Drug Targeting Organ-Specific Strategies

References 329

[33]Ikejima K, Enomoto N, Seabra V, Ikejima A, Brenner DA, Thurman RG, Am. J. Physiol. 1999, 276, G591–G598.

[34]Meijer DKF, Keulemans K, Mulder GJ, Methods Enzymol. 1981, 77, 81–94.

[35]Smith P, Krack G, McKee R, Johnson D, Gandolfi A, Hruby V, Krumdieck C, Brendel K, In Vitro Cell Dev. Biol. 1986, 22, 706–712.

[36]Parrish AR, Gandolfi AJ, Brendel K, Life Sci. 1995, 57, 1887–1901.

[37]Price RJ, Ball SE, Renwick AB, Barton PT, Beamand JA, Lake BG, Xenobiotica 1998, 28, 361–371.

[38]Olinga P, Merema MT, Meijer DKF, Slooff MJH, Groothuis GMM, ATLA 1993, 21, 466–468.

[39]Ekins S, Murray GI, Burke MD, Williams JA, Marchant NC, Hawksworth GM, Drug Metab. Dispos. 1995, 23, 1274–1279.

[40]de Kanter R, Koster HJ, ATLA 1995, 23, 653–665.

[41]Leeman W, van de Gevel I, Rutten A, Toxicol. In Vitro 1995, 9, 291–298.

[42]Fisher RL, Putnam CW, Koep LJ, Sipes IG, Gandolfi AJ, Brendel K, Cryobiology 1991, 28, 131–142.

[43]Fisher RL, Shaughnessy RP, Jenkins PM, Austin ML, Roth GL, Gandolfi AJ, Brendel K, Toxicol. Methods 1995, 5, 99–113.

[44]Fisher RL, Hasal SJ, Sanuik JT, Gandolfi AJ, Brendel K, Toxicol. Methods 1995, 5, 115–130.

[45]Price RJ, Renwick AB, Barton PT, Houston JB, Lake BG, ATLA 1998, 26, 541–548.

[46]Brendel K, Gandolfi A, Krumdieck C, Smith P, TIPS 1987, 8, 11–15.

[47]Smith PF, McKee R, Gandolfi AJ, Krumdieck CL, Fisher R, Brendel K, Precision Cut Liver Slices: A New In Vitro Tool In Toxicology. Telford Press, Caldwell, NJ, 1989.

[48]Bach PH, Vickers AEM, Fisher R, Baumann A, Brittebo E, Carlile DJ, Koster HJ, Lake BG, Salmon F, Sawyer TW, Skibinski G, ATLA 1996, 24, 893–923.

[49]Hart A, Mattheyse J, Balinsky JB, In Vitro 1983, 19, 841–852.

[50]Goethals F, Deboyser D, Lefebvre V, de Coster I, Roberfroid M, Toxicol. In Vitro 1990, 4, 435–438.

[51]Dogterom P, Drug Metab. Dispos. 1993, 21, 699–704.

[52]Olinga P, Groen K, Hof IH, de Kanter R, Koster HJ, Leeman WR, Rutten AAJJL, van Twillert K, Groothuis GMM, J. Pharm. Toxicol. Methods 1997, 38, 59–69.

[53]Kwekkeboom J, Princen H, Van Voorthuizen EM, Meijer P, Kempen H, Biochem. Biophys. Res. Commun. 1989, 162, 619–625.

[54]Paine AJ, Chem. Biol. Interact. 1991, 74, 1–31.

[55]Padgham CR, Boyle CC, Wang XJ, Raleigh SM, Wright MC, Paine AJ, Biochem. Biophys. Res. Commun. 1993, 197, 599–605.

[56]Rogiers V, In: Human Cells In In Vitro Pharmaco-Toxicology (Eds Rogiers V, Sonck W, Shephard E, Vercruysse A), pp. 77–115. VUB Press, Brussels, 1993.

[57]Miyazaki M, Handa Y, Oda M, Yabe T, Miyano K, Sato J, Exp. Cell Res. 1985, 159, 176–190.

[58]Dich J, Vind C, Grunnet N, Hepatology 1988, 8, 39–45.

[59]Jefferson DM, Clayton DF, Darnell Jr J, Reid LM, Mol. Cell Biol. 1984, 4, 1929–1934.

[60]Dunn JC, Tompkins RG, Yarmush ML, J. Cell Biol. 1992, 116, 1043–1053.

