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
Hb87 g/LSaO₂98%PaO₂97 mmHgCaO₂?

Practice exercise (made-up values, not clinical guidance). A patient has Hb 87 g/L, SaO₂ 98% and PaO₂ 97 mmHg (12.9 kPa). Find the arterial oxygen content CaO₂ = 1.34 × Hb (g/dL) × SaO₂ + 0.003 × PaO₂ (mmHg) in mL O₂/dL.

Hb 87 g/LSaO₂ 98%PaO₂ 97 mmHg (12.9 kPa)
CaO₂ = mL/dL
2.Oxygen therapy & respiratory calculationsHard
PaO₂ 13.6 kPa · FiO₂ 0.35 · PEEP 6 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 13.6 kPa on 35% oxygen with a PEEP of 6 cmH₂O. Grade the ARDS severity with the Berlin definition. Click your answer.

PaO₂ 13.6 kPaFiO₂ 35%PEEP 6 cmH₂O
  1. 1above 300: no ARDS grade
  2. 2mild
  3. 3moderate
  4. 4severe
  5. 5not gradable: PEEP below 5
3.Arterial blood gas interpretationMedium
pH7.357.457.31PaCO₂mmHg354568HCO₃⁻mmol/L222633uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.31, PaCO₂ 68 mmHg (9.1 kPa) and HCO₃⁻ 33 mmol/L. The primary disorder is respiratory acidosis. How far is it compensated? Click your answer.

pH 7.31PaCO₂ 68 mmHg (9.1 kPa)HCO₃⁻ 33 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
4.Arterial blood gas interpretationHard
pH7.357.457.31PaCO₂mmHg354533HCO₃⁻mmol/L222616appropriate compensationadded respiratory acidosisadded respiratory alkalosis

A practice gas shows a metabolic acidosis: pH 7.31, PaCO₂ 33 mmHg (4.4 kPa), HCO₃⁻ 16 mmol/L. Compare the measured PaCO₂ with Winter’s formula. Click your interpretation.

pH 7.31PaCO₂ 33 mmHg (4.4 kPa)HCO₃⁻ 16 mmol/L
  1. 1appropriate compensation
  2. 2added respiratory acidosis
  3. 3added respiratory alkalosis
5.Clinical assessment scoresMedium
3210123RR≤89–1112–2021–24≥25SpO₂≤9192–9394–95≥96air / O₂O₂airSBP≤9091–100101–110111–219≥220HR≤4041–5051–9091–110111–130≥131ACVPUAC, V, P, UT °C≤35.035.1–36.036.1–38.038.1–39.0≥39.1

Practice exercise (made-up values, not clinical guidance). Use the NEWS2 chart (SpO₂ scale 1) for these observations: respiration rate 30/min, SpO₂ 89% on supplemental oxygen, blood pressure 78/46 mmHg, pulse 140/min, alert, temperature 37.5 °C. What is the NEWS2 total score?

RR 30SpO₂ 89%O₂SBP 78HR 140AT 37.5 °C
NEWS2 =
6.Clinical assessment scoresHard
108?SBPDBPmmHgMAP = 70

Practice exercise (made-up values, not clinical guidance). The team aims for a mean arterial pressure of at least 70 mmHg. A patient’s systolic pressure is 108 mmHg. Using MAP = (SBP + 2·DBP)/3, what is the lowest diastolic pressure DBP that still gives a MAP of 70 mmHg?

MAP 70 mmHgSBP 108 mmHg
DBP = mmHg
7.Med-surg: cardiovascular & respiratoryMedium

Why should a long-acting beta-2 agonist (LABA) never be used alone in asthma?

  1. AWithout an inhaled steroid, it is linked with severe and fatal attacks
  2. BIt cannot be inhaled without a nebuliser
  3. CIt always causes immediate severe bronchospasm when used on its own
  4. DIt works only when it is taken together with a course of antibiotics
8.Med-surg: cardiovascular & respiratoryHard

Twelve hours after a coronary stent, a patient has sudden severe chest pain again with new ST elevation in the same leads. What is the most likely cause?

  1. APericarditis from the catheter
  2. BAcute stent thrombosis
  3. CIndigestion from the hospital meal
  4. DNormal pain from the procedure site

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: CaO₂ = 11.72 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

87 g/L = 8.7 g/dL

Bound oxygen

1.34·8.7·0.98 = 11.42 mL/dL

Dissolved oxygen

0.003·97 = 0.291 mL/dL

Oxygen content

CaO₂ = 11.42 + 0.291 = 11.72 mL/dL

Answer

CaO₂ = 11.72 mL/dL
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 6 ≥ 5 cmH₂O

PaO₂ in mmHg

13.6·7.5 = 102 mmHg

P/F ratio

P/F = 102/0.35 = 291.4 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 7.31: acidaemia (below 7.35)
PaCO₂ 68 mmHg: high (35–45)
HCO₃⁻ 33 mmol/L: high (22–26)

Compensation

partially compensated

Answer

partially compensated
4.Arterial blood gas interpretation

Answer: appropriate compensation

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: 33 mmHg → appropriate compensation

Answer

appropriate compensation
5.Clinical assessment scores

Answer: NEWS2 = 14

NEWS2 (National Early Warning Score 2, Royal College of Physicians 2017): score each of the seven parameters with the chart (respiration rate, SpO₂ on scale 1, air or supplemental oxygen, systolic blood pressure, pulse, consciousness on the ACVPU scale and temperature) and add the scores. Clinical risk: 0–4 low; a score of 3 in any single parameter low–medium; 5–6 medium; 7 or more high. A total of 5 or more needs an urgent response.

Score each parameter

RR 30/min → 3
SpO₂ 89% → 3
on oxygen → 2
SBP 78 mmHg → 3
HR 140/min → 3
alert (A) → 0
T 37.5 °C → 0

Add

NEWS2 = 3 + 3 + 2 + 3 + 3 + 0 + 0 = 14

Answer

NEWS2 = 14
6.Clinical assessment scores

Answer: DBP = 51 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 = (3·70 − 108)/2 = 102/2 = 51 mmHg

Answer

DBP = 51 mmHg
7.Med-surg: cardiovascular & respiratory

Answer: A · Without an inhaled steroid, it is linked with severe and fatal attacks

Why this is the answer

LABA monotherapy in asthma is linked with severe attacks and asthma deaths because it relieves symptoms while airway inflammation continues. In asthma, LABAs are always given with an inhaled corticosteroid, often in one combination inhaler.

Answer

A · Without an inhaled steroid, it is linked with severe and fatal attacks
8.Med-surg: cardiovascular & respiratory

Answer: B · Acute stent thrombosis

Why this is the answer

Acute stent thrombosis presents with recurrent ischaemic pain and ST elevation, and needs emergency return to the catheter laboratory. Missed antiplatelet doses are a major risk factor, which is why dual antiplatelet adherence is emphasised.

Answer

B · Acute stent thrombosis

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