Anesthesia Pharmacology Chapter 4: Physics and Anesthesiology
photo: Richard Struthers, The Anesthesia Machine
The reason why vaporizers are required in anesthesia is simply that most volatile, potent inhaled agents exists as a liquid at room temperature and atmospheric pressure.
Vaporizers are needed them to convert the liquid-form of the anesthetic to vapor phase and then importantly add a certain amount of this vapor to the anesthetic circuit.
Contemporary vaporizers are quite far removed from the original ether inhalers or even copper kettles and are now described as temperature-compensated, variable-bypass machines.
Since the vapor pressure associated with a potent volatile agent will be dependent only on the agent itself and temperature, it is not surprising that newer systems automatically compensate for temperature.
Review: if we consider an anesthetic agent, residing in liquid form within a container, it is easy to imagine some anesthetic molecules escaping from the liquid in moving into the gas phase. As this process continues over time, eventually a condition will be reached in which the likelihood of a molecule moving from the liquid to the vapor phase is essentially equal to the likelihood of a molecule of anesthetic in the vapor phase moving to the liquid phase. This condition represents the equilibrium case. (Figure 1, below) For a given temperature, and temperature influences this process, once equilibrium condition has been met the anesthetic would be at its saturated vapor pressure (at that temperature).
It is an important point that the vapor pressure (force) associated with the vapor phase will be dependent on the physical properties of the individual agent and temperature. If the temperature is increased to point that the vapor pressure is equal to the atmospheric pressure and that the liquid, all of the liquid, converts to the vapor phase, and the temperature would be equal to the liquid's boiling point.
Boiling point: desflurane (Suprane) 22.8 oC
Boiling point: isoflurane (Forane) 48.5 oC
Boiling point: halothane (Fluothane) 50.2 oC
Boiling point: enflurane (Ethrane) 56.5 oC
Boiling point: sevoflurane (Sevorane, Ultane) 58.5 oC
Different anesthetic agents have different volatilities which means that they have different saturated vapor pressures (SVP) and that the most volatile agents have the highest saturated vapor pressure (Figure 2, below). Boiling points decrease with decreasing pressure, for example and increasing altitude.
29,31In the above figure we note different vapor pressure-temperature relationships between common volatile agents and recognize that desflurane (Suprane) falls outside the grouping.
Not surprisingly, special vaporizer is required for desflurane given that it is very near its boiling point at room temperature.
30Vapor concentration: Anesthetic vapor pressure may be represented as absolute pressure (mmHg) or in volumes percent of one atmosphere which is volume of anesthetic vapor per 100 volumes of total gas.
The relationship between volume percent in the anesthetic agents partial pressure (fractional) is given using Dalton's Law as: volume% = (partial pressure of anesthetic agent / total ambient pressure) x 100.
Dalton's law indicates that each gas will exert pressure independently of the other gasses present.
From kinetic theory it is reasonable that transfer of momentum by molecules colliding with the walls of the container would be independent of other molecules that may or may not be present.
An example could be oxygen gas at atmospheric pressure (760 mm mercury) in which oxygen molecules correspond to 21% of all gas molecules present.
Therefore the partial pressure of O2 would be 21% x 760 mm mercury or about 160 mm mercury
The above calculation assumes dry air; however, if the air is saturated with water vapor at 37 oC, which is the physiological circumstance, then the water vapor pressure must be taken into consideration in calculating the partial pressure of oxygen.
Since vapor pressure will be dependent on temperature, the saturated vapor pressure for H2O will be 47 mm Hg at 37 oC.
Therefore, partial pressure of oxygen must be calculated based on 760 mm Hg - 47 mm Hg or 713 mm Hg, i.e. 21% x 713 mm Hg = about 150 mm Hg for the partial pressure of O2 .
29,30Importantly, volumes percent reflects ratios of gas molecules in a mixture [(partial pressure of anesthetic agent / total ambient pressure) x 100], whereas partial pressure is absolute and anesthetic uptake in potency is directly relatedto partial pressure, but only indirectly to volumes percent.
