20275003 physics measurement 2

Physics & Measurement

Peter C A KamPeter C A KamProfessor of Anaesthesia, UNSWProfessor of Anaesthesia, UNSW

St George HospitalSt George Hospital

The Gas Laws

Boyle’s LawBoyle’s Law

Charles’ LawCharles’ Law

The Third Perfect Gas LawThe Third Perfect Gas Law

The Ideal Gas EquationThe Ideal Gas Equation

Henry’s LawHenry’s Law

Dalton’s LawDalton’s Law

Boyle’s Law or First Gas Law

Boyle's LawBoyle's Law at a constant at a constant temperaturetemperature,,

the volume of a given mass of gasthe volume of a given mass of gasvaries inversely with its absolute pressure,varies inversely with its absolute pressure,

or,or,

PV = k1PV = k1

Charles’ Law or Second Gas Law

Charles' LawCharles' Law at a constant at a constant pressurepressure,,

the volume of a given mass of gasthe volume of a given mass of gasvaries proportionately to its absolute temperature,varies proportionately to its absolute temperature,

or,or,

V/T = k2V/T = k2

The Third Gas Law

The Third Perfect Gas LawThe Third Perfect Gas Law at a constant at a constant volumevolume,,

the absolute pressure of a given mass of gasthe absolute pressure of a given mass of gasvaries proportionately to its absolute temperature,varies proportionately to its absolute temperature,

or,or,

P/T = k3P/T = k3

Ideal Gas Equation

for 1 mol of any perfect gas,for 1 mol of any perfect gas,the the universal gas constantuniversal gas constant

R = PV/TR = PV/T

or, where n = number of mol of gas,or, where n = number of mol of gas,

PV = nRTPV = nRT

A Mole

the quantity of any substance containing the the quantity of any substance containing the

same number of particles as there are atoms in same number of particles as there are atoms in

0.012 kg of 0.012 kg of 1212CarbonCarbon

1 mol ~ 6.0223 x 101 mol ~ 6.0223 x 102323

Avogadro's numberAvogadro's number

Avogadro’s Hypothesis

equal volumes of gases, at the same equal volumes of gases, at the same temperature and pressure contain equal temperature and pressure contain equal numbers of moleculesnumbers of molecules

STPSTP T = T = 273.15 K273.15 K (0°C)(0°C) P = P = 101.325 kPa101.325 kPa (760 mmHg)(760 mmHg) for any gas at STP, 1 mol ~ for any gas at STP, 1 mol ~ 22.4 litre22.4 litre

Henry’s Laws

Henry's LawHenry's Law

at a constant at a constant temperaturetemperature, the amount of a gas , the amount of a gas dissolveddissolved in a liquid is directly proportional to the in a liquid is directly proportional to the partial pressurepartial pressure of that gas in equilibrium with that of that gas in equilibrium with that liquidliquid

Dalton's Law of Partial Pressures

Dalton's Law of Partial PressuresDalton's Law of Partial Pressures

in a mixture of gases, the pressure exerted by each in a mixture of gases, the pressure exerted by each

gas is equal to the pressure which would be exerted if gas is equal to the pressure which would be exerted if

that gas alone were presentthat gas alone were present

Solubility

Bunsen Solubility CoefficientBunsen Solubility Coefficient

the the volumevolume of gas, corrected to of gas, corrected to STPSTP, which dissolves , which dissolves

in one in one unit volumeunit volume of the liquid at the temperature of the liquid at the temperature

concerned, where the partial pressure of the gas concerned, where the partial pressure of the gas

concerned is concerned is 1 atmosphere1 atmosphere

Solubility

Ostwald Solubility CoefficientOstwald Solubility Coefficient the the volumevolume of gas which dissolves in one of gas which dissolves in one unit unit

volumevolume of the liquid at the of the liquid at the temperaturetemperature concerned concerned the temperature must be specifiedthe temperature must be specified it is it is independentindependent of pressure of pressure

as the pressure rises the number of molecules of gas as the pressure rises the number of molecules of gas in the liquid phase increases,in the liquid phase increases, however, when measured at the higher pressure the however, when measured at the higher pressure the volume is the samevolume is the same

Partition Coefficient

Partition CoefficientPartition Coefficient the the ratioratio of the amount of a substance present in one of the amount of a substance present in one

phase as compared with than in anotherphase as compared with than in another

the two phases being of the two phases being of equal volumeequal volume

the the temperaturetemperature must be specified, and must be specified, and

the phases being in the phases being in equilibriumequilibrium eg. blood:gas and tissue:bloodeg. blood:gas and tissue:blood

Diffusion

the spontaneous movement of molecules or the spontaneous movement of molecules or other particles in solution, owing to their random other particles in solution, owing to their random thermal motion, to reach a uniform concentration thermal motion, to reach a uniform concentration throughout the solventthroughout the solvent

the constant random thermal motion of the constant random thermal motion of molecules, in gaseous or liquid phases, which molecules, in gaseous or liquid phases, which leads to the net transfer molecules from a region leads to the net transfer molecules from a region of higher concentration to a region of lower of higher concentration to a region of lower concentration (concentration (thermodynamic activitythermodynamic activity))

Fick’s Law of Diffusion

the the rate of transferrate of transfer of a gas through a sheet of of a gas through a sheet of tissue is,tissue is, proportional to the proportional to the areaarea available for transfer available for transfer proportional to the gas proportional to the gas tension differencetension difference inversely proportional to the tissue inversely proportional to the tissue thicknessthickness

V gas = k.A (P gas 1 - Pgas 2) T

Determinants of diffusion

Characteristics of the GasCharacteristics of the Gas

Pressure GradientPressure Gradient

Membrane CharacteristicsMembrane Characteristics

Gas Characteristics

Molecular WeightMolecular Weight VV 1/ 1/MWMW

Graham's LawGraham's Law: relative rate of diffusion is inversely : relative rate of diffusion is inversely proportional to the square root of the gas molecular proportional to the square root of the gas molecular weightweight thus, lighter gases diffuse faster in gaseous media thus, lighter gases diffuse faster in gaseous media

than heavier gasesthan heavier gases lighter molecules for given energy have faster lighter molecules for given energy have faster

velocitiesvelocities therefore, Otherefore, O22 diffuses more rapidly than CO diffuses more rapidly than CO22 in the in the

gas phase (1.17 : 1)gas phase (1.17 : 1)

Gas Characteristics: Solubility

Henry's LawHenry's Law the amount of a gas which dissolves in unit the amount of a gas which dissolves in unit

volume of a liquid, at a given temperature, volume of a liquid, at a given temperature, is directly proportional to the partial is directly proportional to the partial pressure of the gas in the equilibrium phase pressure of the gas in the equilibrium phase

Gas Characteristics: Solubility

relative solubilities of COrelative solubilities of CO22 & O & O22 in water ~ in water ~

24:124:1 combining this with Graham's Law from combining this with Graham's Law from

above,above,the relative rates of diffusion the relative rates of diffusion

from alveolus to rbc for COfrom alveolus to rbc for CO22:O:O22 ~ ~ 20.7 : 120.7 : 1 solubility determines the limitation to the rate of solubility determines the limitation to the rate of

diffusion, gases being eitherdiffusion, gases being either

• diffusion limiteddiffusion limited, as for CO, as for CO

• perfusion limitedperfusion limited, as for N, as for N22OO

Diffusion, k

further, the diffusion of gas across a further, the diffusion of gas across a membrane, or into or out of a liquid, is membrane, or into or out of a liquid, is proportional to the gases proportional to the gases solubilitysolubility in the in the liquidliquid COCO22 being more soluble than O being more soluble than O22 diffuses far more diffuses far more

rapidly across the alveolar membrane and into the rapidly across the alveolar membrane and into the RBCRBC

NN22O being far more soluble than NO being far more soluble than N22 may diffuse may diffuse

into and expand closed cavities during induction of into and expand closed cavities during induction of anaesthesiaanaesthesia

Osmotic Pressure

Osmosis & pressure

OsmosisOsmosis : the movement of solvent across : the movement of solvent across a semipermeable membrane, down a a semipermeable membrane, down a thermodynamic activity gradient for that thermodynamic activity gradient for that solventsolvent

Osmotic PressureOsmotic Pressure : the pressure which : the pressure which would be required to prevent the movement would be required to prevent the movement of solvent across a semipermeable of solvent across a semipermeable membrane, down a thermodynamic activity membrane, down a thermodynamic activity gradient for that solventgradient for that solvent

Osmolality

the number of osmotically active particles the number of osmotically active particles (osmoles) per (osmoles) per kilogramkilogram of solvent of solvent

depression of depression of freezing pointfreezing point of a solution is of a solution is directly proportional to the osmolalitydirectly proportional to the osmolality 1 mol of a solute added to 1 kg of water 1 mol of a solute added to 1 kg of water

depresses the freezing point by depresses the freezing point by 1.86°C1.86°C presence of increased amounts of solute presence of increased amounts of solute

also lowers the also lowers the vapour pressurevapour pressure of the of the solvent, viz…….solvent, viz…….

Raoult’s Law

the depression or lowering of the the depression or lowering of the vapour vapour pressurepressure of a solvent is proportional to the of a solvent is proportional to the molar concentration of the solutemolar concentration of the solute

as the presence of a solute decreases the as the presence of a solute decreases the vapour pressure, making the solvent less vapour pressure, making the solvent less volatile, so the volatile, so the boiling pointboiling point is raised is raised

Raoult’s Law

These phenomena, These phenomena, depression of freezing point, depression of depression of freezing point, depression of

vapour pressure vapour pressure and elevation of boiling point, being related and elevation of boiling point, being related

to osmolarity to osmolarity are termed are termed colligative propertiescolligative properties of a of a

solutionsolution

Osmotic Pressure

1 mol1 mol of any solute dissolved in of any solute dissolved in 22.4 litres22.4 litres of of solution at solution at 0°C0°C will generate an osmotic will generate an osmotic pressure of pressure of 1 atmosphere1 atmosphere

in mixed solutions the osmotic pressure is the in mixed solutions the osmotic pressure is the sum of the individual molalitiessum of the individual molalities

Osmotic Pressure

> 99% of the plasma osmolality is due to electrolytes> 99% of the plasma osmolality is due to electrolytes

contribution of the plasma proteins: contribution of the plasma proteins: 1 mosmol/l 1 mosmol/l

normal rbc's lyse at osmolalities ~ 200 mosmol/lnormal rbc's lyse at osmolalities ~ 200 mosmol/l

as capillaries are relatively impermeable to protein, as capillaries are relatively impermeable to protein,

this generates an osmotic pressure difference this generates an osmotic pressure difference

between the plasma and the interstitial fluid, the between the plasma and the interstitial fluid, the

plasma oncotic pressure plasma oncotic pressure ~ 26 mmHg~ 26 mmHg

COLLIGATIVE PROPERTIES OF A SOLVENT

• Presence of solute stabilises solvent molecules

• More stable solvent molecules cause

(a) Increase in boiling point

(b) Increase in osmotic pressure

(c) Decrease in freezing point

(d) Decrease in vapour pressure

of solvent.

