Advances in Computational Oncology: Mathematical Modeling, Numerical Methods, and Intelligent Systems

Dear Colleagues,

Cancer remains one of the most complex and devastating diseases worldwide, and the development of accurate, predictive computational models is pivotal to advancing our understanding of tumor initiation, progression, invasion, and response to therapy. The inherent multi-scale and multi-physics nature of tumor dynamics—spanning molecular signaling, cellular mechanics, tissue-level remodeling, and macroscopic growth—demands a synergistic integration of advanced mathematical frameworks, state-of-the-art numerical methods, and modern data-driven approaches.

In this Special Issue we aim to feature high-quality, original contributions that present innovative numerical, mathematical, and deep learning methodologies for modeling and simulating tumor-related phenomena across diverse biological environments. The scope includes, but is not limited to, the following themes:

• Partial differential equation (PDE) models for tumor growth, invasion, and metastasis in heterogeneous tissue environments, including avascular and vascular settings.
• Reaction–diffusion and chemotaxis systems describing tumor angiogenesis, nutrient transport, extracellular matrix degradation, and cell–cell interactions.
• Novel numerical schemes for stiff, multi-scale biological systems, including positivity-preserving schemes, operator-splitting techniques, and adaptive mesh refinement strategies.
• Physics-informed neural networks and neural operators for the forward and inverse solution of PDE-based tumor models.
• Application of deep learning architectures, convolutional neural networks, graph neural networks, and transformers to tumor classification, progression prediction, and treatment optimization.
• High-performance and GPU-accelerated computing strategies for large-scale tumor simulations.
• Fractional-order and non-local models capturing anomalous diffusion and memory effects in tumor microenvironments.
• Uncertainty quantification, sensitivity analysis, and Bayesian inference for parameter estimation in tumor models.
• Hybrid continuum–discrete and agent-based models coupled with machine learning surrogates for multi-scale tumor dynamics.
• Digital twins and patient-specific simulation frameworks integrating clinical imaging data with computational models for personalized oncology.

We welcome both methodological advances and application-driven studies that demonstrate the potential of innovative computational techniques in realistic tumor scenarios. Contributions showcasing rigorous mathematical analysis, efficient numerical implementations, validation against experimental or clinical data, and interdisciplinary collaborations between mathematicians, computer scientists, engineers, and biomedical researchers are particularly encouraged.

We look forward to receiving your contributions and to assembling a collection of works that reflects the state of the art and future directions in computational tumor modeling.

Kind regards,

Dr. Pasquale De Luca
Dr. Annabella Di Mauro
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Bioengineering is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2700 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.