Physics in Anesthesiology:Basic Science ReviewKeith E. Gipson, MD, PhD and Jeffrey B. Gross, MD

Department of AnesthesiologyUniversity of Connecticut School of Medicine

Farmington, Connecticut

Learning Objectives:As a result of completing this activity, the participantwill be able to� Explain how our equipment is supposed to work� Troubleshoot problems with anesthesia equipment

when they occur, thereby avoiding potentialpatient complications

� Use fundamental principles to instruct trainees inthe proper use of anesthesia equipment

Author Disclosure Information:Drs. Gipson and Gross have disclosed that they haveno financial interests in or significant relationshipwith any commercial companies pertaining to thiseducational activity.

Safety in the delivery of anesthesia is inextricablylinked to the proper functioning of anesthesiaequipment and resuscitative equipment, and to the

presence of a consultant in anesthesia who can maintainsafety in the face of equipment failure. This consultantrelies upon basic principles in troubleshooting and evalua-tion of alternatives when equipment malfunction occurs.This chapter reviews the standards and principles that

underlie the function of anesthesia equipment, includingmeasurement of patient variables and prevention ofcommon safety mishaps (see Supplemental Digital Content1, http://links.lww.com/ASA/A124).

PRESSURE

Pressure is defined as force per unit area. The definitionimplies that even a small pressure may exert a large force ifthe area is large, and that even a small force can exert alarge pressure if the area is small. Some common units ofpressure and their clinical applications are listed in Table 1(see Supplemental Digital Content 2, http://links.lww.com/ASA/A125).

Pressure is defined as force per unit area. The

definition implies that even a small pressure

may exert a large force if the area is large, and

that even a small force can exert a large

pressure if the area is small.

Measurements of pressure may be expressed as gaugepressure or absolute pressure. Gauge pressures are meas-ured relative to ambient pressure, e.g. tire pressure, pres-sure in a compressed gas cylinder, blood pressure. Absolutepressures are measured relative to vacuum, e.g. vaporpressures, blood gases, and situations involving gas laws.

40

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Types of pressure gauges in the operating room:

� Diaphragm—Useful for measuring fairly low gas pres-sures, e.g. airway pressures, noninvasive blood pressures.Gas pressure at the inlet expands elastic capsules, whichpush a connecting rod that drives a gear/hair springassembly to turn the indicator needle (Figure 1).

� Bourdon tube—Useful for measuring high gas pressures,e.g. compressed gas cylinder pressures. Gas pressure atthe inlet deforms a curved metal tube to drive a lever armassembly to turn the indicator needle (Figure 2).

� Strain gauge—Useful for precise electronic measurementof time-varying signals, e.g. arterial and central venous

pressure waveforms. Fluid pressure deforms a diaphragmto which a ‘‘zigzag’’ pattern of conductive material isattached. As the conductor is stretched, its electricalresistance increases; a Wheatstone bridge circuit convertsthe changes in resistance into a voltage signal that can bedisplayed by electronic monitors (Figures 3 and 4).

In the operating room, pressure regulators reduce tankpressures (750 to 2,000 psi) to approximately 50 psi forsupply to the anesthesia machine. Wall gas pressures arearound 50 psi as well. The pressure regulation is accom-plished using a spring–diaphragm–valve assembly in anegative feedback relationship between a high-pressurechamber and a low-pressure chamber. The spring providesan opening force for the valve, whereas valve opening is

Table 1. Common Units of Pressure Used in MedicalApplications

Clinical Application UnitsAtmosphericPressure

Compressed gas cylinderpressure

Pounds per squareinch (psi)

14.7 psi

Blood gases Pa¼1N/m2 101.3 kPa(1 kPa¼1,000Pa)

Blood/CSF pressure,blood gases

mm Hg 760mm Hg

Airway pressure cm H2O 1,029 cm H2O

Figure 1. Cutaway view of a ‘‘capsule’’ type pressure gauge commonly usedfor measuring relatively low pressures (e.g., arterial blood pressures,barometric pressure).

Figure 2. Cutaway view of a ‘‘Bourdon tube’’ type pressure gaugecommonly used for measuring relatively high pressures (e.g., pressureswithin compressed gas tanks and gas pipelines).

