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Open research questions in Mathematical Biology Tumor Growth

63 unresolved questions extracted from the limitations and future-work sections of 132 Mathematical Biology Tumor Growth papers in our library. Each links back to the study that raised it.

What the literature leaves open

  • 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

  • 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

  • The occurrence of solution blow-up in higher dimensions is not fully understood. The global boundedness and exponential convergence to a constant stationary solution for quasilinear chemotaxis models is not well-studied.

    Global boundedness in a quasilinear chemotaxis model for tumor angiogenesis · 2026 · DOI

  • Future research should focus on evaluating the effectiveness of the quorum-based system in detecting tumors. Future research should investigate the importance of considering the dependence between channels in the design of immune surveillance systems. Future research should develop new methods for correcting for cell complexity.

    DQIS — Distributed Quorum-Based Independent Immune Surveillance: A Theoretical Framework for Byzantine Fault Tolerance for Multi-Channel Immune Surveillance · 2026 · DOI

  • The gap is the need for a system that can tolerate failures and detect tumors effectively. The current systems rely on a single signal and have a single point of failure. The gap is the lack of consideration of dependence between channels in the design of immune surveillance systems.

    DQIS — Distributed Quorum-Based Independent Immune Surveillance: A Theoretical Framework for Byzantine Fault Tolerance for Multi-Channel Immune Surveillance · 2026 · DOI

  • Cancer is a complex disease and one of the leading causes of death worldwide. The field of study is named Mathematical Oncology. Most studies reported on mathematical modeling in cancer aim to understand the effect of anticancer therapies.

    Close relationship and role of fractal dimension, heterogeneous nucleation, dynamic transformations and cooperativity mechanisms in unperturbed tumor growth · 2026 · DOI

  • Further study of the occurrence of solution blow-up in higher dimensions. Extension of the results to more general models.

    Global boundedness in a quasilinear chemotaxis model for tumor angiogenesis · 2026 · DOI

  • By decoupling radiobiological resistance from RL delivery effects --- which are spatially correlated in real tumours but separated in our model --- we show that hypoxic radioresistance alone is insufficient to prevent cure, identifying compromised RL delivery, rather than intrinsic radioresistance, as the dominant mechanism of hypoxic treatment failure.

    Energy deposition and receptor saturation set a tumour size threshold for radiopharmaceutical therapy: insights from a pharmacokinetic-tumour dynamics model · 2026 · DOI

  • The parameter sensitivity analysis varies all parameters by ±20% uniformly, but the study does not investigate how parameter uncertainty or inter-individual variability in SMC phenotypic switching rates (ηc, αc) and apoptosis rates affects plaque vulnerability predictions. Sensitivity analysis with realistic parameter distributions from experimental literature is needed.

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

  • The bidirectional phenotypic switching between SMCs and SDMs is modeled with switching rates dependent on intracellular lipid loads, but the molecular mechanisms driving SDM-to-SMC restoration (δs parameter) are not experimentally validated in the context of the plaque. The conditions under which SDM lipid offloading triggers reversal to SMC phenotype require investigation with in vitro and in vivo studies.

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

  • The complexity of the underlying PDE systems. The need for customized medical treatments to individual patient characteristics. The development of effective control policies that balance tumor eradication and minimal toxicity.

    Physics-guided deep reinforcement learning for personalized PDE control in cancer therapy optimization · 2026 · DOI

  • The approach is limited to a simulated environment. The paper acknowledges that mapping AUC directly to the kinetic parameter a2 via a linear transformation is a first-order approximation.

    Physics-guided deep reinforcement learning for personalized PDE control in cancer therapy optimization · 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 complexity of the channel network morphology of an actual scaffold. 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

  • 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

  • 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

  • To validate the model using real-world data. To apply the model to predict the effects of different treatments on tumour growth and vascular remodelling. 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 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 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 kinetics

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

  • The lack of systematic consideration of tumor growth kinetics or drug pharmacodynamics in traditional dose-finding studies. The need for more sophisticated approaches to chemotherapy scheduling, integrating pharmacokinetic/pharmacodynamic models with mathematical control theory.

    Personalized optimal dosing strategies for anticancer chemotherapy using mathematical modeling · 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

  • Traditional diffusion models often fall short in capturing the irregular and non-local movements of cells within the tumor microenvironment. There is a need for a comprehensive framework for understanding the complex interactions between glioma cells and immune cells. The development of a novel model that captures anomalous diffusion processes in cancer dynamics is necessary.

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

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63 open questions have been extracted from the limitations and future-work passages of 132 Mathematical Biology Tumor Growth papers in our library. Each one below links back to the study that raised it, so you can read the original claim in context.

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