Introduction to Mathematical Oncology

Kuang, Yang; Nagy, John D.; Eikenberry, Steffen E.

doi:10.1201/9781315365404

Cited by 52 publications

(73 citation statements)

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“…Parameters: N -cell population size (or volume / mass thorough conversion [15]), α -growth rate, β -cell death rate, λ -nutrient limited proliferation rate, k -carrying capacity of cells. to the question, which is the best model to fit cancer data [17]. In our analysis we chose four of the most representative and typically used scalar growth models, namely Logistic, von Bertalanffy, Gompertz and Holling, described in Table 1 and depicted in Figure 2.…”

Section: Model Equationmentioning

confidence: 99%

“…each is priming on a type of tumor), and c) the small amount and irregular sampling of the data (e.g. 15 measurements with at days 6,10,13,17,19,21,24,28,31,34,38,41,45,48 for breast cancer growth in [26]). Although such competing canonical tumor growth models are commonly used, how to decide which of the models to use for which tumor types is still an open question.…”

Section: Model Equationmentioning

confidence: 99%

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Growth pattern Learning for Unsupervised Extraction of Cancer Kinetics

Axenie¹,

Kurz

2020

Preprint

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Neoplastic processes are described by complex and heterogeneous dynamics. The interaction of neoplastic cells with their environment describes tumor growth and is critical for the initiation of cancer invasion. Despite the large spectrum of tumor growth models, there is no clear guidance on how to choose the most appropriate model for a particular cancer and how this will impact its subsequent use in therapy planning. Such models need parametrization that is dependent on tumor biology and hardly generalize to other tumor types and their variability. Moreover, the datasets are small in size due to the limited or expensive measurement methods. Alleviating the limitations that incomplete biological descriptions, the diversity of tumor types, and the small size of the data bring to mechanistic models, we introduce Growth pattern Learning for Unsupervised Extraction of Cancer Kinetics (GLUECK) a novel, data-driven model based on a neural network capable of unsupervised learning of cancer growth curves. Employing mechanisms of competition, cooperation, and correlation in neural networks, GLUECK learns the temporal evolution of the input data along with the underlying distribution of the input space. We demonstrate the superior accuracy of GLUECK, against four typically used tumor growth models, in extracting growth curves from a four clinical tumor datasets. Our experiments show that, without any modification, GLUECK can learn the underlying growth curves being versatile between and within tumor types.

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Section: Model Equationmentioning

confidence: 99%

Section: Model Equationmentioning

confidence: 99%

Growth pattern Learning for Unsupervised Extraction of Cancer Kinetics

Axenie¹,

Kurz

2020

Preprint

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“…There has been little work in investigating the combination of dendritic cell vaccines with any type of androgen deprivation therapy. Portz and Kuang [27,36] examined immunotherapy in conjunction with IAD for prostate cancer which combined the Ideta et. al model [19] with the Kirschner and Panetta [24] model.…”

Section: Model Formulationmentioning

confidence: 99%

“…Our model is based on the Portz and Kuang [27,36] model described above with some appropriate modifications. Their results showed that adding dendritic cell vaccines resulted in an increase in time to androgen independent relapse.…”

Section: Model Formulationmentioning

confidence: 99%

Global dynamics of a model of joint hormone treatment with dendritic cell vaccine for prostate cancer

Rutter

Kuang

2017

Discrete &Amp; Continuous Dynamical Systems - B

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Advanced prostate cancer is often treated by androgen deprivation therapy, which is initially effective but gives rise to fatal treatment-resistant cancer. Intermittent androgen deprivation therapy improves the quality of life of patients and may delay resistance towards treatment. Immunotherapy alters the bodies immune system to help fight cancer and has proven effective in certain types of cancer. We propose a model incorporating androgen deprivation therapy (intermittent and continual) in conjunction with dendritic cell vaccine immunotherapy. Simulations are run to determine the sensitivity of cancer growth to dendritic cell vaccine therapy administration schedule. We consider the limiting case where dendritic cells are administered continuously and perform analysis on the full model and the limiting cases of the model to determine necessary conditions for global stability of cancer eradication.2010 Mathematics Subject Classification. Primary: 92C50, 34D20; Secondary: 34D23.

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“…In order to induce tumor formation, the progeny of the tumor-originating cell must not go extinct but has to establish within the tissue. This establishment is achieved by clonal expansion to a sufficiently large cell population [9]. For some tissues, there is experimental evidence that this establishment is characterized by an outcompetition of wild-type cells within the homeostatic range of competition.…”

Section: Introductionmentioning

confidence: 99%

Patterns of tumor progression predict small and tissue-specific tumor-originating niches

Buder

Deutsch

Klink

et al. 2018

Preprint

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Cancer development is a multistep process in which cells increase in malignancy through progressive alterations. The early phase of this process is hardly observable which aggravates an understanding of later tumor development. We shed light on this initial phase with a cell-based stochastic model calibrated with epidemiological data from the tissue scale. Our model allows to estimate the number of tumor cells needed for tumor formation in human tissues based on data on the diagnosed ratios of benign and malignant tumors. We find that the minimal number of cells needed for tumor formation is surprisingly small and largely depends on the tissue type. Our results point towards the existence of tumor-originating niches in which the fate of tumor development is early decided. Our estimate for the human 1/16 colon agrees well with the size of the stem cell niche in colonic crypts. Our estimates might help to identify the tumor-originating cell type, e.g. our analysis suggests for glioblastoma that the tumors originate from a cell type competing in a range of 300 -1900 cells. SummaryWe estimate the number of tumor cells needed for tumor formation in human tissues and propose the existence of small and tissue-specific tumor-originating niches which might help to find tumor-originating cell types, in particular in glioblastoma.

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Introduction to Mathematical Oncology

Cited by 52 publications

References 0 publications

Growth pattern Learning for Unsupervised Extraction of Cancer Kinetics

Growth pattern Learning for Unsupervised Extraction of Cancer Kinetics

Global dynamics of a model of joint hormone treatment with dendritic cell vaccine for prostate cancer

Patterns of tumor progression predict small and tissue-specific tumor-originating niches

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