[61]Koebe HG, Pahernik S, Eyer P, Schildberg FW, Xenobiotica 1994, 24, 95–107.

[62]Saad B, Scholl FA, Thomas H, Schawalder H, Streit V, Waechter F, Maier P, Eur. J. Biochem. 1993, 213, 805–814.

[63]Guillouzo A, Morel F, Fardel O, Meunier B, Toxicology 1993, 82, 209–219.

[64]Connors S, Rankin DR, Gandolfi AJ, Krumdieck CL, Koep LJ, Brendel K, Toxicology 1990, 61, 171–184.

[65]Connors MS, Larrauri A, Dannecker R, Nufer R, Brendel K, Vickers AEM, Xenobiotica 1996, 26, 133–141.

[66]Vickers AEM, Fischer V, Connors S, Fisher RL, Baldeck JP, Maurer G, Brendel K, Drug Metab. Dispos. 1992, 20, 802–809.

[67]Berridge MV, Tan AS, Arch. Biochem. Biophys. 1993, 303, 474–482.

[68]Hashemi E, Dobrota M, Till C, Ioannides C, Xenobiotica 1999, 29, 11–25.

[69]Olinga P, Merema MT, Sandker GW, Slooff MJH, Meijer DKF, Groothuis GMM, In: The World

Congress on Alternatives and Animal Use in The Life Sciences: Education, Research, Testing (Eds Goldberg AM, Van Zutphen LFM), pp. 197–203. Liebert, New York, 1995.

[70]Fisher RL, Hasal SJ, Sanuik JT, Scott KS, Gandolfi AJ, Brendel K, Cryobiology 1993, 30, 250–261.

[71]Lake BG, Charzat C, Tredger JM, Renwick AB, Beamand JA, Price RJ, Xenobiotica 1996, 26, 297–306.

33012 Use of Human Tissue Slices in Drug Targeting Research

[72]Leeman WR, van de Gevel IA, Rutten AAJJL, Toxicol. In Vitro 1995, 9, 291–298.

[73]de Kanter R, Olinga P, de Jager MH, Merema MT, Meijer DKF, Groothuis GMM, Toxicol. In Vitro 1999, 13, 737–744.

[74]de Kanter R, Olinga P, Hof I, de Jager M, Verwillegen WA, Slooff MJ, Koster HJ, Meijer DK, Groothuis GM, Xenobiotica 1998, 28, 225–234.

[75]Olinga P, Merema M, Hof IH, de Jong KP, Slooff MJH, Meijer DKF, Groothuis GMM, Drug Metab. Dispos. 1998, 26, 5–11.

[76]Valentovic MA, Ball JG, Anestis DK, Rankin GO, Toxicol. In Vitro 1995, 9, 75–81.

[77]Miller MG, Beyer J, Hall GL, Degraffenried LA, Adams PE, Toxicol. Appl. Pharmacol. 1993, 122, 108–116.

[78]Olinga P, Merema MT, Hof IH, De Jager MH, De Jong KP, Slooff MJH, Meijer DKF, Groothuis GMM, Xenobiotica 1998, 28, 349–360.

[79]Jansen RW, Olinga P, Harms G, Meijer DKF, Pharm. Res. 1993, 10, 1611–1614.

[80]Sutto F, Brault A, Lepage R, Huet P-M, J. Hepatol. 1994, 20, 611–616.

[81]Olinga P, Hof IH, Smit M, de Jager MH, Nijenhuis E, Slooff MJH, Meijer DKF, Groothuis GMM, J. Pharm. Toxicol. Methods, 2001 (in press).

[82]Oude Elferink RPJ, Meijer DKF, Kuipers F, Jansen PLM, Groen AK, Groothuis GMM, Biochim. Biophys. Acta 1995, 1241, 215–268.

[83]Tiribelli C, Reichen J, Meijer DKF, J. Hepatol. 1996, 24, 11–34.

[84]Meijer DKF, In: Handbook of Physiology. The Gastrointestinal System, Vol. III (Eds Schulz J, Forte G, Rauner BB), pp. 717–758. Oxford University Press, New York, 1989.

[85]Meijer DKF, Ziegler K, In: Biological Barriers to Protein Delivery (Eds Audus KL, Raub TJ), pp. 339–407. Plenum Press, New York and London, 1993.

