Science AI Journal
Mathematics · Research topic

Open research questions in Mathematical Biology Tumor Growth

92 gap statements mined from Mathematical Biology Tumor Growth papers in our 4.5M-paper local library, which holds 634 papers on the topic — drawn mostly from each paper's own stated research gap, future-work, challenge and limitation notes, and its abstract. The ones listed below are a selection still marked open; each names the study that raised it, with a DOI link where the paper has one.

What the literature leaves open

  • The paper suggests that future research should focus on developing new therapeutic strategies for preventing or treating atherosclerosis. The paper recommends that future studies should investigate the effects of targeting SMC phenotypic switching on plaque progression.

    A Mathematical Model for Smooth Muscle Cell Phenotype Switching In Atherosclerotic Plaque · 2026 · DOI

  • The paper notes that prior studies have not fully explored the impact of SMC phenotypic switching on plaque progression.

    A Mathematical Model for Smooth Muscle Cell Phenotype Switching In Atherosclerotic Plaque · 2026 · DOI

  • Traditional mesh-based solvers are not efficient for 3D simulations. Classical SIPF and FDM methods have limitations in capturing the dynamics of 3D multi-bump solutions.

    An Efficient Particle-Field Algorithm with Neural Interpolation Based on a Parabolic-Hyperbolic Chemotaxis System in 3D · 2026 · DOI

  • In future work, methods such as Bayesian optimization could be explored to overcome the computational bottleneck associated with selecting hyperparameters in higher dimensions.

    Enhancing generalizability of model discovery across parameter space with multi-experiment equation learning for biological systems · 2026 · DOI

  • The need for a comprehensive computational framework to understand hormonal dynamics in breast cancer. The lack of personalized treatment protocols based on computational modeling.

    MODELING THE ROLE OF HORMONAL DYNAMICS AND ANTI-HORMONAL THERAPIES IN BREAST CANCER: A MULTIMODAL COMPUTATIONAL FRAMEWORK · 2026 · DOI

  • The study is limited to a specific type of network structure. The numerical simulations are performed on a specific network with 56 edges.

    Two-Species Chemotaxis Systems on Weighted Graphs: Asymptotic Behavior and Numerical Simulations · 2026 · DOI

  • Future research can focus on extending the analysis to more complex network structures. The study of other types of reaction-diffusion systems on weighted networks can provide further insights.

    Two-Species Chemotaxis Systems on Weighted Graphs: Asymptotic Behavior and Numerical Simulations · 2026 · DOI

  • The need to analyze the choice of values for input parameters. The need to validate the model using experimental data.

    On mathematical modeling of cell proliferation in tissue-engineering scaffolds with branching channels · 2026 · DOI

  • Prior work has focused on global weak solutions in bounded domains. There is a lack of understanding of the long-time dynamics of predator-prey models with cross-diffusion.

    Long‐Time Dynamics of the Cauchy Problem for the Predator–Prey Model with Cross‐Diffusion · 2026 · DOI

  • The lack of existing models that incorporate mechanical interactions between tumour cells and vasculature. The need for a better understanding of the effects of mechanical cell interactions with the tumour microenvironment on tumour growth and vascular remodelling.

    Exploring the relationship between vascular remodelling and tumour growth using agent-based modelling · 2026 · DOI

  • The lack of a tractable model to capture the evolution of the orientation distribution. The need for a model to study vascular remodeling and hypertension. The gap in understanding the response of endothelial cells to cyclic stretching.

    Using stochastic thermodynamics with internal variables to capture orientational spreading in cell populations undergoing cyclic stretch · 2026 · DOI

  • The paper suggests that future research should focus on extending the results to more general systems. The paper also suggests that future research should investigate the behavior of the system in different functional spaces.

    Stability of constant steady states of an attraction-repulsion chemotaxis system · 2026 · DOI

  • The paper identifies a gap in the existing literature on the attraction-repulsion chemotaxis system, namely the lack of a sharp stability criterion for constant steady states. The paper also identifies a gap in the understanding of the behavior of the system in the uniformly local Lebesgue spaces Lpuloc(Rn).

    Stability of constant steady states of an attraction-repulsion chemotaxis system · 2026 · DOI

  • Experimental validation of the model is needed. The model can be extended to account for other factors that may influence tumor growth and immune response. The introduction of the invasion threshold can be explored in other contexts, such as epidemiological modeling.

    Existence results and stability analysis for a fractional spatiotemporal brain tumor and immune system interaction · 2026 · DOI

  • The study is based on a mathematical model and requires further experimental and clinical validation. The model is calibrated using data from mouse models, and its applicability to humans needs to be confirmed. The study uses a simplified model of tumor dynamics and does not account for all possible biological processes.

    Optimizing chemoradiotherapy for malignant gliomas: a validated mathematical approach · 2026 · DOI

  • To extend the model to include the possibility of channels rejoining downstream. To validate the model using experimental data. To use the model to design scaffolds that promote cell growth and tissue development.

    On mathematical modeling of cell proliferation in tissue-engineering scaffolds with branching channels · 2026 · DOI

  • To investigate the effects of other factors, such as immune responses or genetic mutations, on tumour growth and vascular remodelling.

