Breast cancer’s heterogeneous progression demands innovative tools for accurate prediction.We present a hybrid framework that integrates machine learning(ML)and fractional-order dynamics to predict tumor growth acros...Breast cancer’s heterogeneous progression demands innovative tools for accurate prediction.We present a hybrid framework that integrates machine learning(ML)and fractional-order dynamics to predict tumor growth across diagnostic and temporal scales.On the Wisconsin Diagnostic Breast Cancer dataset,seven ML algorithms were evaluated,with deep neural networks(DNNs)achieving the highest accuracy(97.72%).Key morphological features(area,radius,texture,and concavity)were identified as top malignancy predictors,aligning with clinical intuition.Beyond static classification,we developed a fractional-order dynamical model using Caputo derivatives to capture memory-driven tumor progression.The model revealed clinically interpretable patterns:lower fractional orders correlated with prolonged aggressive growth,while higher orders indicated rapid stabilization,mimicking indolent subtypes.Theoretical analyses were rigorously proven,and numerical simulations closely fit clinical data.The framework’s clinical utility is demonstrated through an interactive graphics user interface(GUI)that integrates real-time risk assessment with growth trajectory simulations.展开更多
A fractional-order mathematical model of lung cancer is used to describe the dynamics of tumor growth and the interactions between cancer cells and immune cells.To obtain approximate solutions and better understand th...A fractional-order mathematical model of lung cancer is used to describe the dynamics of tumor growth and the interactions between cancer cells and immune cells.To obtain approximate solutions and better understand the behavior of the state functions,a pseudoo-perational collocation scheme employing shifted Jacobi polynomials as basis functions is introduced.Initially,the existence and uniqueness of solutions to the model are established using the Leray-Schauder fixed-point theorem.Error bounds for the residual functions are estimated within a Jacobi-weighted L2-space.To enhance the accuracy and reliability of the results,two distinct strategies are implemented:sensitivity analysis and feedback control.The feedback control of the proposed pseudo-operational spectral method is performed using the method of Lagrange multipliers,marking its first application in this context.Spectral solutions are derived by applying the pseudo-operational scheme to both the original model and the model with control functions.Improved performance and outputs are anticipated following the application of the feedback control strategy.Finally,comprehensive biological interpretations of the results are provided,offering insights into the practical implications of the model.展开更多
文摘Breast cancer’s heterogeneous progression demands innovative tools for accurate prediction.We present a hybrid framework that integrates machine learning(ML)and fractional-order dynamics to predict tumor growth across diagnostic and temporal scales.On the Wisconsin Diagnostic Breast Cancer dataset,seven ML algorithms were evaluated,with deep neural networks(DNNs)achieving the highest accuracy(97.72%).Key morphological features(area,radius,texture,and concavity)were identified as top malignancy predictors,aligning with clinical intuition.Beyond static classification,we developed a fractional-order dynamical model using Caputo derivatives to capture memory-driven tumor progression.The model revealed clinically interpretable patterns:lower fractional orders correlated with prolonged aggressive growth,while higher orders indicated rapid stabilization,mimicking indolent subtypes.Theoretical analyses were rigorously proven,and numerical simulations closely fit clinical data.The framework’s clinical utility is demonstrated through an interactive graphics user interface(GUI)that integrates real-time risk assessment with growth trajectory simulations.
文摘A fractional-order mathematical model of lung cancer is used to describe the dynamics of tumor growth and the interactions between cancer cells and immune cells.To obtain approximate solutions and better understand the behavior of the state functions,a pseudoo-perational collocation scheme employing shifted Jacobi polynomials as basis functions is introduced.Initially,the existence and uniqueness of solutions to the model are established using the Leray-Schauder fixed-point theorem.Error bounds for the residual functions are estimated within a Jacobi-weighted L2-space.To enhance the accuracy and reliability of the results,two distinct strategies are implemented:sensitivity analysis and feedback control.The feedback control of the proposed pseudo-operational spectral method is performed using the method of Lagrange multipliers,marking its first application in this context.Spectral solutions are derived by applying the pseudo-operational scheme to both the original model and the model with control functions.Improved performance and outputs are anticipated following the application of the feedback control strategy.Finally,comprehensive biological interpretations of the results are provided,offering insights into the practical implications of the model.
