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
Hb103 g/LSaO₂97%PaO₂92 mmHgCaO₂?

Practice exercise (made-up values, not clinical guidance). A patient has Hb 103 g/L, SaO₂ 97% and PaO₂ 92 mmHg (12.3 kPa). Find the arterial oxygen content CaO₂ = 1.34 × Hb (g/dL) × SaO₂ + 0.003 × PaO₂ (mmHg) in mL O₂/dL.

Hb 103 g/LSaO₂ 97%PaO₂ 92 mmHg (12.3 kPa)
CaO₂ = mL/dL
2.Oxygen therapy & respiratory calculationsHard
PaO₂ 9.4 kPa · FiO₂ 0.8 · 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 9.4 kPa on 80% oxygen with a PEEP of 10 cmH₂O. Grade the ARDS severity with the Berlin definition. Click your answer.

PaO₂ 9.4 kPaFiO₂ 80%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

A practice gas shows PaCO₂ 69 mmHg (9.2 kPa). Use the rule that in chronic respiratory acidosis HCO₃⁻ rises by 3.5 mmol/L for every 10 mmHg that PaCO₂ is above 40, starting from HCO₃⁻ 24 mmol/L, to find the expected HCO₃⁻.

PaCO₂ 69 mmHg (9.2 kPa)baseline: 40 mmHg, 24 mmol/L
HCO₃⁻ = mmol/L
4.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 35% oxygen shows PaO₂ 94 mmHg (12.5 kPa) and PaCO₂ 41 mmHg (5.5 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 35%PaO₂ 94 mmHg (12.5 kPa)PaCO₂ 41 mmHg (5.5 kPa)
A–a gradient = mmHg
5.Clinical assessment scoresMedium
H? / 25+D? / 15+Aid? / 30+IV? / 20+G? / 20+MS? / 15Σ?

Practice exercise (made-up values, not clinical guidance). A practice patient is assessed with the Morse fall scale: history of falling in the last 3 months: no; secondary diagnosis: no; ambulatory aid: holds on to furniture; IV therapy or saline lock: no; gait: normal, bed rest or wheelchair; mental status: overestimates or forgets limits. Find the Morse total MFS.

0–125
MFS =
6.Clinical assessment scoresHard
reassuringmoderately abnormallow

Practice exercise (made-up values, not clinical guidance). At 1 minute after birth, a practice newborn has a pink body with blue hands and feet, a heart rate of 85/min, a cry, cough or sneeze when stimulated, active movement and good breathing with a strong cry. Score the APGAR and click how the score is interpreted.

  1. 1reassuring
  2. 2moderately abnormal
  3. 3low
7.Med-surg: cardiovascular & respiratoryMedium

A patient with a mechanical heart valve asks to switch from warfarin to apixaban. What is the correct response?

  1. AAny anticoagulant works equally well once the valve is in place
  2. BDirect oral anticoagulants are not used for mechanical valves
  3. CAspirin alone can replace warfarin once the valve has healed
  4. DMechanical valves do not need anticoagulation after the first month
8.Med-surg: cardiovascular & respiratoryHard

A nurse receives handover on four patients. Which patient should be seen first?

  1. AA patient with asthma who wants a reliever inhaler before a walk
  2. BA patient with pneumonia on IV antibiotics who now has a temperature of 38.2 °C
  3. CA patient on day 1 after surgery who is newly restless, RR 30/min, SpO₂ 88% on 4 L/min
  4. DA patient with COPD on 1 L/min whose SpO₂ has been 89% and stable throughout the night

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: CaO₂ = 13.66 mL/dL

Oxygen content and delivery: CaO₂ = 1.34 × Hb (g/dL) × SaO₂ + 0.003 × PaO₂ (mmHg), in mL O₂ per dL of blood, with SaO₂ as a fraction. Almost all oxygen is bound to haemoglobin; the dissolved part is small. Delivery DO₂ = CaO₂ × cardiac output (L/min) × 10 (mL/min), because 1 L = 10 dL; a normal resting adult value is about 1000 mL/min.

