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 s440 mLf = 16/min · V̇A = ?VD​ = 150 mL

Practice exercise (made-up values, not clinical guidance). A patient breathes 16 times a minute with a tidal volume of 440 mL. The anatomical dead space is 150 mL. Find the alveolar ventilation V̇A in L/min.

VT 440 mL16/minVD 150 mL
V̇A = L/min
2.Oxygen therapy & respiratory calculationsHard
1650psiDf = 0.16 L/psi75 minresidual 200 psiQ = ? L/min

Practice exercise (made-up values, not clinical guidance). A transfer will take 75 minutes. The size D cylinder (factor 0.16 L/psi) reads 1650 psi. Keeping a safe residual of 200 psi, what is the highest whole-number flow Q in L/min that lasts the whole transfer?

75 min1650 psif = 0.16 L/psi200 psi
Q = L/min
3.Arterial blood gas interpretationMedium
pH7.357.457.58PaCO₂mmHg354521HCO₃⁻mmol/L222619uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.58, PaCO₂ 21 mmHg (2.8 kPa) and HCO₃⁻ 19 mmol/L. The primary disorder is respiratory alkalosis. How far is it compensated? Click your answer.

pH 7.58PaCO₂ 21 mmHg (2.8 kPa)HCO₃⁻ 19 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
4.Arterial blood gas interpretationHard
pH7.357.457.17PaCO₂mmHg354551HCO₃⁻mmol/L222618appropriate compensationadded respiratory acidosisadded respiratory alkalosis

A practice gas shows a metabolic acidosis: pH 7.17, PaCO₂ 51 mmHg (6.8 kPa), HCO₃⁻ 18 mmol/L. Compare the measured PaCO₂ with Winter’s formula. Click your interpretation.

pH 7.17PaCO₂ 51 mmHg (6.8 kPa)HCO₃⁻ 18 mmol/L
  1. 1appropriate compensation
  2. 2added respiratory acidosis
  3. 3added respiratory 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: yes; secondary diagnosis: yes; ambulatory aid: crutches, cane or walker; IV therapy or saline lock: yes; gait: weak; mental status: knows own limits. Find the Morse total MFS.

0–125
MFS =
6.Clinical assessment scoresHard
underweighthealthy weightoverweightobesity class Iobesity class IIobesity class III

Practice exercise (made-up values, not clinical guidance). An adult weighs 95 kg and is 156 cm tall. Calculate the BMI and click the WHO weight category.

95 kg156 cm
  1. 1underweight
  2. 2healthy weight
  3. 3overweight
  4. 4obesity class I
  5. 5obesity class II
  6. 6obesity class III
7.Med-surg: cardiovascular & respiratoryMedium

A patient with a regular narrow-complex tachycardia of 180/min is alert with a normal blood pressure. What is usually tried first?

  1. AA large oral dose of digoxin
  2. BVagal manoeuvres such as a modified Valsalva
  3. CAn immediate unsynchronised shock with the defibrillator
  4. DChest compressions until the rate slows
8.Med-surg: cardiovascular & respiratoryHard

A patient with COPD is breathless with SpO₂ 84% on air. A blood gas shows pH 7.30 and a raised PaCO₂ despite optimal medical treatment. Which treatment is likely to be considered?

  1. AStopping the nebulised bronchodilators
  2. BIV sedation to slow the breathing rate
  3. CHigh-concentration oxygen by non-rebreather mask
  4. DNon-invasive ventilation (NIV)

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: V̇A = 4.64 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

440 − 150 = 290 mL

Alveolar ventilation

V̇A = 290·16 = 4640 mL/min = 4.64 L/min

Answer

V̇A = 4.64 L/min
2.Oxygen therapy & respiratory calculations

Answer: Q = 3 L/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

(1650 − 200)·0.16 = 232 L

Highest flow

232/75 = 3.093 L/min → Q = 3 L/min

Answer

Q = 3 L/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 7.58: alkalaemia (above 7.45)
PaCO₂ 21 mmHg: low (35–45)
HCO₃⁻ 19 mmol/L: low (22–26)

Compensation

partially compensated

Answer

partially compensated
4.Arterial blood gas interpretation

Answer: added respiratory 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.

Expected PaCO₂

1.5·18 + 8 = 35 → 33–37 mmHg

Compare

measured: 51 mmHg → added respiratory acidosis

Answer

added respiratory acidosis
5.Clinical assessment scores

Answer: MFS = 85

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: yes → 15
ambulatory aid: crutches, cane or walker → 15
IV therapy or saline lock: yes → 20
gait: weak → 10
mental status: knows own limits → 0

Add

Morse total = 25 + 15 + 15 + 20 + 10 + 0 = 85

Answer

MFS = 85
6.Clinical assessment scores

Answer: obesity class II

Body mass index: BMI = weight (kg)/height (m)², with the height converted to metres first. With pounds and inches, BMI = 703 × weight (lb)/height (in)². WHO adult categories: below 18.5 underweight, 18.5–24.9 healthy weight, 25.0–29.9 overweight, 30.0–34.9 obesity class I, 35.0–39.9 obesity class II and 40 or more obesity class III.

BMI

BMI = 95/1.56² = 39.04

Category

obesity class II

Answer

obesity class II
7.Med-surg: cardiovascular & respiratory

Answer: B · Vagal manoeuvres such as a modified Valsalva

Why this is the answer

In stable supraventricular tachycardia, vagal manoeuvres slow AV node conduction and can stop the rhythm. If they fail, IV adenosine is usually next. Electrical cardioversion is for patients with adverse features such as shock or chest pain.

Answer

B · Vagal manoeuvres such as a modified Valsalva
8.Med-surg: cardiovascular & respiratory

Answer: D · Non-invasive ventilation (NIV)

Why this is the answer

In an acute COPD exacerbation with respiratory acidosis (pH < 7.35 and raised PaCO₂) persisting despite optimal medical therapy, NIV reduces mortality and the need for intubation. Controlled oxygen continues with a target of 88–92%. Uncontrolled high-flow oxygen and sedatives can worsen CO₂ retention.

Answer

D · Non-invasive ventilation (NIV)

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