COLLIGATIVE PROPERTIES

1 Osmole of solute leads to ;

a) Boiling point of water increase by 0.52oC

b) Osmotic pressure increase by 2267kPa (17000)

c) Freezing point 1.85oC depression

d) Vapour pressure 0.04kPa (0.3 mmHg)

FREEZING POINT OSMOMETER

Sample

Thermometer

EthyleneGlycol

Thermocouple

StirringWire

MEASUREMENT OF OSMOLALITY

Supercooling

True freezing pointTemperature

GAS OR LIQUID FLOW

Hagen-Poiseuille

where flow is where flow is laminarlaminar,, etaeta (h) (h) = = viscosityviscosity of the fluid in pascal seconds of the fluid in pascal seconds there are no eddies or turbulencethere are no eddies or turbulence flow flow

• is greatest at the is greatest at the centrecentre, being ~ twice the mean, being ~ twice the mean

• near the wall near the wall 0 0

• is directly proportional to the driving pressureis directly proportional to the driving pressure

Q = r4P

Laminar Flow

but as R = dP/Q, sobut as R = dP/Q, so

thus, resistance in inversely proportional thus, resistance in inversely proportional to the to the (radius)(radius)44

R = 8nl r4

Turbulent Flow

the velocity profile across the lumen is lostthe velocity profile across the lumen is lost flow becomes directly proportional to the flow becomes directly proportional to the

square rootsquare root of the driving pressure of the driving pressure pressure flow is not linear and resistance is not pressure flow is not linear and resistance is not

constantconstant flow at which R is measured must be specifiedflow at which R is measured must be specified

other factors in turbulent flow follow,other factors in turbulent flow follow,

((rho) = densityrho) = density of the fluid in kg.m of the fluid in kg.m-3-3

Q = k r2 P l

Turbulent Flow

thus, radius has less effect, cf. laminarthus, radius has less effect, cf. laminar likelihood of the onset of turbulent flow is likelihood of the onset of turbulent flow is

predicted by the predicted by the Reynold's numberReynold's number

d =d = the the diameterdiameter of the tube of the tube v =v = the the velocityvelocity of flow of flow == rho, the rho, the densitydensity of the fluid in kg.m of the fluid in kg.m-3-3

== eta, the eta, the viscosityviscosity of the fluid in of the fluid in pascal secondspascal seconds

Re = vd

Turbulent Flow

empirical studies show that for empirical studies show that for cylindrical tubes, if cylindrical tubes, if Re > 2000Re > 2000 turbulent turbulent flow becomes more likelyflow becomes more likely

for a given set of conditions there is a for a given set of conditions there is a critical velocitycritical velocity at which Re = 2000 at which Re = 2000

the breakpoint for turbulent flow versus the breakpoint for turbulent flow versus Re also varies with the nature of the Re also varies with the nature of the fluidfluid eg. for blood turbulent flow at eg. for blood turbulent flow at Re > 1000Re > 1000

Viscosity

for a given set of conditions, flow is inversely proportional for a given set of conditions, flow is inversely proportional to viscosityto viscosity

blood viscosity increases with,blood viscosity increases with, low temperatureslow temperatures increasing ageincreasing age cigarette smokingcigarette smoking increasing haematocritincreasing haematocrit abnormal elevations of plasma proteinsabnormal elevations of plasma proteins

the viscosity of blood is anomalous due to the presence of the viscosity of blood is anomalous due to the presence of cellscells behavior is said to be behavior is said to be non-newtoniannon-newtonian

Tension

Laplace's LawLaplace's Law

P = T.h.(1/rP = T.h.(1/r11 + 1/r + 1/r22))

T T = the tangential force in N/m= the tangential force in N/m acting along a length of wallacting along a length of wall

h h = the thickness of the wall (usually = the thickness of the wall (usually smallsmall))

Laplace’s Law

thus, for straight tubes,thus, for straight tubes,

P = T.h./rP = T.h./r

and, for and, for spheresspheres,,

P = 2T.h/rP = 2T.h/r

Laplace’s Law

thus, as vessel diameter becomes thus, as vessel diameter becomes smaller, the collapsing force becomes smaller, the collapsing force becomes greater greater

this can lead to vessel closure at low this can lead to vessel closure at low pressures, the pressures, the critical closing critical closing pressurepressure

seen in alveoli, leading to instability with seen in alveoli, leading to instability with small alveoli tending to fill larger ones small alveoli tending to fill larger ones major action of surfactant is to maintain major action of surfactant is to maintain

alveolar stabilityalveolar stability

Measurement of Gas Volumes and Flows

Direct methodsDirect methods

Indirect methodsIndirect methods

WET SPIROMETER

••

Recorder

CO2 Absorber

Disadvantages1. High inertia2. Inaccurate at high respiratory rate or

VITALOGRAPH

Bellows

Recorder

Patient

Disadvantage : Patient effort dependent Bellows collect expired gas.

Only measures forced expiratory volumes and flows.

WRIGHT RESPIROMETER

Channels

Gas Flow

1. Gas stream directed by tangential slits to vane

2. Gas flow drives spinning vane

3. Spinning vane activates gears to record flow

4. Over reads at peak flow

Under reads at continuous flow

DRAGER VOLUMETER

Gasflow

1. Consists of 2 interlocking dumb bell rotors2. More accurate3. Affected by water vapour

INDIRECT MEASUREMENT OFGAS VOLUMES

1. Magnetometers

2. Pneumographs

3. Capacitance spirometry

4. Respiratory inductance plethysmograph

MAGNETOMETERS

1. Electromagnets attached to chest wall andabdomen

2. Electromagnetic field generated .

3. Chest and abdominal diameter changes –alter magnetic filed.

4. Disadvantage : Inaccurate ++

PNEUMOGRAPH

Pressure Transducer

PressureTransducer

Disadvantage : frequent recalibration required

Chest wall

CAPACITANCE SPIROMETRY

Top plate

Bottom plate

Used for apnoeic monitoring

Chest wall

INDUCTANCE SPIROMETRY

Oscillator

RECORDER COMPUTER

Chest wall

GAS FLOW MEASUREMENT

1. Variable orifice (constant pressure drop)flowmeter eg. rotameter

2. Variable pressure – fixed orifice flowmeter

ROTAMETER

1. Variable orifice flowmeter

2. Gas flow controlled by control value at bottom of rotameter

3. Vertical tube with tapering internal diameter- wider at the top- narrower at the bottom

4. Bobbin - acts as indicator of flow

5. Pressure drops across the annular space around bobbin opposes downward pressure produced by weight of bobbin.

ROTAMETER

Pressure drop [P1 – P2] balances weight [W] of bobbin

Bobbin

Rotameter tube

Gas Flow

ROTAMETER

1. Non – linear scale

2. At lower flow;- bobbin length > distance between bobbin and glass (d)- Laminar flow

3. At high flows;- bobbin length < d- turbulent flow

4. Accuracy + 2%

PNEUMOTACHOGRAPH

1. Measure gas flows.

2. Types(a) Fixed Resistance

Gas flow across fixed resistance differentialpressure signal & flow eg. screen and fleisch pneumotachograph.

(b) Hot wireSignal produced by gas flow cooling a heatedresistance wire.

(c) Pitot tube

SCREEN PNEUMOTACHOGRAPH

ScreenGas

Pressure difference flow

FLEISCH PNEUMOTACHOGRAPH

HEATING COIL

Fine bore parallel tubeEnsure laminar flow

P1 - P2

Heating coil to prevent water condensation

GAS FLOW

PITOT TUBE PNEUMOTACHOGRAPH

Upstream Downstream P2

P1 (total) (static P)

P1 - P2 velocity of gas

GAS FLOW

Heat & Temperature

HeatHeat : a form of energy, being the state : a form of energy, being the state of of thermal agitationthermal agitation of the molecules of of the molecules of a substance, which may be transferred a substance, which may be transferred by,by,

conductionconduction through a substance through a substance

convectionconvection by a substance, and by a substance, and

radiationradiation as electromagnetic waves as electromagnetic waves

Heat & Temperature

TemperatureTemperature : is the physical state of a : is the physical state of a

substance which determines whether or not the substance which determines whether or not the

substance is in thermal equilibrium with its substance is in thermal equilibrium with its

surroundings, surroundings, heat energyheat energy being transferred being transferred

from a region of higher temperature to a region of from a region of higher temperature to a region of

lower temperaturelower temperature

Heat & Temperature

KelvinKelvin

the SI unit of thermodynamic temperaturethe SI unit of thermodynamic temperature

equal to 1/273.16 of the absolute temperature of equal to 1/273.16 of the absolute temperature of

the the triple pointtriple point of water of water

the temperature at which ice, water and water the temperature at which ice, water and water

vapour are all in equilibriumvapour are all in equilibrium Celsius scaleCelsius scale

Temperature (K) = Temperature (°C) + 273.15Temperature (K) = Temperature (°C) + 273.15

in Celsius the triple point of water is in Celsius the triple point of water is 0.01 °C0.01 °C

Critical Temperature

the temperature above which a gas cannot be the temperature above which a gas cannot be

liquified by pressure aloneliquified by pressure alone NN22OO = 36.5 °C= 36.5 °C

OO22 = -119 °C= -119 °C

GasGas:: a substance in the gaseous phasea substance in the gaseous phaseaboveabove its critical T its critical T

VapourVapour:: a substance in the gaseous phasea substance in the gaseous phasebelowbelow its critical its critical TT

Critical Pressure

the pressure at which a gas liquifies at the pressure at which a gas liquifies at its critical Tits critical T

NN22O ~ O ~ 73 bar 73 bar @@ 36.5 °C36.5 °C NN22O ~ 52 bar O ~ 52 bar @ 20.0 °C@ 20.0 °C

Pseudo-Critical TemperaturePseudo-Critical Temperature for a mixture of gases at a specific pressure, the for a mixture of gases at a specific pressure, the

specific temperature at which the individual gases specific temperature at which the individual gases may separate from the gaseous phase may separate from the gaseous phase

NN22O 50% / OO 50% / O22 50% 50% = - 5.5 °C= - 5.5 °C

• for cylinders (most likely at 117 bar)for cylinders (most likely at 117 bar) NN22O 50% / OO 50% / O22 50% 50% = - 30 °C= - 30 °C

• for piped gasfor piped gas

Adiabatic Change

the change of the change of physical statephysical state of a gas, without the of a gas, without the transfer of heat energy to or from the surrounding transfer of heat energy to or from the surrounding environmentenvironment rapid rapid expansionexpansion & energy required to overcome Van & energy required to overcome Van

der Waal's forces of attraction, as this energy cannot be der Waal's forces of attraction, as this energy cannot be

gained from the surroundings, it is taken from the kinetic gained from the surroundings, it is taken from the kinetic

energy of the molecules energy of the molecules basis of the basis of the cryoprobecryoprobe

rapid rapid compressioncompression, the energy level between molecules , the energy level between molecules

is reduced, as this energy cannot be dissipated to the is reduced, as this energy cannot be dissipated to the

surroundings, it is transferred to the kinetic energy of the surroundings, it is transferred to the kinetic energy of the

moleculesmolecules

T Measurement: Non-electrical

mercurymercury thermometers thermometers

accurate, reliable, cheapaccurate, reliable, cheap

readily made into a thermostat, or max. reading readily made into a thermostat, or max. reading

formform

Angulated constriction at base of stem prevents Hg Angulated constriction at base of stem prevents Hg

column returning to bulb via surface tension forcescolumn returning to bulb via surface tension forces

requires 2-3 mins to reach thermal equilibriumrequires 2-3 mins to reach thermal equilibrium

unsuitable for insertion in certain orificesunsuitable for insertion in certain orifices

T Measurement: Non-electrical

alcoholalcohol thermometers thermometers

cheaper than mercurycheaper than mercury

useful for very low T, mercuryuseful for very low T, mercury solid at solid at -39°C-39°C

unsuitable for high T, alcohol boils at unsuitable for high T, alcohol boils at 78.5°C78.5°C

expansion also tends to be less linear than expansion also tends to be less linear than

mercurymercury

Bimetallic stripsBimetallic strips

Bourdon gauge Bourdon gauge pressurepressure

T Measurement: Electrical

resistanceresistance thermometer thermometer

metalsmetals R R linearlylinearly with with TT

frequently use a platinum wire resistor, or frequently use a platinum wire resistor, or

similarsimilar

accuracy improved with a Wheatstone accuracy improved with a Wheatstone

bridgebridge

Resistance Thermometer

Platinum Wire T α R (linear) Disadv. R Not sensitive α R α T wire Battery T

thermistorthermistor metal oxidesmetal oxides R R exponentiallyexponentially with with TT made exceeding smallmade exceeding small rapid thermal equilibrationrapid thermal equilibration narrow reference rangenarrow reference range different thermistors for different scalesdifferent thermistors for different scales accuracy improved with a Wheatstone bridgeaccuracy improved with a Wheatstone bridge Accuracy reduced with exposure to severe T, Accuracy reduced with exposure to severe T,

egeg. . sterilisationsterilisation

Thermistor

Thermistor oxide of R exponentially with Temp. metal Adv : small - rapid change

- accessible to remote location Disadv : Drift in calibration

thermocouplethermocouple based on the Seebeck effectbased on the Seebeck effect at the junction of two dissimilar metals a small at the junction of two dissimilar metals a small

voltage is produced, the magnitude of which is voltage is produced, the magnitude of which is

determined by the temperature determined by the temperature metals such as copper and constantan (Cu+Ni alloy)metals such as copper and constantan (Cu+Ni alloy) requires a constant reference temperature at the requires a constant reference temperature at the

second junction of the electrical circuitsecond junction of the electrical circuit may be made exceeding small and introduced may be made exceeding small and introduced

almost anywherealmost anywhere

Thermocouple – “Seebeck effect”

