The blood–gas partition coefficient

Abstract

A partition coefficient (λ) describes the relative affinity of a volatile anaesthetic for two phases and how that anaesthetic distributes itself between the two phases when equilibrium has been achieved. The blood–gas partition coefficient (λb/g), or Ostwald coefficient for blood–gas, is a pharmacological term used to describe the solubility of a volatile anaesthetic agent. Volatile agents with a low blood–gas partition coefficient (less soluble) will exert a high partial pressure and produce a more rapid onset and offset of anaesthetic action.

Full text

S8
South Afr J Anaesth Analg 2020; 26(6)Supplement http://www.sajaa.co.za
Southern African Journal of Anaesthesia and Analgesia. 2020;26(6 Suppl 3):S8-11
https://doi.org/10.36303/SAJAA.2020.26.6.S3.2528
Open Access article distributed under the terms of the
Creative Commons License [CC BY-NC 3.0]
http://creativecommons.org/licenses/by-nc/3.0
South Afr J Anaesth Analg
ISSN 2220-1181 EISSN 2220 -1173
© 2020 The Author(s)
FCA 1 REFRESHER COURSE
Introduction
Volatile anaesthetic agents produce their eect through their
action on the brain. The depth of anaesthesia is therefore de-
termined by the concentration of volatile anaesthetic agent in
the brain. The speed of induction and recovery from anaesthesia
is governed by the speed at which this concentration in the brain
changes. For a volatile anaesthetic agent to reach the brain it
must be distributed throughout the body. The extent to which
the volatile anaesthetic gets taken up by the body tissues will
have an inuence on the speed of uptake and elimination by the
brain.1
Gas laws and gas exchange
Inhalational anaesthetics are administered as gases or vapours,
therefore a specic set of physical principles applies to the
delivery of these agents. Dalton's law of partial pressures states
that in a mixture of non-reacting gases, the totalpressureexerted
is equal to the sum of the partial pressures of the individual
gases.2
Partial pressure is the pressure a gas exerts proportional to its
fractional mass (Figure 1); this is the same pressure each gas
would have if it alone occupied the same volume:
Ptot = P1 + P2 + P3 … + Pn
Henry's law states that at a constant temperature, the amount
of a given gas that dissolves into a given type and volume of
liquid is directly proportional to the partial pressure of the gas in
equilibrium with that liquid.3,4 An equivalent way of stating the
law is that the solubility of a gas in a liquid is directly proportional
to the partial pressure of the gas above the liquid:2
C = kP
C – Concentration of dissolved gas (mol/l)
k – Henry’s proportionality constant (specic to solute, solvent
and temperature)
P – Partial pressure of the gas above the solution (kPa)
Volatile anaesthetics or gases equilibrate throughout the
body based on their respective partial pressures and not con-
centrations (Figure 2). Once a volatile anaesthetic agent reaches
steady state, the partial pressure of the agent within the alveoli
(PA) is in equilibrium with the partial pressure in arterial blood
(Pa) as well as partial pressure within the brain (PB). The alveolar
partial pressure (PA) is therefore an indirect measure of brain
partial pressure (PB).5
Summary
A partition coecient (λ) describes the relative anity of a volatile anaesthetic for two phases and how that anaesthetic distributes
itself between the two phases when equilibrium has been achieved. The blood–gas partition coecient (λb/g), or Ostwald
coecient for blood–gas, is a pharmacological term used to describe the solubility of a volatile anaesthetic agent. Volatile agents
with a low blood–gas partition coecient (less soluble) will exert a high partial pressure and produce a more rapid onset and oset
of anaesthetic action.
Keywords: blood–gas partition coecient, Ostwald coecient, volatile anaesthetic, solubility
The blood–gas partition coefficient
E Bezuidenhout
Department of Anaesthesiology, Charlotte Maxeke Johannesburg Academic Hospital, University of the Witwatersrand, South Africa
Corresponding author, email: emily.bezuidenhout@gmail.com
Figure 1: Partial pressureof a gas is proportional to its fractional
concentration2

