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
1650psiHf = 3.14 L/psi10 L/minresidual 200 psit = ? min

Practice exercise (made-up values, not clinical guidance). A size H oxygen cylinder (factor 3.14 L/psi) reads 1650 psi and runs at 10 L/min. Keeping a safe residual of 200 psi, how many minutes t will it last? Round down to a whole minute.

1650 psif = 3.14 L/psi10 L/min200 psi
t = min
2.Oxygen therapy & respiratory calculationsHard
1050psiDf = 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 1050 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 min1050 psif = 0.16 L/psi200 psi
Q = L/min
3.Arterial blood gas interpretationMedium
pH7.357.457.56PaCO₂mmHg354549HCO₃⁻mmol/L222642uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.56, PaCO₂ 49 mmHg (6.5 kPa) and HCO₃⁻ 42 mmol/L. The primary disorder is metabolic alkalosis. How far is it compensated? Click your answer.

pH 7.56PaCO₂ 49 mmHg (6.5 kPa)HCO₃⁻ 42 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
4.Arterial blood gas interpretationHard
pH7.357.457.33PaCO₂mmHg354535HCO₃⁻mmol/L222618added normal-gap acidosispure high-gap acidosisadded metabolic alkalosis

A practice gas shows pH 7.33, PaCO₂ 35 mmHg (4.7 kPa) and HCO₃⁻ 18 mmol/L, with Na⁺ 132 and Cl⁻ 87 mmol/L. Use the anion gap and the delta ratio to click the best interpretation.

pH 7.33PaCO₂ 35 mmHg (4.7 kPa)HCO₃⁻ 18 mmol/LNa⁺ 132 mmol/LCl⁻ 87 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 16/min, SpO₂ 97% on supplemental oxygen, blood pressure 84/50 mmHg, pulse 76/min, responds only to pain, temperature 36.3 °C. What is the NEWS2 total score?

RR 16SpO₂ 97%O₂SBP 84HR 76PT 36.3 °C
NEWS2 =
6.Clinical assessment scoresHard
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≥39.1lowlow–mediummediumhigh

Practice exercise (made-up values, not clinical guidance). Use the NEWS2 chart (SpO₂ scale 1) for these observations: respiration rate 20/min, SpO₂ 97% on room air, blood pressure 130/78 mmHg, pulse 82/min, alert, temperature 37.7 °C. Which clinical risk group does the patient fall into? Click it.

RR 20SpO₂ 97%airSBP 130HR 82AT 37.7 °C
  1. 1low
  2. 2low–medium
  3. 3medium
  4. 4high
7.Med-surg: cardiovascular & respiratoryMedium

Why are patients with mitral stenosis at high risk of atrial fibrillation?

  1. AThe left atrium enlarges as it pushes blood through the narrow valve
  2. BThe narrow valve presses on the sinus node and slows it down directly
  3. CThe right ventricle shrinks and stops contracting properly over time
  4. DThe coronary arteries become blocked by the valve
8.Med-surg: cardiovascular & respiratoryHard

Two days after coronary artery bypass surgery, a patient feels palpitations. The pulse is irregularly irregular at 140/min and BP is 112/70 mmHg. Which rhythm is most likely?

  1. AVentricular fibrillation
  2. BSinus tachycardia
  3. CAtrial fibrillation
  4. DComplete heart block

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: t = 455 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)·3.14 = 4553 L

Duration

4553/10 = 455.3 min → t = 455 min

Answer

t = 455 min

That is about 7 h 35 min.

2.Oxygen therapy & respiratory calculations

Answer: Q = 6 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

(1050 − 200)·0.16 = 136 L

Highest flow

136/20 = 6.8 L/min → Q = 6 L/min

Answer

Q = 6 L/min
3.Arterial blood gas interpretation

Answer: partially compensated

Reading a blood gas (ROME): first the pH: below 7.35 is acidaemia, above 7.45 alkalaemia. Then find the value that explains it. PaCO₂ (normal 35–45 mmHg, 4.7–6.0 kPa) is the respiratory part and moves Opposite to the pH in a respiratory disorder; HCO₃⁻ (normal 22–26 mmol/L) is the metabolic part and moves in the same direction as the pH (Respiratory Opposite, Metabolic Equal). The other value shows the compensation: normal means uncompensated; abnormal in the direction that pulls the pH back while the pH is still abnormal means partially compensated; a normal pH with both values abnormal means fully compensated. Ranges differ slightly between laboratories; these are practice values.

ROME, value by value

pH 7.56: alkalaemia (above 7.45)
PaCO₂ 49 mmHg: high (35–45)
HCO₃⁻ 42 mmol/L: high (22–26)

Compensation

partially compensated

Answer

partially compensated
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 = 132 − (87 + 18) = 27

Delta ratio

(27 − 12)/(24 − 18) = 2.5
added metabolic alkalosis

Answer

added metabolic alkalosis
5.Clinical assessment scores

Answer: NEWS2 = 8

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 16/min → 0
SpO₂ 97% → 0
on oxygen → 2
SBP 84 mmHg → 3
HR 76/min → 0
responds only to pain (P) → 3
T 36.3 °C → 0

Add

NEWS2 = 0 + 0 + 2 + 3 + 0 + 3 + 0 = 8

Answer

NEWS2 = 8
6.Clinical assessment scores

Answer: low

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 20/min → 0
SpO₂ 97% → 0
on air → 0
SBP 130 mmHg → 0
HR 82/min → 0
alert (A) → 0
T 37.7 °C → 0

Total and red scores

NEWS2 = 0 + 0 + 0 + 0 + 0 + 0 + 0 = 0
No parameter scores 3.

Risk group

low

Answer

low
7.Med-surg: cardiovascular & respiratory

Answer: A · The left atrium enlarges as it pushes blood through the narrow valve

Why this is the answer

A narrowed mitral valve raises pressure in the left atrium, which dilates. A stretched atrium is prone to atrial fibrillation, and blood stasis there carries a high risk of clots and stroke. Anticoagulation is therefore essential in mitral stenosis with AF.

Answer

A · The left atrium enlarges as it pushes blood through the narrow valve
8.Med-surg: cardiovascular & respiratory

Answer: C · Atrial fibrillation

Why this is the answer

New atrial fibrillation affects a large proportion of patients in the first days after cardiac surgery, often due to inflammation, electrolyte shifts and stress. Management includes a 12-lead ECG, checking potassium and magnesium, rate or rhythm control and considering anticoagulation.

Answer

C · Atrial fibrillation

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