Physiologically Based Pharmacokinetic (PBPK) Modeling and Simulations. Sheila Annie Peters

F is the bioavailability of a non‐IV drug, and τ is the dosing interval, which is 24 hours for a once daily drug. C_ss,av.u is the unbound steady state drug concentration and f_up is the fraction unbound in plasma. According to Equation 1.47, the steady state concentration of the drug increases as clearance decreases. This is the case for drugs exhibiting nonlinear clearance at therapeutic doses either due to enzyme saturation or autoinhibition. In addition, since clearance decreases with increasing doses, the apparent half‐life increases with increasing dose. Consequently, the time to reach steady state increases with dose.

      The magnitude of drug concentrations at steady state compared with that after the first dose is determined by the relationship between dosing interval and the half‐life. The ratio of maximum drug concentration under steady state conditions (C_ss,max ) to the maximum drug concentration after the first dose (C_1,max ) is called the accumulation ratio.

      

Figure 1.8. Steady state concentrations following (a) constant rate infusion (b) oral drug administration.

(1.48)

AUC_SS,τ is the AUC at steady state for a duration of dosing interval, τ. AUC_1,τ is the AUC during the same duration, following administration of the first dose. Equation 1.48 suggests that a drug with a long half‐life compared with its dosing interval is likely to accumulate. According to Equation 1.48, a half‐life greater than approximately six hours will lead to accumulation for a once‐daily regimen. Thus, dosing intervals should consider the half‐lives of drugs to minimize accumulation ratio and thereby to minimize safety risks. For a once daily chronic administration of a drug, a half‐life of around eight hours guarantees an accumulation ratio close to 1.

      Since a drug normally requires at least 3–5 half‐lives to reach steady state, effective plasma levels may be achieved more rapidly by the administration of a single large dose called the loading dose to bring the concentration in plasma quickly to the steady state levels followed by maintenance doses. The loading dose required to achieve the plasma levels present at steady state can be determined from the fraction of drug eliminated during the dosing interval and the maintenance dose.

      (1.49)

1.2.10 Active Metabolite and Prodrug Kinetics

       1.2.10.1 Active Metabolites

      Certain drugs like Tetrahydrocannabinol (THC) and morphine are metabolized to active metabolites (11‐hydroxy‐THC and morphine‐6‐glucuronide, respectively) with pharmacological activity that can be significant. Codeine and tramadol have metabolites (morphine and O‐desmethyltramadol respectively) that are stronger than the parent drug. Metabolites may also produce toxic effects, requiring patient monitoring to ensure they do not accumulate in the body. Metabolites may compete with the parent compound for the same plasma protein binding site, resulting in changes to the disposition of the parent drug. They may also inhibit or induce enzymes that metabolize the parent drug, causing changes to the exposure of the parent drug. The extent of metabolite activity, toxicity, displacement, or interaction depends on its concentration. Thus, examination of metabolite kinetics following drug administration plays a key role in characterizing its relevance for these processes.

       1.2.10.2 Prodrugs

When an active metabolite is part of a therapeutic strategy, the parent compound is called a prodrug. A prodrug is a pharmacologically inert compound that undergoes in vivo biotransformation to release the active drug by chemical or enzymatic cleavage at the desired site. Activation to the active compound should constitute the major pathway (>75%). Broadly, prodrugs can be classified into two types, carrier‐linked and bioprecursor prodrugs. A carrier‐linked prodrug comprises an inert carrier coupled covalently by an ester or amide linkage to an active drug. It is more lipophilic than the active drug. In a bioprecursor prodrug, the active drug is obtained by redox transformation by enzymes without alteration of its lipophilicity.

      A prodrug strategy is employed for multiple reasons – to enhance bioavailability of poorly soluble drugs or drugs that are prone to extensive pre‐systemic metabolism, to reduce side effects of the active drug, to prolong duration of action or to enable drug targeting to desired sites. Prednisolone phosphate is a prodrug activated in vivo by phosphatase to prednisolone which is pharmacologically active and poorly water soluble. Propranolol is a widely used antihypertensive drug which has low oral bioavalability due to first pass metabolism. Its prodrug, hemisuccinate ester of propranolol, blocks the glucuronidation leading to an 8‐fold increase in the plasma levels of propranolol. To reduce the side effects mediated by the pre‐colonic absorption of the pharmacologically active anti‐inflammatory drug 5‐amino salicylic acid (ASA), it is coupled with diazotized sulphanilamide pyridine to its prodrug sulfasalazine. Sulfasalazine remains intact until it reaches the colon, where the azo reductase in the colonic microflora converts it to constituents entities, 5‐ASA and sulphanilamide pyridine making them available for colonic absorption. Prodrugs of nonsteroidaidal anti‐inflammatory drugs (NSAIDs) overcome the gastrointestinal toxicity (irritation, ulcergenocity, and bleeding) caused by the drugs (Shah et al., 2017). L‐dopamine, used for the treatment of Parkinson’s disease, cannot cross the blood–brain barrier to act on the central nervous system (CNS). Its prodrug levodopa can easily cross the blood–brain barrier via an amino acid carrier and is then decarboxylated into dopamine by dopa decarboxylase in the CNS. Prodrugs are also used for masking taste and odor to improve patient compliance. Understanding the pharmacokinetics of a prodrug and its metabolite is key to defining the prodrug dose needed for efficacy.

       1.2.10.3 Metabolite Kinetics

      In principle, a drug or a prodrug may be metabolized to the active metabolite in more than one site. For example, an active metabolite of an orally administered drug/prodrug may be formed in the gut and in the liver. In addition, metabolites other than the active metabolite may be formed in parallel at both sites. The active metabolite may be eliminated in the gut and liver before entry into liver. For the simplest case of a single metabolite formed solely in liver, following IV administration of the parent, under first‐order, linear kinetic conditions, the rate of change in the amount of metabolite (A_M ), in systemic circulation is given by:

(1.50)

      k_f,M and k_el,M are the first‐order rate constants of metabolite formation (strictly, metabolite entry into systemic circulation) and elimination respectively. For simplicity, the metabolic pathway