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Measurement and monitoring > Key equations and laws > Flashcards

Key equations and laws Flashcards

1
Q

Combine the Beer and Lambert law into one definition

A

◦ The measured absorbance for a single compound is directly proportional to the concentration fo the compound and the length of the light path through the sample

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2
Q

beer’s law

A

‣ Beers law deals the the concentration measurement - absorption or attenutation of light is proportional to concentration of the substance

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3
Q

Lamberts law

A

‣ Lamberts law deals with identification fo the pulsatile signal - ababsorption or attentuation is proportional to the distance the light has ti travel

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4
Q

Oxygen saturation equations (not fractional saturations)

A
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5
Q

Draw the equation for calculating HCO3 concentration

A
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6
Q

Joule thomson efffect

A

A gas changes temperature when it moves from higher pressure to lower pressure, and for most gasses they cool e.g. bike tire pumped = hot

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7
Q

Viscocity

A

Fluids resistance to flow

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8
Q

Newtonian fluid

A

Constant viscocity regardless of flow rate

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9
Q

Non newtonian fluid

A

Viscocity changes with flow rate

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10
Q

Surface tension

A

The result of attraction between moleciles across the surface of a liquid - as the molecules on the surface have reduced molecules to interact with compared to those deeper they form stronger bonds leaving the surface with the smallest possibel surface area for a given volume

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11
Q

Wall tension

A

Vessel wall that is an elasticated solid and the attraction between molecules across the surface of the solid (similar ot surface tension)

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12
Q

Laplace’s law

A

The larger the radius of the vessel the greater the wall tension required to withstand a given internal fluid pressure

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13
Q

What is Laplace’s equation for a spherical bubble

A
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14
Q

What is Laplace’s law for a cylinder

A
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15
Q

Work equation

A

Force applied x distance moved

Amount of energy applied to a system
ie. holding a shopping bag is not work because there is no distance moved

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16
Q

Energy definition

A

Capacity to do work
Measured in joules - the energy required to exert a force of one newton through a distance of one metre

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17
Q

Power equation

A

Work done/ time taken
Units watt (1 J/sec)
The rate at which work is done or the rate of transfer of energy

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18
Q

What is pressure by definiition?

A

Force divided by area

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19
Q

Define compliance

A

The change of volume with respect to pressure and a measure of the ease of expansion
Units metres/newton

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20
Q

Compliance equation

A

Change in volume / change in pressure

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21
Q

What is elastance

A

The opposite, or reciprocal of compliance

Chnage in pressure/change in volume

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22
Q

How to calculate the energy required to move a volume througha tube?

A

E = pressure x volume

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23
Q

How are power and flow related? (laminar)

A

If the pressure difference remains constant when E = P x V then

power = pressure x the rate of change of volume (or flow rate)

therefore since pressure is directly related to flow in laminar conditions

Power directly related to flow squared for laminar flow

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24
Q

In turbulent flow how is this related to pressure?

A

Power is directly proportional to flow ^ 3

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25
Q

Explain pressure as a concept then define it

A

Gas in a box contains millions of molecules zipping around in all directions bouncing off one antoher and off the walls, the combined effect of these collisions with the walls of the box create pressure

Pressure = force per unit of area

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26
Q

Define flow

A

the movement of gas through a tube or system

Volume / time

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27
Q

What is the conservation of flow?

A

Flow remains constant although if cross sectional area changes the velocity will also change to account for flow being conserved therefore

Q = A1 x V1 = A2 x V2

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28
Q

What is laminar flow

A

Orderly movement of a fluid that complies with a model in which parallel layers have different velocities relative to one another

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29
Q

What is the velocity profile within a blood vessel

A

Parabolic - fastest at the middle, decreasingly fast either side

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30
Q

Flow occurs when…

A

There is a difference in pressure between two points

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31
Q

What effect does resistance have on flow?

A

If resistance is increased a greater driving pressure is needed to maintain a fixed flow rate, BUT it will not prevent flow

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32
Q

Describe the relationship between flow and resistance

A

Flow = change in pressure or driving pressure / flow resistance of the tube

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33
Q

What is Ohms law

A

Current = potential difference or voltage/ resistance

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34
Q

Flow has what relationship to pressure

A

Directly proportional

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35
Q

What is resistance defined by

A

Hagen Poiseuelle law

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36
Q

What are the assumptions of the hagen Poiseuille equation

A

liquid is incompressible
Viscosity is stable
Flow is laminar

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37
Q

Hagen poiseuelle equation

A
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38
Q

What equation is this

A

Hagen Poiseulle equation

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39
Q

What is the equation for low solved for the Hagen POisuelle equation

A
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40
Q

Define turbulent flow

A

Movement of a fluid in which small scale currrents in the fluid move in irregular patterns while the overall flow is one directoin

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41
Q

What is Reynolds number?