Figure 3. Magnified view of a strain gauge. As pressure is applied, theconductors lengthen slightly, increasing their electrical resistance. Thechange in resistance is measured using a Wheatstone bridge circuit whoseoutput is amplified and sent to the monitor display.

41Physics in Anesthesiology

opposed by force on the diaphragm by gas in the low-pressure chamber (Figure 5).

Gas CylindersIn the operating room, gas storage typically occurs in Ecylinders. For ideal gases (e.g., oxygen, nitrogen, air),the cylinder contains compressed gas. A full E cylindercontains E660 L of oxygen at a pressure of E2,000 psi.The volume of gas remaining in the cylinder is propor-tional to the pressure. Thus, when an oxygen cylinder ishalf full, it reads 1,000 psi and contains 330 L; when it isone-quarter full, it reads 500 psi and contains 165 L.

Some gases form liquids when compressed at roomtemperature (e.g., CO2 [carbon dioxide], N2O [nitrousoxide], C3H8 [propane], C3H6 [cyclopropane]). For thesesubstances, when gas leaves the cylinder it is replaced by

evaporation of some of the pressurized liquid. The pressurein the cylinder depends on the vapor pressure of the liquidat the tank temperature until the liquid is entirely consumed.For N2O, this pressure is E750 psi at room temperature;a full E cylinder of N2O contains 1,590 L. The remainingcylinder content is best determined by weight. The quantityof N2O in a full cylinder has a mass of about 3 kg. Once theliquid is consumed (when the tank is approximately one-quarter full and the pressure in the tank drops below thevapor pressure of the gas), the amount of gas remaining in thecylinder is proportional to gauge pressure.

Whether a gas behaves as an ideal gas or a pressurizedliquid in an E cylinder is determined by its critical tem-perature. The critical temperature (Tc) is the temperatureabove which a gas cannot be liquefied, regardless of pres-sure. For N2O, Tc¼ 36.41C; for CO2, Tc¼ 31.11C; and forO2, Tc¼�118.61C.

Some simple calculations involving gases and vapors:

� What is the mass of N2O in an E cylinder?

1;590 L�mole

24 L�

44 g

mole¼ 2;900 g ¼ 2:9 kg

(Note: The volume of 1 mole of an ideal gas at roomtemperature (201C) is approximately 24 L.)

� What is the internal volume of an E cylinder?Use Boyle’s Law: P1V1¼ P2V2

2;000 PSI� VTANK ¼ 14:7 PSI� 660 L

VTANK ¼14:7� 660

2;000¼ 4:85 L

� How many milliliters of sevoflurane vapor come from1mL of sevoflurane liquid? (see Supplemental Digital Con-tent 3, http://links.lww.com/ASA/A126, and SupplementalDigital Content 4, http://links.lww.com/ASA/A127).

1 mL liquid�1:5 g

mL�

1 mole

200 g�

24 L gas

mole

¼ 0:18 L gas ¼ 180 mL

� If the fresh gas flow is 2 L/min, how many minutes of 2%sevoflurane anesthesia will 5 mL of sevoflurane provide?

5 mL liquid�180 mL gas

mL liquid�

1 minute

0:02� 2;000 mL gas

¼22:5 minutes

Adiabatic Compression. According to the ideal gaslaw (PV¼ nRT), compression of a quantity of gas by in-creasing pressure (P) produces an increase in temperature(T). Adiabatic compression implies that the compressionoccurs rapidly without a chance for heat to escape. Whenadiabatic compression occurs in the presence of fuel (e.g.,in a diesel engine cylinder), ignition can occur. Adiabaticcompression occurs in the yoke or in a pressure regulatorwhen a compressed gas cylinder is opened rapidly. The useof lubricants on these components can provide fuel forignition and lead to explosions in the operating room.

Figure 4. Wheatstone bridge circuit. When no pressure is applied to thestrain gauge, the bridge is ‘‘balanced’’ and the voltmeter reads 0. A slightchange in the resistance of the strain gauge causes a large change in thevoltmeter reading.

Figure 5. Schematic of pressure regulator. Gas from the cylinder (or otherhigh-pressure source) enters the high-pressure chamber on the left side of thefigure. Gas passes through the valve into the low-pressure chamber until theforce of gas pushing the diaphragm to the right exceeds that of the springpushing the diaphragm to the left, at which point the valve closes. When gas isdrawn from the low-pressure outlet, the valve opens slightly, allowing additionalgas to enter the low-pressure chamber keeping the pressure constant.

