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.

New problemsBack to the course

In the print window, choose “Save as PDF” to keep a copy on your device.

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
Hb150 g/LSaO₂86%PaO₂51 mmHgCaO₂?

Practice exercise (made-up values, not clinical guidance). A patient has Hb 150 g/L, SaO₂ 86% and PaO₂ 51 mmHg (6.8 kPa). Find the arterial oxygen content CaO₂ = 1.34 × Hb (g/dL) × SaO₂ + 0.003 × PaO₂ (mmHg) in mL O₂/dL.

Hb 150 g/LSaO₂ 86%PaO₂ 51 mmHg (6.8 kPa)
CaO₂ = mL/dL
2.Oxygen therapy & respiratory calculationsHard
PaO₂ 6.2 kPa · FiO₂ 1 · PEEP 8 cmH₂O0100200300400500P/F (mmHg)above 300: no ARDS grademildmoderateseverenot gradable: PEEP below 5

Practice exercise (made-up values, not clinical guidance). A patient with acute hypoxaemia and bilateral opacities, not explained by heart failure, has PaO₂ 6.2 kPa on 100% oxygen with a PEEP of 8 cmH₂O. Grade the ARDS severity with the Berlin definition. Click your answer.

PaO₂ 6.2 kPaFiO₂ 100%PEEP 8 cmH₂O
  1. 1above 300: no ARDS grade
  2. 2mild
  3. 3moderate
  4. 4severe
  5. 5not gradable: PEEP below 5
3.Arterial blood gas interpretationMedium
pH7.357.457.52PaCO₂mmHg354539HCO₃⁻mmol/L222631uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.52, PaCO₂ 39 mmHg (5.2 kPa) and HCO₃⁻ 31 mmol/L. The primary disorder is metabolic alkalosis. How far is it compensated? Click your answer.

pH 7.52PaCO₂ 39 mmHg (5.2 kPa)HCO₃⁻ 31 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
4.Arterial blood gas interpretationHard
pH7.357.457.31PaCO₂mmHg354529HCO₃⁻mmol/L222614added normal-gap acidosispure high-gap acidosisadded metabolic alkalosis

A practice gas shows pH 7.31, PaCO₂ 29 mmHg (3.9 kPa) and HCO₃⁻ 14 mmol/L, with Na⁺ 137 and Cl⁻ 108 mmol/L. Use the anion gap and the delta ratio to click the best interpretation.

pH 7.31PaCO₂ 29 mmHg (3.9 kPa)HCO₃⁻ 14 mmol/LNa⁺ 137 mmol/LCl⁻ 108 mmol/L
  1. 1added normal-gap acidosis
  2. 2pure high-gap acidosis
  3. 3added metabolic alkalosis
5.Clinical assessment scoresMedium
H? / 25+D? / 15+Aid? / 30+IV? / 20+G? / 20+MS? / 15Σ?

Practice exercise (made-up values, not clinical guidance). A practice patient is assessed with the Morse fall scale: history of falling in the last 3 months: no; secondary diagnosis: yes; ambulatory aid: crutches, cane or walker; IV therapy or saline lock: no; gait: impaired; mental status: knows own limits. Find the Morse total MFS.

0–125
MFS =
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 91% on room air, blood pressure 112/68 mmHg, pulse 82/min, alert, temperature 37.1 °C. Which clinical risk group does the patient fall into? Click it.

RR 12SpO₂ 91%airSBP 112HR 82AT 37.1 °C
  1. 1low
  2. 2low–medium
  3. 3medium
  4. 4high
7.Med-surg: cardiovascular & respiratoryMedium

Which set of side effects is typical of thiazide or thiazide-like diuretics such as indapamide?

  1. AHigh sodium and magnesium, with low blood glucose
  2. BHigh potassium and sodium, low uric acid and low blood glucose
  3. CDry cough, taste disturbance and swelling of the lips
  4. DLow potassium and sodium, raised uric acid and raised glucose
8.Med-surg: cardiovascular & respiratoryHard

A patient's chest drain tubing disconnects from the drainage unit. What should the nurse do first?