Reference Junction Copper Constantan Junction Potential

mV Measuring junction Temp

Thermocouple

Junction of 2 different metals P. Diff (α To) Seebeck effect Metal 1 eg Cu V Metal 2 eg. Constantin

Ref Measured Adv. Large linear range Temp Temp can be very small (eg.Ice) Disadv. Small output 40μv

Specific Heat Capacity

heat required to raise the temperature of 1 kg heat required to raise the temperature of 1 kg

of a substance by 1 K (J/kg/K)of a substance by 1 K (J/kg/K) water SHCwater SHC = 4.18 kJ/kg/K or, 1 kcal/kg/K= 4.18 kJ/kg/K or, 1 kcal/kg/K blood SHCblood SHC = 3.6 kJ/kg/K= 3.6 kJ/kg/K

infusion of 2000 ml of blood at 5°C, requiring infusion of 2000 ml of blood at 5°C, requiring

warming to 35°C, warming to 35°C, require require 2 kg x 3.6 kJ/kg/°C x (35-5)°C = 216 kJ2 kg x 3.6 kJ/kg/°C x (35-5)°C = 216 kJ

would result in the person's temperature falling by would result in the person's temperature falling by

~ 1°C~ 1°C

Specific Latent Heat

the heat required to convert 1 kg of a substance the heat required to convert 1 kg of a substance from one phase to another at a given temperaturefrom one phase to another at a given temperature latent heat of vaporisation latent heat of vaporisation (from liquid to vapour)(from liquid to vapour)

LHV of waterLHV of water at 100°C = 2.26 MJ/kgat 100°C = 2.26 MJ/kg at 37°Cat 37°C = 2.42 MJ/kg = 2.42 MJ/kg the lower the T the greater the latent heat requiredthe lower the T the greater the latent heat required

as T rises, the latent heat falls until ultimately it as T rises, the latent heat falls until ultimately it reaches reaches zerozero at a point which corresponds with the at a point which corresponds with the critical temperaturecritical temperature = 373°C = 373°C

Humidity

ABSOLUTE HUMIDITY

• Mass of water vapour (g) in a given

volume of air (m3)

numerically = mg / 1L

• Fully saturated air

@ 20oC contains 17mg/L water

@ 37oC contains 44mg/L water

RELATIVE HUMIDITY

• Defined as ratio of mass of water vapour in a given volume of air to the mass required

to fully saturate that volume of air at a given temperature. (%).

• By ideal gas equation, mass is proportional to number of moles present.

Relative humidity = actual vapour pressure saturated vapour pressure

HAIR HYGROMETER

Principle : Hair lengthens as humidity increases

Accuracy : - Low - Accurate between RH 15-85% - very simple & cheap

RH LHair

WET AND DRY BULB HYGROMETER

WetGauze

- - - - - - - -- - - -

WET AND DRY BULB HYGROMETER

T1 = temperature of wet bulb decreases because of evaporation in wet gauze.

Lower humidity causes more evaporation and T1 decreases more.

Humidity T1 – T2

δ - % humidity from tables

DEW POINT

• Defined as temperature at which ambient air is fully saturated

• At this point condensation occurs

REGNAULT’S HYGROMETER

Thermometer

Silver Tube

Bubble

Condensation at “ dew point”

RH = SVP at dew point SVP at ambient temperature

OR from tables

HUMIDITY TRANSDUCERS

• Principle : When a substance absorbs water, its resistance or capacitance changes.

• Substance is incorporated into electrical circuit as resistor or dielectric portion of a capacitor.

HUMIDITY TRANSDUCERS

Advantages :1. Extremely sensitive2. Rapid response - can be used as

servo-systems.

Disadvantages :1. Display hysteresis – unsuitable for critical applications where high degrees of accuracy required.

MASS SPECTROMETER for measuring humidity

- Used to measure water vapour pressure

- Rapid response - can be used to measure breath –by- breath changes.

- Disadvantage - very expensive

WEIGHING TECHNIQUES

a) Weighing quantity of water vapour that has condensed in a known volume of air

b) Warming air so that all water droplets areevaporated & then weighing volume of air.

c) Absorption techniquesAbsorption of water vapour in either

concentrated sulphuric acid, silica gel or anhydrous CaCl2

PRESSURE – Physics and Measurement

PRESSURE

• Defined as Force per unit area• Units : Pascal (Pa) or Newton per square meter ( N.m-2).

Newton = Force that will accelerate 1 kg (N) mass at 1ms-2.

1 Pascal = 1 N acting on area of 1m2

• Gravity = 9.81m.s-2

PRESSURE UNITS

1 kPa = 10.2 cm H2O1 kPa = 10.2 cm H2O

= mm Hg= mm Hg

[mercury = 13.6 times as dense as water][mercury = 13.6 times as dense as water]

1 bar = 100 kPa1 bar = 100 kPa

= mm Hg= mm Hg

GAUGE PRESSURE

• Pressure relative to atmospheric pressure. i.e. zero at atmospheric pressure

• Gauge Pressure may be determined by how much pressure is above or below atmospheric pressure.

ABSOLUTE PRESSURE

•Pressure relative to a true zero pressure(i.e.vacuum)

Therefore,

Zero gauge pressure = 1 atmosphere absolute

• Gauge pressure 1 atmosphere = 760 mmHg

= 101.325 kPa

= 2 atmosphere

absolute

MEASUREMENT OF BLOODPRESSURE

UNITS OF PRESSURE

Unit Value

Pascal ( Pa) N/m2 SI Unit

mmHg 133.3Pa 1 mmHg = 7.5kP

bar 105Pa

Torr almost = 1 mmHg

cmH2O ~ 1-Pa

PRESSURE

P = p x g x h

p = density of fluid

g = acceleration due to gravity

H = Height of column

Conversions 10cmH2O = 7.4 mmHg 10mmHg = 13.6 cmH2O

Mercury 13.6 x water density

INDIRECT BLOOD PRESSUREMEASUREMENT

Principlea) Utilise cuff - occlude pulse

a) Detection of return of pulse or blood flow distal to cuff.

OCCLUDING CUFF

• Cuff pressure transmitted to tissues surrounding artery.

• Cuff width = 40% limb circumference

• Bladder - at least half circumference - Centred over artery

• Cuff level with heart

ERRORS WITH CUFF

a) Too narrow or to loose cuff overestimate

SP and DP.

b) Too wide

underestimate SP and DP

(Pressure = F/A)

CUFF – AHA STANDARDS

Small Adult 10 x 24 cm 22 – 26 cm

Adult 13 x 30 cm 27 – 34 cm

Large adult 16 x 38 cm 35 x 44 cm

Adult thigh 20 x 42 cm 45 – 52 cm

Bladder sizeArm

Circumference

DEVICES MEASURING CUFFPRESSURE

Mercury manometers - Used to be standard

- Now phased out

- Column must be vertical

- Air vent on top of column

Aneroid gauges - Convenient

- Commonly under-read BP

- Calibrated 6 monthly

FLOW DETECTION DISTALTO CUFF

Palpation Finger palpation

Finger Photoplethysmograph

Auscultation Audible range – Korotkov sound

Ultrasound (5MH2) range – Arteriosounde

Subaudible (10-40mH2) range – Infrasound

Oscillometry Defection of oscillations

von Recklinghausen’s oscillations

NO2 invasive BP

KOROTKOV SOUNDS

Phase I: First appearance of tapping sounds

Phase II: Brief softening of sounds

Auscultation gap : disappearance of sounds

Phase III: Return of sounds

Phase IV: Muffing of sounds

Phase V: Disappearance of all sounds

KOROTKOV SOUNDS

Cuff deflation rate = 2-3 mm Hg per sec.

Rapid deflation = underestimate BP

Note auscultatory gap may be present

DBP = point of disappearance of sound

Difference between phase IV & V ~ 5 mmHg

OSCILLOMETRY

• Basis of NIBP

• Only one cuff acts as (i) occluding cuff

(ii) Sensor using microprocessor

• Cuff both actuator & transducer

OSCILLOMETRY

Oscillations begins at SBP

Maximal at MAP

Abruptly diminishes at DBP

OSCILLOMETRY - NATURE OFOSCILLATIONS

• Diamond shaped pattern

• Pressures at oscillation between 2 heart beats compared.

• Average is recorded

• MAP most accurate

OSCILLOMETRY

Advantage : 1. Not operator dependent

2. “hands free”

3. Automated

Disadvantage :

1. Inaccurate in shock or

arrhythmia.

2. Cuff placement important

3. Bruising + skin damage

4. Venous congestion

5. Nerve compression

FINAPRES

• Cuff placed around finger

• Changes in volume of arterial blood in

finger detected by plethysmography

• MAP - cuff inflated to maximal

- cuff pressure approximates

arterial pressure waveform

ARTERIAL TONOMETER

• Force transducer placed over artery with under lying bone.

• Electrical signal - reproduces arterial waveform

• Needs to be calibrated 5 – 10 min against oscillometric measurements

INVASIVE (DIRECT) BP MEASUREMENT

Advantages

1. Continuous monitoring

2. Trends observed

3. Accuracy over wide range

4. Enables visual analysis of pulse

pressure

VISUAL ANALYSIS OF WAVEFORM

Myocardial Contractility

Upstroke of pulse pressure ~ LV dp/dtSteep upstroke = strong LV contraction

Stroke Volume

Area under systolic ejection ~ LV stroke volume

Systemic Vascular Resistance

Low diastolic notch = Rapid run off & Steep down stroke low SVR

CIRCULATING BLOOD VOLUME

Exaggerated beat to beat variation with

ventilation = hypovolaemia

INDICATIONS FOR INVASIVE BP

1. Rapid changes in BP

2. Monitor effects of potent hypotensive or

vasopressor agents

3. During CP bypass

4. Operation with volume shifts eg. AAA or

phaeochromocytoma.

5. Shock

6. Difficult access eg. Morbid obesity

VARIATION OF BP

• Waveform distorted the further away from the heart.

• High frequency components eg. incisura damped out / disappear.

• Systolic BP increases distally.

• Hump becomes more prominent in diastolic part of waveform

VARIATION OF BP

• SBP increases towards periphery

• DBP decreases towards periphery

• MAP - only slight drop

eg. MAP radial 5% < MAP aorta

• Pulse Pressure increases towards periphery

Causes : a) Reflection of pressure wave from peripheral arterioles

b) Resonance

BP AND POSTURE

- 42 mmHg

+80 mmHg

COMPONENTS OF INVASIVE BP

• Mechanical coupling of blood to transducerintravascular catheterconnecting tubingstop lock

• TransducerConverts pressure changes to voltage changes

• Electronic processing

• Display + recorder

REQUIREMENTS FOR ACCURACYINVASIVE BP

1. STATIC Accuracy - Ability to measure stationary events- No baseline/sensitivity drifts

- Input & output linearity - No hysteresis

2. DYNAMIC Accuracy - Ability to accurately record over rapid changes.

3. PHYSIOLOGICAL Reactance - measuring system must have effect on event recorded / measured.

TRANSDUCER

• Coverts pressure energy movement electrical signal

• Commonly diaphragm resistance movement change Wire stretch resistance

• Wheatstone bridge used to convert resistance change to voltage signal

STATIC CALIBRATION

• Linear response (straight line) between pressure and output voltage.

OutputGain = slope of line

offset

Pressure

• Offset - Transducer output at zero pressure• Gain - Change in output for given change in pressure

must be constant.• Sensitivity (factory set) at 5V/V/mmHg

MEAN BLOOD PRESSURE

• Average Pressure• Equal to pressure when a = b• Electronically averaged instantaneous measurements• Highly damped system eg. aneroid gauge gives MAP• MAP = diastolic pressure + 1/3 pulse pressure = SBP + 2DBP

DYNAMIC RESPONSE

• Basic or Fundamental Harmonic (1st) Heart Rate 60 beats/min = 1 Hz Heart Rate 120 beats/min = 2 Hz

• By Fourier Analysis Fundamental = f = 2Hz (HR 120) 2nd Harmonic = 2 x f = 4Hz 3rd Harmonic = 3 x f = 6Hz 10th Harmonic = 10 x f = 20Hz

• Accurate waveform without amplitude distortion achieved with 10th harmonic ~ 20Hz

PRACTICAL ASPECTS OF DYNAMIC RESPONSE

• Natural frequencies of clinical systems approx, 30Hz

• Acceptable if damping ratio is optimal

• To achieve dynamic accuracy - fundamental frequency (fo) must be maximised.

