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
Hb106 g/LSaO₂89%PaO₂56 mmHgCaO₂?

Practice exercise (made-up values, not clinical guidance). A patient has Hb 106 g/L, SaO₂ 89% and PaO₂ 56 mmHg (7.5 kPa). Find the arterial oxygen content CaO₂ = 1.34 × Hb (g/dL) × SaO₂ + 0.003 × PaO₂ (mmHg) in mL O₂/dL.

Hb 106 g/LSaO₂ 89%PaO₂ 56 mmHg (7.5 kPa)
CaO₂ = mL/dL
2.Oxygen therapy & respiratory calculationsHard
800psiDf = 0.16 L/psi90 minresidual 200 psiQ = ? L/min

Practice exercise (made-up values, not clinical guidance). A transfer will take 90 minutes. The size D cylinder (factor 0.16 L/psi) reads 800 psi. Keeping a safe residual of 200 psi, what is the highest whole-number flow Q in L/min that lasts the whole transfer?

90 min800 psif = 0.16 L/psi200 psi
Q = L/min
3.Arterial blood gas interpretationMedium

Practice values: Na⁺ 132 mmol/L, glucose 7.1 mmol/L and urea 16.7 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.

Na⁺ 132 mmol/Lglucose 7.1 mmol/Lurea 16.7 mmol/L
Osm = mOsm/kg
4.Arterial blood gas interpretationHard
pH7.357.457.31PaCO₂mmHg354527HCO₃⁻mmol/L222613added normal-gap acidosispure high-gap acidosisadded metabolic alkalosis

A practice gas shows pH 7.31, PaCO₂ 27 mmHg (3.6 kPa) and HCO₃⁻ 13 mmol/L, with Na⁺ 146 and Cl⁻ 95 mmol/L. Use the anion gap and the delta ratio to click the best interpretation.

pH 7.31PaCO₂ 27 mmHg (3.6 kPa)HCO₃⁻ 13 mmol/LNa⁺ 146 mmol/LCl⁻ 95 mmol/L
  1. 1added normal-gap acidosis
  2. 2pure high-gap acidosis
  3. 3added metabolic alkalosis
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 14/min, SpO₂ 99% on room air, blood pressure 88/52 mmHg, pulse 76/min, responds only to pain, temperature 36.7 °C. What is the NEWS2 total score?

RR 14SpO₂ 99%airSBP 88HR 76PT 36.7 °C
NEWS2 =
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: very limited; moisture: constantly moist; activity: bedfast; mobility: completely immobile; nutrition: very poor; friction and shear: no apparent 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

According to current guidance, when should oxygen be given to a patient with an acute coronary syndrome?

  1. AOnly once the troponin result is available
  2. BOnly when SpO₂ is below the target range
  3. CNever, because oxygen harms heart muscle
  4. DAlways at 15 L/min, whatever the saturation
8.Med-surg: cardiovascular & respiratoryHard

A patient with asthma needs their reliever every three hours and their peak flow is falling well below their personal best. What does their action plan most likely advise?

  1. ADo extra exercise to open the airways
  2. BWait two weeks to see whether it improves without any change
  3. CStop the preventer inhaler for a few days to rest the lungs
  4. DFollow the worsening-asthma steps and get a same-day review

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: CaO₂ = 12.81 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

106 g/L = 10.6 g/dL

Bound oxygen

1.34·10.6·0.89 = 12.64 mL/dL

Dissolved oxygen

0.003·56 = 0.168 mL/dL

Oxygen content

CaO₂ = 12.64 + 0.168 = 12.81 mL/dL

Answer

CaO₂ = 12.81 mL/dL
2.Oxygen therapy & respiratory calculations

Answer: Q = 1 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

(800 − 200)·0.16 = 96 L

Highest flow

96/90 = 1.067 L/min → Q = 1 L/min

Answer

Q = 1 L/min
3.Arterial blood gas interpretation

Answer: Osm = 288 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 = 2·132 + 7.1 + 16.7 = 287.8 ≈ 288 mOsm/kg

Answer

Osm = 288 mOsm/kg
4.Arterial blood gas interpretation

Answer: added metabolic alkalosis

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.

Anion gap

AG = 146 − (95 + 13) = 38

Delta ratio

(38 − 12)/(24 − 13) = 2.364
added metabolic alkalosis

Answer

added metabolic alkalosis
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 14/min → 0
SpO₂ 99% → 0
on air → 0
SBP 88 mmHg → 3
HR 76/min → 0
responds only to pain (P) → 3
T 36.7 °C → 0

Add

NEWS2 = 0 + 0 + 0 + 3 + 0 + 3 + 0 = 6

Answer

NEWS2 = 6
6.Clinical assessment scores

Answer: very high 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: very limited → 2
moisture: constantly moist → 1
activity: bedfast → 1
mobility: completely immobile → 1
nutrition: very poor → 1
friction and shear: no apparent problem → 3

Add

Braden total = 2 + 1 + 1 + 1 + 1 + 3 = 9

Risk level

9 → very high risk

Answer

very high risk
7.Med-surg: cardiovascular & respiratory

Answer: B · Only when SpO₂ is below the target range

Why this is the answer

Routine high-flow oxygen in patients who are not hypoxaemic offers no benefit and may increase infarct size. Oxygen is given when saturation falls below the target (for example below 90% in some guidelines, below 94% in others).

Answer

B · Only when SpO₂ is below the target range
8.Med-surg: cardiovascular & respiratory

Answer: D · Follow the worsening-asthma steps and get a same-day review

Why this is the answer

Personal asthma action plans set steps based on symptoms and peak flow compared with the personal best. Increasing reliever need and a falling peak flow mean worsening asthma: treatment is increased as the plan says (sometimes with oral steroids) and urgent review is sought. Severe signs need emergency care.

Answer

D · Follow the worsening-asthma steps and get a same-day review

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