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
1050psiEf = 0.28 L/psi6 L/minresidual 200 psit = ? min

Practice exercise (made-up values, not clinical guidance). A size E oxygen cylinder (factor 0.28 L/psi) reads 1050 psi and runs at 6 L/min. Keeping a safe residual of 200 psi, how many minutes t will it last? Round down to a whole minute.

1050 psif = 0.28 L/psi6 L/min200 psi
t = min
2.Oxygen therapy & respiratory calculationsHard
PaO₂ 18 kPa · FiO₂ 1 · PEEP 5 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 18 kPa on 100% oxygen with a PEEP of 5 cmH₂O. Grade the ARDS severity with the Berlin definition. Click your answer.

PaO₂ 18 kPaFiO₂ 100%PEEP 5 cmH₂O
  1. 1above 300: no ARDS grade
  2. 2mild
  3. 3moderate
  4. 4severe
  5. 5not gradable: PEEP below 5
3.Arterial blood gas interpretationMedium

A practice gas shows PaCO₂ 20 mmHg (2.7 kPa). Use the rule that in chronic respiratory alkalosis HCO₃⁻ falls by 5 mmol/L for every 10 mmHg that PaCO₂ is below 40, starting from HCO₃⁻ 24 mmol/L, to find the expected HCO₃⁻.

PaCO₂ 20 mmHg (2.7 kPa)baseline: 40 mmHg, 24 mmol/L
HCO₃⁻ = mmol/L
4.Arterial blood gas interpretationHard

A practice gas shows a metabolic alkalosis with HCO₃⁻ 35 mmol/L. Use expected PaCO₂ = 0.7·HCO₃⁻ + 21 to find the expected PaCO₂.

HCO₃⁻ 35 mmol/L
PaCO₂ = mmHg
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: no impairment; moisture: occasionally moist; activity: walks frequently; mobility: slightly limited; nutrition: very poor; friction and shear: potential problem. Find the Braden total B.

6–23
B =
6.Clinical assessment scoresHard
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≥39.1lowlow–mediummediumhigh

Practice exercise (made-up values, not clinical guidance). Use the NEWS2 chart (SpO₂ scale 1) for these observations: respiration rate 14/min, SpO₂ 97% on supplemental oxygen, blood pressure 118/70 mmHg, pulse 132/min, alert, temperature 37.0 °C. Which clinical risk group does the patient fall into? Click it.

RR 14SpO₂ 97%O₂SBP 118HR 132AT 37.0 °C
  1. 1low
  2. 2low–medium
  3. 3medium
  4. 4high
7.Med-surg: cardiovascular & respiratoryMedium

A patient on home oxygen has dry, sore lips. Which product is safest to use?

  1. AAn oil-based balm
  2. BA water-based lubricant
  3. CAn alcohol-based gel
  4. DPetroleum jelly
8.Med-surg: cardiovascular & respiratoryHard

A patient with severe chronic kidney disease needs therapeutic anticoagulation for a DVT. Why might unfractionated heparin be chosen instead of a low-molecular-weight heparin?

  1. ALMWH cannot be given to anyone over 60
  2. BUnfractionated heparin is taken by mouth
  3. CLMWH is cleared by the kidneys and can accumulate
  4. DUnfractionated heparin has no bleeding risk at all

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: t = 39 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

(1050 − 200)·0.28 = 238 L

Duration

238/6 = 39.67 min → t = 39 min

Answer

t = 39 min
2.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.

PEEP

PEEP 5 ≥ 5 cmH₂O

PaO₂ in mmHg

18·7.5 = 135 mmHg

P/F ratio

P/F = 135/1 = 135 mmHg

Berlin severity

moderate

Answer

moderate
3.Arterial blood gas interpretation

Answer: HCO₃⁻ = 14 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

|20 − 40| = 20 mmHg → 2 × 10 mmHg

Expected HCO₃⁻

HCO₃⁻ = 24 − 5·2 = 14 mmol/L

Answer

HCO₃⁻ = 14 mmol/L
4.Arterial blood gas interpretation

Answer: PaCO₂ = 45.5 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

0.7·35 + 21 = 45.5 mmHg

Answer

PaCO₂ = 45.5 mmHg

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

5.Clinical assessment scores

Answer: B = 17

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: no impairment → 4
moisture: occasionally moist → 3
activity: walks frequently → 4
mobility: slightly limited → 3
nutrition: very poor → 1
friction and shear: potential problem → 2

Add

Braden total = 4 + 3 + 4 + 3 + 1 + 2 = 17

Answer

B = 17
6.Clinical assessment scores

Answer: medium

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 14/min → 0
SpO₂ 97% → 0
on oxygen → 2
SBP 118 mmHg → 0
HR 132/min → 3
alert (A) → 0
T 37.0 °C → 0

Total and red scores

NEWS2 = 0 + 0 + 2 + 0 + 3 + 0 + 0 = 5
At least one parameter scores 3.

Risk group

medium

Answer

medium

A total of 5 or more calls for an urgent clinical response.

7.Med-surg: cardiovascular & respiratory

Answer: B · A water-based lubricant

Why this is the answer

Oil-based products such as petroleum jelly can ignite or burn intensely in high oxygen concentrations and have caused facial burns. Water-based products are recommended. Oxygen cylinders are kept upright and secured, away from heat and flames.

Answer

B · A water-based lubricant
8.Med-surg: cardiovascular & respiratory

Answer: C · LMWH is cleared by the kidneys and can accumulate

Why this is the answer

Low-molecular-weight heparins are mainly renally excreted, so they accumulate in severe renal impairment and increase bleeding risk. Unfractionated heparin is cleared mainly by other routes, has a short half-life and can be monitored with aPTT and reversed with protamine.

Answer

C · LMWH is cleared by the kidneys and can accumulate

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