Vaporizers designed to support desflurane (Suprane) administration may be based on volume percent delivering, whereas current variable-bypass vaporizers, which are not used for desflurane (Suprane), deliver a constant partial pressure of agent.
The systems respond differently in low or high-pressure circumstances.
30MAC (minimum alveolar concentration): As we have described earlier, the MAC value for an inhalational agent is one that causes a lack of response to painful stimulation in 50% of patients.
The painful stimulation would be equivalent to a surgical incision.
Typically, in order to cover more nearly the entire population, agents will be administered above 1 MAC, say 1.2-1.3 MAC.
MAC values for some inhalational agents are given below:
Sevoflurane (Sevorane, Ultane): 1.7
Desflurane (Suprane): about 6
These MAC numbers referred to volumes % of end-tidal alveolar gas at 760 mm Hg (1 atm).
MAC values can also be expressed in terms of mm Hg by multiplying the MAC value given above times 760 mm Hg.
Considering MAC in terms of a minimum alveolar partial pressure of the specific agent rather than volumes% may be more appropriate because the partial pressure or anesthetic tension in the brain determines the anesthetic effect.
Applying the conversion factor to the anesthetics above would yield the following results for agent partial pressure at 1 MAC (760 mm Hg ambient pressure).
Halothane (Fluothane) 0.75 MAC = 5.7 mm Hg
Enflurane (Ethrane) 1.68 MAC = 12.8 mm Hg
Isoflurane (Forane) 1.15 MAC = 8.7 mm Hg
Methoxyflurane 0.16 MAC = 1.2 mm Hg
Desflurane (Suprane) [for age-dependent MAC range of 6-7.25) = 46 mm Hg-55 mm Hg
Sevoflurane (Sevorane, Ultane) 2.1 MAC = 16 mm Hg
30,29Heat of Vaporization. Energy (heat) is required to promote the vaporization process.
The molecular basis of this requirement is probably be intermolecular forces in the liquid phase that must be overcome in order to promote molecular transfer to the gas phase.
Formally, the latent heat of vaporization would be the amount of calories (heat) needed to convert a unit mass (e.g. one gram) of the liquid into vapor.
Given the molecular basis that underlies the energy required, that is it's easy to imagine that different molecules might have different degrees of intermolecular forces that need to be overcome, the heat to vaporization volatile anesthetics differ one to the next.
Specifically, halothane (Fluothane) requires 35 cal/g; isoflurane (Forane) and enflurane (Ethrane) require 41 cal/g where as methoxyflurane requires 58 cal/g. [Methoxyflurane is not available in United States any longer but it may be a useful reference compound]
Since the vaporization process requires heat, it is not surprising that the vaporization process, which draws heat from the liquid anesthetic itself as well as the container, is a cooling process.
So, as vaporization proceeds the cooling of the liquid anesthetic would tend to retard the vaporization process.
Since vaporization is a temperature dependent process, if no heat is added, vaporizer output would decline.
Accordingly, many vaporizers have temperature compensatory systems to ensure that heat loss due to vaporization is compensated and therefore does not reduce output.
The specific heat is another parameter of interest and is defined began as calories required to raise the temperature of the unit mass (e.g. one gram) by 1 oC--it is a distinct value--only for one gram going one degree.
The technical definition for specific heat is that it is a ratio of the heat capacity of a substance to the capacity of the reference material, typically water.
The heat capacity of water is defined as one calorie per gram per degree Celsius. Here are some examples of specific heats:
gold: 0.0312 cal/ (g deg C) (at 18 oC)
copper: 0.092 cal/ (g oC) (at 20 oC) or 0.389 J/gm oC
lead: 0.031 cal/gm oC or 0.13 J/gm oC
cortical bone: 0.44 cal/ (g oC)
water 1 cal/ (g deg C) (at 18 oC)
The formal equation is Q = cm T, where Q is the heat added, c is the specific heat, and T is the temperature change.
Note above to be specific heat of copper and lead appear quite different; however, if the specific heat is expressed in terms of energy per mole as opposed energy per unit mass the differences minimal and minimal differences are observed among metals or among solids in general at room temperature and above. Therefore, on a molar basis:
copper: 0.386 J/gm oC x 63.6 gm/mole = 26.6 J/mol oC
lead: 0.128 J/gm oC x 207 g/mole = 26.6 J/mol oC
Important in vaporizer design and construction an important characteristic has to do with heat conduction to the liquid anesthetic.