    Exploring the relationship between vascular remodelling and tumour growth using agent-based modelling · 2026 · DOI

  • The study used a simulated dataset, - The performance depended on the model structure, parameter identifiability, and training configuration, - The need for careful loss weighting and further…

    Physics-Informed Neural Network for Parameter Inference in a Tumor Model · 2026 · DOI

  • Further study of piecewise PINNs in realistic therapeutic settings, - Investigation of the effect of different model structures and training configurations…

    Physics-Informed Neural Network for Parameter Inference in a Tumor Model · 2026 · DOI

  • The results are based on a specific model and may not be generalizable to other models - The study only considers the case of strong competition - The analysis is limited to the asymptotic behavior…

    Asymptotic Behavior of Solutions of Two-Species Chemotaxis System with Strong Competition · 2026 · DOI

  • Further study of the asymptotic behavior of solutions for different types of competition - Investigation of the uniform Hölder continuity of solutions for other models - Analysis of the spatial segregation of solutions for different parameter…

    Asymptotic Behavior of Solutions of Two-Species Chemotaxis System with Strong Competition · 2026 · DOI

  • To apply the algorithm to other biological phenomena. To improve the accuracy of the neural interpolation. To extend the algorithm to other types of partial differential equations.

    An Efficient Particle-Field Algorithm with Neural Interpolation Based on a Parabolic-Hyperbolic Chemotaxis System in 3D · 2026 · DOI

  • The development of more sophisticated computational models that incorporate additional biological mechanisms. The integration of computational modeling with clinical trials to validate predictions. The exploration of combination therapies that exploit network vulnerabilities.

    MODELING THE ROLE OF HORMONAL DYNAMICS AND ANTI-HORMONAL THERAPIES IN BREAST CANCER: A MULTIMODAL COMPUTATIONAL FRAMEWORK · 2026 · DOI

  • The paper identifies a gap in the analysis of branching Brownian motion - The paper aims to provide a description for the probabilistic evolution of chemical reaction…

    A new look to branching Brownian motion from a particle-based reaction–diffusion dynamics point of view · 2026 · DOI

  • Experimental validation of the reduced model. Investigation of the viscosity η as a function of the strain amplitude. Application of the reduced model to study vascular remodeling and hypertension.

    Using stochastic thermodynamics with internal variables to capture orientational spreading in cell populations undergoing cyclic stretch · 2026 · DOI

Most-cited papers in Mathematical Biology Tumor Growth

Most recent work

Find a gap in your own Mathematical Biology Tumor Growth sub-topic

This page shows what the Mathematical Biology Tumor Growth literature already flags as unresolved. To narrow it to your specific question, search the Research Gap Finder: the search is free with a free account and lists the papers closest to your topic first. Unlocking that topic (50 credits, charged once) fills the comparison table from our 4.5M-paper local library and writes the gaps from its rows.

Open the Research Gap Finder →

Related topics in Mathematics

Cognitive and developmental aspects of mathematical skills
732 open questions
Statistics Education and Methodologies
348 open questions
Mathematics Education and Pedagogy
344 open questions
History and Theory of Mathematics
309 open questions
Advanced Causal Inference Techniques
282 open questions
Survey Sampling and Estimation Techniques
256 open questions
Mathematics Education and Programs
252 open questions
Advanced Statistical Methods and Models
247 open questions
Open questions raised by papers listed on this page include: (1) The paper suggests that future research should focus on developing new therapeutic strategies for preventing or treating atherosclerosis (“A Mathematical Model for Smooth Muscle Cell Phenotype Switching In…”, 2026); (2) The lack of personalized treatment protocols based on computational modeling (“MODELING THE ROLE OF HORMONAL DYNAMICS AND ANTI-HORMONAL THERAPIES IN BREAST…”, 2026); (3) Future research can focus on extending the analysis to more complex network structures (“Two-Species Chemotaxis Systems on Weighted Graphs: Asymptotic Behavior and…”, 2026); (4) There is a lack of understanding of the long-time dynamics of predator-prey models with cross-diffusion (“Long‐Time Dynamics of the Cauchy Problem for the Predator–Prey Model with…”, 2026); (5) The lack of existing models that incorporate mechanical interactions between tumour cells and vasculature (“Exploring the relationship between vascular remodelling and tumour growth using…”, 2026). 92 gap statements have been mined from Mathematical Biology Tumor Growth papers in our 4.5M-paper local library, which holds 634 papers on the topic; the gaps come from whichever of those papers state one. They are mostly the research gaps the authors state and the papers' abstracts, plus future-work, limitations and challenges passages. The ones listed below are a selection still marked open; each names the study that raised it, with a DOI link where the paper has one, so you can read the original claim in context.

Tools for your next paper

Gaps & Literature SearchFind open questions in any field — 120,000+ open gaps mined from our own library.Pre-CheckIs your paper ready? Acceptance odds for top, mid and open/emerging journals, in seconds.Journal FinderA ranked shortlist of target journals from a 17,500-venue index.Duplicate Publication CheckerCheck for prior publication across 7 sources and our local library.Citation GeneratorFreeA DOI or title → APA, MLA, Vancouver, Chicago, BibTeX, RIS. No signup.Graphical Abstract MakerFreeTurn your findings into a colorblind-safe graphical abstract.

How Pre-Check worksHow AI Review works

Compare the category — Honest roundups of the AI research tools, ours listed alongside the alternatives.

Command palette

Jump anywhere, run any action.