Integrative framework for cancer detection via integro-differential equations using deep learning techniques

Cancer diagnosis remains challenging in clinical practice, motivating the development of computational tools for accurate identification of cancerous regions in medical images. Recent advances in deep learning have shown potential to support these tasks. This study proposes a framework that converts 2D medical images (e.g., mammograms) into 1D signals for efficient feature extraction, followed by classification using a 1D convolutional neural network. Integro-differential equations are incorporated to model tumor growth dynamics and spatial-temporal intensity variations, with the goal of improving interpretability. The approach was evaluated on publicly available mammography datasets (INbreast and MIAS). In preliminary experiments, it achieved 96.4% accuracy in binary classification, comparable to or slightly better than selected conventional deep learning baselines on these benchmarks. The paper discusses advantages in feature extraction and computational aspects, along with limitations related to data dependency, information loss during signal conversion, and simplifications in the mathematical models.