Hb in g/dL

103 g/L = 10.3 g/dL

Bound oxygen

1.34·10.3·0.97 = 13.39 mL/dL

Dissolved oxygen

0.003·92 = 0.276 mL/dL

Oxygen content

CaO₂ = 13.39 + 0.276 = 13.66 mL/dL

Answer

CaO₂ = 13.66 mL/dL
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

9.4·7.5 = 70.5 mmHg

P/F ratio

P/F = 70.5/0.8 = 88.13 mmHg

Berlin severity

severe

Answer

severe
3.Arterial blood gas interpretation

Answer: HCO₃⁻ = 34.15 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

|69 − 40| = 29 mmHg → 2.9 × 10 mmHg

Expected HCO₃⁻

HCO₃⁻ = 24 + 3.5·2.9 = 34.15 mmol/L

Answer

HCO₃⁻ = 34.15 mmol/L
4.Arterial blood gas interpretation

Answer: A–a gradient = 104.3 mmHg

Derived values: calculated serum osmolality is 2·Na⁺ + glucose + urea with all values in mmol/L (2·Na⁺ + glucose/18 + BUN/2.8 with glucose and BUN in mg/dL); normal is about 275–295 mOsm/kg. The P/F ratio is PaO₂ divided by FiO₂ as a fraction. The alveolar oxygen pressure is PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 mmHg at sea level, and the A–a gradient is PAO₂ − PaO₂.

Alveolar oxygen

PAO₂ = 0.35·713 − 41/0.8 = 249.5 − 51.25 = 198.3 mmHg

Gradient

A–a = 198.3 − 94 = 104.3 mmHg

Answer

A–a gradient = 104.3 mmHg
5.Clinical assessment scores

Answer: MFS = 45

Morse fall scale: six items. History of falling: no 0, yes 25. Secondary diagnosis: no 0, yes 15. Ambulatory aid: none, bed rest or nurse assistance 0; crutches, cane or walker 15; holding on to furniture 30. IV therapy or saline lock: no 0, yes 20. Gait: normal, bed rest or wheelchair 0; weak 10; impaired 20. Mental status: knows own limits 0; overestimates or forgets limits 15. The total runs from 0 to 125. Risk cut-offs differ between hospitals; a common set is 0–24 low, 25–44 moderate and 45 or more high.

Score each item

history of falling in the last 3 months: no → 0
secondary diagnosis: no → 0
ambulatory aid: holds on to furniture → 30
IV therapy or saline lock: no → 0
gait: normal, bed rest or wheelchair → 0
mental status: overestimates or forgets limits → 15

Add

Morse total = 0 + 0 + 30 + 0 + 0 + 15 = 45

Answer

MFS = 45
6.Clinical assessment scores

Answer: reassuring

APGAR score: five signs, each scored 0, 1 or 2, checked at 1 and 5 minutes after birth. Appearance (colour): blue or pale 0, pink body with blue extremities 1, pink all over 2. Pulse: absent 0, below 100/min 1, 100/min or more 2. Grimace (reflex irritability): none 0, grimace 1, cry, cough or sneeze 2. Activity (tone): limp 0, some flexion 1, active movement 2. Respiration: absent 0, slow or irregular with a weak cry 1, good with a strong cry 2. A total of 7–10 is reassuring, 4–6 moderately abnormal and 0–3 low.

Score each sign

Appearance: a pink body with blue hands and feet → 1
Pulse: 85/min → 1
Grimace: a cry, cough or sneeze when stimulated → 2
Activity: active movement → 2
Respiration: good breathing with a strong cry → 2

Add

APGAR = 1 + 1 + 2 + 2 + 2 = 8

Interpretation

8 → reassuring

Answer

reassuring
7.Med-surg: cardiovascular & respiratory

Answer: B · Direct oral anticoagulants are not used for mechanical valves

Why this is the answer

Mechanical valves need lifelong anticoagulation with a vitamin K antagonist such as warfarin. Direct oral anticoagulants caused more clots and bleeding in mechanical valve patients and are contraindicated. Biological valves usually need only short-term anticoagulation.

Answer

B · Direct oral anticoagulants are not used for mechanical valves
8.Med-surg: cardiovascular & respiratory

Answer: C · A patient on day 1 after surgery who is newly restless, RR 30/min, SpO₂ 88% on 4 L/min

Why this is the answer

New restlessness, tachypnoea and hypoxaemia despite oxygen suggest acute deterioration such as a PE, pneumonia or bleeding, so this patient is seen first. SpO₂ 89% is within target for a stable COPD patient, a mild fever on antibiotics is expected, and the asthma patient is well.

Answer

C · A patient on day 1 after surgery who is newly restless, RR 30/min, SpO₂ 88% on 4 L/min

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