MAXIMISING Fo

Note : fo = 1 E 2 M

To minimize fo Minimize M (mass)

- Minimal volume of fluid in transducer- Short tubing

Maximise E, modulus of elasticity- Stiff tubing- Stiff diaphragm- Eliminate air bubbles

FACTORS THAT INCREASE DAMPING

• Increase fluid viscosity eg. blood clots

• Narrow tubing eg. kinked catheter

• Increased tubing length

• Decreased stiffness of tubing

LIQUID MANOMETERS(Absolute Pressure)

Mercury Barometer

••

• ••

••

••••

•• •

••

• Mercury

Torricellian Vaccum

Measures Absolute Pressure

LIQUID MANOMETERS (Gauge Pressure)

h - Amount by which pressure exceeds atmospheric

Note tube open at both ends

LIQUID MANOMETERSMethods to increase sensitivity

• Use low density liquid

• Amplify vertical movement of

meniscus.

a) inclined plane manometer

b) differential liquid manometer

MECHANICAL PRESSURE GAUGE

Bourdon Gauge

Pointer

Coiled tube unwinds at high pressure

Pressure

Fixed Point Low

Pressure

HighPressure

Cross Section

• Usually for measuring high pressure• Can be adapted for temperature or flow measurement

MECHANICAL PRESSURE GAUGE

Aneroid Gauge

BellowsExpands with pressure

Pointer

Lever System - amplifies change

Uses : BP, Airway Pressures on IPPV

DIAPHRAGM GAUGE

• Pressure measurement made by sensing movement of flexible diaphragm.

• Diaphragm movement sensed by a) Direct movement of levers etc. (not sensitive) b) Optical method pressure Diaphragm Mirror

stretched more rotated & curved

c) Electromechanical transducers

OPTICAL ELECTROMECHANICALTRANSDUCERS

Principles :

1. Increased pressure Diaphragm more convex

2. Light beam reflected off silvered surface of diaphragm on to photoelectric cell.

3. Reflected light beam more divergent.

4. Light intensity sensed by photo-electric cell decreases and electrical output falls

OPTICAL ELECTROMECHANICALTRANSDUCERS

Mirror Mirror

Photoelectric

CellSlivered surface

Divergent reflected light

Convergent

Reflected light

Sliveredsurface

LightSource

STRAIN GAUGE ELECTROMECHANICALTRANSDUCERS

Principles :

Wire stretched or compressedChange in length and diameteratomic stricture change

Resistance change

STRAIN GAUGE TRANSDUCER

Wired compressed

Movable block

Fixed pointDiaphragm

Resistance wire stretch

1. Resistance wires arranged in 2 sets2. When pressure increases, one set stretches & other set compresses3. Difference in resistance is measured by wheatstone bridge system.

BONDED STAIN GAUGE

PStrain gaugeBonded todiaphragm

Single Bond Double Bond

1. Resistance wires in zig-zag patter cemented to diaphragm surfaces.

2. Robust but subject to hysteresis.3. Resistance wire – low temperature coefficient.4. Double bonded strain gauge one stretched & other

compressed.

WHEATSTONE BRIDGE ARRANGEMENT OF RESISTANCE WIRES

OUTPUT OUTPUT

StrainGaugeelement

Half bridge circuit Full bridge circuit

CAPACITANCE TRANSDUCER

2ND plateDiaphragmas one plate

Charge

Characteristics : 1. Very sensitive 2. High natural frequency 3. Temperature drift

4. Unstable

VARIANCE INDUCTANCE TRANSDUCER

P Iron Core

Diaphragm

Coil magnetic field

WHEATSTONE BRIDGE

Wheatstone bridge is a special arrangement of resistors designed to amplify change in resistance.

Balanced Wheatstone bridge

R adjust R measure

Ammeter readszero

R measure R adjust

FREQUENCY RESPONSE

1. Measurement systems respond to restricted range of frequencies.

2. Input signals of same amplitude at different frequencies will produce output over a limited range of frequencies.

3. Within this frequency range, response may be more sensitive to some frequencies than others.

4. Response of system (system gain) plotted against signal frequency is called “ Frequency Response of System”.

FREQUENCY RESPONSE OFA SYSTEM

Bandwidth

Lower cut off Upper cut off

Frequency

Systemgain

DETERMINANTS OFFREQUENCY RESPONSE

MECHANICAL SYSTEM

Inertial elements (eg. mass)Compliance elements (eg. spring)

ELECTRICAL CIRCUIT

InductanceCapacitance

NATURAL OR RESONANT FREQUENCY

1. When a constant amplitude waveform is applied at increasing amplitude occurs at resonant ornatural frequency (fo) of the system.

2. Beyond fo (higher frequencies), amplitude of oscillations increase and then fall to zero.

3. Fo depends on inertial and compliance etc.

AMPLITUDE AS FREQUENCYINCREASES

Natural or resonantFrequency (fo)(maximal oscillation)

Increasing frequency

Amplitude decreasedBeyond fo

Amplitude of oscillation

ENERGY INTERCHANGE INOSCILLATING SYSTEM

1. Continental interchange between kinetic energy of mass in motion and potential energy.

2. Kinetic energy = ½ mv2.

3. Narrow Tube

(a) More energy required to make given mass of fluid to oscillate because it has to reach higher velocity.

(b) Catheter fluid velocity > fluid velocity at diaphragm.

(c) E, Effective mass catheter > E, diaphragm.

(d) Larger effective mass lower fo.

RESONANT FREQUENCY

OUTPUT

FREQUENCY FO Resonantfrequency

UNDAMPED NATURAL FREQUENCY

Fo = 1 2

Fo = undamped natural frequency

S = stiffness of transducer diaphragm

M = Effective mass

HIGH UNDAMPED NATURALFREQUENCY

Catheter - Transducer System

- Needs high fo

- Occurs when fluid velocity is minimized

- Achieved by;

(a) Stiff diaphragm

(b) Short and wide catheter.

DAMPING

• Defined as tendency of a system to resist oscillations caused by a sudden change.

• In mechanical devices, damping arises from frictional effects on mechanical moving parts.

• In fluid operated devices, damping is caused by vicious forces that oppose fluid movement.

• In electrical devices, electrical resistance oppose passage of electrical currents.

EXTENT OF DAMPING

Underdamping - Results in oscillation and over-estimation of measurement (overshoot ofoutput) .

Overdamping - Results in slow response and underestimation of measurement.

Critical damping - No overshoot of output signal but speed of response is too slow.

SIGNAL AMPLITUDE & DAMPING

0.50.1 0.5 1.0 1.5

0.64D=1.0

RelativeAmplitude

OPTIMAL DAMPING

1. State of damping in which(a) Minimal overshoot(b) Response speed only slightly reduced

2. D = 0.64 (i.e. 64% critical damping)

(a) 7% overshoot

(b) Response speed only minimally reduced

PHASE SHIFT RESPONSE

1. Waveform or signal composed of series of component frequencies.

2. Each component waveform undergoes different time delay or phase shift.

3. Phase shift is time delay expressed as an angle(radians).

4. At fo, waveform delayed by 90%

5. Other frequencies, phase lag is linearly related at D = 0.64 I.e. phase distortion minimal at D = 0.6.

SPECIFICATIONS OF TRANSDUCERS

1. To avoid waveform, amplitude and phase distortion, catheter-transducer system should have undamped natural frequency 25-40Hz .

2. Standard transducer – undamped natural frequency of 100 Hz or more.

3. Catheter - tap - cannula arrangement reduces natural frequency of the system.

DIRECT BP MEASUREMENT SPECIFICATIONS

1. Transducer : - Frequency response > 100 Hz i,.e. resonant frequency > 100Hz.

2. Tubing & cannula : - Lowers fo and adds damping.

Length increase - lower fo, more damping

Compliant tube - lower fo, more damping

Small bore tube - lower fo, more damping

air/clot in tube - lower fo, more damping

Factors that increases fo tend to lower damping.

CARDIAC OUTPUT MEASUREMENT

USES OF CARDIAC OUTPUT MEASUREMENT

1. GENERAL ICU

- Cardiac performance assessment in shocked patients.

- Management of inotropes and vasoconstrictors

- Optimisation of PEEP Therapy.

2. OPERATING THEATRES

- Major Anaesthetic eg. AAA, Liver transplant

- Anaesthesia in severe cardiac disease (eg. L V failure, Recent MI)

CARDIAC OUT MEASUREMENT USES

3. Post-cardiac Surgery Intensive Care Units4. Coronary Care Units / Laboratories

- Assessment of severity of ischaemic & valvular disease

- Management of inotropes vasoconstrictors and vasodilators.

INFORMATION FROM C.O. MEASUREMENT

Cardiac output L/min

Cardiac Index = CO Surface area L/min/m2

Systemic vascular resistance = MAP-RAP mmHg/L/min CO or PRU

dyne.sec.cm-5

Pulmonary Vascular Resistance = MPAP-LAP CO

mmHg/L/min or PRU

dyne.sec.cm-5

INFORMATION FROM C.O. MEASUREMENT

LV stroke work = MAP x SV gm.m

RVstroke work = MPAP x SV gm.m

Oxygen Consumption = CO x (CaO2-Cv-O2) ml/min

Oxygen Delivery = CO x CaO2 ml/min (D O2)

DIRECT CO MEASUREMENT

1. ELECTROMAGNETIC FLOWMETER PROBE

a) Periaorticb) Intraaortic

2. Ultrasonic Flow Probe

3. Intravascular thermal velocity transducer

INDIRECT CO MEASUREMENT

A. INVASIVE METHODS1. Fick method (1970) i) Direct (O2 Consumption) ii) Indirect (CO2 production)2. Dye dilution (Stewart, 1894,

Hamilton, 1979)3. Thermodilution (Fegler, 1954)

NON-INVASIVE METHODS1. Radioactive tracer dilution (radiocardiography)2. Bollisto cardiography3. Pneumocardiography4. Impedance Plethysmography

ELECTROMAGNETIC FLOW PROBE

Faraday’s Law states that :-

“When a conductor moves with a given velocity across theLines of force of a uniform magnetic field, an electromotiveForce will be induced at right angles to the flow, and will be Proportional to the velocity of the conductor”

MAGNETIC FIELD

Blood flow

Magnetic H

Magnetic field is held at right angles to blood flowElectromotive force induced at right angles to moving conductor, the blood flow.

NOTE : EMF technique measures blood velocity

ELECTROMOTIVE FORCE, E

+a E = v. H 2a 10 -8

V = Velocity of bloodH = strength of magnetic field (gauss)2a = length of conductor or diameter of blood vessel.

