Updated: April 27th, 2024 05:01

2024 journal article

Quantifying collective motion patterns in mesenchymal cell populations using topological data analysis and agent-based modeling

*MATHEMATICAL BIOSCIENCES*, *370*.

Sources: Web Of Science, NC State University Libraries

Added: April 22, 2024

2021 review

Learning differential equation models from stochastic agent-based model simulations

[Review of ]. *JOURNAL OF THE ROYAL SOCIETY INTERFACE*, *18*(176).

author keywords: agent-based models; differential equations; equation learning; population dynamics; disease dynamics

MeSH headings : Learning; Models, Biological; Molecular Dynamics Simulation; Monte Carlo Method; Stochastic Processes

TL;DR:
This tutorial proposes that methods from the equation learning field provide a promising, novel and unifying approach for agent-based model analysis, and demonstrates that this framework is easy to use, requires few model simulations, and accurately predicts model dynamics in parameter regions where coarse-grained differential equation models fail to do so.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science; OpenAlex)

Source: Web Of Science

Added: April 12, 2021

2021 journal article

Topological data analysis distinguishes parameter regimes in the Anderson-Chaplain model of angiogenesis

*PLOS COMPUTATIONAL BIOLOGY*, *17*(6).

MeSH headings : Algorithms; Animals; Blood Vessels / anatomy & histology; Blood Vessels / growth & development; Blood Vessels / physiology; Chemotaxis; Computational Biology; Computer Simulation; Humans; Models, Cardiovascular; Neoplasms / blood supply; Neovascularization, Pathologic; Neovascularization, Physiologic; Spatio-Temporal Analysis

TL;DR:
This work simulates the Anderson-Chaplain model of angiogenesis at different parameter values, and proposes a topological data analysis (TDA) pipeline for systematic analysis of the model and shows that TDA of model simulation data stratifies parameter space into regions with similar vessel morphology.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

6. Clean Water and Sanitation
(OpenAlex)

Source: Web Of Science

Added: July 19, 2021

2020 review

A tutorial review of mathematical techniques for quantifying tumor heterogeneity

[Review of ]. *MATHEMATICAL BIOSCIENCES AND ENGINEERING*, *17*(4), 3660–3709.

author keywords: cancer heterogeneity; mathematical oncology; tumor growth; glioblastoma multiforme; virtual populations; nonlinear mixed effects; spatiotemporal data; Bayesian estimation; generative; adversarial networks; non-parametric estimation; variational autoencoders; machine learning

MeSH headings : Bayes Theorem; Humans; Machine Learning; Models, Theoretical; Neoplasms; Precision Medicine

TL;DR:
Several techniques that can be used to aid the mathematical modeller in inferring and quantifying both sources of heterogeneity from patient data are reviewed, including virtual populations, nonlinear mixed effects modeling, non-parametric estimation, Bayesian techniques, and machine learning.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 3, 2020

2020 journal article

Biologically-informed neural networks guide mechanistic modeling from sparse experimental data

*PLOS COMPUTATIONAL BIOLOGY*, *16*(12).

MeSH headings : Computer Simulation; Machine Learning; Neural Networks, Computer; Nonlinear Dynamics

TL;DR:
BINNs are trained in a supervised learning framework to approximate in vitro cell biology assay experiments while respecting a generalized form of the governing reaction-diffusion partial differential equation (PDE).
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: January 4, 2021

2020 journal article

Learning Equations from Biological Data with Limited Time Samples

*BULLETIN OF MATHEMATICAL BIOLOGY*, *82*(9).

author keywords: Equation learning; Numerical differentiation; Sparse regression; Model selection; Partial differential equations; Parameter estimation; Population dynamics; Glioblastoma multiforme

MeSH headings : Computational Biology / methods; Glioblastoma; Humans; Learning; Mathematical Concepts; Models, Biological; Nonlinear Dynamics

TL;DR:
This work presents an equation learning methodology comprised of data denoising, equation learning, model selection and post-processing steps that infers a dynamical systems model from noisy spatiotemporal data and highlights how these results are informative for data-driven modeling-based tumor invasion predictions.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: September 28, 2020

2020 journal article

Learning partial differential equations for biological transport models from noisy spatio-temporal data

author keywords: numerical differentiation; equation learning; sparse regression; partial differential equations; parameter estimation; biological transport

TL;DR:
It is shown that the ANN methodology outperforms previous denoising methods, including finite differences and both local and global polynomial regression splines, in the ability to accurately approximate partial derivatives and learn the correct PDE model.
(via Semantic Scholar)

Source: Web Of Science

Added: March 30, 2020

2019 journal article

The influence of numerical error on parameter estimation and uncertainty quantification for advective PDE models

*INVERSE PROBLEMS*, *35*(6).

author keywords: inverse problems; numerical analysis; uncertainty quantification; autocorrelation

TL;DR:
Results concerning how a least squares cost function and parameter estimator behave in the presence of numerical error in approximating solutions to the underlying advection equation are presented and guidelines are provided to determine when numerical or experimental error is the main source of error in their inference.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: June 17, 2019

2013 journal article

Quantifying CFSE label decay in flow cytometry data

*APPLIED MATHEMATICS LETTERS*, *26*(5), 571–577.

author keywords: Carboxyfluorescein succinimidyl ester (CFSE); Ordinary differential equation models; Inverse problems; Exponential decay; Gompertz growth; Akiake Information

TL;DR:
A series of models for the label decay in cell proliferation assays when the intracellular dye carboxyfluorescein succinimidyl ester is used as a staining agent are developed.
(via Semantic Scholar)

UN Sustainable Development Goal Categories

3. Good Health and Well-being
(Web of Science)

Source: Web Of Science

Added: August 6, 2018

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