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

387
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...
387
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

1.4K
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...
1.4K
Newton’s Method01:30

Newton’s Method

114
Newton’s Method is a powerful iterative technique for approximating the roots of real-valued, differentiable functions, particularly when analytical solutions are impractical. This approach is widely used in scientific computing, engineering, and finance, where equations may be too complex for traditional algebraic methods to handle. The method relies on an iterative process that refines an initial estimate using the function’s derivative to approach the true solution progressively.
114
Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

309
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...
309
Differential Equations: Problem Solving01:21

Differential Equations: Problem Solving

107
When analyzing the motion of falling objects, it is essential to consider not only the force of gravity but also the opposing force of air resistance. A practical example involves releasing a heavy test weight during a safety check on a ship. As the weight falls from rest, gravity accelerates it downward while air resistance exerts an upward force that increases with velocity. This dynamic interplay of forces is well described by differential equations, which provide a mathematical framework...
107
Distributions to Estimate Population Parameter01:26

Distributions to Estimate Population Parameter

5.6K
The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
5.6K

You might also read

Related Articles

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

Sort by
Same author

Dynamic density functional theory for sedimentation processes on complex domains: Modelling, spectral elements, and control problems.

The Journal of chemical physics·2023
Same author

The Impact of Microfibril Orientations on the Biomechanics of Plant Cell Walls and Tissues.

Bulletin of mathematical biology·2016
Same journal

Linearly Implicit Finite Element Methods Approximating the Solution to the Nonlinear Schrödinger Equation with a Schamel-Type Nonlinearity.

Journal of scientific computing·2026
Same journal

Fully Well-Balanced Methods for Schwarzschild-Euler Equation in Gullstrand-Painlevé Coordinates.

Journal of scientific computing·2026
Same journal

Inf-Sup Stable Space-Time Discretization of the Wave Equation Based on a First-Order-In-Time Variational Formulation.

Journal of scientific computing·2026
Same journal

Matrix-Free Inexact Preconditioning Techniques for Isogeometric Tensor-Product Discretizations.

Journal of scientific computing·2026
Same journal

A Robust Finite Element Method for Linearized Magnetohydrodynamics on General Domains.

Journal of scientific computing·2026
Same journal

Multiharmonic Algorithms for Contrast-Enhanced Ultrasound.

Journal of scientific computing·2026
See all related articles

Related Experiment Video

Updated: Mar 20, 2026

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
10:20

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules

Published on: September 5, 2019

8.9K

Fast Numerical Solvers for Parameter Identification Problems in Mathematical Biology.

Karolína Benková1, John W Pearson2, Mariya Ptashnyk3

  • 1The Bayes Centre, The Maxwell Institute for Mathematical Sciences, 47 Potterrow, Edinburgh, EH8 9BT Scotland, UK.

Journal of Scientific Computing
|March 19, 2026
PubMed
Summary
This summary is machine-generated.

This study introduces efficient methods for discretizing and solving nonlinear optimization problems in biological pattern evolution. The approach ensures commutative operations for accurate simulations and uses iterative solvers for performance.

Keywords:
Krylov subspace methodsPDE-constrained optimizationParameter identificationPattern formationPreconditioningTime-stepping

More Related Videos

Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion
09:17

Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion

Published on: March 1, 2022

3.6K
A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates
10:33

A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates

Published on: February 23, 2018

26.3K

Related Experiment Videos

Last Updated: Mar 20, 2026

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules
10:20

Single-Molecule Tracking Microscopy - A Tool for Determining the Diffusive States of Cytosolic Molecules

Published on: September 5, 2019

8.9K
Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion
09:17

Structure-Based Simulation and Sampling of Transcription Factor Protein Movements along DNA from Atomic-Scale Stepping to Coarse-Grained Diffusion

Published on: March 1, 2022

3.6K
A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates
10:33

A Method for Determination and Simulation of Permeability and Diffusion in a 3D Tissue Model in a Membrane Insert System for Multi-well Plates

Published on: February 23, 2018

26.3K

Area of Science:

  • Computational Biology
  • Applied Mathematics
  • Scientific Computing

Background:

  • Nonlinear partial differential equation (PDE)-constrained optimization is crucial for modeling biological pattern evolution.
  • Challenges exist in discretizing these complex models while maintaining optimization accuracy.

Purpose of the Study:

  • To develop effective discretization strategies and iterative solvers for nonlinear PDE-constrained optimization problems.
  • To ensure commutativity between discretization and optimization steps for reliable results.

Main Methods:

  • Linearization of the optimization problem using Sequential Quadratic Programming.
  • Devising time-stepping schemes and discrete approximations for commutative operations.
  • Formulating large-scale linear systems for efficient preconditioned iterative solvers (Krylov subspace methods).

Main Results:

  • The proposed methods achieve commutativity between discretization and optimization.
  • Efficient preconditioned iterative solvers are successfully applied to the formulated linear systems.
  • Numerical experiments validate the viability and efficiency of the approach.

Conclusions:

  • The developed strategies offer a robust framework for simulating biological pattern evolution.
  • The combination of specific discretization techniques and iterative solvers enhances computational efficiency and accuracy.