RT Formula Library

Alveolar Oxygen Tension

PAO₂ = FiO₂ × (Patm − 47) − PaCO₂ / RQ

PAO₂ represents the theoretical oxygen tension in the alveolar gas. It is the driving pressure available to push oxygen across the alveolar-capillary membrane into pulmonary blood. The alveolar gas equation accounts for the dilution of oxygen by water vapor and CO₂. It is not measured directly but calculated from known variables.

Alveolar-Arterial Oxygen Gradient

A-a = PAO₂ − PaO₂

The A-a gradient measures the difference between the oxygen tension in the alveoli (PAO₂) and the oxygen in the arterial blood (PaO₂). An elevated gradient indicates a gas exchange problem: the alveolus is full of oxygen but it is not transferring efficiently into the blood. A normal gradient with hypoxemia points to hypoventilation or low inspired O₂ as the cause.

PaO₂/FiO₂ Ratio (Horowitz Index)

P/F = PaO₂ ÷ FiO₂

The P/F ratio provides a standardized measure of oxygenation efficiency that accounts for the FiO₂ being administered. It allows comparison of oxygenation across different oxygen concentrations. A ratio of 400 means the patient has a normal PaO₂ of 80 on room air (80/0.21 ≈ 381) or a normal response to any oxygen level.

Oxygen Content of Blood

CaO₂ = (Hgb × 1.34 × SaO₂) + (PaO₂ × 0.003)

Oxygen content is the total amount of oxygen carried in blood, both bound to hemoglobin (the dominant component) and dissolved in plasma (minor component). It reveals why anemia can cause tissue hypoxia even when SpO₂ is 100% — hemoglobin is the oxygen carrier, not plasma. The dissolved component contributes < 1.5% of total O₂ at normal PaO₂.

Oxygen Delivery

DO₂ = CaO₂ × CO × 10

Oxygen delivery quantifies the total amount of oxygen transported from the lungs to the systemic circulation per minute. It is the product of how much oxygen the blood carries (CaO₂) and how fast it is delivered (cardiac output). Tissues extract oxygen from this delivery to meet metabolic needs (VO₂).

Oxygenation Index

OI = (FiO₂ × MAP × 100) ÷ PaO₂

The oxygenation index is primarily used in neonatal and pediatric intensive care. It incorporates mean airway pressure (MAP) — the driving force for oxygenation — in addition to FiO₂ and PaO₂. A higher OI indicates more severe oxygenation failure because the patient requires higher MAP and/or FiO₂ to achieve the same PaO₂.

Minute Ventilation

V̇E = VT × RR

Minute ventilation is the total volume of gas moved in and out of the lungs per minute. It is the product of tidal volume and respiratory rate. Not all of this volume participates in gas exchange — a portion (dead space ventilation) ventilates airways that do not contact pulmonary capillaries. Minute ventilation is the primary determinant of PaCO₂.

Alveolar Ventilation

V̇A = (VT − VD) × RR

Alveolar ventilation is the portion of minute ventilation that actually reaches the alveoli and participates in gas exchange. It equals minute ventilation minus dead space ventilation. PaCO₂ is directly and inversely proportional to alveolar ventilation — only alveolar ventilation eliminates CO₂.

Dead Space Fraction (Bohr Equation)

VD/VT = (PaCO₂ − PeCO₂) ÷ PaCO₂

The VD/VT ratio represents the fraction of each breath that is 'wasted' by ventilating areas that receive air but have no blood flow (physiological dead space). Dead space includes anatomic dead space (conducting airways, ~150 mL) and alveolar dead space (alveoli with ventilation but no perfusion, as in PE or ARDS).

Driving Pressure

ΔP = Pplat − PEEP

Driving pressure represents the pressure swing applied to the alveoli with each breath — the actual 'tidal stress' delivered to lung tissue. It normalizes tidal volume to the functional lung size (respiratory system compliance). A high driving pressure indicates that each breath is exerting excessive mechanical stress on available lung units.

Rapid Shallow Breathing Index

RSBI = f ÷ VT (in liters)

The RSBI quantifies the balance between respiratory rate and tidal volume during spontaneous breathing. Patients in respiratory distress who are fatiguing tend to breathe rapidly and shallowly (high f, low VT) — producing a high RSBI. A low RSBI indicates the patient can take adequate breaths without tachypnea.

Static Lung Compliance

Cst = VT ÷ (Pplat − PEEP)

Static compliance reflects the elastic recoil properties of the lung and chest wall combined. Measured during no-flow conditions (end-inspiratory pause), it reflects the true distensibility of the respiratory system without the confounding effect of airway resistance. Low static compliance means the lungs are stiff and require more pressure for the same volume.

Dynamic Lung Compliance

Cdyn = VT ÷ (PIP − PEEP)

Dynamic compliance is measured during active gas flow and therefore reflects BOTH the elastic properties of the lung AND the resistance of the airways. It is always lower than static compliance because additional pressure is needed to overcome airway resistance during flow. The difference between static and dynamic compliance reveals the contribution of airway resistance.

Airway Resistance

Raw = (PIP − Pplat) ÷ Flow

Airway resistance measures how much pressure is required to move gas through the airways at a given flow rate. It reflects the diameter and length of the airways — narrower airways have exponentially higher resistance (Poiseuille's law: resistance ∝ 1/r⁴). The ETT itself contributes significantly to resistance in intubated patients.

Intrapulmonary Shunt Fraction

Qs/Qt = (CcO₂ − CaO₂) ÷ (CcO₂ − CvO₂)

The shunt fraction represents the proportion of cardiac output that passes through non-ventilated lung (or anatomic shunts) without participating in gas exchange. True shunt is distinguished from V/Q mismatch by failure to improve with 100% oxygen — if PaO₂ doesn't improve on FiO₂ 1.0, true shunt is present.

Ideal Body Weight (Male)

IBW (male) = 50 + 2.3 × (Height in inches − 60)

Ideal body weight estimates the weight corresponding to a healthy BMI for a given height. In mechanical ventilation, IBW is critical because lung size is determined by height, not actual body weight. Using actual body weight to calculate tidal volume in obese patients would cause dangerously large tidal volumes and volutrauma.

Ideal Body Weight (Female)

IBW (female) = 45.5 + 2.3 × (Height in inches − 60)

Female IBW uses the same formula structure as male but starts at 45.5 kg for 5 feet of height (versus 50 kg for males). This difference accounts for average gender-based differences in muscle mass and lean body composition relative to height.

Mean Arterial Pressure

MAP = DBP + ⅓ × (SBP − DBP) or MAP = (SBP + 2×DBP) ÷ 3

Mean arterial pressure represents the average arterial pressure throughout the cardiac cycle, weighted to reflect the longer diastolic period (approximately two-thirds of the cycle at rest). MAP is the true driving pressure for tissue perfusion — it better reflects organ blood flow than systolic BP alone. Autoregulation of most vital organs maintains flow constant across a MAP range of approximately 60–150 mmHg.