The biological half-life or terminal half-life of a substance is the time it takes for a substance (for example a metabolite, drug, signalling molecule, radioactive nuclide, or other substance) to lose half of its pharmacologic, physiologic, or radiologic activity.[1] Typically, this refers to the body's cleansing through the function of kidneys and liver in addition to excretion functions to eliminate a substance from the body. In a medical context, half-life may also describe the time it takes for the blood plasma concentration of a substance to halve (plasma half-life) its steady-state. The relationship between the biological and plasma half-lives of a substance can be complex depending on the substance in question, due to factors including accumulation in tissues (protein binding), active metabolites, and receptor interactions.[2] Biological half-life is an important pharmacokinetic parameter and is usually denoted by the abbreviation t 1 2 displaystyle t_ frac 1 2 .[3] While a radioactive isotope decays perfectly according to first order kinetics where the rate constant is fixed, the elimination of a substance from a living organism follows more complex chemical kinetics. See Rate equation. Contents 1 Examples 1.1 Water 1.2 Alcohol 1.3 Common prescription medications 1.4 Metals 1.5 Peripheral half-life 2 Rate equations 2.1 First-order elimination 2.2 Biphasic half-life 3 Sample values and equations 4 See also 5 References Examples[edit] Water[edit] The biological half-life of water in a human is about 7 to 14 days. It can be altered by behavior. Drinking large amounts of alcohol will reduce the biological half-life of water in the body.[4][5] This has been used to decontaminate humans who are internally contaminated with tritiated water (tritium). The basis of this decontamination method (used at Harwell)[citation needed] is to increase the rate at which the water in the body is replaced with new water. Alcohol[edit] The removal of ethanol (drinking alcohol) through oxidation by alcohol dehydrogenase in the liver from the human body is limited. Hence the removal of a large concentration of alcohol from blood may follow zero-order kinetics. Also the rate-limiting steps for one substance may be in common with other substances. For instance, the blood alcohol concentration can be used to modify the biochemistry of methanol and ethylene glycol. In this way the oxidation of methanol to the toxic formaldehyde and formic acid in the human body can be prevented by giving an appropriate amount of ethanol to a person who has ingested methanol. Note that methanol is very toxic and causes blindness and death. A person who has ingested ethylene glycol can be treated in the same way. Half life is also relative to the subjective metabolic rate of the individual in question. Common prescription medications[edit] Substance Biological half-life Adenosine <10 seconds Norepinephrine 2 minutes Oxaliplatin 14 minutes[6] Salbutamol 1.6 hours Zaleplon 1–2 hours Morphine 2–3 hours Methotrexate 3–10 hours (lower doses), 8–15 hours (higher doses)[7] Phenytoin 12–42 hours Methadone 15 hours to 3 days, in rare cases up to 8 days[8] Buprenorphine 16–72 hours Clonazepam 18–50 hours Diazepam 20–100 hours (active metabolite, nordazepam 1.5–8.3 days) Flurazepam 0.8–4.2 days (active metabolite, desflurazepam 1.75–10.4 days) Donepezil 70 hours (approx.) Fluoxetine 4–6 days (active lipophilic metabolite 4–16 days) Dutasteride 5 weeks Amiodarone 25–110 days Bedaquiline 5.5 months Metals[edit]
The biological half-life of caesium in humans is between one and four
months. This can be shortened by feeding the person prussian blue. The
prussian blue in the digestive system acts as a solid ion exchanger
which absorbs the caesium while releasing potassium ions.
For some substances, it is important to think of the human or animal
body as being made up of several parts, each with their own affinity
for the substance, and each part with a different biological half-life
(physiologically-based pharmacokinetic modelling). Attempts to remove
a substance from the whole organism may have the effect of increasing
the burden present in one part of the organism. For instance, if a
person who is contaminated with lead is given
EDTA
Polonium
Peripheral half-life[edit] Some substances may have different half-lives in different parts of the body. For example, oxytocin has a half-life of typically about three minutes in the blood when given intravenously. Peripherally administered (e.g. intravenous) peptides like oxytocin cross the blood-brain-barrier very poorly, although very small amounts (< 1%) do appear to enter the central nervous system in humans when given via this route.[12] In contrast to peripheral administration, when administered intranasally via a nasal spray, oxytocin reliably crosses the blood–brain barrier and exhibits psychoactive effects in humans.[13][14] In addition, also unlike the case of peripheral administration, intranasal oxytocin has a central duration of at least 2.25 hours and as long as 4 hours.[15][16] In likely relation to this fact, endogenous oxytocin concentrations in the brain have been found to be as much as 1000-fold higher than peripheral levels.[12] Rate equations[edit] First-order elimination[edit] There are circumstances where the half-life varies with the concentration of the drug. Thus the half-life, under these circumstances, is proportional to[dubious – discuss] the initial concentration of the drug A0 and inversely proportional to the zero-order rate constant k0 where: t 1 2 = 0.5 A 0 k 0 displaystyle t_ frac 1 2 = frac 0.5A_ 0 k_ 0 , This process[clarification needed] is usually a logarithmic process - that is, a constant proportion of the agent is eliminated per unit time.[17] Thus the fall in plasma concentration after the administration of a single dose is described by the following equation: C t = C 0 e − k t displaystyle C_ t =C_ 0 e^ -kt , Ct is concentration after time t C0 is the initial concentration (t=0) k is the elimination rate constant The relationship between the elimination rate constant and half-life is given by the following equation: k = ln 2 t 1 2 displaystyle k= frac ln 2 t_ frac 1 2 ,
