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 118 mmHg · FiO₂ 0.3 · PEEP 12 cmH₂O0100200300400500P/F (mmHg)above 300mildmoderatesevere

Practice exercise (made-up values, not clinical guidance). A ventilated patient who meets the other Berlin criteria for ARDS has PaO₂ 118 mmHg (15.7 kPa) on 30% oxygen with a PEEP of 12 cmH₂O. Calculate the P/F ratio and click the ARDS severity.

PaO₂ 118 mmHg (15.7 kPa)FiO₂ 30%PEEP 12 cmH₂O
  1. 1above 300
  2. 2mild
  3. 3moderate
  4. 4severe
2.Oxygen therapy & respiratory calculationsHard
114 kg194 cm♂5 mL/kg PBWVT​ = ? mL

Practice exercise (made-up values, not clinical guidance). A ventilated man is 194 cm tall and weighs 114 kg. Lung-protective ventilation is set at 5 mL per kg of predicted body weight. Using PBW = 50 + 0.91 × (height cm − 152.4) kg, find the tidal volume VT to the nearest mL.

194 cm114 kg5 mL/kg
VT = mL
3.Arterial blood gas interpretationMedium

A practice gas shows a metabolic acidosis with HCO₃⁻ 18 mmol/L. Use Winter’s formula to find the expected PaCO₂ (the centre of the range) in mmHg.

HCO₃⁻ 18 mmol/L
PaCO₂ = mmHg
4.Arterial blood gas interpretationHard
pH7.357.457.31PaCO₂mmHg354574HCO₃⁻mmol/L222636acutechronicacute on chronic

A practice gas shows a respiratory acidosis: pH 7.31, PaCO₂ 74 mmHg (9.9 kPa), HCO₃⁻ 36 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 7.31PaCO₂ 74 mmHg (9.9 kPa)HCO₃⁻ 36 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 12/min, SpO₂ 92% on supplemental oxygen, blood pressure 110/66 mmHg, pulse 104/min, alert, temperature 37.6 °C. What is the NEWS2 total score?

RR 12SpO₂ 92%O₂SBP 110HR 104AT 37.6 °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: none, bed rest or nurse assists; IV therapy or saline lock: no; gait: normal, bed rest or wheelchair; mental status: overestimates or forgets 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

Why is a beta-blocker started at a low dose and increased slowly in heart failure?

  1. AIt must be stopped as soon as symptoms improve
  2. BIt works only if the dose is never changed after the first day
  3. CIt is safe only at the highest possible dose from the very start
  4. DIt can briefly worsen symptoms before long-term benefit appears
8.Med-surg: cardiovascular & respiratoryHard

An older inpatient develops sudden fever, muscle aches and a dry cough during the winter influenza season. Which plan is most appropriate?

  1. AIsolate with droplet precautions, test and expect early antivirals
  2. BIsolate only if they develop a rash
  3. CLeave them in the open bay and give a course of antibiotics only
  4. DWait a week to see whether the symptoms settle before testing

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: above 300

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 = 118/0.3 = 393.3 mmHg

Berlin severity

above 300

Answer

above 300
2.Oxygen therapy & respiratory calculations

Answer: VT = 439 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 = 50 + 0.91·(194 − 152.4) = 87.86 kg

Tidal volume

VT = 5·87.86 = 439.3 ≈ 439 mL

Answer

VT = 439 mL
3.Arterial blood gas interpretation

Answer: PaCO₂ = 35 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 = 1.5·18 + 8 = 35 mmHg
range: 33–37 mmHg

Answer

PaCO₂ = 35 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 + 1·3.4 = 27.4 mmol/L
chronic: 24 + 3.5·3.4 = 35.9 mmol/L

Compare

measured: 36 mmol/L → chronic

Answer

chronic
5.Clinical assessment scores

Answer: NEWS2 = 6

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 12/min → 0
SpO₂ 92% → 2
on oxygen → 2
SBP 110 mmHg → 1
HR 104/min → 1
alert (A) → 0
T 37.6 °C → 0

Add

NEWS2 = 0 + 2 + 2 + 1 + 1 + 0 + 0 = 6

Answer

NEWS2 = 6
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: normal, bed rest or wheelchair → 0
mental status: overestimates or forgets limits → 15

Add

Morse total = 0 + 0 + 0 + 0 + 0 + 15 = 15

Risk level

15 → low risk

Answer

low risk
7.Med-surg: cardiovascular & respiratory

Answer: D · It can briefly worsen symptoms before long-term benefit appears

Why this is the answer

Beta-blockers improve survival in heart failure with reduced ejection fraction, but they can cause tiredness, low blood pressure, bradycardia and fluid retention when first started. They are therefore started low and increased gradually in stable patients, with monitoring of weight, pulse and BP.

Answer

D · It can briefly worsen symptoms before long-term benefit appears
8.Med-surg: cardiovascular & respiratory

Answer: A · Isolate with droplet precautions, test and expect early antivirals

Why this is the answer

Influenza spreads mainly by droplets and contact, so the patient is isolated with droplet precautions and tested. Antivirals such as oseltamivir work best if started early, ideally within 48 hours of symptoms, and are recommended for hospitalised and high-risk patients. Vaccination of staff and patients reduces outbreaks.

Answer

A · Isolate with droplet precautions, test and expect early antivirals

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