42 Gipson and Gross

Flows of Liquids and GasesLaminar flows of fluids are characterized by streamlinedflow patterns in which particles are traveling mostly inparallel in the direction of flow. For example, laminar flowpredominates during calm inspiration in the normal air-way. During laminar flow, Pressure¼ Flow�Resistance,where the resistance is given by the Poiseuille law:

Resistance ¼8� L�Z

p�R4

where Z¼ viscosity of fluid, R¼ radius of tube, andL¼ length of tube.

Turbulent flow is a less efficient pattern of flow character-ized by randomness in the direction of flow of individualparticles. Turbulent flow may be favored by changes in thediameter of the ‘‘tube’’ in which flow occurs (e.g., branchpoints or obstructions) as well as by high flow velocitiesand low fluid viscosity (the molecules are less likely to‘‘stick’’ together, making flow more ‘‘chaotic’’). Duringturbulent flow, Pressure aDensity� Flow2.

The tendency of fluid flow to be turbulent is describedby the Reynolds number (Re), where turbulent flow is fa-vored at Re42,300:

Re ¼r�V�D

Z

where r¼ density of fluid, V¼ velocity of flow, D¼diameter of tube, and Z¼ viscosity of fluid.

Flowmeters. The basic construction of a gas flow-meter (Thorpe tube) involves a tapered glass tube whosediameter increases toward the top (Figure 6). A needlevalve is opened to allow gas flow upward through the tube.The gas exerts a drag force as it flows around and raises abobbin in the tube. This drag force at a given flow ratedecreases as the bobbin moves upward and the annularspace around it grows larger. The bobbin assumes anequilibrium position where the upward drag force fromgas flow equals the downward force from gravity.

Meters using spherical bobbins are designed to be readin the center of the bobbin, whereas those using cylindricalbobbins are designed to be read at the top of the bobbin.Rotation of the bobbin in the gas stream is an importantindicator that the bobbin is not stuck, and is encouraged byrifling on cylindrical bobbins. At low flow rates, laminarflow predominates around the bobbin and the upwardforce is proportional to the viscosity of the gas. At highflow rates, turbulent flow predominates around the bobbinand the upward force is proportional to the density of thegas (see equations in previous section). At higher altitudes,both the density and viscosity of gases are decreased; thisreduces the upward force on the bobbin for any given gasflow. As a result, the actual gas flow may be significantlygreater than indicated by the flowmeter.

The arrangement of flowmeters in an anesthesia ma-chine routinely locates the O2 flow tube closest to thecommon gas outlet. This arrangement minimizes the risk

of hypoxia in the case of a cracked flow tube by minimiz-ing the chance that O2 will leak out through a cracked flowtube closer to the common gas outlet of the machine.

Fail-Safe Valve. The fail-safe valve resides in the low-pressure system of the anesthesia machine and is designed toprevent delivery of a hypoxic gas mixture. This mechanismdoes not prevent ‘‘dialing in’’ of a hypoxic gas mixture by theoperator; rather, it prevents the flow of nitrous oxide fromthe wall or tank source unless an adequate O2 supply pres-sure is present. To test the fail-safe, one should turn on bothO2 and N2O flows, then disconnect the wall O2 supply,being sure that the O2 tank is closed. As the O2 pressuredecreases to zero, observe that the N2O flow stops. The O2

flush valve may be pressed to test more quickly.

Proportioning Systems. Proportioning systems aredesigned to prevent the anesthesiologist from dialing in ahypoxic gas mixture involving nitrous oxide. Two generaldesigns (i.e., link- or pressure-operated) limit N2O flow toroughly three times the O2 flow. To test the proportion-ing system, the user should attempt to create a hypoxicmixture by raising the N2O flow or decreasing the O2 flow,then observing the adjustment of the other gas by theproportioning system.

