Drug Targeting Organ-Specific Strategies

350 13 Pharmacokinetic/Pharmacodynamic Modelling in Drug Targeting

13.3 Pharmacokinetic Models for Drug Targeting

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.

13.3.1 Model of Stella and Himmelstein

The model of Stella and Himmelstein [5], depicted in Figure 13.3, was originally derived for pro-drugs, and may be considered as a minimal model for evaluating the pharmacokinetics of pro-drugs and drug targeting systems. Since the drug–carrier conjugate (DC) and the active drug (D) are different entities, and since the model should be able to discriminate between the target site and non-target sites, a pharmacokinetic model for drug–carrier conjugates should include, at least, the following compartments (Figure 13.3):

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 RC(DC) into the central compartment of DC, which is characterized by a volume of distribution VC(DC). DC is transported with an intercompartmental clearance CLCR(DC) to and from the response (target) compartment with volume VR(DC), and is eliminated from the central compartment with a clearance CLC(DC). The active drug

(D) is released from DC in the central and response compartments via saturable processes obeying Michaelis–Menten kinetics defined by Vmax and Km values. D is distributed over the volumes VC(D) and VR(D) of the central and response compartment, respectively. D is transported with an intercompartmental clearance CLCR(D) between the central compartment and response compartment, and is eliminated from the central compartment with a clearance CLC(D).

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eliminating organs to the targeted drug (in the case of release or activation of the drug in the eliminating organs) and to maximize the therapeutic availability, that is, to maximize the fraction of the dose that reaches the target site. Ideally, the elimination of the DC should take place exclusively in the target organ (see Sections 13.3.1.2 and 13.3.1.3). Elimination at other sites reduces the efficiency of targeting. For example, elimination of the DC without release of the active drug implies a waste of a sophisticated and expensive product, and elimination of the DC with release of active drug in non-target tissue increases the concentration of D in non-target tissue, thus lowering the Drug Targeting Index (DTI, see Section 13.4.2) [12].

In general, optimization of the disposition of DC is the simplest part of the design of a drug targeting system. There are many methods by which the retention time of the drug carrier within the target tissue can be prolonged (described in other chapters of this book), and the assessment of the disposition of the DC by measuring its plasma or blood concentra- tion–time profile is relatively simple.

13.3.1.2 Delivery of the DC to the Target Site

The focus of research in the field of drug targeting is mainly on the selectivity of the DC for the target site (see other chapters in this book), undoubtedly because it is the essential process in drug targeting.

Although the delivery of the DC to the target site is a critical step in the efficacy of drug targeting, it is not necessarily the most critical step. In fact, each of the processes involved may be critical, and it is possible that in practice, given the sophisticated principles which are applied to increase the selectivity of DC for the target site, one of the other processes involved (see Sections 13.3.1.1. and 13.3.1.3.6) is responsible for the eventual failures of drug targeting systems.

The general principles of drug transport have been described in Sections 13.2.1.2 and 13.2.1.3.The rate of delivery of the DC to the target site is not critical in absolute terms. Even if the delivery rate is low, as long as the selectivity of the DC for the target site is high efficient targeting is assured. In this case, it will take more time to reach effective steady-state drug levels in the target organ and the duration of the drug effect will be prolonged. However, if the selectivity of DC for the target site is less than 100%, the slow delivery of the DC to the target site may decrease the efficacy of drug targeting [12].

If the rate of delivery of the DC to the target site is high compared to the release of the activated drug (see Section 13.3.1.3), accumulation of DC at the target site might result in a loss of DC from the target site either back into the blood, or via lymphatic drainage, and thus in a decrease of the efficiency of targeting. An example of this is the occurrence of retro-endo- cytosis in which the endocytosed DC is refluxed back into the systemic circulation before it has released the drug to be targeted [41]. The possibility that receptor-mediated endocytosis is a bidirectional rather than a unidirectional process is often not taken into account in drug targeting models. Yet, a secondary release of endocytosed material through reactivation of endocytotic vesicles in the plasma membrane has been demonstrated in various cell types. This process may be of quantitative importance, especially if trafficking to and association with lysosomes is slow or if proteolytic degradation is rate-limiting.

13.3.1.3 Release or Activation of D at the Target Site

The release of the drug from the drug–carrier conjugate or the formation of the active moiety from the pro-drug, is also reported to be of major concern in many research papers on drug targeting (see other chapters in this book). Although this process cannot be measured in vivo in most cases, valuable information can be obtained from in vitro measurements, for example, using cultured cell lines. The mechanism of release or activation may contribute to the selectivity of the target site, for example, in case of the formation of the phosphorylated active forms of nucleoside analogues by viral enzymes. In the case of release or activation by enzymatic processes, the rate of release or activation may be limited by saturation of the enzyme capacity.

In general, rapid release contributes to the efficiency of drug targeting, although in many cases the rate of release may not be critical as a result of rate limitation in the delivery of the DC to the target site. With respect to the selectivity of the target site for the release or activation in comparison to non-target sites, it can be stated that the more selective the delivery of the DC to the target site, the less important is the selectivity of the release or activation at the target site.

13.3.1.4 Removal of D from the Target Site

Little attention has been paid to this aspect in most research papers on drug targeting, despite several reports on the importance of removal of the released drug from the target site [6,12,42]. Most likely, this lack of attention is related to at least three factors: removal of drug from the target site (1) cannot be manipulated by the design of the drug targeting system, (2) is difficult to measure, and (3) may be the bottleneck of the efficiency of drug targeting strategies.