BLOOD VELOCITY

Blood velocity = Flow rate (cm3 / sec) Cross section area of vessel (cm2)

Flow rate = Blood velocity x cross section area

TYPES OF EMF FLOW PROBES

NOTE : Peri or intra-aortic flow probes measure CO (less coronary blood flow)

(a) Periaortic Flow Probe• used in open heart surgery• rarely used clinically

(b) Intravascular Flow Probe• introduced via peripheral artery• invasive• velocity depends on exact site (maximal in centre of blood vessel)

ULTRASONIC FLOW PROBE

Measures velocity of flowing fluid

(a) Pulsed Ultrasound- Cuff transducer around artery- Pulse of 5 MHz from piece-electric crystal

in cuff.- receiver crystal downstream- Transit time between

(B) Doppler EffectPrinciple : frequency shift of emitted wave frombarium titanate crystal when it is reflected frommoving fluid column

Disadvantage :Cannot detect difference between forward and backward flow.eg. aortic blood flow : mean velocity = 40 cm/sec

systolic velocity = 120 cm/sec

1. Probe placed at suprasternal notch with beam directed to aortic arch or

2. Transoesophageal probe with beam directed at descending aorta

3. Velocity of blood flow and cross – sectional area of aorta determined.

ACCUCOM C.O. MONITOR

1. Continuous C.O reading

2. Oesophageal probe containing dual crystal Doppler probe transducer to measure velocity in descending aorta.

3. Second Doppler probe placed at suprasternal notch used to calibrate instrument

4. Aortic diameter determined by echocardiogram or monogram

2 D COLOUR FLOW – ECHO-DOPPLER

1. Pulse ultrasound for imaging of cardiac flow

2. L V outflow tract imaged and cross sectional area determined.

3. Velocity of blood flow in LV – outflow tractmeasured.

4. CO = Cross Section Area x Velocity.

5. Colour Doppler to demonstrate direction of flow

INTRAVASCULAR THERMAL VELOCITY TRANSDUCER

1. Heated thermistor placed in moving liquid stream dissipates heat as a function of flow velocity.

2. Probe maintained at fixed position in blood stream within vessel of fixed diameter.

3. Velocity signal translated into flow.

INDIRECT METHODS OF C.O. MEASUREMENT

I INVASIVE METHODS Direct Fick Method Indirect Fick Method Dye dilution Method Thermodilution technique

II NON INVASIVE METHODS

Radioactive tracer dilution Ballisto cardiography Thoracic impedance plethysmography

FICK PRINCIPLE(Adolph Fick – 1870)

States that : “ the flow of a liquid in a given period ofTime is equal to the amount of substance entering orLeaving the stream / or organ) in the same period of Time, divided by the difference between the concentration of the substance before and after thePoint of entry or exit “

DERIVATION OF FICK PRINCIPLE

Substance added ( M mg)

Amount ofIndicatorAt entry ()

+Amount of IndicatorAdded (M)

=Amount ofIndicator atExit ( o )

Concentration = Amount VolumeAmount = Volume x concentration

DERIVATION OF FICK PRINCIPLE

ConcentrationAt entry ( ) x

Volume at () +

Mass added (M)

= CE VE

Dividing at entry = Vol at exit

Conc. At entry x flow rate + M (amount added/min)

=ConcAtExit

x Flowrate

Therefore Flow Rate

=Amount indicator added per min Exit conc. – entry conc.

HYDRAULIC ANALOGUE MODEL

M mgs-1

Q ml sec –1

C mg / m

INDICATOR CONCENTRATION CHANGE AT CONSTANT INFUSION WITH NO INDICATOR INPUT

Conc.(mg ml-1)

INDICATOR CONCENTRATION(known concentration Co at input with constant infusion)

INDICATOR CONCENTRATION vs TIME (Bolus Injection)

y1 = yoe-ke Conc

FICK METHOD

Used in 3 ways

1. Direct Fick - uses oxygen uptake as indicator Co = ___Vo2____

CaO2 - CVO2

2. Indirect Fick – uses CO2 production as indicator

Co = VCO2

CVCO2 – CaCO2

3. INERT GAS METHODeg. N2O xe137, K85, K7a

- Used for specific organ blood flow measurement- basis of Kety – Schmidt Method

DIRECT FICK METHOD

Assumptions ;

1. Steady State of both flow (Q) and oxygen consumption.

2. CaO2 and CVO2 constant.

3. Closed systemI.e. blood is only source of substance taken up.

DIRECT FICK METHOD

Measurement of O2 consumption

1. Breathe O2 (FIO2) via one-way valve

2. Expires into Douglas bag or Tissot Spirometer

E = Volume measured Time

DIRECT FICK METHOD

Calculation of Oxygen consumption

VO2 = InspiredGas Vol

x FiO2 - ExpiredGas Vol

x FEO2

DIRECT FICK METHODOxygen consumption calculations

Nitrogen is in steady state

V inspired N2 = V expired N2

VI x FIN2 = VE x FEN2

VI = VE x FEN2

FIN2 = I - FIO2

FEN2 = 1 – FEO2 – FECO2

VI = VE x 1 – FEO2 – FECO2

1 – FIN2

VO2 = (VI x FIO2) – VE x FEO2

DIRECT FICK METHOD

CaO2 = Hb (g/L) x SaO2 x 1.34 ( mIO2) + 0.003 x PaO2

SaO2 measured using arterial blood and calibrated oximeter

DIRECT FICK METHOD

( Mixed Venous Oxygen Content)

Need pulmonary artery blood for mixed venousSample.

CVO2 = Hb x SVO2 x 1.34 dissolved component usually ignored

DIRECT FICK METHOD

CO = 250 ml / min_____ 200ml/L - 150 ml/L

= 5 L / Min

Features : 1. Steady state of CO, VO2, CO2 production N2 balance arterial; and venous O2 concentration.

2. Accuracy + 10% used as reference.

3. Slow, cumbersome, unsuitable for rapid measurements.

4. Unsuitable during GA - Not a steady state - Uptake of volatile agents and N2 washout.

INDIRECT FICK METHOD

1. CO2 used as indicator

2. Theoretical advantage :Mixed venous CO2 estimated by rebreathingtechnique - No need for CVP.

3. Problem :Large CO2 stores - steady state not easily

achieved.

DYE DILUTION METHOD

1. Applies to bolus of indicator

2. Also known as Stewart – Hamilton principle.

3. Basis of dye dilution and thermodilution techniques.

DYE DILUTION METHOD

ExitConc.

0 T 00time

Ct = C maxe-kt

Where e = 2.718K = decay constant of exponential

DYE DILUTION METHOD: CALCULATIONS

At any moment c = M V M = C x V

Integrating :

Mdt = Cdt x Vdt

o o oWhere

oMdt = Original injected

= total volume flow

STEWART – HAMILTON FORMULA

cdt x Q

Q = ___M___

DYE – DILUTION INFUSION TECHNIQUE

C exit

C entry

Q = __M__

= __M__Ct1 - Ct0

= _______M________C exit - C entry

DYE – DILUTION METHOD

Dye - Indocyanine green (ICG)

- peak absorption = 805 nm(isobestic point of HbO2)

- non toxic

- rapid removal 18-24% per min

- 2.5-5mg injected into right atrium

DYE DILUTION – GRAPH ANALYSIS

recirculation

Cdt = area under curve

Methods used (a) Trapezoid Method (b) Forward method

Triangle area - Peak Height x width at halve peak height (c) Computer integrator

DYE DILUTION METHOD

EQUIPMENT

1. Withdrawal Pump/syringe ~ 20ml/min

2. Optical densitometer ~ 805 nm

3. Chart Recorder

THERMODILUTION TECHNIQUE

Bolus of “Negative Heat”

Sensor = Thermistor in pulmonary artery

Cardiac Output = ___Amount of –ve Heat (M)__

THERMODILUTION METHOD

Negative Heat M = V1 x (TB – T1) D S

Where M = Amount of negative heat VI = Volume injectable ( 10ml 5% D) TB = Patient’s blood temperature TI = Injectable temperature DI = Injectable density DB = Blood density SI = Specific heat of injectate

SB = Specific heat of blood

For 5% Dextrose = __DS SI__ = 1.08 DB - SB

THERMODILUTION ADJUSTMENTS

(a) Correction factor

(b) AVC = Calculated to 1.22

t where C = _30 Cmax 100

(c) Final Formula

CO = VI x (TB – TI) x 1.08 x CT x 60

THERMODILUTION

1. Room temperature D 5% used

2. Inject within 1.5 sec.

3. Inject at end-expiration

ICED vs ROOM TEMPERATURE INJECTATE

1. Random error greater with injectateat room temperature

2. Iced Injectate slightly overestimates atlow cardiac output.

3. Room temperature significantly overestimatesat CO < 2-3L/min by 20-50%.

FICK METHOD

ADVANTAGES

Correlates with direct measurements referenceMethod.

DISADVANTAGES

Slow and cumbersomeNot suitable for rapid repeated measurements.

DYE DILUTION

ADVANTAGES 1. Correlates well with direct and Fick method

DISADVANTAGES 1. Arterial cannulation needed 2. Limited to 3 measurements 3. Recirculation “Noise” 4. Unsuitable for rapid, repeated measurements

THERMODILUTION METHODS

ADVANTAGES

1. Simple and convenient

2. No blood withdrawal

3. Limited recirculation

4. Unlimited number of measurements

5. Rapid repeated measurements possible

RADIOACTIVE TRACER DILUTION

Risa washout over heart

Scintillation Counter

Difficult to calibrate

Radiation hazard.

BALLISTOCARDIOGRAPHY

Patient coupled to light bed

Ultralow frequency recording

Body acceleration (recoil) measures aortic

Acceleration ( dQ/dt) and stroke volume

I and J waves = dQ/dt

IMPEDANCE PLETHYSMOGRAPHY

-100Yz sinusoidal current 4 mA through chest

-Wheatstone bridge to measure resistance

-Voltage change with constant current I

-R = Voltage change I

-Resistance change reflect pulmonary blood flow

LITHIUM DILUTION CARDIAC OUTPUT

- Indicator = Lithium chloride (150 mM)

- Dose ~ 0.3 mmol via any venous line

- Artyerial litium plasma concentration measured by lithium sensitive electrode aspirated at 4 ml/min.

- Co = LiCl dose x 6- Area (1 – haemocrit)

PULSE PRESSURE ANALYSIS

- Arterial pulse pressure waveform analysed

- Cardiac output ~ Area under systolic portion of arterial waveform from diastole to end-systole

- Calibrated initial using lithium dilution technique.

Measurement of pH

pH = - logpH = - log1010 of the hydrogen ion activity (~ []'n) of the hydrogen ion activity (~ []'n) at 37°C, normal blood at 37°C, normal blood pH = 7.4 ± 0.04pH = 7.4 ± 0.04 circuit consists of,circuit consists of,

capillary tube of pH sensitive glass ® dVcapillary tube of pH sensitive glass ® dV reference buffer solution the other side of the glassreference buffer solution the other side of the glass

+ a silver/silver chloride electrode + a silver/silver chloride electrode an electrolyte solution (KCl) in contact with bloodan electrolyte solution (KCl) in contact with blood

+ a silver/silver chloride electrode+ a silver/silver chloride electrode surrounding water jacket at 37°Csurrounding water jacket at 37°C voltmetervoltmeter

Measurement of pH

MEASUREMENT OF pHpH electrode

- Depends on ion selective electrode

- pH sensitive Glass Electrode

- Utilises glass membrane which is

selectively permeable to hydrogen ions.

- Glass electrode - placed in series with 2 half cells which generate a constant potential gradient

pH ELECTRODE SYSTEMS

• Electrode consists of:

metal – conducts - electrons

electrolyte – conducts ions.

• Ag:AgCl + Hydrochloric Acid

Hg:Hg2Cl2 + saturated KCl Solution

• EMF generated at interface of 2 electrodes.

SCHEMATIC ARRANGEMENT OF pH ELECTRODE

Ag/AgClReferenceElectrodeSAMPLE

KCl Saltbridge

Hg / Hg2Cl2

Calomel Reference Electrode

Porous Plug

pH sensitiveglass

Potential Constant Constant Variable Constant

Voltmeter

pH ELECTRODE

Saturated KCl

• Provides salt bridge

• Completes circuit between blood sample and calomel electrode.