A link-operated system uses a proportioning chain be-tween the N2O and O2 flow knobs. The chain mechanicallyturns down the N2O needle valve if the O2 flow is reduced; italso opens the O2 needle valve if the N2O flow is increasedbeyond the 3:1 ratio. Of note, the chain only affects theN2O:O2 proportion when the user attempts to violate the

Figure 6. Schematic of Thorpe tube flowmeter. When the flow control knobis turned counterclockwise, the needle valve is pulled toward the left,allowing gas to flow from the inlet into the flowmeter. The bobbin then risesto the point where the upward force of the gas acting on the bobbin equalsthe weight of the bobbin. As gas flows increase, the bobbin rises and moregas flows around the bobbin, restoring the balance of forces.

43Physics in Anesthesiology

3:1 ratio. A pressure-operated system uses a diaphragmsystem to keep the N2O:O2 ratio at or below 3:1. In contrastto the link-operated system, if a pressure-operated systemreduces the N2O flow in response to inadequate O2 flow, theN2O will be restored to its previous value when the O2 flowis restored by the user.

ANESTHESIA VAPORIZERS

Copper KettleThe predecessor to modern anesthesia vaporizers was thecopper kettle (Figure 7). Its vapor output depends on theO2 inflow and the vapor pressure of the anesthetic, asshown in Table 2. For example, consider a copper kettlecontaining sevoflurane through which oxygen is flowing.As the vapor pressure of sevoflurane is about 1/4 atm, ap-proximately 1/4 of the output molecules will be sevo-flurane and 3/4 will be oxygen. Hence, the output willcontain 1/3 as much sevoflurane as O2 (1/4 vs. 3/4). Forevery 100 mL O2 input, we would thus expect 100 mL O2

output plus 33 mL sevoflurane¼ 133 mL total output. (Theconcentration of sevoflurane in the copper kettle outputwould be 33/133¼ 25%, as expected from the vapor pres-sure.) When using a copper kettle with sevoflurane, anes-thesiologists typically used a total gas flow (O2 plus eitherN2O or air) of 3,300 mL/min (the so-called ‘‘magic number’’for sevoflurane). Under these conditions, 100 mL of oxygenflowing through the kettle resulted in 1% sevoflurane at thecommon gas outlet (33 mL/3,300 mL). To give 2% sevo-flurane, one simply increased the ‘‘kettle flow’’ to 200 mL/min. Modern vaporizers do the ‘‘calculations’’ automati-cally; the amount of fresh gas diverted through the vaporiz-ing chamber depends upon the dial setting as well as thetemperature of the anesthetic liquid. As the anesthetic is va-porized, cooling the liquid and lowering its vapor pressure, atemperature-sensing mechanism (usually a bellows or bi-metallic strip) slightly increases the flow through the vapor-izing chamber to compensate.

Supplying desflurane vapor poses a particular challenge.Its vapor pressure is close to atmospheric pressure, leadingto its low boiling point of 23.51C. In a copper kettle, each100 mL O2 input would yield E900 mL desflurane outputat 201C. The output would be strongly variable with tem-perature, making precise control difficult. To avoid thisproblem, desflurane is delivered from a heated boilerwhose output is pure desflurane gas. The gas is deliveredthrough a needle valve, much like O2 or N2O. Electronicscontrol the pressure of desflurane flowing through theneedle valve to ensure delivery of a predictable percentageof desflurane at the prevailing fresh gas flow rate.

At higher altitude, both vaporizer output and anestheticeffect change in predictable ways. Even though we speak ofanesthetic minimum alveolar concentration (MAC) interms of a percentage of alveolar gas at sea level, it is im-portant to recognize that anesthetics act on the brain inproportion to their partial pressure in blood. Thus, we could

express the MAC of sevoflurane as 2%� 760 mmHg¼15.2 mmHg. The world’s highest city of La Rinconada,Peru, lies at 5,100 m above sea level and boasts an atmos-pheric pressure of about 380 mmHg (E1/2 atm). Here, weneed a greater percentage of vapor to achieve the same par-tial pressure. In this case, the MAC of sevoflurane is15.2 mmHg/380 mmHg¼ 4%. Despite the difference in at-mospheric pressure, the vapor pressure of sevoflurane is thesame in La Rinconada as at sea level as it depends only ontemperature. However, the vapor pressure of sevoflurane inLa Rinconada is approximately 1/2 of the ambient atmos-pheric pressure; therefore, for every 100 mL O2 flowingthrough the vaporizing chamber, the output is 100 mL of O2

Figure 7. ‘‘Copper kettle’’ vaporizer. Each 100mL of oxygen picks up 33mLof sevoflurane vapor as it bubbles through the liquid sevoflurane. If the totalgas flow is set to 3,300mL (the ‘‘magic number’’), then the deliveredconcentration of sevoflurane will be 1%.

