Physics in Anesthesiology: Basic Science Review

Physics in Anesthesiology: Basic Science Review
Jeffrey B. Gross, M.D. Farmington, Connecticut
Why Physics?
a) Understand how our equipment is SUPPOSED to work
b) Understand what might happen if things go WRONG
c) Function as a CONSULTANT in the medical specialty of Anesthesiology
d) Do well on Content Outline Section 1B of the In-Training and Part I American Board of
Anesthesiology Examinations
Pressure
a) Pressure= Force per unit of area
b) Units
• Pounds / in2 (PSI)
- Atmospheric Pressure PATM=14.7 PSI)
• Pascals (nt / m2) (PATM~100 KPa)
• mmHg (7.5 mmHg = 1 KPa)
• cmH2O (1 mmHg = 1.36 cmH2O)
c) Implications
• Even a small pressure exerts a large force if area is large
• A small force can exert a lot of pressure if the area is small
d) Absolute vs. Gauge Pressures
• Gauge pressures: relative to ambient pressure
- Tire pressure, pressure in compressed gas cylinder, blood pressure
• Absolute pressures
- Vapor pressure of anesthetics, H2O
- Blood gases
- Other cases where you need to use gas laws
e) Pressure Gauges
• Bourdon tube (for high pressure gases such as compressed gas cylinders)
- Deformable tube changes shape when filled with pressurized gas causing pointer to move
• Diaphragm (for low pressures such as aneroid blood pressure cuffs--the kind with a pointer)
- Diaphragm at top of a "pancake" shaped cylinder moves outward causing pointer to move
f) Pressure Regulators
• Reduces high pressure in compressed gas cylinder to approximately 50 PSIG
Gas Cylinders
a) E Cylinder (back of machine)
• For ideal gases (air, nitrogen, oxygen)
- Full cylinder pressure = 2000 PSI
- Full cylinder volume = 660 liters
- Volume remaining is proportional to pressure
- 1000 PSI --> 330 L 500 PSI-->165 L
• For pressurized liquids (N2O, CO2, C3H8 [propane--barbecue grill], C3H6 [cyclopropane])
- Pressure depends on vapor pressure of liquid at tank temperature until liquid is “gone” (740
PSI) for N2O at room temperature
- Full cylinder of N2O – 1590 L
- Remaining quantity of gas best determined by weight
• The N2O in a full E cylinder weighs about 3 Kg
- Critical temperature (Tc): gas cannot be liquefied above this temperature regardless of
pressure
• For N2O TC = 36.5o C

b) Some Simple Calculations
• What is the weight of N2O in an E-cylinder?
• What is the internal volume of an “E” Cylinder?
- Use Boyle's Law: P1V1=P2V2
c) More Simple Calculations
• How many ml of sevoflurane vapor come from 1 ml of sevoflurane liquid?
• If the fresh-gas flow is 2 l/min, how many minutes of 2% sevoflurane anesthesia will 5 ml of
liquid provide?
Adiabatic Compression
a) Rapid compression of gas without giving heat a chance to escape
• Principle of diesel engine (no spark plugs)
b) If there is oil / grease in valve or regulator and tank opened quickly, explosion can occur :-(
Flows of Liquids and Gases
a) Laminar (streamlined)
• Pressure=Flow x Resistance
b) Turbulent
• Pressure α Density x Flow2
• Transition from laminar to turbulent flow when Reynold's number > 2300
Flowmeters
a) Tapered tube with diameter increasing toward the top
b) Bobbin position determined by equilibrium
• Upward force from flowing gas = downward force from gravity
- At low flow rates (laminar flow) upward force depends on viscosity of gas
- At high flow rates (turbulent flow ) upward force depends on density of gas
c) Always want O2 flow tube nearest to the common gas outlet
- Minimizes risk of hypoxia if a flow tube is cracked
η=viscosity of liquid
R=radius of tube
L=length of tube
ρ=density of liquid
V=velocity of flow
D=diameter of tube
η=viscosity of liquid

