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
900psiHf = 3.14 L/psi4 L/minresidual 200 psit = ? min

Practice exercise (made-up values, not clinical guidance). A size H oxygen cylinder (factor 3.14 L/psi) reads 900 psi and runs at 4 L/min. Keeping a safe residual of 200 psi, how many minutes t will it last? Round down to a whole minute.

900 psif = 3.14 L/psi4 L/min200 psi
t = min
2.Oxygen therapy & respiratory calculationsHard
1250psiDf = 0.16 L/psi120 minresidual 200 psiQ = ? L/min

Practice exercise (made-up values, not clinical guidance). A transfer will take 120 minutes. The size D cylinder (factor 0.16 L/psi) reads 1250 psi. Keeping a safe residual of 200 psi, what is the highest whole-number flow Q in L/min that lasts the whole transfer?

120 min1250 psif = 0.16 L/psi200 psi
Q = L/min
3.Arterial blood gas interpretationMedium

Practice values: Na⁺ 140 mmol/L, glucose 13.1 mmol/L and urea 13.5 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.

Na⁺ 140 mmol/Lglucose 13.1 mmol/Lurea 13.5 mmol/L
Osm = mOsm/kg
4.Arterial blood gas interpretationHard

A practice gas shows a metabolic alkalosis with HCO₃⁻ 41 mmol/L. Use expected PaCO₂ = 0.7·HCO₃⁻ + 21 to find the expected PaCO₂.

HCO₃⁻ 41 mmol/L
PaCO₂ = mmHg
5.Clinical assessment scoresMedium
E3 / 4+V4 / 5+M? / 6GCS 10?

Practice exercise (made-up values, not clinical guidance). A practice chart records GCS 10, with E3 and V4. What motor score M was recorded, and which response does it describe? Give the number.

GCS 10E3V4
M =
6.Clinical assessment scoresHard
low riskmoderate riskhigh risk

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: yes; secondary diagnosis: yes; ambulatory aid: none, bed rest or nurse assists; IV therapy or saline lock: no; gait: weak; mental status: knows own limits. Using the cut-offs 0–24 low, 25–44 moderate and 45 or more high, click the fall-risk level.

  1. 1low risk
  2. 2moderate risk
  3. 3high risk
7.Med-surg: cardiovascular & respiratoryMedium

A patient with COPD uses an inhaled corticosteroid combination inhaler. Which risk should the nurse be aware of?

  1. AAn increased risk of high blood pressure crises
  2. BA sharp drop in potassium after each dose
  3. CHearing loss after every dose
  4. DAn increased risk of pneumonia
8.Med-surg: cardiovascular & respiratoryHard

A patient with a confirmed calf DVT has started therapeutic anticoagulation and asks whether they must stay in bed. What is the most accurate answer?

  1. AStrict bed rest is needed for at least two weeks
  2. BWalking is not allowed until the clot has fully dissolved
  3. CThe leg should be massaged before each walk
  4. DWalking as tolerated is usually encouraged once treated

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: t = 549 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

(900 − 200)·3.14 = 2198 L

Duration

2198/4 = 549.5 min → t = 549 min

Answer

t = 549 min

That is about 9 h 09 min.

2.Oxygen therapy & respiratory calculations

Answer: Q = 1 L/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

(1250 − 200)·0.16 = 168 L

Highest flow

168/120 = 1.4 L/min → Q = 1 L/min

Answer

Q = 1 L/min
3.Arterial blood gas interpretation

Answer: Osm = 307 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 = 2·140 + 13.1 + 13.5 = 306.6 ≈ 307 mOsm/kg

Answer

Osm = 307 mOsm/kg
4.Arterial blood gas interpretation

Answer: PaCO₂ = 49.7 mmHg

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

0.7·41 + 21 = 49.7 mmHg

Answer

PaCO₂ = 49.7 mmHg

The rise has a limit: PaCO₂ rarely goes above about 55 mmHg from compensation alone.

5.Clinical assessment scores

Answer: M = 3

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.

Motor score

M = 10 − 3 − 4 = 3
M3: abnormal flexion of the arms (decorticate posture)

Answer

M = 3
6.Clinical assessment scores

Answer: high risk

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: yes → 25
secondary diagnosis: yes → 15
ambulatory aid: none, bed rest or nurse assists → 0
IV therapy or saline lock: no → 0
gait: weak → 10
mental status: knows own limits → 0

Add

Morse total = 25 + 15 + 0 + 0 + 10 + 0 = 50

Risk level

50 → high risk

Answer

high risk
7.Med-surg: cardiovascular & respiratory

Answer: D · An increased risk of pneumonia

Why this is the answer

In COPD, inhaled corticosteroids increase the risk of pneumonia. They are used where there are frequent exacerbations or features of asthma, and their benefit is weighed against this risk. Signs of pneumonia should be reported promptly.

Answer

D · An increased risk of pneumonia
8.Med-surg: cardiovascular & respiratory

Answer: D · Walking as tolerated is usually encouraged once treated

Why this is the answer

Early mobilisation with effective anticoagulation does not increase the risk of pulmonary embolism and may reduce pain, swelling and post-thrombotic syndrome. Routine bed rest is no longer recommended. Massage of the affected leg should be avoided.

Answer

D · Walking as tolerated is usually encouraged once treated

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