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 s610 mLf = 19/min · V̇A = ?VD​ = 150 mL

Practice exercise (made-up values, not clinical guidance). A patient breathes 19 times a minute with a tidal volume of 610 mL. The anatomical dead space is 150 mL. Find the alveolar ventilation V̇A in L/min.

VT 610 mL19/minVD 150 mL
V̇A = L/min
2.Oxygen therapy & respiratory calculationsHard
168 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 168 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 L168 bar10 L/min20 bar
t = min
3.Arterial blood gas interpretationMedium

A practice gas shows PaCO₂ 20 mmHg (2.7 kPa). Use the rule that in chronic respiratory alkalosis HCO₃⁻ falls by 5 mmol/L for every 10 mmHg that PaCO₂ is below 40, starting from HCO₃⁻ 24 mmol/L, to find the expected HCO₃⁻.

PaCO₂ 20 mmHg (2.7 kPa)baseline: 40 mmHg, 24 mmol/L
HCO₃⁻ = mmol/L
4.Arterial blood gas interpretationHard
pH7.357.457.23PaCO₂mmHg354522HCO₃⁻mmol/L22269appropriate compensationadded respiratory acidosisadded respiratory alkalosis

A practice gas shows a metabolic acidosis: pH 7.23, PaCO₂ 22 mmHg (2.9 kPa), HCO₃⁻ 9 mmol/L. Compare the measured PaCO₂ with Winter’s formula. Click your interpretation.

pH 7.23PaCO₂ 22 mmHg (2.9 kPa)HCO₃⁻ 9 mmol/L
  1. 1appropriate compensation
  2. 2added respiratory acidosis
  3. 3added respiratory alkalosis
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 9/min, SpO₂ 90% on room air, blood pressure 150/90 mmHg, pulse 70/min, alert, temperature 38.8 °C. What is the NEWS2 total score?

RR 9SpO₂ 90%airSBP 150HR 70AT 38.8 °C
NEWS2 =
6.Clinical assessment scoresHard
reassuringmoderately abnormallow

Practice exercise (made-up values, not clinical guidance). At 5 minutes after birth, a practice newborn has pink skin all over, a heart rate of 150/min, a grimace when stimulated, some flexion of the arms and legs and good breathing with a strong cry. Score the APGAR and click how the score is interpreted.

  1. 1reassuring
  2. 2moderately abnormal
  3. 3low
7.Med-surg: cardiovascular & respiratoryMedium

A patient on furosemide has a serum potassium of 3.0 mmol/L (3.0 mEq/L). Which symptoms may this cause?

  1. ASevere headache and a stiff neck
  2. BTingling around the lips and painful spasm of the hands
  3. CMuscle weakness, cramps and an irregular pulse
  4. DFacial flushing, fever and a skin rash
8.Med-surg: cardiovascular & respiratoryHard

A patient with a stab wound to the chest has a hole that sucks air with each breath. What is the immediate management?

  1. ACover it with a vented chest seal or a dressing taped on three sides
  2. BSeal it completely with tape on all four sides and leave it alone
  3. CLeave it open and give a nebuliser
  4. DPack the wound tightly with gauze pushed deep into the chest

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: V̇A = 8.74 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

610 − 150 = 460 mL

Alveolar ventilation

V̇A = 460·19 = 8740 mL/min = 8.74 L/min

Answer

V̇A = 8.74 L/min
2.Oxygen therapy & respiratory calculations

Answer: t = 44 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·(168 − 20) = 444 L

Duration

444/10 = 44.4 min → t = 44 min

Answer

t = 44 min
3.Arterial blood gas interpretation

Answer: HCO₃⁻ = 14 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.

Change in PaCO₂

|20 − 40| = 20 mmHg → 2 × 10 mmHg

Expected HCO₃⁻

HCO₃⁻ = 24 − 5·2 = 14 mmol/L

Answer

HCO₃⁻ = 14 mmol/L
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

1.5·9 + 8 = 21.5 → 19.5–23.5 mmHg

Compare

measured: 22 mmHg → appropriate compensation

Answer

appropriate compensation
5.Clinical assessment scores

Answer: NEWS2 = 5

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 9/min → 1
SpO₂ 90% → 3
on air → 0
SBP 150 mmHg → 0
HR 70/min → 0
alert (A) → 0
T 38.8 °C → 1

Add

NEWS2 = 1 + 3 + 0 + 0 + 0 + 0 + 1 = 5

Answer

NEWS2 = 5
6.Clinical assessment scores

Answer: reassuring

APGAR score: five signs, each scored 0, 1 or 2, checked at 1 and 5 minutes after birth. Appearance (colour): blue or pale 0, pink body with blue extremities 1, pink all over 2. Pulse: absent 0, below 100/min 1, 100/min or more 2. Grimace (reflex irritability): none 0, grimace 1, cry, cough or sneeze 2. Activity (tone): limp 0, some flexion 1, active movement 2. Respiration: absent 0, slow or irregular with a weak cry 1, good with a strong cry 2. A total of 7–10 is reassuring, 4–6 moderately abnormal and 0–3 low.

Score each sign

Appearance: pink skin all over → 2
Pulse: 150/min → 2
Grimace: a grimace when stimulated → 1
Activity: some flexion of the arms and legs → 1
Respiration: good breathing with a strong cry → 2

Add

APGAR = 2 + 2 + 1 + 1 + 2 = 8

Interpretation

8 → reassuring

Answer

reassuring
7.Med-surg: cardiovascular & respiratory

Answer: C · Muscle weakness, cramps and an irregular pulse

Why this is the answer

The adult reference range is about 3.5–5.0 mmol/L, so 3.0 mmol/L is low. Hypokalaemia causes weakness, cramps, constipation and arrhythmias, with flattened T waves and U waves on the ECG. Tingling lips and hand spasm suggest low calcium.

Answer

C · Muscle weakness, cramps and an irregular pulse
8.Med-surg: cardiovascular & respiratory

Answer: A · Cover it with a vented chest seal or a dressing taped on three sides

Why this is the answer

An open (sucking) chest wound lets air enter the pleural space. A vented chest seal or a dressing taped on three sides acts as a flap valve, letting air out but not in. A fully sealed dressing can cause a tension pneumothorax. A chest drain is placed away from the wound.

Answer

A · Cover it with a vented chest seal or a dressing taped on three sides

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