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
2000psiDf = 0.16 L/psi5 L/minresidual 200 psit = ? min

Practice exercise (made-up values, not clinical guidance). A size D oxygen cylinder (factor 0.16 L/psi) reads 2000 psi and runs at 5 L/min. Keeping a safe residual of 200 psi, how many minutes t will it last? Round down to a whole minute.

2000 psif = 0.16 L/psi5 L/min200 psi
t = min
2.Oxygen therapy & respiratory calculationsHard
PaO₂ 13 kPa · FiO₂ 0.5 · PEEP 15 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 13 kPa on 50% oxygen with a PEEP of 15 cmH₂O. Grade the ARDS severity with the Berlin definition. Click your answer.

PaO₂ 13 kPaFiO₂ 50%PEEP 15 cmH₂O
  1. 1above 300: no ARDS grade
  2. 2mild
  3. 3moderate
  4. 4severe
  5. 5not gradable: PEEP below 5
3.Arterial blood gas interpretationMedium
pH7.357.457.10PaCO₂mmHg354537HCO₃⁻mmol/L222611uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.10, PaCO₂ 37 mmHg (4.9 kPa) and HCO₃⁻ 11 mmol/L. The primary disorder is metabolic acidosis. How far is it compensated? Click your answer.

pH 7.10PaCO₂ 37 mmHg (4.9 kPa)HCO₃⁻ 11 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
4.Arterial blood gas interpretationHard
pH7.357.457.09PaCO₂mmHg354541HCO₃⁻mmol/L222612appropriate compensationadded respiratory acidosisadded respiratory alkalosis

A practice gas shows a metabolic acidosis: pH 7.09, PaCO₂ 41 mmHg (5.5 kPa), HCO₃⁻ 12 mmol/L. Compare the measured PaCO₂ with Winter’s formula. Click your interpretation.

pH 7.09PaCO₂ 41 mmHg (5.5 kPa)HCO₃⁻ 12 mmol/L
  1. 1appropriate compensation
  2. 2added respiratory acidosis
  3. 3added respiratory alkalosis
5.Clinical assessment scoresMedium
S? / 4+M? / 4+A? / 4+Mob? / 4+N? / 4+F? / 3Σ?

Practice exercise (made-up values, not clinical guidance). A practice patient is assessed with the Braden scale: sensory perception: completely limited; moisture: very moist; activity: chairfast; mobility: slightly limited; nutrition: excellent; friction and shear: potential problem. Find the Braden total B.

6–23
B =
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 98% on supplemental oxygen, blood pressure 136/82 mmHg, pulse 130/min, alert, temperature 36.5 °C. Which clinical risk group does the patient fall into? Click it.

RR 18SpO₂ 98%O₂SBP 136HR 130AT 36.5 °C
  1. 1low
  2. 2low–medium
  3. 3medium
  4. 4high
7.Med-surg: cardiovascular & respiratoryMedium

How should a patient with asthma record their peak flow at home?

  1. ABlow only during an asthma attack, never when well
  2. BTake the average of ten blows after exercise
  3. CTake one gentle blow once a week, at any time of day
  4. DTake the best of three blows, ideally morning and evening
8.Med-surg: cardiovascular & respiratoryHard

An older patient with three rib fractures is breathing shallowly and refuses to cough because of pain. What is the priority intervention?

  1. AEffective analgesia so they can breathe deeply and cough
  2. BWithhold analgesia to avoid depressing breathing
  3. CStrap the chest tightly with bandages to stop the ribs moving
  4. DKeep the patient flat and still in bed until the pain settles

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: t = 57 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

(2000 − 200)·0.16 = 288 L

Duration

288/5 = 57.6 min → t = 57 min

Answer

t = 57 min
2.Oxygen therapy & respiratory calculations

Answer: moderate

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 15 ≥ 5 cmH₂O

PaO₂ in mmHg

13·7.5 = 97.5 mmHg

P/F ratio

P/F = 97.5/0.5 = 195 mmHg

Berlin severity

moderate

Answer

moderate
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 7.10: acidaemia (below 7.35)
PaCO₂ 37 mmHg: normal (35–45)
HCO₃⁻ 11 mmol/L: low (22–26)

Compensation

Clinically, also check the expected compensation: Winter’s formula expects PaCO₂ 22.5–26.5 mmHg, so the measured 37 mmHg points to an additional respiratory acidosis (a mixed disorder). The answer above is the ROME exam classification.

uncompensated

Answer

uncompensated
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

1.5·12 + 8 = 26 → 24–28 mmHg

Compare

measured: 41 mmHg → added respiratory acidosis

Answer

added respiratory acidosis
5.Clinical assessment scores

Answer: B = 14

Braden scale: six subscales for pressure-injury risk. Sensory perception, moisture, activity, mobility and nutrition score 1 to 4, from the worst level (1) to no problem (4); friction and shear scores 1 to 3. The total runs from 6 to 23, and a lower total means a higher risk. Common bands: 19–23 not at risk, 15–18 mild risk, 13–14 moderate risk, 10–12 high risk and 9 or below very high risk.

Score each subscale

sensory perception: completely limited → 1
moisture: very moist → 2
activity: chairfast → 2
mobility: slightly limited → 3
nutrition: excellent → 4
friction and shear: potential problem → 2

Add

Braden total = 1 + 2 + 2 + 3 + 4 + 2 = 14

Answer

B = 14
6.Clinical assessment scores

Answer: low

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 98% → 0
on oxygen → 2
SBP 136 mmHg → 0
HR 130/min → 2
alert (A) → 0
T 36.5 °C → 0

Total and red scores

NEWS2 = 0 + 0 + 2 + 0 + 2 + 0 + 0 = 4
No parameter scores 3.

Risk group

low

Answer

low
7.Med-surg: cardiovascular & respiratory

Answer: D · Take the best of three blows, ideally morning and evening

Why this is the answer

The patient stands or sits upright, takes a full breath and blows as hard and fast as possible, three times, recording the best. Regular readings show variability and guide the action plan, which uses the patient's own best value as the reference.

Answer

D · Take the best of three blows, ideally morning and evening
8.Med-surg: cardiovascular & respiratory

Answer: A · Effective analgesia so they can breathe deeply and cough

Why this is the answer

Pain from rib fractures causes shallow breathing and poor coughing, leading to atelectasis and pneumonia, especially in older adults. Good analgesia (sometimes regional blocks), deep breathing, coughing with support and early mobilisation are key. Chest strapping restricts breathing and is not used.

Answer

A · Effective analgesia so they can breathe deeply and cough

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