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Chapter 220. Important Formulae

Ruchir Gupta, MD

Allowable blood loss (ABL): weight (kg) × EBV × (Hinitial − Hfinal)/ Havg.

Total body deficit of HCO3: weight (kg) × (deviation from 24) × ECF.

Anion gap: Na + (Cl + HCO3).

  Normal 8–16.

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Perfusion to Various Body Compartments
CompartmentBody mass in adults (%)Cardiac output (%)
Vessel-rich group (brain, heart, liver, kidneys)1075
Muscles5019
Fat205
Vessel-poor group (bone, tendons)201
Table 220-1 Respiratory Formulae and Equations
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Table 220-1 Respiratory Formulae and Equations
Fick equation: VO2 (O2 consumption) (N: 250 mL/min)CO × (CaO2 − CvO2)
  • CO: cardiac output
  • CaO2: arterial oxygen content
  • CvO2: venous oxygen content
Alveolar gas equationPAO2 = (PB − 47)FiO2 − PaCO2/RQ
  • PB: barometric pressure
  • PA: alveolar pressure
  • RQ: respiratory quotient (0.8 on a typical diet)
  • Pa: arterial pressure
  • FiO2: fraction of inspired O2
A–a gradientPAO2 − PaO2
O2 content (N: 20 mL O2/dL)CaO2 = 1.39(Hb × SaO2) + (PaO2 × 0.003)
  • CaO2: arterial oxygen content
  • PaO2: arterial oxygen content
  • Hb: hemoglobin
Shunt fraction (N: 5%)
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  • CćO2: end capillary
  • O2 content
  • CaO2: arterial oxygen content
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    : mixed venous oxygen content
Oxygen delivery (N: 400–660 mL/min/m2)DO2 = CO × CaO2
Oxygen extraction(CaO2 − C
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)/CaO2
  • Bohr's equation (physiologic dead space)
  • Normal 25–30%
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: mixed expired CO2
Compliance
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  • PAP: peak airway pressure
  • Pplat: plateau pressure
Time constant definitionTotal compliance × airway resistance
Fractional SaO2
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SaO2: oxygen saturation of hemoglobin in the arterial blood
Laplace's lawT =PR/W

T: tension

W: wall thickness

Boyle's lawPfVf =P0V0, i.e., the PV product is constant
  • T: temperature
  • P: pressure
  • V: volume
Ideal gas lawPV =nRT
  • P: pressure
  • V: volume
  • n: number of moles of gas
  • R: universal gas constant = 8.31 J/moles/kg
  • T: temperature

Adapted from Schwartz's Principles of Surgery, Table 13-3.

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Cardiac Formulae
ParameterFormulaNormal range
Cardiac indexCO/BSA2.2–4.2 L/min/m2
Stroke volume indexSV/BSA40–70 mL/beats/m2
Left ventricular stroke work indexSI × 0.0136(MAP − PAOP)46–60 g m/beat/m2
Right ventricular stroke work indexSI × 0.0136(PA − CVP)30–65 g m/beat/m2
Stroke volumeCO × 1,000/HR40–80 mL
Pulmonary ...

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