Equations Flashcards
Momentum
Momentum = mass x velocity
Ideal gas equation
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)
Reynolds’ number
η
Where v = velocity, p = pressure, d = density, η = viscosity
<2000 = laminar
2000-4000 transitional
>4000 turbulent
NB: number is dimensionless
Laplace’s law
Sphere: P=2T/r
Cylinder: P=T/r
Where P = pressure, T = tension and r = radius
Energy (e.g. stored energy of defibrillator) (5)
1/2 CV2 = 1/2QV = VQ = VIt = Pt
Where C - capacitance, V = voltage, Q = charge, t = time
Power (3)
Power = IV = I2R = E/t
Where I = current, V = voltage, R = resistance, E = energy (can also be work)
Work (2)
Work = force x distance = VQ
Where V = voltage, Q = charge
Resistors
Series: R1 + R2
Parallel: 1/R1 + 1/R2
Wheatstone bridge: R1/R2 = R3/R4
Charge
Q = CV = It = E/V = Pt
Where C = capacitance, V = voltage, I = current, t = time, E = energy, P = power
Loading and maintenance doses (e.g. for TIVA without TCI pump)
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
Force (3)
Force = mass x acceleration (Newton’s second law)
Force = pressure x area
Force = work/distance
Ejection fraction
EF = SV/EDV
Fick principle
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
Henderson-Hasselbalch and pKa
pH = pKa + log [base]/[acid]
pKa = pH - log [base]/[acid]
Osmotic pressure (van’t Hoff)
π = RTC
Where π = osmotic pressure, R = universal gas constant, T = absolute temperature, C = osmolality (mosm/kg H2O)
Gibbs-Donnan
[cation]A x [anion]A = [cation]B x [anion]B
Clearance
Clearance =
(urine conc x urine flow
———————–
plasma conc
Pharmacokinetics
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
Renal equations (RPF, RBF, GFR, FF)
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%)
Osmolarity
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.
Stroke volume
SV = EDV-ESV
SVR and PVR
SVR = (MAP - CVP)/CO x 80 dynes/s/cm to -5 (normal 800-1200)
PVR = (MPAP - PCWP)/CO x 80 (normal 100-200)
O2 and N2O cylinder contents
O2: P1V1 = P2V2
N2O: moles = weight/MW; then volume = moles x 22.4L
MAP
MAP = CO x SVR
Alveolar gas equation
PAO2 = PiO2 - (PACO2/R)
Where R (respiratory quotient) = CO2 production/O2 consumption (about 0.8 depending on fuel source)
PiO2 = FiO2 x (Patm - PH2O)
Shunt equation
Qs = CcO2 - CaO2
— ——————
Qt CcO2 - CvO2
Physiological dead space (Bohr)
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
Paediatric weight formulae
<1y: (age x 0.5) + 4 (age in months)
1-5y: (age x 2) + 8
6-12y: (age x 3) + 7
Therapeutic index
LD50/ED50
Transpulmonary pressure
Alveolar pressure - pleural pressure
Strong ion difference
SID = (Na+ + K+ + Ca2+ + Mg2+) – (Cl- – other strong anions)
A ‘strong’ ion is one which completely dissociates at the pH of interest.
Kinetic energy
1/2 x mass x (velocity2)
SEM
Standard deviation / √n - 1
Graphs
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
Soda lime reactions
CO2 + H2O –> H2CO3
H2CO3 + 2NaOH –> Na2CO3 + 2H2O + heat
Na2CO3 + Ca(OH)2 –> 2NaOH + CaCO3
Impedance
Resistance + reactance
Ideal gas laws
Boyle’s: k = PV
Charles’: k = V/T
Gay-Lussac: k = P/T
‘TPR’ are the constant factors (from laws 1-3)
Bioavailability
AUC (PO)/AUC (IV)
AUC = of a concentration-time curve
Dissociation constant and affinity
kd = [D][R]/[DR]
Affinity = 1/kd
Where kd = dissociation constant for that drug, [D] = free drug, [R] = unoccupied receptors, [DR] = drug-occupied receptors
Absolute pressure
Absolute pressure = gauge pressure + atmospheric pressure
Hagen-Pouseille (laminar flow)
Q = πPd4
——–
128ηl
Turbulent flow (3)
Q ∝ √P
∝ 1/√l
∝ 1/√p (density)
Capacitance
C = Q/V
Relative humidity
RH = actual vapour pressure/SVP
Beer-Lambert
Absorbance = ξcd
Where ξ = molar extinction coefficient, c = molar concentration, d = thickness
Fick’s law
Rate of diffusion = kp.(A/T).C1-C2
Where kp = permeability constant, A = area, T = thickness, C1-C2 = concentration gradient
Nernst and Goldman constant field equation
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.
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)
Cardiac output
CO = HR x SV
Cardiac index = CO/BSA
Bazett’s formula
QTc = QT
—-
√(R-R)
Compliance
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
Oxygen content and delivery (flux)
CaO2 = (Hb x SpO2 x 1.34) + (PaO2 x 0.0225)
DO2 (flux) = CaO2 x CO
Cerebral perfusion pressure
CPP = MAP - (ICP + CVP)
Graham’s law
Rate of diffusion ∝ 1/√MW
Where MW = molecular weight
Closing capacity
CC = CV + RV
Ohm’s law
V = IR
Also V = P/I = Q/C
Doppler equation
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
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)
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.
Circumference and area of a circle
Circumference = πd
Area = πr2
Spinal cord perfusion pressure
SCPP = MAP - CSFP
Anion gap
(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
Coronary perfusion pressure
CPP = aortic diastolic pressure - LVEDP
Endocardial viability ratio
EVR = diastolic pressure time index . HR
——————————————
tension time index
DPTI = myocardial supply TTI = myocardial demand
EVR <0.7 means a high likelihood of ischaemia
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.
Sodium deficit
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.
Parkland formula
4ml x kg x %BSA = first 24h requirement
Half over 8h, rest over 16h
BMI
Weight in kg / height in m2
Specific compliance
Compliance / FRC
compensates for BSA
Paediatric blood transfusion
Volume required = desired Hb rise x weight x 3
Also 5 ml/kg should increment Hb by 10 g/L
Sensitivity
True positives / true positives + false negatives
Specificity
True negatives / true negatives + false positives
Positive predictive value
True positives / all positives
Negative predictive value
True negatives / all negatives
Oxygenation index
OI = (FiO2 x mean airway pressure) x 100
————-
PaO2
P:F ratio
PaO2/FiO2
Normal is over 60kPa (13.3/0.21)
A-a gradient
PAO2 - PaO2
Former calculated from alveolar gas equation
% dehydration in paeds
% = ml per 100g body weight.
e.g. 5% dehydration = 5ml/100g or 50ml/kg.
If shock is present, at least 10% dehydration has occurred.
Servin’s formula (for calculating input mass for TCI in the obese)
IBW + 40% of difference between IBW and actual weight
Density
Mass / volume