Table 2. Vapor Pressure of Commonly AdministeredInhalation Anesthetics

AnestheticsVapor Pressure

(mmHg) (at 251C)Vapor Pressure

(atm)

Sevoflurane 197 E1/4

Enflurane 218 E1/4

Halothane 299 E1/3

Isoflurane 295 E1/3

Desflurane 798 41

44 Gipson and Gross

plus 100 mL of sevoflurane. The vaporizer output is thusthree times as high as at sea level for a given dial setting, so ifwe ‘‘dial in’’ 2% sevoflurane, the vaporizer will actually de-liver 6% of the gas! As the MAC of sevoflurane is only 4%,we actually need to turn the vaporizer down to 1.33% to geta vaporizer output of 4% which will give 1 MAC of anes-thetic effect. For a desflurane ‘‘vaporizer’’ (really a boiler, seeabove), the percentage vapor output is unaffected by alti-tude. However, the MAC of desflurane in La Rinconada,Peru, is 12%, and we thus would need to dial in 12% des-flurane to achieve 1 MAC of anesthetic effect.

Contemporary Anesthesia Machines

Low-pressure Leak Test. The low-pressure leak testperformed during an anesthesia machine checkout is doneto detect leaks in flowmeters, vaporizers, and the commongas manifold. To check for leaks, turn the machine fully‘‘off’’ so that the minimum mandatory flow of O2 does notlook like a leak. Then, apply a suction bulb to the commongas outlet and verify that it remains deflated for at least 5seconds. This test should be repeated with each vaporizerturned ‘‘on’’ to verify that there are no leaks within thevaporizers themselves. On many machines, there is a checkvalve just before the common gas outlet. This allows thepatient to be ventilated with O2 from the flush valve even ifthere is a leak in the low-pressure system. Therefore, thefact that the breathing circuit ‘‘holds pressure’’ does notguarantee that there are no leaks in the low-pressurecomponents of the anesthesia machine.

Breathing Circuits. There are four types:

� Open breathing circuits are characterized by the lack ofrebreathing of exhaled gases and include nasal cannulas,simple face masks, and bag–valve–mask systems (e.g.,Ambus). Bag–valve–mask systems use three valves toallow either spontaneous or controlled ventilation whilepreventing rebreathing (Figure 8).

� Semiopen circuits (e.g., Mapleson or Bain circuits) arevalveless systems in which the fresh gas flow serves towash out the patient’s exhaled gases to reduce rebreath-ing (Figure 9). Semiopen circuits are most efficient atremoving exhaled CO2 for a given gas flow when the‘‘pop off’’ valve is nearest the source of the ventilatorypower. For spontaneous ventilation a Mapleson Acircuit is advantageous, whereas a Mapleson D is themost efficient for controlled ventilation. Of note, theMapleson A is very inefficient (i.e., requires high gasflows to prevent rebreathing) during controlled ventila-tion, whereas the Mapleson D is reasonably efficient forboth controlled and spontaneous ventilation. Due to itsversatility, the Mapleson D design is preferred for mostapplications; fresh gas flows of twice the minuteventilation are usually sufficient to minimize rebreath-ing. The Bain circuit uses a Mapleson D design withcoaxial circuit tubing.

� Semiclosed circle systems involve partial rebreathing ofexhaled gas after removal of CO2 by an absorber. Thisimplies that the fresh gas flow is greater than the patientuptake of gases but less than the minute ventilation. Inmodern semiclosed systems, direct rebreathing is preventedby a pair of one-way valves so that the patient alwaysinhales from the ‘‘fresh gas’’ side of the circuit and exhalesthrough the ‘‘waste gas’’ side of the circuit. The ‘‘dead space’’of such a system begins at the ‘‘Y-piece’’ where the circuitconnects to the mask or endotracheal tube (Figure 10).

