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
60 s470 mLf = 14/min · V̇A = ?VD​ = 140 mL

Practice exercise (made-up values, not clinical guidance). A patient breathes 14 times a minute with a tidal volume of 470 mL. The anatomical dead space is 140 mL. Find the alveolar ventilation V̇A in L/min.

VT 470 mL14/minVD 140 mL
V̇A = L/min
2.Oxygen therapy & respiratory calculationsHard
94 kg187 cm♂5 mL/kg PBWVT​ = ? mL

Practice exercise (made-up values, not clinical guidance). A ventilated man is 187 cm tall and weighs 94 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.

187 cm94 kg5 mL/kg
VT = mL
3.Arterial blood gas interpretationMedium
pH7.357.457.43PaCO₂mmHg354525HCO₃⁻mmol/L222616uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.43, PaCO₂ 25 mmHg (3.3 kPa) and HCO₃⁻ 16 mmol/L. The primary disorder is respiratory alkalosis. How far is it compensated? Click your answer.

pH 7.43PaCO₂ 25 mmHg (3.3 kPa)HCO₃⁻ 16 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
4.Arterial blood gas interpretationHard

Practice values: Na⁺ 140, Cl⁻ 99, HCO₃⁻ 21 mmol/L and albumin 27 g/L. Find the albumin-corrected anion gap AGc = AG + 0.25·(40 − albumin).

Na⁺ 140 mmol/LCl⁻ 99 mmol/LHCO₃⁻ 21 mmol/Lalbumin 27 g/L
AGc = mmol/L
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: rarely moist; activity: chairfast; mobility: no limitation; nutrition: very poor; 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 97% on room air, blood pressure 90/54 mmHg, pulse 58/min, alert, temperature 37.1 °C. Which clinical risk group does the patient fall into? Click it.

RR 14SpO₂ 97%airSBP 90HR 58AT 37.1 °C
  1. 1low
  2. 2low–medium
  3. 3medium
  4. 4high
7.Med-surg: cardiovascular & respiratoryMedium

Why is pyridoxine (vitamin B6) often given with isoniazid?

  1. ATo prevent orange discolouration of urine
  2. BTo prevent peripheral neuropathy
  3. CTo prevent gout attacks
  4. DTo prevent loss of colour vision
8.Med-surg: cardiovascular & respiratoryHard

A patient with pneumonia has a heart rate of 118/min, BP 86/50 mmHg, RR 28/min and a high lactate. Sepsis is recognised. Which action should not be delayed?

  1. AGive oral antibiotics and reassess the next day
  2. BDelay fluids until a chest X-ray has been reported
  3. CTake blood cultures and give IV antibiotics within the first hour
  4. DWait for the sputum culture result before choosing an antibiotic

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: V̇A = 4.62 L/min

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).

Alveolar part of a breath

470 − 140 = 330 mL

Alveolar ventilation

V̇A = 330·14 = 4620 mL/min = 4.62 L/min

Answer

V̇A = 4.62 L/min
2.Oxygen therapy & respiratory calculations

Answer: VT = 407 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·(187 − 152.4) = 81.49 kg

Tidal volume

VT = 5·81.49 = 407.4 ≈ 407 mL

Answer

VT = 407 mL
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 7.43: within 7.35–7.45
PaCO₂ 25 mmHg: low (35–45)
HCO₃⁻ 16 mmol/L: low (22–26)

Compensation

fully compensated

Answer

fully compensated
4.Arterial blood gas interpretation

Answer: AGc = 23.25 mmol/L

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 = 140 − (99 + 21) = 20

Correction for albumin

20 + 0.25·(40 − 27) = 23.25 mmol/L

Answer

AGc = 23.25 mmol/L

Above about 12 after correction: a high anion gap.

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: rarely moist → 4
activity: chairfast → 2
mobility: no limitation → 4
nutrition: very poor → 1
friction and shear: no apparent problem → 3

Add

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

Answer

B = 15
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 14/min → 0
SpO₂ 97% → 0
on air → 0
SBP 90 mmHg → 3
HR 58/min → 0
alert (A) → 0
T 37.1 °C → 0

Total and red scores

NEWS2 = 0 + 0 + 0 + 3 + 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 prevent peripheral neuropathy

Why this is the answer

Isoniazid increases pyridoxine loss, which can cause peripheral neuropathy, especially in people with diabetes, alcohol dependence, malnutrition or HIV. Pyridoxine prevents this. Isoniazid can also cause hepatitis. Ethambutol affects vision; pyrazinamide can cause gout.

Answer

B · To prevent peripheral neuropathy
8.Med-surg: cardiovascular & respiratory

Answer: C · Take blood cultures and give IV antibiotics within the first hour

Why this is the answer

In sepsis with shock, blood cultures, IV antibiotics within the first hour, IV fluids, lactate measurement, oxygen if hypoxic and urine output monitoring are started together. Cultures should not delay antibiotics. Persistent hypotension may need vasopressors in critical care.

Answer

C · Take blood cultures and give IV antibiotics within the first hour

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