Introductory Physics for Anesthesiologists

T. Turkstra, M. Eng, P. Eng, MD, FRCPC

April 15 2009

Royal College of Physicians and Surgeons of Canada:

Objectives of Training and Training requirements for certification

• Specific Requirements • Demonstrate knowledge of the basic

sciences as applicable to anesthesia, including anatomy, physiology, pharmacology, biochemistry and physics.

Royal College of Physicians and Surgeons of Canada:

Objectives of Training and Training requirements for certification

• Specific Requirements • Demonstrate knowledge of the basic

sciences as applicable to anesthesia, including anatomy, physiology, pharmacology, biochemistry and physics??

Training Objectives (Resident Handbook)

• “The Anaesthetist will possess the scientific knowledge to provide a sound basis for good clinical practice. This will include…..

• Physics – especially the physics of gases and fluids, and the principles of electrical safety.”

Patient Scenario

• 52 yr old male, prev healthy, Ø med/allergy

• ~2 week Hx of dyspepsia, 10 lb wt loss

• AXR/CT shows obstructing 5 cm mass near cecum

• Admitted to floor, no resolution of symptoms, NPO, has NG insitu

• Exam unremarkable including airway

• Anesthetic plan?

Patient Anesthetic Concerns

• Airway?

• RSI?

• Cricoid pressure?

• How much “cricoid pressure”?• Brimacombe JR et al: “Cricoid pressure”

CJA 1997; 44: 414-25

• Recommendations: 20-44 N.

• “Cricoid pressure is a force.”

Physics? Why Bother?

• Fewer and fewer physics MCQ’s since about 2000

• Still fair game…

• Fairly important aspect of much of our daily practice

Today's Objectives

• To outline some of the core principles and definitions as applicable to:

1. Force2. Pressure3. Gases4. Fluids5. Flow6. Work and Power7. Electrical Safety8. Thermodynamics9. Light transmission/optics

Today's Objectives

• To outline some of the core principles and definitions as applicable to:

1. Force2. Pressure3. Gases4. Fluids5. Flow6. Work and Power7. Electrical and Fire Safety8. Thermodynamics9. Light transmission/optics

Sample Exam Question

• (2004) According to NIOSH, exposure to N2O should be limited to?

• a) Time-weighted 8 hours of 10 ppm.

• b) Time-weighted 8 hours of 25 ppm.

• c) Time-weighted 8 hours of 100 ppm.

• d) Max exposure 200 ppm per case.

• e) Max exposure 50 ppm per day.

Force

• 1 Newton (N) of force applied to 1 kg of matter, will accelerate it by 1m/s2

– How much is that?

Pressure

• Pressure is defined as force exerted over a given area P = F/A

• 1 Pascal of Pressure = 1Nm-2 = 1N/m2 – 1kPa = 1000 Pa

• 1 PSI = 1 pound per square inch (lb/in2)

• 1bar = 101.3 kPa = 1 atmosphere = 760 mmHg = 14.7 psi

Force in Context

• Consider the Pressure Reducing Valve– High pipeline pressure has to be reduced to

low anaesthesia machine or breathing system pressure, to prevent injury

• The Pressure Reducing Valve uses a diaphragm attached to a spring to open or close a piston valve in a high pressure chamber.

The Pressure Reducing Valve

The low pressure (P2) is applied over a the large area diaphragm, exerting sufficient force against the spring to raise the piston and stop flow from the High Pressure inlet. (F=PA)

As the pressure falls in the low pressure system, the spring pushes the diaphragm down, allowing more gas into the system

Question

• (2004) An anesthesiologist is working in Vancouver (Patm = 760 mmHg) and sets oxygen at 2L/min, nitrous oxide at 1L/min and the Halothane vaporizer at 1 volume %. Which of the following is true?

a) The gas mixture at the common gas outlet will be 1 MAC.

b) All of the fresh gas flow will pass through the vaporizing chamber of the halothane vaporizer.

c) The partial pressure of halothane at the common gas outlet will be 7.6 mmHg.

d) 3 mL per min of halothane will enter the gas mixture.e) 300 mL per min of halothane will enter the gas mixture.

What is a Gas?

• Molecular theory; Substances are composed of a lattice of molecules.

