# Viva B(i)

This viva refers to  Section B(i) of the 2017 CICM Primary Syllabus, which asks the trainees to "explain the concept of pharmacokinetic modeling of single and multiple compartment models".

###### Define a compartment as related to pharmacokinetics.

A pharmacokinetic compartment is a mathematical concept which describes a space in the body which a  drug appears to occupy. It does not need to correspond to any specific anatomical space or physiological volume.

###### What is a single compartment model of pharmacokinetics?

A single compartment model of pharmacokinetics describes a drug being distributed in a single volume inside the body, from which it is then cleared.

• The compartment is characterised by a distribution volume,  V
• Drug concentration is determined by the dose (I) and distribution volume
• Clearance is determined by the compartment elimination rate (k)

This can be represented as a diagram:

###### What assumptions are made when using this model?
• The drug is instantly and completely dispersed to every part of the compartment
• The drug is thereafter homogeneously distributed throughout the volume.
• The drug is not distributed to anywhere other than this compartment, i.e. it is not absorbed into the tissues.
###### For which drugs might this model be sufficient?

Drugs which are highly water soluble and which are confined to body water as a single compartment, for example aminoglycosides.

Thus:

• High water solubility
• High molecular weight (confined to blood)
• Low protein/tissue binding
• No tissue metabolism
• Chemically stable (no spontaneous degradation)
###### Which properties of a drug might make it unsuitable for a single compartment model? Give some examples.
• Highly lipophilic, eg. anaesthetics
• Highly tissue bound, eg. amiodarone
• Unpredictable elimination, eg. exhaled, metabolised by tissues, chemically unstable (spontaneous degradation)
###### What is a multi-compartment model?

A multi-compartment model accounts for the differences in the rate and volume of drug distribution to different tissues and body fluids. Each compartment represents a space which has distinct pharmacokinetic distribution characteristics.

Distribution of drugs from the blood into the tissues is an important factor in pharmacokinetics of anaesthetic drugs

###### What are the phases of distribution? Can you draw a diagram illustrating the three phases of distribution?

The three phases of distribution are

• Initial rapid distribution
• Second rapid elimination phase
• Terminal "slow elimination" phase

These phases can be expressed as a polyexponential curve of drug concentration over time:

The polyexponential curve has multiple exponents which can be interpreted as half-lives of each distribution phase.

###### What are the limitations of compartment modeling? What are the common incorrect assumptions made by these models?

Some of the common assumptions and fallacies are as follows:

1) That the central compartment is the only compartment from which the drug is eliminated. Of course that is not the case, as for example in the case of cisatracurium where the drug degrades spontaneously no matteer where it is in the body, i.e. elimination takes place in numerous compartments simultaneously.

2) That the multicompartment model is more accurate the more compartments it has. Of course it is not, and often the plasma concentration data derived from a two-compartment model matches the empiric data at least as well as the multicompartment prediction. For instance, Levy et al (1969) found that the plasma concentration of LSD was predicted very well by using only two compartments, and that it was "virtually impossible, in most instances, to distinguish between a two-compartment and more complex pharmacokinetic system on the basis of plasma concentrations alone". For the record, the authors gave 2μg/kg of LSD to five volunteers and then measured their ability to solve maths problems.

3) The mathematical model may include various compartments (eg. brain), but it may be highly inconvenient to verify the concentration of drug in that compartment by sampling it (eg. by brain biopsy). We end up relying on samples from more easily accessible compartments (eg. blood plasma) but as mentioned above the multicompartment models and the two and three compartment models are virtually indistinguishable when you are sampling only plasma, which renders modeling of specific organs highly unreliable.

## References

Mould, D. R., and Richard Neil Upton. "Basic Concepts in Population Modeling, Simulation, and Model‐Based Drug Development—Part 2: Introduction to Pharmacokinetic Modeling Methods." CPT: pharmacometrics & systems pharmacology 2.4 (2013): 1-14.

Nikkelen, Eric, Willem L. van Meurs, and Maria AK Öhrn. "Hydraulic analog for simultaneous representation of pharmacokinetics and pharmacodynamics: application to vecuronium." Journal of clinical monitoring and computing 14.5 (1998): 329-337.

Gupta, D. K., and E. I. Eger. "Inhaled Anesthesia: The Original Closed‐Loop Drug Administration Paradigm." Clinical Pharmacology & Therapeutics 84.1 (2008): 15-18.

Eger, E. I. "A mathematical model of uptake and distribution" Uptake and Distribution of Anesthetic Agents, ed EM Papper and RJ Kitz." (1963).

Peng, Philip WH, and Alan N. Sandler. "A review of the use of fentanyl analgesia in the management of acute pain in adults." The Journal of the American Society of Anesthesiologists 90.2 (1999): 576-599.

Hug Jr, C. C., and Michael R. Murphy. "Tissue redistribution of fentanyl and termination of its effects in rats." Anesthesiology 55.4 (1981): 369-375.

Gerlowski, Leonard E., and Rakesh K. Jain. "Physiologically based pharmacokinetic modeling: principles and applications." Journal of pharmaceutical sciences 72.10 (1983): 1103-1127.

Levy, Gerhard, Milo Gibaldi, and William J. Jusko. "Multicompartment pharmacokinetic models and pharmacologic effects." Journal of pharmaceutical sciences 58.4 (1969): 422-424.

Rescigno, Aldo. "Synthesis of a multicompartmented biological model." Biochimica et biophysica acta 37.3 (1960): 463-468.

Nestorov, Ivan A., et al. "Lumping of whole-body physiologically based pharmacokinetic models." Journal of pharmacokinetics and biopharmaceutics26.1 (1998): 21-46.

Gerlowski, Leonard E., and Rakesh K. Jain. "Physiologically based pharmacokinetic modeling: principles and applications." Journal of pharmaceutical sciences 72.10 (1983): 1103-1127.