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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
Beer-Lambert
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.
26
Fick's law of diffusion
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
Starling forces
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
Cardiac output | Cardiac index
CO = HR x SV Cardiac index = CO/BSA
29
Bazett's formula
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
Compliance - Specific - Total respiratory system - Static - Dynamic
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
Oxygen content and delivery (flux)
CaO2 = (Hb x SpO2 x 1.34) + (PaO2 x 0.0225) DO2 (flux) = CaO2 x CO
32
Perfusion pressures - Cerebral - Spinal cord - Coronary
CPP = MAP - (ICP + CVP) SCPP = MAP - CSFP CoPP = DBP - LVEDP
33
Closing capacity
CC = CV + RV
34
Doppler equation
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
Stewart-Hamilton equation
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
Inverse square law
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
Anion gap Correction for albumin
(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
Stroke volume variation
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
Sodium deficit
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
Parkland formula
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
BMI
Weight in kg / height in m2
42
Sensitivity
True positives / true positives + false negatives
43
Specificity
True negatives / true negatives + false positives
44
Positive predictive value
True positives / all positives
45
Negative predictive value
True negatives / all negatives
46
P:F ratio
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
A-a gradient
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
Rapid Shallow Breathing Index (RSBI)
RSBI = RR/Vt (L)
49
Energy requirements
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
RQ
RQ = CO2 produced / O2 consumed ``` Carbs = 1.0 Protein = 0.8 Fat = 0.7 ```
51
Osmolar gap
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
Free water deficit
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
Corrected Na+ in hyperglycaemia
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
Oxygen requirement for transfer
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
Nasal specs FiO2
21% + (O2 flow rate x 3) e.g. 2L/m 21 + (2 x 3) = 27%
56
(H)SMR
(Actual deaths/expected deaths) x 100
57
ABPI
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
Shock index
HR/SBP Normal = 0.5-0.7 0. 8 or more predicts hypotension at induction for emergency intubation, hyperlactataemia in sepsis and 28-day mortality in sepsis 1. 0 or more even more strongly associated with sepsis outcomes above
59
Maddrey's discriminant function
Bilirubin + (4.6 x (PT - control PT)) >32 in alc hep suggests poor prognosis + may benefit from steroids
60
ICU capacity (Hill-Burton formula)
Calculated ICU capacity = (adms/yr x av LoS in days) / (ideal occupancy rate x 365)
61
Pleural effusion volume estimate
Max depth in mm on US x 20ml
62
Paediatric fluid maintenance
First 10kg 4ml/kg/h Next 10kg 2ml/kg/h All further kg 1ml/kg/h
63
CPP
CPP = MAP-ICP (or CVP if CVP>ICP)

FFICM (8 decks)

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