Related Experiment Video
Updated: Nov 5, 2025
09:44
Use of Principal Components for Scaling Up Topographic Models to Map Soil Redistribution and Soil Organic Carbon
Published on: October 16, 2018
10.4K
A systematic approach to the scale separation problem in the development of multiscale models
Pinaki Bhattacharya1,2, Qiao Li1,2, Damien Lacroix1,2
1Department of Mechanical Engineering, University of Sheffield, Sheffield, United Kingdom.
Plos One
|May 18, 2021
Summary
This study defines "scale" for multiscale engineering problems, addressing a key challenge in biomedical engineering. A new methodology for multiscale modeling is presented, adaptable to various engineering applications.
Area of Science:
- Engineering
- Biomedical Engineering
- Computational Science
Background:
- Multiscale problems in engineering involve predicting quantities with variations across different time and space ranges.
- Defining 'scale' in these multiscale problems is a significant, poorly addressed challenge, causing confusion, especially in biomedical engineering.
Purpose of the Study:
- To propose a novel definition of 'scale' for multiscale problems.
- To develop a comprehensive multiscale modeling methodology based on this definition.
- To illustrate the methodology's application and adaptability in engineering.
Main Methods:
- Defining scale based on instrument limitations, computational power, and characteristic variation ranges.
- Constructing a start-to-finish multiscale modeling methodology.
- Algorithmic orchestration of mathematical models at different scales.
Main Results:
- A clear definition of scale is proposed, addressing a fundamental challenge.
- A practical multiscale modeling methodology is developed and illustrated.
- The methodology demonstrates adaptability to related engineering problems.
Conclusions:
- The proposed definition of scale clarifies a critical concept in multiscale engineering.
- The developed multiscale modeling methodology offers a structured approach for complex problems.
- The methodology is adaptable and has potential for wide application across engineering disciplines.
Related Concept Videos
01:30Typical Model Studies
502
Fluid mechanics model studies often utilize scaled-down systems to predict fluid behavior in full-scale environments, such as river flows, dam spillways, and structures interacting with open surfaces. Maintaining Froude number similarity in river models is crucial, as it replicates surface flow features like wave patterns and velocities.
502
01:29Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving
153
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...
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
153
01:14Multicompartment Models: Overview
328
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,...
These models offer a more comprehensive representation of drug behavior in the body than one-compartment models. They accommodate the complexity of drug distribution,...
328
01:21Design Example: Creating a Hydraulic Model of a Dam Spillway
444
Scaled hydraulic models of dam spillways provide a practical way to replicate and study the intricate flow dynamics of these structures. Often built to a 1:15 ratio, these models allow for observing critical water behavior, such as velocity distribution, flow patterns, and energy dissipation.
444
01:23Mechanistic Models: Compartment Models in Individual and Population Analysis
122
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...
122
01:06Model Approaches for Pharmacokinetic Data: Distributed Parameter Models
153
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...
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...
153