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
1550psiHf = 3.14 L/psi12 L/minresidual 200 psit = ? min

Practice exercise (made-up values, not clinical guidance). A size H oxygen cylinder (factor 3.14 L/psi) reads 1550 psi and runs at 12 L/min. Keeping a safe residual of 200 psi, how many minutes t will it last? Round down to a whole minute.

1550 psif = 3.14 L/psi12 L/min200 psi
t = min
2.Oxygen therapy & respiratory calculationsHard
105 kg179 cm♀6 mL/kg PBWVT​ = ? mL

Practice exercise (made-up values, not clinical guidance). A ventilated woman is 179 cm tall and weighs 105 kg. Lung-protective ventilation is set at 6 mL per kg of predicted body weight. Using PBW = 45.5 + 0.91 × (height cm − 152.4) kg, find the tidal volume VT to the nearest mL.

179 cm105 kg6 mL/kg
VT = mL
3.Arterial blood gas interpretationMedium
pH7.357.457.52PaCO₂mmHg354539HCO₃⁻mmol/L222631uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.52, PaCO₂ 39 mmHg (5.2 kPa) and HCO₃⁻ 31 mmol/L. The primary disorder is metabolic alkalosis. How far is it compensated? Click your answer.

pH 7.52PaCO₂ 39 mmHg (5.2 kPa)HCO₃⁻ 31 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
4.Arterial blood gas interpretationHard
pH7.357.457.31PaCO₂mmHg354529HCO₃⁻mmol/L222614appropriate compensationadded respiratory acidosisadded respiratory alkalosis

A practice gas shows a metabolic acidosis: pH 7.31, PaCO₂ 29 mmHg (3.9 kPa), HCO₃⁻ 14 mmol/L. Compare the measured PaCO₂ with Winter’s formula. Click your interpretation.

pH 7.31PaCO₂ 29 mmHg (3.9 kPa)HCO₃⁻ 14 mmol/L
  1. 1appropriate compensation
  2. 2added respiratory acidosis
  3. 3added respiratory alkalosis
5.Clinical assessment scoresMedium
9054SBPDBPmmHgHR 120/min · SI = ?

Practice exercise (made-up values, not clinical guidance). A patient has a pulse of 120/min and a blood pressure of 90/54 mmHg. Find the shock index SI = HR/SBP. Round to two decimal places.

HR 120/minBP 90/54 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 32/min, SpO₂ 99% on room air, blood pressure 84/50 mmHg, pulse 64/min, alert, temperature 38.8 °C. Which clinical risk group does the patient fall into? Click it.

RR 32SpO₂ 99%airSBP 84HR 64AT 38.8 °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 nitrate such as isosorbide mononitrate
  2. BAn angiotensin II receptor blocker such as losartan
  3. CA non-selective beta-blocker such as propranolol
  4. DA loop diuretic such as furosemide
8.Med-surg: cardiovascular & respiratoryHard

A patient on spironolactone and an ACE inhibitor has a potassium of 6.8 mmol/L (6.8 mEq/L) with peaked T waves. What is usually given first to protect the heart?

  1. AA dose of digoxin
  2. BOral potassium supplements
  3. CAn IV furosemide bolus as the only treatment
  4. DIntravenous calcium gluconate or chloride

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: t = 353 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

(1550 − 200)·3.14 = 4239 L

Duration

4239/12 = 353.3 min → t = 353 min

Answer

t = 353 min

That is about 5 h 53 min.

2.Oxygen therapy & respiratory calculations

Answer: VT = 418 mL

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).

Predicted body weight

PBW = 45.5 + 0.91·(179 − 152.4) = 69.71 kg

Tidal volume

VT = 6·69.71 = 418.2 ≈ 418 mL

Answer

VT = 418 mL
3.Arterial blood gas interpretation

Answer: uncompensated

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 7.52: alkalaemia (above 7.45)
PaCO₂ 39 mmHg: normal (35–45)
HCO₃⁻ 31 mmol/L: high (22–26)

Compensation

Clinically, also check the expected compensation: for a metabolic alkalosis PaCO₂ ≈ 0.7·HCO₃⁻ + 21 = 40.7–44.7 mmHg, so the measured 39 mmHg points to an additional respiratory alkalosis (a mixed disorder). The answer above is the ROME exam classification.

uncompensated

Answer

uncompensated
4.Arterial blood gas interpretation

Answer: appropriate compensation

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

1.5·14 + 8 = 29 → 27–31 mmHg

Compare

measured: 29 mmHg → appropriate compensation

Answer

appropriate compensation
5.Clinical assessment scores

Answer: SI = 1.33

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 = 120/90 = 1.333 ≈ 1.33

Answer

SI = 1.33

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

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 32/min → 3
SpO₂ 99% → 0
on air → 0
SBP 84 mmHg → 3
HR 64/min → 0
alert (A) → 0
T 38.8 °C → 1

Total and red scores

NEWS2 = 3 + 0 + 0 + 3 + 0 + 0 + 1 = 7
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: B · 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

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

Answer: D · Intravenous calcium gluconate or chloride

Why this is the answer

Severe hyperkalaemia with ECG changes is an emergency. IV calcium stabilises the myocardium within minutes. Insulin with glucose and nebulised salbutamol shift potassium into cells, and the cause (here spironolactone and the ACE inhibitor) is stopped. Cardiac monitoring is essential.

Answer

D · Intravenous calcium gluconate or chloride

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