Equations

• Concentration = Dose/Volume of distribution
• Loading dose = volume of distribution x desired concentration
• Infusion rate = desired concentration x clearance

• Rate of elimination = Css x clearance
• Half life = 0.693 x Volume of distribution/Clearance
• Half life = 0.693/Ke
• τ =1/Ke
• τ =Vd/Cl
• Ke = Clearance/Vd

Css = steady state concentration

Ke = elimination rate constant

Explanation here

• Clearance = Ke x Volume of distribution
• Clearance = Urine concentration x urinary flow/plasma concentration
• Clearance = Dose/AUC

• Lumbosacral block - 0.5 ml/kg
• Thoracolumbar block - 1 ml/kg
• Midthoracic block - 1.25 ml/kg

This is for 0.25% bupivacaine.

The following are all equivalent doses

• Methylprednisolone - 4mg
• Prednisolone - 5mg
• Hydrocortisone - 20mg
• Cortisone - 25 mg

• Volts = Current x Resistance

• Charge = Voltage x capacitance
• Power = Current x Voltage
• Power = Energy/Time
• Volts = Energy/Charge
• Energy = Charge x voltage/2
• Energy = (Capacitance x voltage^2) /2
• Energy = Mass x specific heat capacity x temperature

For a series circuit

• Total resistance = R1 + R2 + ... + Rn

For a parallel circuit

• 1/Total resistance = 1/R1 + 1/R2 + ... + 1/Rn

• Energy = Force x distance
• Energy = pressure x volume
• Force = mass x acceleration
• Kinetic energy = 0.5 x mass x velocity^2
• Potential energy = mass x gravitational acceleration x height

• Q = πΔPr4/8ɳl

Q = Flow, ΔP - change in pressure, ɳ - viscosity, l - length of tube

Re = pvD/ɳ

p - density, D - diameter of tube, ɳ - viscosity

Turbulent flow is more affected by density

Laminar flow is more affected by viscosity

• Fd= 2FtVCos θ / C

Ft -transmitted Doppler frequency, V i- speed of blood flow, Cos θ - Cosine of the blood flow to beam angle, C - speed of sound in tissue

The following are all the same:

• 101 kPa
• 1 atm
• 760 mmHg
• 1033 cmH2O
• 101 325 N/M^2
• 101 325 Dynes/cm^2
• 14.4 PSI

Universal gas law

• PV = nRT

Boyle's law

• V1P1 = V2P2 at a given temperature

Charles' law

• V is proportional to T for a given pressure

Gay-Lussac's law

• P is proportional to T for any given volume

Dalton's law

• Total pressure = sum of all the partial pressures

Fick's law of diffusion

• Volume of gas is proportional to (Area/Thickness) x diffusion constant x pressure gradient
• Diffusion constant is proportional to gas solubility/√molecular weight

More here

• Cardiac output = Stroke volume x Heart rate
• Blood pressure = Cardiac output x Systemic vascular resistance
• Mean arterial pressure = diastolic + (systolic - diastolic)/3
• Systemic vascular resistnace = (MAP - CVP/CO) x 80
• Pulmonary vascular resistance = (MPAP-PAWP/CO) x 80

• Oxygen content = cardiac output x (Hb x SaO2 x 1.34) + (0.02 x PaO2)
• Saturations = HbO2 x 100%/Hb + HbO2

• The pressure inside a sphere is proportional to the surface tension in the wall
• The pressure inside a sphere is inversely proportional to the radius of the sphere
• Wall stress is the wall tension divided by 2 times the wall thickness
• P = 2 x Surface Tension /radius

• SI = HR​/SBP

>0.9 is suggestive of circulatory failure

• Physiological dead space = anatomical + alveolar

Explanations here

• Total airway resistance = airway resistance + tissue resistance
• Compliance = Δ volume/ Δ pressure
• 1/total compliance = 1/lung compliance + 1/thoracic wall compliance

• Delivered FiO2 = (O2 flow rate + (0.21 x air flow rate))/Total flow rate

The air flow rate can be calculated from the entrainment ratio

Here's our post on venturi stuff

• VD/VT = PaCO2 - PeCO2/PaCO2

Explanation here

• QS/QT = CCO2 - CaO2/ CCO2 – CvO2

Explanation here

• PAO2 = FiO2 x (PATM – PH20) – PACO2/RQ

Explanation here

• pH = pKₐ + log([A⁻]/[HA])
• pH = -log10 [H+]

For an acid:

• pH = pKa + log[A-/HA]

For a base:

• pH = pKa + log[B/BA+]

More acid base stuff here

• 1 MET = 3.5 ml O2/kg/min

Explanation here

• [Na+ + K+] - [Cl- + HCO3-]

Explanation here

• (2x[Na+]) + [Glu] + [Urea]
• Osmolality = per kg, osmolarity = per litre
• Normally 275 - 290 mOsmol/kg
• Normal urine osmolality = 500 - 850 mOsm/kg

Fluids and stuff here

• Corrected Na =Measured Na +2.4 x Glucose​/100

• CPP = MAP - (ICP + CVP)

Explanation here

• ICP∝Brain Volume+CSF Volume+Blood Volume

where:

• Compensation: If one increases, the others must decrease to maintain normal ICP.
• Decompensation: Once compensation fails, ICP rises steeply.

• CSF Production ≈ 0.3−0.4 mL/min ≈ 500 mL/day

• CBF=CPP/CVR

where CVR = Cerebrovascular Resistance

• Normal CBF = 50 mL/100g/min
• CBF is autoregulated between a MAP of 50–150 mmHg

• CMRO₂=CBF×(CaO₂−CjvO₂)

where:

• CaO2​ = arterial oxygen content
• CjvO2​ = jugular venous oxygen content

• Ex​ = RT/zF​ x ln([X]extracellular​/[X]intracellular​​)

where:

• Ex​ = equilibrium potential for an ion
• R = universal gas constant
• T = temperature in Kelvin
• z = charge of the ion
• F = Faraday’s constant

• Weight = (age+4) x 2
• Energy = 4 J/kg
• Tube = (age/4) + 4
• Fluids = 10ml/kg
• Lorazepam = 0.1mg/kg
• Adrenaline = 0.1ml/kg of 1:10 000 (1mg in 10ml)
• Glucose = 2mls/kg 10% dextrose

Atropine = 20mcg/kg

More here

• Maintenance=4 mL/kg/hr (first 10 kg)+2 mL/kg/hr (next 10 kg)+1 mL/kg/hr (>20 kg)

Sensitivity = Likelihood of detecting a true case of the disease

• true positive/(true positive + false negative)

Specificity = Likelihood of testing negative if you don't have the disease

• true negative/(true negative + false positive)

Positive predictive value = Likelihood you actually have it if test positive

• true positive/(true positive + false positive)

Negative predictive value = Likelihood that a negative test means you don't have the disease

• true negative/(true negative + false negative)

When presented with a 2 x 2 table

Odds ratio = (a/b)/(c/d)

Relative risk = (a/(a + b))/(c/(c + d))

Absolute risk reduction = (c/(c + d)) - (c/(c + b))

Number needed to treat = 1/ARR