� Closed systems use complete rebreathing of exhaledgases with fresh gas flows equal to the patient’s uptakeof O2 and anesthetic. If using a sidestream gas analyzer,one must route the exhaust gases back into thepatient circuit to achieve a truly closed circle system.Flow rates for closed-circuit anesthesia can be titratedusing FiO2 and inhaled anesthetic data from the gasanalyzer. Starting values for flow rates should include3 to 4 mL/kg/min O2. Anesthetic flow rates shouldmatch their rates of uptake, which can be estimated as:

First-minute uptakeffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiTime ðminutesÞ

p

Some sample starting uptakes are listed in Table 3.

Figure 8. Bag–valve–mask system showing the three valves used toprevent rebreathing while allowing either spontaneous or positive-pressureventilation. When the bag is squeezed, the inlet andmushroom valves close,forcing air into the patient’s lungs. When the bag is released, the mushroomvalve opens, allowing the patient to exhale to the atmosphere; the inlet valveopens, allowing fresh gas to fill the bag; and the inspiratory valve closes,preventing exhaled air from reentering the bag.

45Physics in Anesthesiology

In modern semiclosed systems, direct

rebreathing is prevented by a pair of one-way

valves so that the patient always inhales from

the ‘‘fresh gas’’ side of the circuit and exhales

through the ‘‘waste gas’’ side of the circuit.

Once closed-circuit anesthesia has been established,total flow of gas into the circuit should be adjusted tomaintain the volume of the bag or bellows constant andsubmaximal (to prevent gas from ‘‘popping off’’). The ratioof O2 to N2O or air should be adjusted to maintain thedesired FiO2, and the vaporizer setting should be adjustedto maintain the desired inspired anesthetic concentration.

CO2 Absorption. Granules of CO2 absorbent are sizedsmall enough to have a large surface area for reaction butlarge enough to avoid ‘‘channeling’’ of gas flow. This size istypically 4 to 8 mesh; this means that the granules are smallenough to pass through a ‘‘4 mesh’’ (i.e., wire grid spacedat 1/4-inch intervals), but not so small that they can passthrough an 8 mesh (i.e., wire grid spaced at 1/8-inch in-tervals). Granules are composed of a weak base (Ca(OH)2

or Ba(OH)2) plus a strong base catalyst (NaOH or KOH).Soda lime is composed of NaOH and Ca(OH)2, whereasBaralyme contains KOH, Ca(OH)2, and Ba(OH)2. Bar-alyme is more likely to react with anesthetics to form CO(with desflurane) or compound A (with sevoflurane).

Moisture is necessary for CO2 absorption and reduces thelikelihood of anesthetic breakdown (Supplemental DigitalContent 5, http://links.lww.com/ASA/A128).

The chemistry of CO2 absorption includes the followingthree steps:

CO2þH2O-H2CO3

H2CO3þ 2 NaOH-Na2CO3þ 2H2Oþ heat

Na2CO3þCa(OH)2-CaCO3þ 2NaOH

The zone of maximum absorption in the canister feelswarm to the touch, or could feel hot in the case of malig-nant hyperthermia. When there is insufficient Ca(OH)2 toregenerate the NaOH, acidification causes the indicator(ethyl violet) to turn violet in color; when the violet zoneextends more than halfway through the canister, it is timeto replace the absorbent. Note that if it is allowed to ‘‘rest’’overnight, the residual Ca(OH)2 may be sufficient to de-colorize the violet indicator, making it appear as if theabsorber is ‘‘fresh’’ despite the fact that little absorbingcapacity remains. Thus, the decision to change the ab-sorbent should be made at the end of the day.

BLOOD PRESSURE AND CARDIAC OUTPUT

Invasive Blood Pressure MeasurementPressure transducers measure pressures using the variableresistance of a strain gauge incorporated into a Wheat-stone bridge circuit. In most cases, a continuous flush de-

Figure 9. The two most common semiopen circuits, Mapleson ‘‘A’’ and ‘‘D.’’The ‘‘A’’ circuit is very efficient for spontaneous ventilation, but very inefficientfor controlled ventilation. The ‘‘D’’ circuit is most efficient for controlledventilation, but also reasonably efficient for spontaneous ventilation.

Table 3. Approximate First-minute Uptake ofSelected Anesthetics in an 80-kg Patient

Agent (%) First-minute Uptake (mL)

Nitrous oxide (80%) 1,600

Sevoflurane (2%) 50

Desflurane (6%) 100

Figure 10. Circle absorber breathing system. Exhaled, CO2-containing gasis indicated in gray; CO2-free gas is indicated in green. ‘‘Dead space’’ beginsat the ‘‘Y’’ piece and extends down through the patient’s conductingairways.

