Tumour eradication by antiangiogenic therapy: analysis and extensions of the model by Hahnfeldt et al. (1999)

d’Onofrio, Alberto; Gandolfi, Alberto

doi:10.1016/j.mbs.2004.06.003

Cited by 167 publications

(162 citation statements)

References 32 publications

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“…This work validated the theory of dose escalation proposed by Norton and Simon [29,30]. D'Onofrio and Gandolfi [31] also considered a modified version of the mathematical model given in [26] in which they determined conditions that guarantee the eradication of the tumor under a protocol of periodic anti-angiogenic therapy.…”

Section: Introductionsupporting

confidence: 62%

An Optimal Control Approach for the Treatment of Solid Tumors with Angiogenesis Inhibitors

Glick

Mastroberardino

2017

Mathematics

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Abstract:Cancer is a disease of unregulated cell growth that is estimated to kill over 600,000 people in the United States in 2017 according to the National Institute of Health. While there are several therapies to treat cancer, tumor resistance to these therapies is a concern. Drug therapies have been developed that attack proliferating endothelial cells instead of the tumor in an attempt to create a therapy that is resistant to resistance in contrast to other forms of treatment such as chemotherapy and radiation therapy. In this study, a two-compartment model in terms of differential equations is presented in order to determine the optimal protocol for the delivery of anti-angiogenesis therapy. Optimal control theory is applied to the model with a range of anti-angiogenesis doses to determine optimal doses to minimize tumor volume at the end of a two week treatment and minimize drug toxicity to the patient. Applying a continuous optimal control protocol to our model of angiogenesis and tumor cell growth shows promising results for tumor control while minimizing the toxicity to the patients. By investigating a variety of doses, we determine that the optimal angiogenesis inhibitor dose is in the range of 10-20 mg/kg. In this clinically useful range of doses, good tumor control is achieved for a two week treatment period. This work shows that varying the toxicity of the treatment to the patient will change the optimal dosing scheme but tumor control can still be achieved.

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Section: Introductionsupporting

confidence: 62%

An Optimal Control Approach for the Treatment of Solid Tumors with Angiogenesis Inhibitors

Glick

Mastroberardino

2017

Mathematics

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“…To describe the interplay between the tumour and its vasculature, we adopt a family of models previously proposed (d 'Onofrio and Gandolfi 2009), which includes as particular cases the models in (Hahnfeldt et al 1999, Sachs et al 2001, d'Onofrio and Gandolfi 2004. In this family of models, we assume that (i) the carrying capacity of the tumour vasculature is simply proportional to the amount of vessels, and (ii) the specific growth rate of the tumour, V /V , and the specific "birth" rate of vessels depend on the ratio between the carrying capacity and the tumour size.…”

Section: A Family Of Models For the Tumour Growthmentioning

confidence: 99%

Chemotherapy of vascularised tumours: Role of vessel density and the effect of vascular “pruning”

d’Onofrio

Gandolfi

2010

Journal of Theoretical Biology

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“…Pharmacokinetic (PK) and pharmacodynamic (PD) models are used for the cytotoxic action of the chemotherapeutic agents on the cancer cells and for the hematological toxicities. We also can mention few optimization problems analyzed to determine optimal drug infusion schedules taking into account drug toxicity [6,7,20,40,[48][49][50]56]. Note that these articles studied the optimization of one anti-cancer therapy (chemotherapy, anti-angiogenic therapy, ...) or of combination of several ones.…”

Section: Introductionmentioning

confidence: 99%

Mathematical model of cancer growth controled by metronomic chemotherapies

et al. 2013

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Abstract. We propose in this article to compare the efficiency of two chemotherapeutic schedules: the traditional and the metronomic. For this, we develop a new mathematical model describing the growth dynamics of tumor and endothelial cells as well as the impact of molecules as oxygen or vascular endothelial growth factor on this dynamics. The model construction: biological assumptions, description of the equations and their discretization, constitutes the core of the article. Numerical experiments illustrate the expected behavior of the disease under the two chemotherapeutic schedules.Résumé. Nous proposons dans cet article de comparer l'action de deux protocoles d'administration de chimiothérapie. Pour cela, nous développons un nouveau modèle mathématique décrivant la dynamique de croissance de diverses cellules tumorales et endothéliales et l'impact sur cette dynamique de molécules comme l'oxygène et de facteurs de croissances endothéliales. La construction du modèle, a savoir les hypothèses biologiques sous-jacentes, la description deséquations et leur discrétisation constitue le coeur de cet article. Nous donnons quelques illustrations numériques de l'évolution de la maladie sous l'action des deux protocoles thérapeutiques et retrouvons les résultats attendus par les oncologues.

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Tumour eradication by antiangiogenic therapy: analysis and extensions of the model by Hahnfeldt et al. (1999)

Cited by 167 publications

References 32 publications

An Optimal Control Approach for the Treatment of Solid Tumors with Angiogenesis Inhibitors

An Optimal Control Approach for the Treatment of Solid Tumors with Angiogenesis Inhibitors

Chemotherapy of vascularised tumours: Role of vessel density and the effect of vascular “pruning”

Mathematical model of cancer growth controled by metronomic chemotherapies

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