Respiratory Care and Oxygen Therapy: cram pack

Formula sheets, the key method steps for every topic and 8 practice problems, with full solutions at the back.

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1Formulas and methods

Oxygen therapy & respiratory calculations

Nasal cannula
FiO₂ ≈ 21% + 4% × L/min (1–6 L/min)
Cylinder duration
min = (psi − 200) × factor / (L/min); D 0.16, E 0.28, H 3.14 L/psi
Minute and alveolar ventilation
V̇E = VT·f, V̇A = (VT − VD)·f
Predicted body weight
men 50 + 0.91 × (cm − 152.4); women 45.5 + 0.91 × (cm − 152.4)
P/F ratio (Berlin, PEEP ≥ 5)
mild > 200–300, moderate > 100–200, severe ≤ 100 mmHg
Oxygen content
CaO₂ = 1.34·Hb·SaO₂ + 0.003·PaO₂
Oxygen delivery
DO₂ = CaO₂ × CO × 10
ROX index
(SpO₂/FiO₂)/RR

Method

  1. Put every value in the units of the formula: FiO₂ and SaO₂ as fractions, PaO₂ in mmHg, Hb in g/dL.
  2. For a cylinder, subtract the safe residual, multiply by the cylinder factor and divide by the flow.
  3. Round cylinder times and flows down, never up.
  4. For the P/F ratio, check the PEEP first, then divide PaO₂ by FiO₂ and compare with 300, 200 and 100 mmHg.
  5. For ventilation, subtract the dead space for alveolar ventilation and use the predicted body weight for tidal volumes.

Arterial blood gas interpretation

Normal ranges
pH 7.35–7.45, PaCO₂ 35–45 mmHg (4.7–6.0 kPa), HCO₃⁻ 22–26 mmol/L
ROME
Respiratory: PaCO₂ opposite to pH; Metabolic: HCO₃⁻ equal to pH
Winter’s formula
PaCO₂ = 1.5·HCO₃⁻ + 8 ± 2
Metabolic alkalosis
PaCO₂ ≈ 0.7·HCO₃⁻ + 21
Anion gap
AG = Na⁺ − (Cl⁻ + HCO₃⁻) ≈ 8–12
Albumin-corrected gap
AG + 2.5·(4.0 − alb g/dL) = AG + 0.25·(40 − alb g/L)
Delta ratio
(AG − 12)/(24 − HCO₃⁻)
P/F ratio
PaO₂/FiO₂
Alveolar gas equation
PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8
Serum osmolality
2·Na⁺ + glucose + urea (2·Na⁺ + glucose/18 + BUN/2.8)

Method

  1. Read the pH: below 7.35 is acidosis, above 7.45 alkalosis.
  2. Find the value that explains it: PaCO₂ moving opposite to the pH is respiratory, HCO₃⁻ moving with the pH is metabolic.
  3. Look at the other value: normal means uncompensated, abnormal in the compensating direction means partial compensation, and a normal pH with both abnormal means full compensation.
  4. In a metabolic acidosis, compare PaCO₂ with Winter’s formula, 1.5·HCO₃⁻ + 8 ± 2, and calculate the anion gap Na⁺ − (Cl⁻ + HCO₃⁻).
  5. Check a high anion gap with the delta ratio and, when albumin is low, with the corrected gap.

Clinical assessment scores

Glasgow Coma Scale
GCS = E (1–4) + V (1–5) + M (1–6) = 3–15
APGAR
5 signs × 0–2 = 0–10; 7–10 reassuring, 4–6 moderately abnormal, 0–3 low
Braden scale
5 × (1–4) + 1 × (1–3) = 6–23; ≤ 18 at risk
Morse fall scale
falls 25, diagnosis 15, aid 15/30, IV 20, gait 10/20, mental status 15
NEWS2 risk
0–4 low; single 3 low–medium; 5–6 medium; ≥ 7 high
Mean arterial pressure
MAP = (SBP + 2·DBP)/3 = DBP + PP/3
Pulse pressure and shock index
PP = SBP − DBP, SI = HR/SBP
Body mass index
BMI = kg/m² = 703·lb/in²

Method

  1. Find the score sheet that the question uses and its range (GCS 3–15, APGAR 0–10, Braden 6–23, Morse 0–125).
  2. Score every item separately, matching the description to its level.
  3. Add the item scores and check that the total lies inside the range.
  4. Apply the cut-offs: for NEWS2 also look for any single parameter scoring 3.
  5. For derived values use MAP = (SBP + 2·DBP)/3, PP = SBP − DBP, SI = HR/SBP and BMI = kg/m².

Med-surg: cardiovascular & respiratory

Method

  1. Name the problem: pump failure, blocked artery, rhythm, clot, airway narrowing, infection or a device problem.
  2. Check the danger signs first: hypoxia, hypotension, chest pain, new confusion, a cold pulseless limb.
  3. Match the oxygen to the patient: 94–98% for most, 88–92% for those at risk of CO₂ retention.
  4. Link each drug to its test and its risk: warfarin and INR, heparin and aPTT and platelets, diuretics and potassium.
  5. Choose the safe first action, then escalate and reassess.

