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
2050psiDf = 0.16 L/psi3 L/minresidual 200 psit = ? min

Practice exercise (made-up values, not clinical guidance). A size D oxygen cylinder (factor 0.16 L/psi) reads 2050 psi and runs at 3 L/min. Keeping a safe residual of 200 psi, how many minutes t will it last? Round down to a whole minute.

2050 psif = 0.16 L/psi3 L/min200 psi
t = min
2.Oxygen therapy & respiratory calculationsHard
Hb162 g/LSaO₂97%PaO₂90 mmHgCaO₂mL/dL× CO5.7 L/minDO₂?

Practice exercise (made-up values, not clinical guidance). A patient has Hb 162 g/L, SaO₂ 97%, PaO₂ 90 mmHg (12.0 kPa) and a cardiac output of 5.7 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 162 g/LSaO₂ 97%PaO₂ 90 mmHg (12.0 kPa)CO 5.7 L/min
DO₂ = mL/min
3.Arterial blood gas interpretationMedium

A practice gas shows a metabolic acidosis with HCO₃⁻ 8 mmol/L. Use Winter’s formula to find the expected PaCO₂ (the centre of the range) in mmHg.

HCO₃⁻ 8 mmol/L
PaCO₂ = mmHg
4.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 21% oxygen shows PaO₂ 57 mmHg (7.6 kPa) and PaCO₂ 47 mmHg (6.3 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 21%PaO₂ 57 mmHg (7.6 kPa)PaCO₂ 47 mmHg (6.3 kPa)
A–a gradient = 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: slightly limited; moisture: constantly moist; activity: walks occasionally; mobility: very limited; nutrition: very poor; friction and shear: 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 12/min, SpO₂ 86% on room air, blood pressure 110/66 mmHg, pulse 76/min, alert, temperature 37.1 °C. Which clinical risk group does the patient fall into? Click it.

RR 12SpO₂ 86%airSBP 110HR 76AT 37.1 °C
  1. 1low
  2. 2low–medium
  3. 3medium
  4. 4high
7.Med-surg: cardiovascular & respiratoryMedium

A patient's ankle–brachial pressure index (ABPI) is 0.6. What does this suggest?

  1. AA deep vein thrombosis
  2. BNormal leg circulation
  3. CSignificant peripheral arterial disease
  4. DStiff, calcified arteries that read falsely high
8.Med-surg: cardiovascular & respiratoryHard

Why is humidification used with high-flow oxygen?

  1. AWater vapour filters bacteria from the oxygen supply
  2. BHumidification stops oxygen toxicity from developing
  3. CHumidified gas carries more oxygen per litre than dry gas
  4. DDry gas at high flow dries the airway and thickens secretions

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: t = 98 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 litres

(2050 − 200)·0.16 = 296 L

Duration

296/3 = 98.67 min → t = 98 min

Answer

t = 98 min

That is about 1 h 38 min.

2.Oxygen therapy & respiratory calculations

Answer: DO₂ = 1216 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

162 g/L = 16.2 g/dL
CaO₂ = 1.34·16.2·0.97 + 0.003·90 = 21.33 mL/dL

Oxygen delivery

DO₂ = 21.33·5.7·10 = 1216 mL/min

Answer

DO₂ = 1216 mL/min

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

3.Arterial blood gas interpretation

Answer: PaCO₂ = 20 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 = 1.5·8 + 8 = 20 mmHg
range: 18–22 mmHg

Answer

PaCO₂ = 20 mmHg
4.Arterial blood gas interpretation

Answer: A–a gradient = 33.98 mmHg

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.

Alveolar oxygen

PAO₂ = 0.21·713 − 47/0.8 = 149.7 − 58.75 = 90.98 mmHg

Gradient

A–a = 90.98 − 57 = 33.98 mmHg

Answer

A–a gradient = 33.98 mmHg
5.Clinical assessment scores

Answer: B = 11

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: constantly moist → 1
activity: walks occasionally → 3
mobility: very limited → 2
nutrition: very poor → 1
friction and shear: problem → 1

Add

Braden total = 3 + 1 + 3 + 2 + 1 + 1 = 11

Answer

B = 11
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 12/min → 0
SpO₂ 86% → 3
on air → 0
SBP 110 mmHg → 1
HR 76/min → 0
alert (A) → 0
T 37.1 °C → 0

Total and red scores

NEWS2 = 0 + 3 + 0 + 1 + 0 + 0 + 0 = 4
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: C · Significant peripheral arterial disease

Why this is the answer

An ABPI of roughly 1.0–1.3 is normal, and below 0.9 indicates peripheral arterial disease; lower values mean more severe disease. A value above about 1.3 suggests calcified, incompressible vessels, common in diabetes, and is unreliable.

Answer

C · Significant peripheral arterial disease
8.Med-surg: cardiovascular & respiratory

Answer: D · Dry gas at high flow dries the airway and thickens secretions

Why this is the answer

High-flow dry gas overwhelms the nose's ability to humidify, causing dry mucosa, thick secretions and discomfort. Warmed, humidified high-flow systems improve tolerance and help clear secretions.

Answer

D · Dry gas at high flow dries the airway and thickens secretions

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