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 s500 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 500 mL. The anatomical dead space is 150 mL. Find the alveolar ventilation V̇A in L/min.

VT 500 mL19/minVD 150 mL
V̇A = L/min
2.Oxygen therapy & respiratory calculationsHard
1050psiEf = 0.28 L/psi90 minresidual 200 psiQ = ? L/min

Practice exercise (made-up values, not clinical guidance). A transfer will take 90 minutes. The size E cylinder (factor 0.28 L/psi) reads 1050 psi. Keeping a safe residual of 200 psi, what is the highest whole-number flow Q in L/min that lasts the whole transfer?

90 min1050 psif = 0.28 L/psi200 psi
Q = L/min
3.Arterial blood gas interpretationMedium

A practice gas shows PaCO₂ 80 mmHg (10.7 kPa). Use the rule that in acute respiratory acidosis HCO₃⁻ rises by 1 mmol/L for every 10 mmHg that PaCO₂ is above 40, starting from HCO₃⁻ 24 mmol/L, to find the expected HCO₃⁻.

PaCO₂ 80 mmHg (10.7 kPa)baseline: 40 mmHg, 24 mmol/L
HCO₃⁻ = mmol/L
4.Arterial blood gas interpretationHard
pH7.357.457.33PaCO₂mmHg354535HCO₃⁻mmol/L222618appropriate compensationadded respiratory acidosisadded respiratory alkalosis

A practice gas shows a metabolic acidosis: pH 7.33, PaCO₂ 35 mmHg (4.7 kPa), HCO₃⁻ 18 mmol/L. Compare the measured PaCO₂ with Winter’s formula. Click your interpretation.

pH 7.33PaCO₂ 35 mmHg (4.7 kPa)HCO₃⁻ 18 mmol/L
  1. 1appropriate compensation
  2. 2added respiratory acidosis
  3. 3added respiratory alkalosis
5.Clinical assessment scoresMedium
7340SBPDBPmmHgHR 114/min · SI = ?

Practice exercise (made-up values, not clinical guidance). A patient has a pulse of 114/min and a blood pressure of 73/40 mmHg. Find the shock index SI = HR/SBP. Round to two decimal places.

HR 114/minBP 73/40 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 30/min, SpO₂ 91% on room air, blood pressure 118/70 mmHg, pulse 104/min, alert, temperature 36.9 °C. Which clinical risk group does the patient fall into? Click it.

RR 30SpO₂ 91%airSBP 118HR 104AT 36.9 °C
  1. 1low
  2. 2low–medium
  3. 3medium
  4. 4high
7.Med-surg: cardiovascular & respiratoryMedium

Which emergency equipment should be kept at the bedside of a patient with a tracheostomy?

  1. AA urinary catheter set, a blood glucose meter and a thermometer
  2. BOnly a spare oxygen mask, since the tube rarely causes problems
  3. CSpare tubes (same size and one smaller), suction and oxygen
  4. DA nasogastric tube and a feeding pump
8.Med-surg: cardiovascular & respiratoryHard

A 25-year-old non-smoker has wheeze and cough that come and go, worse at night and after exercise. Spirometry improves markedly after a bronchodilator. Which diagnosis is most likely?

  1. AIdiopathic pulmonary fibrosis
  2. BCOPD
  3. CHeart failure
  4. DAsthma

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: V̇A = 6.65 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

500 − 150 = 350 mL

Alveolar ventilation

V̇A = 350·19 = 6650 mL/min = 6.65 L/min

Answer

V̇A = 6.65 L/min
2.Oxygen therapy & respiratory calculations

Answer: Q = 2 L/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

(1050 − 200)·0.28 = 238 L

Highest flow

238/90 = 2.644 L/min → Q = 2 L/min

Answer

Q = 2 L/min
3.Arterial blood gas interpretation

Answer: HCO₃⁻ = 28 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

|80 − 40| = 40 mmHg → 4 × 10 mmHg

Expected HCO₃⁻

HCO₃⁻ = 24 + 1·4 = 28 mmol/L

Answer

HCO₃⁻ = 28 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

1.5·18 + 8 = 35 → 33–37 mmHg

Compare

measured: 35 mmHg → appropriate compensation

Answer

appropriate compensation
5.Clinical assessment scores

Answer: SI = 1.56

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 = 114/73 = 1.562 ≈ 1.56

Answer

SI = 1.56

1 or more: a warning sign of shock in this practice case.

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 30/min → 3
SpO₂ 91% → 3
on air → 0
SBP 118 mmHg → 0
HR 104/min → 1
alert (A) → 0
T 36.9 °C → 0

Total and red scores

NEWS2 = 3 + 3 + 0 + 0 + 1 + 0 + 0 = 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: C · Spare tubes (same size and one smaller), suction and oxygen

Why this is the answer

Bedside equipment usually includes spare tracheostomy tubes (same size and one size smaller), an obturator if used, suction with catheters, oxygen, a bag-valve-mask and tracheal dilators where policy requires. It is checked at every shift.

Answer

C · Spare tubes (same size and one smaller), suction and oxygen
8.Med-surg: cardiovascular & respiratory

Answer: D · Asthma

Why this is the answer

Asthma typically causes variable symptoms with reversible airflow obstruction. COPD usually affects older people with a smoking history and causes persistent, poorly reversible obstruction. Fibrosis gives a restrictive pattern.

Answer

D · Asthma

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