Lab Values for Nurses: 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

Lab values & electrolytes

Method

  1. Compare the value with the laboratory’s own reference range, then with the patient’s baseline and trend.
  2. Check the sample: hemolysis, a delay, or blood drawn near an IV can give false results.
  3. Link the value to its typical signs and to the drugs and conditions that cause it.
  4. Look for interactions: low potassium or magnesium increases digoxin toxicity; dehydration raises lithium.
  5. Act on the patient: assess, hold a drug if the level is unsafe, read back critical values and inform the prescriber.

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 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
Renal adjustment
dose × CrCl/normal; Dettli Q = 1 − fe·(1 − CrCl/normal)

Method

  1. Convert the half-life to a rate constant: k = 0.693/t½.
  2. Turn per-kg values into totals: Vd (L) = L/kg × weight, CL (L/h) = L/kg/h × weight.
  3. Pick the relation: C = C₀·e−kt, LD = Vd·C/(S·F), maintenance rate = CL·Css/(S·F), τ = ln(Cpeak/Ctrough)/k.
  4. For kidney function, estimate CrCl with Cockcroft–Gault first, then scale the dose or the interval.
  5. Check the result: levels fall by half every half-life, and steady state takes about five half-lives.

2Practice problems

1.Lab values & electrolytesMedium

A patient with ventricular arrhythmia shows a twisting pattern (torsades de pointes) on the monitor. Which electrolyte is commonly given IV as treatment?

  1. AMagnesium sulfate
  2. BPotassium phosphate
  3. CSodium bicarbonate
  4. DCalcium carbonate
2.Lab values & electrolytesHard

A patient on IV gentamicin has a trough level above the target, and the creatinine has risen since yesterday. The next dose is due. What is the best action?

  1. AGive the dose now and recheck the levels next week
  2. BHold the dose and report the results to the prescriber
  3. CGive the dose with extra oral fluids to protect the kidneys
  4. DGive half of the dose and document the reason for it
3.Arterial blood gas interpretationMedium
pH7.357.457.38PaCO₂mmHg354533HCO₃⁻mmol/L222619uncompensatedpartially compensatedfully compensated

A practice arterial blood gas shows pH 7.38, PaCO₂ 33 mmHg (4.4 kPa) and HCO₃⁻ 19 mmol/L. The primary disorder is metabolic acidosis. How far is it compensated? Click your answer.

pH 7.38PaCO₂ 33 mmHg (4.4 kPa)HCO₃⁻ 19 mmol/L
  1. 1uncompensated
  2. 2partially compensated
  3. 3fully compensated
4.Arterial blood gas interpretationHard
pH7.357.457.22PaCO₂mmHg354520HCO₃⁻mmol/L22268appropriate compensationadded respiratory acidosisadded respiratory alkalosis

A practice gas shows a metabolic acidosis: pH 7.22, PaCO₂ 20 mmHg (2.7 kPa), HCO₃⁻ 8 mmol/L. Compare the measured PaCO₂ with Winter’s formula. Click your interpretation.

pH 7.22PaCO₂ 20 mmHg (2.7 kPa)HCO₃⁻ 8 mmol/L
  1. 1appropriate compensation
  2. 2added respiratory acidosis
  3. 3added respiratory alkalosis
5.Clinical pharmacokineticsMedium
VCss​ = 10 mg/LR = ? mg/hCL = 0.045 L/kg/h93 kg

Practice exercise (made-up values, not clinical guidance). A 93 kg patient receives a theophylline infusion. The clearance is 0.045 L/kg/h. What infusion rate R in mg/h gives a steady-state level of 10 mg/L?

93 kgCL = 0.045 L/kg/hCss = 10 mg/L
R = mg/h
6.Clinical pharmacokineticsHard
VCss,avg​ = ?1500 mg · q12hCL = 3.5 L/hS = 1 · F = 1

Practice exercise (made-up values, not clinical guidance). A patient receives vancomycin IV every 12 h; the vancomycin clearance is 3.5 L/h. Each dose is 1500 mg of vancomycin. Find the average steady-state level Css,avg.

CL = 3.5 L/hτ = 12 hS = 1F = 1D = 1500 mg
Css,avg = mg/L
7.Clinical nursingMedium

How does CPAP help a patient with obstructive sleep apnoea?

  1. AIt delivers bronchodilator drugs deep into the lungs overnight
  2. BIt keeps the upper airway open during sleep with continuous air pressure
  3. CIt strengthens the breathing muscles during the day
  4. DIt removes excess carbon dioxide from the lungs by gentle suction
8.Clinical nursingHard

A patient with cirrhosis and a large tense abdomen undergoes paracentesis. Why may albumin be given?

  1. ATo increase urine potassium
  2. BTo reduce the risk of circulatory dysfunction after large-volume fluid removal
  3. CTo treat infection in the fluid
  4. DTo stop the liver making more bile

3Solutions

1.Lab values & electrolytes

Answer: A · Magnesium sulfate

Why this is the answer

IV magnesium sulfate is the standard drug treatment for torsades de pointes, even when serum magnesium is normal. Low magnesium and low potassium both prolong the QT interval and raise the risk.

Answer

A · Magnesium sulfate
2.Lab values & electrolytes

Answer: B · Hold the dose and report the results to the prescriber

Why this is the answer

A high aminoglycoside trough with rising creatinine means the drug is accumulating, which increases the risk of kidney damage and hearing loss. The nurse holds the dose, reports to the prescriber and asks about hearing changes and tinnitus. Only the prescriber or pharmacist changes the regimen.

Answer

B · Hold the dose and report the results to the prescriber
3.Arterial blood gas interpretation

Answer: fully 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 7.38: within 7.35–7.45
PaCO₂ 33 mmHg: low (35–45)
HCO₃⁻ 19 mmol/L: low (22–26)

Compensation

Clinically, also check the expected compensation: Winter’s formula expects PaCO₂ 34.5–38.5 mmHg, so the measured 33 mmHg points to an additional respiratory alkalosis (a mixed disorder). The answer above is the ROME exam classification.

fully compensated

Answer

fully 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

1.5·8 + 8 = 20 → 18–22 mmHg

Compare

measured: 20 mmHg → appropriate compensation

Answer

appropriate compensation
5.Clinical pharmacokinetics

Answer: R = 41.85 mg/h

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.

Clearance

CL = 0.045·93 = 4.185 L/h

Infusion rate

R = 4.185·10 = 41.85 mg/h

Answer

R = 41.85 mg/h
6.Clinical pharmacokinetics

Answer: Css,avg = 35.71 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.

Average steady-state level

Css,avg = S·F·D/(CL·τ) = 1·1·1500/(3.5·12) = 35.71 mg/L

Answer

Css,avg = 35.71 mg/L
7.Clinical nursing

Answer: B · It keeps the upper airway open during sleep with continuous air pressure

Why this is the answer

Continuous positive airway pressure acts as a splint for the upper airway, preventing collapse and apnoeas. Patients should bring their CPAP machine into hospital.

Answer

B · It keeps the upper airway open during sleep with continuous air pressure
8.Clinical nursing

Answer: B · To reduce the risk of circulatory dysfunction after large-volume fluid removal

Why this is the answer

Large-volume paracentesis can cause hypotension and renal impairment. Albumin infusion helps maintain the circulating volume.

Answer

B · To reduce the risk of circulatory dysfunction after large-volume fluid removal

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