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
PaO₂ 59 mmHg · FiO₂ 0.7 · PEEP 14 cmH₂O0100200300400500P/F (mmHg)above 300: no ARDS grademildmoderatesevere

Practice exercise (made-up values, not clinical guidance). A ventilated patient who meets the other Berlin criteria for ARDS has PaO₂ 59 mmHg (7.9 kPa) on 70% oxygen with a PEEP of 14 cmH₂O. Calculate the P/F ratio and click the ARDS severity.

PaO₂ 59 mmHg (7.9 kPa)FiO₂ 70%PEEP 14 cmH₂O
  1. 1above 300: no ARDS grade
  2. 2mild
  3. 3moderate
  4. 4severe
2.Oxygen therapy & respiratory calculationsHard
83 bar3 L12 L/min20 bart = ? min

Practice exercise (made-up values, not clinical guidance). A cylinder with a water capacity of 3 L is filled to 83 bar and runs at 12 L/min. The gas volume is about the water capacity × the pressure. In this exercise the cylinder is changed at 20 bar. How many minutes t until it must be changed? Round down to a whole minute.

3 L83 bar12 L/min20 bar
t = min
3.Arterial blood gas interpretationMedium

A practice gas shows PaCO₂ 20 mmHg (2.7 kPa). Use the rule that in acute respiratory alkalosis HCO₃⁻ falls by 2 mmol/L for every 10 mmHg that PaCO₂ is below 40, starting from HCO₃⁻ 24 mmol/L, to find the expected HCO₃⁻.

PaCO₂ 20 mmHg (2.7 kPa)baseline: 40 mmHg, 24 mmol/L
HCO₃⁻ = mmol/L
4.Arterial blood gas interpretationHard
pH7.357.457.32PaCO₂mmHg354532HCO₃⁻mmol/L222616appropriate compensationadded respiratory acidosisadded respiratory alkalosis

A practice gas shows a metabolic acidosis: pH 7.32, PaCO₂ 32 mmHg (4.3 kPa), HCO₃⁻ 16 mmol/L. Compare the measured PaCO₂ with Winter’s formula. Click your interpretation.

pH 7.32PaCO₂ 32 mmHg (4.3 kPa)HCO₃⁻ 16 mmol/L
  1. 1appropriate compensation
  2. 2added respiratory acidosis
  3. 3added respiratory alkalosis
5.Clinical assessment scoresMedium
mildmoderatesevere

Practice exercise (made-up values, not clinical guidance). A practice patient after a head injury opens the eyes when spoken to, talks in sentences but is confused and shows as the best motor response: abnormal flexion of the arms (decorticate posture). Work out the GCS and classify the head injury by it. Click your answer.

  1. 1mild
  2. 2moderate
  3. 3severe
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 16/min, SpO₂ 97% on supplemental oxygen, blood pressure 222/134 mmHg, pulse 82/min, alert, temperature 36.3 °C. Which clinical risk group does the patient fall into? Click it.

RR 16SpO₂ 97%O₂SBP 222HR 82AT 36.3 °C
  1. 1low
  2. 2low–medium
  3. 3medium
  4. 4high
7.Med-surg: cardiovascular & respiratoryMedium

A patient with heart failure is comfortable at rest but becomes breathless walking across a room. Which NYHA class fits best?

  1. AClass II
  2. BClass I
  3. CClass III
  4. DClass IV
8.Med-surg: cardiovascular & respiratoryHard

A day after a myocardial infarction, a patient has frequent ventricular ectopic beats on the monitor. Which blood results should be checked first?

  1. AAlbumin and bilirubin
  2. BAmylase and lipase
  3. CPotassium and magnesium
  4. DFerritin and vitamin B12

3Solutions

1.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.

P/F ratio

P/F = 59/0.7 = 84.29 mmHg

Berlin severity

severe

Answer

severe
2.Oxygen therapy & respiratory calculations

Answer: t = 15 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 gas

3·(83 − 20) = 189 L

Duration

189/12 = 15.75 min → t = 15 min

Answer

t = 15 min
3.Arterial blood gas interpretation

Answer: HCO₃⁻ = 20 mmol/L

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.

Change in PaCO₂

|20 − 40| = 20 mmHg → 2 × 10 mmHg

Expected HCO₃⁻

HCO₃⁻ = 24 − 2·2 = 20 mmol/L

Answer

HCO₃⁻ = 20 mmol/L
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

1.5·16 + 8 = 32 → 30–34 mmHg

Compare

measured: 32 mmHg → appropriate compensation

Answer

appropriate compensation
5.Clinical assessment scores

Answer: moderate

Glasgow Coma Scale: add the best response in three areas. Eye opening E: 4 spontaneous, 3 to sound or speech, 2 to pressure, 1 none. Verbal V: 5 oriented, 4 confused, 3 inappropriate words, 2 incomprehensible sounds, 1 none. Motor M: 6 obeys commands, 5 localises, 4 normal flexion (withdraws), 3 abnormal flexion, 2 extension, 1 none. The total runs from 3 to 15. After a head injury, 13–15 is usually called mild, 9–12 moderate and 3–8 severe.

Score each area

E: opens the eyes when spoken to → 3
V: talks in sentences but is confused → 4
M: abnormal flexion of the arms (decorticate posture) → 3

Add

GCS = 3 + 4 + 3 = 10

Severity

GCS 10 → moderate

Answer

moderate
6.Clinical assessment scores

Answer: 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 16/min → 0
SpO₂ 97% → 0
on oxygen → 2
SBP 222 mmHg → 3
HR 82/min → 0
alert (A) → 0
T 36.3 °C → 0

Total and red scores

NEWS2 = 0 + 0 + 2 + 3 + 0 + 0 + 0 = 5
At least one parameter scores 3.

Risk group

medium

Answer

medium

A total of 5 or more calls for an urgent clinical response.

7.Med-surg: cardiovascular & respiratory

Answer: C · Class III

Why this is the answer

NYHA class I has no limitation, class II slight limitation with ordinary activity, class III marked limitation with less than ordinary activity but comfortable at rest, and class IV symptoms at rest. The class guides treatment and prognosis.

Answer

C · Class III
8.Med-surg: cardiovascular & respiratory

Answer: C · Potassium and magnesium

Why this is the answer

Low potassium and low magnesium both increase ventricular irritability and the risk of VT and VF after an MI. They are checked and corrected, usually keeping potassium in the upper part of the normal range. The patient is also assessed for ischaemia and haemodynamic change.

Answer

C · Potassium and magnesium

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