46 Gipson and Gross

vice is located between the pressurized flush solution andthe tubing connected to the patient. Since the flow throughthe flush device is only a few mL/h, the flush solution doesnot usually affect pressure measurements. However, if themonitoring catheter is totally occluded (as in a kinkedarterial catheter), the flush solution will pressurize thepatient connection and the pressure reading will quicklyrise to that of the flush solution.

The accuracy with which the transducer system re-produces the intravascular pressure depends on the reso-nant frequency (higher is better) and the degree ofdamping. The resonant frequency of the transducer systemis increased by keeping the connecting tubing short andnoncompliant. Damping is increased if the diameter of thetubing is small, or if there is air in the tubing, resultingin increased motion of the fluid and friction within thesystem. If the resonant frequency of the system is approx-imately 1/rise-time of the pressure waveform, the wave-form may be exaggerated; this will cause overestimation ofsystolic pressures and underestimation of diastolic pres-sures, particularly if the system is ‘‘underdamped.’’ Incontrast, if the system has too much damping, peaks andtroughs of the pressure waveform tend to be ‘‘smoothed out,’’resulting in underestimation of systolic pressures and over-estimation of diastolic pressures. Damping can be assessed byobserving the pressure waveform while squeezing and thenreleasing the manual flush valve. If the pressure trace returnsvery slowly to its baseline, then the system is overdamped; ifit returns very quickly and oscillates around the baselinewaveform, then the system is underdamped. The ideal sit-uation is for the trace to return quickly to the baseline with-out excessive oscillation (critical damping) (Figure 11).

Zeroing the pressure transducer requires attention to afew factors. At the time of zeroing, the transducer may be atany height relative to the patient, but the system should be‘‘opened to air’’ at heart level while zeroing is performed.After zeroing, the height of the transducer relative to thepatient must remain constant. The site of arterial pressuremeasurement has some effect on the arterial waveform. Wavereflection causes systolic pressure to be higher and diastolicpressure to be lower when there is an acute change in vesseldiameter (e.g., at the radial or dorsalis pedis arteries). Themean pressure is unaffected by wave reflection, but resistanceto flow does produce a very slight decrement in the meanpressure as we progress from the aorta to more distal vessels.

Noninvasive Blood Pressure MeasurementMost standard blood pressure cuff systems detect bloodpressures using oscillometry. The cuff is inflated until ar-terial flow is occluded, then pulsations in the cuff pressureare monitored as the cuff deflates. The initial pulsationsoccur just above systolic pressure, and the maximal pul-sations correspond to the mean pressure. The diastolicpressure is determined using a mathematical algorithm.Most continuous noninvasive blood pressure monitoringsystems use a sensor placed over the radial artery at thewrist, with stronger pulsations corresponding to a higher

blood pressure. Many of these systems require calibrationwith a standard blood pressure cuff (located on the sameextremity) that inflates at regular intervals.

Cardiac Output MeasurementCardiac output is measured most purely using the Fickprinciple, which is based on conservation of mass. In theabsence of a cardiopulmonary shunt, the patient’s oxygenuptake (VO2) equals the difference between arterial andmixed venous oxygen content (CaO2�CvO2) times thecardiac output (Q). Rearranged, this yields:

Q ¼VO2

CaO2�CvO2ð Þ

Cardiac output is measured most purely using

the Fick principle, which is based on

conservation of mass. In the absence of a

cardiopulmonary shunt, the patient’s oxygen

uptake (VO2) equals the difference between

arterial and mixed venous oxygen content

(CaO2�CvO2) times the cardiac output (Q).

Figure 11. Pressure waveforms after the flush valve is squeezed and thenreleased. Critical damping provides the best response to the rapid upstroke ofthe arterial pressure waveform without excessive overshoot or undershoot.