A

A number used to predict whether turbulent or laminar flow would occur in a given system. It has no units

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42
Q

Reynaulds number equation

A
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43
Q

Reynaulds number equation

A
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44
Q

What is the unit for density

A

kg/m cubed

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45
Q

What is the unit for viscocity

A

newton x seconds/ metres cubed

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46
Q

What are the cutoffs for the Reynolds number

A

<2000 predominantly laminar
>4000 turbulen flow predominant
2000-4000 transitional with eddies and vortices

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47
Q

What effect does viscocity have on laminar flow?

A

Increasing viscocity reduces the reynolds number proportionally and therefore makes flow more laminar

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48
Q

What effect does density have on laminar flow

A

the more dense something is the hgiher the reynolds number and the more turbulent the flow will be

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49
Q

What is the COanda effect

A

fluid or gas stream will hug the convex contour when directed at a tangent to the surface

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50
Q

Explain the coanda effect

A

As has already been seen with the Venturi effect, when the water leaves the tap at speed, the flowing fluid entrains fluid (in this case air) into the stream of flow. When there is an obstruction, such as the spoon’s surface, this entrainment is dramatically reduced on the spoon side. There is a drop in pressure on the spoon side of the jet and this causes a deflection in the flow towards the spoon.

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51
Q

Define an ideal gas

A

An ideal gas has 3 conditions
- the molecules are assumed to be so far apart there is no attraction between them
- volume of the molecules themselves is negligible
- moleculears in random motion obeying newtons laws of motion

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52
Q

Avogadros law

A

equal volumes of gasses at the same temperature and pressure contain the same number of molecules

53
Q

What is a mole

A

one mole is 6.02 x 10 ^ 23 atoms/molecules such that it represents a standard amount - it is derived from 12g of carbon

54
Q

What is molar mass

A

the mass of 6.02 x 10 ^23 partiicles of the substance measured in g / mol

55
Q

Daltons law

A

for a gas the total pressure is simply all the partial pressures added up

Pt = P1 + P2 + P3

56
Q

How would you calculate the partial pressure of oxygen change between dry air at standard H20 pressures, and alveolar gas pressures?

A
57
Q

Boyles law

A

the volume of gas is inversely proportional to its pressure at a fixed temperature

58
Q

Describe the relationship between pressure and volume in gasses and draw a diagram to represent the same

A
59
Q

What is Charle’s law

A

at a given pressure the temperature is directly proportional to the volume of the gas - linera relationship

60
Q

Guy-Lussac’s law

A

the pressure of a gas is directly proportional to its temperature within a fixed volume

61
Q

Draw a curve representing Guy Lussacs law

A

Benedict Roth spirometer - collecting gas passing through an airway opening. It is an expandable compartment consistent of a moveable statically counterbalanced rigid chamber or bell, a stationary base and a dynamic seal between them. The bell can move up and down freely so pressure inside it is close to atmospheric, the seal is often water but dry seals have been used. Changes in internal volume are proportional to displacement

62
Q

What is the combined gas law

A
63
Q

What is the univertsal gas equation

A
64
Q

Define diffusion

A

Passive movemen tof a substance from an area of high concentration to that of lower concentration

65
Q

Ficks law of diffusion

A
66
Q

Add the diffusion constant to Fick’s law of diffusion

A
67
Q

What factors lead to a faster rate of diffusion

A

Large surface area
Large concentration gradient
Small thickness ot diffuse through
High solubility in medium diffusing thorugh
Low molecular weight or density

68
Q

Grahams law of diffusion

A

rate at which gasses diffuse are inversely proportional to the square root of their densities

69
Q

Why is Grahams law of diffusion based on density? How can it be rearranged for molecular mass?

A
70
Q

When does solubility of a gas matter to diffusion rate?