S9
The blood–gas partition coecient
South Afr J Anaesth Analg 2020; 26(6)Supplement http://www.sajaa.co.za
How long it takes for each volatile anaesthetic agent to reach
steady state conditions depends on the individual properties
of the agent and numerous physiological factors.6 Kety6 deter-
mined that the alveolar partial pressure curves for all inert gases
(volatile anaesthetics are considered to behave as inert gases)
have the same characteristics.
When an inert gas is introduced at a constant partial pressure in
the inspired air, it takes time for the tissues in the body to obtain
the gas at this partial pressure. Pulmonary ventilation carries the
gas to the alveolar membrane where it diuses to the pulmonary
blood and gets distributed via the systemic circulation to the
tissues. Diusion across the capillary membranes, interstitial uid
and cellular membrane takes place so that venous blood leaving
the capillary is in equilibrium with the tissue. The blood returning
to the lungs carries a fraction of the inspired gas concentration
and is again equilibrated with the alveolar gas. In this way the
alveolar (or arterial) and venous (or tissue) partial pressures of
the inhaled anaesthetic gradually rise towards equilibrium with
the partial pressure of the inspired gas.7 If this rise in partial
pressure is plotted against time, it produces a curve that is similar
for every inert gas or volatile anaesthetic (Figure 3).6
This curve has an initial rise, a knee and a tail. The steep initial
rise represents the phase where ventilation moves the inhaled
agent rapidly into the lungs. Following this, the knee stage
arrives where lung washout gives place to tissue
saturation. The slope of the knee is determined by
the rate of uptake by the vessel-rich tissues such as
the heart, liver and brain. Lastly, the slope of the tail
is determined by the more gradual rate of uptake of
volatile anaesthetic by the vessel-poor tissues such
as the muscles and fat. The dierence in slopes
between the volatile anaesthetic agents is mainly
determined by the dierence in their solubilities in
tissue and blood (Figure 4).
Recovery from volatile anaesthesia results from
the elimination of anaesthetic from the brain. This
process is simply the reversal (or wash-out) of the
uptake process so the principal factors determining
induction and recovery are the same.7
Blood-gas partition coefficients and
volatile anaesthetic solubility
A partition coecient describes the relative a-
inity of an anaesthetic for two phases and how
that anaesthetic partitions itself between the two phases when
equilibrium has been achieved.3,8,9 The blood gas partition
coecient is dened as the ratio of the amount of anaesthetic
in blood and gas when the two phases are of equal volume and
pressure and in equilibrium at 37 °C.3
A partition coecient is simply the ratio of the concentration
ofanaestheticin one phase compared to another and therefore
has no units (Table I).8,9 For example, halothane has a λB/G of 2.3; if
we had an equal volume of air in contact with an equal volume
of blood and halothane is allowed to move freely between these
compartments until the pressure is equal in each compartment,
we have the equivalent of 1 molecule of halothane in the air to
every 2.3 molecules dissolved in the blood (Figure 5).
Partition coecientsare used to describe the solubility ofvolatile
anaesthetics in a number of dierent solvents. Theblood–gas
partition coecientis an important determinant of the speed of
Figure 2: Partial pressure (P) of the gas is equal between the two
phases even though concentration of the gas in solution (C1 and C2)
differs
Figure 3: Kety’s alveolar partial pressure curve of inhalant during
uptake6
Figure 4: The rise of alveolar partial pressure (PA) towards inspired partial pressure (PI) in
different volatile anaesthetics8