47Physics in Anesthesiology

Determining Q using this method requires access to ar-terial and mixed venous (via pulmonary artery [PA] cath-eter) blood samples. More problematic during anesthesiais measurement of VO2, which requires collection andanalysis of mixed exhaled gases or determination viaclosed-circuit techniques. The NICOs monitor applies theFick principle to elimination of CO2 rather than uptake ofO2. In this case, intermittent insertion of a partial-re-breathing circuit allows estimation of arterial and mixedvenous CO2 content. These, along with measurement ofCO2 elimination, allow for calculation of cardiac output asfollows:

Q¼VCO2

CaCO2�CvCO2ð Þ

In a patient with a PA catheter, cardiac output is fre-quently measured by thermodilution. This method reliesupon injection of a fixed of quantity of room-temperatureor ice-cold fluid via a proximal port in the PA catheter andmeasuring the time course of the temperature change at adistal point on the catheter within the PA. When bloodflow (Q) is low, the bolus of cold fluid remains in the PA fora relatively long time, causing the area under the temper-ature versus time curve to be large. In contrast, when bloodflow is high, the cold fluid is rapidly washed out of the PA,resulting in a smaller area under the temperature versustime curve. As shown in Figure 12, the temperature curvedoes not return all the way to baseline because of re-circulation; the cardiac output computer accounts for thisby extrapolating the return to baseline. The cardiac outputis computed from the extrapolated curve by the formula:

Q ¼Quantity of indicator

R1

t¼0

DTemp dt

where Quantity of indicator¼ (Volume of indicator)�(TPatient�TIndicator) (Supplemental Digital Content 6,http://links.lww.com/ASA/A129).

There are a few important sources of error to keep inmind with thermodilution measurements. The Quantity ofindicator is entered into the computer based on the volumeof indicator to be injected and the temperature of the in-jectate. If the volume injected is lower than expected, the

temperature changeR1

t¼0

DTemp dt will be artificially small

and the calculated cardiac output will be falsely high. Ifthe injectate is too cold (e.g., using iced rather thanroom-temperature saline), the temperature changeR1

t¼0

DTemp dt will be artificially large and the calculated

cardiac output will be falsely low.In the absence of a PA catheter, cardiac output can be

estimated by a variety of less invasive approaches. One suchapproach involves a Doppler probe in the esophagus thatmeasures blood flow velocities in the descending aorta.Esophageal Doppler relies on detection of a change in

the frequency of ultrasound waves when reflected frommoving objects (e.g., erythrocytes). Erythrocyte velocity(v) is related to Doppler shift (fd), ultrasound frequency(fi), the velocity of the ultrasound wave (c), and angle (y) atwhich the ultrasound waves penetrate the vessel by theformula:

v ¼ fd�c

2ficosy

The esophageal Doppler monitor computes a velocity-time integral (VTI) by integrating erythrocyte velocitiesthrough the cardiac cycle. VTI, along with heart rate (HR)and an estimate of aortic cross-sectional area (CSA, esti-mated on the basis of patient weight, height, and age) areused to calculate cardiac output (Q):

Q¼HR�CSA�VTI

There are two potential sources of error in estimat-ing the cardiac output by this method: (1) unless theultrasound beam is directed to the center of the aorta,flow velocity may not be accurately estimated; and (2)

Figure 12. Thermodilution curve for cold saline injection. The temperaturedoes not return to baseline as quickly as predicted because of recirculationof the cold ‘‘indicator’’ through the coronary vessels (dotted line). Thecardiac output computer compensates for this by extrapolating the curveback to baseline temperature. When cardiac output is increased, the coldindicator passes the temperature sensor more quickly, decreasing the areaunder the middle curve. When the cardiac output is decreased, the cold fluidremains in proximity to the temperature sensor for a longer period of time,increasing the area under the bottom curve.

48 Gipson and Gross

the ultrasound beam should be nearly parallel to the di-rection of blood flow, so that cosyE1. Otherwise, the ve-locity needs to be corrected according to the formulaabove.

CONCLUSIONS

On a daily basis, anesthesiologists use equipment whosefunction depends upon basic physical principles. Onlythrough an understanding of how these devices functioncan we appropriately apply them to clinical situations, in-

terpret results, recognize and troubleshoot malfunction,and ensure the safety of our patients.

FURTHER READING

1. DorschJA, DorschSE: Understanding AnesthesiaEquipment. 5th ed. Philadelphia: Lippincott Williams& Wilkins, 2008.

2. ScurrC, FeldmanSA, SoniN: Scientific Foundations ofAnesthesia. 4th ed. London: Butterworth-Heinemann,1991.

49Physics in Anesthesiology