2Practice problems

1.Oxygen therapy & respiratory calculationsMedium
Hb81 g/LSaO₂98%PaO₂102 mmHgCaO₂?

Practice exercise (made-up values, not clinical guidance). A patient has Hb 81 g/L, SaO₂ 98% and PaO₂ 102 mmHg (13.6 kPa). Find the arterial oxygen content CaO₂ = 1.34 × Hb (g/dL) × SaO₂ + 0.003 × PaO₂ (mmHg) in mL O₂/dL.

Hb 81 g/LSaO₂ 98%PaO₂ 102 mmHg (13.6 kPa)
CaO₂ = mL/dL
2.Oxygen therapy & respiratory calculationsHard
94 kg182 cm♀6 mL/kg PBWVT​ = ? mL

Practice exercise (made-up values, not clinical guidance). A ventilated woman is 182 cm tall and weighs 94 kg. Lung-protective ventilation is set at 6 mL per kg of predicted body weight. Using PBW = 45.5 + 0.91 × (height cm − 152.4) kg, find the tidal volume VT to the nearest mL.

182 cm94 kg6 mL/kg
VT = mL
3.Arterial blood gas interpretationMedium
pH7.357.457.53PaCO₂mmHg354530HCO₃⁻mmol/L222624uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.53, PaCO₂ 30 mmHg (4.0 kPa) and HCO₃⁻ 24 mmol/L. The primary disorder is respiratory alkalosis. How far is it compensated? Click your answer.

pH 7.53PaCO₂ 30 mmHg (4.0 kPa)HCO₃⁻ 24 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
4.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 24% oxygen shows PaO₂ 55 mmHg (7.3 kPa) and PaCO₂ 35 mmHg (4.7 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 24%PaO₂ 55 mmHg (7.3 kPa)PaCO₂ 35 mmHg (4.7 kPa)
A–a gradient = mmHg
5.Clinical assessment scoresMedium
S? / 4+M? / 4+A? / 4+Mob? / 4+N? / 4+F? / 3Σ?

Practice exercise (made-up values, not clinical guidance). A practice patient is assessed with the Braden scale: sensory perception: completely limited; moisture: rarely moist; activity: chairfast; mobility: completely immobile; nutrition: probably inadequate; friction and shear: problem. Find the Braden total B.

6–23
B =
6.Clinical assessment scoresHard
3210123RR≤89–1112–2021–24≥25SpO₂≤9192–9394–95≥96air / O₂O₂airSBP≤9091–100101–110111–219≥220HR≤4041–5051–9091–110111–130≥131ACVPUAC, V, P, UT °C≤35.035.1–36.036.1–38.038.1–39.0≥39.1lowlow–mediummediumhigh

Practice exercise (made-up values, not clinical guidance). Use the NEWS2 chart (SpO₂ scale 1) for these observations: respiration rate 20/min, SpO₂ 97% on room air, blood pressure 112/68 mmHg, pulse 70/min, responds only to pain, temperature 37.8 °C. Which clinical risk group does the patient fall into? Click it.

RR 20SpO₂ 97%airSBP 112HR 70PT 37.8 °C
  1. 1low
  2. 2low–medium
  3. 3medium
  4. 4high
7.Med-surg: cardiovascular & respiratoryMedium

A patient with a mechanical heart valve asks to switch from warfarin to apixaban. What is the correct response?

  1. AMechanical valves do not need anticoagulation after the first month
  2. BAny anticoagulant works equally well once the valve is in place
  3. CDirect oral anticoagulants are not used for mechanical valves
  4. DAspirin alone can replace warfarin once the valve has healed
8.Med-surg: cardiovascular & respiratoryHard

A patient with pneumonia on high-flow nasal oxygen at 50 L/min with FiO₂ 0.6 has SpO₂ 90%, RR 34/min and is using accessory muscles. What is the most appropriate action?

  1. AContinue the same support and recheck in four hours
  2. BChange to a nasal cannula at 4 L/min to reduce nasal dryness
  3. CEscalate urgently to critical care for review of respiratory support
  4. DLay the patient flat so they can rest the breathing muscles

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: CaO₂ = 10.94 mL/dL

Oxygen content and delivery: CaO₂ = 1.34 × Hb (g/dL) × SaO₂ + 0.003 × PaO₂ (mmHg), in mL O₂ per dL of blood, with SaO₂ as a fraction. Almost all oxygen is bound to haemoglobin; the dissolved part is small. Delivery DO₂ = CaO₂ × cardiac output (L/min) × 10 (mL/min), because 1 L = 10 dL; a normal resting adult value is about 1000 mL/min.

