Model of Stella and Himmelstein

An example of the use of Michaelis-Menten kinetics in a compartmental model is given in the model of Stella and Himmelstein [5], depicted in Figure 13.3. 

In 1980, Stella and Himmelstein [5] introduced the principles of pharmacokinetic modelling into the field of pro-drugs and site-specific delivery. In 1986, Hunt et al. [6] extended the model of Stella and Himmelstein by taking into account a specific area where toxicity occurs. Their work may be considered as the frame of reference for later work in this area. 

Figure 13.3. Model of Stella and Himmelstein, adapted from reference [5] (Section 13.3.1). The drug-carrier conjugate (DC) is administered at a rate i c(DC) into the central compartment of DC, which is characterized by a volume of distribution Fc(DC). DC is transported with an inter-compartmental clearance CLcr(DC) to and from the response (target) compartment with volume Fr(DC), and is eliminated from the central compartment with a clearance CZ.c(DC). The active drug (D) is released from DC in the central and response compartments via saturable processes obeying Michaelis-Menten kinetics defined by Fmax and Km values. D is distributed over the volumes Fc(D) and Fr(D) of the central and response compartment, respectively. D is transported with an inter-compartmental clearance CLcr(D) between the central compartment and response compartment, and is eliminated from the central compartment with a clearance CLc(D).

Stella and Himmelstein [95,97,99] examined mathematical models of several hypotheses and concluded that an additional condition is necessary for transport parent drug site retention. They identified three factors for successful targeting via prodrugs [95] ... 

MZ Southard, DW Green, VJ Stella, KJ Himmelstein. Dissolution of ionizable drugs into unbuffered solution A comprehensive model for mass transport and reaction in the rotating disk geometry. Pharm Res 9 58-69, 1992. 

---