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 s480 mLf = 13/min · V̇A = ?VD​ = 180 mL

Practice exercise (made-up values, not clinical guidance). A patient breathes 13 times a minute with a tidal volume of 480 mL. The anatomical dead space is 180 mL. Find the alveolar ventilation V̇A in L/min.

VT 480 mL13/minVD 180 mL
V̇A = L/min
2.Oxygen therapy & respiratory calculationsHard
195 bar3 L4 L/min20 bart = ? min

Practice exercise (made-up values, not clinical guidance). A cylinder with a water capacity of 3 L is filled to 195 bar and runs at 4 L/min. The gas volume is about the water capacity × the pressure. In this exercise the cylinder is changed at 20 bar. How many minutes t until it must be changed? Round down to a whole minute.

3 L195 bar4 L/min20 bar
t = min
3.Arterial blood gas interpretationMedium
pH7.357.457.36PaCO₂mmHg354533HCO₃⁻mmol/L222618uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.36, PaCO₂ 33 mmHg (4.4 kPa) and HCO₃⁻ 18 mmol/L. The primary disorder is metabolic acidosis. How far is it compensated? Click your answer.

pH 7.36PaCO₂ 33 mmHg (4.4 kPa)HCO₃⁻ 18 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
4.Arterial blood gas interpretationHard
pH7.357.457.31PaCO₂mmHg354533HCO₃⁻mmol/L222616added normal-gap acidosispure high-gap acidosisadded metabolic alkalosis

A practice gas shows pH 7.31, PaCO₂ 33 mmHg (4.4 kPa) and HCO₃⁻ 16 mmol/L, with Na⁺ 134 and Cl⁻ 102 mmol/L. Use the anion gap and the delta ratio to click the best interpretation.

pH 7.31PaCO₂ 33 mmHg (4.4 kPa)HCO₃⁻ 16 mmol/LNa⁺ 134 mmol/LCl⁻ 102 mmol/L
  1. 1added normal-gap acidosis
  2. 2pure high-gap acidosis
  3. 3added metabolic alkalosis
5.Clinical assessment scoresMedium
mildmoderatesevere

Practice exercise (made-up values, not clinical guidance). A practice patient after a head injury opens the eyes only to pressure (a painful stimulus), says inappropriate, random words and shows as the best motor response: extension of the arms and legs (abnormal extension). Work out the GCS and classify the head injury by it. Click your answer.

  1. 1mild
  2. 2moderate
  3. 3severe
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 14/min, SpO₂ 91% on room air, blood pressure 92/56 mmHg, pulse 130/min, alert, temperature 35.2 °C. Which clinical risk group does the patient fall into? Click it.

RR 14SpO₂ 91%airSBP 92HR 130AT 35.2 °C
  1. 1low
  2. 2low–medium
  3. 3medium
  4. 4high
7.Med-surg: cardiovascular & respiratoryMedium

Which finding shows that long-standing hypertension has caused target organ damage?

  1. ALeft ventricular hypertrophy on the ECG
  2. BA heart rate of 72/min
  3. CA normal fasting glucose
  4. DClear lung fields on the chest X-ray
8.Med-surg: cardiovascular & respiratoryHard

A woman starting rifampicin (rifampin) for tuberculosis uses a combined oral contraceptive pill. What advice is correct?

  1. ATake two pills a day to make up for the drug
  2. BContinue the pill as usual, because there is no interaction with TB drugs
  3. CStop all contraception during TB treatment, as pregnancy cannot occur
  4. DUse another reliable method, as rifampicin reduces the pill's effect

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: V̇A = 3.9 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

480 − 180 = 300 mL

Alveolar ventilation

V̇A = 300·13 = 3900 mL/min = 3.9 L/min

Answer

V̇A = 3.9 L/min
2.Oxygen therapy & respiratory calculations

Answer: t = 131 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 gas

3·(195 − 20) = 525 L

Duration

525/4 = 131.3 min → t = 131 min

Answer

t = 131 min

That is about 2 h 11 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 33 mmHg: low (35–45)
HCO₃⁻ 18 mmol/L: low (22–26)

Compensation

fully compensated

Answer

fully compensated
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 = 134 − (102 + 16) = 16

Delta ratio

(16 − 12)/(24 − 16) = 0.5
added normal-gap acidosis

Answer

added normal-gap acidosis
5.Clinical assessment scores

Answer: severe

Glasgow Coma Scale: add the best response in three areas. Eye opening E: 4 spontaneous, 3 to sound or speech, 2 to pressure, 1 none. Verbal V: 5 oriented, 4 confused, 3 inappropriate words, 2 incomprehensible sounds, 1 none. Motor M: 6 obeys commands, 5 localises, 4 normal flexion (withdraws), 3 abnormal flexion, 2 extension, 1 none. The total runs from 3 to 15. After a head injury, 13–15 is usually called mild, 9–12 moderate and 3–8 severe.

Score each area

E: opens the eyes only to pressure (a painful stimulus) → 2
V: says inappropriate, random words → 3
M: extension of the arms and legs (abnormal extension) → 2

Add

GCS = 2 + 3 + 2 = 7

Severity

GCS 7 → severe

Answer

severe
6.Clinical assessment scores

Answer: high

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 14/min → 0
SpO₂ 91% → 3
on air → 0
SBP 92 mmHg → 2
HR 130/min → 2
alert (A) → 0
T 35.2 °C → 1

Total and red scores

NEWS2 = 0 + 3 + 0 + 2 + 2 + 0 + 1 = 8
At least one parameter scores 3.

Risk group

high

Answer

high

A total of 5 or more calls for an urgent clinical response.

7.Med-surg: cardiovascular & respiratory

Answer: A · Left ventricular hypertrophy on the ECG

Why this is the answer

Target organ damage from hypertension includes left ventricular hypertrophy, retinopathy, chronic kidney disease with proteinuria, and stroke. Its presence changes treatment urgency and targets.

Answer

A · Left ventricular hypertrophy on the ECG
8.Med-surg: cardiovascular & respiratory

Answer: D · Use another reliable method, as rifampicin reduces the pill's effect

Why this is the answer

Rifampicin induces liver enzymes that break down oestrogen and progestogen, so hormonal contraception may fail. A non-hormonal or unaffected method, such as a copper IUD, is advised during and for a time after treatment. The interaction also affects warfarin and many other drugs.

Answer

D · Use another reliable method, as rifampicin reduces the pill's effect

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