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
Hb80 g/LSaO₂88%PaO₂55 mmHgCaO₂?

Practice exercise (made-up values, not clinical guidance). A patient has Hb 80 g/L, SaO₂ 88% and PaO₂ 55 mmHg (7.3 kPa). Find the arterial oxygen content CaO₂ = 1.34 × Hb (g/dL) × SaO₂ + 0.003 × PaO₂ (mmHg) in mL O₂/dL.

Hb 80 g/LSaO₂ 88%PaO₂ 55 mmHg (7.3 kPa)
CaO₂ = mL/dL
2.Oxygen therapy & respiratory calculationsHard
86 kg175 cm♀6 mL/kg PBWVT​ = ? mL

Practice exercise (made-up values, not clinical guidance). A ventilated woman is 175 cm tall and weighs 86 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.

175 cm86 kg6 mL/kg
VT = mL
3.Arterial blood gas interpretationMedium

A practice gas shows PaCO₂ 73 mmHg (9.7 kPa). Use the rule that in acute respiratory acidosis HCO₃⁻ rises by 1 mmol/L for every 10 mmHg that PaCO₂ is above 40, starting from HCO₃⁻ 24 mmol/L, to find the expected HCO₃⁻.

PaCO₂ 73 mmHg (9.7 kPa)baseline: 40 mmHg, 24 mmol/L
HCO₃⁻ = mmol/L
4.Arterial blood gas interpretationHard
pH7.357.457.20PaCO₂mmHg354537HCO₃⁻mmol/L222614appropriate compensationadded respiratory acidosisadded respiratory alkalosis

A practice gas shows a metabolic acidosis: pH 7.20, PaCO₂ 37 mmHg (4.9 kPa), HCO₃⁻ 14 mmol/L. Compare the measured PaCO₂ with Winter’s formula. Click your interpretation.

pH 7.20PaCO₂ 37 mmHg (4.9 kPa)HCO₃⁻ 14 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: slightly limited; moisture: very moist; activity: chairfast; mobility: completely immobile; nutrition: very poor; friction and shear: potential problem. Find the Braden total B.

6–23
B =
6.Clinical assessment scoresHard
not at riskmild riskmoderate riskhigh riskvery high risk

Practice exercise (made-up values, not clinical guidance). A practice patient is assessed with the Braden scale: sensory perception: very limited; moisture: occasionally moist; activity: chairfast; mobility: completely immobile; nutrition: probably inadequate; friction and shear: no apparent problem. Use the bands 19–23 not at risk, 15–18 mild, 13–14 moderate, 10–12 high and 9 or below very high. Click the risk level.

  1. 1not at risk
  2. 2mild risk
  3. 3moderate risk
  4. 4high risk
  5. 5very high risk
7.Med-surg: cardiovascular & respiratoryMedium

Why are nitrates used with great caution in right ventricular infarction?

  1. ANitrates are not absorbed when the right ventricle is affected
  2. BThe right ventricle depends on preload, so BP can fall sharply
  3. CNitrates cause dangerous hyperkalaemia in this type of infarct
  4. DNitrates make the infarct spread into the left ventricle
8.Med-surg: cardiovascular & respiratoryHard

A patient on warfarin for atrial fibrillation is prescribed clarithromycin. Which action is most appropriate?

  1. AAsk whether the INR should be checked sooner, as it may rise
  2. BStop the warfarin for the whole antibiotic course
  3. CChange nothing, as antibiotics do not affect warfarin
  4. DDouble the warfarin dose during the course

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: CaO₂ = 9.599 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

80 g/L = 8 g/dL

Bound oxygen

1.34·8·0.88 = 9.434 mL/dL

Dissolved oxygen

0.003·55 = 0.165 mL/dL

Oxygen content

CaO₂ = 9.434 + 0.165 = 9.599 mL/dL

Answer

CaO₂ = 9.599 mL/dL
2.Oxygen therapy & respiratory calculations

Answer: VT = 396 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·(175 − 152.4) = 66.07 kg

Tidal volume

VT = 6·66.07 = 396.4 ≈ 396 mL

Answer

VT = 396 mL
3.Arterial blood gas interpretation

Answer: HCO₃⁻ = 27.3 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

|73 − 40| = 33 mmHg → 3.3 × 10 mmHg

Expected HCO₃⁻

HCO₃⁻ = 24 + 1·3.3 = 27.3 mmol/L

Answer

HCO₃⁻ = 27.3 mmol/L
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

1.5·14 + 8 = 29 → 27–31 mmHg

Compare

measured: 37 mmHg → added respiratory acidosis

Answer

added respiratory acidosis
5.Clinical assessment scores

Answer: B = 11

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: slightly limited → 3
moisture: very moist → 2
activity: chairfast → 2
mobility: completely immobile → 1
nutrition: very poor → 1
friction and shear: potential problem → 2

Add

Braden total = 3 + 2 + 2 + 1 + 1 + 2 = 11

Answer

B = 11
6.Clinical assessment scores

Answer: moderate risk

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: very limited → 2
moisture: occasionally moist → 3
activity: chairfast → 2
mobility: completely immobile → 1
nutrition: probably inadequate → 2
friction and shear: no apparent problem → 3

Add

Braden total = 2 + 3 + 2 + 1 + 2 + 3 = 13

Risk level

13 → moderate risk

Answer

moderate risk
7.Med-surg: cardiovascular & respiratory

Answer: B · The right ventricle depends on preload, so BP can fall sharply

Why this is the answer

In right ventricular infarction cardiac output depends heavily on venous filling. Venodilators such as nitrates (and diuretics or opioids) can cause a dramatic fall in blood pressure. These patients often need careful fluid administration instead.

Answer

B · The right ventricle depends on preload, so BP can fall sharply
8.Med-surg: cardiovascular & respiratory

Answer: A · Ask whether the INR should be checked sooner, as it may rise

Why this is the answer

Several antibiotics, including macrolides such as clarithromycin, some fluoroquinolones and co-trimoxazole, can raise the INR and the bleeding risk. Closer INR monitoring and possible dose adjustment are needed. Stopping or doubling warfarin without advice is unsafe.

Answer

A · Ask whether the INR should be checked sooner, as it may rise

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