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
Hb175 g/LSaO₂96%PaO₂82 mmHgCaO₂?

Practice exercise (made-up values, not clinical guidance). A patient has Hb 175 g/L, SaO₂ 96% and PaO₂ 82 mmHg (10.9 kPa). Find the arterial oxygen content CaO₂ = 1.34 × Hb (g/dL) × SaO₂ + 0.003 × PaO₂ (mmHg) in mL O₂/dL.

Hb 175 g/LSaO₂ 96%PaO₂ 82 mmHg (10.9 kPa)
CaO₂ = mL/dL
2.Oxygen therapy & respiratory calculationsHard
Hb140 g/LSaO₂97%PaO₂93 mmHgCaO₂mL/dL× CO4.4 L/minDO₂?

Practice exercise (made-up values, not clinical guidance). A patient has Hb 140 g/L, SaO₂ 97%, PaO₂ 93 mmHg (12.4 kPa) and a cardiac output of 4.4 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 140 g/LSaO₂ 97%PaO₂ 93 mmHg (12.4 kPa)CO 4.4 L/min
DO₂ = mL/min
3.Arterial blood gas interpretationMedium

A practice gas shows a metabolic acidosis with HCO₃⁻ 10 mmol/L. Use Winter’s formula to find the expected PaCO₂ (the centre of the range) in mmHg.

HCO₃⁻ 10 mmol/L
PaCO₂ = mmHg
4.Arterial blood gas interpretationHard

Practice values: Na⁺ 137, Cl⁻ 94 and HCO₃⁻ 15 mmol/L. Calculate the delta ratio (AG − 12)/(24 − HCO₃⁻), using AG = Na⁺ − (Cl⁻ + HCO₃⁻). Give two decimals.

Na⁺ 137 mmol/LCl⁻ 94 mmol/LHCO₃⁻ 15 mmol/L
delta ratio =
5.Clinical assessment scoresMedium
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≥39.1

Practice exercise (made-up values, not clinical guidance). Use the NEWS2 chart (SpO₂ scale 1) for these observations: respiration rate 8/min, SpO₂ 95% on room air, blood pressure 136/82 mmHg, pulse 120/min, alert, temperature 36.8 °C. What is the NEWS2 total score?

RR 8SpO₂ 95%airSBP 136HR 120AT 36.8 °C
NEWS2 =
6.Clinical assessment scoresHard
122?SBPDBPmmHgMAP = 70

Practice exercise (made-up values, not clinical guidance). The team aims for a mean arterial pressure of at least 70 mmHg. A patient’s systolic pressure is 122 mmHg. Using MAP = (SBP + 2·DBP)/3, what is the lowest diastolic pressure DBP that still gives a MAP of 70 mmHg?

MAP 70 mmHgSBP 122 mmHg
DBP = mmHg
7.Med-surg: cardiovascular & respiratoryMedium

A patient with heart failure asks why salt is being limited. Which explanation is correct?

  1. ASodium raises the heart rate during sleep
  2. BSodium directly weakens the contracting heart muscle
  3. CSodium stops the diuretic tablets from being absorbed properly
  4. DSodium makes the body retain water, which adds to congestion
8.Med-surg: cardiovascular & respiratoryHard

After cardiac catheterisation via the radial artery, which assessment is most important?

  1. ACirculation, sensation and movement of the hand, and the site
  2. BBowel sounds and abdominal girth every hour after the test
  3. CUrine specific gravity every four hours
  4. DPupil size and reaction to light every 15 minutes

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: CaO₂ = 22.76 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

175 g/L = 17.5 g/dL

Bound oxygen

1.34·17.5·0.96 = 22.51 mL/dL

Dissolved oxygen

0.003·82 = 0.246 mL/dL

Oxygen content

CaO₂ = 22.51 + 0.246 = 22.76 mL/dL

Answer

CaO₂ = 22.76 mL/dL
2.Oxygen therapy & respiratory calculations

Answer: DO₂ = 813 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

140 g/L = 14 g/dL
CaO₂ = 1.34·14·0.97 + 0.003·93 = 18.48 mL/dL

Oxygen delivery

DO₂ = 18.48·4.4·10 = 813 mL/min

Answer

DO₂ = 813 mL/min

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

3.Arterial blood gas interpretation

Answer: PaCO₂ = 23 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.

Winter’s formula

PaCO₂ = 1.5·10 + 8 = 23 mmHg
range: 21–25 mmHg

Answer

PaCO₂ = 23 mmHg
4.Arterial blood gas interpretation

Answer: delta ratio = 1.778

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 = 137 − (94 + 15) = 28

Delta ratio

(28 − 12)/(24 − 15) = 16/9 = 1.778

Answer

delta ratio = 1.778

Between 1 and 2: a pure high anion gap acidosis.

5.Clinical assessment scores

Answer: NEWS2 = 6

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 8/min → 3
SpO₂ 95% → 1
on air → 0
SBP 136 mmHg → 0
HR 120/min → 2
alert (A) → 0
T 36.8 °C → 0

Add

NEWS2 = 3 + 1 + 0 + 0 + 2 + 0 + 0 = 6

Answer

NEWS2 = 6
6.Clinical assessment scores

Answer: DBP = 44 mmHg

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.

Rearrange

DBP = (3·MAP − SBP)/2

Substitute

DBP = (3·70 − 122)/2 = 88/2 = 44 mmHg

Answer

DBP = 44 mmHg
7.Med-surg: cardiovascular & respiratory

Answer: D · Sodium makes the body retain water, which adds to congestion

Why this is the answer

Sodium retention leads to water retention, increasing circulating volume, preload and congestion. Limiting sodium and, in some patients, fluid helps control oedema and breathlessness. The exact limits are set by the prescriber.

Answer

D · Sodium makes the body retain water, which adds to congestion
8.Med-surg: cardiovascular & respiratory

Answer: A · Circulation, sensation and movement of the hand, and the site

Why this is the answer

After radial access, the compression device and puncture site are checked for bleeding or haematoma, and the hand for colour, warmth, capillary refill, sensation and movement. Radial artery occlusion and forearm compartment syndrome are possible complications.

Answer

A · Circulation, sensation and movement of the hand, and the site

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