S10
The blood–gas partition coecient
South Afr J Anaesth Analg 2020; 26(6)Supplement http://www.sajaa.co.za
anaesthetic induction and recovery. It describes the distribution
of an inhalational agent between a gaseous phase (alveolar air)
and the blood.The greater the blood–gas partition coecient,
the greater the solubility in blood.4,9
Table I: Partition coefficients of volatile anaesthetic at 37 °C 8
Agent Blood/
Gas
Brain/
Blood
Muscle/
Blood
Fat/
Blood
MAC
(%)
Nitrous oxide 0.47 1.1 1.2 2.3 104
Desflurane 0.42 1.3 2.0 27 6
Sevoflurane 0.65 1.7 3.1 48 2
Isoflurane 1.4 2.6 4.0 45 1.4
Halothane 2.4 2.9 3.5 60 0.75
Poorly soluble agents (λB/G < 1) generate a high partial pressure,
which creates a steep gradient between Pa and PB. Volatile
anaesthetic agents with a low blood–gas partition coecient
will therefore exert a high partial pressure and produce a more
rapid onset and oset of action.9
Conversely, soluble volatile anaesthetic agents with a low blood–
gas partition coecient (λB/G > 1) dissolve easily into pulmonary
blood without substantially increasing the partial pressure (Pa).
This leads to a slow onset of anaesthesia due to a large fall in PA as
the agent leaves the alveolus, decreasing the gradient for further
diusion and a small gradient between PA and PB.9
Uptake of volatile anaesthetic agents
The rate of uptake of anaesthetic agent by the bloodstream is
predicted by the Fick equation:10
VB = λB/G * Q ((PA-PV)/PB)
VB – uptake by blood
λB/G – blood–gas partition coecient (solubility of the volatile
anaesthetic)
Q – cardiac output
PA – alveolar partial pressure of anaesthetic
Pv – venous partial pressure of anaesthetic
PB – barometric pressure
Factors affecting the blood–gas partition coefficient
Temperature
Hypothermia increases the solubility of volatile anaesthetics in
blood. The λB/G therefore increases as temperature decreases and
vice versa.11-13
Haematocrit
Haemodilution or a reduction in haematocrit will generally de-
crease the solubility (λB/G) of volatile anaesthetics in blood.11,13,14
The extent to which the λB/G changes is variable and depends on
the particular agent’s anity for red cells. An agent that is less
soluble in red cells, e.g. isourane, will have a decreased blood–
gas partition coecient in anaemia. The λB/G for sevourane and
desurane are mostly unaected by changes in haemoglobin or
haematocrit.14
Serum constituents
Concentrations of serum constituents such as albumin, globulin,
triglycerides, and cholesterol can inuence the λB/G.15 These
serum molecules eectively act as molecular sinks to bind
anaesthetic agents, thereby increasing their blood solubility.
Serum triglyceride concentrations have an important eect
on the blood–gas partition coecient for halothane because
of its much higher solubility compared to the other volatile
anaesthetics.16
Obesity
An increase in BMI causes a modest increase in FI/FA and λB/G of
volatile anaesthetic agents; this eect is more pronounced in
those agents with a higher solubility. An increased BMI increases
anaesthetic uptake and the need for the delivered anaesthetic to
sustain a constant alveolar concentration.17
Age
Lower blood–gas partition coecients in children explain in part
the more rapid rise of alveolar anaesthetic partial pressure in
this age group.18,19 λB/G in neonates were found to be 18% lower
than in adults, and for children and the elderly 12% lower than in
adults.18 Halothane, isourane and nitrous oxide are signicantly
less soluble in fetal compared to maternal blood; this nding is
independent of the known dierences in lipid concentration,
protein and haemoglobin content of fetal blood.20,21
Conclusion
The blood–gas partition coecient is a ratio of the concentration
of volatile anaesthetic in blood compared to alveolar gas once
the partial pressure has equilibrated. It is a pharmacological
term used to describe the solubility of a volatile anaesthetic
agent. Volatile agents with a low blood–gas partition coecient
(λB/G < 1) are poorly soluble with subsequent rapid rise in partial
pressure and onset of anaesthetic action.
Figure 5: Blood–gas partition coefficients for halothane and nitrous
oxide2

