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FRCA > Equations > Flashcards

Equations Flashcards

1
Q

Momentum

A

Momentum = mass x velocity

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2
Q

Ideal gas equation

A

PV = nRT (or P1V1/T1 = P2V2/T2)

Where n = number of moles of gas present and R = universal gas constant (8.32J per 1C at 0C and 1 atm)

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3
Q

Reynolds’ number

A

η

Where v = velocity, p = pressure, d = density, η = viscosity

<2000 = laminar
2000-4000 transitional
>4000 turbulent
NB: number is dimensionless

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4
Q

Laplace’s law

A

Sphere: P=2T/r

Cylinder: P=T/r

Where P = pressure, T = tension and r = radius

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5
Q

Energy (e.g. stored energy of defibrillator) (5)

A

1/2 CV2 = 1/2QV = VQ = VIt = Pt

Where C - capacitance, V = voltage, Q = charge, t = time

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6
Q

Power (3)

A

Power = IV = I2R = E/t

Where I = current, V = voltage, R = resistance, E = energy (can also be work)

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7
Q

Work (2)

A

Work = force x distance = VQ

Where V = voltage, Q = charge

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8
Q

Resistors

A

Series: R1 + R2

Parallel: 1/R1 + 1/R2

Wheatstone bridge: R1/R2 = R3/R4

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9
Q

Charge

A

Q = CV = It = E/V = Pt

Where C = capacitance, V = voltage, I = current, t = time, E = energy, P = power

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10
Q

Loading and maintenance doses (e.g. for TIVA without TCI pump)

A

Loading dose = desired conc x Vd

Maintenance dose = desired conc x clearance

Bolus dose to achieve new conc (in TCI) = [difference btwn current and desired concs] x Vd

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11
Q

Force (3)

A

Force = mass x acceleration (Newton’s second law)

Force = pressure x area

Force = work/distance

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12
Q

Ejection fraction

A

EF = SV/EDV

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13
Q

Fick principle

A

Rate of flow to an organ = clearance of substance / A-V difference in substance concentration

e.g. CO = VO2 / (CaO2-CvO2) or RPF = PAH clearance / A-V conc diff

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14
Q

Henderson-Hasselbalch and pKa

A

pH = pKa + log [base]/[acid]

pKa = pH - log [base]/[acid]

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15
Q

Osmotic pressure (van’t Hoff)

A

π = RTC

Where π = osmotic pressure, R = universal gas constant, T = absolute temperature, C = osmolality (mosm/kg H2O)

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16
Q

Gibbs-Donnan

A

[cation]A x [anion]A = [cation]B x [anion]B

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17
Q

Clearance

A

Clearance =
(urine conc x urine flow
———————–
plasma conc

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18
Q

Pharmacokinetics

A

k = 0.693/t1/2 = clearance/Vd

This is the only pharmacokinetics formula to remember; if τ needed, substitute it for k and switch the other two values (because k and τ are reciprocals).

Where k = rate constant, τ = time constant

Also k = rate/quantity

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19
Q

Renal equations (RPF, RBF, GFR, FF)

A

RPF = clearance/[A-V PAH difference]

RBF = RPF/(1-Hct)

GFR (inulin or creatinine) = urine conc x (urine flow/plasma conc)

Filtration fraction = GFR/RPF (normally 20%)

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20
Q

Osmolarity

A

2(Na+ + K+) + urea + glucose

Normal = 285-295 mosm/L

Na+ and K+ are doubled to account for the Cl- which accompanies most Na+/K+ ions in the body. Urea reduces the freezing point, although it is not osmotically active. Proteins are osmotically active but not ionic so not included.

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21
Q

Stroke volume

A

SV = EDV-ESV

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22
Q

SVR and PVR

A

SVR = (MAP - CVP)/CO x 80 dynes/s/cm to -5 (normal 800-1200)

PVR = (MPAP - PCWP)/CO x 80 (normal 100-200)

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23
Q

O2 and N2O cylinder contents

A

O2: P1V1 = P2V2

N2O: moles = weight/MW; then volume = moles x 22.4L

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24
Q

MAP

A

MAP = CO x SVR

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25
Q

Alveolar gas equation

A

PAO2 = PiO2 - (PACO2/R)

