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
Hb127 g/LSaO₂91%PaO₂60 mmHgCaO₂?

Practice exercise (made-up values, not clinical guidance). A patient has Hb 127 g/L, SaO₂ 91% and PaO₂ 60 mmHg (8.0 kPa). Find the arterial oxygen content CaO₂ = 1.34 × Hb (g/dL) × SaO₂ + 0.003 × PaO₂ (mmHg) in mL O₂/dL.

Hb 127 g/LSaO₂ 91%PaO₂ 60 mmHg (8.0 kPa)
CaO₂ = mL/dL
2.Oxygen therapy & respiratory calculationsHard
64 kg164 cm♀6 mL/kg PBWVT​ = ? mL

Practice exercise (made-up values, not clinical guidance). A ventilated woman is 164 cm tall and weighs 64 kg. Lung-protective ventilation is set at 6 mL per kg of predicted body weight. Using PBW = 45.5 + 0.91 × (height cm − 152.4) kg, find the tidal volume VT to the nearest mL.

164 cm64 kg6 mL/kg
VT = mL
3.Arterial blood gas interpretationMedium
pH7.357.457.56PaCO₂mmHg354542HCO₃⁻mmol/L222636uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.56, PaCO₂ 42 mmHg (5.6 kPa) and HCO₃⁻ 36 mmol/L. The primary disorder is metabolic alkalosis. How far is it compensated? Click your answer.

pH 7.56PaCO₂ 42 mmHg (5.6 kPa)HCO₃⁻ 36 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
4.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 24% oxygen shows PaO₂ 72 mmHg (9.6 kPa) and PaCO₂ 42 mmHg (5.6 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 24%PaO₂ 72 mmHg (9.6 kPa)PaCO₂ 42 mmHg (5.6 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 16/min, SpO₂ 95% on supplemental oxygen, blood pressure 112/68 mmHg, pulse 44/min, alert, temperature 38.8 °C. What is the NEWS2 total score?

RR 16SpO₂ 95%O₂SBP 112HR 44AT 38.8 °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: no impairment; moisture: occasionally moist; activity: bedfast; mobility: completely immobile; nutrition: excellent; 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

After a permanent pacemaker is inserted, which instruction is commonly given for the first few weeks?

  1. AAvoid raising the arm on that side above shoulder height
  2. BDo not shower or wash at all for six weeks
  3. CKeep the arm completely still in a sling for six months or more
  4. DMassage the wound firmly twice a day
8.Med-surg: cardiovascular & respiratoryHard

Which approach to chest drain removal is commonly taught?

  1. ARemove it and leave the site open to drain for a day
  2. BRemove it during a held breath or expiration, then seal the site
  3. CRemove it with the suction still running at full power
  4. DRemove it slowly while the patient takes a long, deep breath in

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: CaO₂ = 15.67 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

127 g/L = 12.7 g/dL

Bound oxygen

1.34·12.7·0.91 = 15.49 mL/dL

Dissolved oxygen

0.003·60 = 0.18 mL/dL

Oxygen content

CaO₂ = 15.49 + 0.18 = 15.67 mL/dL

Answer

CaO₂ = 15.67 mL/dL
2.Oxygen therapy & respiratory calculations

Answer: VT = 336 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 = 45.5 + 0.91·(164 − 152.4) = 56.06 kg

Tidal volume

VT = 6·56.06 = 336.3 ≈ 336 mL

Answer

VT = 336 mL
3.Arterial blood gas interpretation

Answer: uncompensated

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 42 mmHg: normal (35–45)
HCO₃⁻ 36 mmol/L: high (22–26)

Compensation

Clinically, also check the expected compensation: for a metabolic alkalosis PaCO₂ ≈ 0.7·HCO₃⁻ + 21 = 44.2–48.2 mmHg, so the measured 42 mmHg points to an additional respiratory alkalosis (a mixed disorder). The answer above is the ROME exam classification.

uncompensated

Answer

uncompensated
4.Arterial blood gas interpretation

Answer: A–a gradient = 46.62 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 = 0.24·713 − 42/0.8 = 171.1 − 52.5 = 118.6 mmHg

Gradient

A–a = 118.6 − 72 = 46.62 mmHg

Answer

A–a gradient = 46.62 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 16/min → 0
SpO₂ 95% → 1
on oxygen → 2
SBP 112 mmHg → 0
HR 44/min → 1
alert (A) → 0
T 38.8 °C → 1

Add

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

Answer

NEWS2 = 5
6.Clinical assessment scores

Answer: moderate 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: no impairment → 4
moisture: occasionally moist → 3
activity: bedfast → 1
mobility: completely immobile → 1
nutrition: excellent → 4
friction and shear: problem → 1

Add

Braden total = 4 + 3 + 1 + 1 + 4 + 1 = 14

Risk level

14 → moderate risk

Answer

moderate risk
7.Med-surg: cardiovascular & respiratory

Answer: A · Avoid raising the arm on that side above shoulder height

Why this is the answer

Limiting arm movement on the device side for a few weeks reduces the risk of lead displacement. Patients are also taught to watch the wound for infection, carry their device card and follow advice on magnets and certain medical scans.

Answer

A · Avoid raising the arm on that side above shoulder height
8.Med-surg: cardiovascular & respiratory

Answer: B · Remove it during a held breath or expiration, then seal the site

Why this is the answer

Many guidelines suggest removing the tube at the end of a deep breath held (Valsalva) or during expiration, so that the pressure in the chest is positive. The wound is closed with a suture or occlusive dressing, the patient monitored for recurrent pneumothorax and a chest X-ray done if indicated. Analgesia beforehand is good practice.

Answer

B · Remove it during a held breath or expiration, then seal the site

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