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
2150psiEf = 0.28 L/psi4 L/minresidual 200 psit = ? min

Practice exercise (made-up values, not clinical guidance). A size E oxygen cylinder (factor 0.28 L/psi) reads 2150 psi and runs at 4 L/min. Keeping a safe residual of 200 psi, how many minutes t will it last? Round down to a whole minute.

2150 psif = 0.28 L/psi4 L/min200 psi
t = min
2.Oxygen therapy & respiratory calculationsHard
PaO₂ 9.1 kPa · FiO₂ 1 · PEEP 10 cmH₂O0100200300400500P/F (mmHg)above 300: no ARDS grademildmoderateseverenot gradable: PEEP below 5

Practice exercise (made-up values, not clinical guidance). A patient with acute hypoxaemia and bilateral opacities, not explained by heart failure, has PaO₂ 9.1 kPa on 100% oxygen with a PEEP of 10 cmH₂O. Grade the ARDS severity with the Berlin definition. Click your answer.

PaO₂ 9.1 kPaFiO₂ 100%PEEP 10 cmH₂O
  1. 1above 300: no ARDS grade
  2. 2mild
  3. 3moderate
  4. 4severe
  5. 5not gradable: PEEP below 5
3.Arterial blood gas interpretationMedium
pH7.357.457.22PaCO₂mmHg354523HCO₃⁻mmol/L22269uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.22, PaCO₂ 23 mmHg (3.1 kPa) and HCO₃⁻ 9 mmol/L. The primary disorder is metabolic acidosis. How far is it compensated? Click your answer.

pH 7.22PaCO₂ 23 mmHg (3.1 kPa)HCO₃⁻ 9 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
4.Arterial blood gas interpretationHard

A practice gas shows a metabolic alkalosis with HCO₃⁻ 32 mmol/L. Use expected PaCO₂ = 0.7·HCO₃⁻ + 21 to find the expected PaCO₂.

HCO₃⁻ 32 mmol/L
PaCO₂ = mmHg
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 22/min, SpO₂ 96% on room air, blood pressure 150/90 mmHg, pulse 82/min, alert, temperature 37.6 °C. What is the NEWS2 total score?

RR 22SpO₂ 96%airSBP 150HR 82AT 37.6 °C
NEWS2 =
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 20/min, SpO₂ 98% on room air, blood pressure 150/90 mmHg, pulse 140/min, alert, temperature 36.8 °C. Which clinical risk group does the patient fall into? Click it.

RR 20SpO₂ 98%airSBP 150HR 140AT 36.8 °C
  1. 1low
  2. 2low–medium
  3. 3medium
  4. 4high
7.Med-surg: cardiovascular & respiratoryMedium

Unless fluids are restricted, why are patients with pneumonia encouraged to drink plenty?

  1. ATo flush the bacteria out through the urine
  2. BTo prevent dehydration and keep secretions thinner
  3. CTo lower the temperature by diluting the blood plasma
  4. DTo make the cough completely stop
8.Med-surg: cardiovascular & respiratoryHard

A frightened young woman is breathing fast and has tingling fingers. Her blood gas shows pH 7.50 and a low PaCO₂. SpO₂ is 99% on air. What does this show?

  1. AMetabolic alkalosis from vomiting
  2. BRespiratory alkalosis from hyperventilation
  3. CRespiratory acidosis from hypoventilation
  4. DMetabolic acidosis from kidney failure

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: t = 136 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

(2150 − 200)·0.28 = 546 L

Duration

546/4 = 136.5 min → t = 136 min

Answer

t = 136 min

That is about 2 h 16 min.

2.Oxygen therapy & respiratory calculations

Answer: severe

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.

PEEP

PEEP 10 ≥ 5 cmH₂O

PaO₂ in mmHg

9.1·7.5 = 68.25 mmHg

P/F ratio

P/F = 68.25/1 = 68.25 mmHg

Berlin severity

severe

Answer

severe
3.Arterial blood gas interpretation

Answer: partially 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 7.22: acidaemia (below 7.35)
PaCO₂ 23 mmHg: low (35–45)
HCO₃⁻ 9 mmol/L: low (22–26)

Compensation

partially compensated

Answer

partially compensated
4.Arterial blood gas interpretation

Answer: PaCO₂ = 43.4 mmHg

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

0.7·32 + 21 = 43.4 mmHg

Answer

PaCO₂ = 43.4 mmHg

The rise has a limit: PaCO₂ rarely goes above about 55 mmHg from compensation alone.

5.Clinical assessment scores

Answer: NEWS2 = 2

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 22/min → 2
SpO₂ 96% → 0
on air → 0
SBP 150 mmHg → 0
HR 82/min → 0
alert (A) → 0
T 37.6 °C → 0

Add

NEWS2 = 2 + 0 + 0 + 0 + 0 + 0 + 0 = 2

Answer

NEWS2 = 2
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 20/min → 0
SpO₂ 98% → 0
on air → 0
SBP 150 mmHg → 0
HR 140/min → 3
alert (A) → 0
T 36.8 °C → 0

Total and red scores

NEWS2 = 0 + 0 + 0 + 0 + 3 + 0 + 0 = 3
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: B · To prevent dehydration and keep secretions thinner

Why this is the answer

Fever, sweating and tachypnoea increase insensible fluid loss. Good hydration prevents dehydration and helps keep secretions less sticky. Patients with heart failure or other restrictions need individual plans.

Answer

B · To prevent dehydration and keep secretions thinner
8.Med-surg: cardiovascular & respiratory

Answer: B · Respiratory alkalosis from hyperventilation

Why this is the answer

Hyperventilation blows off CO₂, causing respiratory alkalosis. The alkalosis lowers ionised calcium, causing tingling and carpopedal spasm. Normal oxygen saturation is reassuring, but organic causes such as PE, asthma or diabetic ketoacidosis must still be excluded.

Answer

B · Respiratory alkalosis from hyperventilation

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