• Molecules all vibrate, oscillating about a mean position.

• Molecules exert force (attraction) on surrounding molecules

• If heat is added, the vibration amplitude is increased, and molecules exert less force on their ‘neighbours’

• With increased kinetic energy, some molecules ‘break free’ to enter atmosphere as a gas or vapour

Gas vs. Vapour

• Molecules may transfer from the liquid phase to the vapour phase and back again

• Once equilibrium of transfer has been reached, the vapour is saturated

• If the liquid is heated to its boiling point, all the molecules escape to the gaseous phase

• As gas molecules collide with the wall of the container holding it, they exert a net force, which when exerted over a certain area is defined as pressure

The Ideal Gas Laws

• BOYLE’S LAW (First perfect gas law)

The Ideal Gas Laws

• BOYLE’S LAW (First perfect gas law)

At a constant temperature, the volume of a given mass of gas varies inversely with the absolute pressure

V 1/P

or, PV = Constant (k1)

Practical Application

• Consider a patient who needs high flow O2 being transferred to a different Hospital.

• You have a10 L O2 cylinder, with a gauge pressure of 13,700kPa

• How long do you have on that O2 cylinder?

Boyle’s Law Quiz

• If a 10 litre oxygen cylinder has a gauge pressure of 13,700 kPa, how many litres of oxygen does it hold?

• Hint: from PV = Constant (k1);P1V1 = P2V2

Answer

• Absolute pressure = gauge pressure plus atmospheric pressure

Using P1V1 = P2V2

(13,700 +100) x 10 = 100 x V2

V2 = 13800 10 = 1380 litres(10 litres will stay behind in the cylinder, so

1370 litres are available for delivery at atmospheric pressure

At 10 l/min 1370/10 = 137 min…=just over 2 hours

Question

• (2004) You are transporting a patient by ambulance. The patient requires 4l/min O2. You are taking along a full E tank of O2. The trip takes 2 hours. At the end of the trip, how much O2 is left in the tank?

• a) 60 L• b) 180 L• c) 360 L• d) 400 L• e) 620 L

The Ideal Gas Laws

• CHARLES’ LAW (Second perfect gas law – also known as Gay Lussac’s law)

At a constant Pressure, the volume of a given mass of gas varies directly with

the absolute temperature

V T

or V/T = Constant (k2)

The Ideal Gas Laws

• The Third Perfect Gas Law (The pressure law)

At a constant volume, the absolute pressure of a given mass of gas varies directly with the absolute temperature

P T

or P/T = Constant (k3)

Question

• Consider an Oxygen cylinder filled to absolute pressure of 138 atmospheres (bar) or 13800kPa, at 17°C.

• Cylinders are tested to withstand 210 bar

• If this cylinder accidentally makes it into a furnace at 100°C, what happens to the cylinder?

EXPLOSION?

• Doubling the temperature will double the pressure. Why does the cylinder not explode at 340C…….?

EXPLOSION?

• Doubling the temperature will double the pressure. Why does the cylinder not explode at 340C…….?

• Because the equation relates to absolute temperature. 170C = 290K, and 1000C = 3900K.

• At 1000C the pressure is ‘only’ 185 atmospheres (P1/ T1 = P2 / T2)

Standard Pressure and Temperature: s.t.p.

• Because gas volumes are so greatly affected by changes of pressure and temperature, it is important to specify the temperature and pressure at which volumes are measured

• s.t.p. is 273.15 K and 101.325kPa or 760 mmHg

AVAGADRO

• Avagadro’s Hypothesis states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules

• Because the molecular weights of gases differ, there will be a different mass of any gas in a given volume at the same temperature and pressure

• Therefore it is more convenient to express a quantity of a gas in terms of the number of molecules, rather than in terms of mass.

AVAGADRO and the MOLE

• A MOLE is the quantity of a substance containing the same number of particles as there are atoms in 0.012kg of carbon12

• There are 6.022 x 1023 atoms in 12 g of carbon 12. This is called Avagadro’s Number

• One mole of any gas at s.t.p. occupies 22.4litres

The Mole

THUS:

• 2g of Hydrogen

• 32g of Oxygen

• 44g of Carbon Dioxide

All occupy 22.4 litres at s.t.p

Physics in Context

• Calibration of vaporizers is done using Avagadro’s hypothesis.

