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
500psiEf = 0.28 L/psi10 L/minresidual 200 psit = ? min

Practice exercise (made-up values, not clinical guidance). A size E oxygen cylinder (factor 0.28 L/psi) reads 500 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.

500 psif = 0.28 L/psi10 L/min200 psi
t = min
2.Oxygen therapy & respiratory calculationsHard
Hb70 g/LSaO₂98%PaO₂107 mmHgCaO₂mL/dL× CO4.6 L/minDO₂?

Practice exercise (made-up values, not clinical guidance). A patient has Hb 70 g/L, SaO₂ 98%, PaO₂ 107 mmHg (14.3 kPa) and a cardiac output of 4.6 L/min. With CaO₂ = 1.34 × Hb (g/dL) × SaO₂ + 0.003 × PaO₂ (mmHg), find the oxygen delivery DO₂ = CaO₂ × CO × 10 in mL/min.

Hb 70 g/LSaO₂ 98%PaO₂ 107 mmHg (14.3 kPa)CO 4.6 L/min
DO₂ = mL/min
3.Arterial blood gas interpretationMedium
pH7.357.457.65PaCO₂mmHg354537HCO₃⁻mmol/L222639uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.65, PaCO₂ 37 mmHg (4.9 kPa) and HCO₃⁻ 39 mmol/L. The primary disorder is metabolic alkalosis. How far is it compensated? Click your answer.

pH 7.65PaCO₂ 37 mmHg (4.9 kPa)HCO₃⁻ 39 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
4.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 40% oxygen shows PaO₂ 66 mmHg (8.8 kPa) and PaCO₂ 36 mmHg (4.8 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 40%PaO₂ 66 mmHg (8.8 kPa)PaCO₂ 36 mmHg (4.8 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 18/min, SpO₂ 94% on supplemental oxygen, blood pressure 106/64 mmHg, pulse 92/min, alert, temperature 36.0 °C. What is the NEWS2 total score?

RR 18SpO₂ 94%O₂SBP 106HR 92AT 36.0 °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 21/min, SpO₂ 91% on supplemental oxygen, blood pressure 142/86 mmHg, pulse 40/min, alert, temperature 36.9 °C. Which clinical risk group does the patient fall into? Click it.

RR 21SpO₂ 91%O₂SBP 142HR 40AT 36.9 °C
  1. 1low
  2. 2low–medium
  3. 3medium
  4. 4high
7.Med-surg: cardiovascular & respiratoryMedium

A patient with COPD is prescribed long-term oxygen therapy. How many hours a day is it usually needed to improve survival?

  1. AAt least 15 hours a day
  2. BOnly during meals
  3. COnly when walking outside
  4. DAbout one hour each morning
8.Med-surg: cardiovascular & respiratoryHard

Two days after a coronary stent, a patient on aspirin and ticagrelor has black, tarry stools and feels faint on standing. What should the nurse do?

  1. AReassure the patient that iron tablets cause black stools
  2. BStop both antiplatelet drugs permanently on the nurse's own decision
  3. CGive a laxative and repeat the observations tomorrow
  4. DCheck vital signs, report urgently and anticipate a blood count

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: t = 8 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

(500 − 200)·0.28 = 84 L

Duration

84/10 = 8.4 min → t = 8 min

Answer

t = 8 min
2.Oxygen therapy & respiratory calculations

Answer: DO₂ = 437.6 mL/min

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.

Oxygen content

70 g/L = 7 g/dL
CaO₂ = 1.34·7·0.98 + 0.003·107 = 9.513 mL/dL

Oxygen delivery

DO₂ = 9.513·4.6·10 = 437.6 mL/min

Answer

DO₂ = 437.6 mL/min

A normal resting adult value is about 1000 mL/min.

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 7.65: alkalaemia (above 7.45)
PaCO₂ 37 mmHg: normal (35–45)
HCO₃⁻ 39 mmol/L: high (22–26)

Compensation

Clinically, also check the expected compensation: for a metabolic alkalosis PaCO₂ ≈ 0.7·HCO₃⁻ + 21 = 46.3–50.3 mmHg, so the measured 37 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 = 174.2 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 = 0.4·713 − 36/0.8 = 285.2 − 45 = 240.2 mmHg

Gradient

A–a = 240.2 − 66 = 174.2 mmHg

Answer

A–a gradient = 174.2 mmHg
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 18/min → 0
SpO₂ 94% → 1
on oxygen → 2
SBP 106 mmHg → 1
HR 92/min → 1
alert (A) → 0
T 36.0 °C → 1

Add

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

Answer

NEWS2 = 6
6.Clinical assessment scores

Answer: high

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 21/min → 2
SpO₂ 91% → 3
on oxygen → 2
SBP 142 mmHg → 0
HR 40/min → 3
alert (A) → 0
T 36.9 °C → 0

Total and red scores

NEWS2 = 2 + 3 + 2 + 0 + 3 + 0 + 0 = 10
At least one parameter scores 3.

Risk group

high

Answer

high

A total of 5 or more calls for an urgent clinical response.

7.Med-surg: cardiovascular & respiratory

Answer: A · At least 15 hours a day

Why this is the answer

Long-term oxygen therapy improves survival in COPD with chronic hypoxaemia when used for at least 15 hours a day, including overnight. Patients must not smoke, because of the fire risk. Ambulatory oxygen for exercise is a separate assessment.

Answer

A · At least 15 hours a day
8.Med-surg: cardiovascular & respiratory

Answer: D · Check vital signs, report urgently and anticipate a blood count

Why this is the answer

Melaena with postural dizziness suggests upper gastrointestinal bleeding, a risk with dual antiplatelet therapy. The nurse assesses for shock, informs the team urgently and expects bloods, a group and save (type and screen) and possibly endoscopy. Stopping antiplatelets after a stent risks stent thrombosis, so the decision belongs to the medical and cardiology team.

Answer

D · Check vital signs, report urgently and anticipate a blood count

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