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
PaO₂ 122 mmHg · FiO₂ 0.5 · PEEP 8 cmH₂O0100200300400500P/F (mmHg)above 300: no ARDS grademildmoderatesevere

Practice exercise (made-up values, not clinical guidance). A ventilated patient who meets the other Berlin criteria for ARDS has PaO₂ 122 mmHg (16.3 kPa) on 50% oxygen with a PEEP of 8 cmH₂O. Calculate the P/F ratio and click the ARDS severity.

PaO₂ 122 mmHg (16.3 kPa)FiO₂ 50%PEEP 8 cmH₂O
  1. 1above 300: no ARDS grade
  2. 2mild
  3. 3moderate
  4. 4severe
2.Oxygen therapy & respiratory calculationsHard
750psiDf = 0.16 L/psi20 minresidual 200 psiQ = ? L/min

Practice exercise (made-up values, not clinical guidance). A transfer will take 20 minutes. The size D cylinder (factor 0.16 L/psi) reads 750 psi. Keeping a safe residual of 200 psi, what is the highest whole-number flow Q in L/min that lasts the whole transfer?

20 min750 psif = 0.16 L/psi200 psi
Q = L/min
3.Arterial blood gas interpretationMedium

Practice values: Na⁺ 136 mmol/L, glucose 21.2 mmol/L and urea 20.4 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.

Na⁺ 136 mmol/Lglucose 21.2 mmol/Lurea 20.4 mmol/L
Osm = mOsm/kg
4.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 28% oxygen shows PaO₂ 52 mmHg (6.9 kPa) and PaCO₂ 33 mmHg (4.4 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 28%PaO₂ 52 mmHg (6.9 kPa)PaCO₂ 33 mmHg (4.4 kPa)
A–a gradient = mmHg
5.Clinical assessment scoresMedium
mildmoderatesevere

Practice exercise (made-up values, not clinical guidance). A practice patient after a head injury opens the eyes only to pressure (a painful stimulus), makes only incomprehensible sounds such as moaning and shows as the best motor response: no movement at all. Work out the GCS and classify the head injury by it. Click your answer.

  1. 1mild
  2. 2moderate
  3. 3severe
6.Clinical assessment scoresHard
not at riskmild riskmoderate riskhigh riskvery high risk

Practice exercise (made-up values, not clinical guidance). A practice patient is assessed with the Braden scale: sensory perception: no impairment; moisture: very moist; activity: walks occasionally; mobility: very limited; nutrition: adequate; friction and shear: problem. Use the bands 19–23 not at risk, 15–18 mild, 13–14 moderate, 10–12 high and 9 or below very high. Click the risk level.

  1. 1not at risk
  2. 2mild risk
  3. 3moderate risk
  4. 4high risk
  5. 5very high risk
7.Med-surg: cardiovascular & respiratoryMedium

A patient with heart failure starts spironolactone in addition to an ACE inhibitor. Which blood result needs close monitoring?

  1. APotassium, because both drugs can raise it
  2. BHaemoglobin, because both drugs can cause bleeding
  3. CCalcium, because both drugs can lower it
  4. DGlucose, because both drugs can cause hypoglycaemia
8.Med-surg: cardiovascular & respiratoryHard

A healthcare assistant (unlicensed assistive personnel) reports four observations. Which one needs the nurse's attention first?

  1. AA patient with heart failure who is newly confused, with SpO₂ 89%
  2. BA patient after a PCI asking for a cup of tea
  3. CA patient with a DVT whose leg is less swollen today
  4. DA patient with COPD whose SpO₂ is 90% on 1 L/min, which is usual for him

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: mild

P/F ratio and ARDS (Berlin definition): P/F = PaO₂ (mmHg)/FiO₂ (as a fraction). With PEEP or CPAP of at least 5 cmH₂O, ARDS is graded mild for 200 < P/F ≤ 300, moderate for 100 < P/F ≤ 200 and severe for P/F ≤ 100 mmHg. The other Berlin criteria (onset within a week, bilateral opacities, not fully explained by heart failure) must also be met. PaO₂ in kPa × 7.5 gives mmHg. The ROX index (SpO₂/FiO₂)/respiratory rate is used to follow patients on high-flow nasal oxygen.

P/F ratio

P/F = 122/0.5 = 244 mmHg

Berlin severity

mild

Answer

mild
2.Oxygen therapy & respiratory calculations

Answer: Q = 4 L/min

Cylinder duration: usable litres = (gauge pressure − safe residual) × cylinder factor, with the safe residual usually 200 psi. Cylinder factors in L/psi: D 0.16, E 0.28, H (and K) 3.14. Duration (min) = usable litres/flow (L/min). Round a duration down, never up, so the cylinder is changed in time. In bar-based systems, the gas volume is the water capacity (L) × the pressure (bar).

Usable litres

(750 − 200)·0.16 = 88 L

Highest flow

88/20 = 4.4 L/min → Q = 4 L/min

Answer

Q = 4 L/min
3.Arterial blood gas interpretation

Answer: Osm = 314 mOsm/kg

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.

Calculated osmolality

Osm = 2·136 + 21.2 + 20.4 = 313.6 ≈ 314 mOsm/kg

Answer

Osm = 314 mOsm/kg
4.Arterial blood gas interpretation

Answer: A–a gradient = 106.4 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 − 33/0.8 = 199.6 − 41.25 = 158.4 mmHg

Gradient

A–a = 158.4 − 52 = 106.4 mmHg

Answer

A–a gradient = 106.4 mmHg
5.Clinical assessment scores

Answer: severe

Glasgow Coma Scale: add the best response in three areas. Eye opening E: 4 spontaneous, 3 to sound or speech, 2 to pressure, 1 none. Verbal V: 5 oriented, 4 confused, 3 inappropriate words, 2 incomprehensible sounds, 1 none. Motor M: 6 obeys commands, 5 localises, 4 normal flexion (withdraws), 3 abnormal flexion, 2 extension, 1 none. The total runs from 3 to 15. After a head injury, 13–15 is usually called mild, 9–12 moderate and 3–8 severe.

Score each area

E: opens the eyes only to pressure (a painful stimulus) → 2
V: makes only incomprehensible sounds such as moaning → 2
M: no movement at all → 1

Add

GCS = 2 + 2 + 1 = 5

Severity

GCS 5 → severe

Answer

severe
6.Clinical assessment scores

Answer: mild risk

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: no impairment → 4
moisture: very moist → 2
activity: walks occasionally → 3
mobility: very limited → 2
nutrition: adequate → 3
friction and shear: problem → 1

Add

Braden total = 4 + 2 + 3 + 2 + 3 + 1 = 15

Risk level

15 → mild risk

Answer

mild risk
7.Med-surg: cardiovascular & respiratory

Answer: A · Potassium, because both drugs can raise it

Why this is the answer

ACE inhibitors reduce aldosterone production and spironolactone blocks its receptor, so both reduce potassium excretion. Together they can cause dangerous hyperkalaemia, especially with impaired renal function. Potassium and renal function are monitored, and potassium supplements are usually avoided.

Answer

A · Potassium, because both drugs can raise it
8.Med-surg: cardiovascular & respiratory

Answer: A · A patient with heart failure who is newly confused, with SpO₂ 89%

Why this is the answer

New confusion with hypoxaemia suggests acute deterioration and needs immediate assessment. A COPD patient within their usual target range, a request for tea and an improving DVT are not urgent. Delegated observations must be reported and acted on promptly.

Answer

A · A patient with heart failure who is newly confused, with SpO₂ 89%

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