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
1250psiHf = 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 1250 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.

1250 psif = 3.14 L/psi6 L/min200 psi
t = min
2.Oxygen therapy & respiratory calculationsHard
SpO₂ 95% · FiO₂ 0.4ROX = ?RR 25/minROX = (SpO₂/FiO₂)/RR

Practice exercise (made-up values, not clinical guidance). A patient on high-flow nasal oxygen has SpO₂ 95% on FiO₂ 0.4 and a respiratory rate of 25/min. Find the ROX index ROX = (SpO₂/FiO₂)/RR, with SpO₂ in percent and FiO₂ as a fraction. Round to two decimal places.

SpO₂ 95%FiO₂ 0.4RR 25/min
ROX =
3.Arterial blood gas interpretationMedium

Practice values: Na⁺ 149 mmol/L, glucose 4.5 mmol/L and urea 7.9 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.

Na⁺ 149 mmol/Lglucose 4.5 mmol/Lurea 7.9 mmol/L
Osm = mOsm/kg
4.Arterial blood gas interpretationHard
pH7.357.457.12PaCO₂mmHg354535HCO₃⁻mmol/L222611appropriate compensationadded respiratory acidosisadded respiratory alkalosis

A practice gas shows a metabolic acidosis: pH 7.12, PaCO₂ 35 mmHg (4.7 kPa), HCO₃⁻ 11 mmol/L. Compare the measured PaCO₂ with Winter’s formula. Click your interpretation.

pH 7.12PaCO₂ 35 mmHg (4.7 kPa)HCO₃⁻ 11 mmol/L
  1. 1appropriate compensation
  2. 2added respiratory acidosis
  3. 3added respiratory alkalosis
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 23/min, SpO₂ 99% on supplemental oxygen, blood pressure 92/56 mmHg, pulse 98/min, alert, temperature 37.9 °C. What is the NEWS2 total score?

RR 23SpO₂ 99%O₂SBP 92HR 98AT 37.9 °C
NEWS2 =
6.Clinical assessment scoresHard
reassuringmoderately abnormallow

Practice exercise (made-up values, not clinical guidance). At 5 minutes after birth, a practice newborn has a pink body with blue hands and feet, a heart rate of 125/min, a cry, cough or sneeze when stimulated, active movement and good breathing with a strong cry. Score the APGAR and click how the score is interpreted.

  1. 1reassuring
  2. 2moderately abnormal
  3. 3low
7.Med-surg: cardiovascular & respiratoryMedium

A patient has chest pain at rest in the early morning with brief ST elevation that resolves. Coronary arteries are later found to be clear. Which condition is most likely?

  1. AAortic stenosis
  2. BVasospastic (Prinzmetal) angina
  3. CAcute pericarditis
  4. DStable exertional angina from a fixed plaque
8.Med-surg: cardiovascular & respiratoryHard

A patient with heart failure is breathless at rest, with cool peripheries, a systolic BP of 80 mmHg and falling urine output. What does this suggest?

  1. ACardiogenic shock with poor tissue perfusion
  2. BStable, well-compensated chronic heart failure
  3. CMild dehydration that oral fluids will correct
  4. DAnxiety causing a vasovagal response

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: t = 549 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

(1250 − 200)·3.14 = 3297 L

Duration

3297/6 = 549.5 min → t = 549 min

Answer

t = 549 min

That is about 9 h 09 min.

2.Oxygen therapy & respiratory calculations

Answer: ROX = 9.5

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.

SpO₂/FiO₂

95/0.4 = 237.5

ROX

ROX = 237.5/25 = 9.5

Answer

ROX = 9.5

At or above 4.88, a value linked in studies with success of high-flow oxygen.

3.Arterial blood gas interpretation

Answer: Osm = 310 mOsm/kg

Derived values: calculated serum osmolality is 2·Na⁺ + glucose + urea with all values in mmol/L (2·Na⁺ + glucose/18 + BUN/2.8 with glucose and BUN in mg/dL); normal is about 275–295 mOsm/kg. The P/F ratio is PaO₂ divided by FiO₂ as a fraction. The alveolar oxygen pressure is PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 mmHg at sea level, and the A–a gradient is PAO₂ − PaO₂.

Calculated osmolality

Osm = 2·149 + 4.5 + 7.9 = 310.4 ≈ 310 mOsm/kg

Answer

Osm = 310 mOsm/kg
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

1.5·11 + 8 = 24.5 → 22.5–26.5 mmHg

Compare

measured: 35 mmHg → added respiratory acidosis

Answer

added respiratory acidosis
5.Clinical assessment scores

Answer: NEWS2 = 7

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 23/min → 2
SpO₂ 99% → 0
on oxygen → 2
SBP 92 mmHg → 2
HR 98/min → 1
alert (A) → 0
T 37.9 °C → 0

Add

NEWS2 = 2 + 0 + 2 + 2 + 1 + 0 + 0 = 7

Answer

NEWS2 = 7
6.Clinical assessment scores

Answer: reassuring

APGAR score: five signs, each scored 0, 1 or 2, checked at 1 and 5 minutes after birth. Appearance (colour): blue or pale 0, pink body with blue extremities 1, pink all over 2. Pulse: absent 0, below 100/min 1, 100/min or more 2. Grimace (reflex irritability): none 0, grimace 1, cry, cough or sneeze 2. Activity (tone): limp 0, some flexion 1, active movement 2. Respiration: absent 0, slow or irregular with a weak cry 1, good with a strong cry 2. A total of 7–10 is reassuring, 4–6 moderately abnormal and 0–3 low.

Score each sign

Appearance: a pink body with blue hands and feet → 1
Pulse: 125/min → 2
Grimace: a cry, cough or sneeze when stimulated → 2
Activity: active movement → 2
Respiration: good breathing with a strong cry → 2

Add

APGAR = 1 + 2 + 2 + 2 + 2 = 9

Interpretation

9 → reassuring

Answer

reassuring
7.Med-surg: cardiovascular & respiratory

Answer: B · Vasospastic (Prinzmetal) angina

Why this is the answer

Vasospastic angina is caused by temporary coronary artery spasm, often at rest or at night, with transient ST elevation. It responds to calcium channel blockers and nitrates. Triggers include smoking, cold and cocaine.

Answer

B · Vasospastic (Prinzmetal) angina
8.Med-surg: cardiovascular & respiratory

Answer: A · Cardiogenic shock with poor tissue perfusion

Why this is the answer

Cardiogenic shock is pump failure with hypotension and hypoperfusion (cool skin, oliguria, confusion, raised lactate), often with pulmonary congestion. It needs urgent critical care review. Large fluid boluses can worsen congestion unless guided by careful assessment.

Answer

A · Cardiogenic shock with poor tissue perfusion

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