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
60 s560 mLf = 28/min · V̇A = ?VD​ = 160 mL

Practice exercise (made-up values, not clinical guidance). A patient breathes 28 times a minute with a tidal volume of 560 mL. The anatomical dead space is 160 mL. Find the alveolar ventilation V̇A in L/min.

VT 560 mL28/minVD 160 mL
V̇A = L/min
2.Oxygen therapy & respiratory calculationsHard
70 kg164 cm♂6 mL/kg PBWVT​ = ? mL

Practice exercise (made-up values, not clinical guidance). A ventilated man is 164 cm tall and weighs 70 kg. Lung-protective ventilation is set at 6 mL per kg of predicted body weight. Using PBW = 50 + 0.91 × (height cm − 152.4) kg, find the tidal volume VT to the nearest mL.

164 cm70 kg6 mL/kg
VT = mL
3.Arterial blood gas interpretationMedium
pH7.357.457.44PaCO₂mmHg354523HCO₃⁻mmol/L222615uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.44, PaCO₂ 23 mmHg (3.1 kPa) and HCO₃⁻ 15 mmol/L. The primary disorder is respiratory alkalosis. How far is it compensated? Click your answer.

pH 7.44PaCO₂ 23 mmHg (3.1 kPa)HCO₃⁻ 15 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
4.Arterial blood gas interpretationHard
pH7.357.457.30PaCO₂mmHg354577HCO₃⁻mmol/L222637acutechronicacute on chronic

A practice gas shows a respiratory acidosis: pH 7.30, PaCO₂ 77 mmHg (10.3 kPa), HCO₃⁻ 37 mmol/L. Use the rules ‘HCO₃⁻ rises 1 mmol/L per 10 mmHg (acute) or 3.5 mmol/L per 10 mmHg (chronic)’ to classify it. Click your answer.

pH 7.30PaCO₂ 77 mmHg (10.3 kPa)HCO₃⁻ 37 mmol/L
  1. 1acute
  2. 2chronic
  3. 3acute on chronic
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: rarely moist; activity: bedfast; mobility: no limitation; nutrition: probably inadequate; friction and shear: problem. Find the Braden total B.

6–23
B =
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 grimace when stimulated, limp limbs with no muscle tone and slow, irregular breathing with a weak cry. Score the APGAR and click how the score is interpreted.

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

Why is intravenous furosemide given slowly rather than as a rapid push of a large dose?

  1. ARapid doses cause the potassium level to rise
  2. BRapid doses cause severe constipation
  3. CSlow injection makes the urine output larger
  4. DRapid high doses can damage hearing
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 acidosis from hypoventilation
  3. CMetabolic acidosis from kidney failure
  4. DRespiratory alkalosis from hyperventilation

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: V̇A = 11.2 L/min

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).

Alveolar part of a breath

560 − 160 = 400 mL

Alveolar ventilation

V̇A = 400·28 = 11200 mL/min = 11.2 L/min

Answer

V̇A = 11.2 L/min
2.Oxygen therapy & respiratory calculations

Answer: VT = 363 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 = 50 + 0.91·(164 − 152.4) = 60.56 kg

Tidal volume

VT = 6·60.56 = 363.3 ≈ 363 mL

Answer

VT = 363 mL
3.Arterial blood gas interpretation

Answer: fully 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 7.44: within 7.35–7.45
PaCO₂ 23 mmHg: low (35–45)
HCO₃⁻ 15 mmol/L: low (22–26)

Compensation

fully compensated

Answer

fully compensated
4.Arterial blood gas interpretation

Answer: chronic

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 HCO₃⁻

acute: 24 + 1·3.7 = 27.7 mmol/L
chronic: 24 + 3.5·3.7 = 36.95 mmol/L

Compare

measured: 37 mmol/L → chronic

Answer

chronic
5.Clinical assessment scores

Answer: B = 15

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: rarely moist → 4
activity: bedfast → 1
mobility: no limitation → 4
nutrition: probably inadequate → 2
friction and shear: problem → 1

Add

Braden total = 3 + 4 + 1 + 4 + 2 + 1 = 15

Answer

B = 15
6.Clinical assessment scores

Answer: moderately abnormal

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 grimace when stimulated → 1
Activity: limp limbs with no muscle tone → 0
Respiration: slow, irregular breathing with a weak cry → 1

Add

APGAR = 1 + 1 + 1 + 0 + 1 = 4

Interpretation

4 → moderately abnormal

Answer

moderately abnormal
7.Med-surg: cardiovascular & respiratory

Answer: D · Rapid high doses can damage hearing

Why this is the answer

High plasma levels of loop diuretics can cause tinnitus and hearing loss (ototoxicity), especially with fast injection, renal impairment or other ototoxic drugs such as aminoglycosides. Large IV doses are therefore given slowly.

Answer

D · Rapid high doses can damage hearing
8.Med-surg: cardiovascular & respiratory

Answer: D · 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

D · Respiratory alkalosis from hyperventilation

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