[86]Jansen RW, Kruijt JK, van Berkel TJ, Meijer DK, Hepatology 1993, 18, 146–152.

[87]Olinga P, Merema MT, Hof IH, Slooff MJH, Proost JH, Meijer DKF, Groothuis GMM, J. Pharmacol. Exp. Ther. 1998, 285, 506–510.

[88]Sandker GW, Weert B, Olinga P, Wolters H, Slooff MJH, Meijer DKF, Groothuis GMM,

Biochem. Pharmacol. 1994, 47, 2193–2200.

[89]Schanker LS, Solomon HM, Am. J. Physiol. 1963, 204, 829–832.

[90]Hedman A, Meijer DKF, J. Pharm. Sci. 1998, 87, 457–461.

[91]Hedman A, Meijer DK, J. Hepatol. 1998, 28, 240–249.

[92]Olinga P, de Kanter R, Hof IH, de Jager MH, Slooff MJH, Koster HJ, Meijer DKF, Groothuis GMM, Hepatology 1996, 24, 468A.

[93]Thompson MB, Davis DG, Morris RW, J. Lipid Res. 1993, 34, 553–561.

[94]Beljaars L, Molema G, Weert B, Bonnema H, Olinga P, Groothuis GMM, Meijer DKF, Poelstra K, Hepatology 1999, 29, 1486–1493.

[95]Beljaars L, Molema G, Schuppan D, Geerts A, De Bleser PJ, Weert B, Meijer DKF, Poelstra K, J. Biol. Chem. 2000, 275, 12743–12751.

[96]Aono K, Isobe K, Kiuchi K, Fan ZH, Ito M, Takeuchi A, Miyachi M, Nakashima I, Nimura Y, J. Cell Biochem. 1997, 65, 349–358.

[97]Van Bossuyt H, De Zanger RB, Wisse E, J. Hepatol. 1988, 7, 325–337.

[98]Billiar TR, Curran RD, Ferrari FK, Williams DL, Simmons RL, J. Surg. Res. 1990, 48, 349–353.

[99]Vos TA, Gouw AS, Klok PA, Havinga R, van Goor H, Huitema S, Roelofsen H, Kuipers F, Jansen PL, Moshage H, Gastroenterology 1997, 113, 1323–1333.

[100]Nussler AK, Di Silvio M, Liu ZZ, Geller DA, Freeswick P, Dorko K, Bartoli F, Billiar TR, Hepatology 1995, 21, 1552–1560.

[101]Luster MI, Germolec DR, Yoshida T, Kayama F, Thompson M, Hepatology 1994, 19, 480–488.

[102]Sultan K, Hartung J, Bade EG, FEBS Lett. 1996, 394, 51–54.

[103]Melgert BN, Olinga P, Jack VK, Molema G, Meijer DKF, Poelstra K, J. Hepatol. 2000, 32, 603–611.

[104]Olinga P, Merema MT, de Jager MH, Slooff MJH, Limburg PC, Bijzet J, Poelstra K, Meijer DKF, Groothuis GMM, Hepatology 1998, 28, 184A.

[105]Stijntjes GJ, Commandeur JN, te Koppele JM, McGuinness S, Gandolfi AJ, Vermeulen NP, Toxicology 1993, 79, 67–79.

[106]Vickers AEM, Fisher RL, Brendel K, Guertler J, Dannecker R, Keller B, Fischer V, Drug Metab. Dispos. 1995, 23, 327–333.

[107]Foulkes EC, Proc. Soc. Exp. Biol. Med. 1996, 211, 155–162.

[108]Ruegg CE, Gandolfi AJ, Nagle RB, Krumdieck CL, Brendel K, J. Pharmacol. Methods 1987, 17, 111–123.

References 331

[109]Dutt A, Priebe TS, Teeter LD, Kuo MT, Nelson JA, J. Pharmacol. Exp. Ther. 1992, 261, 1222–1230.

[110]Drieman JC, Thijssen HH, Struyker-Boudier HA, Br. J. Pharmacol. 1993, 108, 204-208.

[111]Rump LC, Schwertfeger E, Schaible U, Schuster MJ, Frankenschmidt A, Schollmeyer P, Eur. J. Clin. Pharmacol. 1993, 44 (Suppl. 1), S47–S49.

[112]Stubenitsky BM, Ametani M, Danielewicz R, Southard JH, Belzer FO, Transplant. Int. 1995, 8, 293–297.

