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 107 mmHg · FiO₂ 0.3 · PEEP 6 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 107 mmHg (14.3 kPa) on 30% oxygen with a PEEP of 6 cmH₂O. Calculate the P/F ratio and click the ARDS severity.

PaO₂ 107 mmHg (14.3 kPa)FiO₂ 30%PEEP 6 cmH₂O
  1. 1above 300: no ARDS grade
  2. 2mild
  3. 3moderate
  4. 4severe
2.Oxygen therapy & respiratory calculationsHard
89 bar2 L8 L/min20 bart = ? min

Practice exercise (made-up values, not clinical guidance). A cylinder with a water capacity of 2 L is filled to 89 bar and runs at 8 L/min. The gas volume is about the water capacity × the pressure. In this exercise the cylinder is changed at 20 bar. How many minutes t until it must be changed? Round down to a whole minute.

2 L89 bar8 L/min20 bar
t = min
3.Arterial blood gas interpretationMedium
pH7.357.457.30PaCO₂mmHg354568HCO₃⁻mmol/L222632uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.30, PaCO₂ 68 mmHg (9.1 kPa) and HCO₃⁻ 32 mmol/L. The primary disorder is respiratory acidosis. How far is it compensated? Click your answer.

pH 7.30PaCO₂ 68 mmHg (9.1 kPa)HCO₃⁻ 32 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
4.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 50% oxygen shows PaO₂ 69 mmHg (9.2 kPa) and PaCO₂ 51 mmHg (6.8 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 50%PaO₂ 69 mmHg (9.2 kPa)PaCO₂ 51 mmHg (6.8 kPa)
A–a gradient = mmHg
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 20/min, SpO₂ 96% on supplemental oxygen, blood pressure 96/58 mmHg, pulse 50/min, alert, temperature 36.2 °C. What is the NEWS2 total score?

RR 20SpO₂ 96%O₂SBP 96HR 50AT 36.2 °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: completely limited; moisture: rarely moist; activity: walks frequently; 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 asthma uses their reliever inhaler more than three times a week. What does this suggest?

  1. AAsthma control is poor and treatment needs review
  2. BThe reliever no longer works and should be stopped
  3. CAsthma is well controlled with the current plan
  4. DThe preventer inhaler is no longer needed
8.Med-surg: cardiovascular & respiratoryHard

Two adults with cystic fibrosis are admitted to the same ward. What is the correct infection-control plan?

  1. AUse standard precautions only, as CF is not infectious
  2. BLet them share physiotherapy sessions and equipment
  3. CPut them in the same bay so they can support each other
  4. DNurse them in separate single rooms and keep them apart

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: above 300: no ARDS grade

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 = 107/0.3 = 356.7 mmHg

Berlin severity

above 300: no ARDS grade

Answer

above 300: no ARDS grade
2.Oxygen therapy & respiratory calculations

Answer: t = 17 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 gas

2·(89 − 20) = 138 L

Duration

138/8 = 17.25 min → t = 17 min

Answer

t = 17 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 7.30: acidaemia (below 7.35)
PaCO₂ 68 mmHg: high (35–45)
HCO₃⁻ 32 mmol/L: high (22–26)

Compensation

partially compensated

Answer

partially compensated
4.Arterial blood gas interpretation

Answer: A–a gradient = 223.8 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 = 0.5·713 − 51/0.8 = 356.5 − 63.75 = 292.8 mmHg

Gradient

A–a = 292.8 − 69 = 223.8 mmHg

Answer

A–a gradient = 223.8 mmHg
5.Clinical assessment scores

Answer: NEWS2 = 5

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 96% → 0
on oxygen → 2
SBP 96 mmHg → 2
HR 50/min → 1
alert (A) → 0
T 36.2 °C → 0

Add

NEWS2 = 0 + 0 + 2 + 2 + 1 + 0 + 0 = 5

Answer

NEWS2 = 5
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: completely limited → 1
moisture: rarely moist → 4
activity: walks frequently → 4
mobility: very limited → 2
nutrition: adequate → 3
friction and shear: problem → 1

Add

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

Risk level

15 → mild risk

Answer

mild risk
7.Med-surg: cardiovascular & respiratory

Answer: A · Asthma control is poor and treatment needs review

Why this is the answer

Needing a reliever often, waking at night with symptoms or limiting activity indicates poorly controlled asthma. Inhaler technique, adherence and triggers should be checked and the regular preventer treatment stepped up.

Answer

A · Asthma control is poor and treatment needs review
8.Med-surg: cardiovascular & respiratory

Answer: D · Nurse them in separate single rooms and keep them apart

Why this is the answer

People with CF are colonised with organisms such as Pseudomonas aeruginosa and Burkholderia cepacia complex that can pass between patients and worsen outcomes. They are cared for in single rooms and kept apart, without sharing equipment or sessions.

Answer

D · Nurse them in separate single rooms and keep them apart

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