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
1300psiHf = 3.14 L/psi12 L/minresidual 200 psit = ? min

Practice exercise (made-up values, not clinical guidance). A size H oxygen cylinder (factor 3.14 L/psi) reads 1300 psi and runs at 12 L/min. Keeping a safe residual of 200 psi, how many minutes t will it last? Round down to a whole minute.

1300 psif = 3.14 L/psi12 L/min200 psi
t = min
2.Oxygen therapy & respiratory calculationsHard
PaO₂ 7.3 kPa · FiO₂ 0.7 · 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 7.3 kPa on 70% oxygen with a PEEP of 12 cmH₂O. Grade the ARDS severity with the Berlin definition. Click your answer.

PaO₂ 7.3 kPaFiO₂ 70%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
pH7.357.457.10PaCO₂mmHg354543HCO₃⁻mmol/L222613uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.10, PaCO₂ 43 mmHg (5.7 kPa) and HCO₃⁻ 13 mmol/L. The primary disorder is metabolic acidosis. How far is it compensated? Click your answer.

pH 7.10PaCO₂ 43 mmHg (5.7 kPa)HCO₃⁻ 13 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
4.Arterial blood gas interpretationHard

Practice values: Na⁺ 132, Cl⁻ 94 and HCO₃⁻ 18 mmol/L. Calculate the delta ratio (AG − 12)/(24 − HCO₃⁻), using AG = Na⁺ − (Cl⁻ + HCO₃⁻). Give two decimals.

Na⁺ 132 mmol/LCl⁻ 94 mmol/LHCO₃⁻ 18 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: very limited; moisture: occasionally moist; activity: walks occasionally; mobility: no limitation; nutrition: probably inadequate; friction and shear: potential problem. Find the Braden total B.

6–23
B =
6.Clinical assessment scoresHard
underweighthealthy weightoverweightobesity class Iobesity class IIobesity class III

Practice exercise (made-up values, not clinical guidance). An adult weighs 71 kg and is 183 cm tall. Calculate the BMI and click the WHO weight category.

71 kg183 cm
  1. 1underweight
  2. 2healthy weight
  3. 3overweight
  4. 4obesity class I
  5. 5obesity class II
  6. 6obesity class III
7.Med-surg: cardiovascular & respiratoryMedium

Rheumatic heart disease most often follows which infection?

  1. AA group A streptococcal throat infection
  2. BStaphylococcal infection of the skin
  3. CA viral infection of the upper airway
  4. DA fungal infection of the lungs
8.Med-surg: cardiovascular & respiratoryHard

As the defibrillator charges, a nurse sees a colleague still holding the patient's bed rail. What should the nurse do?

  1. ATurn off the defibrillator and start a new cycle of CPR
  2. BDeliver the shock now, as the bed rail is not part of the patient
  3. CAsk the colleague to hold the patient's hand instead
  4. DCall clearly for everyone to stand clear and check before the shock

3Solutions

1.Oxygen therapy & respiratory calculations

Answer: t = 287 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

(1300 − 200)·3.14 = 3454 L

Duration

3454/12 = 287.8 min → t = 287 min

Answer

t = 287 min

That is about 4 h 47 min.

2.Oxygen therapy & respiratory calculations

Answer: severe

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

7.3·7.5 = 54.75 mmHg

P/F ratio

P/F = 54.75/0.7 = 78.21 mmHg

Berlin severity

severe

Answer

severe
3.Arterial blood gas interpretation

Answer: uncompensated

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 7.10: acidaemia (below 7.35)
PaCO₂ 43 mmHg: normal (35–45)
HCO₃⁻ 13 mmol/L: low (22–26)

Compensation

Clinically, also check the expected compensation: Winter’s formula expects PaCO₂ 25.5–29.5 mmHg, so the measured 43 mmHg points to an additional respiratory acidosis (a mixed disorder). The answer above is the ROME exam classification.

uncompensated

Answer

uncompensated
4.Arterial blood gas interpretation

Answer: delta ratio = 1.333

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 = 132 − (94 + 18) = 20

Delta ratio

(20 − 12)/(24 − 18) = 8/6 = 1.333

Answer

delta ratio = 1.333

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

5.Clinical assessment scores

Answer: B = 16

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: very limited → 2
moisture: occasionally moist → 3
activity: walks occasionally → 3
mobility: no limitation → 4
nutrition: probably inadequate → 2
friction and shear: potential problem → 2

Add

Braden total = 2 + 3 + 3 + 4 + 2 + 2 = 16

Answer

B = 16
6.Clinical assessment scores

Answer: healthy weight

Body mass index: BMI = weight (kg)/height (m)², with the height converted to metres first. With pounds and inches, BMI = 703 × weight (lb)/height (in)². WHO adult categories: below 18.5 underweight, 18.5–24.9 healthy weight, 25.0–29.9 overweight, 30.0–34.9 obesity class I, 35.0–39.9 obesity class II and 40 or more obesity class III.

BMI

BMI = 71/1.83² = 21.2

Category

healthy weight

Answer

healthy weight
7.Med-surg: cardiovascular & respiratory

Answer: A · A group A streptococcal throat infection

Why this is the answer

Rheumatic fever is an autoimmune reaction weeks after group A streptococcal pharyngitis. It can permanently damage heart valves, most often the mitral valve. Prompt antibiotic treatment of strep throat prevents it.

Answer

A · A group A streptococcal throat infection
8.Med-surg: cardiovascular & respiratory

Answer: D · Call clearly for everyone to stand clear and check before the shock

Why this is the answer

Before every shock, the operator states a clear warning, checks that nobody is touching the patient or bed and that oxygen is moved away from the chest. Compressions continue during charging in many protocols, then everyone stands clear for the shock. Touching the bed can conduct current to staff.

Answer

D · Call clearly for everyone to stand clear and check before the shock

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