Multiple Dosing PK/PD

This interactive module demonstrates multiple dosing pharmacokinetics using patient-specific parameters.

Controls

Patient Generator

• Age: - years
• Sex: -
• Height: - cm
• Weight: - kg
• Creatinine: - mg/dL

Drug Name:

Formulation: Slow (Extended Release) Medium (Standard Oral) Fast (IV Bolus) Medium (Standard Oral)

PK Model: One-Compartment Two-Compartment Non-Compartmental Analysis (NCA)

Elimination Kinetics: Zero-Order First-Order Second-Order Third-Order Non-Linear (Michaelis-Menten)

PK Parameters

Bioavailability (F): 1.0

Fraction Unbound: 1.0

Volume of Distribution (L/kg): 0.7 L/kg

Peripheral Volume V2 (L/kg): 0.5 L/kg

Intercompartmental Clearance Q (L/h): 2.0 L/h

Fraction Renally Cleared: 1.0

Dosing

Loading Dose (mg): 0 mg

Dose (mg): 250 mg

Dosing Interval (hrs): 24 hrs

Treatment Duration (days): 10 days

Reference Lines

Toxicity (mg/L): 20 mg/L

Efficacy (mg/L): 5 mg/L

Data

Subject	Drug Name	PK Model	Kinetics	Age	Sex	Ht (cm)	Wt (kg)	BMI	IBW (kg)	Adj IBW (kg)	Creatinine (mg/dL)	CrCl (mL/min)	Loading Dose (mg)	Dose (mg)	Interval (hrs)	Duration (days)	Clearance (L/h)	Volume (L)	Fraction Unbound	Vss,u (L)	Bioavailability	Half-life (h)	Css,avg	AUC0-24h	Cmax	Tmax (h)	AUC/Efficacy	Cmax/Efficacy	Time>Efficacy (%)

Education

Blood Sampling Strategy

In this simulation, blood samples are collected every 1 hour to provide a detailed view of how pharmacokinetic data is collected in clinical practice. This sampling frequency allows us to:

• Capture both peak and trough concentrations
• Observe the full absorption and elimination phases
• Reduce the burden on patients compared to more frequent sampling
• Provide sufficient data points for pharmacokinetic analysis

Simplified Pharmacokinetic Model

This simulation supports three pharmacokinetic modeling approaches:

One-Compartment Model (Default)

The one-compartment model with first-order absorption focuses on the minimum essential parameters needed to generate a multiple dosing pharmacokinetic plot:

Essential PK Parameters: - Clearance (CL): Automatically calculated from patient’s creatinine clearance using Cockcroft-Gault equation - Volume of Distribution (Vd): Drug-specific volume per kg multiplied by patient weight - Bioavailability (F): Fraction of dose reaching systemic circulation

Patient-Specific Factors: - Creatinine Clearance: Calculated using Cockcroft-Gault: CrCl = [(140 - age) × weight × (0.85 if female)] / (72 × serum creatinine) - Weight-Based Dosing: Volume of distribution scales directly with patient weight

Dosing Parameters: - Dose: Amount of drug administered per dose - Dosing Interval: Time between doses - Treatment Duration: Total length of treatment

Two-Compartment Model

The two-compartment model adds peripheral distribution to capture drugs with slow tissue distribution:

Additional Parameters: - Peripheral Volume (V2): Volume of the peripheral compartment (L/kg) - Intercompartmental Clearance (Q): Rate of drug transfer between central and peripheral compartments (L/h)

This model is particularly useful for drugs that: - Show multi-phasic elimination (initial rapid decline followed by slower terminal phase) - Have extensive tissue distribution (e.g., lipophilic drugs) - Require loading doses to account for peripheral distribution

Two-Compartment Equations: - Central compartment: dA1/dt = -k10·A1 - k12·A1 + k21·A2 + ka·Absorption - Peripheral compartment: dA2/dt = k12·A1 - k21·A2 - Where: k10 = CL/V1, k12 = Q/V1, k21 = Q/V2

Non-Compartmental Analysis (NCA)

NCA calculates pharmacokinetic parameters directly from observed concentration-time data without assuming a specific compartmental model:

Key NCA Parameters: - AUC (Area Under the Curve): Total drug exposure calculated using the trapezoidal rule - Cmax: Maximum observed concentration - Tmax: Time to maximum concentration - Terminal Half-life: Calculated from the terminal elimination phase (regression of log-concentration vs time) - Clearance (CL/F): Dose/AUC for extravascular administration

Advantages of NCA: - No model assumptions required - Robust to sparse sampling - Regulatory gold standard for bioequivalence studies - Less prone to bias than compartmental methods

Elimination Kinetics

This simulation supports multiple elimination kinetic models:

First-Order Kinetics (Default): - Elimination rate proportional to drug concentration: dC/dt = -ke × C - Constant half-life independent of dose - Most common for therapeutic drugs - Linear pharmacokinetics (dose proportional)

Zero-Order Kinetics: - Constant elimination rate regardless of concentration: dC/dt = -k0 - Seen when elimination pathways are saturated - Examples: Alcohol, phenytoin at high doses - Non-linear pharmacokinetics

Second-Order Kinetics: - Elimination rate proportional to concentration squared: dC/dt = -k2 × C² - Faster elimination at higher concentrations - Rare in clinical practice

Third-Order Kinetics: - Elimination rate proportional to concentration cubed: dC/dt = -k3 × C³ - Even faster elimination at higher concentrations - Theoretical interest, rarely observed clinically

Non-Linear (Michaelis-Menten) Kinetics: - Saturable elimination: dC/dt = -Vmax × C / (Km + C) - Combination of first-order (low C) and zero-order (high C) - Examples: Phenytoin, salicylates, theophylline at high doses - Dose-dependent half-life

This approach incorporates key patient-specific factors (age, sex, weight, creatinine) while maintaining the core functionality needed to understand multiple dosing pharmacokinetics and the clinical application of the Cockcroft-Gault equation.

Quiz

Test your understanding by calculating the following parameters for the current patient:

1. Creatinine Clearance (mL/min):

2. Adjusted Body Weight (kg):

3. Volume of Distribution of Unbound Drug (L):

4. Time to Steady State - tss (hours):

5. Average Steady-State Concentration - Css,avg (mg/L):

Plot

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