  1. AReconnect it, or put the tube end in sterile water, then assess
  2. BClamp the tube for several hours and recheck the patient later
  3. CLeave it open to air until the doctor arrives to review it
  4. DRemove the drain from the chest and cover the site

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: CaO₂ = 17.44 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

150 g/L = 15 g/dL

Bound oxygen

1.34·15·0.86 = 17.29 mL/dL

Dissolved oxygen

0.003·51 = 0.153 mL/dL

Oxygen content

CaO₂ = 17.29 + 0.153 = 17.44 mL/dL

Answer

CaO₂ = 17.44 mL/dL
2.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.

PEEP

PEEP 8 ≥ 5 cmH₂O

PaO₂ in mmHg

6.2·7.5 = 46.5 mmHg

P/F ratio

P/F = 46.5/1 = 46.5 mmHg

Berlin severity

severe

Answer

severe
3.Arterial blood gas interpretation

Answer: uncompensated

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 7.52: alkalaemia (above 7.45)
PaCO₂ 39 mmHg: normal (35–45)
HCO₃⁻ 31 mmol/L: high (22–26)

Compensation

Clinically, also check the expected compensation: for a metabolic alkalosis PaCO₂ ≈ 0.7·HCO₃⁻ + 21 = 40.7–44.7 mmHg, so the measured 39 mmHg points to an additional respiratory alkalosis (a mixed disorder). The answer above is the ROME exam classification.

uncompensated

Answer

uncompensated
4.Arterial blood gas interpretation

Answer: added normal-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 = 137 − (108 + 14) = 15

Delta ratio

(15 − 12)/(24 − 14) = 0.3
added normal-gap acidosis

Answer

added normal-gap acidosis
5.Clinical assessment scores

Answer: MFS = 50

Morse fall scale: six items. History of falling: no 0, yes 25. Secondary diagnosis: no 0, yes 15. Ambulatory aid: none, bed rest or nurse assistance 0; crutches, cane or walker 15; holding on to furniture 30. IV therapy or saline lock: no 0, yes 20. Gait: normal, bed rest or wheelchair 0; weak 10; impaired 20. Mental status: knows own limits 0; overestimates or forgets limits 15. The total runs from 0 to 125. Risk cut-offs differ between hospitals; a common set is 0–24 low, 25–44 moderate and 45 or more high.

Score each item

history of falling in the last 3 months: no → 0
secondary diagnosis: yes → 15
ambulatory aid: crutches, cane or walker → 15
IV therapy or saline lock: no → 0
gait: impaired → 20
mental status: knows own limits → 0

Add

Morse total = 0 + 15 + 15 + 0 + 20 + 0 = 50

Answer

MFS = 50
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 91% → 3
on air → 0
SBP 112 mmHg → 0
HR 82/min → 0
alert (A) → 0
T 37.1 °C → 0

Total and red scores

NEWS2 = 0 + 3 + 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: D · Low potassium and sodium, raised uric acid and raised glucose

Why this is the answer

Thiazides cause hypokalaemia, hyponatraemia, hypomagnesaemia, hyperuricaemia (gout), hyperglycaemia and hypercalcaemia (they reduce calcium excretion). Dry cough and angioedema are ACE inhibitor effects.

Answer

D · Low potassium and sodium, raised uric acid and raised glucose
8.Med-surg: cardiovascular & respiratory

Answer: A · Reconnect it, or put the tube end in sterile water, then assess

Why this is the answer

A disconnected tube lets atmospheric air enter the pleural space. Reconnecting quickly, or submerging the tube end 2–3 cm in sterile water as a temporary seal, restores the one-way valve. Then assess for respiratory distress and inform the team. Prolonged clamping risks tension pneumothorax.

Answer

A · Reconnect it, or put the tube end in sterile water, then assess

ExamProblems · examproblems.com/courses/respiratory-care-and-oxygen-therapy