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Biological halflife
The biological halflife or terminal halflife 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, as per the MeSH definition. 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, halflife may also describe the time it takes for the blood plasma concentration of a substance to halve (plasma halflife) its steadystate. The relationship between the biological and plasma halflives 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.^{[1]}
Biological halflife is an important pharmacokinetic parameter and is usually denoted by the abbreviation <math>t_{\frac{1}{2}}</math>.^{[2]}
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, into the environment, follows more complex kinetics. See the article rate equation.
Contents
Examples
Water
The biological halflife 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 halflife of water in the body.^{[3]}^{[4]} This has been used to decontaminate humans who are internally contaminated with tritiated water (tritium). Drinking the same amount of water would have a similar effect, but many would find it difficult to drink a large volume of water. The basis of this decontamination method (used at Harwell) is to increase the rate at which the water in the body is replaced with new water.
Alcohol
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 zeroorder kinetics. Also the ratelimiting 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
Substance  Biological halflife 

Adenosine  <10 seconds 
Norepinephrine  2 minutes 
Oxaliplatin  14 minutes^{[5]} 
Salbutamol  1.6 hours 
Zaleplon  1–2 hours 
Morphine  2–3 hours 
Methadone  15 hours to 3 days, in rare cases up to 8 days^{[6]} 
Phenytoin  12–42 hours 
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  25110 days 
Bedaquiline  5.5 months 
Metals
The biological halflife 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 halflife (physiologicallybased 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 in a chelation therapy, then while the rate at which lead is lost from the body will be increased, the lead within the body tends to relocate into the brain where it can do the most harm.^{[citation needed]}
 Polonium in the body has a biological halflife of about 30 to 50 days.
 Caesium in the body has a biological halflife of about one to four months.
 Mercury (as methylmercury) in the body has a halflife of about 65 days.
 Lead in the blood has a half life of 28–36 days.^{[7]}^{[8]}
 Lead in bone has a biological halflife of about ten years.
 Cadmium in bone has a biological halflife of about 30 years.
 Plutonium in bone has a biological halflife of about 100 years.
 Plutonium in the liver has a biological halflife of about 40 years.
Rate equations
Firstorder elimination
There are circumstances where the halflife varies with the concentration of the drug. Thus the halflife, under these circumstances, is proportional to the initial concentration of the drug A_{0} and inversely proportional to the zeroorder rate constant k_{0} where:
 <math>t_\frac{1}{2} = \frac{0.5 A_{0}}{k_{0}} \,</math>
This process is usually a logarithmic process  that is, a constant proportion of the agent is eliminated per unit time.^{[9]} Thus the fall in plasma concentration after the administration of a single dose is described by the following equation:
 <math>C_{t} = C_{0} e^{kt} \,</math>
 C_{t} is concentration after time t
 C_{0} is the initial concentration (t=0)
 k is the elimination rate constant
The relationship between the elimination rate constant and halflife is given by the following equation:
 <math>k = \frac{\ln 2}{t_\frac{1}{2}} \,</math>
Halflife is determined by clearance (CL) and volume of distribution (V_{D}) and the relationship is described by the following equation:
 <math>t_\frac{1}{2} = \frac{{\ln 2}\cdot{V_D}}{CL} \,</math>
In clinical practice, this means that it takes 4 to 5 times the halflife 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 halflife (or t_{½}) 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 halflife (e.g., amiodarone, elimination t_{½} of about 58 days) are usually started with a loading dose to achieve their desired clinical effect more quickly.
Sample values and equations
Characteristic  Description  Example value  Symbol  Formula 

Dose  Amount of drug administered.  500 mg  <math>D</math>  Design parameter 
Dosing interval  Time between drug dose administrations.  24 h  <math>\tau</math>  Design parameter 
C_{max}  The peak plasma concentration of a drug after administration.  60.9 mg/L  <math>C_\text{max}</math>  Direct measurement 
t_{max}  Time to reach C_{max}.  3.9 h  <math>t_\text{max}</math>  Direct measurement 
C_{min}  The lowest (trough) concentration that a drug reaches before the next dose is administered.  27.7 mg/L  <math>C_{\text{min}, \text{ss}}</math>  Direct measurement 
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  <math>V_\text{d}</math>  <math>= \frac{D}{C_0}</math> 
Concentration  Amount of drug in a given volume of plasma.  83.3 mg/L  <math>C_{0}, C_\text{ss}</math>  <math>= \frac{D}{V_\text{d}}</math> 
Elimination halflife  The time required for the concentration of the drug to reach half of its original value.  12 h  <math>t_\frac{1}{2}</math>  <math>= \frac{\ln(2)}{k_\text{e}}</math> 
Elimination rate constant  The rate at which a drug is removed from the body.  0.0578 h^{−1}  <math>k_\text{e}</math>  <math>= \frac{\ln(2)}{t_\frac{1}{2}} = \frac{CL}{V_\text{d}}</math> 
Infusion rate  Rate of infusion required to balance elimination.  50 mg/h  <math>k_\text{in}</math>  <math>= C_\text{ss} \cdot CL</math> 
Area under the curve  The integral of the concentrationtime curve (after a single dose or in steady state).  1,320 mg/L·h  <math>AUC_{0  \infty}</math>  <math>= \int_{0}^{\infty}C\, \operatorname{d}t</math> 
<math>AUC_{\tau, \text{ss}}</math>  <math>= \int_{t}^{t + \tau}C\, \operatorname{d}t</math>  
Clearance  The volume of plasma cleared of the drug per unit time.  0.38 L/h  <math>CL</math>  <math>= V_\text{d} \cdot k_\text{e} = \frac{D}{AUC}</math> 
Bioavailability  The systemically available fraction of a drug.  0.8  <math>f</math>  <math>= \frac{AUC_\text{po} \cdot D_\text{iv}}{AUC_\text{iv} \cdot D_\text{po}}</math> 
Fluctuation  Peak trough fluctuation within one dosing interval at steady state  41.8 %  <math>\%PTF</math>  <math>= \frac{C_{\text{max}, \text{ss}}  C_{\text{min}, \text{ss}}}{C_{\text{av}, \text{ss}}} \cdot 100</math> where <math>C_{\text{av},\text{ss}} = \frac{1}{\tau}AUC_{\tau, \text{ss}}</math> 
[  ]
See also
 Halflife, pertaining to the general mathematical concept in physics or pharmacology.
 Effective halflife
References
 ^ Lin VW; Cardenas DD (2003). Spinal cord medicine. Demos Medical Publishing, LLC. p. 251. ISBN 1888799617.
 ^ 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 0123694132.
 ^ Silk, Kenneth R.; Tyrer, Peter J. (2008). Cambridge textbook of effective treatments in psychiatry. Cambridge, UK: Cambridge University Press. p. 295. ISBN 052184228X.
 ^ Ehrsson, Hans et al. (Winter 2002). "Pharmacokinetics of oxaliplatin in humans". Medical Oncology. Retrieved 20070328.
 ^ Manfredonia, John (March 2005). "Prescribing Methadone for Pain Management in EndofLife Care". JAOA—The Journal of the American Osteopathic Association 105 (3 supplement): 18S. Retrieved 20070129.
 ^ Griffin et al. 1975 as cited in ATSDR 2005
 ^ Rabinowitz et al. 1976 as cited in ATSDR 2005
 ^ Birkett DJ (2002). For example, ethanol may be consumed in sufficient quantity to saturate the metabolic enzymes in the liver, and so is eliminated from the body at an approximately constant rate (zeroorder eliminationPharmacokinetics Made Easy (Revised Edition). Sydney: McGrawHill Australia. ISBN 0074710729.
