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
1050psiHf = 3.14 L/psi15 L/minresidual 200 psit = ? min

Practice exercise (made-up values, not clinical guidance). A size H oxygen cylinder (factor 3.14 L/psi) reads 1050 psi and runs at 15 L/min. Keeping a safe residual of 200 psi, how many minutes t will it last? Round down to a whole minute.

1050 psif = 3.14 L/psi15 L/min200 psi
t = min
2.Oxygen therapy & respiratory calculationsHard
Hb106 g/LSaO₂94%PaO₂73 mmHgCaO₂mL/dL× CO7.5 L/minDO₂?

Practice exercise (made-up values, not clinical guidance). A patient has Hb 106 g/L, SaO₂ 94%, PaO₂ 73 mmHg (9.7 kPa) and a cardiac output of 7.5 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 106 g/LSaO₂ 94%PaO₂ 73 mmHg (9.7 kPa)CO 7.5 L/min
DO₂ = mL/min
3.Arterial blood gas interpretationMedium
pH7.357.457.57PaCO₂mmHg354542HCO₃⁻mmol/L222637uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.57, PaCO₂ 42 mmHg (5.6 kPa) and HCO₃⁻ 37 mmol/L. The primary disorder is metabolic alkalosis. How far is it compensated? Click your answer.

pH 7.57PaCO₂ 42 mmHg (5.6 kPa)HCO₃⁻ 37 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
4.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 35% oxygen shows PaO₂ 80 mmHg (10.7 kPa) and PaCO₂ 39 mmHg (5.2 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 35%PaO₂ 80 mmHg (10.7 kPa)PaCO₂ 39 mmHg (5.2 kPa)
A–a gradient = mmHg
5.Clinical assessment scoresMedium
H? / 25+D? / 15+Aid? / 30+IV? / 20+G? / 20+MS? / 15Σ?

Practice exercise (made-up values, not clinical guidance). A practice patient is assessed with the Morse fall scale: history of falling in the last 3 months: no; secondary diagnosis: yes; ambulatory aid: holds on to furniture; IV therapy or saline lock: yes; gait: normal, bed rest or wheelchair; mental status: overestimates or forgets limits. Find the Morse total MFS.

0–125
MFS =
6.Clinical assessment scoresHard
126?SBPDBPmmHgMAP = 70

Practice exercise (made-up values, not clinical guidance). The team aims for a mean arterial pressure of at least 70 mmHg. A patient’s systolic pressure is 126 mmHg. Using MAP = (SBP + 2·DBP)/3, what is the lowest diastolic pressure DBP that still gives a MAP of 70 mmHg?

MAP 70 mmHgSBP 126 mmHg
DBP = mmHg
7.Med-surg: cardiovascular & respiratoryMedium

A patient is starting doxazosin, an alpha-blocker, for hypertension. Which advice is most important?

  1. AStop it suddenly if the heart rate rises after the first few doses
  2. BTake the first dose at bedtime, as dizziness and fainting can occur
  3. CTake it with a large glass of grapefruit juice to improve absorption
  4. DAvoid all potassium-containing foods
8.Med-surg: cardiovascular & respiratoryHard

A patient regains a pulse after a ventricular fibrillation arrest that was probably caused by a heart attack. Which investigation is most urgent?

  1. AA lumbar puncture
  2. BAn abdominal ultrasound
  3. CA 12-lead ECG
  4. DSpirometry

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: t = 177 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)·3.14 = 2669 L

Duration

2669/15 = 177.9 min → t = 177 min

Answer

t = 177 min

That is about 2 h 57 min.

2.Oxygen therapy & respiratory calculations

Answer: DO₂ = 1018 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

106 g/L = 10.6 g/dL
CaO₂ = 1.34·10.6·0.94 + 0.003·73 = 13.57 mL/dL

Oxygen delivery

DO₂ = 13.57·7.5·10 = 1018 mL/min

Answer

DO₂ = 1018 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 7.57: alkalaemia (above 7.45)
PaCO₂ 42 mmHg: normal (35–45)
HCO₃⁻ 37 mmol/L: high (22–26)

Compensation

Clinically, also check the expected compensation: for a metabolic alkalosis PaCO₂ ≈ 0.7·HCO₃⁻ + 21 = 44.9–48.9 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 = 120.8 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 = 0.35·713 − 39/0.8 = 249.5 − 48.75 = 200.8 mmHg

Gradient

A–a = 200.8 − 80 = 120.8 mmHg

Answer

A–a gradient = 120.8 mmHg
5.Clinical assessment scores

Answer: MFS = 80

Morse fall scale: six items. History of falling: no 0, yes 25. Secondary diagnosis: no 0, yes 15. Ambulatory aid: none, bed rest or nurse assistance 0; crutches, cane or walker 15; holding on to furniture 30. IV therapy or saline lock: no 0, yes 20. Gait: normal, bed rest or wheelchair 0; weak 10; impaired 20. Mental status: knows own limits 0; overestimates or forgets limits 15. The total runs from 0 to 125. Risk cut-offs differ between hospitals; a common set is 0–24 low, 25–44 moderate and 45 or more high.

Score each item

history of falling in the last 3 months: no → 0
secondary diagnosis: yes → 15
ambulatory aid: holds on to furniture → 30
IV therapy or saline lock: yes → 20
gait: normal, bed rest or wheelchair → 0
mental status: overestimates or forgets limits → 15

Add

Morse total = 0 + 15 + 30 + 20 + 0 + 15 = 80

Answer

MFS = 80
6.Clinical assessment scores

Answer: DBP = 42 mmHg

Blood pressure values: pulse pressure PP = SBP − DBP. Mean arterial pressure MAP ≈ (SBP + 2·DBP)/3 = DBP + PP/3, an estimate based on the heart spending about two thirds of each beat in diastole at a normal heart rate (less accurate when the heart rate is fast); a MAP of at least about 65 mmHg is a common target for organ perfusion. The shock index SI = heart rate/SBP is normally about 0.5–0.7; a value above about 1 is a warning sign of shock.

Rearrange

DBP = (3·MAP − SBP)/2

Substitute

DBP = (3·70 − 126)/2 = 84/2 = 42 mmHg

Answer

DBP = 42 mmHg
7.Med-surg: cardiovascular & respiratory

Answer: B · Take the first dose at bedtime, as dizziness and fainting can occur

Why this is the answer

Alpha-blockers can cause marked first-dose postural hypotension. Taking the first dose at bedtime and rising slowly reduces the risk of falls. They are also used for symptoms of an enlarged prostate.

Answer

B · Take the first dose at bedtime, as dizziness and fainting can occur
8.Med-surg: cardiovascular & respiratory

Answer: C · A 12-lead ECG

Why this is the answer

After return of spontaneous circulation, a 12-lead ECG looks for STEMI, which needs urgent coronary angiography and PCI. Post-resuscitation care also aims for normal oxygen and CO₂ levels, blood pressure support, glucose control and avoiding fever.

Answer

C · A 12-lead ECG

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