Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

103
Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
103
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

89
Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
89
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

131
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...
131
Multicompartment Models: Overview01:14

Multicompartment Models: Overview

260
Multicompartment models are mathematical constructs that depict how drugs are distributed and eliminated within the body. They segment the body into several compartments, symbolizing various physiological or anatomical areas connected through drug transfer processes such as absorption, metabolism, distribution, and elimination.
These models offer a more comprehensive representation of drug behavior in the body than one-compartment models. They accommodate the complexity of drug distribution,...
260
One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation01:24

One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

729
This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
729
Mechanistic Models: Overview of Compartment Models01:21

Mechanistic Models: Overview of Compartment Models

170
Mechanistic models, a category encompassing both physiological and compartmental modeling, differ from empirical models' approaches to incorporating known factors about the systems being modeled. Empirical models describe data with minimal assumptions, while mechanistic models aim to provide a robust description of available data by specifying assumptions and integrating known factors about the system. Compartmental analysis is a key example of a mechanistic model in pharmacokinetics and...
170

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

General oblique projections for model reduction via spectral submanifolds.

Chaos (Woodbury, N.Y.)·2026
Same author

Data-driven nonlinear model reduction to spectral submanifolds via oblique projection.

Chaos (Woodbury, N.Y.)·2025
Same author

Data-driven linearization of dynamical systems.

Nonlinear dynamics·2024
Same author

Nonautonomous spectral submanifolds for model reduction of nonlinear mechanical systems under parametric resonance.

Chaos (Woodbury, N.Y.)·2024
Same author

Nonlinear model reduction to temporally aperiodic spectral submanifolds.

Chaos (Woodbury, N.Y.)·2024
Same author

Data-driven modeling and forecasting of chaotic dynamics on inertial manifolds constructed as spectral submanifolds.

Chaos (Woodbury, N.Y.)·2024
Same journal

Kat5 deficiency in alveolar type II cells licenses STAT6-driven glycolytic reprogramming and pulmonary fibrosis.

Nature communications·2026
Same journal

Continuous nonthermal slab gap formed by progressive tearing beneath Northeast Asia.

Nature communications·2026
Same journal

Zeolitic isolated protonic acid sites-mediated NH<sub>3</sub> storage for robust NO<sub>x</sub> removal.

Nature communications·2026
Same journal

Coaxially nested component with asymmetric fiber resonant cavity and separation membrane for gaseous and dissolved gases detection.

Nature communications·2026
Same journal

Near-unity charge readout signal in a nonlinear resonator without matching the sensor dissipation.

Nature communications·2026
Same journal

Prokaryotic Schlafen proteins cleave tRNAs during type III CRISPR immunity.

Nature communications·2026
See all related articles

Related Experiment Video

Updated: Sep 17, 2025

Lumped-Parameter and Finite Element Modeling of Heart Failure with Preserved Ejection Fraction
09:20

Lumped-Parameter and Finite Element Modeling of Heart Failure with Preserved Ejection Fraction

Published on: February 13, 2021

6.6K

Globalizing manifold-based reduced models for equations and data.

Bálint Kaszás1, George Haller2

  • 1Institute for Mechanical Systems, ETH Zürich, Zurich, Switzerland. bkaszas@ethz.ch.

Nature Communications
|July 1, 2025
PubMed
Summary
This summary is machine-generated.

This study enhances nonlinear model reduction by using Padé approximants to extend invariant manifold analysis beyond local polynomial approximations. This method enables more accurate reduced modeling of complex global phenomena in dynamical systems.

More Related Videos

A Rapid Method for Modeling a Variable Cycle Engine
04:58

A Rapid Method for Modeling a Variable Cycle Engine

Published on: August 13, 2019

7.7K
Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

3.4K

Related Experiment Videos

Last Updated: Sep 17, 2025

Lumped-Parameter and Finite Element Modeling of Heart Failure with Preserved Ejection Fraction
09:20

Lumped-Parameter and Finite Element Modeling of Heart Failure with Preserved Ejection Fraction

Published on: February 13, 2021

6.6K
A Rapid Method for Modeling a Variable Cycle Engine
04:58

A Rapid Method for Modeling a Variable Cycle Engine

Published on: August 13, 2019

7.7K
Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

3.4K

Area of Science:

  • Applied Mathematics
  • Computational Mechanics
  • Dynamical Systems Theory

Background:

  • Model reduction is crucial for analyzing complex dynamical systems.
  • Current methods using invariant manifolds are limited by local polynomial approximations and convergence domains.
  • Rigorous nonlinear model reduction relies on identifying attracting invariant manifolds.

Purpose of the Study:

  • To overcome limitations of local polynomial approximations in invariant manifold identification.
  • To extend the applicability of manifold-based model reduction techniques.
  • To enable reduced modeling of global phenomena in complex systems.

Main Methods:

  • Extending local expansions for invariant manifolds using Padé approximants.
  • Re-expressing Taylor expansions as rational functions for broader utility.
  • Applying globalized manifold-based model reduction to equation- and data-driven examples.

Main Results:

  • Padé approximants significantly expand the utility of local expansions for invariant manifolds.
  • The enhanced method broadens the applicability of manifold-reduced models.
  • Successful application to solid and fluid mechanics examples, including large-scale oscillations and chaotic attractors.

Conclusions:

  • Padé approximant-based manifold extension offers a mathematically rigorous approach to nonlinear model reduction.
  • This method enhances the capability to model global phenomena accurately.
  • The approach is effective for both equation-driven and data-driven modeling in mechanics.