Urbana, IL, USA

INTRODUCTION

Pharmacokinetics (PK) is the science that studies the time-course of a drug journey in the body of patients. The efficacy of a drug is typically correlated to the administered dose and the concentrations achieved at the site of therapeutic action. Concentrations in plasma are often adequate markers of these and therefore may be related to the observed drug action, biological effect or clinical response. The objective of pharmacokinetics is usually to study the phenomena of drug absorption, distribution, and elimination (metabolism and excretion) in order to develop models that allow predicting the concentration of drugs in plasma sometime after its administration. Given the predictive nature of pharmacokinetics, its language is one of mathematics. This is usually the first and foremost obstacle for its practical use in the clinical setting. However, dosage regimens can be easily adjusted to adapt to changing clinical scenarios without the need of heavy mathematical knowledge. Understanding the conceptual basis of pharmacokinetic parameters and the factors (e.g., species, age, disease status...) that affect their magnitude is the first step in learning how to use this tool that we call pharmacokinetics. The purpose of this paper is to review some of the most common pharmacokinetic concepts and to illustrate some of their applications in the clinical setting. We will not discuss how to analyze pharmacokinetic data but how to use available pharmacokinetic information to modify dosage regimens.

CLINICAL APPLICATION OF PHARMACOKINETIC CONCEPTS

The pharmacokinetic behaviour of a drug depends on the animal physiology (i.e., renal and hepatic function, organ perfusion...) and the drug's physicochemical features (lipid solubility, ionization...). The two main pharmacokinetic parameters are clearance and volume of distribution. Changes on these parameters due to disease, organ disfunction, age, etc, may require adjusting dosages of drugs given to animals. A brief overview of these and other parameters follows:

**Clearance:** The systemic clearance is representative of the elimination of the drug from the body. Physiologically it represents the rate of elimination of a drug relative to the plasma concentration. The concept of clearance is extremely useful for dosage adjustment because at the typical therapeutic doses, the systemic clearance of a drug is usually constant over the interval of plasma concentrations of clinical importance. For certain drugs, like phenylbutazone in dogs or salicylate in cats, the elimination is dose-dependent due to saturation of the process at high concentrations, and clearance cannot be considered constant beyond a certain level. The systemic clearance of a variety of drugs differs greatly between dogs and cats, reflecting the diverse metabolic capacity in both species. This parameter is the most relevant in dose calculation. This will be better understood by reviewing secondary parameters such as the area under the curve and the peak concentration.

**Area Under the Curve (AUC):** This parameter is a reflection of the extent of drug bioavailability and graphically consists of the area that is contained by the concentration-time profile. This parameter represents better than most the exposure of the animal to the drug after each dose. AUC is usually obtained by a numerical integration procedure known as the trapezoidal rule method (Figure 1).

Figure 1. Area under the curve and the trapezoidal method for its calculation

The AUC is independent of the administration route and the drug elimination, as long as the processes of elimination are constant. When dose-independent (linear) kinetics apply, the AUC is directly proportional to the dose and is related to this and to the clearance by this useful expression:

where **F** is the fraction of dose absorbed, **D** is the dose and **Cl** is the systemic clearance. As we can deduct from this expression, when clearance is constant (linear kinetics) an increase in dose (with unchanged **F**) will lead to a proportional increase in AUC. This is a measure of drug availability that for certain drugs can be used as a target exposure to modify dosage regimens accordingly. For example, in the case of fluoroquinolone antibiotics, the AUC_{24 hr}/MIC ratio seems to be the best indicator of efficacy, with reported optimum values oscillating between 125-250. Whatever is the appropriate value for each drug and species (still to be determined) if a new bacterial colony with a higher MIC (or lower, for that matter) is isolated from a patient, the total daily dose could be modified just by calculating the AUC that is needed to keep the optimum ratio (e.g., 200), and then calculating the dose required to obtain such AUC. This assumes that clearance and *F* do not change.

Likewise, clearance is related to average concentration at steady state as follows:

where **Css _{avg} **is the average concentration at steady state and

*t*is the interdose interval. The combination of both expressions allow to easily modify the dose to achieve a new target average concentration at steady state, if this is needed. For example, if a dog is being medicated long-term with phenobarbital and after a few months on therapy the average steady state concentration decreases 25% due to a similar increase in clearance, the dose will need to be increased by 25% in order to revert to the target concentration at steady state.

**Peak concentration:** This parameter, also known as C_{max} represents the maximum plasma drug concentration obtained after extravascular administration of the drug. C_{max} is a measure of dose intensity and may be related to both the therapeutic and toxic effects. When the absorption and elimination processes are linear (not saturated) and the volume of distribution and *F* are unchanged, the Cmax is proportional to the dose. This relationship can be used to modify drug concentrations to achieve new therapeutic targets. For example, when a concentration-dependent antibiotic such as an aminoglycoside is administered to an animal the aim is usually obtaining a certain Cmax to MIC ratio (e.g., Cmax/MIC = 10). If a new bacterial isolate has a higher MIC, the dose may need to be modified to account for this new target. Under the conditions expressed before the dose could just be multiplied by the ratio of MIC's, unless toxicity is a limiting factor. In the case of aminoglycosides, this adjustment may be followed by an increase in the interdose interval in order to decrease the likelihood of toxicity (in such case the total daily dose might remain the same).

**Volume of distribution:** This parameter provides an indication of "how far" the drug travels inside of the patient body. For lipophilic drugs that easily cross membranes, this parameter is usually high (close to 1 L/kg or higher), indicating that the drug reaches concentrations (perhaps therapeutic) in many tissues. The rate at which a drug distributes extravascularly can be limited either by perfusion (e.g., lipophilic drugs) or by diffusion (e.g., polar drugs). There are several types of volumes of distribution. For a drug exhibiting a biexponential concentration-time profile, the volume of distribution "area" can be calculated from the following equation:

where **ß** is the slope of the elimination phase of the semi logarithmic concentration-time profile after IV bolus administration. The volume of distribution "area" is a proportionality factor between the plasma concentration and the total amount of drug in the body during the terminal phase according to the following expression:

where **C _{t}** is a plasma concentration within the therapeutic range (which might be the optimum MIC multiple for an antimicrobial). This expression can be used to calculate the dose required to achieve a desired plasma concentration. The volume of distribution "at steady state" is useful to calculate the loading dose. This may be necessary in the case of drugs with long half-lives in order to quickly obtain steady-state concentrations.

**Half-life:** This is a hybrid parameter that depends on both volume of distribution and clearance. It is a good indicator of how quickly a drug disappears from the body. It has also de advantage of being a rather familiar term. It is the time necessary for a plasma concentration to decrease by half after pseudo-distribution equilibrium is achieved. This is not necessarily the time required for the amount of drug in the body to decrease by half. Half-life is calculated as:

Half-life increases when the volume of distribution increases or when the clearance decreases. Although the latter case is more common in practice, an increase in half-life cannot be automatically considered a reflection of a decrease in clearance. Therefore, dose adaptation should be based in clearance and not half-life. This parameter is useful in the case of multiple administrations to predict drug accumulation, time to steady-state, and dosage interval. It takes 5 half-lives to reach 97% of the concentration at steady-state.

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**
Tomas Martín-Jiménez, DVM, PhD, Diplomate ACVCP, Diplomate ECVPT
**

Assistant Professor of Clinical Pharmacology

College of Veterinary Medicine, University of Illinois

Urbana, IL, USA