2D reaction-diffusion model-based biopsy simulation for dynamic tumor growth parameter estimation
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 √(D/γ) could be retrieved with a relative root mean squared error (RRMSE) of around 8% and an R2-value of 0.97. In long-term experiments, the RRMSEs ranged from 8 to 14% and the R2-values from 0.75 to 0.98. The scaled front velocity √(D ·γ), which can only be estimated if information about tumor age is available, was retrieved with an RRMSE of 7% and an R2 of 0.98 in both, the short-term and the long-term experiments.
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BibTeX
@misc{hofmann2026reactiondiffusion,
title = {{2D reaction-diffusion model-based biopsy simulation for dynamic tumor growth parameter estimation}},
author = {Veronika Hofmann and Pirmin Schlicke and Jan Zawallich and Heiko Enderling and Christina Kuttler},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.22363},
eprint = {2609.22363},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.22363},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - 2D reaction-diffusion model-based biopsy simulation for dynamic tumor growth parameter estimation
AU - Veronika Hofmann
AU - Pirmin Schlicke
AU - Jan Zawallich
AU - Heiko Enderling
AU - Christina Kuttler
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.22363
UR - https://arxiv.org/abs/2609.22363
AB - 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 √(D/γ) could be retrieved with a relative root mean squared error (RRMSE) of around 8% and an R^2-value of 0.97. In long-term experiments, the RRMSEs ranged from 8 to 14% and the R^2-values from 0.75 to 0.98. The scaled front velocity √(D ·γ), which can only be estimated if information about tumor age is available, was retrieved with an RRMSE of 7% and an R^2 of 0.98 in both, the short-term and the long-term experiments.
ER -