S11
The blood–gas partition coecient
South Afr J Anaesth Analg 2020; 26(6)Supplement http://www.sajaa.co.za
Conflict of interest
The author declares no conict of interest.
Funding source
None.
ORCID
E Bezuidenhout https://orcid.org/0000-0002-9233-8142
References
1. Eger EI, Larson CP. Anaesthetic solubility in blood and tissues: values and
significance. Br J Anaesth. 1964;36:140-9. https://doi.org/10.1093/bja/36.3.140.
2. Hendrickx JFA, De Wolf A. Special aspects of pharmacokinetics of inhalation
anaesthesia. Handb Exp Pharmacol. 2008;182:159-86. https://doi.
org/10.1007/978-3-540-74806-9_8.
3. Soares JHN, Brosnan RJ, Fukushima FB, Hodges J, Liu H. Solubility of haloether
anaesthetics in human and animal blood. Anaesthesiology. 2012;117:48-55.
https://doi.org/10.1097/ALN.0b013e3182557cc9.
4. Gropper MA, Miller RD. Miller’s anaesthesia. 9th ed. Philadelphia (PA):
Elsevier;2020. p. 509-39.
5. Carpenter RL, Eger EI. Alveolar-to-arterial-to-venous anesthetic partial
pressure differences in humans. Anaesthesiology. 1989;70:630-5. https://doi.
org/10.1097/00000542-198904000-00014.
6. Kety SS. The theory and applications of the exchange of inert gas at the lungs
and tissues. Pharmacol Rev. 1951;3:1-41.
7. Bourne JG. Uptake, elimination and potency of the inhalational anaesthetics.
Anaesthesia. 1964;19:12-32. https://doi.org/10.1111/j.1365-2044.1964.tb03674.x.
8. Butterworth JF. Morgan & Mikhail’s clinical anesthesiology. 6th ed. New York:
McGraw-Hill; 2018. p. 1393.
9. Khan KS, Hayes I, Buggy DJ. Pharmacology of anaesthetic agents II: inhalation
anaesthetic agents. Contin Educ Anaesth Crit Care Pain. 2014;14:106-11. https://
doi.org/10.1093/bjaceaccp/mkt038.
10. Peyton PJ, Fortuin M, Robinson GJB, et al. The rate of alveolar-capillary uptake
of sevoflurane and nitrous oxide following anaesthetic induction. Anaesthesia.
2008;63:358-63. https://doi.org/10.1111/j.1365-2044.2007.05355.x.
11. Zhou J-X, Liu J. Dynamic changes in blood solubility of desflurane, isoflurane,
and halothane during cardiac surgery. J Cardiothorac Vasc Anesth. 2001;15:555-
9. https://doi.org/10.1053/jcan.2001.26529.
12. Stoelting RK, Longshore RE. The effects of temperature on fluroxene,
halothane, and methoxyflurane blood-gas and cerebrospinal fluid-gas
partition coefficients. Anaesthesiology. 1972;36:503-5. https://doi.
org/10.1097/00000542-197205000-00018.
13. Sada T, Macuire HT, Antonio Aldrete J. Halothane solubility in blood during
cardiopulmonary bypass: the effect of haemodilution and hypothermia. Can
Anaesth Soc J. 1979;26:164-7. https://doi.org/10.1007/BF03006975.
14. Esper T, Wehner M, Meinecke C-D, Rueffert H. Blood-gas partition coefficients for
isoflurane, sevoflurane, and desflurane in a clinically relevant patient population.
Anesth Analg. 2015;120:45-50. https://doi.org/10.1213/ANE.0000000000000516.
15. Shim JC, Kaminoh Y, Tashiro C, Miyamoto Y, Yoo HK. Solubility of volatile
anesthetics in plasma substitutes, albumin, intravenous fat emulsions,
perfluorochemical emulsion, and aqueous solutions. J Anesth. 1996;10:276-81.
https://doi.org/10.1007/BF02483395.
16. Saraiva RA, Willis BA, Steward A, Lunn JA, Mapleson WW. Halothane solubility in
human blood. Br J Anaesth. 1977;49:115-9. https://doi.org/10.1093/bja/49.2.115.
17. Lemmens HJM, Saidman LJ, Eger EI, Laster MJ. Obesity modestly affects inhaled
anaesthetic kinetics in humans. Anaesth Analg. 2008;107:1864-70. https://doi.
org/10.1213/ane.0b013e3181888127.
18. Lerman J, Gregory GA, Willis MM. Age and solubility of volatile
anaesthetics in blood. Anaesthesiology. 1984;61:139-43. https://doi.
org/10.1097/00000542-198408000-00005.
19. Zhou J-X, Liu J. The effect of temperature on solubility of volatile
anaesthetics in human tissues. Anaesth Analg. 2001;234-8. https://doi.
org/10.1097/00000539-200107000-00047.
20. Gibbs CP, Munson ES, Tham MK. Anaesthetic solubility coefficients for
maternal and fetal blood. Anaesthesiology. 1975;43:100-2. https://doi.
org/10.1097/00000542-197507000-00020.
21. Malviya S, Lerman J. The blood/gas solubilities of sevoflurane,
isoflurane, halothane, and serum constituent concentrations in
neonates and adults. Anaesthesiology. 1990;72:793-6. https://doi.
org/10.1097/00000542-199005000-00003.