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
Hb156 g/LSaO₂98%PaO₂101 mmHgCaO₂?

Practice exercise (made-up values, not clinical guidance). A patient has Hb 156 g/L, SaO₂ 98% and PaO₂ 101 mmHg (13.5 kPa). Find the arterial oxygen content CaO₂ = 1.34 × Hb (g/dL) × SaO₂ + 0.003 × PaO₂ (mmHg) in mL O₂/dL.

Hb 156 g/LSaO₂ 98%PaO₂ 101 mmHg (13.5 kPa)
CaO₂ = mL/dL
2.Oxygen therapy & respiratory calculationsHard
81 kg162 cm♀5 mL/kg PBWVT​ = ? mL

Practice exercise (made-up values, not clinical guidance). A ventilated woman is 162 cm tall and weighs 81 kg. Lung-protective ventilation is set at 5 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.

162 cm81 kg5 mL/kg
VT = mL
3.Arterial blood gas interpretationMedium

A practice gas shows PaCO₂ 24 mmHg (3.2 kPa). Use the rule that in acute respiratory alkalosis HCO₃⁻ falls by 2 mmol/L for every 10 mmHg that PaCO₂ is below 40, starting from HCO₃⁻ 24 mmol/L, to find the expected HCO₃⁻.

PaCO₂ 24 mmHg (3.2 kPa)baseline: 40 mmHg, 24 mmol/L
HCO₃⁻ = mmol/L
4.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 21% oxygen shows PaO₂ 50 mmHg (6.7 kPa) and PaCO₂ 33 mmHg (4.4 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 21%PaO₂ 50 mmHg (6.7 kPa)PaCO₂ 33 mmHg (4.4 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: none, bed rest or nurse assists; IV therapy or saline lock: no; gait: weak; mental status: knows own limits. Find the Morse total MFS.

0–125
MFS =
6.Clinical assessment scoresHard
low riskmoderate riskhigh risk

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: none, bed rest or nurse assists; IV therapy or saline lock: no; gait: weak; mental status: knows own limits. Using the cut-offs 0–24 low, 25–44 moderate and 45 or more high, click the fall-risk level.

  1. 1low risk
  2. 2moderate risk
  3. 3high risk
7.Med-surg: cardiovascular & respiratoryMedium

What is the main difference between CPAP and bilevel NIV (often called BiPAP)?

  1. ACPAP is mainly used to lower a raised PaCO₂ in COPD exacerbations
  2. BBilevel NIV gives oxygen only, without any positive airway pressure
  3. CCPAP is given only through a tracheostomy
  4. DBilevel NIV adds a higher inspiratory pressure, helping remove CO₂
8.Med-surg: cardiovascular & respiratoryHard

Shortly after a thoracentesis, a patient becomes breathless with sharp chest pain and reduced breath sounds on the same side. What complication is most likely?

  1. APulmonary embolism from the leg
  2. BPneumothorax
  3. CInfection at the puncture site
  4. DRe-accumulation of the effusion

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: CaO₂ = 20.79 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

156 g/L = 15.6 g/dL

Bound oxygen

1.34·15.6·0.98 = 20.49 mL/dL

Dissolved oxygen

0.003·101 = 0.303 mL/dL

Oxygen content

CaO₂ = 20.49 + 0.303 = 20.79 mL/dL

Answer

CaO₂ = 20.79 mL/dL
2.Oxygen therapy & respiratory calculations

Answer: VT = 271 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·(162 − 152.4) = 54.24 kg

Tidal volume

VT = 5·54.24 = 271.2 ≈ 271 mL

Answer

VT = 271 mL
3.Arterial blood gas interpretation

Answer: HCO₃⁻ = 20.8 mmol/L

Expected compensation: in metabolic acidosis Winter’s formula predicts PaCO₂ = 1.5·HCO₃⁻ + 8 ± 2 mmHg; a measured value above that range points to an additional respiratory acidosis, below it to an additional respiratory alkalosis. The anion gap AG = Na⁺ − (Cl⁻ + HCO₃⁻), normally about 8–12 mmol/L, separates high-gap from normal-gap metabolic acidosis; low albumin hides a high gap (add 2.5 per g/dL that albumin is below 4.0). The delta ratio (AG − 12)/(24 − HCO₃⁻) between about 0.8 and 2 fits a pure high-gap acidosis (some texts use 1 instead of 0.8), below that an added normal-gap acidosis, and above 2 an added metabolic alkalosis.

Change in PaCO₂

|24 − 40| = 16 mmHg → 1.6 × 10 mmHg

Expected HCO₃⁻

HCO₃⁻ = 24 − 2·1.6 = 20.8 mmol/L

Answer

HCO₃⁻ = 20.8 mmol/L
4.Arterial blood gas interpretation

Answer: A–a gradient = 58.48 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 = 0.21·713 − 33/0.8 = 149.7 − 41.25 = 108.5 mmHg

Gradient

A–a = 108.5 − 50 = 58.48 mmHg

Answer

A–a gradient = 58.48 mmHg
5.Clinical assessment scores

Answer: MFS = 50

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: none, bed rest or nurse assists → 0
IV therapy or saline lock: no → 0
gait: weak → 10
mental status: knows own limits → 0

Add

Morse total = 25 + 15 + 0 + 0 + 10 + 0 = 50

Answer

MFS = 50
6.Clinical assessment scores

Answer: low risk

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: none, bed rest or nurse assists → 0
IV therapy or saline lock: no → 0
gait: weak → 10
mental status: knows own limits → 0

Add

Morse total = 0 + 0 + 0 + 0 + 10 + 0 = 10

Risk level

10 → low risk

Answer

low risk
7.Med-surg: cardiovascular & respiratory

Answer: D · Bilevel NIV adds a higher inspiratory pressure, helping remove CO₂

Why this is the answer

CPAP gives one continuous pressure that splints the airways and alveoli open, improving oxygenation (for example in pulmonary oedema or OSA). Bilevel NIV adds a higher inspiratory pressure that supports ventilation, so it is used for hypercapnic respiratory failure such as COPD exacerbations.

Answer

D · Bilevel NIV adds a higher inspiratory pressure, helping remove CO₂
8.Med-surg: cardiovascular & respiratory

Answer: B · Pneumothorax

Why this is the answer

Pneumothorax is a common complication of thoracentesis, caused by the needle puncturing the lung or air entering the chest. The nurse assesses the patient, gives oxygen and informs the team, who will arrange a chest X-ray. An effusion re-accumulates over days, and infection appears later.

Answer

B · Pneumothorax

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