Half-life
t 1 2 = ln 2 ⋅ V D C L displaystyle t_ frac 1 2 = frac ln 2 cdot V_ D CL , In clinical practice, this means that it takes 4 to 5 times the half-life for a drug's serum concentration to reach steady state after regular dosing is started, stopped, or the dose changed. So, for example, digoxin has a half-life (or t½) of 24–36 h; this means that a change in the dose will take the best part of a week to take full effect. For this reason, drugs with a long half-life (e.g., amiodarone, elimination t½ of about 58 days) are usually started with a loading dose to achieve their desired clinical effect more quickly. Biphasic half-life[edit] Many drugs follow a biphasic elimination curve — first a steep slope then a shallow slope:[18] STEEP (initial) part of curve —> initial distribution of the drug in the body. SHALLOW part of curve —> ultimate excretion of drug, which is dependent on the release of the drug from tissue compartments into the blood. For a more detailed description see Pharmacokinetics--Multi-compartmental_models. Sample values and equations[edit] Characteristic Description Example value Symbol Formula Dose Amount of drug administered. 500 mg D displaystyle D Design parameter Dosing interval Time between drug dose administrations. 24 h τ displaystyle tau Design parameter Cmax The peak plasma concentration of a drug after administration. 60.9 mg/L C max displaystyle C_ text max Direct measurement tmax Time to reach Cmax. 3.9 h t max displaystyle t_ text max Direct measurement Cmin The lowest (trough) concentration that a drug reaches before the next dose is administered. 27.7 mg/L C min , ss displaystyle C_ text min , text ss Direct measurement Volume of distribution The apparent volume in which a drug is distributed (i.e., the parameter relating drug concentration in plasma to drug amount in the body). 6.0 L V d displaystyle V_ text d = D C 0 displaystyle = frac D C_ 0 Concentration Amount of drug in a given volume of plasma. 83.3 mg/L C 0 , C ss displaystyle C_ 0 ,C_ text ss = D V d displaystyle = frac D V_ text d Elimination half-life The time required for the concentration of the drug to reach half of its original value. 12 h t 1 2 displaystyle t_ frac 1 2 = ln ( 2 ) k e displaystyle = frac ln(2) k_ text e Elimination rate constant The rate at which a drug is removed from the body. 0.0578 h−1 k e displaystyle k_ text e = ln ( 2 ) t 1 2 = C L V d displaystyle = frac ln(2) t_ frac 1 2 = frac CL V_ text d Infusion rate Rate of infusion required to balance elimination. 50 mg/h k in displaystyle k_ text in = C ss ⋅ C L displaystyle =C_ text ss cdot CL Area under the curve The integral of the concentration-time curve (after a single dose or in steady state). 1,320 mg/L·h A U C 0 − ∞ displaystyle AUC_ 0-infty = ∫ 0 ∞ C d t displaystyle =int _ 0 ^ infty C,operatorname d t A U C τ , ss displaystyle AUC_ tau , text ss = ∫ t t + τ C d t displaystyle =int _ t ^ t+tau C,operatorname d t Clearance The volume of plasma cleared of the drug per unit time. 0.38 L/h C L displaystyle CL = V d ⋅ k e = D A U C displaystyle =V_ text d cdot k_ text e = frac D AUC Bioavailability The systemically available fraction of a drug. 0.8 f displaystyle f = A U C po ⋅ D iv A U C iv ⋅ D po displaystyle = frac AUC_ text po cdot D_ text iv AUC_ text iv cdot D_ text po Fluctuation Peak trough fluctuation within one dosing interval at steady state. 41.8 % % P T F displaystyle %PTF = C max , ss − C min , ss C av , ss ⋅ 100 displaystyle = frac C_ text max , text ss -C_ text min , text ss C_ text av , text ss cdot 100 where C av , ss = 1 τ A U C τ , ss displaystyle C_ text av , text ss = frac 1 tau AUC_ tau , text ss [ v t e ] See also[edit] Half-life, pertaining to the general mathematical concept in physics or pharmacology. Effective half-life References[edit] ^ "Half-Life". Medical Subject Headings. United States National
Library of Medicine. 2016. Tree No. G01.910.405. Retrieved June 3,
2016.
^ Lin VW; Cardenas DD (2003). Spinal Cord Medicine. Demos Medical
Publishing, LLC. p. 251. ISBN 1-888799-61-7.
^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book")
(1997). Online corrected version: (2006–) "Biological Half
Life".
^ Nordberg, Gunnar (2007). Handbook on the toxicology of metals.
Amsterdam: Elsevier. p. 119. ISBN 0-12-369413-2.
^ Silk, Kenneth R.; Tyrer, Peter J. (2008). Cambridge textbook of
effective treatments in psychiatry. Cambridge, UK: Cambridge
University Press. p. 295. ISBN 0-521-84228-X.
^ Ehrsson, Hans; et al. (Winter 2002). "
Pharmacokinetics
v t e Concepts in pharmacology Pharmacokinetics (L)ADME: (Liberation)
Absorption
Distribution
Metabolism
Excretion
Loading dose Volume of distribution (Initial) Rate of infusion Compartment Bioequivalence Bioavailability Onset of action Biological half-life Mean residence time Plasma protein binding Therapeutic index (Median lethal dose, Effective dose) Pharmacodynamics Mechanism of action
Toxicity
Antimicrobial pharmacodynamics: Minimum inhibitory concentration (Bacteriostatic) Minimum bactericidal concentration (Bactericide) Agonism and antagonism Agonist: Inverse agonist Irreversible agonist Partial agonist Superagonist Physiological agonist Antagonist: Competitive antagonist Irreversible antagonist Physiological antagonist Other: Binding Affinity Binding selectivity Functional selectivity Other
Drug
Drug
Drug
Classical pharmacology Reverse pharmacology Related fields/subfields Pharmacogenetics Pharmacogenomics Neuropsychopharmacology (Neuropharmacology, P |