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
1650psiDf = 0.16 L/psi6 L/minresidual 200 psit = ? min

Practice exercise (made-up values, not clinical guidance). A size D oxygen cylinder (factor 0.16 L/psi) reads 1650 psi and runs at 6 L/min. Keeping a safe residual of 200 psi, how many minutes t will it last? Round down to a whole minute.

1650 psif = 0.16 L/psi6 L/min200 psi
t = min
2.Oxygen therapy & respiratory calculationsHard
1650psiEf = 0.28 L/psi30 minresidual 200 psiQ = ? L/min

Practice exercise (made-up values, not clinical guidance). A transfer will take 30 minutes. The size E cylinder (factor 0.28 L/psi) reads 1650 psi. Keeping a safe residual of 200 psi, what is the highest whole-number flow Q in L/min that lasts the whole transfer?

30 min1650 psif = 0.28 L/psi200 psi
Q = L/min
3.Arterial blood gas interpretationMedium

A practice gas shows a metabolic acidosis with HCO₃⁻ 8 mmol/L. Use Winter’s formula to find the expected PaCO₂ (the centre of the range) in mmHg.

HCO₃⁻ 8 mmol/L
PaCO₂ = mmHg
4.Arterial blood gas interpretationHard
pH7.357.457.30PaCO₂mmHg354582HCO₃⁻mmol/L222639acutechronicacute on chronic

A practice gas shows a respiratory acidosis: pH 7.30, PaCO₂ 82 mmHg (10.9 kPa), HCO₃⁻ 39 mmol/L. Use the rules ‘HCO₃⁻ rises 1 mmol/L per 10 mmHg (acute) or 3.5 mmol/L per 10 mmHg (chronic)’ to classify it. Click your answer.

pH 7.30PaCO₂ 82 mmHg (10.9 kPa)HCO₃⁻ 39 mmol/L
  1. 1acute
  2. 2chronic
  3. 3acute on chronic
5.Clinical assessment scoresMedium
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≥39.1

Practice exercise (made-up values, not clinical guidance). Use the NEWS2 chart (SpO₂ scale 1) for these observations: respiration rate 32/min, SpO₂ 97% on supplemental oxygen, blood pressure 150/90 mmHg, pulse 64/min, unresponsive, temperature 39.0 °C. What is the NEWS2 total score?

RR 32SpO₂ 97%O₂SBP 150HR 64UT 39.0 °C
NEWS2 =
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: crutches, cane or walker; IV therapy or saline lock: no; gait: impaired; 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

A patient with supraventricular tachycardia is to receive IV adenosine. What should the nurse warn them about?

  1. ABrief flushing or chest tightness and a pause of a few seconds
  2. BSeveral hours of drowsiness, slurred speech and confusion afterwards
  3. CA headache that lasts for several days afterwards
  4. DA burning pain along the arm vein for about a week
8.Med-surg: cardiovascular & respiratoryHard

A patient with squamous cell lung cancer becomes confused, thirsty and constipated, with abdominal pain. Which electrolyte disturbance is most likely?

  1. AHypomagnesaemia
  2. BHypercalcaemia
  3. CHypokalaemia
  4. DHyponatraemia

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: t = 38 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

(1650 − 200)·0.16 = 232 L

Duration

232/6 = 38.67 min → t = 38 min

Answer

t = 38 min
2.Oxygen therapy & respiratory calculations

Answer: Q = 13 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

(1650 − 200)·0.28 = 406 L

Highest flow

406/30 = 13.53 L/min → Q = 13 L/min

Answer

Q = 13 L/min
3.Arterial blood gas interpretation

Answer: PaCO₂ = 20 mmHg

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.

Winter’s formula

PaCO₂ = 1.5·8 + 8 = 20 mmHg
range: 18–22 mmHg

Answer

PaCO₂ = 20 mmHg
4.Arterial blood gas interpretation

Answer: chronic

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.

Expected HCO₃⁻

acute: 24 + 1·4.2 = 28.2 mmol/L
chronic: 24 + 3.5·4.2 = 38.7 mmol/L

Compare

measured: 39 mmol/L → chronic

Answer

chronic
5.Clinical assessment scores

Answer: NEWS2 = 9

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 32/min → 3
SpO₂ 97% → 0
on oxygen → 2
SBP 150 mmHg → 0
HR 64/min → 0
unresponsive (U) → 3
T 39.0 °C → 1

Add

NEWS2 = 3 + 0 + 2 + 0 + 0 + 3 + 1 = 9

Answer

NEWS2 = 9
6.Clinical assessment scores

Answer: moderate 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: crutches, cane or walker → 15
IV therapy or saline lock: no → 0
gait: impaired → 20
mental status: knows own limits → 0

Add

Morse total = 0 + 0 + 15 + 0 + 20 + 0 = 35

Risk level

35 → moderate risk

Answer

moderate risk
7.Med-surg: cardiovascular & respiratory

Answer: A · Brief flushing or chest tightness and a pause of a few seconds

Why this is the answer

Adenosine is given as a rapid IV bolus followed by a saline flush, with continuous ECG monitoring. It briefly blocks AV node conduction, often causing a few seconds of asystole, flushing, chest discomfort, breathlessness or a sense of doom. The effects last only seconds.

Answer

A · Brief flushing or chest tightness and a pause of a few seconds
8.Med-surg: cardiovascular & respiratory

Answer: B · Hypercalcaemia

Why this is the answer

Squamous cell lung cancer can secrete PTH-related protein, and bone metastases can release calcium. Hypercalcaemia causes confusion, thirst, polyuria, constipation, abdominal pain and arrhythmias ("bones, stones, groans and psychiatric overtones"). Treatment includes IV fluids and bisphosphonates.

Answer

B · Hypercalcaemia

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