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FFICM > Equations > Flashcards

Equations Flashcards

1
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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2
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

Turbulent flow is ∝ √P ∝ 1/√l ∝ 1/√d

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3
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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4
Q

Resistors

A

Series: R1 + R2

Parallel: 1/R1 + 1/R2

Wheatstone bridge: R1/R2 = R3/R4

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5
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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6
Q

Ejection fraction

Stroke volume

A

EF = SV/EDV

SV = EDV-ESV

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7
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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8
Q

Henderson-Hasselbalch and pKa

A

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

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

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9
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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10
Q

Gibbs-Donnan

A

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

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11
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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12
Q

Renal equations (GFR, RPF, RBF, FF)

A

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

RPF = clearance/[A-V PAH difference]

RBF = RPF/(1-Hct)

Filtration fraction = GFR/RPF (normally 20%)

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13
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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14
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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15
Q

MAP

A

MAP = CO x SVR

MAP = DBP + 1/3 (SBP - DBP)

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16
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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17
Q

Shunt equation

A

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

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18
Q

Physiological dead space (Bohr)

A

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

Where PECO2 = mixed expired PCO2

Physiological dead space = anatomical dead space (2ml/kg) + alveolar dead space (0 in health)

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19
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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20
Q

Therapeutic index

A

LD50/ED50

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21
Q

Transpulmonary pressure

A

Alveolar pressure - pleural pressure

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22
Q

Strong ion difference

A

Apparent SID = (Na+ + K+ + Ca2+ + Mg2+) – (Cl- + lactate)

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

Apparent SID is normally about 40 mEq/L.

True or ‘effective’ SID is much more complicated to calculate.

Strong ion gap = difference between apparent and effective SID. Principle is similar to the anion gap.

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23
Q

Bioavailability

A

AUC (PO)/AUC (IV)

AUC = of a concentration-time curve

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24
Q

Hagen-Pouseille (laminar flow)

A

Q = πPd4
——–
128ηl

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25
Q

Beer-Lambert

A

Absorbance = ξcd

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

Transmission decreases exponentially as the concentration of the medium (Beer) and the thickness of the medium (Lambert) increase.

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26
Q

Fick’s law of diffusion

A

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

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

Rate is also ∝ 1/√MW (Graham’s law)

27
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)

28
Q

Cardiac output

Cardiac index

A

CO = HR x SV

Cardiac index = CO/BSA

29
Q

Bazett’s formula

A

QTc = QT
—-
√(R-R)

The QT interval is ‘corrected’ to a HR of 60 bpm.

QTc is prolonged if >440ms in males or >460ms in females.
>500ms is high risk for torsades.

30
Q

Compliance

  • Specific
  • Total respiratory system
  • Static
  • Dynamic
A

Compliance = ΔV/ΔP
Specific compliance = (ΔV/ΔP) / FRC

1/Cresp = 1/Clung + 1/Ccw

Static compliance = Vt / (Pplat - PEEP)
Dynamic compliance = Vt / (Ppeak - PEEP)

Where V = volume, P = pressure, Cresp = overall respiratory system compliance, Clung = lung compliance, Ccw = chest wall compliance

31
Q

Oxygen content and delivery (flux)

A

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

DO2 (flux) = CaO2 x CO

32
Q

Perfusion pressures

  • Cerebral
  • Spinal cord
  • Coronary
A

CPP = MAP - (ICP + CVP)

SCPP = MAP - CSFP

CoPP = DBP - LVEDP

33
Q

Closing capacity

A

CC = CV + RV

34
Q

Doppler equation

A

V = 2 Fo
——–
C Fd Cos Theta

V = blood velocity
Fo = original US frequency
Fd = Doppler shift
C = constant (velocity of US in tissue - 1540m/s)
Cos Theta = cosine of angle of incidence (corrects for probe misalignment)

Velocity is then used to calculate flow:

Flow = area x velocity

35
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)

Or:

CO = k(core temp - indicator temp) x vol indicator
———————————————-
Change in blood temp

36
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.

37
Q

Anion gap

Correction for albumin

A

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

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

High anion gap metabolic acidosis: lactate, ketones, alcohols, renal, salicylate, chronic paracetamol
Normal anion gap metabolic acidosis: Cl- excess, GI losses, diuretics, bicarb loss, ileostomy, RTA, TPN, ileal conduit

Anion gap can be falsely low/negative or ‘normal’ if the albumin is low; low/negative anion gap can also be caused by high Ca/Mg and Li intoxication.

AG (corrected for albumin) = AG + (albumin gap/4)

Where albumin gap = 40 - apparent albumin

38
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.

39
Q

Sodium deficit

A

Na+ deficit = (0.6 x weight) x (desired Na+ - current Na+)

0.6 indicates 60% TBW being H2O.

Desired Na+ usually taken as 140.

Normal Na+ content is about 60 mmol/kg.
Normal H2O content is about 60% total body weight.