Since we know that will be a tendency during the vaporization process for a reduction in temperature and that constant outflow would require compensation for this heat loss, thermal conductivity is an important factor.
Substances with both a high specific heat and high thermal conductivity are thought best for vaporizer construction.
Copper approximates an ideal substance and more currently stainless-steel and bronze are also used in vaporizer fabrication.
A vaporizer type known as "Copper Kettle ®" will be considered later.
Heat flow (Q) = A dT/dx where is the thermal conductivity value, A is the cross-sectional area, and dT/dx is the temperature/thickness gradient.
Substances which have large (thermoconductivity values) promote good heat conduction.
The above equation form is derived from Fourier's Law of heat conduction, q* = -k(dT/dx) where q* is the heat flux which is the rate at which heat moves through unit surface (area) and which has the units of energy/(time x area). x is the x-direction distance and T is the temperature. k in this formulation corresponds to above.
With the assumption that the lines of heat flow are parallel then q* = -k(dT/dx) can be written as Q/t (1/A) = -k (Tcold - Thot)/x where Q/t is the rate of heat supplied, A is the heat flow area and Tcold , Thot are the boundary temperatures.
This term refers to energy per unit mass that is either absorbed or evolved when a substance changes phases.
Phase change is relevant in anesthesia because the volatile agents transition from the liquid phase to the gas phase.
There are two types of specific latent heat to consider:
(a) Latent heat of fusion which is heat given off when a liquid changes into a solid and
(b) Latent heat of vaporization which involves heat absorption when a liquid turns into the gas.
The general idea is that a liquid is in a higher energy state compared to solid and that the vapor his and a higher energy state compared to the liquid.
Accordingly, energy (heat) must be provided to induce phase change from solid to liquid as well as from liquid to vapor.
Because the standard vapor pressures (SVP) of commonly used inhaled anesthetics are in substantial excess compared to anesthetic requirements, a dilutional step is needed. [halothane (Fluothane) SVP: 243 mm Hg; isoflurane (Forane) SVP: 238 mm Hg; enflurane (Ethrane) SVP: 175 mm Hg; sevoflurane (Sevorane, Ultane) SVP: 160 mm Hg].
The dilutional step is accomplished by the vaporizer in accord with mixing gas that has bypassed the chamber containing volatile agent with gas that contains saturated vapor.
Figure below adapted from reference 30 and from Eisenkraft, JB: Vaporizers and vaporization of volatile anesthetics. In Eisenkraft JB, editor, Progress in Anesthesiology, vol 2, San Antonio,1988, Dannemiller Memorial Educational Foundation) (reference 40)
30Most vaporizers in current use are of the variable-bypass type and are concentration-calibrated.
This description is not applicable to the Ohmeda Tec 6, which is specific for the anesthetic agent desflurane (Suprane).
As shown above, in the variable bypass design which would include the Ohmeda Tec series (except 6) and the Drager Vapor 19.1 the total gas from the anesthesia machine flow meters is split with some gas flowing into the vaporizing chamber, picking up anesthetic agent molecules, while a larger gas pass bypasses the chamber completely.
Vaporizer outflow is based on the re- mixing of the two gas pass and results in administration to the patient of the anesthetic concentration indicated on the dial.
30The Ohmeda 855A field anesthetic machine is used by the United States military and is classified as a measured flow vaporizer.
Other than in this context, measured flow machines are rarely encountered but are often referred to as Copper Kettle® (Foregger, Puritan-Bennett) or Verni-Trol ®(Ohmeda).
This system is referred to as measured flow because measured flow is sent by separate O2 flowmeter to pass to the vaporizer with the output being at saturated vapor pressure for the anesthetic (SVP).
