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Related Concept Videos

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
Model Approaches for Pharmacokinetic Data: Physiological Models01:15

Model Approaches for Pharmacokinetic Data: Physiological Models

Physiological models in pharmacokinetics are instrumental in understanding the distribution and elimination of drugs within the body. These models describe the drug concentration within target organs, influenced by factors such as drug uptake, tissue volume, and blood flow. Drug uptake is governed by the partition coefficient, which signifies the drug concentration ratio in tissue to that in the blood. The blood flow rate to a specific tissue is expressed as Qt, and the rate of change in tissue...
Model Approaches for Pharmacokinetic Data: Compartment Models01:14

Model Approaches for Pharmacokinetic Data: Compartment Models

Compartmental analysis is a widely adopted approach to characterizing drug pharmacokinetics. It uses compartment models that conceptualize the body as a collection of reversibly communicating compartments, each representing a group of tissues exhibiting similar drug distribution characteristics. The movement rate of the drug between these compartments is typically described by first-order kinetics.
Two primary types of compartment models are recognized: mammillary and catenary. The more...
Pharmacokinetic Models: Comparison and Selection Criterion01:26

Pharmacokinetic Models: Comparison and Selection Criterion

Physiological and compartmental models are valuable tools used in studying biological systems. These models rely on differential equations to maintain mass balance within the system, ensuring an accurate representation of the dynamic processes at play.
Physiological models take a detailed approach by considering specific molecular processes. They can predict drug distribution, metabolism, and elimination changes, providing a comprehensive understanding of how drugs interact with the body.
Analysis Methods of Pharmacokinetic Data: Model and Model-Independent Approaches01:14

Analysis Methods of Pharmacokinetic Data: Model and Model-Independent Approaches

Drug disposition in the body is a complex process and can be studied using two major approaches: the model and the model-independent approaches.
The model approach uses mathematical models to describe changes in drug concentration over time. Pharmacokinetic models help characterize drug behavior in patients, predict drug concentration in the body fluids, calculate optimum dosage regimens, and evaluate the risk of toxicity. However, ensuring that the model fits the experimental data accurately...
Pharmacokinetic Models: Overview01:20

Pharmacokinetic Models: Overview

Pharmacokinetic models utilize mathematical analysis to achieve a detailed quantitative understanding of a drug's life cycle within the body. They are instrumental in simulating a drug's pharmacokinetic parameters, predicting drug concentrations over time, optimizing dosage regimens, linking concentrations with pharmacologic activity, and estimating potential toxicity.
There are three primary types of models: empirical, compartment, and physiological. Empirical models, with minimal assumptions,...

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Related Experiment Video

Updated: May 11, 2026

Qualitative and Comparative Cortical Activity Data Analyses from a Functional Near-Infrared Spectroscopy Experiment Applying Block Design
06:18

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A HIERARCHICAL FUNCTIONAL DATA ANALYTIC APPROACH FOR ANALYZING PHYSIOLOGICALLY BASED PHARMACOKINETIC MODELS.

Siddhartha Mandal1, Pranab K Sen, Shyamal D Peddada

  • 1Norwegian Institute of Public Health, Oslo 0473, Norway, siddharta.mandal@fhi.no.

Environmetrics
|May 18, 2013
PubMed
Summary

This study introduces a new functional data analytic framework for parameter inference in ordinary differential equation (ODE) models, accounting for biological variability. The method improves understanding of chemical mechanisms in toxicology and PBPK modeling.

Keywords:
benzene kineticscubic splinesdifferential equationsfunctional basis

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Area of Science:

  • Mathematical biology
  • Toxicology
  • Pharmacokinetics

Background:

  • Ordinary differential equation (ODE) models are crucial for biological and physiological phenomena, including gene networks, viral dynamics, and toxicology.
  • Physiologically based pharmacokinetic (PBPK) models use ODEs to describe chemical absorption, distribution, metabolism, and excretion (ADME).
  • Parameter estimation in ODE models, often via non-linear least squares, faces challenges, particularly with experimental variability.

Purpose of the Study:

  • To develop a general framework for parameter inference in systems of differential equations using functional data analysis.
  • To incorporate variability between and within experimental units into the modeling framework.
  • To provide a robust methodology for analyzing complex biological and toxicological models.

Main Methods:

  • Application of functional data analytic methodology to ODE-based models.
  • Development of a framework for drawing inferences on model parameters.
  • Accounting for inter- and intra-experimental unit variability.

Main Results:

  • A novel functional data analytic framework for parameter inference in ODE models was developed.
  • The methodology effectively accounts for variability in experimental data.
  • Performance was validated through simulation studies and a benzene inhalation study.

Conclusions:

  • The proposed functional data analytic approach offers a robust method for parameter inference in ODE models.
  • This framework enhances the understanding of chemical mechanisms in toxicology and PBPK modeling.
  • An R-based software package is available to facilitate the application of this methodology.