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
Hb94 g/LSaO₂94%PaO₂72 mmHgCaO₂?

Practice exercise (made-up values, not clinical guidance). A patient has Hb 94 g/L, SaO₂ 94% and PaO₂ 72 mmHg (9.6 kPa). Find the arterial oxygen content CaO₂ = 1.34 × Hb (g/dL) × SaO₂ + 0.003 × PaO₂ (mmHg) in mL O₂/dL.

Hb 94 g/LSaO₂ 94%PaO₂ 72 mmHg (9.6 kPa)
CaO₂ = mL/dL
2.Oxygen therapy & respiratory calculationsHard
PaO₂ 11.2 kPa · FiO₂ 0.7 · PEEP 15 cmH₂O0100200300400500P/F (mmHg)above 300: no ARDS grademildmoderateseverenot gradable: PEEP below 5

Practice exercise (made-up values, not clinical guidance). A patient with acute hypoxaemia and bilateral opacities, not explained by heart failure, has PaO₂ 11.2 kPa on 70% oxygen with a PEEP of 15 cmH₂O. Grade the ARDS severity with the Berlin definition. Click your answer.

PaO₂ 11.2 kPaFiO₂ 70%PEEP 15 cmH₂O
  1. 1above 300: no ARDS grade
  2. 2mild
  3. 3moderate
  4. 4severe
  5. 5not gradable: PEEP below 5
3.Arterial blood gas interpretationMedium

Practice values: Na⁺ 138 mmol/L, glucose 9.5 mmol/L and urea 24 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.

Na⁺ 138 mmol/Lglucose 9.5 mmol/Lurea 24 mmol/L
Osm = mOsm/kg
4.Arterial blood gas interpretationHard

Practice values: Na⁺ 134, Cl⁻ 105, HCO₃⁻ 20 mmol/L and albumin 37 g/L. Find the albumin-corrected anion gap AGc = AG + 0.25·(40 − albumin).

Na⁺ 134 mmol/LCl⁻ 105 mmol/LHCO₃⁻ 20 mmol/Lalbumin 37 g/L
AGc = mmol/L
5.Clinical assessment scoresMedium
15694SBPDBPmmHgHR 120/min · SI = ?

Practice exercise (made-up values, not clinical guidance). A patient has a pulse of 120/min and a blood pressure of 156/94 mmHg. Find the shock index SI = HR/SBP. Round to two decimal places.

HR 120/minBP 156/94 mmHg
SI =
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 97% on room air, blood pressure 150/90 mmHg, pulse 76/min, alert, temperature 36.7 °C. Which clinical risk group does the patient fall into? Click it.

RR 14SpO₂ 97%airSBP 150HR 76AT 36.7 °C
  1. 1low
  2. 2low–medium
  3. 3medium
  4. 4high
7.Med-surg: cardiovascular & respiratoryMedium

After a bronchoscopy with throat anaesthesia, when can the patient eat and drink?

  1. AImmediately after the scope is removed
  2. BWhen the gag and cough reflexes have returned
  3. CAfter a full 24 hours without food
  4. DOnly after a chest X-ray has been reported
8.Med-surg: cardiovascular & respiratoryHard

One hour after cardiac surgery, a mediastinal chest drain has drained 350 mL of bright red blood and the heart rate is rising. What should the nurse do?

  1. ARecord the volume and continue hourly checks
  2. BReport it to the surgical team at once
  3. CClamp the drain to stop further blood loss
  4. DStrip the tubing hard every five minutes

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: CaO₂ = 12.06 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

94 g/L = 9.4 g/dL

Bound oxygen

1.34·9.4·0.94 = 11.84 mL/dL

Dissolved oxygen

0.003·72 = 0.216 mL/dL

Oxygen content

CaO₂ = 11.84 + 0.216 = 12.06 mL/dL

Answer

CaO₂ = 12.06 mL/dL
2.Oxygen therapy & respiratory calculations

Answer: moderate

P/F ratio and ARDS (Berlin definition): P/F = PaO₂ (mmHg)/FiO₂ (as a fraction). With PEEP or CPAP of at least 5 cmH₂O, ARDS is graded mild for 200 < P/F ≤ 300, moderate for 100 < P/F ≤ 200 and severe for P/F ≤ 100 mmHg. The other Berlin criteria (onset within a week, bilateral opacities, not fully explained by heart failure) must also be met. PaO₂ in kPa × 7.5 gives mmHg. The ROX index (SpO₂/FiO₂)/respiratory rate is used to follow patients on high-flow nasal oxygen.

PEEP

PEEP 15 ≥ 5 cmH₂O

PaO₂ in mmHg

11.2·7.5 = 84 mmHg

P/F ratio

P/F = 84/0.7 = 120 mmHg

Berlin severity

moderate

Answer

moderate
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 + 9.5 + 24 = 309.5 ≈ 310 mOsm/kg

Answer

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

Answer: AGc = 9.75 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.

Anion gap

AG = 134 − (105 + 20) = 9

Correction for albumin

9 + 0.25·(40 − 37) = 9.75 mmol/L

Answer

AGc = 9.75 mmol/L

Still within about 8–12 after correction.

5.Clinical assessment scores

Answer: SI = 0.77

Blood pressure values: pulse pressure PP = SBP − DBP. Mean arterial pressure MAP ≈ (SBP + 2·DBP)/3 = DBP + PP/3, an estimate based on the heart spending about two thirds of each beat in diastole at a normal heart rate (less accurate when the heart rate is fast); a MAP of at least about 65 mmHg is a common target for organ perfusion. The shock index SI = heart rate/SBP is normally about 0.5–0.7; a value above about 1 is a warning sign of shock.

Shock index

SI = 120/156 = 0.7692 ≈ 0.77

Answer

SI = 0.77

Above the usual 0.5–0.7.

6.Clinical assessment scores

Answer: low

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 97% → 0
on air → 0
SBP 150 mmHg → 0
HR 76/min → 0
alert (A) → 0
T 36.7 °C → 0

Total and red scores

NEWS2 = 0 + 0 + 0 + 0 + 0 + 0 + 0 = 0
No parameter scores 3.

Risk group

low

Answer

low
7.Med-surg: cardiovascular & respiratory

Answer: B · When the gag and cough reflexes have returned

Why this is the answer

Local anaesthetic sprayed on the throat abolishes the gag and cough reflexes for a time, so food or fluid could be aspirated. The nurse checks that the reflexes have returned (often after about one to two hours) before giving sips of water and then food.

Answer

B · When the gag and cough reflexes have returned
8.Med-surg: cardiovascular & respiratory

Answer: B · Report it to the surgical team at once

Why this is the answer

Drainage of more than about 100–200 mL/h (or a sudden large volume of fresh blood), especially with tachycardia or hypotension, may indicate surgical bleeding and needs urgent review. Clamping could cause cardiac tamponade. A sudden stop in drainage with falling blood pressure can also signal tamponade.

Answer

B · Report it to the surgical team at once

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