A

When diffusion is moving from a gas through a membrane into a liquid the rate of diffusion is proportional to soliubility of the gas

71
Q

What two factors does the diffusion constant involve

A
72
Q

What is osmotic pressure

A

the pressure required to stop the flow from one side of a semi permeable membrane to another

73
Q

Henry’s law

A

at a cosntant temperature the amount of gas that dissolves in a given type and volume of liquid is directly proportional to the partial pressure of that gas in equilibrium wiht that liquid

74
Q

Define partition coefficient

A

the ratio of conentrations of a substance in two phases of a mixture of two immiscible solvents

75
Q

Blood gas coefficient- what does this mean and reflect?

A

The ratio fo the concentration of an anaesthetic agent in blood to that in the same volume of gas in contact with that blood at equilibrium

This reflects the solubility of the gas in blood

76
Q

Oil/gas coefficeint - what does it reflect and why does it matter

A

the ratio of the concentration of an anaeshtetic agent in oil (adipose) to that in the same volume of gas in contact with that oil at equilibrium

this reflects the solubility of the gas in adipose/brain tissues in comparison to blood - it will reflect how easily it crosses the BBB. If the oil:blood coefficient is >1 (or blood:oil <1) then the concentration or amount of gas dissolved in adipose tissue will be higher than that in blood

77
Q

What characteristics are ideal in an inhaled agent?

A

Low solubility in blood

If highly soluble it transfers quickly from the lungs, but has a lower partial pressure in blood once dissolved therefore staying in solution rather than passing to brian tissue therefore taking longer to work, longer to exit the body.

78
Q

Raoults law

A

the fall in vapour pressure of a solvent is proportional to the molar concentration of the solute

79
Q

Mathematics of the Beer-Lambert law

A
80
Q

Define current

A

the flow of an electric charge - this can be electrons or flow of charged particles e.g. ions

81
Q

Wire resistance is proportional to?

A

Increases with length
Decreases with cross sectoinal area increases
Conduct better at lower temperatures

82
Q

What is voltage

A

an informal term for electrical potential difference - this is the amount of energy required to move a unit of charge between two points.

1 volt is if 1 coulomb were to move through a potential differenceof 1 volt it would require 1 joule of energy ; or the electrical potential required to move 1 ampere through 1 ohm resistor

83
Q

Ohms law

A

the potential difference between two points is the product of the resitance and the current flowing

84
Q

Draw the Ohm;s law pyramid

A
85
Q

Kirchoffs first law

A

current in = current out
Or the sum of all currents going in and out is zero

86
Q

Kirchoffs second law

A

closed loop netowrk the total voltage around the loop is equal tot he sum of all voltage drops within the same loop - this is also equal to zero (as the battery produces the voltage gain)

87
Q

What is power in electircal terms

A

the rate of electrical energy usage/transferrance per second measured in watts - 1 watt is 1 joule transfered per second

88
Q

Power in electrical terms =

A

Voltage x current
voltage squared / resistance
Current squared x resistance

89
Q

Resistance in series calculation

A

the total resistance is greater than the largest reisstors

90
Q

Resistors in parallel equation

A

the total resisstance is smaller than the smallest resistor

91
Q

Impedence

A

the resistance to thef low of an alternating current - instead of resistance using in DC

Calculations for power remain the same

92
Q

What is capacitance

A

a measure of the charge a device can hold measured in Farads

The cpacitance = charge stored in coulombs/ potential difference in volts

Energy stored = 1/2 capacitance x voltage squared

93
Q

The charge Q in a capacitor is given by what equation

A

Q = C x Vc
C is caacitance
Vc is appplied voltage

94
Q

How do you calculate distance in the pulse echo principle

A

2d = v x t

95
Q

What is the equation for natural frequency

A
96
Q

What is the Windkessel effect and how does it apply to arterial lines?

A

◦ The reflected wave in the upper aorta is more prominent however they merge as you progress down the vascular tree, amplification increases as the vascular tree becomes less compliant and more and more reflection waves accumulate —> windkessel effect as the stored energy

97
Q

In the simple flow model of dye calculation of cardiac output what equation is used to calculate the rate of dye removal from a tank?

