Read the pH: below 7.35 is acidosis, above 7.45 alkalosis.
Find the value that explains it: PaCO₂ moving opposite to the pH is respiratory, HCO₃⁻ moving with the pH is metabolic.
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.
In a metabolic acidosis, compare PaCO₂ with Winter’s formula, 1.5·HCO₃⁻ + 8 ± 2, and calculate the anion gap Na⁺ − (Cl⁻ + HCO₃⁻).
Check a high anion gap with the delta ratio and, when albumin is low, with the corrected gap.
Clinical pharmacokinetics
Rate constant and half-life
k = ln 2/t½ = 0.693/t½
First-order decay
C = C₀·e−kt = C₀·(1/2)t/t½
Two levels
k = ln(C₁/C₂)/Δt
Volume and clearance
Vd = dose/C₀, CL = k·Vd
Loading dose
LD = Vd·C/(S·F)
Maintenance rate
R = CL·Css/(S·F)
Average steady state
Css,avg = S·F·D/(CL·τ)
Steady state
1 − (1/2)ⁿ after n half-lives; ≈ 97% after 5
Infusion
C = (R/CL)(1 − e−kt)
Interval and dose from peak and trough
τ = ln(Cpeak/Ctrough)/k, D = Vd·(Cpeak − Ctrough)
Cockcroft–Gault
CrCl = (140 − age) × kg/(72 × SCr mg/dL), × 0.85 for women
Pick the relation: C = C₀·e−kt, LD = Vd·C/(S·F), maintenance rate = CL·Css/(S·F), τ = ln(Cpeak/Ctrough)/k.
For kidney function, estimate CrCl with Cockcroft–Gault first, then scale the dose or the interval.
Check the result: levels fall by half every half-life, and steady state takes about five half-lives.
2Practice problems
1.Lab values & electrolytesMedium
When should a blood sample for a digoxin level be drawn to be interpreted correctly?
AOnly after a meal, because food is needed for absorption
BWithin 30 minutes after an oral dose to show the peak level
CAt least 6–8 hours after a dose, often just before the next one
DAt any time, because digoxin levels do not change during the day
2.Lab values & electrolytesHard
A patient's creatinine was 0.9 mg/dL (80 µmol/L) on admission and is 1.3 mg/dL (115 µmol/L) 36 hours later. Using the common KDIGO criteria, what does this show?
ANo kidney injury, because the creatinine is still within the normal range
BAcute kidney injury, because it rose by at least 0.3 mg/dL within 48 hours
CA laboratory error, because creatinine cannot change within 2 days
DChronic kidney disease, because creatinine has risen above baseline
3.Arterial blood gas interpretationMedium
A practice arterial blood gas shows pH 7.27, PaCO₂ 54 mmHg (7.2 kPa) and HCO₃⁻ 24 mmol/L. The primary disorder is respiratory acidosis. How far is it compensated? Click your answer.
pH 7.27PaCO₂ 54 mmHg (7.2 kPa)HCO₃⁻ 24 mmol/L
1uncompensated
2partially compensated
3fully compensated
4.Arterial blood gas interpretationHard
A practice gas shows a metabolic alkalosis with HCO₃⁻ 42 mmol/L. Use expected PaCO₂ = 0.7·HCO₃⁻ + 21 to find the expected PaCO₂.
HCO₃⁻ 42 mmol/L
PaCO₂ = mmHg
5.Clinical pharmacokineticsMedium
Practice exercise (made-up values, not clinical guidance). After an IV dose of vancomycin, the level is 35 mg/L at 1 h and 13 mg/L at 11 h. Assume first-order elimination. Find the elimination rate constant k.
C1 = 35 mg/L (1 h)C2 = 13 mg/L (11 h)
k = h⁻¹
6.Clinical pharmacokineticsHard
Practice exercise (made-up values, not clinical guidance). A vancomycin infusion runs at 60 mg/h with no loading dose. The patient's clearance is 3 L/h and the half-life is 6 h. What is the level C after 16 h?