• Porous plug prevents diffusion of KCl into blood sample.

pH ELECTRODE

• Measures activity of H+; not concentration

• Calibrated against 2 standard buffers;

(a) pH 6.841 = Zero (b) pH 7.383

pH ELECTRODE

Ag : AgClelectrode

SENDING CIRCUITAND DISPLAY

SAMPLECUVETTE

Platinum Wire

Mercurous chloride

Mercury

Saturated KCl

Porous Plug

pH sensitive glass

Measurement of Gases

GAS ANALYSIS

CHEMICAL METHODSAbsorption in chemicals using Haldane apparatusCO2 : 10 – 20% KOH or NaOHO2 : Alkaline pyrogallol or sodium anthraquinone

PHYSICAL METHODS :• Mass spectrometers• Infra-red absorption• Polarography• Galvanic fuel cell• Ultra violet absorption• Paramagnetism• Thermal conductivity

Spectrophotometry

first used to determine the [Hb] the 1930's, by first used to determine the [Hb] the 1930's, by application of the application of the Lambert-Beer LawLambert-Beer Law

IIii = the incident light= the incident light IItt = the transmitted light= the transmitted light DD = the distance through the medium= the distance through the medium CC = the concentration of the solute= the concentration of the solute = the = the extinction coefficientextinction coefficient of the of the

solutesolute

ITrans = ISource x e- DC

Spectrophotometry

the the extinction coefficientextinction coefficient is specific for is specific for a given solute at a given wavelength of a given solute at a given wavelength of lightlight

therefore, for each wavelength of light therefore, for each wavelength of light used an independent Lambert-Beer used an independent Lambert-Beer equation can be writtenequation can be written

if the number of equations = the number if the number of equations = the number of solutes, then the concentration for of solutes, then the concentration for each one can be solvedeach one can be solved

Spectrophotometry

by convention oxyhaemoglobin by convention oxyhaemoglobin concentration, HbOconcentration, HbO22 is the fractional is the fractional

concentration as measured by concentration as measured by cooximetrycooximetry

a 4 wavelength device, and includes a 4 wavelength device, and includes COHbCOHb and and MetHbMetHb in the denominator in the denominator

%HbO2 = 100 [ HbO2 ]

Hb + HbO2 + COHb + Met Hb

ULTRA-VIOLET ABSORPTION

• Halogenated vapours absorb uv light

• used for measuring halothane

• Disadvantage : Slow response time produce toxic product

THERMAL CONDUCTIVITY (KATHAROMETERS)

1. High thermal conductivity gas - more rapid heat conductioneg. Helium 600%CO2 35% compared with air

2. Gas passed over heated wire which cools.

3. Decreased wire temperature – depends on flow rate and thermal conductivity of gas.

4. Temperature leads to wire resistance

5. Advantages : Simple and inexpensive

6. Disadvantage : Slow response time ( ~ 5s)

Measurement: Methods

Mass spectrometryMass spectrometry

Raman spectrographyRaman spectrography

Photo-acoustic spectrographyPhoto-acoustic spectrography

Infra-red spectrographyInfra-red spectrography

RAMAN LIGHT SCATTERING

1. Photon of light passes thro’ gas

2. Photon energy partly given to gas molecule

3. Light is re-emitted at longer wavelengthcharacteristic to gas.

Measurement: Raman Spectrography

Raman scatteringRaman scattering occurs with illumination with high intensity occurs with illumination with high intensity argon laserargon laser light light

absorbed light energy produces unstable energy states absorbed light energy produces unstable energy states (rotational & vibration)(rotational & vibration)

emitted low energy light, Raman lightemitted low energy light, Raman light measured at 90° to the laser pathmeasured at 90° to the laser path

can be used to identify all types of molecules in the gas can be used to identify all types of molecules in the gas sample, and has been incorporated into new monitors sample, and has been incorporated into new monitors (RASCAL) which instantaneously identify & quantify CO(RASCAL) which instantaneously identify & quantify CO22 and and inhalational agentsinhalational agents

Measurement: Photo-acoustic spect.

relies on the absorbance of IR light by COrelies on the absorbance of IR light by CO22 gas expansiongas expansion

IR light is pulsed at IR light is pulsed at acoustic frequenciesacoustic frequencies and the and the energy absorbed is detected by a microphoneenergy absorbed is detected by a microphone

amount of light absorbed is measured amount of light absorbed is measured directlydirectly without the need for a reference chamberwithout the need for a reference chamber no zero point driftno zero point drift

other claimed advantages over IR spectrometry,other claimed advantages over IR spectrometry, higher accuracyhigher accuracy increased reliabilityincreased reliability reduced maintenance & reduced need for reduced maintenance & reduced need for calibrationcalibration

MASS SPECTROMETER

PRINCIPLE :

1. Gas passed into ionizing chamber

2. Electron beam ionizes gas

3. Ions diffuse thro’ slit in chambers

4. Negatively charge plate accelerate ions

5. Different particles streams separate according to mass & charge.

6. Detector plate

MASS SPECTROMETER

Detector

Low charge / mass ratio

Deflection Angle

High charge / mass ratio

AcceleratorPotentialOn screen electrode

Magnetic field

MASS SPECTROMETER

ADVANTAGES

1. Rapid response time ( < 0.1s)2. Can measure variety of gases (May be affected by water vapour)

DISADVANTAGES

1. Complex2. Expensive

Capnometry

capnometrycapnometry is the measurement and display of is the measurement and display of COCO22 concentrations on a digital or analogue concentrations on a digital or analogue displaydisplay

capnographycapnography is the graphic recording of is the graphic recording of instantaneous respired COinstantaneous respired CO22 concentrations concentrations during the respiratory cycleduring the respiratory cycle

Capnometry

first IR COfirst IR CO22 measuring and recording apparatus measuring and recording apparatus was introduced by was introduced by LuftLuft in 1943 in 1943

expensive, bulky and principally only used for expensive, bulky and principally only used for researchresearch

widespread use within the last 10-15 years with widespread use within the last 10-15 years with cost and size reductioncost and size reduction

ASA closed claims ASA closed claims 93%93% of anaesthetic of anaesthetic mishaps preventable by mishaps preventable by ETCOETCO22 / SpO / SpO22

INFRA-RED ABSORPTION

PRINCIPLE :

1. Molecule composed of 2 or more dissimilar atoms absorb infra red light.

2. Absorption of 2.5 - 25 m cause covalent bonds to bend and vibrate; increasing rotational speed.

3. Different gas molecules absorb specific of infra red light.

4. Detecting increased absorption allows their concentrations to be determined

Measurement: IR Spectroscopy

Lambert-Beer lawLambert-Beer law applies, (cf. Hb) applies, (cf. Hb) more compact and less expensivemore compact and less expensive assymetric, assymetric, polyatomicpolyatomic gases gases of two or more of two or more

molecules, absorb IR radiation (> 1.0 µm)molecules, absorb IR radiation (> 1.0 µm) HH22O, NO, N22O, COO, CO22

absorbance peak is characteristic for a gasabsorbance peak is characteristic for a gas COCO22 ~ 4.28 µm ~ 4.28 µm

glass absorbs IR radiationglass absorbs IR radiation chamber windows must be made of a crystalchamber windows must be made of a crystal

sodium chloride or sodium bromidesodium chloride or sodium bromide

calibration may be achieved by filling the chamber calibration may be achieved by filling the chamber with a COwith a CO22 free gas, or by splitting the incident beam free gas, or by splitting the incident beam

and passing this through a and passing this through a reference chamberreference chamber

the use of a reference beam also allows for the use of a reference beam also allows for compensation for variations in the output of the compensation for variations in the output of the IR sourceIR source

the sample chamber is made small, so that the sample chamber is made small, so that continuous analysis is possible continuous analysis is possible

the the response timeresponse time ~ 100 ms~ 100 ms enabling end-tidal COenabling end-tidal CO22 estimations and real-time estimations and real-time

graphical analysisgraphical analysis

INFRA-RED GAS ANALYSER(SPECTROPHOTOMETER)

1. LED split infra-red into different .

2. Sample chamber is transilluminated and IR absorption measured.

3. Reference chamber transilluminated & absorption allowscalibration.

4. IR absorption in sample chamber compared with reference chamber.

INFRA-RED SPECTROPHOTOMETER

REFERENCE

Known CO2

SAMPLE CELL

Light splitterChopper

Detector

ADVANTAGES : Fast response for CO2 N2O and volatile anaesthetic agentDISADVANTAGES : Rapid respiratory rates

decrease accuracy

ETCO2 : Classification 1

side-streamside-stream sensor is located within the main unit and gas is aspirated sensor is located within the main unit and gas is aspirated

from the circuitfrom the circuit sampling flow rate may besampling flow rate may be

highhigh > 400 ml/min, or> 400 ml/min, or lowlow < 400 ml/min< 400 ml/min

optimal gas flowoptimal gas flow is considered to be 50-200 ml/min, is considered to be 50-200 ml/min, ensuring reliability with both adults and childrenensuring reliability with both adults and children

exhaust gases contain anaesthetic agentsexhaust gases contain anaesthetic agents & should be & should be routed to the routed to the scavengingscavenging unit unit

ETCO2 : Classification 2

mainstreammainstream sensor is located at the patient, with a curvette placed sensor is located at the patient, with a curvette placed

within the circuitwithin the circuit

these are heated to > 39° to prevent occlusion by water these are heated to > 39° to prevent occlusion by water vapourvapour

no mixing of gases occurs during sampling and the no mixing of gases occurs during sampling and the response time is more rapidresponse time is more rapid

curvettes tend to be bulky, add dead space, are heated, curvettes tend to be bulky, add dead space, are heated, and are expensive if dropped & brokenand are expensive if dropped & broken

ETCO2 : Sources of Error

Atmospheric pressure differencesAtmospheric pressure differences NN22OO HH22OO OthersOthers

alinearityalinearity volatile agentsvolatile agents

ETCO2 : PAtm

direct effectsdirect effects gas densitygas density

for a given chamber thickness, no. of molecules for a given chamber thickness, no. of molecules increasesincreases

eliminated by calibration against a known Peliminated by calibration against a known PCO2CO2 (% (%

x Atm.)x Atm.) units calibrated against Cunits calibrated against CCO2CO2 require correction require correction

(1%:1%)(1%:1%) IR absorbanceIR absorbance

intermolecular forces ® IR absorbance for a given [COintermolecular forces ® IR absorbance for a given [CO22]]

PPAtmAtm ~ 1% ~ 1% absorbance ~ 0.5-0.8%absorbance ~ 0.5-0.8%

ETCO2 : PAtm

direct effects (continued)direct effects (continued) sampling sampling flow rateflow rate may reduce sample chamber may reduce sample chamber

pressurepressure units should be calibrated for a given sample rateunits should be calibrated for a given sample rate

PEEPPEEP maymay PPCO2CO2 reading (some unit compensate reading (some unit compensate automatically)automatically)

PEEP ~ 20 cmHPEEP ~ 20 cmH22O O PPCO2CO2 ~ 1.5 mmHg ~ 1.5 mmHg

ETCO2 : PAtm

indirect effectindirect effect : volume percent : volume percent, ,

where Pwhere PCO2CO2 = F = FCO2CO2 x Atm. x Atm.

where Pwhere PAtmAtm at calibration is different to the time of measurement at calibration is different to the time of measurement

ETCO2 : N2O

absorbs IR at absorbs IR at 4.5 µm4.5 µm (cf. CO(cf. CO22 ~ 4.28 µm) ~ 4.28 µm)

NN22OO falsely elevatedfalsely elevated CO CO22 readings readings effect minimised by a narrow bandwidth filtereffect minimised by a narrow bandwidth filter

however, presence of Nhowever, presence of N22O molecules results in O molecules results in collision broadeningcollision broadening of the absorbance peak of of the absorbance peak of COCO22

resulting in apparently resulting in apparently elevated COelevated CO22 readings readings

ETCO2 : N2O

simplest correction is to calibrate the monitor with simplest correction is to calibrate the monitor with the same background gas as is to be used during the same background gas as is to be used during anaesthesiaanaesthesia

alternatively correction factors may be applied,alternatively correction factors may be applied, 50% N50% N22OO P'P'CO2CO2 ~ P ~ PCO2CO2 x 0.9 x 0.9 70% N70% N22OO P'P'CO2CO2 ~ P ~ PCO2CO2 x 0.94 x 0.94

ETCO2 : H2O

condensed watercondensed water

result in falsely result in falsely highhigh readings readings

prevented in mainstream units by heating the sensorprevented in mainstream units by heating the sensor

side-stream units use water trapsside-stream units use water traps

some units use semipermeable Nafionsome units use semipermeable Nafion®® tubing tubing

ETCO2 : H2O

water vapourwater vapour mainstream analysers measure breathing circuit gasmainstream analysers measure breathing circuit gas

generally saturated at body T. but may be affected by the generally saturated at body T. but may be affected by the

use of humidifiers, FGF's, and the ambient T.use of humidifiers, FGF's, and the ambient T.

