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
Hb145 g/LSaO₂88%PaO₂55 mmHgCaO₂?

Practice exercise (made-up values, not clinical guidance). A patient has Hb 145 g/L, SaO₂ 88% and PaO₂ 55 mmHg (7.3 kPa). Find the arterial oxygen content CaO₂ = 1.34 × Hb (g/dL) × SaO₂ + 0.003 × PaO₂ (mmHg) in mL O₂/dL.

Hb 145 g/LSaO₂ 88%PaO₂ 55 mmHg (7.3 kPa)
CaO₂ = mL/dL
2.Oxygen therapy & respiratory calculationsHard
Hb142 g/LSaO₂98%PaO₂104 mmHgCaO₂mL/dL× CO3.6 L/minDO₂?

Practice exercise (made-up values, not clinical guidance). A patient has Hb 142 g/L, SaO₂ 98%, PaO₂ 104 mmHg (13.9 kPa) and a cardiac output of 3.6 L/min. With CaO₂ = 1.34 × Hb (g/dL) × SaO₂ + 0.003 × PaO₂ (mmHg), find the oxygen delivery DO₂ = CaO₂ × CO × 10 in mL/min.

Hb 142 g/LSaO₂ 98%PaO₂ 104 mmHg (13.9 kPa)CO 3.6 L/min
DO₂ = mL/min
3.Arterial blood gas interpretationMedium

A practice gas shows a metabolic acidosis with HCO₃⁻ 14 mmol/L. Use Winter’s formula to find the expected PaCO₂ (the centre of the range) in mmHg.

HCO₃⁻ 14 mmol/L
PaCO₂ = mmHg
4.Arterial blood gas interpretationHard
pH7.357.457.21PaCO₂mmHg354541HCO₃⁻mmol/L222616appropriate compensationadded respiratory acidosisadded respiratory alkalosis

A practice gas shows a metabolic acidosis: pH 7.21, PaCO₂ 41 mmHg (5.5 kPa), HCO₃⁻ 16 mmol/L. Compare the measured PaCO₂ with Winter’s formula. Click your interpretation.

pH 7.21PaCO₂ 41 mmHg (5.5 kPa)HCO₃⁻ 16 mmol/L
  1. 1appropriate compensation
  2. 2added respiratory acidosis
  3. 3added respiratory alkalosis
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: yes; 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 1 minute after birth, a practice newborn has a pink body with blue hands and feet, a heart rate of 65/min, a grimace when stimulated, limp limbs with no muscle tone 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

After thrombolysis for a myocardial infarction, which complication is the nurse most concerned to detect?

  1. AConstipation from bed rest
  2. BA skin rash appearing at the sites of the ECG electrodes
  3. CA high blood glucose caused by the thrombolytic drug itself
  4. DBleeding, including a sudden change in neurological status
8.Med-surg: cardiovascular & respiratoryHard

A patient with COPD on a 28% Venturi mask (SpO₂ 90%) wants to eat a meal. What is the most appropriate plan?

  1. ARemove all oxygen during the meal and replace it afterwards
  2. BKeep the Venturi mask on and give only liquids through a straw
  3. CChange to a non-rebreather mask at 15 L/min during the meal
  4. DSwitch to nasal cannula at low flow, keeping SpO₂ at 88–92%

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: CaO₂ = 17.26 mL/dL

Oxygen content and delivery: CaO₂ = 1.34 × Hb (g/dL) × SaO₂ + 0.003 × PaO₂ (mmHg), in mL O₂ per dL of blood, with SaO₂ as a fraction. Almost all oxygen is bound to haemoglobin; the dissolved part is small. Delivery DO₂ = CaO₂ × cardiac output (L/min) × 10 (mL/min), because 1 L = 10 dL; a normal resting adult value is about 1000 mL/min.

Hb in g/dL

145 g/L = 14.5 g/dL

Bound oxygen

1.34·14.5·0.88 = 17.1 mL/dL

Dissolved oxygen

0.003·55 = 0.165 mL/dL

Oxygen content

CaO₂ = 17.1 + 0.165 = 17.26 mL/dL

Answer

CaO₂ = 17.26 mL/dL
2.Oxygen therapy & respiratory calculations

Answer: DO₂ = 682.5 mL/min

Oxygen content and delivery: CaO₂ = 1.34 × Hb (g/dL) × SaO₂ + 0.003 × PaO₂ (mmHg), in mL O₂ per dL of blood, with SaO₂ as a fraction. Almost all oxygen is bound to haemoglobin; the dissolved part is small. Delivery DO₂ = CaO₂ × cardiac output (L/min) × 10 (mL/min), because 1 L = 10 dL; a normal resting adult value is about 1000 mL/min.

Oxygen content

142 g/L = 14.2 g/dL
CaO₂ = 1.34·14.2·0.98 + 0.003·104 = 18.96 mL/dL

Oxygen delivery

DO₂ = 18.96·3.6·10 = 682.5 mL/min

Answer

DO₂ = 682.5 mL/min

A normal resting adult value is about 1000 mL/min.

3.Arterial blood gas interpretation

Answer: PaCO₂ = 29 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.

Winter’s formula

PaCO₂ = 1.5·14 + 8 = 29 mmHg
range: 27–31 mmHg

Answer

PaCO₂ = 29 mmHg
4.Arterial blood gas interpretation

Answer: added respiratory acidosis

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

1.5·16 + 8 = 32 → 30–34 mmHg

Compare

measured: 41 mmHg → added respiratory acidosis

Answer

added respiratory acidosis
5.Clinical assessment scores

Answer: MFS = 80

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: yes → 15
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 + 15 + 30 + 20 + 0 + 15 = 80

Answer

MFS = 80
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: 65/min → 1
Grimace: a grimace when stimulated → 1
Activity: limp limbs with no muscle tone → 0
Respiration: slow, irregular breathing with a weak cry → 1

Add

APGAR = 1 + 1 + 1 + 0 + 1 = 4

Interpretation

4 → moderately abnormal

Answer

moderately abnormal
7.Med-surg: cardiovascular & respiratory

Answer: D · Bleeding, including a sudden change in neurological status

Why this is the answer

The main risk of thrombolysis is bleeding, from puncture sites, gums or the gut, and most seriously intracranial haemorrhage. The nurse monitors puncture sites, vital signs and neurological status and minimises invasive procedures. Reperfusion arrhythmias are also common.

Answer

D · Bleeding, including a sudden change in neurological status
8.Med-surg: cardiovascular & respiratory

Answer: D · Switch to nasal cannula at low flow, keeping SpO₂ at 88–92%

Why this is the answer

Oxygen is prescribed to a target range and should not be stopped for meals in a patient who needs it. Nasal cannulae allow eating and talking; the flow (for example 1–2 L/min) is titrated to keep the saturation in the target range. High-concentration oxygen risks hypercapnia.

Answer

D · Switch to nasal cannula at low flow, keeping SpO₂ at 88–92%

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