A striking example of the importance of the secondary removal of a drug from the target site are the multi-drug-resistance (MDR) processes of tumour cells. For instance antineoplastic drugs can be extruded efficiently by P-glycoprotein [43]. Although this example is only relevant for a limited category of drugs, it clearly demonstrates that the delivery of a drug into a cell does not guarantee an optimal retention time in the cell nor an optimal drug effect. Levy [42] assumed that in many cases drug elimination from the target site will be much more rapid that drug elimination from the body, as exemplified for intracerebroventricular injections of barbiturates.

Removal of active drug from the target site can occur by two different routes: direct removal by a local elimination process (typically a metabolic process, causing inactivation of the drug), or removal by the blood flow following diffusion out of the target cell. In both cases removal reduces the efficiency of drug targeting by lowering the concentration of the active drug at the target site. However, in case of local removal, the active drug is not transported to non-target tissues, and does not contribute to toxicity. In contrast, removal by the bloodstream causes an increase of concentration in the non-target tissue, thus lowering the targeting efficiency further. It may be noted that a high blood flow to the target tissue favours the delivery of the DC to the target site, but also increases the rate of removal of the active drug. Ideally, the active drug should be eliminated slowly from the target site, so that effec-

354 13 Pharmacokinetic/Pharmacodynamic Modelling in Drug Targeting

tive drug levels are maintained at the site after administration of relatively low maintenance doses of the drug targeting system. Obviously, a low, but substantial, rate of active drug removal is a prerequisite for controlling the intensity and duration of the drug effect.

13.3.1.5 Release of D at Non-target Sites

The release or activation of a drug at non-target sites is the undesirable counterpart of release at the target site (see Section 13.3.1.3), determining the selectivity of the release or activation of the drug, and thus of the drug targeting.

In principle, the release at non-target sites can be measured by the same methods as used for the target site (Section 13.3.1.3). In practice, however, measurement must be limited to one or more selected cell lines, which do not necessarily include all the non-target sites in which the drug may be released outside the intended target tissue.

13.3.1.6 Disposition of D

The distribution and elimination characteristics of the active drug have a profound influence on the efficiency of drug targeting. This topic is dealt with in Section 13.5.

13.3.2 Model of Hunt

Hunt et al. [6] extended the model of Stella and Himmelstein by adding two compartments, that is, a specific area where toxicity occurs, and an elimination compartment consisting of the liver and kidney (Figure 13.4). Their model may be regarded as a simplified physiologi- cally-based pharmacokinetic model (Section 13.2.4.2). It is assumed that the drug concentration in the blood or plasma (whichever is the reference fluid) exiting the compartments is a function of the concentrations within the corresponding compartments. This implies that tissue perfusion rather than permeability of the drug between blood and tissue is assumed to be the rate-limiting step of the transport between the central compartment and each of the other compartments (Section 13.2.1.3).

The model does not use a pharmacokinetic model for the drug–carrier conjugate. Instead, the release of the active drug is modelled as an input function in each of the four compartments: ‘blood’ (central compartment), ‘response’ (target site), ‘toxicity’, and ‘elimination’. The aim of their model was the derivation of the Therapeutic Availability (TA, Section 13.4.1) and the Drug Targeting Index (Section 13.4.2). For the particular derivations, several simplifications were made; for example, the aforementioned drug input replaces the model for DC. As a result, their simplified approach cannot be used for the prediction of the time course of the drug concentrations in the various compartments. This limitation does not affect the ability of the model to evaluate steady-state drug concentrations, which can also be used as an appropriate measure of the average concentration over a single dose interval after repeated administration. However, their analysis does not give insight into the time course of drug action, that is, the time needed to reach steady state, and the duration of the

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13.4.1 Therapeutic Availability (TA)

Hunt et al. [6] introduced the term Therapeutic Availability as the ratio of the fraction of the dose reaching the target sites, if the dose is administered as the drug–carrier conjugate, to the fraction of the dose which reaches the same sites if an equal dose of the active drug is administered intravenously, as formulated below.

where AUC denotes the area under the curve (normalized for dose) after a single dose or over one dosing interval in the case of steady state; Css denotes the average steady-state concentration; the subscript ‘target’ refers to the target site; DC refers to administration of the drug–carrier conjugate, and D to the intravenous administration of the active drug.

In contrast to the parameter Bioavailability (the fraction of the administered dose reaching the systemic circulation), the Therapeutic Availability may exceed a value of 1. A value exceeding 1 implies that the drug has been targeted successfully, the concentration at the target site being higher than that following a conventional intravenous administration of the same dose, and (see gueries) that a lower dose can be administered to reach the same concentration. Thus, an increase in TA is effectively equivalent to an increase in potency.

Boddy et al. [7] defined the Therapeutic Availability as the ratio of the rate of input of free drug divided by that of the drug carrier for the same degree of maximal therapeutic effect. When considering steady-state conditions, this definition is equivalent to that shown in Eq. 13.20 and 13.21.

13.4.2 Drug Targeting Index (DTI)

Hunt et al. [6] also introduced the Drug Targeting Index, which was defined as the ratio of drug delivered to the target and toxicity sites when the drug–carrier conjugate is administered, divided by the same ratio when the active drug is administered intravenously and is formulated as follows.

where AUC denotes the area under the curve (normalized for dose) after a single dose or over one dosing interval in the case of steady state; Css denotes the average steady-state concentration; subscripts ‘target’ and ‘tox’ refer to the target and toxicity sites, respectively; DC