side-stream units, cooling of the gases results inside-stream units, cooling of the gases results in water vapour pressure, andwater vapour pressure, and

apparent apparent increaseincrease in P in PCO2CO2 ~ ~ 1.5-2%1.5-2%

transit timetransit time creating a creating a phase shiftphase shift, but no distortion, but no distortion gas is subject to gas is subject to mixingmixing with overdamping of a with overdamping of a

square waveformsquare waveform results in underestimation of ETCOresults in underestimation of ETCO22, especially in , especially in

childrenchildren this error increases both with,this error increases both with,

increased width and length of the sample tubingincreased width and length of the sample tubing reduced sample flow rates < 50 ml/minreduced sample flow rates < 50 ml/min higher frequency breathing patternshigher frequency breathing patterns

rise timerise time TT10-9010-90

time to change from 10% to 90% of the final valuetime to change from 10% to 90% of the final value

depends on size of the depends on size of the sample chambersample chamber and and flow rateflow rate

capnographs used clinically ~ 50-600 mseccapnographs used clinically ~ 50-600 msec

prolongation may decrease the slope of phase II, and prolongation may decrease the slope of phase II, and

underestimation of anatomical dead spaceunderestimation of anatomical dead space

ETCOETCO22 in adults at < 30 bpm with in adults at < 30 bpm with ± 5% ± 5% accuracyaccuracy

faster units are required in children, Tfaster units are required in children, T7070 < 80 msec < 80 msec

rise timerise time TT10-90 10-90 (continued)(continued)

response times have been markedly response times have been markedly reduced by,reduced by,

more powerful signal amplifiersmore powerful signal amplifiers minimising the volume of the sample minimising the volume of the sample

chamberchamber use of relatively high sample flow rates > use of relatively high sample flow rates >

150 ml/min150 ml/min

ETCO2 : Other Factors

oxygenoxygen OO22 does not directly absorb IR light does not directly absorb IR light

may affect reading by collision broadeningmay affect reading by collision broadening

results in falsely results in falsely lowlow P PCO2CO2 readings readings

not as great as with Nnot as great as with N22O (some units incorporate O (some units incorporate correction)correction)

ETCO2 : Other Factors

halogenated agentshalogenated agents absorb IR light at absorb IR light at ~ 3.3 µm~ 3.3 µm

interference is not clinically significantinterference is not clinically significant

alinearityalinearity of CO of CO22 analysis analysis

the concentration of the calibration gas should be as close the concentration of the calibration gas should be as close as possible to the measured gas sampleas possible to the measured gas sample

Severinghaus CO2 Electrode

Severinghaus developed the COSeveringhaus developed the CO22 electrode in electrode in

19581958

modern arterial blood gas analysis was bornmodern arterial blood gas analysis was born Essentially a modified pH electrodeEssentially a modified pH electrode

provides a direct measure of Pprovides a direct measure of PCO2CO2 from the from the change in pHchange in pH

circuit consists of,circuit consists of, a closed cylinder of a closed cylinder of pH sensitive glasspH sensitive glass in the centre in the centre 2 electrodes, 1 inside, the other outside the cylinder2 electrodes, 1 inside, the other outside the cylinder a surrounding solution of a surrounding solution of sodium bicarbonatesodium bicarbonate

a thin film of bicarbonate impregnated nylon mesh a thin film of bicarbonate impregnated nylon mesh covering the end of the cylinder covering the end of the cylinder

a thin, a thin, COCO22 permeable membrane permeable membrane covering the end covering the end

of the electrodeof the electrode

COCO22 diffuses from the blood sample through the diffuses from the blood sample through the membrane into the nylon mesh and by the membrane into the nylon mesh and by the formation of formation of carbonic acidcarbonic acid lowers the pH of the lowers the pH of the bicarbonate solutionbicarbonate solution

the change in pH alters the dV across the glass, the change in pH alters the dV across the glass, such that,such that,

pH ~ pH ~ loglog1010PPCO2CO2

CO2 Electrode

output of output of voltmetervoltmeter calibrated in terms of P calibrated in terms of PCO2CO2

electrode accuracy ~ 1 mmHgelectrode accuracy ~ 1 mmHg

response time ~ 2-3 minsresponse time ~ 2-3 mins

as for the pH electrode, the COas for the pH electrode, the CO22 electrode kept at electrode kept at 37°C and regularly calibrated with known 37°C and regularly calibrated with known concentrations of COconcentrations of CO22

Measurement of OXYGEN

OXYGEN MEASUREMENT ELECTROCHEMICAL METHODS

• Based on electrochemical reaction in buffer

solution occurring between 2 electrodes,

involving gas molecules.

• 2 Devices

(a) Polarographic electrode

(b) Fuel cell.

Measurement of Oxygen

Leyland Clarke developed the Leyland Clarke developed the

polarographic oxygen electrode in 1956polarographic oxygen electrode in 1956

prior to this the POprior to this the PO22 had not been measured had not been measured

Other Methods

POPO22 may also be measured by, may also be measured by, Volumetric - van Slyke/NeillVolumetric - van Slyke/Neill Clarke electrodeClarke electrode Fuel cellFuel cell ParamagneticParamagnetic Hummel Cell - paramagneticHummel Cell - paramagnetic Optode - photoluminescence quenchingOptode - photoluminescence quenching Raman scatteringRaman scattering Mass spectrometerMass spectrometer

PARAMAGNETISM

• Paramagnetic : attracted toward magnetic field eg. oxygen

• Diamagnetic : repelled by magnetic field eg. nitrogen

• Paramagnetic molecules = 2 unpaired electrons in outer electron shell spinning in the same direction.

PAULING TYPE OF PARAMAGNETICOXYGEN ANALYSER

MAGNET POLE

Gas O2

Nitrogen In GlassDumb-Bell

Light beam Detector

Slow response ( 5 – 20 s)

RAPID PARAMAGNETIC O2 ANALYSERS

Sample Reference Gas

Magnetic field

Gas Mixture out

Made more compactRapid response time

DifferentialPressure transducer

POLAROGRAPHIC ELECTRODE

PRINCIPLE

• 1 pair of electrodes in electrolyte solution

• Electrodes maintained at potential difference

• Current through electrolyte solution dependent on gas concentration in solution

• Reaction driven by voltage applied to electrodes

CLARKE OXYGEN ELECTRODE

• Cathode - Platinum covered by permeable membrane

• Anode - Silver/Silver chloride covered by membrane

• Electrolyte Solution - KCl

• Electrodes connected to DC voltage 0.6V

• Electrons produced by Ag / AgCl anode migrate to cathode to reduce O2 molecules.

Clarke Electrode

the circuit consists of,the circuit consists of, DC voltage source (0.6 V)DC voltage source (0.6 V)

ammeterammeter

platinum cathodeplatinum cathode

silver/silver chloride anodesilver/silver chloride anode

electrolyte solution (KCl), andelectrolyte solution (KCl), and

OO22-permeable membrane-permeable membrane

Clarke Electrode

Ohm’s Law: for any resistive Ohm’s Law: for any resistive circuit:circuit: I I V V

for the Clarkefor the Clarkeelectrode there is aelectrode there is aplateau voltage rangeplateau voltage range I does not change withI does not change with VV however:however: II POPO22

this occurs as the cathode this occurs as the cathode reaction requires both Oreaction requires both O22

and free electronsand free electrons

Clarke Oxygen Electrodes (Cont’d)

• Platinum Cathode - O2 + 4e 2 O

(reduction) 2 O + 2 H2O 4 OH

reaction at the platinum cathode,reaction at the platinum cathode,OO22 + 2H + 2H22O + 4eO + 4e-- 4OH4OH--

At Ag / AgCl Anode (oxidation) :

4 Ag 4 Ag+ + 4e-

Current flow between both electrodes measured

Clarke Electrode

current flow being in direct proportion to the current flow being in direct proportion to the consumption of oxygenconsumption of oxygen

the platinum electrode cannot be inserted directly the platinum electrode cannot be inserted directly into the blood stream as protein deposits form an into the blood stream as protein deposits form an affect its accuracyaffect its accuracy

CLARKE ELECTRODES

Advantages : Robust

Portable

Disadvantages : Limited life span

Silver anode eventually used

up by current

FUEL CELL

Cathode : Silver - reduces O2 molecules in solution.

Anode : Lead : 2Pb + 40H 2Pbo +2H2O + 4e-

Electrolyte : potassium bicarbonate

SAMPLE

No polarising current required

Lead Anode

M Potassium Bicarbonate Solution

Silver CathodeO2 + 4e + 2H2O 4OH-

FUEL CELL

Advantages :CompactNo power supply requiredUnaffected by N2O

Disadvantage :

Slow response timelife-span 6-12 months

OPTODES - PRINCIPLE

1. Oxygen has the property of “quenching” fluorescenceof certain dyes.

2. Dyes exposed to light – electrons excited and release photons when they return to their original state (fluorescence).

3. Oxygen absorbs energy from excited electrons electrons return to original state without releasing photon

4. Absorption of light and reduction in light emitted is proportional to PO2

OPTODE - MECHANISM

• Optical fibre with dye coated tip

• O2 permeable membrane cover

• Sequential illumination of fibre causes dye to fluorescence

• Intensity of fluorescence depends on oxygen concentration at tip

• Fluorescence measured by photo multiplication.

OPTODE : Uses

• Intravascular PO2 monitoring

• Advantages :Independent of blood flowStableRapid response times

• Disadvantage :expensiveDye deteriorate with timeFibrin deposition

Oximetry

Kramer optically measured the OKramer optically measured the O22 in animals in the early in animals in the early 1930's1930's

Karl Matthes in 1936 was the first to measure OKarl Matthes in 1936 was the first to measure O22 from from transmission of transmission of redred and and blue-greenblue-green light through the human light through the human earear

the term oximeter was coined by Millikan the term oximeter was coined by Millikan et alet al. in the 1940's. in the 1940's they developed a lightweight oximeter, a smaller version they developed a lightweight oximeter, a smaller version

of Matthes' design, which measured SaOof Matthes' design, which measured SaO22 by by transillumination of the earlobe using red & green filters transillumination of the earlobe using red & green filters covering Kramer's barrier layer photocellscovering Kramer's barrier layer photocells

Oximetry

the signal detected from the photocell under the the signal detected from the photocell under the green filter later proved to be in the green filter later proved to be in the IR rangeIR range

there were two technical problems with this approach,there were two technical problems with this approach,

there are many non-Hb light absorbers in tissuethere are many non-Hb light absorbers in tissue

the tissues contain capillary & venous blood in addition to the tissues contain capillary & venous blood in addition to arterial bloodarterial blood

TRANSMISSION OXIMETRY

Based on absorbance laws

Blood consists of a mixture of

Oxyhaemoglobin and Deoxyhaemoglobin

ABSORBANCE CURVES FOR HbO2 AND Hb

Absorbance

660 805 940

RED INFRARED

OXY Hb

DEOXY Hb

wavelength

ISOBESTIC WAVELENGTH

ABSORBANCE CURVES

Secondary Peaks of Absorbance

660 nm - Deoxyhaemoglobin

940 nm - Oxyhaemoglobin

805 nm - Isobestic point

defined as point at which absorbances of HbO2 and Hb are equal.

Depends on haemoglobin concentration

CO - OXIMETER

• Measures Oxygen saturation

• Based on absorbance curves

• Requires haemolysis of blood sample before “sats” measurement

• 2 types - Reflectance

- Transmission

Measure at 4 wavelength to enable measurement of metHb and HbCO

CO-OXIMETER

ADVANTAGES :

Light absorbance measured at several

wavelength enables fraction estimation.