In order to dilute this otherwise lethal anesthetic concentration, output from that gas flow pass is combined with gas passing from main flowmeters, perhaps containing nitrous oxide and O2 with the resultant gas mixture exhibiting proper anesthetic concentration for the patient. See Figure below adapted from reference 30 and from Eisenkraft, JB: Vaporizers and vaporization of volatile anesthetics. In Eisenkraft JB, editor, Progress in Anesthesiology, vol 2, San Antonio,1988, Dannemiller Memorial Educational Foundation) (reference 40)
243 mm Hg
(volume % at 1 atm)
238 mm Hg
172 mm Hg
sevoflurane (Sevorane, Ultane)
160 mm Hg
As can be appreciated from examination of figures 1 & 2 above, gas flow paths are designed to ensure development of a saturated vapor concentration in the vaporizing compartment.
30This requirement may be satisfied by having sufficient surface area in the case of variable bypass systems or "flow-over" systems or in the case of copper kettle-type systems bubbling O2 through the liquid agent.
Various techniques may be used to achieve adequate surface areas for evaporation including, in the "flow-over" system use of baffles/wicks; analogously, for the bubble through systems small bubbles can be created by passing through sintered bronze disks.
Desflurane (Suprane) vaporizers will be considered separately because of the requirements peculiar to desflurane (Suprane) and related to its very high saturated vapor pressure at room temperature (669 mm Hg at 20oC).
In other words, a special vaporizer (Ohmeda Tec-6) for desflurane (Suprane) has a specific, unique design to accommodate special requirements.
Assumptions: a temperature = 20oC; Saturated vapor pressures as described in Table 1 are present in the vaporizing chamber
For each quantity of carrier gas entering the vaporizing compartment (i.e. not bypass gas), the same quantity of carrier gas gas will be leaving the chamber.
Given that the carrier gas represents 100% upon entering the chamber, the carrier gas can no longer represent 100% in the chamber because of the presence of the volatile agent at its saturated vapor pressure.
30Using halothane (Fluothane) as an example, we note from table 1, that its percent contribution in the vaporizing chamber at 20oC is about 32% which is calculated like taking halothane's (Fluothane) SVP which is 243 mm Hg and dividing by atmospheric pressure which would be 760 mm Hg, i.e. (243 mm Hg/760 mm Hg) x 100.
Knowing that in the vaporizing compartment halothane (Fluothane) contributes 32% we can readily calculate the% contributed by the carrier gas as 100% - 32% = 68%.
If we specify that the volume of carrier gas entering the chamber were 100 ml, we can now calculate in ml the volume of the agent vapor using this relationship:
SVPvapor (mm Hg)/total pressure (mm Hg) and = agent vapor (x ml)/(carrier gas (y ml) + agent vapor (x ml) and by substitution
243mm Hg/760 mm Hg =x mls/(100mls + x mls) noting that the 100 in the denominator comes from the carrier gas volume of 100
0.32 = x / (100 + x )
x = 0.32 (100 + x)
x = (0.32 * 100) + 0.32 x
1x = 32 + 0.32x
0.68 x = 32
x = 47 mls (if we knew the agent volume , i.e x and didn't know y, the amount of carrier gas entering the bypass chamber, we could calculate y by an analagous approach.
This analysis leads to the conclusion that a greater total volume of gas will be leaving the chamber than entering it because anesthetic gas vapor volume adds to the fresh gas volume entering the system.
We can qualitatively check this result by the use of the Equation of State Calculator below: setting volume as the dependent variable and increasing the number of moles while keeping pressure and temperature constant we can see the increase in volume in accord with Avogadro's Law. The volume must increase in response to the additional anesthetic agent molecules added to the vapor phase.
29Andrews, J.J. "Inhaled Anesthetic Delivery Systems" in Anesthesia 5th edition vol. 1 (Miller, R.D. editor; Cucchiara, R.F., Miller, Jr., E.D., Reves, J.G., Roizen, M.F. and Savarese, J.J., consulting editors) Churchill Livingstone, Philadelphia, 2000, pp 174-206.
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40Eisenkraft, JB: Vaporizers and vaporization of volatile anesthetics. In Eisenkraft JB, editor, Progress in Anesthesiology, vol 2, San Antonio,1988, Dannemiller Memorial Educational Foundation)