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
500psiHf = 3.14 L/psi5 L/minresidual 200 psit = ? min

Practice exercise (made-up values, not clinical guidance). A size H oxygen cylinder (factor 3.14 L/psi) reads 500 psi and runs at 5 L/min. Keeping a safe residual of 200 psi, how many minutes t will it last? Round down to a whole minute.

500 psif = 3.14 L/psi5 L/min200 psi
t = min
2.Oxygen therapy & respiratory calculationsHard
PaO₂ 6.7 kPa · FiO₂ 1 · PEEP 6 cmH₂O0100200300400500P/F (mmHg)above 300: no ARDS grademildmoderateseverenot gradable: PEEP below 5

Practice exercise (made-up values, not clinical guidance). A patient with acute hypoxaemia and bilateral opacities, not explained by heart failure, has PaO₂ 6.7 kPa on 100% oxygen with a PEEP of 6 cmH₂O. Grade the ARDS severity with the Berlin definition. Click your answer.

PaO₂ 6.7 kPaFiO₂ 100%PEEP 6 cmH₂O
  1. 1above 300: no ARDS grade
  2. 2mild
  3. 3moderate
  4. 4severe
  5. 5not gradable: PEEP below 5
3.Arterial blood gas interpretationMedium
pH7.357.457.42PaCO₂mmHg354549HCO₃⁻mmol/L222631uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.42, PaCO₂ 49 mmHg (6.5 kPa) and HCO₃⁻ 31 mmol/L. The primary disorder is metabolic alkalosis. How far is it compensated? Click your answer.

pH 7.42PaCO₂ 49 mmHg (6.5 kPa)HCO₃⁻ 31 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 92 mmHg (12.3 kPa) and PaCO₂ 52 mmHg (6.9 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 40%PaO₂ 92 mmHg (12.3 kPa)PaCO₂ 52 mmHg (6.9 kPa)
A–a gradient = mmHg
5.Clinical assessment scoresMedium
mildmoderatesevere

Practice exercise (made-up values, not clinical guidance). A practice patient after a head injury opens the eyes only to pressure (a painful stimulus), says inappropriate, random words and shows as the best motor response: extension of the arms and legs (abnormal extension). Work out the GCS and classify the head injury by it. Click your answer.

  1. 1mild
  2. 2moderate
  3. 3severe
6.Clinical assessment scoresHard
121?SBPDBPmmHgMAP = 65

Practice exercise (made-up values, not clinical guidance). The team aims for a mean arterial pressure of at least 65 mmHg. A patient’s systolic pressure is 121 mmHg. Using MAP = (SBP + 2·DBP)/3, what is the lowest diastolic pressure DBP that still gives a MAP of 65 mmHg?

MAP 65 mmHgSBP 121 mmHg
DBP = mmHg
7.Med-surg: cardiovascular & respiratoryMedium

A patient with hypertension takes amlodipine. Which side effect is the nurse most likely to observe?

  1. AHyperkalaemia
  2. BWheeze
  3. CAnkle swelling
  4. DDry, tickly cough
8.Med-surg: cardiovascular & respiratoryHard

A patient with asthma has a peak flow of 40% of their best, a respiratory rate of 28/min and cannot complete sentences. SpO₂ is 94%. How should this attack be classified?

  1. ANear-fatal asthma
  2. BModerate asthma exacerbation
  3. CLife-threatening asthma
  4. DAcute severe asthma

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: t = 188 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)·3.14 = 942 L

Duration

942/5 = 188.4 min → t = 188 min

Answer

t = 188 min

That is about 3 h 08 min.

2.Oxygen therapy & respiratory calculations

Answer: severe

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.

PEEP

PEEP 6 ≥ 5 cmH₂O

PaO₂ in mmHg

6.7·7.5 = 50.25 mmHg

P/F ratio

P/F = 50.25/1 = 50.25 mmHg

Berlin severity

severe

Answer

severe
3.Arterial blood gas interpretation

Answer: fully 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 7.42: within 7.35–7.45
PaCO₂ 49 mmHg: high (35–45)
HCO₃⁻ 31 mmol/L: high (22–26)

Compensation

Clinically, also check the expected compensation: for a metabolic alkalosis PaCO₂ ≈ 0.7·HCO₃⁻ + 21 = 40.7–44.7 mmHg, so the measured 49 mmHg points to an additional respiratory acidosis (a mixed disorder). The answer above is the ROME exam classification.

fully compensated

Answer

fully compensated
4.Arterial blood gas interpretation

Answer: A–a gradient = 128.2 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 − 52/0.8 = 285.2 − 65 = 220.2 mmHg

Gradient

A–a = 220.2 − 92 = 128.2 mmHg

Answer

A–a gradient = 128.2 mmHg
5.Clinical assessment scores

Answer: severe

Glasgow Coma Scale: add the best response in three areas. Eye opening E: 4 spontaneous, 3 to sound or speech, 2 to pressure, 1 none. Verbal V: 5 oriented, 4 confused, 3 inappropriate words, 2 incomprehensible sounds, 1 none. Motor M: 6 obeys commands, 5 localises, 4 normal flexion (withdraws), 3 abnormal flexion, 2 extension, 1 none. The total runs from 3 to 15. After a head injury, 13–15 is usually called mild, 9–12 moderate and 3–8 severe.

Score each area

E: opens the eyes only to pressure (a painful stimulus) → 2
V: says inappropriate, random words → 3
M: extension of the arms and legs (abnormal extension) → 2

Add

GCS = 2 + 3 + 2 = 7

Severity

GCS 7 → severe

Answer

severe
6.Clinical assessment scores

Answer: DBP = 37 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 = (3·65 − 121)/2 = 74/2 = 37 mmHg

Answer

DBP = 37 mmHg
7.Med-surg: cardiovascular & respiratory

Answer: C · Ankle swelling

Why this is the answer

Dihydropyridine calcium channel blockers such as amlodipine dilate arterioles, raising capillary pressure and causing peripheral oedema, flushing and headache. Dry cough is typical of ACE inhibitors, and wheeze of non-selective beta-blockers in asthma.

Answer

C · Ankle swelling
8.Med-surg: cardiovascular & respiratory

Answer: D · Acute severe asthma

Why this is the answer

In common guidance (for example BTS/SIGN), a peak flow of 33–50% of best, a respiratory rate of 25/min or more, a heart rate of 110/min or more or inability to complete sentences indicate acute severe asthma. Life-threatening features include peak flow below 33%, SpO₂ under 92%, a silent chest, cyanosis, exhaustion or confusion; near-fatal asthma means a raised PaCO₂ or the need for ventilation.

Answer

D · Acute severe asthma

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