[113]Gonzalez-Flecha B, Evelson P, Sterin-Speziale N, Boveris A, Biochim. Biophys. Acta 1993, 1157, 155–161.

[114]Hoet PH, Lewis CP, Demedts M, Nemery B, Biochem. Pharmacol. 1994, 48, 517–524.

[115]Placke ME, Fisher GL, Toxicol. Appl. Pharmacol. 1987, 90, 284–298.

[116]Price RJ, Renwick AB, Wield PT, Beamand JA, Lake BG, Arch. Toxicol. 1995, 69, 405–409.

[117]Price RJ, Renwick AB, Beamand JA, Esclangon F, Wield PT, Walters DG , Lake BG, Food Chem. Toxicol. 1995, 33, 233–237.

[118]Fisher RL, Smith MS, Hasal SJ, Hasal KS, Gandolfi AJ, Brendel K, Hum. Exp. Toxicol. 1994, 13, 466–471.

Drug Targeting Organ-Specific Strategies. Edited by G. Molema, D. K. F. Meijer Copyright © 2001 Wiley-VCH Verlag GmbH ISBNs: 3-527-29989-0 (Hardcover); 3-527-60006-X (Electronic)

13Pharmacokinetic/Pharmacodynamic Modelling in Drug Targeting

Johannes H. Proost

13.1 Introduction

13.1.1 Drug Targeting and Effectiveness: The Role of Pharmacokinetics

The key issue in drug targeting is the improvement of the effectiveness of the intended drug therapy in comparison to conventional drug administration. In the present context, effectiveness is defined as the net benefit of drug administration, that is, the balance of the therapeutic drug effect and any harmful effect, including minor and major side-effects and toxicity. For the sake of simplicity, any harmful effect of the drug will be referred to as toxicity throughout this chapter. Also, effectiveness may be defined in terms of the increased apparent potency and/or therapeutic effect of the administered drug. A drug targeting system produces a larger and/or more prolonged pharmacologic effect than an equimolar dose of the free drug, and a lower single dose and/or dosing rate is needed to reach the same effect.

To demonstrate an improvement in effectiveness, relevant and reliable measures of the effect of drug administration should be available. Generally speaking, the best measure of the effectiveness of drug therapy should be a measure of the ultimate goal: the benefit to the patient. Although this approach is conceptually sound and logical, in practice the leap between the experimental development of drug targeting preparations and the ultimate benefit to the patient is extremely large. First, the experiments in the early development phase of a drug are usually carried out in small laboratory animals. Second, the pathogenesis in these animals is, in general, different from that in the patient for whom the therapy is intended. Third, the measures of effectiveness and toxicity may differ between laboratory animals and man. In laboratory animals the range of potential parameters or end-points is practically not limited, since the complete animal can be analysed after sacrifice. On the other hand, the eventual goal of the therapy, efficacy in the patient, cannot be readily assessed in objective terms.

Despite limitations, the measurement of the effectiveness of drug therapy in laboratory animals, for example, by the reduction in size of a solid tumour or decreased levels of surrogate tumour markers, is indispensable for the development of drug targeting preparations. However, during rational drug development it is not sufficient to ascertain that one drug preparation is more effective than another, it is important to find out the reasons why this is the case. This will enable the introduction of further improvements in the process of optimizing the design of the drug preparation. In the understanding of the effectiveness of drug therapy, pharmacokinetics (relating drug administration to drug concentration at the site of action) and pharmacodynamics (relating drug concentration to drug effect) are essential elements [1,2]. It should be stressed that PK and PK/PD modelling (Section 13.2) are essential

334 13 Pharmacokinetic/Pharmacodynamic Modelling in Drug Targeting

tools in the evaluation of the effectiveness of any dosing strategy, including drug targeting. In some cases, it is sufficient to measure the drug concentration in the target tissue, if the relationship between concentration and drug effect is relatively simple (Section 13.2.5). In other case, however, the complex relationship between concentration and effect, for example due to dependence on time, dose, rate of drug administration, drug concentration, or rate of drug concentration change, requires the application of PK/PD modelling [3]. A detailed review of the pharmacodynamic aspects of drug delivery has been published recently [4].

