<p>In this study, we develop and analyze a novel mathematical model for colon cancer progression in intestinal epithelial cells incorporating the role of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\hbox {CD8}^+$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mtext>CD8</mtext> <mo>+</mo> </msup> </math></EquationSource> </InlineEquation> immune response. While traditional numerical techniques are commonly employed for studying such biological systems, we employ a machine learning–driven physics-informed neural network (PINN) approach to address the nonlinear system of ordinary differential equations arising from the model. The PINN approach integrates biological domain knowledge (e.g., tumor growth kinetics and immune interactions) into the training process of a neural network, thereby combining data-driven learning with governing biological laws to estimate system dynamics and unknown parameters with improved accuracy and efficiency. A rigorous analytical investigation ensures positivity, boundedness, and local stability of equilibrium states, characterized by a threshold parameter analogous to the basic reproduction number (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\mathscr {R}_0$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>) from infectious disease modeling. Sensitivity analysis highlights the critical influence of mutation rates and immune efficacy on long-term disease dynamics. In particular, an enhanced <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\hbox {CD8}^+$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mtext>CD8</mtext> <mo>+</mo> </msup> </math></EquationSource> </InlineEquation> immune response significantly reduces cancerous cell populations while promoting healthy epithelial cell survival. PINN-based simulations not only validate the theoretical predictions but also reveal critical thresholds for treatment effectiveness and early detection. Overall, this hybrid mathematical machine learning framework provides a powerful tool for modeling cancer progression, offering insights for improving early intervention strategies and optimizing therapeutic and screening policies in colon cancer management.</p>

A machine learning approach to colon cancer modeling of intestinal epithelial cells using physics-informed neural networks

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发表日期：

2026年2月24日

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Rafiqur Rahaman,
Biswadip Pal,
Purnendu Sardar,
Santosh Biswas,
Md Firoj Ali,
Krishna Pada Das,
Tshering Dorjee Bhutia

摘要

In this study, we develop and analyze a novel mathematical model for colon cancer progression in intestinal epithelial cells incorporating the role of $\hbox {CD8}^+$ ${CD8}^{+}$ immune response. While traditional numerical techniques are commonly employed for studying such biological systems, we employ a machine learning–driven physics-informed neural network (PINN) approach to address the nonlinear system of ordinary differential equations arising from the model. The PINN approach integrates biological domain knowledge (e.g., tumor growth kinetics and immune interactions) into the training process of a neural network, thereby combining data-driven learning with governing biological laws to estimate system dynamics and unknown parameters with improved accuracy and efficiency. A rigorous analytical investigation ensures positivity, boundedness, and local stability of equilibrium states, characterized by a threshold parameter analogous to the basic reproduction number ( $\mathscr {R}_0$ $R_{0}$ ) from infectious disease modeling. Sensitivity analysis highlights the critical influence of mutation rates and immune efficacy on long-term disease dynamics. In particular, an enhanced $\hbox {CD8}^+$ ${CD8}^{+}$ immune response significantly reduces cancerous cell populations while promoting healthy epithelial cell survival. PINN-based simulations not only validate the theoretical predictions but also reveal critical thresholds for treatment effectiveness and early detection. Overall, this hybrid mathematical machine learning framework provides a powerful tool for modeling cancer progression, offering insights for improving early intervention strategies and optimizing therapeutic and screening policies in colon cancer management.