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
PaO₂ 104 mmHg · FiO₂ 1 · PEEP 10 cmH₂O0100200300400500P/F (mmHg)above 300: no ARDS grademildmoderatesevere

Practice exercise (made-up values, not clinical guidance). A ventilated patient who meets the other Berlin criteria for ARDS has PaO₂ 104 mmHg (13.9 kPa) on 100% oxygen with a PEEP of 10 cmH₂O. Calculate the P/F ratio and click the ARDS severity.

PaO₂ 104 mmHg (13.9 kPa)FiO₂ 100%PEEP 10 cmH₂O
  1. 1above 300: no ARDS grade
  2. 2mild
  3. 3moderate
  4. 4severe
2.Oxygen therapy & respiratory calculationsHard
65 kg160 cm♂5 mL/kg PBWVT​ = ? mL

Practice exercise (made-up values, not clinical guidance). A ventilated man is 160 cm tall and weighs 65 kg. Lung-protective ventilation is set at 5 mL per kg of predicted body weight. Using PBW = 50 + 0.91 × (height cm − 152.4) kg, find the tidal volume VT to the nearest mL.

160 cm65 kg5 mL/kg
VT = mL
3.Arterial blood gas interpretationMedium
pH7.357.457.50PaCO₂mmHg354525HCO₃⁻mmol/L222619uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.50, PaCO₂ 25 mmHg (3.3 kPa) and HCO₃⁻ 19 mmol/L. The primary disorder is respiratory alkalosis. How far is it compensated? Click your answer.

pH 7.50PaCO₂ 25 mmHg (3.3 kPa)HCO₃⁻ 19 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
4.Arterial blood gas interpretationHard

At sea level, a practice gas taken on 21% oxygen shows PaO₂ 57 mmHg (7.6 kPa) and PaCO₂ 57 mmHg (7.6 kPa). Use PAO₂ = FiO₂·(760 − 47) − PaCO₂/0.8 to find the A–a gradient.

FiO₂ 21%PaO₂ 57 mmHg (7.6 kPa)PaCO₂ 57 mmHg (7.6 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 when spoken to, talks in sentences but is confused and shows as the best motor response: moves a hand to the site of pressure (localises). Work out the GCS and classify the head injury by it. Click your answer.

  1. 1mild
  2. 2moderate
  3. 3severe
6.Clinical assessment scoresHard
reassuringmoderately abnormallow

Practice exercise (made-up values, not clinical guidance). At 1 minute after birth, a practice newborn has a pink body with blue hands and feet, a heart rate of 80/min, a cry, cough or sneeze when stimulated, some flexion of the arms and legs and slow, irregular breathing with a weak cry. Score the APGAR and click how the score is interpreted.

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

Why is active tuberculosis treated with several drugs for at least six months?

  1. ATo kill slow-growing bacteria and prevent drug resistance
  2. BBecause each drug works on a different organ only
  3. CBecause the bacteria are resistant to all drugs at first
  4. DTo reduce the number of side effects compared with one drug
8.Med-surg: cardiovascular & respiratoryHard

A nurse looked after a patient for a shift before smear-positive pulmonary TB was diagnosed, without wearing a respirator. What should happen?

  1. ATake no action, as healthcare workers are immune to TB
  2. BReport it so occupational health can arrange follow-up screening
  3. CStay off work for six months in case symptoms develop
  4. DStart a full six-month course of TB drugs at once without any tests

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: moderate

P/F ratio and ARDS (Berlin definition): P/F = PaO₂ (mmHg)/FiO₂ (as a fraction). With PEEP or CPAP of at least 5 cmH₂O, ARDS is graded mild for 200 < P/F ≤ 300, moderate for 100 < P/F ≤ 200 and severe for P/F ≤ 100 mmHg. The other Berlin criteria (onset within a week, bilateral opacities, not fully explained by heart failure) must also be met. PaO₂ in kPa × 7.5 gives mmHg. The ROX index (SpO₂/FiO₂)/respiratory rate is used to follow patients on high-flow nasal oxygen.

P/F ratio

P/F = 104/1 = 104 mmHg

Berlin severity

moderate

Answer

moderate
2.Oxygen therapy & respiratory calculations

Answer: VT = 285 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 = 50 + 0.91·(160 − 152.4) = 56.92 kg

Tidal volume

VT = 5·56.92 = 284.6 ≈ 285 mL

Answer

VT = 285 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 7.50: alkalaemia (above 7.45)
PaCO₂ 25 mmHg: low (35–45)
HCO₃⁻ 19 mmol/L: low (22–26)

Compensation

partially compensated

Answer

partially compensated
4.Arterial blood gas interpretation

Answer: A–a gradient = 21.48 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 − 57/0.8 = 149.7 − 71.25 = 78.48 mmHg

Gradient

A–a = 78.48 − 57 = 21.48 mmHg

Answer

A–a gradient = 21.48 mmHg
5.Clinical assessment scores

Answer: moderate

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 when spoken to → 3
V: talks in sentences but is confused → 4
M: moves a hand to the site of pressure (localises) → 5

Add

GCS = 3 + 4 + 5 = 12

Severity

GCS 12 → moderate

Answer

moderate
6.Clinical assessment scores

Answer: moderately abnormal

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: a pink body with blue hands and feet → 1
Pulse: 80/min → 1
Grimace: a cry, cough or sneeze when stimulated → 2
Activity: some flexion of the arms and legs → 1
Respiration: slow, irregular breathing with a weak cry → 1

Add

APGAR = 1 + 1 + 2 + 1 + 1 = 6

Interpretation

6 → moderately abnormal

Answer

moderately abnormal
7.Med-surg: cardiovascular & respiratory

Answer: A · To kill slow-growing bacteria and prevent drug resistance

Why this is the answer

Mycobacterium tuberculosis grows slowly and has resistant mutants in any large population. A combination (for example rifampicin, isoniazid, pyrazinamide and ethambutol at first) kills susceptible and resistant bacteria and prevents resistance. Stopping early risks relapse and multidrug-resistant TB.

Answer

A · To kill slow-growing bacteria and prevent drug resistance
8.Med-surg: cardiovascular & respiratory

Answer: B · Report it so occupational health can arrange follow-up screening

Why this is the answer

Contact tracing includes staff exposed without respiratory protection. Occupational health assesses the risk, checks for symptoms and arranges testing (for example IGRA) at suitable intervals. Treatment is offered for latent infection if found. Exposed people do not usually need to stop work unless they become unwell.

Answer

B · Report it so occupational health can arrange follow-up screening

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