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
Hb96 g/LSaO₂91%PaO₂60 mmHgCaO₂?

Practice exercise (made-up values, not clinical guidance). A patient has Hb 96 g/L, SaO₂ 91% and PaO₂ 60 mmHg (8.0 kPa). Find the arterial oxygen content CaO₂ = 1.34 × Hb (g/dL) × SaO₂ + 0.003 × PaO₂ (mmHg) in mL O₂/dL.

Hb 96 g/LSaO₂ 91%PaO₂ 60 mmHg (8.0 kPa)
CaO₂ = mL/dL
2.Oxygen therapy & respiratory calculationsHard
86 kg175 cm♀6 mL/kg PBWVT​ = ? mL

Practice exercise (made-up values, not clinical guidance). A ventilated woman is 175 cm tall and weighs 86 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.

175 cm86 kg6 mL/kg
VT = mL
3.Arterial blood gas interpretationMedium
pH7.357.457.42PaCO₂mmHg354527HCO₃⁻mmol/L222617uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.42, PaCO₂ 27 mmHg (3.6 kPa) and HCO₃⁻ 17 mmol/L. The primary disorder is respiratory alkalosis. How far is it compensated? Click your answer.

pH 7.42PaCO₂ 27 mmHg (3.6 kPa)HCO₃⁻ 17 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
4.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 28% oxygen shows PaO₂ 83 mmHg (11.1 kPa) and PaCO₂ 51 mmHg (6.8 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 28%PaO₂ 83 mmHg (11.1 kPa)PaCO₂ 51 mmHg (6.8 kPa)
A–a gradient = mmHg
5.Clinical assessment scoresMedium
H? / 25+D? / 15+Aid? / 30+IV? / 20+G? / 20+MS? / 15Σ?

Practice exercise (made-up values, not clinical guidance). A practice patient is assessed with the Morse fall scale: history of falling in the last 3 months: no; secondary diagnosis: no; ambulatory aid: crutches, cane or walker; IV therapy or saline lock: yes; gait: weak; mental status: overestimates or forgets limits. Find the Morse total MFS.

0–125
MFS =
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 18/min, SpO₂ 94% on room air, blood pressure 130/78 mmHg, pulse 88/min, alert, temperature 35.8 °C. Which clinical risk group does the patient fall into? Click it.

RR 18SpO₂ 94%airSBP 130HR 88AT 35.8 °C
  1. 1low
  2. 2low–medium
  3. 3medium
  4. 4high
7.Med-surg: cardiovascular & respiratoryMedium

A patient on warfarin has started eating large spinach and kale salads every day. What is the main concern?

  1. AThe extra vitamin K may lower the INR
  2. BThe extra vitamin K may raise the INR
  3. CGreen vegetables damage the liver on warfarin
  4. DThere is no interaction between food and warfarin
8.Med-surg: cardiovascular & respiratoryHard

A patient with an inferior myocardial infarction develops complete heart block with a heart rate of 38/min. What is the most likely reason?

  1. AThe left anterior descending artery supplies the SA node only
  2. BHeart block is caused by the thrombolytic drug
  3. CThe right coronary artery usually supplies the AV node
  4. DInferior infarcts always destroy the bundle of His permanently

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: CaO₂ = 11.89 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

96 g/L = 9.6 g/dL

Bound oxygen

1.34·9.6·0.91 = 11.71 mL/dL

Dissolved oxygen

0.003·60 = 0.18 mL/dL

Oxygen content

CaO₂ = 11.71 + 0.18 = 11.89 mL/dL

Answer

CaO₂ = 11.89 mL/dL
2.Oxygen therapy & respiratory calculations

Answer: VT = 396 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·(175 − 152.4) = 66.07 kg

Tidal volume

VT = 6·66.07 = 396.4 ≈ 396 mL

Answer

VT = 396 mL
3.Arterial blood gas interpretation

Answer: fully compensated

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 7.42: within 7.35–7.45
PaCO₂ 27 mmHg: low (35–45)
HCO₃⁻ 17 mmol/L: low (22–26)

Compensation

fully compensated

Answer

fully compensated
4.Arterial blood gas interpretation

Answer: A–a gradient = 52.89 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 = 0.28·713 − 51/0.8 = 199.6 − 63.75 = 135.9 mmHg

Gradient

A–a = 135.9 − 83 = 52.89 mmHg

Answer

A–a gradient = 52.89 mmHg
5.Clinical assessment scores

Answer: MFS = 60

Morse fall scale: six items. History of falling: no 0, yes 25. Secondary diagnosis: no 0, yes 15. Ambulatory aid: none, bed rest or nurse assistance 0; crutches, cane or walker 15; holding on to furniture 30. IV therapy or saline lock: no 0, yes 20. Gait: normal, bed rest or wheelchair 0; weak 10; impaired 20. Mental status: knows own limits 0; overestimates or forgets limits 15. The total runs from 0 to 125. Risk cut-offs differ between hospitals; a common set is 0–24 low, 25–44 moderate and 45 or more high.

Score each item

history of falling in the last 3 months: no → 0
secondary diagnosis: no → 0
ambulatory aid: crutches, cane or walker → 15
IV therapy or saline lock: yes → 20
gait: weak → 10
mental status: overestimates or forgets limits → 15

Add

Morse total = 0 + 0 + 15 + 20 + 10 + 15 = 60

Answer

MFS = 60
6.Clinical assessment scores

Answer: low

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 18/min → 0
SpO₂ 94% → 1
on air → 0
SBP 130 mmHg → 0
HR 88/min → 0
alert (A) → 0
T 35.8 °C → 1

Total and red scores

NEWS2 = 0 + 1 + 0 + 0 + 0 + 0 + 1 = 2
No parameter scores 3.

Risk group

low

Answer

low
7.Med-surg: cardiovascular & respiratory

Answer: A · The extra vitamin K may lower the INR

Why this is the answer

A sudden increase in vitamin K intake can reduce the INR and increase clot risk. Patients do not have to avoid these foods but should keep their intake consistent and tell the anticoagulation service about big dietary changes.

Answer

A · The extra vitamin K may lower the INR
8.Med-surg: cardiovascular & respiratory

Answer: C · The right coronary artery usually supplies the AV node

Why this is the answer

In most people the right coronary artery supplies the inferior wall and the AV node, so inferior MI can cause AV block. It is often temporary and may respond to atropine, but symptomatic or persistent block may need temporary pacing.

Answer

C · The right coronary artery usually supplies the AV node

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