# Viva B(v)

This viva is relevant to Section B(v) of the 2017 CICM Primary Syllabus, which expects the exam candidate to "describe the concepts of effect-site and context sensitive half time".

###### Define the term "half life"

"Half-life (t½) is the time required to change the amount of a drug in the body by one-half during elimination" - College answer to Question 11 from the second paper of 2012

Alternatively:

"Half-life is the time take for the amount of the drug in the body (or the plasma concentration) to fall by half." - Birkett, 2009

###### How do you calculate half life from clearance and volume of distribution?

t½ = 0.693 × Vd /CL

where

• 0.693 is the logarithm of 2 (i.e. for a "tenth-life" you'd use a logarithm of 10)
• Vd is the volume of distribution
• CL is clearance
###### Which factors influence the half-life of drugs?
• Volume of distribution, which is in turn influenced by:
• Properties of the drug, including molecule size, charge, pKa, protein binding, tissue binding and lipid-water partition coefficient
• Properties of the patient's body fluids, including volume status, protein content, body fluid pH and presence of drugs which compete for binding sites
• Pathophysiological states, including age, gender, obesity, pregnancy, and oedema
• Presence of extracorporeal sites of distribution, eg. circuit fluid content and drug-adsorbing circuit components
• Clearance, which is in turn influenced by:
• Concentration of the drug
• Susceptibility of the drug to biotransformation (i.e. clearance by metabolism, usually hepatic)
• Susceptibility of the drug to removal by filtration or diffusion (i.e. clearance by the kidneys, lungs etc)
• Active excretion of the drug (its removal by active transort mechanisms)
• Functional status of clearance organs (eg. liver and kidneys)
• Blood delivery to organs of clearance
###### How does elimination rate influence half-life?

Half life is dependent on a first-order elimination rate.

If the drug is eliminated by first-order kinetics, one can plot the concentration on a linear scale over time and achieve a familiar concentration/time curve, with predictable halving of the concentration with each passing time interval. This does not work if the elimination of the drug occurs at a constant rate which is independent of concentration.

###### How does volume of distribution influence half-life?
• Volume of distribution influences the elimination rate constant, because:
• Drug clearance is dependent on the the availability of the drug to the organs of clearance
• That availability is dependent on the volume of distribution
###### What is meant by "α half-life" and "β half-life"?
• A multicompartment model produces a polyexponential curve of concentration over time, with multiple exponents describing different phases of drug distribution and elimination.
• By convention the distribution exponent is called "α" and the elimination exponent is called "β".
• α half-life is the distribution half-life
• β half-life is the terminal elimination half-life
###### How does increasing the drug dose influence the duration of drug action ?
• If elimination is first-order, doubling the dose will lead to an increase of the duration of action by approximately one half-life.
• If elimination is zero-order, doubling the administered dose would lead to the doubling of the duration of action
###### How does the concept of half-life affect sustained dosing?
• If one continues to administer the same dose at half-life time intervals, the drug concentration at the end of every dose will increase.
• However, because elimination is concentration-dependent, the elimination rate will also increase.
• Thus the drug concentration will increase by halves: first to 50%, then to 75%, then to 87.5% and so on.
• Ultimately, the drug will reach close enough to the steady state after about 5 half-lives
###### What are the limitations of the concept of half-life?
• It may be irrelevant if the effect of the drug has little relationship with its plasma concentration
• It usually refers to β half-life, which has less relevance for widely and rapidly distributed drugs
###### Define the term "context-sensitive half time"

"Context-sensitive half time is the time required for a 50% decrease in the central compartment drug concentration after an infusion of the drug is ceased; where the "context" is the prior duration of drug infusion." - Hughes Glass and Jacobs (1992)

Context-sensitive half time  is the concept which relates the drug distribution into and out of tissue compartments to the change in plasma concentration after sustained infusion. It is defined as the time required for the plasma concentration to fall to half of the value at the time of stopping an infusion.

###### How does context-sensitive half-time relate to half-life?
• "Half time" concept is not a "half-life", even though both concepts involve the concentration declining by 50%.
• The main reason for this is :
• all half-lives of a drug are always going to be the same duration in first-order kinetics;
• all the half-times are generally going to be different (i.e., after the first one the next one is likely to be much longer)
• If the infusion has not achieved a steady-state of concentration, the context-sensitive half time will more closely resemble the α half-life (distribution half-life).
• If the infusion is at steady-state and the tissue compartment is well-saturated with drug molecules, the context-sensitive half time will resemble the β half-life (elimination half-life).
###### What factors increase context-sensitive half time?
• Higher the ratio of distribution clearance to clearance due to elimination
• Rapid tissue distribution
• High volume of distribution, eg. high lipophilicity
• Slow elimination
• Increased volume of tissue compartments (eg. increased fat compartment in morbid obesity)
• Smaller volume of plasma compartment (eg. dehydration, old age)
• Clearance of the drug only from the plasma compartment
###### When is the maximum context-sensitive half-time achieved?
• As an infusion continues, the rate of distribution into the tissue compartment slows as the drug concentration within it increases
• Eventually the flow of drug into the compartment is the same as the flow of drug out of the compartment
• At this stage, a steady state is achieved during an infusion, when the infusion distribution and redistribution of a drug is at an equilibrium with elimination.
• The longest possible CSHT is seen when such a steady state is achieved.
• Because infused drugs have maximum dose rates, when equilibrium is established at a maximum dose rate the maximum half-time is achieved
###### What is the maximum context-sensitive half time of propofol and fentanyl?
• Propofol: 20 min
• Fentanyl: 6 hours