Fail Safe Valve
a) Cuts off N2O if O2 supply fails
• Does NOT prevent accidental or intentional “dialing in” of a hypoxic gas mixture
b) Testing
• Turn on O2 and N2O flows
• Disconnect wall O2 supply (be sure O2 tank is "off")
• Press O2 flush valve
• Verify that N2O flow ceases when O2 pressure drops to zero
Proportioning Systems
a) Limit N2O flow to 3 times O2 flow
b) Link vs. pressure operated systems
• Link system: mechanically turns down N2O needle valve if O2 flow reduced
- N2O flow will NOT return to initial value if O2 flow increased
• Pressure system: pneumatically decreases N2O flow if O2 flow reduced
- N2O flow will return to initial value if O2 flow increased
Anesthetic Vaporizers
a) Ye Olde Copper Kettle
• Vapor output depends on O2 inflow and vapor pressure of anesthetic
• For sevoflurane, Pv=190 mmHg = 1/4 ATM
- 1/4 of output molecules will be Sevoflurane; 3/4 of output molecules will be O2
- For every 100 ml O2 input, will get 133 ml of total output
• 100 ml O2 (3/4 of total)
• 33 ml sevoflurane (1/4 of total)
- If you use a total gas flow of 3.3 l/min (magic number :-), each 100 ml of O2 through the
vaporizer gives you 1% of sevoflurane concentration
b) Desflurane “Vaporizer”
• Boiling point of desflurane 23.5o C (vapor pressure at room temp nearly atmospheric
• Variable bypass vaporizer not controllable
- Each 100 ml of O2 through vaporizing chamber would give about 900 ml of desflurane output
- Large output swings with changes in temperature
• Alternative: Use a “boiler” and deliver as a gas
- Desflurane output determined by a "needle" valve, just like O2 and N2O
- Uses electronics to make desflurane flow proportional to total gas flow, so a constant
percentage is given regardless of fresh gas flow settings
c) Vaporizers at Altitude
• Recall that MAC is really a partial pressure
- Sevoflurane MAC = 2% x 760 mmHg =15.2 mmHg
• In Tibet PATM = 380 mmHg
• 15.2 / 380 = 4% (MAC of sevoflurane in Tibet)
- Vapor pressure of sevoflurane in Tibet (depends on temperature only) = 190 mmHg (same as
at sea level)
• Since vapor pressure = 1/2 barometric pressure, for every 100 ml of O2 flowing into
vaporizer the output will be 100 ml of sevoflurane plus 100 ml of O2
• This is 3 times as much as at sea level--vaporizer output triples
• Since MAC is only twice as great as at sea level, actually need to turn vaporizer DOWN
to 1.33% in order to get 1 MAC of anesthetic effect
• Desflurane “vaporizer”
- Percentage output unaffected by altitude
- MAC of desflurane in Tibet is 12%
- Need to “dial in” 12% desflurane to get 1 MAC of anesthetic effect