A second, and equally important, application of pharmacokinetics in the field of drug targeting is the evaluation of the potentials and limitations in the drug targeting approach in relation to the properties of the drug and the drug–carrier conjugate. The theoretical framework designed by Stella and Himmelstein [5], and explored further by Hunt et al. [6], Boddy et al. [7], and others, is a useful tool to investigate the desirable properties of the drug and the drug–carrier conjugate, including the selection of therapeutic agents to be targeted by the chosen drug carrier.

Finally, pharmacokinetic and pharmacokinetic/pharmacodynamic modelling can be used for the purpose of prediction of the concentration–time profile of the drug and drug–carrier conjugate after repeated administration from single dose data, as well as for the prediction of the dose needed to maintain the concentration at the target site within a therapeutic window.

13.1.2 Pro-drugs and Drug–Carrier Conjugates

From the point of view of pharmacokinetics, there is no principal difference between prodrugs and drug–carrier conjugates [5,6,8]. In both cases the active drug is administered as a part of a molecule that has pharmacokinetic and pharmacodynamic properties that are usually largely different from that of the active moiety (‘drug’). The kinetics of pro-drugs which are converted in the body to the active form by conjugation (for example, the formation of the phosphorylated active forms of nucleoside analogues) can be modelled using the same approach. In general, however, the pharmacokinetic properties of pro-drugs and drug–carri- er conjugates are quite different due to their different physicochemical properties, for example, with respect to their molecular weights, hydrophilic/hydrophobic character or exposed functional groups, among other structural features. The pharmacokinetic properties of prodrugs and drug–carrier conjugates can be further optimized during the development phase of a product, the objective of which is to improve the pharmacokinetic properties by conjugation of the compounds to targeting devices which have a wide variety of physicochemical properties, without affecting the intrinsic potency of the coupled agent. In contrast, the pharmacokinetic properties of the active drug itself cannot usually be modified without affecting its pharmacologic profile. However, there are examples in which novel compounds were designed with improved pharmacokinetic properties without loss of potency or changes in the spectrum of activity.

Drug targeting technology may increase the drug concentration at the target site, may decrease the drug concentration at the sites where toxicity may occur, may prolong the retention time at the target site, and thus may improve the efficacy of drug administration.

For the sake of simplicity, in this chapter it is assumed that both the drug–carrier conjugate and the drug carrier itself, or the pro-drug, do not exert any pharmacologic or toxicologic ef-

fect, and that any therapeutic or toxic effect is due to the released or activated drug.This does not take into account the possibility of using intrinsically active carriers, which not only deliver the coupled drug to the appropriate site, but also contribute to the overall therapeutic effect, an approach known as ‘dual targeting’ [9].

13.1.3 Scope of this Chapter

The aim of this chapter is to provide an overview of the application of PK and PK/PD modelling and analysis to the field of drug targeting research. For those readers not familiar with the general principles of pharmacokinetics and pharmacodynamics, modelling, simulation, and data analysis, these topics are described in some detail in Section 13.2. These methods can be used for advanced PK and PK/PD modelling and analysis, as well as for conventional analysis of plasma concentration–time profiles of drugs, drug carriers, and drug–carrier conjugates. Conventional pharmacokinetic approaches, including descriptive methods for the evaluation of the concentration or concentration ratio profiles in different tissues, are not dealt with in this chapter.

The particular models used in drug targeting research are dealt with in Section 13.3, and quantitative measures of the effectiveness of drug targeting are described in Section 13.4, followed by a discussion relating to their application in Section 13.5.

Drug targeting by direct regional drug administration, controlled drug release, and pharmacokinetic modelling and analysis of in vitro experimental data, are outside the scope of this chapter. For the sake of completeness, some references to relevant papers in these areas are given in Section 13.6. After a short section (13.7) on software for pharmacokinetic modelling and data analysis, the perspectives of the application of PK and PK/PD modelling are discussed (Section 13.8).

13.2Pharmacokinetics and Pharmacodynamics, Modelling, Simulation, and Data Analysis

13.2.1 Pharmacokinetics

13.2.1.1 Pharmacokinetic Processes

‘Pharmacokinetics’ (PK) can be defined as the study of the mechanisms and kinetics of drug disposition in the body (acronym ‘LADME’), and includes the following:

•Liberation of drug from the dosage form. For example, the dissolution of drug from a tablet;

•Absorption, the transport from the site of administration to the general circulation. For example the transport of a drug from the gastrointestinal lumen, via the portal vein and the liver to the central venous blood pool;

336 13 Pharmacokinetic/Pharmacodynamic Modelling in Drug Targeting

•Distribution of the drug throughout the body, characterized by the volume of distribution (V) which is defined as the amount of drug in the body divided by the drug concentration in plasma;

•Metabolism, the biotransformation of the drug into metabolites, which may be inert, active, or toxic;

•Excretion of the intact drug, and its metabolites, into urine and faeces.

