# Pharmacokinetics

Pharmacokinetics may be simply defined as what the body does to the drug, as opposed to pharmacodynamics which may be defined as what the drug does to the body.

Benet LZ (1984). "Pharmacokinetics: Basic Principles and Its Use as a Tool in Drug Metabolism". In Horning MG, Mitchell J. Drug metabolism and drug toxicity. New York: Raven Press. ISBN 0-89004-997-1.

Pharmacokinetics, sometimes abbreviated as PK, (from Ancient Greek pharmakon "drug" and kinetikos "to do with motion"; see chemical kinetics) is a branch of pharmacology dedicated to the determination of the fate of substances administered externally to a living organism. The substances of interest include pharmaceutical agents, hormones, nutrients, and toxins.

Pharmacokinetics includes the study of the mechanisms of absorption and distribution of an administered drug, the chemical changes of the substance in the body (e.g. by metabolic enzymes such as CYP or UGT enzymes), and the effects and routes of excretion of the metabolites of the drug.[1] Pharmacokinetics is often studied in conjunction with pharmacodynamics, the study of a drug's pharmacological effect on the body.

Pharmacokinetics is divided into several areas including the extent and rate of absorption, distribution, metabolism and excretion. This is commonly referred to as the ADME scheme:

• Absorption - the process of a substance entering the blood circulation.
• Distribution - the dispersion or dissemination of substances throughout the fluids and tissues of the body.
• Metabolism (or Biotransformation) - the irreversible transformation of parent compounds into daughter metabolites.
• Excretion - the removal of the substances from the body. In rare cases, some drugs irreversibly accumulate in body tissue.

Elimination is the result of metabolism and excretion.

Pharmacokinetics describes how the body affects a specific drug after administration. Pharmacokinetic properties of drugs may be affected by elements such as the site of administration and the dose of administered drug. These may affect the absorption rate.[2]

A fifth process, Liberation has been highlighted as playing an important role in pharmacokinetics:[3][4]

• Liberation - the process of release of drug from the formulation.

Hence LADME may sometimes be used in place of ADME in reference to the core aspects of pharmacokinetics.

## Plasma concentration curves

Plasma drug concentration vs time after an IV dose

Drugs injected intravenously are removed from the plasma through two primary mechanisms: (1) Distribution to body tissues and (2) metabolism + excretion of the drugs. The resulting decrease of the drug's plasma concentration follows a biphasic pattern (see figure).

Alpha phase: An initial phase of rapid decrease in plasma concentration. The decrease is primarily attributed to drug distribution from the central compartment (circulation) into the peripheral compartments (body tissues). This phase ends when a pseudo-equilibrium of drug concentration is established between the central and peripheral compartments.

Beta phase: A phase of gradual decrease in plasma concentration after the alpha phase. The decrease is primarily attributed to drug metabolism and excretion.[5]

Additional phases (gamma, delta, etc.) are sometimes seen.[6]

## Metrics

The following are the most commonly measured pharmacokinetic metrics:[7]

Characteristic Description Example value Abbreviation(s) Formula
Dose Amount of drug administered. 500 mg $\textstyle D$ design parameter
τ Dosing interval. 24 h $\textstyle \tau$ design parameter
Volume of distribution The apparent volume in which a drug is distributed (i.e. the parameter relating drug concentration to drug amount in the body). 6.0 L $\textstyle V_d$ $\textstyle = D / C_0$
Concentration Amount of drug in a given volume of plasma. 83.3 µg/mL $\textstyle C_{0} \ or \ C_{ss}$ $\textstyle = D / V_d$
Elimination half-life The time required for the concentration of the drug to reach half of its original value. 12 h $\textstyle t_{1/2}$ $\textstyle = ln (2) / k_{e}$
Elimination rate constant The rate at which a drug is removed from the body. 0.0578 h-1 $\textstyle k_e$ $\textstyle = ln (2) / t_{1/2} = CL / V_{d}$
Infusion rate Rate of infusion required to balance elimination. 50 mg/h $\textstyle k_{in}$ $\textstyle = C_{ss} \cdot CL$
Area under the curve The integral of the concentration-time curve (after a single dose or in steady state). 1320 µg/mL×h $\textstyle AUC_{0-\infty}$

$\textstyle AUC_{\tau,ss}$
$= \int_{0}^{\infty}C\, dt$
$= \int_{t}^{t+\tau}C\, dt$
Clearance The volume of plasma cleared of the drug per unit time. 0.38 L/h $\textstyle CL$ $\textstyle= V_{d} \cdot k_{e} = D/AUC$
Bioavailability The systemically available fraction of a drug. 0.8 $\textstyle f$ $= \frac{AUC_{po}\cdot D_{iv}}{AUC_{iv}\cdot D_{po}}$
Cmax The peak plasma concentration of a drug after administration. 60.9 µg/mL $\textstyle C_{max}$ direct measurement
tmax Time to reach Cmax. 3.9 h $\textstyle t_{max}$ direct measurement
Cmin The lowest (trough) concentration that a drug reaches before the next dose is administered. 27.7 µg/mL $\textstyle C_{min,ss}$ direct measurement
Fluctuation Peak trough fluctuation within one dosing interval at steady state 41.8 % $\textstyle %PTF$ $\textstyle =100 \cdot \frac{(C_{max,ss} - C_{min,ss})}{C_{av,ss}}$
where
$\textstyle C_{av,ss}=\frac{AUC_{\tau,ss}}{\tau}$
[ ]

In pharmacokinetics, steady state refers to the situation where the overall intake of a drug is fairly in dynamic equilibrium with its elimination. In practice, it is generally considered that steady state is reached when a time of 4 to 5 times the half-life for a drug after regular dosing is started.

