From cell population models to tumor control probability: Including cell cycle effects

Hillen, Thomas; Vries, Gerda de; Gong, Jiafen; Finlay, Chris

doi:10.3109/02841861003631487

Cited by 23 publications

(29 citation statements)

References 32 publications

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“…Note that since active cells are more radiosensitive, we have h A ( t ) > h Q ( t ). The original model of Dawson and Hillen have been taken and extended to describe more complex systems or models with more compartments [25, 32, 59, 68]. Analysis of Dawson and Hillen active-quiescent radiation model and its comparison to LQ model confirms that a larger α / β ratio relates to a fast cell cycle and indicates the presence of a significant quiescent compartment, while a smaller ratio is associated with a slow cell cycle [23].…”

Section: Modeling and Optimization In Radiotherapymentioning

confidence: 99%

Optimal treatment and stochastic modeling of heterogeneous tumors

Badri

Leder

2016

Biol Direct

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In this work we review past articles that have mathematically studied cancer heterogeneity and the impact of this heterogeneity on the structure of optimal therapy. We look at past works on modeling how heterogeneous tumors respond to radiotherapy, and take a particularly close look at how the optimal radiotherapy schedule is modified by the presence of heterogeneity. In addition, we review past works on the study of optimal chemotherapy when dealing with heterogeneous tumors.Reviewers: This article was reviewed by Thomas McDonald, David Axelrod, and Leonid Hanin.

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Section: Modeling and Optimization In Radiotherapymentioning

confidence: 99%

Optimal treatment and stochastic modeling of heterogeneous tumors

Badri

Leder

2016

Biol Direct

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“…Naturally, such analysis can be extended to weekends off schedules. Table 2 lists typical prostate cancer parameters used in our simulations: the initial number of tumour cells (active and quiescent ones), the net mean rates for mitosis   0 0 N  and migration  (both ones discounted   from natural death rates in the active and quiescent compartments, respectively, as in reference [3]) and the parameters i  and i  related to the radiosensitivities in the compartment. The chosen parameters are the same ones as used by Gong et al [6] when studying the DH two-compartment model.…”

Section: Maxmentioning

confidence: 99%

“…Prostate tumours have different radiosensitivities [20] (and thus react differently to the treatment) since cancer cells properties differ from one tumour to another and even in the same tumour. Nevertheless, cells in the same compartment of the model are considered to be identical [3].…”

Section: Maxmentioning

confidence: 99%

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ROC Analysis in Radiotherapy: A TCP Model-Based Test

Santos

Neves²

2013

OJAppS

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Several mathematical models have been proposed to describe the dynamics of irradiated cancer cells and to evaluate the tumour control probability (TCP). In this article, we propose a TCP model-based statistical test for predicting the outcome of a radiation treatment. We determine the foresight capability of prostate tumour erradication (cure) from Monte Carlo simulations of the Dawson-Hillen TCP model. We construct the receiver operating characteristic (ROC) curves of the test from the probability distributions of the fraction of remaining tumour cells for simulated experiments that evolve either to cure or non-cure. Simulations show that a similar procedure may be applicable to clinical data. Results suggest that the evaluation of tumour sizes after the treatment has started may be used for short-term prognosis.

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“…The mathematical framework comes directly from ecological applications, but the interpretations, and some of the details are specific to cancer modelling. This direction of research has blossomed in beautiful theories on brith-death processes and branching processes, which are able to include cell cycle dynamics and differential radiosensitivities depending on the cell cycle state (see [22,25,26,31,43,61,66]). In a recent PhD thesis, Gong [21] included cancer stem cells into the TCP models and she confirmed that it is critical to control the stem cells for treatment to be successful.…”

Section: Tumor Control and Treatmentmentioning

confidence: 99%

Mathematical Ecology of Cancer

Hillen

Lewis

2014

Managing Complexity, Reducing Perplexity

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It is an emerging understanding that cancer does not describe one disease, or one type of aggressive cell, but, rather, a complicated interaction of many abnormal features and many different cell types, which is situated in a heterogeneous habitat of normal tissue. Hence, as proposed by Gatenby, and Merlo et al., cancer should be seen as an ecosystem; issues such as invasion, competition, predator-prey interaction, mutation, selection, evolution and extinction play an important role in determining outcomes. It is not surprising that many methods from mathematical ecology can be adapted to the modeling of cancer. This paper is a statement about the important connections between ecology and cancer modelling. We present a brief overview about relevant similarities and then focus on three aspects; treatment and control, mutations and evolution, and invasion and metastasis. The goal is to spark curiosity and to bring together mathematical oncology and mathematical ecology to initiate cross fertilization between these fields. We believe that, in the long run, ecological methods and models will enable us to move ahead in the design of treatment to fight this devastating disease.

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From cell population models to tumor control probability: Including cell cycle effects

Abstract: The cell cycle can be understood as the sequestration of cells in the quiescent compartment, where they are less sensitive to radiation. We suggest that our model can be used in combination with synchronization methods to optimize treatment timing.

Cited by 23 publications

References 32 publications

Optimal treatment and stochastic modeling of heterogeneous tumors

Optimal treatment and stochastic modeling of heterogeneous tumors

ROC Analysis in Radiotherapy: A TCP Model-Based Test

Mathematical Ecology of Cancer

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