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
Hb138 g/LSaO₂96%PaO₂79 mmHgCaO₂?

Practice exercise (made-up values, not clinical guidance). A patient has Hb 138 g/L, SaO₂ 96% and PaO₂ 79 mmHg (10.5 kPa). Find the arterial oxygen content CaO₂ = 1.34 × Hb (g/dL) × SaO₂ + 0.003 × PaO₂ (mmHg) in mL O₂/dL.

Hb 138 g/LSaO₂ 96%PaO₂ 79 mmHg (10.5 kPa)
CaO₂ = mL/dL
2.Oxygen therapy & respiratory calculationsHard
99 kg170 cm♂5 mL/kg PBWVT​ = ? mL

Practice exercise (made-up values, not clinical guidance). A ventilated man is 170 cm tall and weighs 99 kg. Lung-protective ventilation is set at 5 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.

170 cm99 kg5 mL/kg
VT = mL
3.Arterial blood gas interpretationMedium

A practice gas shows a metabolic acidosis with HCO₃⁻ 14 mmol/L. Use Winter’s formula to find the expected PaCO₂ (the centre of the range) in mmHg.

HCO₃⁻ 14 mmol/L
PaCO₂ = mmHg
4.Arterial blood gas interpretationHard
pH7.357.457.27PaCO₂mmHg354529HCO₃⁻mmol/L222613added normal-gap acidosispure high-gap acidosisadded metabolic alkalosis

A practice gas shows pH 7.27, PaCO₂ 29 mmHg (3.9 kPa) and HCO₃⁻ 13 mmol/L, with Na⁺ 135 and Cl⁻ 97 mmol/L. Use the anion gap and the delta ratio to click the best interpretation.

pH 7.27PaCO₂ 29 mmHg (3.9 kPa)HCO₃⁻ 13 mmol/LNa⁺ 135 mmol/LCl⁻ 97 mmol/L
  1. 1added normal-gap acidosis
  2. 2pure high-gap acidosis
  3. 3added metabolic 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: completely limited; moisture: very moist; activity: walks occasionally; mobility: no limitation; 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 23/min, SpO₂ 97% on room air, blood pressure 96/58 mmHg, pulse 88/min, alert, temperature 38.1 °C. Which clinical risk group does the patient fall into? Click it.

RR 23SpO₂ 97%airSBP 96HR 88AT 38.1 °C
  1. 1low
  2. 2low–medium
  3. 3medium
  4. 4high
7.Med-surg: cardiovascular & respiratoryMedium

A patient has had atrial fibrillation for more than 48 hours and is listed for elective cardioversion. Why is anticoagulation needed beforehand?

  1. AAtrial clots may be dislodged when sinus rhythm returns
  2. BAnticoagulants make the shock less painful
  3. CAnticoagulants reduce the electrical energy needed for the shock
  4. DAnticoagulants convert AF back to sinus rhythm
8.Med-surg: cardiovascular & respiratoryHard

After cardiac catheterisation via the radial artery, which assessment is most important?

  1. ABowel sounds and abdominal girth every hour after the test
  2. BUrine specific gravity every four hours
  3. CPupil size and reaction to light every 15 minutes
  4. DCirculation, sensation and movement of the hand, and the site

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: CaO₂ = 17.99 mL/dL

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.

Hb in g/dL

138 g/L = 13.8 g/dL

Bound oxygen

1.34·13.8·0.96 = 17.75 mL/dL

Dissolved oxygen

0.003·79 = 0.237 mL/dL

Oxygen content

CaO₂ = 17.75 + 0.237 = 17.99 mL/dL

Answer

CaO₂ = 17.99 mL/dL
2.Oxygen therapy & respiratory calculations

Answer: VT = 330 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·(170 − 152.4) = 66.02 kg

Tidal volume

VT = 5·66.02 = 330.1 ≈ 330 mL

Answer

VT = 330 mL
3.Arterial blood gas interpretation

Answer: PaCO₂ = 29 mmHg

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.

Winter’s formula

PaCO₂ = 1.5·14 + 8 = 29 mmHg
range: 27–31 mmHg

Answer

PaCO₂ = 29 mmHg
4.Arterial blood gas interpretation

Answer: pure high-gap acidosis

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 = 135 − (97 + 13) = 25

Delta ratio

(25 − 12)/(24 − 13) = 1.182
pure high-gap acidosis

Answer

pure high-gap acidosis
5.Clinical assessment scores

Answer: B = 15

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: completely limited → 1
moisture: very moist → 2
activity: walks occasionally → 3
mobility: no limitation → 4
nutrition: probably inadequate → 2
friction and shear: no apparent problem → 3

Add

Braden total = 1 + 2 + 3 + 4 + 2 + 3 = 15

Answer

B = 15
6.Clinical assessment scores

Answer: 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 23/min → 2
SpO₂ 97% → 0
on air → 0
SBP 96 mmHg → 2
HR 88/min → 0
alert (A) → 0
T 38.1 °C → 1

Total and red scores

NEWS2 = 2 + 0 + 0 + 2 + 0 + 0 + 1 = 5
No parameter scores 3.

Risk group

medium

Answer

medium

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

7.Med-surg: cardiovascular & respiratory

Answer: A · Atrial clots may be dislodged when sinus rhythm returns

Why this is the answer

After 48 hours of AF, atrial thrombus may be present. Restoring organised contraction can expel it and cause a stroke. Patients are usually anticoagulated for at least three weeks before (or a transoesophageal echo excludes clot) and for at least four weeks afterwards.

Answer

A · Atrial clots may be dislodged when sinus rhythm returns
8.Med-surg: cardiovascular & respiratory

Answer: D · Circulation, sensation and movement of the hand, and the site

Why this is the answer

After radial access, the compression device and puncture site are checked for bleeding or haematoma, and the hand for colour, warmth, capillary refill, sensation and movement. Radial artery occlusion and forearm compartment syndrome are possible complications.

Answer

D · Circulation, sensation and movement of the hand, and the site

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