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
650psiEf = 0.28 L/psi10 L/minresidual 200 psit = ? min

Practice exercise (made-up values, not clinical guidance). A size E oxygen cylinder (factor 0.28 L/psi) reads 650 psi and runs at 10 L/min. Keeping a safe residual of 200 psi, how many minutes t will it last? Round down to a whole minute.

650 psif = 0.28 L/psi10 L/min200 psi
t = min
2.Oxygen therapy & respiratory calculationsHard
68 kg167 cm♀6 mL/kg PBWVT​ = ? mL

Practice exercise (made-up values, not clinical guidance). A ventilated woman is 167 cm tall and weighs 68 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.

167 cm68 kg6 mL/kg
VT = mL
3.Arterial blood gas interpretationMedium

Practice values: Na⁺ 129 mmol/L, glucose 12.4 mmol/L and urea 5.4 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.

Na⁺ 129 mmol/Lglucose 12.4 mmol/Lurea 5.4 mmol/L
Osm = mOsm/kg
4.Arterial blood gas interpretationHard
pH7.357.457.26PaCO₂mmHg354523HCO₃⁻mmol/L222610added normal-gap acidosispure high-gap acidosisadded metabolic alkalosis

A practice gas shows pH 7.26, PaCO₂ 23 mmHg (3.1 kPa) and HCO₃⁻ 10 mmol/L, with Na⁺ 145 and Cl⁻ 98 mmol/L. Use the anion gap and the delta ratio to click the best interpretation.

pH 7.26PaCO₂ 23 mmHg (3.1 kPa)HCO₃⁻ 10 mmol/LNa⁺ 145 mmol/LCl⁻ 98 mmol/L
  1. 1added normal-gap acidosis
  2. 2pure high-gap acidosis
  3. 3added metabolic alkalosis
5.Clinical assessment scoresMedium
mildmoderatesevere

Practice exercise (made-up values, not clinical guidance). A practice patient after a head injury opens the eyes only to pressure (a painful stimulus), makes only incomprehensible sounds such as moaning 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
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: completely limited; moisture: occasionally moist; activity: bedfast; mobility: very limited; nutrition: adequate; friction and shear: potential 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

After coronary artery bypass surgery through a median sternotomy, which instruction is usually given for the first several weeks?

  1. ALift the arms above the head often to stretch the chest
  2. BAvoid walking until the stitches are removed
  3. CAvoid heavy lifting and pushing up with the arms
  4. DSleep only on the stomach to protect the wound
8.Med-surg: cardiovascular & respiratoryHard

After four days of antibiotics for pneumonia, a patient still has fever and pleuritic pain. There is dullness and reduced breath sounds at the right base. What complication should be suspected?

  1. ANormal recovery from pneumonia
  2. BAn allergic reaction to the antibiotic
  3. CAsthma triggered by the infection
  4. DA parapneumonic effusion or empyema

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: t = 12 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

(650 − 200)·0.28 = 126 L

Duration

126/10 = 12.6 min → t = 12 min

Answer

t = 12 min
2.Oxygen therapy & respiratory calculations

Answer: VT = 353 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·(167 − 152.4) = 58.79 kg

Tidal volume

VT = 6·58.79 = 352.7 ≈ 353 mL

Answer

VT = 353 mL
3.Arterial blood gas interpretation

Answer: Osm = 276 mOsm/kg

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.

Calculated osmolality

Osm = 2·129 + 12.4 + 5.4 = 275.8 ≈ 276 mOsm/kg

Answer

Osm = 276 mOsm/kg
4.Arterial blood gas interpretation

Answer: pure high-gap 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.

Anion gap

AG = 145 − (98 + 10) = 37

Delta ratio

(37 − 12)/(24 − 10) = 1.786
pure high-gap acidosis

Answer

pure high-gap acidosis
5.Clinical assessment scores

Answer: severe

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 only to pressure (a painful stimulus) → 2
V: makes only incomprehensible sounds such as moaning → 2
M: abnormal flexion of the arms (decorticate posture) → 3

Add

GCS = 2 + 2 + 3 = 7

Severity

GCS 7 → severe

Answer

severe
6.Clinical assessment scores

Answer: high 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: completely limited → 1
moisture: occasionally moist → 3
activity: bedfast → 1
mobility: very limited → 2
nutrition: adequate → 3
friction and shear: potential problem → 2

Add

Braden total = 1 + 3 + 1 + 2 + 3 + 2 = 12

Risk level

12 → high risk

Answer

high risk
7.Med-surg: cardiovascular & respiratory

Answer: C · Avoid heavy lifting and pushing up with the arms

Why this is the answer

The sternum is wired and takes weeks to heal. Patients are advised to avoid heavy lifting, pulling and pushing with the arms, and to support the chest with a pillow when coughing. Walking is encouraged as part of cardiac rehabilitation.

Answer

C · Avoid heavy lifting and pushing up with the arms
8.Med-surg: cardiovascular & respiratory

Answer: D · A parapneumonic effusion or empyema

Why this is the answer

Persistent fever and signs of pleural fluid suggest a parapneumonic effusion, which may become infected (empyema). Ultrasound and diagnostic pleural aspiration are needed, and an infected collection usually needs a chest drain in addition to antibiotics.

Answer

D · A parapneumonic effusion or empyema

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