Mathematical modeling of tumor growth and treatment: Triple negative breast cancer

Wei, Hao-Ji

doi:10.1016/j.matcom.2022.09.005

Cited by 5 publications

(2 citation statements)

References 45 publications

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“…Despite significant efforts to develop models that predict slower tumor growth in the late stages, recent studies have suggested growth that is even faster than exponential growth [132]. More details of ODEs in tumor growth can be found in [111,[133][134][135][136]. Recently, a thorough investigation was undertaken to compare the outcomes of six ODE models, including the exponential, logistic, 6) [130,131] classic Bertalanffy, general Bertalanffy, classic Gompertz, and general Gompertz models.…”

Section: Continuum Models For Tumor Growthmentioning

confidence: 99%

Biomechanical modelling of tumor growth with chemotherapeutic treatment: a review

Xu,

Wang,

Gomez

et al. 2023

Smart Mater. Struct.

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The efficiency of chemotherapy in the treatment of cancer depends on the administration schedule, such as dosage, timing and frequency, and the release control if self-assembled drugs are administered, in addition to the drug transport in the tumor microenvironment. Biomechanical models can help deepen our understanding of drug pharmacokinetics and pharmacodynamics, tumor response and resistance to treatment, as well as enable the use of personalized treatment and optimal therapies. This review aims to provide an overview of computational modeling for vascular tumor growth, drug biotransport, and tumor response with integration of microenvironmental biology phenomena, e.g., angiogensis, blood flow, and mechanical stress. We first review some discrete and continuum models for vascular tumors, highlighting the advantages and challenges of each approach. Then, we discuss mathematical models that include chemotherapeutic treatment and provide potential strategies to promote drug effectiveness through numerical observations. We finalize discussing several aspects that warrant further research including multiscale modeling of cancer, incorporation of patient-specific parameters and coupling of models with emerging medical imaging technologies.

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Section: Continuum Models For Tumor Growthmentioning

confidence: 99%

Biomechanical modelling of tumor growth with chemotherapeutic treatment: a review

Xu,

Wang,

Gomez

et al. 2023

Smart Mater. Struct.

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“…These treatment response models have been developed to predict response of cancer cells to different treatment strategies [33][34]. Additionally, these models aim to optimize treatment schedules by identifying optimal and combination regimens, thus improving treatment outcomes [35][36][37]. Several mathematical models have been validated in preclinical studies and trials, demonstrating their potential in designing successful clinical trials [38][39][40][41][42][43][44].…”

Section: Mathematical Models For Cap Treatment Response In Cancermentioning

confidence: 99%

Personalized Plasma Medicine for Cancer: Transforming Treatment Strategies with Mathematical Modeling and AI Algorithms

Devi,

Keidar

2023

Preprint

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Plasma technology shows tremendous potential for revolutionizing oncology research and treatment. Reactive oxygen and nitrogen species, electromagnetic emissions generated through gas plasma jets, have attracted significant attention due to their selective cytotoxicity towards cancer cells. To leverage the full potential of plasma medicine, researchers have explored the use of mathematical models and various subsets of machine learning, such as reinforcement learning, and deep learning. This review emphasizes the significant application of AI algorithms in the adaptive plasma system, paving the way for precision and dynamic cancer treatment. Realizing the full potential of AI in plasma medicine, requires research efforts, data sharing and interdisciplinary collaborations. Unravelling the complex mechanisms, developing real-time diagnostics, and optimizing AI models will be crucial to harness the true power of plasma technology in oncology. The integration of personalized and dynamic plasma therapies, alongside AI and diagnostic sensors, presents a transformative approach to cancer treatment with the potential to improve outcomes globally.

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An optimal solution for tumor growth model using generalized Bessel polynomials

Saeidi,

Dahaghin,

Mehrabi

et al. 2024

Math Methods in App Sciences

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In this paper, a mathematical model is given that depicts the interactions between cancer cells and viruses in the setting of oncolytic virotherapy. The model is separated into three classes, namely, concentrations of uninfected tumor cells in the population “ ”, free virus “ ”, and cancerous cells infected “ ”. Applying Caputo fractional derivative, the model is fractionalized, and using generalized Bessel polynomials, an optimal problem is solved utilizing Lagrange multipliers method. The results show that the presented method has high accuracy and is suitable for solving the nonlinear systems based on partial differential equations especially tumors models.

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Mathematical modeling of tumor growth and treatment: Triple negative breast cancer

Cited by 5 publications

References 45 publications

Biomechanical modelling of tumor growth with chemotherapeutic treatment: a review

Biomechanical modelling of tumor growth with chemotherapeutic treatment: a review

Personalized Plasma Medicine for Cancer: Transforming Treatment Strategies with Mathematical Modeling and AI Algorithms

An optimal solution for tumor growth model using generalized Bessel polynomials

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