DISADVANTAGES :

Cannot provide continuous monitoring

Expensive cost and maintenance

PULSE OXIMETRY

Pulse Oximetry

early 1970's, Japanese engineer Takuo Aoyagi working on a early 1970's, Japanese engineer Takuo Aoyagi working on a

dye dilution method for CO, using an earpiece densitometerdye dilution method for CO, using an earpiece densitometer noted that the noted that the pulsatile componentspulsatile components of the red & IR of the red & IR

absorbances were related to SaOabsorbances were related to SaO22

prototype, built by Nihon Khoden, was tested clinically in prototype, built by Nihon Khoden, was tested clinically in

1973 and the first commercial prototype available in 19741973 and the first commercial prototype available in 1974 further refinements were required and widespread use did further refinements were required and widespread use did

not eventuate until the early not eventuate until the early 1980's1980's

Pulse Oximetry

the signal detected from the photocell under the the signal detected from the photocell under the green filter later proved to be in the green filter later proved to be in the IR rangeIR range

there were two technical problems with this approach,there were two technical problems with this approach, there are many non-Hb light absorbers in tissuethere are many non-Hb light absorbers in tissue the tissues contain capillary & venous blood in addition to the tissues contain capillary & venous blood in addition to

arterial bloodarterial blood

Pulse Oximetry

these were overcome by first measuring the these were overcome by first measuring the absorbance of the ear while it was compressed absorbance of the ear while it was compressed to remove all bloodto remove all blood

after this after this bloodless "baseline"bloodless "baseline" measurement measurement the ear was heated to the ear was heated to "arterialise""arterialise" the blood the blood

this device was shown to accurately predict this device was shown to accurately predict intraoperative desaturations, however, due to the intraoperative desaturations, however, due to the technical difficulties was never adopted on masstechnical difficulties was never adopted on mass

Nomenclature

SaOSaO22 = 100.(O = 100.(O22 content)/(O content)/(O22 capacity) capacity) arterial blood saturation measured arterial blood saturation measured in vitroin vitro OO22 capacity the amount of O capacity the amount of O22 which can combine with which can combine with

reduced Hb, reduced Hb, withoutwithout removing COHb or MetHb removing COHb or MetHb thus, at high Pthus, at high PaO2aO2 the SaO the SaO22 = 100% = 100%

irrespective of the [COHb + MetHb]irrespective of the [COHb + MetHb] HbOHbO22= = oxyhaemoglobin concentrationoxyhaemoglobin concentration

multiwavelength spectrometers measure all speciesmultiwavelength spectrometers measure all species SaOSaO22 computed from P computed from PO2O2 and pH approximates SaO and pH approximates SaO22, not , not

HbOHbO22

SpOSpO22 = = pulse oximeter saturationpulse oximeter saturation

Methodology

2 wavelengths of light,2 wavelengths of light, redred = 660 nm= 660 nm IRIR = 910-940 nm= 910-940 nm

the signal is divided into two components,the signal is divided into two components, acac == pulsatile arterial bloodpulsatile arterial blood dcdc == non-pulsatile arterial bloodnon-pulsatile arterial blood

+ tissue + capillary blood + venous + tissue + capillary blood + venous bloodblood

NB: all pulse oximeters assume that only the NB: all pulse oximeters assume that only the pulsatile absorbancepulsatile absorbance is arterial blood is arterial blood

AC AND DC SIGNALSRECEIVED BY PULSE OXIMETER

ACVariable absorption due to pulsatile arterial blood

Absorption due to arterial blood

Absorption due to venous blood

Tissue absorptionTISSUE

VENOUS BLOOD

Methodology

for each wavelength, the oximeter for each wavelength, the oximeter determines the ac/dc fractiondetermines the ac/dc fraction independent of the incident light intensityindependent of the incident light intensity

= = pulse added absorbancepulse added absorbance the the ratio (R)ratio (R) of these is calculated, of these is calculated,

R =R = (ac absorbance/dc absorbance)(ac absorbance/dc absorbance)RedRed

(ac absorbance/dc absorbance)(ac absorbance/dc absorbance)IRIR

= A= A660nm660nm / A / A940nm940nm

R and SpO2

this value varies from,this value varies from,

SaOSaO22 = 100% = 100% R = 0.4R = 0.4 (0.3)(0.3)

SaOSaO22 = 85% = 85% R = 1.0R = 1.0

SaOSaO22 = 0% = 0% R = 3.4R = 3.4

R and SpO2

Methodology

the photo-detector diodes of the sensor will also the photo-detector diodes of the sensor will also register register ambient lightambient light

interference is reduced by cycling the lightinterference is reduced by cycling the light red only red only infrared only infrared only both off both off repeated at 480-1000 Hz in an attempt to subtract the repeated at 480-1000 Hz in an attempt to subtract the

ambient light signal, even when this is oscillatingambient light signal, even when this is oscillating this allows accurate estimation of SpOthis allows accurate estimation of SpO22 at arterial at arterial

pulse frequencies ~ 0.5-4 Hz (30-240 bpm)pulse frequencies ~ 0.5-4 Hz (30-240 bpm) data is averaged over several cyclesdata is averaged over several cycles

Uses: Oxygenation

anaesthesia & recoveryanaesthesia & recovery intensive careintensive care emergency care & transportemergency care & transport labourlabour premature & newborn infantspremature & newborn infants home & hospital monitoring for SIDShome & hospital monitoring for SIDS patients in remote locations eg XRay, MRIpatients in remote locations eg XRay, MRI "office" procedures eg. dentistry, endoscopy"office" procedures eg. dentistry, endoscopy

Uses: Circulation

systolic BP & pleth waveform appearancesystolic BP & pleth waveform appearance inflation better than deflationinflation better than deflation

sympathetic blockade with central neuraxis anaesthesiasympathetic blockade with central neuraxis anaesthesia autonomic dysfunction with valsalva manoeuvreautonomic dysfunction with valsalva manoeuvre anecdotally reported usesanecdotally reported uses

patency of the ductus arteriosuspatency of the ductus arteriosus level of ischaemia in PVDlevel of ischaemia in PVD patency of arterial graftspatency of arterial grafts circulation in reimplanted digits or graftscirculation in reimplanted digits or grafts

Uses: Therapy

optimise Foptimise FIIOO22 in ventilated patients in ventilated patients

optimise CPAP or PEEPoptimise CPAP or PEEP

extubation of ventilated patientsextubation of ventilated patients

adjust Oadjust O22 therapy in preterm infants therapy in preterm infants

no consensus on optimal levelsno consensus on optimal levels

optimisation of home Ooptimisation of home O22 therapy therapy

Signal:Noise

Freund Freund et al.et al. 1.12%1.12% failure failure cumulative > 30 mins in 11,046 anaestheticscumulative > 30 mins in 11,046 anaesthetics

Gilles Gilles et al.et al. found a found a 1.1%1.1% incidence incidence 2 x 15 mins in 1,403 anaesthetics2 x 15 mins in 1,403 anaesthetics

automatic gain controlsautomatic gain controls amplification of low signal strengthsamplification of low signal strengths

low signal to noise ratio low signal to noise ratio most new meters give "low signal strength" warnings once most new meters give "low signal strength" warnings once

the ac component falls below an arbitrary fraction of the the ac component falls below an arbitrary fraction of the total transmitted light (0.2% for the Biox-Ohmeda)total transmitted light (0.2% for the Biox-Ohmeda)

Low S:N Causes

low perfusion pressurelow perfusion pressure

motion artefactmotion artefact

ambient lightambient light

skin pigments & dyesskin pigments & dyes

probe positionprobe position the "penumbra effect" the "penumbra effect"

Ventilation - a large paradox may lead to searchingVentilation - a large paradox may lead to searching

venous pressure wavesvenous pressure waves - TI, reflectance operation- TI, reflectance operation

electrocauteryelectrocautery - most unit are now immune- most unit are now immune

MRI interferenceMRI interference - rare, usually lead distorts MRI- rare, usually lead distorts MRI imageimage

Ultrasound and anaesthesia

ULTRASOUND

• Sound = disturbance propagating in material (Air, water, tissue or solid)

• Characterized by frequency and intensity.

• Frequency measured in hertz

• ULTRASOUND = sounds waves > 20 KHz Cannot be perceived by human ear.

WAVELENGTH OF SOUND

• Sound Wavelength = Velocity frequency

• Shorter wavelength higher resolution less penetration

• Compromise between penetration and resolution required.

SOUND PRODUCTION

• Ultra-sound probe = Transducer containing an array of piezo-electric crystals.

• Electrical voltage applied to crystals causes piezo- electric crystals to oscillate at resonant

frequency.

• Electrical energy - converted to sound energy.

ELECTRICAL ENERGY

Electrical Energy

Piezo – electriccrystals oscillate

Electrical energy

ULTRASOUND PROPAGATION

In homogenous tissues : -

ultrasound is absorbedAbsorption – least in fluids greatest in solid tissues

Absorbed energy converted to heat (small)

Amount of heat dissipated hence useless

ULTRASOUND PROPAGATION

In heterogenous tissues :

• Ultrasound strikes interfaces

• Wave is either a) refracted - transmitted – thro’ interface b) reflected - depends on smooth (specular) or non-smooth

surfaces.

• Bone and calcium more reflective

PULSED SOUND WAVES

• Used to prevent transmitted and reflected sound waves.

• Pulse repetition frequency = 10 – 20 Hz

• Longer path sound wave travels - lower is PRF

PULSES OF ULTRASOUND

Usually 2.5 to 7.5 MHz

Frequency - resolution - penetration

IncidentReflected Wave

Surface

Incident Wave

“Scattering” of Ultrasound

ULTRASOUND REFLECTION

REFLECTED ULTRASOUND (ECHO)

Two quantities measured :

(a) Time delay between sound transmission and reception of reflected echo.

(b) Intensity of reflected signal High echo reflection - whiteLess reflection - greyNo reflection - Black

A - MODE (AMPLITUDE)

Brief ultrasound pulses in one direction.

Reflected ultrasound amplitude plottedAgainst time

Time & distance from probe

Amplitude

Peaks = reflective interface

Time (distance)

B - MODE (BRIGHTNESS)

Brief ultrasound pulse in one direction

Reflected ultrasound measured

Amplitude = Brightness of reflected ultrasound

M – MODE (MOTION)

• Repeated B-Mode pulses graphed against time base.

• > 1000 pulses per second

• Good resolution

• Provides one-dimension image against time.

• useful for value motion

2-D ULTRASOUND

• Multiple crystals (linear or phased array) or moving crystals

• Sequential B-mode pulses across 90o

• Single image displayed

• Real time movement

DOPPLER PRINCIPLE

• Frequency of transmitted sound from a moving object

alters depending on velocity and direction of object.

• Change in frequency proportional to

a) ultrasound frequency

b) Cosine of angle between ultrasound beam

direction and moving object.

DOPPLER SIGNAL

• Maximal signal when sound moves towards probe – higher pitch (frequency).

• Lower pitch when sound moves away from probe.

• Pitch change is due to compression and rarefaction of sound waves.

USES OF DOPPLER

• Examine direction and velocity of blood flow in vessels and heart

• Estimate velocities and therefore measure pressure gradients, using Bernoulli equation

P = 4V2

• Types of Doppler used ;

a) Pulse wave b) Continuous Doppler

PULSED-WAVE DOPPLER

• Depends on Doppler shift

• Doppler shift frequency of reflected waves which depends on velocity or reflected wave.

• Used to measure velocity of red blood cells V = FDC

2fo Cos Q V = Velocity of red blood cells FD = Doppler shift

Fo = Ultrasound frequency Q = angle between flow and sound wave.

PULSED-WAVE DOPPLER- Limitations -

• Large angles - results inaccurate

• High velocity flows > 0.6m/s cannot be accurately

measured by intermittent pulses (causes “aliasing”)

CONTINUOUS WAVE DOPPLER

Separate crystals - emit & receive ultrasound continuously along 1 axis

Frequency Spectrum & velocity of interfaces

Graph of Velocity range vs time plotted

CONTINUOUS WAVE DOPPLER

Advantages :

Can measure fast flows

Calculate valve gradients

Disadvantages :

Small incident angle required

COLOURED DOPPLER

Pulsed wave used on 2 D scan

Velocity depicted as colour

Advantage : Easy visualisation

Disadvantage : high velocity – colour reversal rapid turbulent flow produce colour “jets”

TOE PROBE

Phase array 2 D probe

64 piezo-electric crystals

Mounted on gastroscope (9mm)

Can be monoplane biplane (2 array) multiplane (rotating array)

CLINICAL APPLICATIONS OF ULTRASOUND

1. Examination of structure

Chest - pleural fluid

Obstetrics

Abdominal structures

Blood vessels

2. Interventional Procedures

Guide placement of needles

CLINICAL APPLICATIONS - DOPPLER

1. Sense blood flow in blood vessels

e.g. Thrombo-embolism

Thrombosis

2. Measurement of blood pressure

a) sense onset of blood flow

b) sense movement of arterial wall

CLINICAL APPLICATIONS –DOPPLER (CONT’D)

3. Cardiac output measurement

a) mean velocity

b) cross-sectional area of aorta or left ventricular

outflow tract.

4. Fetal Heart movements and heart rate

5. Valve functional, Myocardial wall movement

6. Transcranial Doppler - Velocity of blood flow in

cerebral vessels.

20275003 physics measurement 2

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