell and capillary walls is perfusion-limited, (4) all xenobiotic disappearing from inspired air appears in arterial blood (i.e., there is no storage of xenobiotic in the lung tissue and insignificant lung mass), and (5) vapor in the alveolar air and arterial blood within the lung compartment are in rapid equilibrium.

In the lung compartment depicted in , the rate of inhalation of xenobiotic is controlled by the ventilation rate (Qp ) and the inhaled concentration (Cinh ). The rate of exhalation of a xenobiotic is a product of the ventilation rate and the xenobiotic concentration in the alveoli (Calv ). Xenobiotic also can enter the lung compartment in venous blood returning from the heart, represented by the product of cardiac output (Qc ) and the concentration of xenobiotic in venous blood (Cven ). Xenobiotic leaving the lungs in the blood is a function of both cardiac output and the concentration of xenobiotic in arterial blood (Cart ). Putting these four processes together, a mass balance differential equation can be written for the rate of change in the amount of xenobiotic in the lung compartment (L):

Figure 7-6. Simple model of gas exchange in the alveolar region of the respiratory tract.

Rapid exchange in the lumped lung compartment between the alveolar gas (blue) and the pulmonary blood (light blue) maintains the equilibrium between them as symbolized by the dashed line. Qp is alveolar ventilation (L/h), Qc is cardiac output (L/h), Cinh is inhaled vapor concentration (mg/L), Cart is concentration of vapor in the arterial blood, and Cven is concentration of vapor in the mixed venous blood. The equilibrium relationship between the chemical in the alveolar air (Calv ) and the chemical in the arterial blood (Cart ) is determined by the blood/air partition coefficient Pb , e.g., Calv = Cart /Pb .Because of some of these assumptions, the rate of change in the amount of xenobiotic in the lung compartment becomes equal to zero (dl/dt = 0). Calv can be replaced by Cart /Pb , and the differential equation can be solved for the arterial blood concentration:

The lung is viewed here as a portal of entry and not as a target organ, and the concentration of a xenobiotic delivered to other organs by the blood, or the arterial concentration of that xenobiotic, is of primary interest.

Liver

The liver often is represented as a compartment in physiologic models because hepatic biotransformation is an important aspect of the toxicokinetics of many xenobiotics. A simple compartmental structure for the liver is assumed to be flow-limited, and this compartment is similar to the general tissue compartment shown in , except that the liver compartment contains an additional process for metabolic elimination. One of the simplest expressions for this process is first-order elimination:

where R is the rate of metabolism (milligrams per hour), Cf is the free concentration of xenobiotic in the liver (milligrams per liter), Vl is the liver volume (liters), and Kf is the first-order rate constant for metabolism in units of h–1.

In physiologic models, the Michaelis-Menten expression for saturable metabolism, which employs two parameters, Vmax and KM , is written as follows:

where Vmax is the maximum rate of metabolism (in milligrams per hour) and KM is the Michaelis constant, or xenobiotic concentration at one-half the maximum rate of metabolism (in milligrams per liter). Because many xenobiotics are metabolized by enzymes that display saturable metabolism, this equation is a key factor in the success of physiologic models for the simulation of chemical disposition across a range of doses.

Other, more complex expressions for metabolism also can be incorporated into physiologic models. Bisubstrate second-order reactions—reactions involving the destruction of enzymes, the inhibition of enzymes, or the depletion of cofactors—have been simulated by using physiologic models. Metabolism also can be included in other compartments in much the same way as was described for the liver.Conclusion

This chapter has overviewed the simpler elements of physiologic models and the important and often neglected assumptions that underlie model structures. The field of physiologic modeling is

expanding rapidly. Physiologic models of a parent chemical linked in series with one or more active metabolites, models describing biochemical interactions among xenobiotics, and more biologically realistic descriptions of tissues previously viewed as simple lumped compartments are just a few of the most recent applications. Finally, physiologically based toxicokinetic models are beginning to be linked to biologically based toxicodynamic models to simulate the entire

exposure dose response paradigm that is basic to the science of toxicology.