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
500psiHf = 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 500 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.

500 psif = 3.14 L/psi4 L/min200 psi
t = min
2.Oxygen therapy & respiratory calculationsHard
Hb120 g/LSaO₂95%PaO₂75 mmHgCaO₂mL/dL× CO3.5 L/minDO₂?

Practice exercise (made-up values, not clinical guidance). A patient has Hb 120 g/L, SaO₂ 95%, PaO₂ 75 mmHg (10.0 kPa) and a cardiac output of 3.5 L/min. With CaO₂ = 1.34 × Hb (g/dL) × SaO₂ + 0.003 × PaO₂ (mmHg), find the oxygen delivery DO₂ = CaO₂ × CO × 10 in mL/min.

Hb 120 g/LSaO₂ 95%PaO₂ 75 mmHg (10.0 kPa)CO 3.5 L/min
DO₂ = mL/min
3.Arterial blood gas interpretationMedium

Practice values: Na⁺ 138 mmol/L, glucose 23.5 mmol/L and urea 10.5 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.

Na⁺ 138 mmol/Lglucose 23.5 mmol/Lurea 10.5 mmol/L
Osm = mOsm/kg
4.Arterial blood gas interpretationHard
pH7.357.457.29PaCO₂mmHg354526HCO₃⁻mmol/L222612appropriate compensationadded respiratory acidosisadded respiratory alkalosis

A practice gas shows a metabolic acidosis: pH 7.29, PaCO₂ 26 mmHg (3.5 kPa), HCO₃⁻ 12 mmol/L. Compare the measured PaCO₂ with Winter’s formula. Click your interpretation.

pH 7.29PaCO₂ 26 mmHg (3.5 kPa)HCO₃⁻ 12 mmol/L
  1. 1appropriate compensation
  2. 2added respiratory acidosis
  3. 3added respiratory alkalosis
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
3210123RR≤89–1112–2021–24≥25SpO₂≤9192–9394–95≥96air / O₂O₂airSBP≤9091–100101–110111–219≥220HR≤4041–5051–9091–110111–130≥131ACVPUAC, V, P, UT °C≤35.035.1–36.036.1–38.038.1–39.0≥39.1lowlow–mediummediumhigh

Practice exercise (made-up values, not clinical guidance). Use the NEWS2 chart (SpO₂ scale 1) for these observations: respiration rate 14/min, SpO₂ 90% on supplemental oxygen, blood pressure 118/70 mmHg, pulse 92/min, alert, temperature 38.4 °C. Which clinical risk group does the patient fall into? Click it.

RR 14SpO₂ 90%O₂SBP 118HR 92AT 38.4 °C
  1. 1low
  2. 2low–medium
  3. 3medium
  4. 4high
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. AAspirin alone can replace warfarin once the valve has healed
  2. BDirect oral anticoagulants are not used for mechanical valves
  3. CMechanical valves do not need anticoagulation after the first month
  4. DAny anticoagulant works equally well once the valve is in place
8.Med-surg: cardiovascular & respiratoryHard

A patient recovering from an MI is anxious about returning to normal life. Which intervention best supports recovery?

  1. AAdvice to stop tablets once they feel well
  2. BAdvice to rest in bed for three months
  3. CReferral to cardiac rehabilitation
  4. DAdvice to avoid all exercise permanently

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: t = 235 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

(500 − 200)·3.14 = 942 L

Duration

942/4 = 235.5 min → t = 235 min

Answer

t = 235 min

That is about 3 h 55 min.

2.Oxygen therapy & respiratory calculations

Answer: DO₂ = 542.5 mL/min

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.

Oxygen content

120 g/L = 12 g/dL
CaO₂ = 1.34·12·0.95 + 0.003·75 = 15.5 mL/dL

Oxygen delivery

DO₂ = 15.5·3.5·10 = 542.5 mL/min

Answer

DO₂ = 542.5 mL/min

A normal resting adult value is about 1000 mL/min.

3.Arterial blood gas interpretation

Answer: Osm = 310 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 = 2·138 + 23.5 + 10.5 = 310 ≈ 310 mOsm/kg

Answer

Osm = 310 mOsm/kg
4.Arterial blood gas interpretation

Answer: appropriate compensation

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

1.5·12 + 8 = 26 → 24–28 mmHg

Compare

measured: 26 mmHg → appropriate compensation

Answer

appropriate compensation
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

NEWS2 (National Early Warning Score 2, Royal College of Physicians 2017): score each of the seven parameters with the chart (respiration rate, SpO₂ on scale 1, air or supplemental oxygen, systolic blood pressure, pulse, consciousness on the ACVPU scale and temperature) and add the scores. Clinical risk: 0–4 low; a score of 3 in any single parameter low–medium; 5–6 medium; 7 or more high. A total of 5 or more needs an urgent response.

Score each parameter

RR 14/min → 0
SpO₂ 90% → 3
on oxygen → 2
SBP 118 mmHg → 0
HR 92/min → 1
alert (A) → 0
T 38.4 °C → 1

Total and red scores

NEWS2 = 0 + 3 + 2 + 0 + 1 + 0 + 1 = 7
At least one parameter scores 3.

Risk group

high

Answer

high

A total of 5 or more calls for an urgent clinical response.

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 · Referral to cardiac rehabilitation

Why this is the answer

Cardiac rehabilitation combines supervised exercise, risk factor education, medication advice and psychological support. It improves quality of life and reduces cardiovascular mortality and readmissions. Patients are encouraged to return gradually to activity, including work, driving and sex, according to advice.

Answer

C · Referral to cardiac rehabilitation

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