The following graph depicts a typical time course of drug plasma concentration and illustrates main pharmacokinetic metrics:

The time course of drug plasma concentrations over 96 hours following oral administrations every 24 hours. Note that the AUC in steady state equals AUC after the first dose.

## Analysis

Pharmacokinetic analysis is performed by noncompartmental or compartmental methods. Noncompartmental methods estimate the exposure to a drug by estimating the area under the curve of a concentration-time graph. Compartmental methods estimate the concentration-time graph using kinetic models. Noncompartmental methods are often more versatile in that they do not assume any specific compartmental model and produce accurate results also acceptable for bioequivalence studies.

### Noncompartmental analysis

Noncompartmental PK analysis is highly dependent on estimation of total drug exposure. 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.

### Compartmental analysis

Compartmental PK analysis uses kinetic models to describe and predict the concentration-time curve. 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 some noncompartmental analyses is the ability to predict the concentration at any time. The disadvantage is the difficulty in developing and validating the proper model. Compartment-free modeling based on curve stripping does not suffer this limitation. The simplest PK compartmental model is the one-compartmental PK model with IV bolus administration and first-order elimination. The most complex PK models (called PBPK models) rely on the use of physiological information to ease development and validation.

### Bioanalytical methods

Bioanalytical methods are necessary to construct a concentration-time profile. Chemical techniques are employed to measure the concentration of drugs in biological matrix, most often plasma. Proper bioanalytical methods should be selective and sensitive. For example microscale thermophoresis can be used to quantify how the biological matrix/liquid affects the affinity of a drug to its target.[8][9]

#### Mass spectrometry

Pharmacokinetics is often studied using mass spectrometry because of the complex nature of the matrix (often plasma or urine) and the need for high sensitivity to observe concentrations after a low dose and a long time period. The most common instrumentation used in this application is LC-MS with a triple quadrupole mass spectrometer. Tandem mass spectrometry is usually employed for added specificity. Standard curves and internal standards are used for quantitation of usually a single pharmaceutical in the samples. The samples represent different time points as a pharmaceutical is administered and then metabolized or cleared from the body. Blank samples taken before administration are important in determining background and insuring data integrity with such complex sample matrices. Much attention is paid to the linearity of the standard curve; however it is not uncommon to use curve fitting with more complex functions such as quadratics since the response of most mass spectrometers is less than linear across large concentration ranges.[10][11][12]

There is currently considerable interest in the use of very high sensitivity mass spectrometry for microdosing studies, which are seen as a promising alternative to animal experimentation.[13]

## Population pharmacokinetics

Population pharmacokinetics is the study of the sources and correlates of variability in drug concentrations among individuals who are the target patient population receiving clinically relevant doses of a drug of interest.[14][15][16] Certain patient demographic, pathophysiological, and therapeutical features, such as body weight, excretory and metabolic functions, and the presence of other therapies, can regularly alter dose-concentration relationships. For example, steady-state concentrations of drugs eliminated mostly by the kidney are usually greater in patients suffering from renal failure than they are in patients with normal renal function receiving the same drug dosage. Population pharmacokinetics seeks to identify the measurable pathophysiologic factors that cause changes in the dose-concentration relationship and the extent of these changes so that, if such changes are associated with clinically significant shifts in the therapeutic index, dosage can be appropriately modified. An advantage of population pharmacokinetic modelling is its ability to analyze sparse data sets (sometimes only one concentration measurement per patient is available).

Software packages used in population pharmacokinetics modeling include NONMEM, which was developed at the UCSF.

## Ecotoxicology

Ecotoxicology is the study of toxic effects on a wide range of organisms and includes considerations of toxicokinetics and toxicodynamics.[17][18]

## Software

### Simulation

All model based software above.

