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
1000psiDf = 0.16 L/psi10 L/minresidual 200 psit = ? min

Practice exercise (made-up values, not clinical guidance). A size D oxygen cylinder (factor 0.16 L/psi) reads 1000 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.

1000 psif = 0.16 L/psi10 L/min200 psi
t = min
2.Oxygen therapy & respiratory calculationsHard
1100psiDf = 0.16 L/psi60 minresidual 200 psiQ = ? L/min

Practice exercise (made-up values, not clinical guidance). A transfer will take 60 minutes. The size D cylinder (factor 0.16 L/psi) reads 1100 psi. Keeping a safe residual of 200 psi, what is the highest whole-number flow Q in L/min that lasts the whole transfer?

60 min1100 psif = 0.16 L/psi200 psi
Q = L/min
3.Arterial blood gas interpretationMedium

A practice gas shows PaCO₂ 79 mmHg (10.5 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 79 mmHg (10.5 kPa)baseline: 40 mmHg, 24 mmol/L
HCO₃⁻ = mmol/L
4.Arterial blood gas interpretationHard

A practice gas shows a metabolic alkalosis with HCO₃⁻ 38 mmol/L. Use expected PaCO₂ = 0.7·HCO₃⁻ + 21 to find the expected PaCO₂.

HCO₃⁻ 38 mmol/L
PaCO₂ = mmHg
5.Clinical assessment scoresMedium
H? / 25+D? / 15+Aid? / 30+IV? / 20+G? / 20+MS? / 15Σ?

Practice exercise (made-up values, not clinical guidance). A practice patient is assessed with the Morse fall scale: history of falling in the last 3 months: no; secondary diagnosis: no; ambulatory aid: holds on to furniture; IV therapy or saline lock: yes; gait: normal, bed rest or wheelchair; mental status: overestimates or forgets limits. Find the Morse total MFS.

0–125
MFS =
6.Clinical assessment scoresHard
reassuringmoderately abnormallow

Practice exercise (made-up values, not clinical guidance). At 5 minutes after birth, a practice newborn has a pink body with blue hands and feet, a heart rate of 85/min, a grimace 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

A 70 kg patient has passed 20 mL of urine per hour for the last three hours. How should this be interpreted?

  1. ANormal, because the target is 0.1 mL/kg/h
  2. BHigh, suggesting fluid overload that needs a diuretic
  3. CNormal, because any measurable urine output is reassuring
  4. DBelow 0.5 mL/kg/h, suggesting poor kidney perfusion
8.Med-surg: cardiovascular & respiratoryHard

A patient's chest drain tubing disconnects from the drainage unit. What should the nurse do first?

  1. ARemove the drain from the chest and cover the site
  2. BReconnect it, or put the tube end in sterile water, then assess
  3. CLeave it open to air until the doctor arrives to review it
  4. DClamp the tube for several hours and recheck the patient later

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: t = 12 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

(1000 − 200)·0.16 = 128 L

Duration

128/10 = 12.8 min → t = 12 min

Answer

t = 12 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

(1100 − 200)·0.16 = 144 L

Highest flow

144/60 = 2.4 L/min → Q = 2 L/min

Answer

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

Answer: HCO₃⁻ = 27.9 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

|79 − 40| = 39 mmHg → 3.9 × 10 mmHg

Expected HCO₃⁻

HCO₃⁻ = 24 + 1·3.9 = 27.9 mmol/L

Answer

HCO₃⁻ = 27.9 mmol/L
4.Arterial blood gas interpretation

Answer: PaCO₂ = 47.6 mmHg

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

0.7·38 + 21 = 47.6 mmHg

Answer

PaCO₂ = 47.6 mmHg

The rise has a limit: PaCO₂ rarely goes above about 55 mmHg from compensation alone.

5.Clinical assessment scores

Answer: MFS = 65

Morse fall scale: six items. History of falling: no 0, yes 25. Secondary diagnosis: no 0, yes 15. Ambulatory aid: none, bed rest or nurse assistance 0; crutches, cane or walker 15; holding on to furniture 30. IV therapy or saline lock: no 0, yes 20. Gait: normal, bed rest or wheelchair 0; weak 10; impaired 20. Mental status: knows own limits 0; overestimates or forgets limits 15. The total runs from 0 to 125. Risk cut-offs differ between hospitals; a common set is 0–24 low, 25–44 moderate and 45 or more high.

Score each item

history of falling in the last 3 months: no → 0
secondary diagnosis: no → 0
ambulatory aid: holds on to furniture → 30
IV therapy or saline lock: yes → 20
gait: normal, bed rest or wheelchair → 0
mental status: overestimates or forgets limits → 15

Add

Morse total = 0 + 0 + 30 + 20 + 0 + 15 = 65

Answer

MFS = 65
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: 85/min → 1
Grimace: a grimace when stimulated → 1
Activity: some flexion of the arms and legs → 1
Respiration: slow, irregular breathing with a weak cry → 1

Add

APGAR = 1 + 1 + 1 + 1 + 1 = 5

Interpretation

5 → moderately abnormal

Answer

moderately abnormal

Below 7 at 5 minutes, the score is usually repeated every 5 minutes up to 20 minutes.

7.Med-surg: cardiovascular & respiratory

Answer: D · Below 0.5 mL/kg/h, suggesting poor kidney perfusion

Why this is the answer

A urine output below about 0.5 mL/kg/h (35 mL/h for 70 kg) for several hours is oliguria and may indicate hypovolaemia, shock or acute kidney injury. It should be reported along with the other observations, and the catheter checked for blockage.

Answer

D · Below 0.5 mL/kg/h, suggesting poor kidney perfusion
8.Med-surg: cardiovascular & respiratory

Answer: B · Reconnect it, or put the tube end in sterile water, then assess

Why this is the answer

A disconnected tube lets atmospheric air enter the pleural space. Reconnecting quickly, or submerging the tube end 2–3 cm in sterile water as a temporary seal, restores the one-way valve. Then assess for respiratory distress and inform the team. Prolonged clamping risks tension pneumothorax.

Answer

B · Reconnect it, or put the tube end in sterile water, then assess

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