• Molecular weight of Sevoflurane is 200, so 200 g Sevo is 1 mole, and would occupy 22.4 l at s.t.p.

• If we put 20g of Sevo (0.1 mole) into a vaporizer, and allow it all to vaporize, it would occupy 2.24 litres

Physics in context

• If we ran oxygen through the vaporizer to a volume of 224 litres, the Sevo would make up 22.4l of the 224 litres, so would make up 1% of the 224 litres

• Similarly 40 g of Sevo would occupy 44.8l or 2 % of the 224l volume…….

20 g of Sevo in 224 litres = 1%

The Universal Gas Constant

PV = Constant (k1) Boyle

V/T = Constant (k2) Charles

P/T = Constant (k3) (3rd Law)

• By combining the perfect gas laws with Avagadro’s hypothesis we arrive at the following equation:

PV/T = Constant (k4), for any given quantity of gas

The Universal Gas Equation

• For any 1 mole of any gas, this constant (k4) is the UNIVERSAL GAS CONSTANT – R

• Rearranging this equation we come to the generally applicable equation (Universal Gas Law) of:

PV = nRT

Where n is the number of moles of the gas

R depends on the units.

Metric: Its value is 8.3144 J/°K/mol

Dalton’s Law

• Dalton’s law of Partial Pressures states that in a mixture of gases, the pressure exerted by each gas is the same as that which it would exert if it alone occupied the cylinder

• By Applying Boyle’s Law (PV = Constant ) and Dalton’s Law we can conclude that the the partial pressure of a gas in a mixture is obtained by multiplying the total pressure by the fractional concentration of the gas

Dalton’s Law in Practice

• For example, in a cylinder of entonox pressurised to 100kPa, The Oxygen is exerting 50 kPa, and the Nitrous Oxide is also exerting 50 kPa

• In a cylinder of air at an ambient pressure of 100kPa, the oxygen exerts a pressure of 20.93kPa, and the Nitrogen a pressure of 79.07kPa

Dalton’s Law in Practice

• Consider alveolar gas:

– If the end tidal CO2 is measured as 5.6% at 101.3 kPa, what is the true pressure of the alveolar CO2 (PACO2)

Answer

• The presence of water vapour must be taken into account for humidified gas when calculating partial pressures, and Water Vapour pressure in humidified alveolar gas is 6.3kPa (x7.5 for mmHg)

• CO2 is measured as a dry gas, so:

PACO2 =(101.3 – 6.3) x 5.6 kPa = 5.3 kPa

100

Adiabatic Changes of State

• The three gas laws describe the behaviour of a gas when one of the three variables (P/V/T) is constant

• If these conditions are applied, heat energy must be added or taken from a gas if it changes pressure or volume

Adiabatic Changes of State

• The state of a gas can however be changed without allowing the gas to exchange heat energy with it’s surroundings – the heat is retained within the system

• Example is the theoretic hazard when high pressure pipelines are opened into a low pressure anaesthetic machine, without regulator valves. The rapid pressurization is associated with a local large temperature rise, and risk of fire and explosion

Question

• (2004) What is the least likely cause of decreased ETCO2?

• a) endobronchial intubation

• b) hypothermia

• c) hyperventilation

• d) increased cardiac output

• e) pulmonary embolism

Question

• (2004) All of the following are disadvantages of a closed circuit system, EXCEPT?

• a) Need to vent the circuit intermittently to remove nitrogen build-up.

• b) Cannot monitor ventilation. • c) Cannot easily increase depth of

anesthesia.• d) There is a 200 mL/min loss through the

gas sampler.

Flow

• Flow can be defined as the amount of a substance (gas or liquid) passing over a given point per unit time

F = Q

t

• Flow may be Laminar or Turbulent• Many clinical measurements assume

laminar flow

Laminar Flow

• Smooth tubes at low flow rates

• There is a linear relationship between pressure difference across the tube, and the rate of flow

• i.e resistance to flow is constant

• (2005) According to the Hagen-Poisseuille equation which parameter will be inversely proportional to laminar flow?

