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Biomedical & Clinical formula solvers

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Arterial Oxygen Content (CaO₂)

CaO2=1.34 Hb SaO2+0.003 PaO2C_a\mathrm{O_2} = 1.34\,\mathrm{Hb}\,S_a\mathrm{O_2} + 0.003\,P_a\mathrm{O_2}

Biomedical & ClinicalOxygen carried per decilitre of arterial blood: the large amount bound to haemoglobin, plus the small amount dissolved in plasma.

Basal Metabolic Rate (Harris-Benedict, Men)

BMR=88.362+13.397 m+4.799 h−5.677 a\mathrm{BMR} = 88.362 + 13.397\,m + 4.799\,h - 5.677\,a

Biomedical & ClinicalEveryday & HealthResting energy expenditure for men in kcal per day, by the 1984 Roza and Shizgal revision of the 1919 Harris-Benedict equations.

Basal Metabolic Rate (Harris-Benedict, Women)

BMR=447.593+9.247 m+3.098 h−4.330 a\mathrm{BMR} = 447.593 + 9.247\,m + 3.098\,h - 4.330\,a

Biomedical & ClinicalEveryday & HealthResting energy expenditure for women in kcal per day, by the 1984 Roza and Shizgal revision of the 1919 Harris-Benedict equations.

Basal Metabolic Rate (Mifflin-St Jeor)

BMR=10 m+6.25 h−5 a+s\mathrm{BMR} = 10\,m + 6.25\,h - 5\,a + s

Biomedical & ClinicalEveryday & HealthMifflin and St Jeor's 1990 fit for resting energy expenditure in kcal per day, from mass in kilograms, height in centimetres and age in years.

Body Surface Area Dosing (mg per m²)

D=DA⋅BSAD = D_A \cdot \mathrm{BSA}

Biomedical & ClinicalThe dose for a person from a protocol quoted per square metre of body surface area, the convention used across oncology.

Cardiac Output (Heart Rate × Stroke Volume)

CO=HR⋅SV\mathrm{CO} = \mathrm{HR} \cdot \mathrm{SV}

Biomedical & ClinicalCardiac output: the volume the left ventricle ejects each beat, multiplied by the number of beats each minute.

Corrected Calcium for Albumin

Cacorr=Ca+0.8 (4.0−Alb)\mathrm{Ca}_{corr} = \mathrm{Ca} + 0.8\,(4.0 - \mathrm{Alb})

Biomedical & ClinicalTotal serum calcium adjusted upward for low albumin, since roughly 40 % of calcium travels bound to albumin and is not biologically active.

Creatinine Clearance (Cockcroft-Gault)

CrCl=(140−a) m F72 Scr\mathrm{CrCl} = \frac{(140 - a)\,m\,F}{72\,S_{cr}}

Biomedical & ClinicalCockcroft and Gault's 1976 estimate of creatinine clearance in mL/min from age, body mass, serum creatinine and a sex factor.

Drug Half-Life from Clearance and Volume of Distribution

t1/2=ln⁡2⋅VdCLt_{1/2} = \frac{\ln 2 \cdot V_d}{\mathrm{CL}}

Biomedical & ClinicalElimination half-life for a one-compartment drug: the time to fall by half, set entirely by the volume of distribution and the clearance.

Estimated GFR (MDRD 4-Variable, IDMS-Traceable)

eGFR=175⋅Scr−1.154⋅a−0.203⋅F\mathrm{eGFR} = 175 \cdot S_{cr}^{-1.154} \cdot a^{-0.203} \cdot F

Biomedical & ClinicalEstimated glomerular filtration rate in mL/min per 1.73 m² by the IDMS-traceable four-variable MDRD equation.

Fick Principle for Oxygen Consumption

V˙O2=CO⋅(CaO2−CvO2)⋅10\dot{V}\mathrm{O_2} = \mathrm{CO} \cdot (C_a\mathrm{O_2} - C_v\mathrm{O_2}) \cdot 10

Biomedical & ClinicalAdolf Fick's 1870 principle: oxygen consumption equals blood flow times the oxygen the blood gives up crossing the tissues.

IV Drip Rate (Drops per Minute)

Rgtt=V⋅ftR_{gtt} = \frac{V \cdot f}{t}

Biomedical & ClinicalDrops per minute for a gravity-fed IV set: the volume, multiplied by the tubing's drop factor, divided by the time.

IV Infusion Rate (mL per Hour)

R=VtR = \frac{V}{t}

Biomedical & ClinicalEveryday & HealthThe rate to set on a volumetric infusion pump: the volume to be infused divided by the time it should take.

Loading Dose from Volume of Distribution

DL=Vd⋅CpD_L = V_d \cdot C_p

Biomedical & ClinicalThe dose that fills the apparent volume of distribution to a target plasma concentration in one step, before any elimination.

Maintenance Dose Rate from Clearance

R=CL⋅CpR = \mathrm{CL} \cdot C_p

Biomedical & ClinicalThe rate of drug administration that exactly replaces what clearance removes, holding a steady-state plasma concentration.

Mean Arterial Pressure (MAP)

MAP=DBP+SBP−DBP3\mathrm{MAP} = \mathrm{DBP} + \frac{\mathrm{SBP} - \mathrm{DBP}}{3}

Biomedical & ClinicalThe time-weighted average arterial pressure over a cardiac cycle, estimated as the diastolic pressure plus one third of the pulse pressure.

Minute Ventilation (Tidal Volume × Respiratory Rate)

V˙E=VT⋅RR\dot{V}_E = V_T \cdot \mathrm{RR}

Biomedical & ClinicalThe total volume of gas moved into the lungs each minute: the volume of one breath multiplied by the number of breaths.

Nernst Equilibrium Potential for a Membrane Ion (37 °C)

Eion=61.5zlog⁡10CoutCinE_{ion} = \frac{61.5}{z}\log_{10}\frac{C_{out}}{C_{in}}

Biomedical & ClinicalThe membrane voltage at which an ion's electrical and chemical driving forces cancel, in the millivolt form physiologists use at 37 °C.

Serum Anion Gap

AG=Na+−(Cl−+HCO3−)\mathrm{AG} = \mathrm{Na^+} - (\mathrm{Cl^-} + \mathrm{HCO_3^-})

Biomedical & ClinicalChemistryThe difference between the measured cation and the measured anions in serum, the standard first split in the workup of a metabolic acidosis.

Systemic Vascular Resistance (SVR)

SVR=80 (MAP−CVP)CO\mathrm{SVR} = \frac{80\,(\mathrm{MAP} - \mathrm{CVP})}{\mathrm{CO}}

Biomedical & ClinicalSystemic vascular resistance in dyn·s·cm⁻⁵: the pressure drop across the systemic circuit divided by the flow through it, with the 80 that converts the units.