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 128 mmHg · FiO₂ 1 · PEEP 6 cmH₂O0100200300400500P/F (mmHg)above 300mildmoderatesevere

Practice exercise (made-up values, not clinical guidance). A ventilated patient who meets the other Berlin criteria for ARDS has PaO₂ 128 mmHg (17.1 kPa) on 100% oxygen with a PEEP of 6 cmH₂O. Calculate the P/F ratio and click the ARDS severity.

PaO₂ 128 mmHg (17.1 kPa)FiO₂ 100%PEEP 6 cmH₂O
  1. 1above 300
  2. 2mild
  3. 3moderate
  4. 4severe
2.Oxygen therapy & respiratory calculationsHard
69 bar10 L12 L/min20 bart = ? min

Practice exercise (made-up values, not clinical guidance). A cylinder with a water capacity of 10 L is filled to 69 bar and runs at 12 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.

10 L69 bar12 L/min20 bar
t = min
3.Arterial blood gas interpretationMedium
pH7.357.457.59PaCO₂mmHg354540HCO₃⁻mmol/L222637uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.59, PaCO₂ 40 mmHg (5.3 kPa) and HCO₃⁻ 37 mmol/L. The primary disorder is metabolic alkalosis. How far is it compensated? Click your answer.

pH 7.59PaCO₂ 40 mmHg (5.3 kPa)HCO₃⁻ 37 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
4.Arterial blood gas interpretationHard
pH7.357.457.19PaCO₂mmHg354519HCO₃⁻mmol/L22267appropriate compensationadded respiratory acidosisadded respiratory alkalosis

A practice gas shows a metabolic acidosis: pH 7.19, PaCO₂ 19 mmHg (2.5 kPa), HCO₃⁻ 7 mmol/L. Compare the measured PaCO₂ with Winter’s formula. Click your interpretation.

pH 7.19PaCO₂ 19 mmHg (2.5 kPa)HCO₃⁻ 7 mmol/L
  1. 1appropriate compensation
  2. 2added respiratory acidosis
  3. 3added respiratory alkalosis
5.Clinical assessment scoresMedium
S? / 4+M? / 4+A? / 4+Mob? / 4+N? / 4+F? / 3Σ?

Practice exercise (made-up values, not clinical guidance). A practice patient is assessed with the Braden scale: sensory perception: slightly limited; moisture: occasionally moist; activity: chairfast; mobility: slightly limited; nutrition: probably inadequate; friction and shear: no apparent problem. Find the Braden total B.

6–23
B =
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 14/min, SpO₂ 89% on room air, blood pressure 78/46 mmHg, pulse 88/min, newly confused, temperature 39.0 °C. Which clinical risk group does the patient fall into? Click it.

RR 14SpO₂ 89%airSBP 78HR 88CT 39.0 °C
  1. 1low
  2. 2low–medium
  3. 3medium
  4. 4high
7.Med-surg: cardiovascular & respiratoryMedium

Why are patients with mitral stenosis at high risk of atrial fibrillation?

  1. AThe left atrium enlarges as it pushes blood through the narrow valve
  2. BThe narrow valve presses on the sinus node and slows it down directly
  3. CThe right ventricle shrinks and stops contracting properly over time
  4. DThe coronary arteries become blocked by the valve
8.Med-surg: cardiovascular & respiratoryHard

An adult inhales a peanut while laughing and now has a persistent cough and wheeze on one side. Where is the peanut most likely to have lodged?

  1. AThe nasal cavity
  2. BThe oesophagus
  3. CThe right main bronchus
  4. DThe left main bronchus

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: moderate

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 = 128/1 = 128 mmHg

Berlin severity

moderate

Answer

moderate
2.Oxygen therapy & respiratory calculations

Answer: t = 40 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

10·(69 − 20) = 490 L

Duration

490/12 = 40.83 min → t = 40 min

Answer

t = 40 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 7.59: alkalaemia (above 7.45)
PaCO₂ 40 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 40 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: appropriate compensation

Expected compensation: in metabolic acidosis Winter’s formula predicts PaCO₂ = 1.5·HCO₃⁻ + 8 ± 2 mmHg; a measured value above that range points to an additional respiratory acidosis, below it to an additional respiratory alkalosis. The anion gap AG = Na⁺ − (Cl⁻ + HCO₃⁻), normally about 8–12 mmol/L, separates high-gap from normal-gap metabolic acidosis; low albumin hides a high gap (add 2.5 per g/dL that albumin is below 4.0). The delta ratio (AG − 12)/(24 − HCO₃⁻) between about 0.8 and 2 fits a pure high-gap acidosis (some texts use 1 instead of 0.8), below that an added normal-gap acidosis, and above 2 an added metabolic alkalosis.

Expected PaCO₂

1.5·7 + 8 = 18.5 → 16.5–20.5 mmHg

Compare

measured: 19 mmHg → appropriate compensation

Answer

appropriate compensation
5.Clinical assessment scores

Answer: B = 16

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: slightly limited → 3
moisture: occasionally moist → 3
activity: chairfast → 2
mobility: slightly limited → 3
nutrition: probably inadequate → 2
friction and shear: no apparent problem → 3

Add

Braden total = 3 + 3 + 2 + 3 + 2 + 3 = 16

Answer

B = 16
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 14/min → 0
SpO₂ 89% → 3
on air → 0
SBP 78 mmHg → 3
HR 88/min → 0
newly confused (C) → 3
T 39.0 °C → 1

Total and red scores

NEWS2 = 0 + 3 + 0 + 3 + 0 + 3 + 1 = 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 · The left atrium enlarges as it pushes blood through the narrow valve

Why this is the answer

A narrowed mitral valve raises pressure in the left atrium, which dilates. A stretched atrium is prone to atrial fibrillation, and blood stasis there carries a high risk of clots and stroke. Anticoagulation is therefore essential in mitral stenosis with AF.

Answer

A · The left atrium enlarges as it pushes blood through the narrow valve
8.Med-surg: cardiovascular & respiratory

Answer: C · The right main bronchus

Why this is the answer

Inhaled foreign bodies most often enter the right main bronchus and right lower lobe, because the right bronchus is wider, shorter and more vertical. Signs include a unilateral wheeze, reduced breath sounds and recurrent infection. Bronchoscopy is used for removal.

Answer

C · The right main bronchus

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