Low pressure leak test
a) Checks for leaks in flowmeters, vaporizers, common gas manifold
b) Check valve just before common gas outlet on many machines
• Allows patient to be ventilated with O2 from flush valve even if there is a leak in low pressure
system--therefore, the fact that the breathing circuit "holds pressure" does not guarantee that there
are no low-pressure leaks
• To check for leaks
- Turn machine fully off (otherwise minimum mandatory O2 flow will look like a leak
- Apply suction bulb to common gas outlet and verify that it remains deflated for at least 5 sec
Breathing Circuits
a) Open (non-rebreathing)
• Simple face mask or nasal cannula (CO2 diffuses away from the face)
• Bag-Valve-Mask system (Ambu®): uses 3 valves to allow either spontaneous or controlled
ventilation while preventing rebreathing
b) Semi-Open (Mapleson / Bain)
• Most efficient removal of CO2 for a given gas flow when the "pop off" valve is nearest the source
of the ventilatory power
- Spontaneous ventilation: Mapleson A
- Controlled ventilation: Mapleson D
• However, the "A" system is very inefficient (requires high gas flows) to prevent rebreathing
during controlled ventilation, while the "D" system is reasonably efficient for both controlled and
spontaneous ventilation, so the "D" is preferred for most applications.
- Bain circuit is a coaxial Mapleson D
c) Semi Closed Circle System
• Patient gas uptake < fresh gas flow < minute ventilation
• Some rebreathing of exhaled gas (following removal of CO2 by absorber)
d) Closed System
• Gas inflow = Patient Uptake
• If using sidestream agent / CO2 analyzer, must route exhaust back into circuit
• Starting values
- O2: 3-4 ml/kg/min
- Anesthetics: First minute uptake / √time (minutes)
• N2O (80% concentration, 80 kg patient): First minute uptake 1600 ml
• Sevoflurane (2%, 80 kg patient): First minute uptake 50 ml
• Desflurane (6%, 80 kg patient): First minute uptake 100 ml
• Closed System-Adjustments
- Total flow: Adjust N2O and O2 in proportion to keep volume of bag or bellows constant
- FIO2 : Adjust ratio of N2O and O2 to maintain desired FIO2 keeping total flow constant
- Depth of anesthesia: Adjust vaporizer setting to maintain desired depth or inspired
concentration
CO2 Absorption
a) Granules
• Small enough to have large surface area but large enough to avoid “channeling”
• Typically 4-8 mesh
b) Composition
• Sodalime: NaOH, Ca(OH)2
• Baralyme: KOH, Ca(OH)2, Ba(OH)2
- More likely to react with anesthetics to form CO (desflurane) or compound A (sevoflurane)
c) Moisture
• Necessary for CO2 absorption
• Reduces likelihood of anesthetic breakdown
d) Absorption Chemistry
• CO2 + H2O-->H2CO3
• H2CO3 + 2 NaOH-->Na2CO3+2H2O + heat
• Na2CO3 + Ca(OH)2 -->CaCO3 +2NaOH
• When the NaOH is gone, acidification causes indicator (ethyl violet) to turn “violet”
e) Zone of maximum absorption feels warm to touch (may be “hot” if malignant hyperthermia)

Pressure Transducer Systems
a) Accuracy with which transducer system reproduces actual intravascular pressure depends on
• Resonant frequency (higher is better)
• Degree of damping (most important if resonant frequency similar to 1/rise-time of waveform)
b) Zeroing Pressure Transducers
• Height of patient relative to transducer must remain constant after zeroing
• At time of zeroing
- Transducer may be at any height relative to patient (need not be at heart level)
- System should be “opened to air” by a stopcock at heart level before zeroing is performed
c) Site of Arterial Pressure Measurement
• Wave reflection causes systolic pressure to be higher and diastolic pressure to be lower when there
is an acute change in vessel diameter (radial / dorsalis pedis)
• This does NOT affect the mean pressure
• Resistance to flow causes a (very slight) decrease in mean pressure as pressure measurement
progresses from aorta to more distal vessels
Non-Invasive Blood Pressure Measurement
a) Most “standard cuff” systems use oscillometry
• Pulsations in the cuff pressure monitored as cuff deflates
• Initial pulsations--just above systolic pressure
• Maximal pulsations--mean arterial pressure
• Diastolic pressure by mathematical algorithm
b) Continuous non-invasive monitoring
• Most systems require intermittent calibration with a cuff
Cardiac Output Measurement
a) Fick Principle
• Conservation of mass
• Q=VO2/[CaO2-CvO2]
• Required measurements
- VO2 (Oxygen uptake--difficult to measure during anesthesia)
- CvO2 (requires PA catheter)
• NICO
- Fick formula applied to CO2 elimination
- Partial rebreathing to estimate mixed venous CO2
- Requires constant ventilatory pattern (controlled ventilation only)
b) Esophageal Doppler Monitor
• Doppler: Change in frequency of sound / ultrasound / light waves when reflected from a moving
object (e.g., RBC)
•
- v=RBC velocity fd= Doppler shift fi=frequency of ultrasound
- θ=angle between ultrasound beam and direction of blood flow
• CO = HR x CSA x VTI
- CO=Cardiac Output CSA=Cross Sectional Area VTI=Velocity-Time Integral
c) Thermodilution
• Quantity of indicator = Volume x (TPATIENT-TINDICATOR)
• Sources of error
- Quantity of indicator is "dialed in" to the C.O. computer based on the intended volume and
temperature of injectate

- If volume injected is lower than intended, then will be too low and the Cardiac
Output reading will be falsely high
- If the temperature of the indicator is colder than intended (e.g. using iced rather than room
temperature saline) then will be too high, and the Cardiac Output reading will
be falsely low