OpenAlex ·
2D reaction-diffusion model-based biopsy simulation for dynamic tumor growth parameter estimation
- Published
- Source
- OpenAlex
- Published in
- arXiv (Cornell University)
- DOI
- 10.48550/arxiv.2609.22363
- Original
- Read it at the publisher
- Topics
Abstract
Once diagnosed, cancer requires a fast, reliable and preferably cost-efficient assessment of the current state and potential progression of the disease. A new method for estimating tumor cell diffusivity $D$ and proliferation rate $γ$ in the context of the mechanistic reaction-diffusion equation from single-point-in-time routine biopsies aims to deliver just that, and quantities computed from the parameter estimates have recently been tested as a new biomarkers for risk-stratification in radiotherapy. Here, we extend the findings of this previous work by providing a first theoretical validation. The method is applied to in-silico biopsies which are generated by solving the two-dimensional reaction-diffusion equation for different growth terms (exponential and logistic) with a Dirac-Delta initial condition, and transforming the continuous results into spatial point patterns via a form of reverse coarse-graining. If no information about tumor age is used, in short-term experiments the original dispersion length $\sqrt{D/γ}$ could be retrieved with a relative root mean squared error (RRMSE) of around 8% and an $\text{R}^2$-value of 0.97. In long-term experiments, the RRMSEs ranged from 8 to 14% and the $\text{R}^2$-values from 0.75 to 0.98. The scaled front velocity $\sqrt{D \cdotγ}$, which can only be estimated if information about tumor age is available, was retrieved with an RRMSE of 7% and an $\text{R}^2$ of 0.98 in both, the short-term and the long-term experiments.
The authors’ abstract, as arXiv lists it. arXiv’s listings, abstracts included, are free for anyone to reuse.
Read it on ReadSearch
Each opens after you create an account, and brings you back to this paper.
More in Numerical Analysis
Nutrient Competition as a General Mechanism of Regulation in Photosymbiosis
Spread of Chronic Wasting Disease under Stochastic Environmental Conditions and its Control using Deep Reinforcement Learning
Bistability with equal and independent removal in small bimolecular networks
Beyond species area curves: a theoretical approach to the relationship between diversity and area
Mutation--selection balance on an infinite trait space: confinement, drift and equilibrium
Get the few papers worth your time in Numerical Analysis every morning.
ReadSearch reads the new papers in your field each day and brings you the few worth reading, each with its key finding in a sentence.