# Clinical Pharmacy Calculations

Clinical calculations are critical to the delivery of safe, effective, and competent patient care and professional practice.  To perform clinical pharmacy calculation few pharmacokinetic parameters are need to understand. These are –

• Area under the curve (AUC)
• Maximum plasma concentration (Cmax)
• Time of maximum concentration (Tmax)
• Elimination half-life (t1/2)
• Elimination rate constant (Kel)
• Volume of distribution (Vd)

#### Common formula for clinical calculation

• Elimination half-life (t1/2) = 0.693/Kel
• Elimination rate constant (Kel) = 0.693/t1/2
• Volume of distribution (Vd) = Ab/C [Ab = amount of drug administered, C = concentration of drug in plasma]

#### Clinical Pharmacy Calculation Practices

1. Calculate AUC, Cmax & Tmax from below graph.

Here (from the above graph),

• Time in hours: 0, 0.5, 1, 2, 4, 6, 8, 10
• Plasma Conc. (mcg/ml): 0, 1, 3, 4, 2, 1, 0.5, 0.1

AUC calculation for above segment:

• Segment 1: (w × h)/2 = (0.5 × 1)/2 = 0.25 mcg.hr/ml (w = time difference)
• Segment 2: 1/2 × w × sum of parallel sides = 1/2 × 0.5 × (1 + 3) = 1 mcg.hr/ml
• Segment 3: 1/2 × w × sum of parallel sides = 1/2 × 1 × (3 + 4) = 3.5 mcg.hr/ml
• Segment 4: 1/2 × w × sum of parallel sides = 1/2 × 2 × (4 + 2) = 6 mcg.hr/ml
• Segment 5: 1/2 × w × sum of parallel sides = 1/2 × 2 × (2 + 1) = 3 mcg.hr/ml
• Segment 6: 1/2 × w × sum of parallel sides = 1/2 × 2 × (1 + 0.5) = 1.5 mcg.hr/ml
• Segment 7: (w × h)/2 = (2 × 0.5)/2 = 0.5 mcg.hr/ml
Therefore, AUC = 0.25 + 1 + 3.5 + 6 + 3 + 1.5 + 0.5 = 15.75 mcg.hr/ml

Cmax = 4 mcg/ml

Tmax = 2 hrs

2. A drug has elimination half-life of 4 hours. After the administration of a 250 mg dose, plasma concentration at zero time point was found 5.65 mcg/ml. What is the volume of distribution of drug?

Vd= D0/C0 = 250,000 mcg/5.65 mcg/ml = 44248 ml = 44.2 L