Models have been developed to simplify conceptualization of the many processes that take place in the interaction between an organism and a chemical substance. Pharmacokinetic modelling may be performed either by noncompartmental or
compartmental methods.
Multi-compartment models provide the best approximations to reality; however, the complexity involved in adding parameters with that modelling approach means that
monocompartmental models and above all
two compartmental models are the most-frequently used. The model outputs for a drug can be used in industry (for example, in calculating
bioequivalence when designing generic drugs) or in the clinical application of pharmacokinetic concepts. Clinical pharmacokinetics provides many performance guidelines for effective and efficient use of drugs for human-health professionals and in
veterinary medicine. Models generally take the form of
mathematical formulas that have a corresponding
graphical representation. The use of these models allows an understanding of the characteristics of a
molecule, as well as how a particular drug will behave given information regarding some of its basic characteristics such as its
acid dissociation constant (pKa),
bioavailability and
solubility, absorption capacity and distribution in the organism. A variety of analysis techniques may be used to develop models, such as
nonlinear regression or curve stripping.
Noncompartmental analysis Noncompartmental methods estimate PK parameters directly from a table of concentration-time measurements. Noncompartmental methods are versatile in that they do not assume any specific model and generally produce accurate results acceptable for bioequivalence studies. Total drug exposure is most often estimated by area under the curve (AUC) methods, with the
trapezoidal rule (
numerical integration) the most common method. Due to the dependence on the length of
x in the trapezoidal rule, the area estimation is highly dependent on the blood/plasma sampling schedule. That is, the closer time points are, the closer the trapezoids reflect the actual shape of the concentration-time curve. The number of time points available in order to perform a successful NCA analysis should be enough to cover the absorption, distribution and elimination phase to accurately characterize the drug. Beyond AUC exposure measures, parameters such as Cmax (maximum concentration), Tmax (time to maximum concentration), CL and Vd can also be reported using NCA methods.
Compartmental analysis Compartment models methods estimate the concentration-time graph by modeling it as a system of differential equations. These models are based on a consideration of an organism as a number of related
compartments. Both single compartment and
multi-compartment models are in use. PK compartmental models are often similar to kinetic models used in other scientific disciplines such as
chemical kinetics and
thermodynamics. The advantage of compartmental over noncompartmental analysis is the ability to modify parameters and to extrapolate to novel situations. The disadvantage is the difficulty in developing and validating the proper model. Although compartment models have the potential to realistically model the situation within an organism, models inevitably make simplifying assumptions and will not be applicable in all situations. However complicated and precise a model may be, it still does not truly represent reality despite the effort involved in obtaining various distribution values for a drug. This is because the concept of distribution volume is a relative concept that is not a true reflection of reality. The choice of model therefore comes down to deciding which one offers the lowest margin of error for the drug involved.
Single-compartment model The simplest PK compartmental model is the one-compartmental PK model. This models an organism as one homogenous compartment. This
monocompartmental model presupposes that
blood plasma concentrations of the drug are the only information needed to determine the drug's concentration in other fluids and tissues. For example, the concentration in other areas may be approximately related by known, constant factors to the blood plasma concentration. In this one-compartment model, the most common model of elimination is
first order kinetics, where the elimination of the drug is directly proportional to the drug's concentration in the organism. This is often called
linear pharmacokinetics, as the change in concentration over time can be expressed as a linear differential equation \frac{dC}{dt} = -k_\text{el} C. Assuming a single IV bolus
dose resulting in a concentration C_\text{initial} at time t=0, the equation can be solved to give C=C_\text{initial} \times e^{-k_\text{el} \times t}.
Two-compartment model Not all body tissues have the same
blood supply, so the distribution of the drug will be slower in those tissues than in others with a better blood supply. Furthermore, there are some tissues (such as the
brain tissue) that present a real barrier to the distribution of drugs, which may be breached with greater or lesser ease depending on the drug's characteristics. If these relative conditions for the different tissue types are considered along with the rate of elimination, the organism can be considered to be acting like two compartments: one that we can call the
central compartment, which has a more rapid distribution and consists of organs and systems with a well-developed blood supply; and the
peripheral compartment, which is made up of organs with a lower blood flow. Other tissues, such as the brain, can occupy a variable position depending on a drug's ability to
passively transport (high lipophilicity) and evade
active efflux to cross the
blood–brain barrier (BBB) that separates the organ from the blood supply. Two-compartment models vary depending on which compartment elimination occurs in. The most common situation is that elimination occurs in the central compartment as the
liver and
kidneys are organs with a good blood supply. However, in some situations, elimination occurs in the peripheral compartment or even in both compartments. This can mean that there are three possible variations in the two compartment model, which still do not cover all possibilities.
Multi-compartment models In the real world, each tissue will have its own distribution characteristics and none of them will be strictly linear. The two-compartment model may not be applicable in situations where some of the enzymes responsible for metabolizing the drug become saturated, or where an active elimination mechanism is present that is independent of the drug's plasma concentration. If we label the drug's
volume of distribution within the organism
VdF and its volume of distribution in a tissue
VdT the former will be described by an equation that takes into account all the tissues that act in different ways, that is: : Vd_F = Vd_{T1} + Vd_{T2} + Vd_{T3} + \cdots + Vd_{Tn}\, This represents the
multi-compartment model with a number of curves that express complicated equations in order to obtain an overall curve. A number of
computer programs have been developed to plot these equations. • Additional phases (gamma, delta, etc.) are sometimes seen. • A drug's characteristics make a clear distinction between tissues with high and low blood flow. • Enzymatic
saturation: When the dose of a drug whose elimination depends on biotransformation is increased above a certain threshold the enzymes responsible for its metabolism become saturated. The drug's plasma concentration will then increase disproportionately and its elimination will no longer be constant. • Induction or
enzymatic inhibition: Some drugs have the capacity to inhibit or stimulate their own metabolism, in negative or
positive feedback reactions (e.g. this occurs with
fluvoxamine,
fluoxetine and
phenytoin). As larger doses of these pharmaceuticals are administered the plasma concentrations of the unmetabolized drug increases and the
elimination half-life increases. It is therefore necessary to adjust the dose or other treatment parameters when a high dosage is required. • The kidneys can also establish active elimination mechanisms for some drugs, independent of plasma concentrations. It can therefore be seen that non-linearity can occur because of reasons that affect the entire pharmacokinetic sequence: absorption, distribution, metabolism and elimination. == Bioavailability ==