A

rate of dye removal = liquid flow x dye concentration

98
Q

In the simple flow model of dye dilution cardiac output calculation what is flow rate equal to

A

amount of dye added / area under the graph

99
Q

What is cardiac output equal to in the circulatory flow model diagram dye dilution technique

A

Amount of dye injected / area under graph

100
Q

Describe the Fick principle in words where oxygen is the substrate

A
  • Total uptake of oxygen by the body is equal to the product of the cardiac output and the arterial-venous oygen content difference
101
Q

FICK EQUATION

A
  • CO = VO2/ Ca - Cv
    ◦ Blood flow to an organ = rate of uptake or excretion of a substance / arterio-venous concentration difference
102
Q

How is VO2 measured in the direct Fick method

A
  • VO2 measurement
    ◦ patients breaths through a spirometer containing a known volume of 100% oxygen and a CO2 absorbed, after a minute the volume of O2 remaining in the spirometer allows the calculation of O2 uptake
103
Q

What is a typical VO2 normal value

A

250ml/min

104
Q

What is a typical CaO2 value in the direct Fick equation

A

0.2mL O2 per mL of blood

105
Q

What is a typical CvO2 in the Fick equation

A

0.15mL of O2 per mL of venous blood

106
Q

What is the Stewart Hamilton equation

A
107
Q

How is the Fick principle used indirectly?

A
  • Measured of cardiac outptu using the Fick equation but substituting estimated values for the some of the measured variables
  • Estimations
    ◦ Uses age/weight and sex based nomogram to estimate VO2 - especially inaccurate if morbidly obese, paralysed, thyrotoxicosis, burns, sepsis, hypothermia where metabolically not normal patients. Additionally pulmonary O2 consumption can be dramatically increased in pnumonia overestimating cardiac output
    ◦ Mixed venous blood assumed on the basis of normal vlues or estimated from CVC samplws; or from end tidal
    ◦ Arterial oxygen content can be estimated from pulse oximetry
108
Q

What different methods of indicator dilution are there? What underlying prinicple is there?

A

Stewart Hamilton equation underlies

Methods
* Thermodilution by PAC or PICCO
* Lithium dilution
* Conductivity dilution using saline
* Indicator dye dilution

109
Q

What is the equation for cardiac output when an indicator dye is used?

A
110
Q

What is the equationf or cardiac output when temperature change is used?

A
111
Q

How is stroke volume derived from pulse contour analysis? How is it calibrated? What is the calibration factor?

A
112
Q

What is the doppler equation for measuring velocity? How does velocity relate to flow?

A

◦ V = F (d)c / 2 F(O) cos (theta)
‣ V = velocity of blood in descending aorta
‣ F(d)c = change in frequency of the reflected ultrasound x speed of ultrasound in tissue
‣ F(O) = transmitted ultrasound freqeuncy
◦ Blood flow is then determined by velocity x cross sectional area of the descending aorta (thoracic) estimated from patients height and weight

113
Q

What is the equation for SVR

A
114
Q

What is a normal BSA for males and females

A

These are indexed to BSA- The normal average adult BSA is 1.9 m2 for males and 1.6 m2 for females. Thus, a normal adult male with a cardiac output of 5.0 L/min would score a cardiac index (CI) of 2.6 L/min/m2.

115
Q

BSA calculation

A
116
Q

When does BSA measurement break down

A
  • Morbidly obese - BSA higher than actual required output, so required index may be below expected
  • Children - BSA and metabolic rate do not correlate as well, so even with normal index can be insufficent
117
Q

What is cardiac index? How is it calculated? What are its normal values?

A

Cardiac output / BSA

COmparison between cardiac output of patients of a different size

Normal 2.5 - 4 L/min/metre squared

118
Q

Define stroke volume

A

the volume of blood pumped out fo the L of the heart during each systolic contraction

119
Q

How is stroke volume determined using cardiac measurement devices

A

cardiac output / HR –> i.e. average SV over 1 minute

120
Q

Normal stroke volume values

A

60 -100mL/beat

121
Q

SVI define? Normal values

A

CI / HR x 1000

Indexed for body size

33 - 47 mL/metre squared / beat

122
Q

SVR calculation and normal values

A

80 x (MAP - CVP) / cardiac output

Normal 800 - 1200 dynes-sec/cm ^ -5

123
Q

SVRI - Define?

A

SVR indxed to body size

80 x (MAP - CVP) / CI

Normal vlue 1970 - 2390 dynes-sec/cm^-5 x metres squared

124
Q

Pulmonary vascular resistance calculation

A

80 x (MPAP - PAWP) / cardiac output

Normal value <250 dynes - sec / cm^ -5

125
Q

Hagen Poiseuille law

A
126
Q

Turbulent flow is proportional to? and inversely proportional to?

A
127
Q

Reynolds number

A
128
Q

What affects flow

A

Measurement and monitoring (6 decks)

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