Where R (respiratory quotient) = CO2 production/O2 consumption (about 0.8 depending on fuel source)

PiO2 = FiO2 x (Patm - PH2O)

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26
Q

Shunt equation

A

Qs = CcO2 - CaO2
— ——————
Qt CcO2 - CvO2

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27
Q

Physiological dead space (Bohr)

A

Vd = PaCO2 - PECO2
— ———————-
Vt PaCO2

Where PECO2 = mixed expired PCO2

Physiological dead space is usually about 30% of the Vt

Physiological dead space = anatomical dead space + alveolar dead space

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28
Q

Paediatric weight formulae

A

<1y: (age x 0.5) + 4 (age in months)

1-5y: (age x 2) + 8

6-12y: (age x 3) + 7

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29
Q

Therapeutic index

A

LD50/ED50

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30
Q

Transpulmonary pressure

A

Alveolar pressure - pleural pressure

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31
Q

Strong ion difference

A

SID = (Na+ + K+ + Ca2+ + Mg2+) – (Cl- – other strong anions)

A ‘strong’ ion is one which completely dissociates at the pH of interest.

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32
Q

Kinetic energy

A

1/2 x mass x (velocity2)

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33
Q

SEM

A

Standard deviation / √n - 1

34
Q

Graphs

A 
y = x - perfect measuring system 
y = k/x - Boyle's law 
y = mx + c - resistance wire 
y = kx2
y = a.e kt - bacterial multiplication 
y = a.e -kt - IV drug elimination or passive expiration 
y = a-b.e -kt - wash-in curve or PCV inspiration
35
Q

Soda lime reactions

A

CO2 + H2O –> H2CO3
H2CO3 + 2NaOH –> Na2CO3 + 2H2O + heat
Na2CO3 + Ca(OH)2 –> 2NaOH + CaCO3

36
Q

Impedance

A

Resistance + reactance

37
Q

Ideal gas laws

A

Boyle’s: k = PV
Charles’: k = V/T
Gay-Lussac: k = P/T

‘TPR’ are the constant factors (from laws 1-3)

38
Q

Bioavailability

A

AUC (PO)/AUC (IV)

AUC = of a concentration-time curve

39
Q

Dissociation constant and affinity

A

kd = [D][R]/[DR]

Affinity = 1/kd

Where kd = dissociation constant for that drug, [D] = free drug, [R] = unoccupied receptors, [DR] = drug-occupied receptors

40
Q

Absolute pressure

A

Absolute pressure = gauge pressure + atmospheric pressure

41
Q

Hagen-Pouseille (laminar flow)

A

Q = πPd4
——–
128ηl

42
Q

Turbulent flow (3)

A

Q ∝ √P
∝ 1/√l
∝ 1/√p (density)

43
Q

Capacitance

A

C = Q/V

44
Q

Relative humidity

A

RH = actual vapour pressure/SVP

45
Q

Beer-Lambert

A

Absorbance = ξcd

Where ξ = molar extinction coefficient, c = molar concentration, d = thickness

46
Q

Fick’s law

A

Rate of diffusion = kp.(A/T).C1-C2

Where kp = permeability constant, A = area, T = thickness, C1-C2 = concentration gradient

47
Q

Nernst and Goldman constant field equation

A

For example, sodium:

Capillary wall potential (mV) = RT/FZ x log(e) [Na]int/[Na]cap

Where R = universal gas constant, T = absolute temperature, F = Faraday constant, Z = valency, int = interstitial, cap = capillary

Goldman calculates overall membrane potential, taking into account the permeabilities and concentration gradients of each ion.

48
Q

Starling forces

A

Pressure gradient = (P cap + π inst) - (P inst + π cap)

Rate of filtration = k x pressure gradient

Where π = colloid osmotic pressure, P = hydrostatic pressure, inst = interstitial, cap = capillary, k = filtration coefficient

In the kidney, equation changes to hydrostatic forces - osmotic forces:

GFR = kf (P gc - P bc) - (π gc - π bc)

Where kf = glomerular filtration coefficient (permeability x capillary bed surface area)

49
Q

Cardiac output

A

CO = HR x SV

Cardiac index = CO/BSA

50
Q

Bazett’s formula

A

QTc = QT
—-
√(R-R)

