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
1150psiHf = 3.14 L/psi8 L/minresidual 200 psit = ? min

Practice exercise (made-up values, not clinical guidance). A size H oxygen cylinder (factor 3.14 L/psi) reads 1150 psi and runs at 8 L/min. Keeping a safe residual of 200 psi, how many minutes t will it last? Round down to a whole minute.

1150 psif = 3.14 L/psi8 L/min200 psi
t = min
2.Oxygen therapy & respiratory calculationsHard
PaO₂ 12.4 kPa · FiO₂ 0.4 · PEEP 12 cmH₂O0100200300400500P/F (mmHg)above 300: no ARDS grademildmoderateseverenot gradable: PEEP below 5

Practice exercise (made-up values, not clinical guidance). A patient with acute hypoxaemia and bilateral opacities, not explained by heart failure, has PaO₂ 12.4 kPa on 40% oxygen with a PEEP of 12 cmH₂O. Grade the ARDS severity with the Berlin definition. Click your answer.

PaO₂ 12.4 kPaFiO₂ 40%PEEP 12 cmH₂O
  1. 1above 300: no ARDS grade
  2. 2mild
  3. 3moderate
  4. 4severe
  5. 5not gradable: PEEP below 5
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

Practice values: Na⁺ 134, Cl⁻ 88 and HCO₃⁻ 11 mmol/L. Calculate the delta ratio (AG − 12)/(24 − HCO₃⁻), using AG = Na⁺ − (Cl⁻ + HCO₃⁻). Give two decimals.

Na⁺ 134 mmol/LCl⁻ 88 mmol/LHCO₃⁻ 11 mmol/L
delta ratio =
5.Clinical assessment scoresMedium
S? / 4+M? / 4+A? / 4+Mob? / 4+N? / 4+F? / 3Σ?

Practice exercise (made-up values, not clinical guidance). A practice patient is assessed with the Braden scale: sensory perception: completely limited; moisture: constantly moist; activity: walks occasionally; mobility: slightly limited; nutrition: probably inadequate; friction and shear: no apparent problem. Find the Braden total B.

6–23
B =
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 60/min, a cry, cough or sneeze 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

Which combination of drug classes improves survival in heart failure with reduced ejection fraction?

  1. AAn NSAID, aspirin, a statin and a thiazide diuretic
  2. BACE inhibitor or ARNI, beta-blocker, MRA and SGLT2 inhibitor
  3. CA loop diuretic alone at the highest tolerated dose
  4. DLoop diuretic, digoxin, nitrate and a calcium channel blocker
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. AHeart failure
  2. BIdiopathic pulmonary fibrosis
  3. CAsthma
  4. DCOPD

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: t = 372 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

(1150 − 200)·3.14 = 2983 L

Duration

2983/8 = 372.9 min → t = 372 min

Answer

t = 372 min

That is about 6 h 12 min.

2.Oxygen therapy & respiratory calculations

Answer: mild

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.

PEEP

PEEP 12 ≥ 5 cmH₂O

PaO₂ in mmHg

12.4·7.5 = 93 mmHg

P/F ratio

P/F = 93/0.4 = 232.5 mmHg

Berlin severity

mild

Answer

mild
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: delta ratio = 1.769

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 = 134 − (88 + 11) = 35

Delta ratio

(35 − 12)/(24 − 11) = 23/13 = 1.769

Answer

delta ratio = 1.769

Between 1 and 2: a pure high anion gap acidosis.

5.Clinical assessment scores

Answer: B = 13

Braden scale: six subscales for pressure-injury risk. Sensory perception, moisture, activity, mobility and nutrition score 1 to 4, from the worst level (1) to no problem (4); friction and shear scores 1 to 3. The total runs from 6 to 23, and a lower total means a higher risk. Common bands: 19–23 not at risk, 15–18 mild risk, 13–14 moderate risk, 10–12 high risk and 9 or below very high risk.

Score each subscale

sensory perception: completely limited → 1
moisture: constantly moist → 1
activity: walks occasionally → 3
mobility: slightly limited → 3
nutrition: probably inadequate → 2
friction and shear: no apparent problem → 3

Add

Braden total = 1 + 1 + 3 + 3 + 2 + 3 = 13

Answer

B = 13
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: a pink body with blue hands and feet → 1
Pulse: 60/min → 1
Grimace: a cry, cough or sneeze when stimulated → 2
Activity: some flexion of the arms and legs → 1
Respiration: good breathing with a strong cry → 2

Add

APGAR = 1 + 1 + 2 + 1 + 2 = 7

Interpretation

7 → reassuring

Answer

reassuring
7.Med-surg: cardiovascular & respiratory

Answer: B · ACE inhibitor or ARNI, beta-blocker, MRA and SGLT2 inhibitor

Why this is the answer

Current guidelines recommend four disease-modifying classes for HFrEF: ACE inhibitor, ARB or ARNI (sacubitril/valsartan); an evidence-based beta-blocker; an MRA (spironolactone or eplerenone); and an SGLT2 inhibitor. Loop diuretics and digoxin improve symptoms but not survival. NSAIDs worsen heart failure.

Answer

B · ACE inhibitor or ARNI, beta-blocker, MRA and SGLT2 inhibitor
8.Med-surg: cardiovascular & respiratory

Answer: C · 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

C · Asthma

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