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
1900psiHf = 3.14 L/psi15 L/minresidual 200 psit = ? min

Practice exercise (made-up values, not clinical guidance). A size H oxygen cylinder (factor 3.14 L/psi) reads 1900 psi and runs at 15 L/min. Keeping a safe residual of 200 psi, how many minutes t will it last? Round down to a whole minute.

1900 psif = 3.14 L/psi15 L/min200 psi
t = min
2.Oxygen therapy & respiratory calculationsHard
1600psiEf = 0.28 L/psi30 minresidual 200 psiQ = ? L/min

Practice exercise (made-up values, not clinical guidance). A transfer will take 30 minutes. The size E cylinder (factor 0.28 L/psi) reads 1600 psi. Keeping a safe residual of 200 psi, what is the highest whole-number flow Q in L/min that lasts the whole transfer?

30 min1600 psif = 0.28 L/psi200 psi
Q = L/min
3.Arterial blood gas interpretationMedium
pH7.357.457.42PaCO₂mmHg354530HCO₃⁻mmol/L222619uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.42, PaCO₂ 30 mmHg (4.0 kPa) and HCO₃⁻ 19 mmol/L. The primary disorder is respiratory alkalosis. How far is it compensated? Click your answer.

pH 7.42PaCO₂ 30 mmHg (4.0 kPa)HCO₃⁻ 19 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
4.Arterial blood gas interpretationHard
pH7.357.457.31PaCO₂mmHg354535HCO₃⁻mmol/L222617added normal-gap acidosispure high-gap acidosisadded metabolic alkalosis

A practice gas shows pH 7.31, PaCO₂ 35 mmHg (4.7 kPa) and HCO₃⁻ 17 mmol/L, with Na⁺ 141 and Cl⁻ 92 mmol/L. Use the anion gap and the delta ratio to click the best interpretation.

pH 7.31PaCO₂ 35 mmHg (4.7 kPa)HCO₃⁻ 17 mmol/LNa⁺ 141 mmol/LCl⁻ 92 mmol/L
  1. 1added normal-gap acidosis
  2. 2pure high-gap acidosis
  3. 3added metabolic alkalosis
5.Clinical assessment scoresMedium
7750SBPDBPmmHgHR 146/min · SI = ?

Practice exercise (made-up values, not clinical guidance). A patient has a pulse of 146/min and a blood pressure of 77/50 mmHg. Find the shock index SI = HR/SBP. Round to two decimal places.

HR 146/minBP 77/50 mmHg
SI =
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 18/min, SpO₂ 88% on room air, blood pressure 136/82 mmHg, pulse 70/min, alert, temperature 35.2 °C. Which clinical risk group does the patient fall into? Click it.

RR 18SpO₂ 88%airSBP 136HR 70AT 35.2 °C
  1. 1low
  2. 2low–medium
  3. 3medium
  4. 4high
7.Med-surg: cardiovascular & respiratoryMedium

A patient stops ramipril because of a troublesome dry cough. Which drug class is a common alternative?

  1. AA loop diuretic such as furosemide
  2. BA nitrate such as isosorbide mononitrate
  3. CA non-selective beta-blocker such as propranolol
  4. DAn angiotensin II receptor blocker such as losartan
8.Med-surg: cardiovascular & respiratoryHard

A patient with COPD is going home on long-term oxygen. Which teaching point is most important for safety?

  1. ATurn the flow up as high as needed when breathless
  2. BUse petroleum jelly to soothe dry nostrils
  3. CNever smoke or allow open flames near the oxygen
  4. DStore spare cylinders next to the cooker

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: t = 355 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

(1900 − 200)·3.14 = 5338 L

Duration

5338/15 = 355.9 min → t = 355 min

Answer

t = 355 min

That is about 5 h 55 min.

2.Oxygen therapy & respiratory calculations

Answer: Q = 13 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

(1600 − 200)·0.28 = 392 L

Highest flow

392/30 = 13.07 L/min → Q = 13 L/min

Answer

Q = 13 L/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 7.42: within 7.35–7.45
PaCO₂ 30 mmHg: low (35–45)
HCO₃⁻ 19 mmol/L: low (22–26)

Compensation

fully compensated

Answer

fully compensated
4.Arterial blood gas interpretation

Answer: added metabolic alkalosis

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 = 141 − (92 + 17) = 32

Delta ratio

(32 − 12)/(24 − 17) = 2.857
added metabolic alkalosis

Answer

added metabolic alkalosis
5.Clinical assessment scores

Answer: SI = 1.9

Blood pressure values: pulse pressure PP = SBP − DBP. Mean arterial pressure MAP ≈ (SBP + 2·DBP)/3 = DBP + PP/3, an estimate based on the heart spending about two thirds of each beat in diastole at a normal heart rate (less accurate when the heart rate is fast); a MAP of at least about 65 mmHg is a common target for organ perfusion. The shock index SI = heart rate/SBP is normally about 0.5–0.7; a value above about 1 is a warning sign of shock.

Shock index

SI = 146/77 = 1.896 ≈ 1.9

Answer

SI = 1.9

1 or more: a warning sign of shock in this practice case.

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 18/min → 0
SpO₂ 88% → 3
on air → 0
SBP 136 mmHg → 0
HR 70/min → 0
alert (A) → 0
T 35.2 °C → 1

Total and red scores

NEWS2 = 0 + 3 + 0 + 0 + 0 + 0 + 1 = 4
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: D · An angiotensin II receptor blocker such as losartan

Why this is the answer

Angiotensin receptor blockers (ending in -sartan) block the effects of angiotensin II without inhibiting ACE, so bradykinin does not build up and cough is much less common. They share other effects, such as raising potassium, and ACE inhibitors and ARBs are not normally combined.

Answer

D · An angiotensin II receptor blocker such as losartan
8.Med-surg: cardiovascular & respiratory

Answer: C · Never smoke or allow open flames near the oxygen

Why this is the answer

Smoking while using oxygen is a major cause of burns and fatal fires. Patients must keep oxygen away from flames and heat sources, use water-based (not oil-based) lubricants and follow the prescribed flow, because unsupervised increases can worsen CO₂ retention.

Answer

C · Never smoke or allow open flames near the oxygen

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