• A. Radius of the tube to the power of 4

• B. Pressure gradient across the tube

• C. Velocity of fluid

• D. Viscosity of fluid

Laminar Flow

• Laminar flow is governed by :– Pressure gradient across the tube; P – Radius of the tube; r– Length of the tube; l– Viscosity of the fluid;

• The Hagen-Poiseuille equation describes the relationship between these factors

The Hagen-Poiseuille Equation

Turbulent Flow

• A constriction results in an increase of the velocity of the fluid

• Flow eddies, with resulting higher resistance

• Flow is no longer directly proportional to pressure

Turbulent Flow

• The analysis of turbulent flow is highly complex• With Turbulent Flow, in a rough tube, the

following approximations apply:

– Q P or P Q2

– Q l-1 thus P l– Q -1 thus P

Where Q is Flow, P is pressure across the tube, l is length of the tube and is the density of the fluid

Turbulent Flow

• For turbulent flow in a smooth tube, the resistance shows behaviour intermediate between turbulent flow in rough tubes, and laminar flow.

• Thus there is some dependence on viscosity as well as density

Onset of Turbulent Flow

• The following factors influence the type of flow: = Linear Velocity of fluid = Density of fluid– d = Diameter of tube = Viscosity of fluid

Reynolds Number

• If Reynolds number exceeds 2000, in a cylindrical tube, turbulent flow is likely to be present

• The Reynolds number is calculated as follows

• Reynolds number = d

Clinical Applications

• Turbulent flow often occurs where there is an orifice, a sharp bend or other irregularity causing an increase in velocity

• Helium reduces the density of inhaled gas, reducing Reynolds number, and converting turbulent flow to laminar flow with resultant reduction in resistance

• Warming and humidification of inhaled gases reduces their density, and also reduces resistance to flow

Work

• One Joule of work is done when one Newton of force moves an object one metre

W = F x D

• Remember that P = F/A, or F = P x A and Volume = D x A, or D = V/A. Substituting;

W = PA x V/A = PV or

Work = Pressure x Volume

Power

• Power is the rate of work, and is expressed in watts

• 1 watt is 1 joule / second

Question

• (2004) Regarding the line isolation monitor, all of the following are true, EXCEPT?

• a) Faulty equipment plugged into the wall converts the system to a standard grounded system.

• b) It will alarm when a 2-5 mA leak is detected.

• c) The number displayed on the gauge is the total current running on the system at that time.

• d) It continuously monitors the integrity of an isolated power system.

Question

• (2005) Regarding power isolation:

• A. prevents macroshock

• B. prevents explosion of flammable gases

• C. prevents interruption of power in the case of short circuit

• D. prevents burns from high frequency electrical cautery

Electrical Safety

• Electrical safety in the OR is often regarded as being of historical interest only

• Reality is that the OR environment is becoming more electrically complex by the year

• More complications arise with the networking of electronic equipment which may not conform to the rigid safety standards of conventional medical equipment

• 10 000 device related injuries in USA every year• Electrocution 5th leading cause of accidental

death in US

Historical Perspective

• As the paranoia of the era of flammable anaesthetics recedes, so does the concern re electrical safety

• Dr.W Stanley Sykes’ ‘‘Essays on the First Hundred Years of Anaesthesia” has a chapter entitled ‘‘Thirty seven little things that have all caused death’’:

• ‘‘One thing is certain—all of them have happened. All have killed, and they are waiting to do the same thing again unless you know about them.Therein lies the value of history’’

• That chapter effectively opens and closes with events related to electrical risks.

Definitions

• When electrons move from one atom to another in a consistent direction, current is said to flow

• The applied force to do this is described as potential difference, and energy is used up by the process (volts)

• This energy can both fulfill its function or injure our patients if care is not taken

• Materials that permit easy transfer of their electrons from one atom to another are termed conductors

• Those that do so reluctantly are termed resistors

Definitions

• Materials that will not transfer electrons under normal circumstances are termed insulators

• An excess of charge may be carried by some materials as a result of friction (static electricity)

• This may later be discharged by contact with a conductor, or if the potential is sufficiently high by jumping a gap as a spark.