51
Q

Compliance

A

Compliance = ΔV/ΔP

1/Cr = 1/Cl + 1/Cw

Where V = volume, P = pressure, Cr = respiratory system compliance, Cl = lung compliance, Cw = chest wall compliance

52
Q

Oxygen content and delivery (flux)

A

CaO2 = (Hb x SpO2 x 1.34) + (PaO2 x 0.0225)

DO2 (flux) = CaO2 x CO

53
Q

Cerebral perfusion pressure

A

CPP = MAP - (ICP + CVP)

54
Q

Graham’s law

A

Rate of diffusion ∝ 1/√MW

Where MW = molecular weight

55
Q

Closing capacity

A

CC = CV + RV

56
Q

Ohm’s law

A

V = IR

Also V = P/I = Q/C

57
Q

Doppler equation

A

V = 2 Fo
——–
C Fd Cos Theta

V = blood velocity 
Fo = transmitted US frequency 
Fd = Doppler shift 
C = constant (velocity of US in blood) 
Cos Theta = cosine of angle of incidence (corrects for probe misalignment)

Velocity is then used to calculate flow:

Flow = area x velocity

58
Q

Stewart-Hamilton equation

A

Q = I / integral Ci dt

Q = cardiac output
I = indicator amount in moles
Ci dt = integral of indicator conc over time (AUC)

59
Q

Inverse square law

A

Point sources of gravitational force, electric field, light, sound or radiation obey the inverse square law.

Intensity = source strength
———————-
4πr2

i.e. doubling the distance from the source will quarter the intensity.

60
Q

Circumference and area of a circle

A

Circumference = πd

Area = πr2

61
Q

Spinal cord perfusion pressure

A

SCPP = MAP - CSFP

62
Q

Anion gap

A

(Na+ + K+) - (Cl- + HCO3-)

Normal = 4-12 mmol/L (older assays 8-16)

High anion gap metabolic acidosis: lactate, ketones, alcohols, renal
Normal anion gap metabolic acidosis: Cl- excess, GI losses, diuretics, bicarb loss

63
Q

Coronary perfusion pressure

A

CPP = aortic diastolic pressure - LVEDP

64
Q

Endocardial viability ratio

A

EVR = diastolic pressure time index . HR
——————————————
tension time index

DPTI = myocardial supply 
TTI = myocardial demand

EVR <0.7 means a high likelihood of ischaemia

65
Q

Stroke volume variation

A

SVV = SV(max) - SV (min)
————————-
SV(mean)

SVV >10% suggests fluid responsivenes as SV is sensitive to fluctuations in preload due to the respiratory cycle.

BP falls in inspiration and rises in expiration in spontaneous ventilation.
In PPV, BP rises in inspiration and falls in expiration.

66
Q

Sodium deficit

A

Na+ deficit = total body water x (desired Na+ - actual Na+)

Where total body water = 60% of total body weight

Normal Na+ content = 58mmol/kg

NB: formula not very accurate.

67
Q

Parkland formula

A

4ml x kg x %BSA = first 24h requirement

Half over 8h, rest over 16h

68
Q

BMI

A

Weight in kg / height in m2

69
Q

Specific compliance

A

Compliance / FRC

compensates for BSA

70
Q

Paediatric blood transfusion

A

Volume required = desired Hb rise x weight x 3

Also 5 ml/kg should increment Hb by 10 g/L

71
Q

Sensitivity

A

True positives / true positives + false negatives

72
Q

Specificity

A

True negatives / true negatives + false positives

73
Q

Positive predictive value

A

True positives / all positives

74
Q

Negative predictive value

A

True negatives / all negatives

75
Q

Oxygenation index

A

OI = (FiO2 x mean airway pressure) x 100
————-
PaO2

76
Q

P:F ratio

A

PaO2/FiO2

Normal is over 60kPa (13.3/0.21)

77
Q

A-a gradient

A

PAO2 - PaO2

Former calculated from alveolar gas equation

78
Q

% dehydration in paeds

A

% = ml per 100g body weight.

e.g. 5% dehydration = 5ml/100g or 50ml/kg.

If shock is present, at least 10% dehydration has occurred.

79
Q

Servin’s formula (for calculating input mass for TCI in the obese)

A

IBW + 40% of difference between IBW and actual weight

80
Q

Density

A

Mass / volume

FRCA (11 decks)

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