(Peck & Hill)
###### What is meant by the term "effect site concentration"?
• Effect site concentration is the concentration of drug at the site of its biological activity, eg. bound to the receptors.
• The "effect site" is a virtual compartment.
###### How does effect site concentration relate to pharmacological effect and rate of effect onset?
• Effect site concentration is proportional to pharmacological effect, whereas plasma concentration may not be.
• The rate of effect onset is determined by the rate of distribution of the drug from other compartments (i.e. central compartment) into the effect site.
• Equilibration between the central and the effect-site compartment follows first-order kinetics, described by the constant ke0
###### What is the effect-site equilibration half-time?
• Effect-site equilibration half-time is the time required for the effect-site compartment to reach 50% of the plasma concentration as an infusion of the drug is running to maintain a constant plasma concentration.
###### How does the effect-site equilibration half-time influence drug dosing? Give an example.
• The slower the effect-site equilibration half-time, the more drug needs to be given as a bolus dose.
• For example, alfentanil:
• Quick effect-site equilibration half-time
• Thus, rapid onset of effect (1.4 minutes to peak effect)
• At 1.4 minutes, only 60% of the total drug dose has been distributed into the tissues
• Whereas for fentanyl, effect-site equilibration half-time is 3.6 minutes - by that stage, 80% of the drug has distributed into fat.

## References

Gibaldi, Milo, and Gerhard Levy. "Pharmacokinetics in clinical practice: I. concepts." Jama 235.17 (1976): 1864-1867.

Rowland, Malcolm, Leslie Z. Benet, and Garry G. Graham. "Clearance concepts in pharmacokinetics." Journal of pharmacokinetics and biopharmaceutics 1.2 (1973): 123-136.

Greenblatt, David J. "Elimination half-life of drugs: value and limitations.Annual review of medicine 36.1 (1985): 421-427.

Toutain, Pierre-Louis, and Alain BOUSQUET‐MÉLOU. "Plasma terminal half‐life." Journal of veterinary pharmacology and therapeutics 27.6 (2004): 427-439.

Goel et al; "Clinical significance of half-life of drugs" Inter. J. of Pharmacotherapy / 4(1), 2014, 6-7

Hughes, Michael A., Peter S. Glass, and James R. Jacobs. "Context-sensitive half-time in multicompartment pharmacokinetic models for intravenous anesthetic drugs.Anesthesiology 76.3 (1992): 334-341.

Shafer, Steven L., and John R. Varvel. "Pharmacokinetics, pharmacodynamics, and rational opioid selection." Anesthesiology74.1 (1991): 53-63.

Bailey, James M. "Context-sensitive half-times." Clinical pharmacokinetics 41.11 (2002): 793-799.

Cortinez, L. I. "What is the ke0 and what does it tell me about propofol?." Anaesthesia 69.5 (2014): 399-402.

Minto, Charles F., et al. "Using the time of maximum effect site concentration to combine pharmacokinetics and pharmacodynamics." Anesthesiology: The Journal of the American Society of Anesthesiologists 99.2 (2003): 324-333.

Coppens, Marc, et al. "Study of the time course of the clinical effect of propofol compared with the time course of the predicted effect-site concentration: performance of three pharmacokinetic–dynamic models." British journal of anaesthesia 104.4 (2010): 452-458.

Sneyd, J. R., and A. E. Rigby-Jones. "Effect site: who needs it?." (2007): 701-704.

Hull, C. J., et al. "A pharmacodynamic model for pancuronium." BJA: British Journal of Anaesthesia 50.11 (1978): 1113-1123.

FURCHGOTT, ROBERT F. "The pharmacology of vascular smooth muscle." Pharmacological Reviews 7.2 (1955): 183-265.

Shafer, Steven L., and John R. Varvel. "Pharmacokinetics, pharmacodynamics, and rational opioid selection.Anesthesiology74.1 (1991): 53-63.

Cortinez, L. I. "What is the ke0 and what does it tell me about propofol?." Anaesthesia 69.5 (2014): 399-402.