The Effects of Current On The Human Body - (Source -Hand)

Around 1mA Mild Tingling

1-5 mA Painful

>15 mA Tonic Muscle Contraction - unable to release grip, risk of asphyxia

75-100mA Risk of VF

>5000mA Tonic Ventricular Contraction, cardiac standstill and death

Protecting the Operator

• Adequate earthing of casing

• Don’t let operator touch casing

• Don’t assume all equipment is always in good shape - regular checks

• Extension cables are frowned upon - frayed from over use, on floor, exposed to saline etc…….

Protecting the Patient

• In modern OR’s patients are rarely grounded• We use Floating Circuitry to ensure this• OR table may be source of grounding, so make

sure no contact to metal e.g. Ether screen etc• Diathermy safety• Use bipolar diathermy if pt has cardiac device• Remember that leakage can occur and is source

for microshock:

Microshock

• Of the current passing through a human hand, less than 0.1% passes through the heart

• Therefore any cardiac effects result from tiny currents

• The implication is that if you passed a current directly through the heart, much smaller currents can cause injury

• 5 seconds of sustained 50 A AC current produces sustained VF

• This phenomenon is known as microshock.

Microshock

• Anaesthetist can be earthing point for patient, and source for microshock -

• IF you touch a faulty apparatus and SG catheter at the same time, small leakage current from poorly grounded device can be sufficient to cause VF, even though you don’t feel a thing…

Capacitative Linkage

• If a material carries a negative charge, other nearby electrons will tend to move away

• If the potential at that point varies from positive to negative, such as happens with all alternating current sources (most obviously with mains electricity) then the surrounding electrons will be attracted and repelled alternately

• In other words, an alternating current can be induced in a material without an electrical source being directly connected to it. This is termed capacitative linkage.

Inductive Linkage

• Moving electrons generate a magnetic field• A moving magnetic field causes movement of

electrons • AC current source will produces a moving

magnetic field and therefore induces secondary current in any nearby wires without the need for direct contact

• Inductive linkage is intentionally utilized in some devices e.g. transformers

Inductive Linkage

• When two transformers are placed in series in a power supply it allows the power source for a medical device to be separated from any other parts of the circuitry

• Consequent reduction in the risk of direct transmission of mains energy to the patient

• This is known as a floating circuit—indicated by the surrounding box in the symbols and the letter F in the description of equipment

Electrical Safety Standards for Medical Equipment

• Complex description, detailed in a series of International Standards - IEC 60601

• Risk to Operator usually occurs when a wire within the device breaks, and contact is made with the metal casing

• Operator can ground the circuit from metal casing if he / she touches it, getting a shock

Safety Standards

• As monitoring devices proliferated in OR’s, awareness of leakage currents grew

• Because of capacitative and inductive linkage within medical devices, there will virtually always be some tiny current floating down wires to patients

• Moderate currents are not a big issue, and the maximum permitted level is below that which can be sensed, or cause harm

Classification by maximum tolerated leakage currents

Class Maximum leakage

Normal condition (A)

Single fault condition (A)

B (BF) 100 500

C (CF) 10 50

Single fault condition: condition in which one means for protection against hazard is defective. If a single fault condition results unavoidably in another single fault condition, the two failures are considered as one single fault condition.

Symbols indicating Class B Equipment

Class B Earthed Class BF, Floating Earth Class BF, Floating Earth, defibrillators may be used while equipment is connected

Symbols indicating Class C Equipment

Class C Earthed Class CF, Floating Earth Class CF, Floating Earth,

defibrillators may be used

while equipment is connected

Question

• (1998, 1999, 2002, 2004) What reduces the incidence of intra-operative fires with CO2 lasers?

a) Using a red rubber ETT

b) Wrapping a PVC ETT with lead foil

c) Using FiO2 > 0.40

d) Using N2O/O2 mixture

e) Using the CO2 laser in noncontiguous mode

Question

• (2004) Which of the following is True about laser surgery?

• a) CO2 laser is absorbed by water and has deep penetration

• b) ND-YAG laser penetrates tissue to 200 um

• c) Nitrous oxide supports combustion• d) PVC tubes are safe in laser surgery• e) Rubber tubes are safe for CO2 laser

Fire Risk

• Flammable anaesthetics largely abandoned – No change in OR Fire incidence

• Diethyl Ether still widely used in dev countries• Perceived need to prevent build up of static

electricity has been progressively abandoned• Risk of flammable skin prep is real, particularly

with electrical OR beds• Most equipment not marked any more

Pause

• Show of hands:– Who can tell me the location of the fire extinguisher in

the OR they were working in this morning?