R = 60 mg/hCL = 3 L/ht½ = 6 ht = 16 h
C = mg/L
7.Clinical nursingMedium
Which adverse effects should be monitored for in a patient receiving IV gentamicin?
AHair loss and weight gain
BHyperglycaemia and tremor
CKidney damage and hearing loss
DConstipation and urinary retention
8.Clinical nursingHard
An arterial blood gas shows a low PaO2 with a low or normal PaCO2. How is this classified?
ANormal blood gas
BMetabolic acidosis
CType 1 respiratory failure
DType 2 respiratory failure
3Solutions
1.Lab values & electrolytes
Answer: C · At least 6–8 hours after a dose, often just before the next one
Why this is the answer
Digoxin distributes slowly from blood to tissues, so a sample taken too soon after a dose is falsely high. Levels are drawn at least 6–8 hours after a dose, commonly as a trough before the next dose.
Answer
C · At least 6–8 hours after a dose, often just before the next one
2.Lab values & electrolytes
Answer: B · Acute kidney injury, because it rose by at least 0.3 mg/dL within 48 hours
Why this is the answer
KDIGO defines AKI as a creatinine rise of at least 0.3 mg/dL (26.5 µmol/L) within 48 hours, a rise to 1.5 times baseline within 7 days, or urine output below 0.5 mL/kg/h for 6 hours. A result inside the reference range can still be a significant rise.
Answer
B · Acute kidney injury, because it rose by at least 0.3 mg/dL within 48 hours
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 7.27: acidaemia (below 7.35)
PaCO₂ 54 mmHg: high (35–45)
HCO₃⁻ 24 mmol/L: normal (22–26)
Compensation
uncompensated
Answer
uncompensated
4.Arterial blood gas interpretation
Answer: PaCO₂ = 50.4 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
0.7·42 + 21 = 50.4 mmHg
Answer
PaCO₂ = 50.4 mmHg
The rise has a limit: PaCO₂ rarely goes above about 55 mmHg from compensation alone.
5.Clinical pharmacokinetics
Answer: k = 0.09904 h⁻¹
Clearance and volume: at steady state the dosing rate equals the elimination rate, so the maintenance rate = CL × Css. A loading dose is LD = Vd × C/(S × F), with S the salt factor (fraction of active drug in the salt) and F the bioavailability (1 for IV). From two levels, k = ln(C₁/C₂)/Δt; for an IV bolus Vd = dose/C₀ and CL = k × Vd. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Elimination rate constant
k = ln(35/13)/10 = 0.9904/10 = 0.09904 h⁻¹
Answer
k = 0.09904 h⁻¹
6.Clinical pharmacokinetics
Answer: C = 16.85 mg/L
Designing a regimen: with rapid IV doses the level falls from peak to trough during the interval, so τ = ln(Cpeak/Ctrough)/k and the dose that restores the peak is Vd × (Cpeak − Ctrough). The average steady-state level is Css,avg = S·F·dose/(CL·τ). An infusion rises as C = (R/CL)(1 − e−kt). For a drug cleared by the kidneys, the dose is scaled with the creatinine clearance. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.
Steady-state level
Css = 60/3 = 20 mg/L
Rate constant
k = 0.693/6 = 0.1155 h⁻¹
Level after the given time
C = 20·(1 − e−0.1155·16) = 16.85 mg/L
Answer
C = 16.85 mg/L
7.Clinical nursing
Answer: C · Kidney damage and hearing loss
Why this is the answer
Gentamicin is nephrotoxic and ototoxic. Blood levels and renal function are monitored, and any tinnitus, dizziness or hearing change is reported.
Answer
C · Kidney damage and hearing loss
8.Clinical nursing
Answer: C · Type 1 respiratory failure
Why this is the answer
Type 1 respiratory failure is hypoxaemia without hypercapnia, as in pneumonia or pulmonary embolism. Type 2 includes a raised PaCO2 from inadequate ventilation, as in COPD exacerbations.