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
Hb121 g/LSaO₂98%PaO₂103 mmHgCaO₂?

Practice exercise (made-up values, not clinical guidance). A patient has Hb 121 g/L, SaO₂ 98% and PaO₂ 103 mmHg (13.7 kPa). Find the arterial oxygen content CaO₂ = 1.34 × Hb (g/dL) × SaO₂ + 0.003 × PaO₂ (mmHg) in mL O₂/dL.

Hb 121 g/LSaO₂ 98%PaO₂ 103 mmHg (13.7 kPa)
CaO₂ = mL/dL
2.Oxygen therapy & respiratory calculationsHard
60 kg153 cm♀6 mL/kg PBWVT​ = ? mL

Practice exercise (made-up values, not clinical guidance). A ventilated woman is 153 cm tall and weighs 60 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.

153 cm60 kg6 mL/kg
VT = mL
3.Arterial blood gas interpretationMedium
pH7.357.457.59PaCO₂mmHg354526HCO₃⁻mmol/L222624uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.59, PaCO₂ 26 mmHg (3.5 kPa) and HCO₃⁻ 24 mmol/L. The primary disorder is respiratory alkalosis. How far is it compensated? Click your answer.

pH 7.59PaCO₂ 26 mmHg (3.5 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 40% oxygen shows PaO₂ 80 mmHg (10.7 kPa) and PaCO₂ 30 mmHg (4.0 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 40%PaO₂ 80 mmHg (10.7 kPa)PaCO₂ 30 mmHg (4.0 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: yes; secondary diagnosis: yes; ambulatory aid: crutches, cane or walker; IV therapy or saline lock: yes; gait: normal, bed rest or wheelchair; mental status: knows own limits. Find the Morse total MFS.

0–125
MFS =
6.Clinical assessment scoresHard
reassuringmoderately abnormallow

Practice exercise (made-up values, not clinical guidance). At 5 minutes after birth, a practice newborn has a pink body with blue hands and feet, a heart rate of 75/min, a grimace when stimulated, active movement and no breathing. Score the APGAR and click how the score is interpreted.

  1. 1reassuring
  2. 2moderately abnormal
  3. 3low
7.Med-surg: cardiovascular & respiratoryMedium

Why is intravenous furosemide given slowly rather than as a rapid push of a large dose?

  1. ARapid doses cause the potassium level to rise
  2. BRapid high doses can damage hearing
  3. CRapid doses cause severe constipation
  4. DSlow injection makes the urine output larger
8.Med-surg: cardiovascular & respiratoryHard

A 70-year-old man has a small abdominal aortic aneurysm found on screening and is placed under surveillance. Which advice is most important?

  1. AStop smoking, control BP and seek help at once for sudden back pain
  2. BAvoid all exercise and lifting for the rest of his life to protect the aorta
  3. CStop all blood pressure medicines to avoid low pressure
  4. DHave the aneurysm repaired immediately, whatever its size or growth rate

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: CaO₂ = 16.2 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

121 g/L = 12.1 g/dL

Bound oxygen

1.34·12.1·0.98 = 15.89 mL/dL

Dissolved oxygen

0.003·103 = 0.309 mL/dL

Oxygen content

CaO₂ = 15.89 + 0.309 = 16.2 mL/dL

Answer

CaO₂ = 16.2 mL/dL
2.Oxygen therapy & respiratory calculations

Answer: VT = 276 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·(153 − 152.4) = 46.05 kg

Tidal volume

VT = 6·46.05 = 276.3 ≈ 276 mL

Answer

VT = 276 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 7.59: alkalaemia (above 7.45)
PaCO₂ 26 mmHg: low (35–45)
HCO₃⁻ 24 mmol/L: normal (22–26)

Compensation

uncompensated

Answer

uncompensated
4.Arterial blood gas interpretation

Answer: A–a gradient = 167.7 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 = 0.4·713 − 30/0.8 = 285.2 − 37.5 = 247.7 mmHg

Gradient

A–a = 247.7 − 80 = 167.7 mmHg

Answer

A–a gradient = 167.7 mmHg
5.Clinical assessment scores

Answer: MFS = 75

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: yes → 25
secondary diagnosis: yes → 15
ambulatory aid: crutches, cane or walker → 15
IV therapy or saline lock: yes → 20
gait: normal, bed rest or wheelchair → 0
mental status: knows own limits → 0

Add

Morse total = 25 + 15 + 15 + 20 + 0 + 0 = 75

Answer

MFS = 75
6.Clinical assessment scores

Answer: moderately abnormal

APGAR score: five signs, each scored 0, 1 or 2, checked at 1 and 5 minutes after birth. Appearance (colour): blue or pale 0, pink body with blue extremities 1, pink all over 2. Pulse: absent 0, below 100/min 1, 100/min or more 2. Grimace (reflex irritability): none 0, grimace 1, cry, cough or sneeze 2. Activity (tone): limp 0, some flexion 1, active movement 2. Respiration: absent 0, slow or irregular with a weak cry 1, good with a strong cry 2. A total of 7–10 is reassuring, 4–6 moderately abnormal and 0–3 low.

Score each sign

Appearance: a pink body with blue hands and feet → 1
Pulse: 75/min → 1
Grimace: a grimace when stimulated → 1
Activity: active movement → 2
Respiration: no breathing → 0

Add

APGAR = 1 + 1 + 1 + 2 + 0 = 5

Interpretation

5 → moderately abnormal

Answer

moderately abnormal

Below 7 at 5 minutes, the score is usually repeated every 5 minutes up to 20 minutes.

7.Med-surg: cardiovascular & respiratory

Answer: B · Rapid high doses can damage hearing

Why this is the answer

High plasma levels of loop diuretics can cause tinnitus and hearing loss (ototoxicity), especially with fast injection, renal impairment or other ototoxic drugs such as aminoglycosides. Large IV doses are therefore given slowly.

Answer

B · Rapid high doses can damage hearing
8.Med-surg: cardiovascular & respiratory

Answer: A · Stop smoking, control BP and seek help at once for sudden back pain

Why this is the answer

Small aneurysms are usually monitored with regular ultrasound, with repair considered when they reach a threshold size or grow fast. Stopping smoking slows growth, and BP and cardiovascular risk are managed. Sudden abdominal or back pain may mean rupture and needs emergency care.

Answer

A · Stop smoking, control BP and seek help at once for sudden back pain

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