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 48 mmHg · FiO₂ 0.7 · PEEP 5 cmH₂O0100200300400500P/F (mmHg)above 300: no ARDS grademildmoderatesevere

Practice exercise (made-up values, not clinical guidance). A ventilated patient who meets the other Berlin criteria for ARDS has PaO₂ 48 mmHg (6.4 kPa) on 70% oxygen with a PEEP of 5 cmH₂O. Calculate the P/F ratio and click the ARDS severity.

PaO₂ 48 mmHg (6.4 kPa)FiO₂ 70%PEEP 5 cmH₂O
  1. 1above 300: no ARDS grade
  2. 2mild
  3. 3moderate
  4. 4severe
2.Oxygen therapy & respiratory calculationsHard
131 kg182 cm♂4 mL/kg PBWVT​ = ? mL

Practice exercise (made-up values, not clinical guidance). A ventilated man is 182 cm tall and weighs 131 kg. Lung-protective ventilation is set at 4 mL per kg of predicted body weight. Using PBW = 50 + 0.91 × (height cm − 152.4) kg, find the tidal volume VT to the nearest mL.

182 cm131 kg4 mL/kg
VT = mL
3.Arterial blood gas interpretationMedium

Practice values: Na⁺ 144 mmol/L, glucose 19.4 mmol/L and urea 5.1 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.

Na⁺ 144 mmol/Lglucose 19.4 mmol/Lurea 5.1 mmol/L
Osm = mOsm/kg
4.Arterial blood gas interpretationHard

Practice values: Na⁺ 139, Cl⁻ 88 and HCO₃⁻ 17 mmol/L. Calculate the delta ratio (AG − 12)/(24 − HCO₃⁻), using AG = Na⁺ − (Cl⁻ + HCO₃⁻). Give two decimals.

Na⁺ 139 mmol/LCl⁻ 88 mmol/LHCO₃⁻ 17 mmol/L
delta ratio =
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: very limited; moisture: rarely moist; activity: walks occasionally; 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 7/min, SpO₂ 96% on room air, blood pressure 112/68 mmHg, pulse 58/min, alert, temperature 36.9 °C. Which clinical risk group does the patient fall into? Click it.

RR 7SpO₂ 96%airSBP 112HR 58AT 36.9 °C
  1. 1low
  2. 2low–medium
  3. 3medium
  4. 4high
7.Med-surg: cardiovascular & respiratoryMedium

What is the purpose of cardiac resynchronisation therapy (a biventricular pacemaker)?

  1. ATo deliver a shock whenever the heart rate exceeds 100/min
  2. BTo make both ventricles contract together and more efficiently
  3. CTo replace a damaged heart valve
  4. DTo slow the atrial rate in patients with atrial fibrillation
8.Med-surg: cardiovascular & respiratoryHard

A patient taking dabigatran has a serious gastrointestinal bleed. Which specific reversal agent may be used?

  1. APhytomenadione (vitamin K)
  2. BIdarucizumab
  3. CProtamine sulfate
  4. DTranexamic acid alone

3Solutions

1.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.

P/F ratio

P/F = 48/0.7 = 68.57 mmHg

Berlin severity

severe

Answer

severe
2.Oxygen therapy & respiratory calculations

Answer: VT = 308 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 = 50 + 0.91·(182 − 152.4) = 76.94 kg

Tidal volume

VT = 4·76.94 = 307.7 ≈ 308 mL

Answer

VT = 308 mL
3.Arterial blood gas interpretation

Answer: Osm = 313 mOsm/kg

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.

Calculated osmolality

Osm = 2·144 + 19.4 + 5.1 = 312.5 ≈ 313 mOsm/kg

Answer

Osm = 313 mOsm/kg
4.Arterial blood gas interpretation

Answer: delta ratio = 3.143

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.

Anion gap

AG = 139 − (88 + 17) = 34

Delta ratio

(34 − 12)/(24 − 17) = 22/7 = 3.143

Answer

delta ratio = 3.143

Above 2: an added metabolic alkalosis.

5.Clinical assessment scores

Answer: B = 17

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: very limited → 2
moisture: rarely moist → 4
activity: walks occasionally → 3
mobility: slightly limited → 3
nutrition: probably inadequate → 2
friction and shear: no apparent problem → 3

Add

Braden total = 2 + 4 + 3 + 3 + 2 + 3 = 17

Answer

B = 17
6.Clinical assessment scores

Answer: low–medium

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 7/min → 3
SpO₂ 96% → 0
on air → 0
SBP 112 mmHg → 0
HR 58/min → 0
alert (A) → 0
T 36.9 °C → 0

Total and red scores

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

Risk group

low–medium

Answer

low–medium

A single score of 3 needs an urgent review even when the total is low.

7.Med-surg: cardiovascular & respiratory

Answer: B · To make both ventricles contract together and more efficiently

Why this is the answer

In heart failure with a wide QRS (often left bundle branch block), the ventricles contract out of step. Pacing both ventricles restores coordinated contraction, improving symptoms and survival. Many devices also include a defibrillator.

Answer

B · To make both ventricles contract together and more efficiently
8.Med-surg: cardiovascular & respiratory

Answer: B · Idarucizumab

Why this is the answer

Idarucizumab binds dabigatran and reverses its effect within minutes. Andexanet alfa (or prothrombin complex concentrate where it is not available) is used for factor Xa inhibitors. Protamine reverses heparin and vitamin K reverses warfarin. Tranexamic acid may support haemostasis but is not a reversal agent.

Answer

B · Idarucizumab

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