BP101T • Unit 3Topic 3 of 4⏱ 5 Min Read

3. Area Under the Curve (AUC) by Linear Trapezoidal Rule

💡 Core Concept & Clinical Context:

Area Under the Curve ($\text{AUC}_{0\rightarrow t}$) represents the total cumulative drug exposure over time and is the primary metric for calculating absolute and relative bioavailability. Because plasma samples are drawn at discrete time intervals ($t_0, t_1, t_2, \dots, t_n$), the area is calculated geometrically by dividing the curve into vertical trapezoids and summing their individual areas.

Pharmaceutical Code & Calculation Examples:

1Linear Trapezoidal AUC Calculation Implementation

Formula for segment area: $\text{Area}_i = \frac{C_i + C_{i+1}}{2} \times (t_{i+1} - t_i)$.

example_1.py

def calculate_trapezoidal_auc(time_pts, cp_pts):
    """Calculates AUC(0->t) using the linear trapezoidal rule"""
    total_auc = 0.0
    for i in range(len(time_pts) - 1):
        dt = time_pts[i+1] - time_pts[i]
        avg_conc = (cp_pts[i] + cp_pts[i+1]) / 2.0
        segment_area = avg_conc * dt
        total_auc += segment_area
    return total_auc

time_data = [0.0, 1.0, 2.0, 4.0, 6.0, 8.0]
cp_data = [0.0, 10.0, 8.0, 4.0, 2.0, 0.5]

auc_value = calculate_trapezoidal_auc(time_data, cp_data)
print(f"Total AUC(0-8h): {auc_value:.2f} ug*hr/mL")

📋Key Takeaways & Exam Highlights

Bioavailability ($F$): Fraction of administered dose that reaches systemic circulation intact.
Relative Bioavailability: $F_{rel} = \frac{\text{AUC}_{test}}{\text{AUC}_{standard}} \times \frac{\text{Dose}_{standard}}{\text{Dose}_{test}}$.
Bioequivalence Criterion: 90% confidence intervals of geometric mean ratio of Test/Reference for AUC and $C_{max}$ must fall within 80.00% to 125.00%.

🇮🇳 हिन्दी व्याख्या (3. Area Under the Curve (AUC) by Linear Trapezoidal Rule)

AUC यह नापता है कि कुल कितनी दवा शरीर में अवशोषित हुई। इसे ट्रेपेज़ॉइडल (Trapezoidal) फॉर्मूले से छोटे-छोटे हिस्सों का क्षेत्रफल जोड़कर निकाला जाता है।