James A Uchizono

Thomas J. Long School of Pharmacy and Health Sciences University of the Pacific Stockton, California

1.1 Introduction 2

1.2 Pharmacokinetics and Pharmacodynamics 3

1.3 LADME Scheme and Meaning of Pharmacokinetic Parameters 4

1.3.1 Maximum concentration, time to maximum 4 concentration, and first-order absorption rate constant

1.3.2 Bioavailability F 5

1.3.3 Volume of distribution Vd 6

1.3.4 Clearance Cl 6

1.3.5 First-order elimination rate constant K

and half-life t1/2 6

1.4 Pharmacokinetics and Classes of Models 7

1.4.1 Linear versus nonlinear pharmacokinetics 8

1.4.2 Time- and state-varying pharmacokinetics and pharmacodynamics 9

1.5 Pharmacokinetics:Input, Disposition, and Convolution 11

1.5.1 Input 11

1.5.2 Disposition 13

1.5.3 Convolution of input and disposition 15

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1.6 Compartmental Pharmacokinetic Modeling 16

1.6.1 Single-dose input systems 16

1.6.2 Multiple-dosing input systems and steady-state kinetics. 25

1.7 Applications of Pharmacokinetics in the Design of Controlled Release Delivery Systems 29

1.7.1 Design challenges for controlled release delivery systems 29

1.7.2 Limitations of using pharmacokinetics only to design controlled release delivery systems 32

1.7.3 Examples of pharmacokinetic/pharmacodynamic considerations in controlled release delivery systems design 33

1.8 Conclusions 35 References 35

1.1 Introduction

In biopharmaceutics, more specifically drug delivery, pharmaceutical scientists generally are faced with an engineering problem: develop drug delivery systems that hit a desired target. The target in pharmacokinetics is generally a plasma/blood drug concentration that lies between the minimum effect concentration (MEC) and minimum toxic concentration (MTC) (Fig. 1.1).

In 1937, Teorell's two articles,1a,1b "Kinetics of Distribution of Substances Administered to the Body," spawned the birth of pharmacokinetics. Thus his work launched an entire area of science that deals


Figure 1.1 Therapeutic window.


Figure 1.1 Therapeutic window.

with the quantitative aspects that undergird the kinetic foundation of controlled release delivery systems: designing a delivery device or system that achieves a desired drug plasma concentration Cp or a desired concentration profile. To be effective clinically but not toxic, the desired steady-state Cp must be greater than the MEC and less than the MTC. This desired or target steady-state Cp may be achieved by using a variety of dosage forms and delivery/dosage strategies.

1.2 Pharmacokinetics and Pharmacodynamics

Pharmacokinetics and pharmacodynamics provide the time-course dynamics between drug concentration and desired target effect/outcome necessary in the development of optimal drug delivery strategies. The basic premise is that if one is able to model the dynamics governing the translation of drug input into drug concentration in the plasma Cp or drug effect accurately, one potentially can design input drug delivery devices or strategies that maximize the effectiveness of drug therapy while simultaneously minimizing adverse effects. Figure 1.2 shows the relationship between the three main processes that convert the dose into an effect. The pharmacokinetic model translates the dose into a plasma concentration Cp; the link model maps Cp into the drug concentration at the effect site Ce; finally, the pharmacodynamic model converts Ce into the measured effect. For most drugs, Cp is in one-to-one correspondence with the corresponding effect; therefore, most delivery devices can focus primarily on achieving a desired steady-state drug plasma concentration Cp,ss. Therefore, in this chapter the focus will be on the use of pharmacokinetics to guide the design of controlled release delivery systems that achieve their intended concentration. Some issues arising owing to Cp versus effect nonstationarity (either time- or state-varying pharmacokinetics or pharmacodynamics) will be discussed in the section entitled, "Limitations of Using Pharmacokinetics Only to Design Controlled Release Delivery Systems."

Pharmacokinetic model (dose

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