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
850psiHf = 3.14 L/psi6 L/minresidual 200 psit = ? min

Practice exercise (made-up values, not clinical guidance). A size H oxygen cylinder (factor 3.14 L/psi) reads 850 psi and runs at 6 L/min. Keeping a safe residual of 200 psi, how many minutes t will it last? Round down to a whole minute.

850 psif = 3.14 L/psi6 L/min200 psi
t = min
2.Oxygen therapy & respiratory calculationsHard
Hb100 g/LSaO₂98%PaO₂103 mmHgCaO₂mL/dL× CO4.5 L/minDO₂?

Practice exercise (made-up values, not clinical guidance). A patient has Hb 100 g/L, SaO₂ 98%, PaO₂ 103 mmHg (13.7 kPa) and a cardiac output of 4.5 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 100 g/LSaO₂ 98%PaO₂ 103 mmHg (13.7 kPa)CO 4.5 L/min
DO₂ = mL/min
3.Arterial blood gas interpretationMedium
pH7.357.457.36PaCO₂mmHg354551HCO₃⁻mmol/L222628uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.36, PaCO₂ 51 mmHg (6.8 kPa) and HCO₃⁻ 28 mmol/L. The primary disorder is respiratory acidosis. How far is it compensated? Click your answer.

pH 7.36PaCO₂ 51 mmHg (6.8 kPa)HCO₃⁻ 28 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
4.Arterial blood gas interpretationHard

Practice values: Na⁺ 140, Cl⁻ 107 and HCO₃⁻ 17 mmol/L. Calculate the delta ratio (AG − 12)/(24 − HCO₃⁻), using AG = Na⁺ − (Cl⁻ + HCO₃⁻). Give two decimals.

Na⁺ 140 mmol/LCl⁻ 107 mmol/LHCO₃⁻ 17 mmol/L
delta ratio =
5.Clinical assessment scoresMedium
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≥39.1

Practice exercise (made-up values, not clinical guidance). Use the NEWS2 chart (SpO₂ scale 1) for these observations: respiration rate 20/min, SpO₂ 93% on room air, blood pressure 92/56 mmHg, pulse 70/min, alert, temperature 39.0 °C. What is the NEWS2 total score?

RR 20SpO₂ 93%airSBP 92HR 70AT 39.0 °C
NEWS2 =
6.Clinical assessment scoresHard
underweighthealthy weightoverweightobesity class Iobesity class IIobesity class III

Practice exercise (made-up values, not clinical guidance). An adult weighs 149 kg and is 169 cm tall. Calculate the BMI and click the WHO weight category.

149 kg169 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

After repair of an abdominal aortic aneurysm, which regular assessment helps detect a blocked graft or clots in the legs?

  1. AMeasuring the blood glucose every hour through the night
  2. BTesting the gag reflex every four hours after surgery
  3. CChecking leg pulses, colour, warmth and sensation
  4. DChecking the pupils' response to light
8.Med-surg: cardiovascular & respiratoryHard

A patient with crushing chest pain has ST elevation in leads V1–V4. Which coronary artery is most likely blocked?

  1. AThe left anterior descending artery
  2. BThe circumflex artery
  3. CThe right coronary artery and its branches
  4. DThe left subclavian artery

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: t = 340 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

(850 − 200)·3.14 = 2041 L

Duration

2041/6 = 340.2 min → t = 340 min

Answer

t = 340 min

That is about 5 h 40 min.

2.Oxygen therapy & respiratory calculations

Answer: DO₂ = 604.8 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

100 g/L = 10 g/dL
CaO₂ = 1.34·10·0.98 + 0.003·103 = 13.44 mL/dL

Oxygen delivery

DO₂ = 13.44·4.5·10 = 604.8 mL/min

Answer

DO₂ = 604.8 mL/min

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

3.Arterial blood gas interpretation

Answer: fully 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 7.36: within 7.35–7.45
PaCO₂ 51 mmHg: high (35–45)
HCO₃⁻ 28 mmol/L: high (22–26)

Compensation

fully compensated

Answer

fully compensated
4.Arterial blood gas interpretation

Answer: delta ratio = 0.5714

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 = 140 − (107 + 17) = 16

Delta ratio

(16 − 12)/(24 − 17) = 4/7 = 0.5714

Answer

delta ratio = 0.5714

Below 1: an added normal anion gap acidosis.

5.Clinical assessment scores

Answer: NEWS2 = 5

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 20/min → 0
SpO₂ 93% → 2
on air → 0
SBP 92 mmHg → 2
HR 70/min → 0
alert (A) → 0
T 39.0 °C → 1

Add

NEWS2 = 0 + 2 + 0 + 2 + 0 + 0 + 1 = 5

Answer

NEWS2 = 5
6.Clinical assessment scores

Answer: obesity class III

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 = 149/1.69² = 52.17

Category

obesity class III

Answer

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

Answer: C · Checking leg pulses, colour, warmth and sensation

Why this is the answer

After aortic surgery, distal pulses, skin colour, temperature, capillary refill, movement and sensation are checked often and compared with baseline. Loss of pulses, pallor or pain suggests graft occlusion or emboli and must be reported at once. Urine output is also monitored for renal perfusion.

Answer

C · Checking leg pulses, colour, warmth and sensation
8.Med-surg: cardiovascular & respiratory

Answer: A · The left anterior descending artery

Why this is the answer

ST elevation in V1–V4 indicates an anteroseptal STEMI, usually from LAD occlusion. Anterior MIs damage a large area of muscle and carry a high risk of heart failure and arrhythmias. Leads II, III and aVF suggest an inferior MI, usually from the right coronary artery.

Answer

A · The left anterior descending artery

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