40
Q

Parkland formula

A

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

Half over 8h, rest over 16h
Children get maintenance as well
Originally used to include a colloid bolus after the above, no longer used

41
Q

BMI

A

Weight in kg / height in m2

42
Q

Sensitivity

A

True positives / true positives + false negatives

43
Q

Specificity

A

True negatives / true negatives + false positives

44
Q

Positive predictive value

A

True positives / all positives

45
Q

Negative predictive value

A

True negatives / all negatives

46
Q

P:F ratio

A

PaO2/FiO2

Normal is over 60kPa (13.3/0.21)

An alternative is the oxygenation index:
OI = ((FiO2 x mean airway pressure)/PaO2) x 100
Used esp in paeds to determine need for ECMO. OI<25 good, 25-40 = 40% mortality, >40 consider ECMO.

47
Q

A-a gradient

A

PAO2 - PaO2

(Former calculated from alveolar gas equation: PAO2 = PiO2 - (PACO2/R) and PiO2 = FiO2 x (Patm - PH2O))

Normal

  • On air: 7mmHg young, 14 elderly
  • On 100% O2: 31 young, 56 elderly
48
Q

Rapid Shallow Breathing Index (RSBI)

A

RSBI = RR/Vt (L)

49
Q

Energy requirements

A

REE/BMR + DIT + activity factor + stress factor +/- specific disease state factor

REE/BMR calculated by Harris-Benedict or Schofield equations

HB:
Male: 66.5 + (13.8 x IBW) + (5 x height) - (6.8 x age)
Female: 66.5 + (9.6 x IBW) + (1.7 x height) - (4.7 x age)

95% CI is about +/- 200kCal/day.

1g protein or carb = 4 kCal
1g fat = 9 kCal

50
Q

RQ

A

RQ = CO2 produced / O2 consumed

Carbs = 1.0 
Protein = 0.8 
Fat = 0.7
51
Q

Osmolar gap

A

Measured osmolality - calculated osmolarity

Normal = <10

Note the units are different so it doesn’t make mathematical sense - it is just a rough clinical aid.

A high osmolar gap indicates presence of other osmotically active particles e.g. methanol, ethylene glycol, mannitol, sorbitol, polyethylene glycol/propylene glycol (found in IV lorazepam and others), glycine (TURP) and maltose (IGIg).

52
Q

Free water deficit

A

H2O deficit = (0.6 x weight) x (current Na+ - desired Na+)/desired Na+

Desired Na+ usually taken as 140.

Normal Na+ content is about 60 mmol/kg.
Normal H2O content is about 60% total body weight.

53
Q

Corrected Na+ in hyperglycaemia

A

Corrected Na+ = measured Na+ x (0.3 x (plasma glucose - 5.5))

Basically, for every 5.5mmol/L increase above a standard glucose of 5.5, add 2.4mmol/L to the serum sodium.

54
Q

Oxygen requirement for transfer

A

O2 req = MV (L) x FiO2 (as fraction) x time (mins)

Then double it for margin of safety.

Be mindful that basic transport vents may only do 100% O2 and may also use O2 to drive the vent.

Size CD cylinder = 460L (hence at 15L/m a full one will last about 30m) 
Size E (anaesthetic machine) = 680L (45m) 
Size F (under trolleys) = 1360L (90m)
55
Q

Nasal specs FiO2

A

21% + (O2 flow rate x 3)

e.g. 2L/m

21 + (2 x 3) = 27%

56
Q

(H)SMR

A

(Actual deaths/expected deaths) x 100

57
Q

ABPI

A

ABPI = SBP at site of interest (e.g. injured/diseased limb) / brachial SBP

Despite the name, can be performed on upper or lower limbs.

ABPI > 0.9 is highly unlikely to have a vascular injury/insufficiency
API < 0.9 indicates possible vascular injury/insufficiency - likely to need CT angiography

58
Q

Shock index

A

HR/SBP

Normal = 0.5-0.7

  1. 8 or more predicts hypotension at induction for emergency intubation, hyperlactataemia in sepsis and 28-day mortality in sepsis
  2. 0 or more even more strongly associated with sepsis outcomes above
59
Q

Maddrey’s discriminant function

A

Bilirubin + (4.6 x (PT - control PT))

> 32 in alc hep suggests poor prognosis + may benefit from steroids

60
Q

ICU capacity (Hill-Burton formula)

A

Calculated ICU capacity = (adms/yr x av LoS in days) / (ideal occupancy rate x 365)

61
Q

Pleural effusion volume estimate

A

Max depth in mm on US x 20ml

62
Q

Paediatric fluid maintenance

A

First 10kg 4ml/kg/h
Next 10kg 2ml/kg/h
All further kg 1ml/kg/h

63
Q

CPP

A

CPP = MAP-ICP (or CVP if CVP>ICP)

FFICM (8 decks)

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