The term ‘elimination’ is used as a common term for the disappearance of the drug from the body by either metabolism or excretion. The term ‘clearance’ (CL) is used as a measure of the collective capacity of the eliminating organs to remove a certain drug, and is defined as the rate of drug elimination (amount/time) divided by the drug concentration in plasma, and indicates the volume of plasma that is cleared from the drug per unit of time (dimension volume/time). The elimination rate constant (k) is defined as the rate of drug elimination (amount/time) by the amount of drug in the body, and is equal to the clearance divided by volume of distribution (CL/V). The (elimination) half-life (t1/2) is the time taken for the plasma concentration, as well as for the amount of drug in the body, to fall by 50%, and is approximately equal to 0.7/k [10].

In the field of drug targeting, the LADME processes refer to both the drug–carrier conjugate and the active drug. Liberation would refer to the release of the drug from a drug–carri- er conjugate or the conversion of a pro-drug to the active moiety.

13.2.1.2 Transport Mechanisms

The transport mechanisms that operate in distribution and elimination processes of drugs, drug–carrier conjugates and pro-drugs include convective transport (for example, by blood flow), passive diffusion, facilitated diffusion and active transport by carrier proteins, and, in the case of macromolecules, endocytosis. The kinetics of the particular transport processes depend on the mechanism involved. For example, convective transport is governed by fluid flow and passive diffusion is governed by the concentration gradient, whereas facilitated diffusion, active transport and endocytosis obey saturable Michaelis–Menten kinetics.

13.2.1.3 Perfusion and Permeability

Both distribution of the drug within the body and elimination from the body require two sequential steps: the transport of the drug by blood flow to the organ or tissue (perfusion), and transport from the capillary to the tissue, and then to receptors on or in the cells of the tissue. The latter processes are governed by the permeability of the barriers between the capillary lumen and the receptor site, and may imply passive or carrier-mediated membrane passage. If there are hardly any barriers for the transport to the tissue, that is, if permeability is high, the supply of drug by the blood flow, that is, the perfusion of the organ or tissue may become the rate-limiting step of transport. In this case a large fraction of the drug present in blood is transported to the tissue, so the extraction ratio is high. On the other hand, if the perfusion is high, and the barriers for the transport within the tissue are considerable, permeability, may

become the rate-limiting step of transport. In this case a small fraction of the drug present in blood is transported to the tissue, and the extraction ratio is low. So, depending on the ratelimiting step, the net transport may be perfusion-limited or permeability-limited. In any case, the upper limit to the rate of delivery is provided by the product of blood flow and the blood concentration of the drug.

13.2.1.4 Plasma Protein Binding and Tissue Binding

Many drugs are partly bound to plasma proteins, primarily albumin for acidic drugs and α1- acid-glycoprotein for basic drugs, and to various macromolecular structures in the tissues [10].An extensive discussion of the influence of plasma protein binding and tissue binding on pharmacokinetics is beyond the scope of this chapter. However, it should be noted that the binding of drugs has a major influence on pharmacokinetic and PK/PD modelling [11]. The unbound drug concentration is the driving force for transport within the body, including distribution, metabolism, and excretion, and for interaction with receptors, and thus for the pharmacologic effect. Unfortunately, the majority of PK and PK/PD models do not take into account plasma protein binding and tissue binding, and describe only the total drug concentration. It should be noted that this approach may lead to erroneous interpretations of PK and PK/PD.

13.2.2 Pharmacodynamics

‘Pharmacodynamics’ (PD) can be defined as the study of the mechanisms of drug action, including the relationship between drug concentration at the site of action and the drug effect. In many cases drug action is the result of the interaction of the drug and a receptor. However, many PD models (Section 13.2.5) do not take into account the precise mechanism of action, and are applicable to both receptor-mediated drug effects and effects initiated by other mechanisms.

