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
Hb74 g/LSaO₂98%PaO₂104 mmHgCaO₂?

Practice exercise (made-up values, not clinical guidance). A patient has Hb 74 g/L, SaO₂ 98% and PaO₂ 104 mmHg (13.9 kPa). Find the arterial oxygen content CaO₂ = 1.34 × Hb (g/dL) × SaO₂ + 0.003 × PaO₂ (mmHg) in mL O₂/dL.

Hb 74 g/LSaO₂ 98%PaO₂ 104 mmHg (13.9 kPa)
CaO₂ = mL/dL
2.Oxygen therapy & respiratory calculationsHard
Hb90 g/LSaO₂96%PaO₂82 mmHgCaO₂mL/dL× CO6.6 L/minDO₂?

Practice exercise (made-up values, not clinical guidance). A patient has Hb 90 g/L, SaO₂ 96%, PaO₂ 82 mmHg (10.9 kPa) and a cardiac output of 6.6 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 90 g/LSaO₂ 96%PaO₂ 82 mmHg (10.9 kPa)CO 6.6 L/min
DO₂ = mL/min
3.Arterial blood gas interpretationMedium
pH7.357.457.32PaCO₂mmHg354526HCO₃⁻mmol/L222613uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.32, PaCO₂ 26 mmHg (3.5 kPa) and HCO₃⁻ 13 mmol/L. The primary disorder is metabolic acidosis. How far is it compensated? Click your answer.

pH 7.32PaCO₂ 26 mmHg (3.5 kPa)HCO₃⁻ 13 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
4.Arterial blood gas interpretationHard
pH7.357.457.29PaCO₂mmHg354562HCO₃⁻mmol/L222629acutechronicacute on chronic

A practice gas shows a respiratory acidosis: pH 7.29, PaCO₂ 62 mmHg (8.3 kPa), HCO₃⁻ 29 mmol/L. Use the rules ‘HCO₃⁻ rises 1 mmol/L per 10 mmHg (acute) or 3.5 mmol/L per 10 mmHg (chronic)’ to classify it. Click your answer.

pH 7.29PaCO₂ 62 mmHg (8.3 kPa)HCO₃⁻ 29 mmol/L
  1. 1acute
  2. 2chronic
  3. 3acute on chronic
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: yes; secondary diagnosis: no; ambulatory aid: crutches, cane or walker; IV therapy or saline lock: yes; gait: normal, bed rest or wheelchair; 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 96% on room air, blood pressure 84/50 mmHg, pulse 70/min, alert, temperature 37.4 °C. Which clinical risk group does the patient fall into? Click it.

RR 12SpO₂ 96%airSBP 84HR 70AT 37.4 °C
  1. 1low
  2. 2low–medium
  3. 3medium
  4. 4high
7.Med-surg: cardiovascular & respiratoryMedium

Which position is usually best for the legs of a patient with chronic venous insufficiency and ankle swelling?

  1. ACrossed at the knees while sitting
  2. BRaised above the level of the heart when resting
  3. CHanging down over the side of the bed
  4. DKept still in a standing position for long periods
8.Med-surg: cardiovascular & respiratoryHard

A patient with severe chronic kidney disease needs therapeutic anticoagulation for a DVT. Why might unfractionated heparin be chosen instead of a low-molecular-weight heparin?

  1. AUnfractionated heparin is taken by mouth
  2. BLMWH cannot be given to anyone over 60
  3. CUnfractionated heparin has no bleeding risk at all
  4. DLMWH is cleared by the kidneys and can accumulate

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: CaO₂ = 10.03 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

74 g/L = 7.4 g/dL

Bound oxygen

1.34·7.4·0.98 = 9.718 mL/dL

Dissolved oxygen

0.003·104 = 0.312 mL/dL

Oxygen content

CaO₂ = 9.718 + 0.312 = 10.03 mL/dL

Answer

CaO₂ = 10.03 mL/dL
2.Oxygen therapy & respiratory calculations

Answer: DO₂ = 780.4 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

90 g/L = 9 g/dL
CaO₂ = 1.34·9·0.96 + 0.003·82 = 11.82 mL/dL

Oxygen delivery

DO₂ = 11.82·6.6·10 = 780.4 mL/min

Answer

DO₂ = 780.4 mL/min

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

3.Arterial blood gas interpretation

Answer: partially 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 7.32: acidaemia (below 7.35)
PaCO₂ 26 mmHg: low (35–45)
HCO₃⁻ 13 mmol/L: low (22–26)

Compensation

partially compensated

Answer

partially compensated
4.Arterial blood gas interpretation

Answer: acute on chronic

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 HCO₃⁻

acute: 24 + 1·2.2 = 26.2 mmol/L
chronic: 24 + 3.5·2.2 = 31.7 mmol/L

Compare

measured: 29 mmol/L → acute on chronic

Answer

acute on chronic
5.Clinical assessment scores

Answer: MFS = 60

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: yes → 25
secondary diagnosis: no → 0
ambulatory aid: crutches, cane or walker → 15
IV therapy or saline lock: yes → 20
gait: normal, bed rest or wheelchair → 0
mental status: knows own limits → 0

Add

Morse total = 25 + 0 + 15 + 20 + 0 + 0 = 60

Answer

MFS = 60
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 96% → 0
on air → 0
SBP 84 mmHg → 3
HR 70/min → 0
alert (A) → 0
T 37.4 °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 · Raised above the level of the heart when resting

Why this is the answer

Elevating the legs above heart level reduces venous pressure and oedema. Compression therapy, walking and avoiding long periods of standing also help. By contrast, patients with arterial disease often find that lowering the legs eases pain.

Answer

B · Raised above the level of the heart when resting
8.Med-surg: cardiovascular & respiratory

Answer: D · LMWH is cleared by the kidneys and can accumulate

Why this is the answer

Low-molecular-weight heparins are mainly renally excreted, so they accumulate in severe renal impairment and increase bleeding risk. Unfractionated heparin is cleared mainly by other routes, has a short half-life and can be monitored with aPTT and reversed with protamine.

Answer

D · LMWH is cleared by the kidneys and can accumulate

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