• At a recent meeting of NA hospital CEOs:– More than 20 percent were aware of a “recent” OR fire…

• Annual incidence ~100/year in USA• Top priority for JCAHO in 2008• I’m on Fire! OR Blazes on the Rise, Roane KR.

US News & World Report, Aug 2003.

OR Fire

• Staring a fire needs three factors:– Oxidizer:

• O2, N2O

– Ignition source:• (electric) spark in 100% of closed claims

– Combustible substances:• ETT, circuit, drape, clothe etc…• Surgical Prep vapour

Case 1

A 25-year-old man was admitted for laparoscopic appendectomy and general anesthesia was induced. The fiberoptic scope was assembled with the proximal end attached to the fiberoptic light source, and the scope was turned on with the distal end laid on the surgical drapes. Within 1 min, the anesthesiologist smelled smoke.

Case 2

A 62-year-old man with copious body hair underwent tracheostomy in the operating room. The neck was prepared with DuraPrep surgical solution, and after drying for at least 3 min, the operative field was draped. Activation of electrocautery ignited a fire, and the patient was burned on his neck and shoulders.

Fuel Sources

Case 3

A 45-year-old man needed emergency tracheostomy. He was intubated with a cuffed oral polyvinylchloride endotracheal tube and ventilated with 100% oxygen prior to tracheal incision. During opening of the trachea using diathermy, a popping sound was heard and flames originating from the tracheal incision were observed.

Case 4•A 73-year-old man was scheduled for bilateral parietal burr-holes to evacuate a subdural hematoma under monitored anesthesia care (MAC). The patient was brought to the OR and a clear plastic mask was loosely strapped to his face, and oxygen introduced at 6 L/min. The head was shaved, and the skin was prepared with a surgical solution of iodine in 74% isopropyl alcohol. After allowing at least 2min drying time as recommended in the manufacturer’s instructions, the surgical field was draped. The electrosurgical unit (ESU) was used to incise the pericranium. During the first activation of the ESU, a muffled ‘pop’ was heard, which was followed almost immediately by the appearance of smoke from under the paper drapes. The entire drape was removed, the head was fully engulfed in a ‘ball of flame’, and the oxygen mask was also observed to be in flames. The paper drapes themselves were not on fire, and the surgeon used these to smother the flames while the anesthesiologist turned off the oxygen flow to the mask.

Symbols of equipment safety in presence of flammable vapours

AP - Anaesthetic Proof

Unsafe to use in zone of risk where vapor is mixed with an oxidising gas mixture (N2O is better oxidiser than O2

Safe to use in zone of risk where vapor is mixed with air

Classification by electrocution risk from contact with chassis

Class 1 Earthed metal casing. 3 pin plug required. If a cable inside breaks, current is directed via metal casing safely to ground. High current blows fuse and shuts off power supply

Class 2 Outer casing is double insulated. No possibility of contact with chassis. No earth wire needed

Class 3 Electricity supplied at < 24V. Usually battery powered, low risk to operator

Question

• (2005) Regarding Pulse oximeter all true EXCEPT:

• A. Pulse oximeter function is not altered by low cardiac output state

• B. Normal saturation may be associated with carbon monoxide

• C. Function may be affected by ambient light• D. Function may be affected by vasoactive

drugs

Additional Reading:

• GD Parbrook: Basic Physics and Measurement in Anaesthesia

• PG Barash: Clinical Anesthesia• Miller: Anesthesia• Dorsch and Dorsch - Understanding Anesthesia

equipment• Current Anaes & Crit Care 2004;15 350-354, Electrical

Safety in the operating theatre, Graham S• Curr Opin Anaesthesiol 21:790-795, Fire safety in the

operating room, Rinder CS• BJA 1994 Jun;72(6):710-22, A short history of fires and

explosions caused by anaesthetic agents, MacDonald AG

Thank you

Questions and Comments Welcome