Hb in g/dL

81 g/L = 8.1 g/dL

Bound oxygen

1.34·8.1·0.98 = 10.64 mL/dL

Dissolved oxygen

0.003·102 = 0.306 mL/dL

Oxygen content

CaO₂ = 10.64 + 0.306 = 10.94 mL/dL

Answer

CaO₂ = 10.94 mL/dL
2.Oxygen therapy & respiratory calculations

Answer: VT = 435 mL

Ventilation: minute ventilation V̇E = tidal volume × respiratory rate (normal adult about 5–8 L/min). Alveolar ventilation V̇A = (tidal volume − dead space) × rate, because the air in the airways (about 150 mL in an adult) takes no part in gas exchange. Lung-protective ventilation uses about 6 mL per kg of predicted body weight (PBW): men 50 + 0.91 × (height in cm − 152.4) kg, women 45.5 + 0.91 × (height in cm − 152.4) kg (with inches: 2.3 per inch above 60 in).

Predicted body weight

PBW = 45.5 + 0.91·(182 − 152.4) = 72.44 kg

Tidal volume

VT = 6·72.44 = 434.6 ≈ 435 mL

Answer

VT = 435 mL
3.Arterial blood gas interpretation

Answer: uncompensated

Reading a blood gas (ROME): first the pH: below 7.35 is acidaemia, above 7.45 alkalaemia. Then find the value that explains it. PaCO₂ (normal 35–45 mmHg, 4.7–6.0 kPa) is the respiratory part and moves Opposite to the pH in a respiratory disorder; HCO₃⁻ (normal 22–26 mmol/L) is the metabolic part and moves in the same direction as the pH (Respiratory Opposite, Metabolic Equal). The other value shows the compensation: normal means uncompensated; abnormal in the direction that pulls the pH back while the pH is still abnormal means partially compensated; a normal pH with both values abnormal means fully compensated. Ranges differ slightly between laboratories; these are practice values.

ROME, value by value

pH 7.53: alkalaemia (above 7.45)
PaCO₂ 30 mmHg: low (35–45)
HCO₃⁻ 24 mmol/L: normal (22–26)

Compensation

uncompensated

Answer

uncompensated
4.Arterial blood gas interpretation

Answer: A–a gradient = 72.37 mmHg

Derived values: calculated serum osmolality is 2·Na⁺ + glucose + urea with all values in mmol/L (2·Na⁺ + glucose/18 + BUN/2.8 with glucose and BUN in mg/dL); normal is about 275–295 mOsm/kg. The P/F ratio is PaO₂ divided by FiO₂ as a fraction. The alveolar oxygen pressure is PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 mmHg at sea level, and the A–a gradient is PAO₂ − PaO₂.

Alveolar oxygen

PAO₂ = 0.24·713 − 35/0.8 = 171.1 − 43.75 = 127.4 mmHg

Gradient

A–a = 127.4 − 55 = 72.37 mmHg

Answer

A–a gradient = 72.37 mmHg
5.Clinical assessment scores

Answer: B = 11

Braden scale: six subscales for pressure-injury risk. Sensory perception, moisture, activity, mobility and nutrition score 1 to 4, from the worst level (1) to no problem (4); friction and shear scores 1 to 3. The total runs from 6 to 23, and a lower total means a higher risk. Common bands: 19–23 not at risk, 15–18 mild risk, 13–14 moderate risk, 10–12 high risk and 9 or below very high risk.

Score each subscale

sensory perception: completely limited → 1
moisture: rarely moist → 4
activity: chairfast → 2
mobility: completely immobile → 1
nutrition: probably inadequate → 2
friction and shear: problem → 1

Add

Braden total = 1 + 4 + 2 + 1 + 2 + 1 = 11

Answer

B = 11
6.Clinical assessment scores

Answer: low–medium

NEWS2 (National Early Warning Score 2, Royal College of Physicians 2017): score each of the seven parameters with the chart (respiration rate, SpO₂ on scale 1, air or supplemental oxygen, systolic blood pressure, pulse, consciousness on the ACVPU scale and temperature) and add the scores. Clinical risk: 0–4 low; a score of 3 in any single parameter low–medium; 5–6 medium; 7 or more high. A total of 5 or more needs an urgent response.

Score each parameter

RR 20/min → 0
SpO₂ 97% → 0
on air → 0
SBP 112 mmHg → 0
HR 70/min → 0
responds only to pain (P) → 3
T 37.8 °C → 0

Total and red scores

NEWS2 = 0 + 0 + 0 + 0 + 0 + 3 + 0 = 3
At least one parameter scores 3.

Risk group

low–medium

Answer

low–medium

A single score of 3 needs an urgent review even when the total is low.

7.Med-surg: cardiovascular & respiratory

Answer: C · Direct oral anticoagulants are not used for mechanical valves

Why this is the answer

Mechanical valves need lifelong anticoagulation with a vitamin K antagonist such as warfarin. Direct oral anticoagulants caused more clots and bleeding in mechanical valve patients and are contraindicated. Biological valves usually need only short-term anticoagulation.

Answer

C · Direct oral anticoagulants are not used for mechanical valves
8.Med-surg: cardiovascular & respiratory

Answer: C · Escalate urgently to critical care for review of respiratory support

Why this is the answer

High oxygen requirements with tachypnoea and increased work of breathing despite high-flow oxygen indicate worsening respiratory failure. Early critical care review is needed for escalation such as CPAP, NIV or intubation. Reducing support or waiting risks a respiratory arrest.

Answer

C · Escalate urgently to critical care for review of respiratory support

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