## Educational centers

Global centres with the highest profiles for providing in-depth training include the Universities of Buffalo, Florida, Gothenburg, Leiden, Otago, San Francisco, Tokyo, Uppsala, Washington, Manchester and University of Sheffield.[19]

## References

1. ^ Pharmacokinetics. (2006). In Mosby's Dictionary of Medicine, Nursing, & Health Professions. Philadelphia, PA: Elsevier Health Sciences. Retrieved December 11, 2008, from http://www.credoreference.com/entry/6686418
2. ^ Kathleen Knights; Bronwen Bryant (2002). Pharmacology for Health Professionals. Amsterdam: Elsevier. ISBN 0-7295-3664-5.
3. ^ Koch HP, Ritschel WA (1986). "Liberation". Synopsis der Biopharmazie und Pharmakokinetik (in German). Landsberg, München: Ecomed. pp. 99–131. ISBN 3-609-64970-4.
4. ^ Ruiz-Garcia A, Bermejo M, Moss A, Casabo VG (February 2008). "Pharmacokinetics in drug discovery". J Pharm Sci 97 (2): 654–90. doi:10.1002/jps.21009. PMID 17630642.
5. ^ Gill SC, Moon-Mcdermott L, Hunt TL, Deresinski S, Blaschke T, Sandhaus RA (Sep 1999). "Phase I Pharmacokinetics of Liposomal Amikacin (MiKasome) in Human Subjects: Dose Dependence and Urinary Clearance". Abstr Intersci Conf Antimicrob Agents Chemother Intersci Conf Antimicrob Agents Chemother 39: 33 (abstract no. 1195).
6. ^ Weiner, Daniel; Johan Gabrielsson (2000). "PK24 - Non-linear kinetics - flow II". Pharmacokinetic/pharmacodynamic data analysis: concepts and applications. Apotekarsocieteten. pp. 527–36. ISBN 91-86274-92-9.
7. ^ AGAH working group PHARMACOKINETICS (2004-02-16). "Collection of terms, symbols, equations, and explanations of common pharmacokinetic and pharmacodynamic parameters and some statistical functions" (PDF). Arbeitsgemeinschaft für Angewandte Humanpharmakologie (AGAH) (Association for Applied Human Pharmacology). Retrieved 2011-04-04.
8. ^ Baaske P, Wienken CJ, Reineck P, Duhr S, Braun D (Feb 2010). "Optical Thermophoresis quantifies Buffer dependence of Aptamer Binding". Angew. Chem. Int. Ed. 49 (12): 1–5. doi:10.1002/anie.200903998. PMID 20186894. Lay summaryPhsyorg.com.
9. ^ Wienken CJ et al. (2010). "Protein-binding assays in biological liquids using microscale thermophoresis". Nature Communications 1 (7): 100. Bibcode:2010NatCo...1E.100W. doi:10.1038/ncomms1093. PMID 20981028.
10. ^ Hsieh Y, Korfmacher WA (June 2006). "Increasing speed and throughput when using HPLC-MS/MS systems for drug metabolism and pharmacokinetic screening". Current Drug Metabolism 7 (5): 479–89. doi:10.2174/138920006777697963. PMID 16787157.
11. ^ Covey TR, Lee ED, Henion JD (October 1986). "High-speed liquid chromatography/tandem mass spectrometry for the determination of drugs in biological samples". Anal. Chem. 58 (12): 2453–60. doi:10.1021/ac00125a022. PMID 3789400.
12. ^ Covey TR, Crowther JB, Dewey EA, Henion JD (February 1985). "Thermospray liquid chromatography/mass spectrometry determination of drugs and their metabolites in biological fluids". Anal. Chem. 57 (2): 474–81. doi:10.1021/ac50001a036. PMID 3977076.
13. ^ Committee for Medicinal Products for Human Use (CHMP) (June 23, 2004). "Position Paper on Non-Clinical Studies to Support Clinical Trials with a Single Microdose" (PDF). CPMP/SWP/2599/02 Rev 1. European Medicines Agency, Evaluation of Medicines for Human Use. Retrieved September 13, 2010.
14. ^ Sheiner LB, Rosenberg B, Marathe VV (October 1977). "Estimation of population characteristics of pharmacokinetic parameters from routine clinical data". J Pharmacokinet Biopharm 5 (5): 445–79. doi:10.1007/BF01061728. PMID 925881.
15. ^ Sheiner LB, Beal S, Rosenberg B, Marathe VV (September 1979). "Forecasting individual pharmacokinetics". Clin. Pharmacol. Ther. 26 (3): 294–305. PMID 466923.
16. ^ Bonate PL (2005). "Recommended reading in population pharmacokinetic pharmacodynamics". AAPS J 7 (2): E363–73. doi:10.1208/aapsj070237. PMC 2750974. PMID 16353916.
17. ^ Jager T, Albert C, Preuss TG, Ashauer R (April 2011). "General unified threshold model of survival--a toxicokinetic-toxicodynamic framework for ecotoxicology". Environ. Sci. Technol. 45 (7): 2529–40. doi:10.1021/es103092a. PMID 21366215.
18. ^ Ashauer R. "Toxicokinetic-Toxicodynamic Models - Ecotoxicology and Models". Swiss Federal Institute of Aquatic Science and Technology. Retrieved 2011-12-03.
19. ^ Tucker GT (June 2012). "Research priorities in pharmacokinetics". Br J Clin Pharmacol 73 (6): 924–6. doi:10.1111/j.1365-2125.2012.04238.x. PMID 22360418.