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
60 s550 mLf = 27/min · V̇A = ?VD​ = 120 mL

Practice exercise (made-up values, not clinical guidance). A patient breathes 27 times a minute with a tidal volume of 550 mL. The anatomical dead space is 120 mL. Find the alveolar ventilation V̇A in L/min.

VT 550 mL27/minVD 120 mL
V̇A = L/min
2.Oxygen therapy & respiratory calculationsHard
118 bar3 L10 L/min20 bart = ? min

Practice exercise (made-up values, not clinical guidance). A cylinder with a water capacity of 3 L is filled to 118 bar and runs at 10 L/min. The gas volume is about the water capacity × the pressure. In this exercise the cylinder is changed at 20 bar. How many minutes t until it must be changed? Round down to a whole minute.

3 L118 bar10 L/min20 bar
t = min
3.Arterial blood gas interpretationMedium

Practice values: Na⁺ 134 mmol/L, glucose 31.5 mmol/L and urea 4.3 mmol/L. Calculate the serum osmolality Osm = 2·Na⁺ + glucose + urea to the nearest whole number.

Na⁺ 134 mmol/Lglucose 31.5 mmol/Lurea 4.3 mmol/L
Osm = mOsm/kg
4.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 21% oxygen shows PaO₂ 71 mmHg (9.5 kPa) and PaCO₂ 43 mmHg (5.7 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 21%PaO₂ 71 mmHg (9.5 kPa)PaCO₂ 43 mmHg (5.7 kPa)
A–a gradient = mmHg
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 no sounds 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
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 room air, blood pressure 130/78 mmHg, pulse 82/min, unresponsive, temperature 36.1 °C. Which clinical risk group does the patient fall into? Click it.

RR 14SpO₂ 90%airSBP 130HR 82UT 36.1 °C
  1. 1low
  2. 2low–medium
  3. 3medium
  4. 4high
7.Med-surg: cardiovascular & respiratoryMedium

How should subcutaneous enoxaparin from a prefilled syringe be given?

  1. AInto the same abdominal site each day, then massaged
  2. BAs a rapid intravenous bolus through a cannula
  3. CInto the deltoid muscle, after first expelling the air bubble
  4. DInto the abdomen, leaving the air bubble in, without rubbing
8.Med-surg: cardiovascular & respiratoryHard

A patient's blood gas shows pH 7.26, PaCO₂ 9.0 kPa (68 mmHg) and bicarbonate 25 mmol/L. What does this show?

  1. AAcute respiratory acidosis
  2. BRespiratory alkalosis
  3. CMetabolic acidosis with compensation
  4. DMetabolic alkalosis

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: V̇A = 11.61 L/min

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).

Alveolar part of a breath

550 − 120 = 430 mL

Alveolar ventilation

V̇A = 430·27 = 11610 mL/min = 11.61 L/min

Answer

V̇A = 11.61 L/min
2.Oxygen therapy & respiratory calculations

Answer: t = 29 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 gas

3·(118 − 20) = 294 L

Duration

294/10 = 29.4 min → t = 29 min

Answer

t = 29 min
3.Arterial blood gas interpretation

Answer: Osm = 304 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 = 2·134 + 31.5 + 4.3 = 303.8 ≈ 304 mOsm/kg

Answer

Osm = 304 mOsm/kg
4.Arterial blood gas interpretation

Answer: A–a gradient = 24.98 mmHg

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.

Alveolar oxygen

PAO₂ = 0.21·713 − 43/0.8 = 149.7 − 53.75 = 95.98 mmHg

Gradient

A–a = 95.98 − 71 = 24.98 mmHg

Answer

A–a gradient = 24.98 mmHg
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 no sounds → 1
M: abnormal flexion of the arms (decorticate posture) → 3

Add

GCS = 2 + 1 + 3 = 6

Severity

GCS 6 → severe

Answer

severe
6.Clinical assessment scores

Answer: medium

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 air → 0
SBP 130 mmHg → 0
HR 82/min → 0
unresponsive (U) → 3
T 36.1 °C → 0

Total and red scores

NEWS2 = 0 + 3 + 0 + 0 + 0 + 3 + 0 = 6
At least one parameter scores 3.

Risk group

medium

Answer

medium

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

7.Med-surg: cardiovascular & respiratory

Answer: D · Into the abdomen, leaving the air bubble in, without rubbing

Why this is the answer

Prefilled LMWH syringes contain an air bubble that is usually left in so the full dose is delivered. Injecting into a skin fold of the abdomen (away from the umbilicus), rotating sites and not rubbing afterwards reduce bruising and haematoma.

Answer

D · Into the abdomen, leaving the air bubble in, without rubbing
8.Med-surg: cardiovascular & respiratory

Answer: A · Acute respiratory acidosis

Why this is the answer

A low pH with raised PaCO₂ is respiratory acidosis. A normal bicarbonate (about 22–26 mmol/L) shows the kidneys have not yet compensated, so the problem is acute, as in opioid toxicity, exhaustion or an acute COPD exacerbation. Treatment targets ventilation.

Answer

A · Acute respiratory acidosis

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