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
Hb104 g/LSaO₂97%PaO₂86 mmHgCaO₂?

Practice exercise (made-up values, not clinical guidance). A patient has Hb 104 g/L, SaO₂ 97% and PaO₂ 86 mmHg (11.5 kPa). Find the arterial oxygen content CaO₂ = 1.34 × Hb (g/dL) × SaO₂ + 0.003 × PaO₂ (mmHg) in mL O₂/dL.

Hb 104 g/LSaO₂ 97%PaO₂ 86 mmHg (11.5 kPa)
CaO₂ = mL/dL
2.Oxygen therapy & respiratory calculationsHard
Hb163 g/LSaO₂90%PaO₂58 mmHgCaO₂mL/dL× CO6.8 L/minDO₂?

Practice exercise (made-up values, not clinical guidance). A patient has Hb 163 g/L, SaO₂ 90%, PaO₂ 58 mmHg (7.7 kPa) and a cardiac output of 6.8 L/min. With CaO₂ = 1.34 × Hb (g/dL) × SaO₂ + 0.003 × PaO₂ (mmHg), find the oxygen delivery DO₂ = CaO₂ × CO × 10 in mL/min.

Hb 163 g/LSaO₂ 90%PaO₂ 58 mmHg (7.7 kPa)CO 6.8 L/min
DO₂ = mL/min
3.Arterial blood gas interpretationMedium

A practice gas shows PaCO₂ 71 mmHg (9.5 kPa). Use the rule that in acute respiratory acidosis HCO₃⁻ rises by 1 mmol/L for every 10 mmHg that PaCO₂ is above 40, starting from HCO₃⁻ 24 mmol/L, to find the expected HCO₃⁻.

PaCO₂ 71 mmHg (9.5 kPa)baseline: 40 mmHg, 24 mmol/L
HCO₃⁻ = mmol/L
4.Arterial blood gas interpretationHard

A practice gas shows a metabolic alkalosis with HCO₃⁻ 39 mmol/L. Use expected PaCO₂ = 0.7·HCO₃⁻ + 21 to find the expected PaCO₂.

HCO₃⁻ 39 mmol/L
PaCO₂ = mmHg
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: occasionally moist; activity: walks frequently; mobility: completely immobile; nutrition: adequate; 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 91% on room air, blood pressure 88/52 mmHg, pulse 76/min, alert, temperature 38.1 °C. Which clinical risk group does the patient fall into? Click it.

RR 14SpO₂ 91%airSBP 88HR 76AT 38.1 °C
  1. 1low
  2. 2low–medium
  3. 3medium
  4. 4high
7.Med-surg: cardiovascular & respiratoryMedium

Why are patients with severe COPD encouraged to eat small, frequent meals?

  1. ALarge meals cause the airways to narrow permanently
  2. BSmall meals reduce how often the inhalers are needed
  3. CA full stomach limits the diaphragm and eating is tiring
  4. DFrequent meals prevent chest infections directly
8.Med-surg: cardiovascular & respiratoryHard

After a pneumonectomy, how is the patient usually positioned?

  1. AHead down with the legs raised, to drain secretions from the lung
  2. BOn the back or the operated side, not fully on the remaining lung
  3. CFully on the non-operated side, to help drain the empty space
  4. DFlat and prone for the whole of the first day after surgery

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: CaO₂ = 13.78 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

104 g/L = 10.4 g/dL

Bound oxygen

1.34·10.4·0.97 = 13.52 mL/dL

Dissolved oxygen

0.003·86 = 0.258 mL/dL

Oxygen content

CaO₂ = 13.52 + 0.258 = 13.78 mL/dL

Answer

CaO₂ = 13.78 mL/dL
2.Oxygen therapy & respiratory calculations

Answer: DO₂ = 1349 mL/min

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.

Oxygen content

163 g/L = 16.3 g/dL
CaO₂ = 1.34·16.3·0.9 + 0.003·58 = 19.83 mL/dL

Oxygen delivery

DO₂ = 19.83·6.8·10 = 1349 mL/min

Answer

DO₂ = 1349 mL/min

A normal resting adult value is about 1000 mL/min.

3.Arterial blood gas interpretation

Answer: HCO₃⁻ = 27.1 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.

Change in PaCO₂

|71 − 40| = 31 mmHg → 3.1 × 10 mmHg

Expected HCO₃⁻

HCO₃⁻ = 24 + 1·3.1 = 27.1 mmol/L

Answer

HCO₃⁻ = 27.1 mmol/L
4.Arterial blood gas interpretation

Answer: PaCO₂ = 48.3 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.

Expected PaCO₂

0.7·39 + 21 = 48.3 mmHg

Answer

PaCO₂ = 48.3 mmHg

The rise has a limit: PaCO₂ rarely goes above about 55 mmHg from compensation alone.

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: occasionally moist → 3
activity: walks frequently → 4
mobility: completely immobile → 1
nutrition: adequate → 3
friction and shear: no apparent problem → 3

Add

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

Answer

B = 15
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 91% → 3
on air → 0
SBP 88 mmHg → 3
HR 76/min → 0
alert (A) → 0
T 38.1 °C → 1

Total and red scores

NEWS2 = 0 + 3 + 0 + 3 + 0 + 0 + 1 = 7
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: C · A full stomach limits the diaphragm and eating is tiring

Why this is the answer

Many people with severe COPD lose weight because breathing uses a lot of energy and large meals cause bloating and breathlessness. Small, nutrient-dense meals help maintain weight and muscle strength.

Answer

C · A full stomach limits the diaphragm and eating is tiring
8.Med-surg: cardiovascular & respiratory

Answer: B · On the back or the operated side, not fully on the remaining lung

Why this is the answer

After a pneumonectomy, the remaining lung needs room to expand, and the mediastinum must not shift. Patients usually lie on their back or on the operated side, semi-upright. Lying fully on the non-operated side can compress the remaining lung. Chest drains, if present, are managed per surgical instructions.

Answer

B · On the back or the operated side, not fully on the remaining lung

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