The effectiveness of drug targeting should be evaluated by taking into account not only pharmacokinetic aspects, but also the pharmacodynamic aspects. The latter include the con- centration–effect relationship in the target tissue and at the sites where toxicity may occur [7,12]. The therapeutic effect of the drug and its toxic effect may be different with regard to their mechanisms, and hence their concentration–effect relationship may also be different, both qualitatively (different PD models) and quantitatively (different model parameters).

13.2.3 Model and Modelling

The relationship between drug administration and the drug concentration at the site of action (PK) and the relationship between drug concentration at the site of action and the drug effect (PD), may be quantified by mathematical models describing the PK and PD processes involved in the drug activity profile. Combining PK and PD models allows the quantification of the relationship between drug administration and drug action (PK/PD models).

338 13 Pharmacokinetic/Pharmacodynamic Modelling in Drug Targeting

PK models (Section 13.2.4), PD models (Section 13.2.5), and PK/PD models (Section 13.2.6) can be used in two different ways, that is, in simulations (Section 13.2.7) and in data analysis (Section 13.2.8). Simulations can be performed if the model structure and its underlying parameter values are known. In fact, for any arbitrary dose or dosing schedule the drug concentration profile in each part of the model can be calculated. The quantitative measures of the effectiveness of drug targeting (Section 13.4) can also be evaluated. If actual measurements have been performed in in-vivo experiments in laboratory animals or man, the relevant model structure and its parameter values can be assessed by analysis of plasma disappearance curves, excretion rate profiles, tissue concentration data, and so forth (Section 13.2.8).

13.2.4 Pharmacokinetic Models

There are many types of PK models, which can be divided in two classes.

13.2.4.1 Compartmental Models

These are relatively simple models describing drug transport between compartments which are not necessarily specified in a physiological or anatomical context. The quantity of drug in each compartment is assumed to be evenly distributed throughout the volume of the compartment, and the rates of drug elimination and transport to other compartments are assumed to be proportional to the drug concentration in the original compartment. In pharmacokinetic literature these compartments are called well-stirred compartments [10,13,14].

Figure 13.1. Compartmental model based on clearance and volume (Section 13.2.4.1). The drug is administered at a rate R1 into the central compartment, which is characterized by a volume of distribution V1. The drug is transported to and from the peripheral compartment with intercompartmental clearance CL12 and CL21, respectively (usually it is assumed that there is no net transport between the two compartments if the concentrations in both compartments are equal; in this case CL21 = CL12). The peripheral compartment is characterized by a volume of distribution V2. Elimination may take place from both compartments and is characterized by clearance CL10 and CL20, respectively.

These models have relatively few parameters, and the parameters have a limited physiological or anatomical meaning. For example, a compartmental volume relates the quantity of the drug to its concentration in a compartment, and does not refer to an anatomicallyor physi- ologically-defined area of the body.

The differential equations defining a compartmental model are derived from logical and simple principles. As an example, consider a model with two compartments as depicted in Figure 13.1.The change in the quantity of a drug in a compartment is the net result of the rate of entry of the drug, that is, the sum of the amount of drug administered to the compartment (for example, an intravenous infusion) or formed within the compartment (for example, release from a drug–carrier conjugate) and the rate of transport from other compartments, reduced by the rate of exit, that is, the sum of the rates of removal from the compartment by elimination or by transport to other compartments.

The rate of transport from a certain compartment is governed by the concentration in that compartment and a proportionality constant, denoted (elimination or distribution) clearance (dimension: volume time-1) as formulated below.

where V1 is the apparent volume of compartment 1, C1 is the drug concentration in compartment 1, R1 is the rate of drug administration or drug release in compartment 1, CL12 is the distribution clearance from compartment 1 to compartment 2, and CL10 is the elimination clearance from compartment 1.

Usually, it is assumed that there is no net transport between two compartments if the concentrations in both compartments are equal; in this specific case CL21 = CL12.

Similar equations can be written for compartment 2. The same principle can be applied to any compartmental model, irrespective of its complexity.

R1

Figure 13.2. Compartmental model based on rate constants (Section 13.2.4.1). The drug is administered at a rate R1 into the central compartment, which is characterized by a volume of distribution V1. The drug is transported to and from the peripheral compartment with rate constants k12 and k21, respectively. The peripheral compartment is characterized by a volume of distribution V2 (usually it is assumed that there is no net transport between the two compartments if the concentrations in both compartments are equal; in this case k21 · V2 = k12 · V1). Elimination may take place from both compartments and is characterized by rate constants k10 and k20, respectively.