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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...
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Estimation of Parameter Distributions for Reaction-Diffusion Equations with Competition using Aggregate

Kyle Nguyen1,2, Erica M Rutter3, Kevin B Flores4,5

  • 1Biomathematics Graduate Program, North Carolina State University, Raleigh, NC, USA.

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|June 2, 2023
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Summary
This summary is machine-generated.

This study introduces a new random differential equation model to accurately predict cell density in competing subpopulations, outperforming traditional models. The approach enhances understanding of biological population dynamics and cancer growth.

Keywords:
Glioblastoma multiformeParameter estimationRandom differential equationk-Means clustering

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Area of Science:

  • Mathematical Biology
  • Computational Biology
  • Cancer Modeling

Background:

  • Reaction-diffusion equations model population dynamics but often assume homogeneous rates.
  • Real-world populations frequently consist of competing subpopulations with varying traits.
  • Existing methods for inferring phenotypic heterogeneity have limitations with competing subpopulations.

Purpose of the Study:

  • To extend existing methods for inferring phenotypic heterogeneity to reaction-diffusion models with competing subpopulations.
  • To develop and test a novel random differential equation model for analyzing complex population dynamics.
  • To apply the developed model to glioblastoma multiforme (GBM) cancer growth.

Main Methods:

  • Developed a novel random differential equation model by converting a reaction-diffusion model.
  • Utilized the Prokhorov metric framework for parameter distribution estimation.
  • Applied k-means clustering to predict the number of subpopulations based on estimated distributions.
  • Simulated data mimicking practical measurements for model validation.

Main Results:

  • The new random differential equation model demonstrated superior accuracy in predicting cell density compared to traditional partial differential equation models.
  • The model proved to be more time-efficient than existing methods.
  • Successfully estimated joint distributions of diffusion and growth rates among heterogeneous subpopulations.
  • K-means clustering effectively predicted the number of subpopulations.

Conclusions:

  • The developed random differential equation approach effectively models phenotypic heterogeneity in competing subpopulations.
  • This method offers a more accurate and efficient tool for analyzing complex biological systems, including cancer proliferation.
  • The findings provide a robust framework for understanding and potentially controlling population dynamics in various biological contexts.