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
850psiHf = 3.14 L/psi10 L/minresidual 200 psit = ? min

Practice exercise (made-up values, not clinical guidance). A size H oxygen cylinder (factor 3.14 L/psi) reads 850 psi and runs at 10 L/min. Keeping a safe residual of 200 psi, how many minutes t will it last? Round down to a whole minute.

850 psif = 3.14 L/psi10 L/min200 psi
t = min
2.Oxygen therapy & respiratory calculationsHard
89 kg178 cm♀6 mL/kg PBWVT​ = ? mL

Practice exercise (made-up values, not clinical guidance). A ventilated woman is 178 cm tall and weighs 89 kg. Lung-protective ventilation is set at 6 mL per kg of predicted body weight. Using PBW = 45.5 + 0.91 × (height cm − 152.4) kg, find the tidal volume VT to the nearest mL.

178 cm89 kg6 mL/kg
VT = mL
3.Arterial blood gas interpretationMedium
pH7.357.457.32PaCO₂mmHg354526HCO₃⁻mmol/L222613uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.32, PaCO₂ 26 mmHg (3.5 kPa) and HCO₃⁻ 13 mmol/L. The primary disorder is metabolic acidosis. How far is it compensated? Click your answer.

pH 7.32PaCO₂ 26 mmHg (3.5 kPa)HCO₃⁻ 13 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
4.Arterial blood gas interpretationHard

Practice values: Na⁺ 139, Cl⁻ 93 and HCO₃⁻ 17 mmol/L. Calculate the delta ratio (AG − 12)/(24 − HCO₃⁻), using AG = Na⁺ − (Cl⁻ + HCO₃⁻). Give two decimals.

Na⁺ 139 mmol/LCl⁻ 93 mmol/LHCO₃⁻ 17 mmol/L
delta ratio =
5.Clinical assessment scoresMedium
E3 / 4+V2 / 5+M? / 6GCS 8?

Practice exercise (made-up values, not clinical guidance). A practice chart records GCS 8, with E3 and V2. What motor score M was recorded, and which response does it describe? Give the number.

GCS 8E3V2
M =
6.Clinical assessment scoresHard
121?SBPDBPmmHgMAP = 65

Practice exercise (made-up values, not clinical guidance). The team aims for a mean arterial pressure of at least 65 mmHg. A patient’s systolic pressure is 121 mmHg. Using MAP = (SBP + 2·DBP)/3, what is the lowest diastolic pressure DBP that still gives a MAP of 65 mmHg?

MAP 65 mmHgSBP 121 mmHg
DBP = mmHg
7.Med-surg: cardiovascular & respiratoryMedium

A patient with COPD is prescribed long-term oxygen therapy. How many hours a day is it usually needed to improve survival?

  1. AOnly when walking outside
  2. BAt least 15 hours a day
  3. COnly during meals
  4. DAbout one hour each morning
8.Med-surg: cardiovascular & respiratoryHard

A fit 24-year-old marathon runner has a resting heart rate of 46/min on admission for minor surgery. He has no dizziness, chest pain or breathlessness, and his BP is 118/70 mmHg. What is the appropriate response?

  1. ACancel the surgery and arrange a permanent pacemaker urgently
  2. BStart chest compressions
  3. CDocument and report it, as this is often normal in an athlete
  4. DGive IV atropine straight away to bring the rate above 60/min

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: t = 204 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

(850 − 200)·3.14 = 2041 L

Duration

2041/10 = 204.1 min → t = 204 min

Answer

t = 204 min

That is about 3 h 24 min.

2.Oxygen therapy & respiratory calculations

Answer: VT = 413 mL

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).

Predicted body weight

PBW = 45.5 + 0.91·(178 − 152.4) = 68.8 kg

Tidal volume

VT = 6·68.8 = 412.8 ≈ 413 mL

Answer

VT = 413 mL
3.Arterial blood gas interpretation

Answer: partially compensated

Reading a blood gas (ROME): first the pH: below 7.35 is acidaemia, above 7.45 alkalaemia. Then find the value that explains it. PaCO₂ (normal 35–45 mmHg, 4.7–6.0 kPa) is the respiratory part and moves Opposite to the pH in a respiratory disorder; HCO₃⁻ (normal 22–26 mmol/L) is the metabolic part and moves in the same direction as the pH (Respiratory Opposite, Metabolic Equal). The other value shows the compensation: normal means uncompensated; abnormal in the direction that pulls the pH back while the pH is still abnormal means partially compensated; a normal pH with both values abnormal means fully compensated. Ranges differ slightly between laboratories; these are practice values.

ROME, value by value

pH 7.32: acidaemia (below 7.35)
PaCO₂ 26 mmHg: low (35–45)
HCO₃⁻ 13 mmol/L: low (22–26)

Compensation

partially compensated

Answer

partially compensated
4.Arterial blood gas interpretation

Answer: delta ratio = 2.429

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 = 139 − (93 + 17) = 29

Delta ratio

(29 − 12)/(24 − 17) = 17/7 = 2.429

Answer

delta ratio = 2.429

Above 2: an added metabolic alkalosis.

5.Clinical assessment scores

Answer: M = 3

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.

Motor score

M = 8 − 3 − 2 = 3
M3: abnormal flexion of the arms (decorticate posture)

Answer

M = 3
6.Clinical assessment scores

Answer: DBP = 37 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 = (3·65 − 121)/2 = 74/2 = 37 mmHg

Answer

DBP = 37 mmHg
7.Med-surg: cardiovascular & respiratory

Answer: B · At least 15 hours a day

Why this is the answer

Long-term oxygen therapy improves survival in COPD with chronic hypoxaemia when used for at least 15 hours a day, including overnight. Patients must not smoke, because of the fire risk. Ambulatory oxygen for exercise is a separate assessment.

Answer

B · At least 15 hours a day
8.Med-surg: cardiovascular & respiratory

Answer: C · Document and report it, as this is often normal in an athlete

Why this is the answer

Endurance training increases vagal tone and stroke volume, so resting rates in the 40s can be normal. Without symptoms or haemodynamic compromise, no treatment is needed, though it is recorded and the team informed. Symptomatic bradycardia is treated.

Answer

C · Document and report it, as this is often normal in an athlete

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