### INTRODUCTION

### PHARMACOKINETICS

### PHARMACODYNAMICS

*E*

_{max}model (the Hill equation [7,10], Eq. 1):

*E*

_{max}is the maximum effect,

*EC*

_{50}is the concentration of the drug producing half of

*E*

_{max}and n is the so-called steepness factor (n does not necessarily have a direct biological meaning, but it determines the slope of the curve. In the ordinary

*E*

_{max}model, n is equal to 1). This model can be used extensively in other areas; for example, in the receptor theory,

*EC*

_{50}reflects the potency of the drug in the system (the sensitivity of the organ or tissue to the drug) and

*E*

_{max}is the efficacy of the drug. If n is less than 1, the curve becomes hyperbolic, implying active metabolites or multiple receptor sites [5,7]. Fig. 2 presents the excitatory sigmoid

*E*

_{max}model including the baseline effect (

*E*

_{0}), and the equation is functionally described as follows (Eq. 2):

### KINETIC-DYNAMIC (PK-PD) MODELING

### WHAT IS HYSTERESIS IN THE PK-PD RELATIONSHIP?

### EFFECT COMPARTMENT LINK MODEL

*k*, defined as the loss of drug from the effect compartment, is not directed toward any of the PK compartments, implying excretion from the body. Therefore,

_{e0}*k*(called ‘equilibration rate constant’) determines the concentration equilibrium between the plasma and effect compartment (the larger

_{e0}*k*, the faster the equilibrium, so the effect of the drug is faster) [2,3,5-7]. The relationship between the concentration at the effect compartment (

_{e0}*C*) and the plasma concentration (

_{e}*C*) is expressed by the differential equation as below Eq. 3:

_{p}### SEMI-COMPARTMENTAL MODEL

*k*are estimated, the semi-compartmental model does not require PK parameters (compartmental PK modeling) to estimate PD parameters and

_{e0}*k*[7,15] (In ‘NONMEM’, a computer program for modeling, the effect compartment link model is named ‘sequential PK-PD modeling’ and the semicompartmental model is named ‘direct PD fit’).

_{e0}*C*) obtained by assuming a piecewise linear PK model is expressed as Eq. 5.

_{p}*C*-

_{p}*C*relationship and Eq. 5 yields the solution for concentration at the effect site (

_{e}*C*) given as Eq. 6:

_{e}*C*) is expressed in exponential form as Eq. 7, assuming a piecewise log-linear PK model.

_{p}