Rates of growth of human neoplasms: Part II

Spratt, John S.; Meyer, John S.; Spratt, John A.

doi:10.1002/1096-9098(199601)61:1<68::aid-jso2930610102>3.0.co;2-e

Cited by 142 publications

(93 citation statements)

References 45 publications

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“…The carrying capacity of the tumour is taken to be 10 6 cells per unit volume because a tumour nodule contains about 10 5 -10 9 tumour cells [54]. The tumour growth rate was taken to be 0.26 day −1 because several experimental tumour growth models estimate it to be in the range of 0.1-1 [5].…”

Section: Tumour Growth and Carrying Capacitymentioning

confidence: 99%

Modelling the spatiotemporal dynamics of chemovirotherapy cancer treatment

Malinzi

Eladdadi

Sibanda

2017

Journal of Biological Dynamics

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Chemovirotherapy is a combination therapy with chemotherapy and oncolytic viruses. It is gaining more interest and attracting more attention in the clinical setting due to its effective therapy and potential synergistic interactions against cancer. In this paper, we develop and analyse a mathematical model in the form of parabolic nonlinear partial differential equations to investigate the spatiotemporal dynamics of tumour cells under chemovirotherapy treatment. The proposed model consists of uninfected and infected tumour cells, a free virus, and a chemotherapeutic drug. The analysis of the model is carried out for both the temporal and spatiotemporal cases. Travelling wave solutions to the spatiotemporal model are used to determine the minimum wave speed of tumour invasion. A sensitivity analysis is performed on the model parameters to establish the key parameters that promote cancer remission during chemovirotherapy treatment. Model analysis of the temporal model suggests that virus burst size and virus infection rate determine the success of the virotherapy treatment, whereas travelling wave solutions to the spatiotemporal model show that tumour diffusivity and growth rate are critical during chemovirotherapy. Simulation results reveal that chemovirotherapy is more effective and a good alternative to either chemotherapy or virotherapy, which is in agreement with the recent experimental studies. ARTICLE HISTORY

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Section: Tumour Growth and Carrying Capacitymentioning

confidence: 99%

Modelling the spatiotemporal dynamics of chemovirotherapy cancer treatment

Malinzi

Eladdadi

Sibanda

2017

Journal of Biological Dynamics

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“…In the second visit dataset, total SLD is a sum of target lesions, 32 mm+25 mm equals to 57 mm of thickness. And for non-target lesion calculating the SLD is not possible due to its unequivocal increase (Lavin et al, 1980;Spratt et al, 1996). The actual SLD is difference of volumes between two lesion and percentage change (Lavin and Flowerdew, 1980).…”

Section: 2375 Volumetric Measurement In Oncology Imaging Trials For mentioning

confidence: 99%

Importance of Volumetric Measurement Processes in Oncology Imaging Trials for Screening and Evaluation of Tumors as Per Response Evaluation Criteria in Solid Tumors

Vemuri¹,

Jarecha²,

Hwi³

et al. 2014

Asian Pacific Journal of Cancer Prevention

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“…The characteristics of the critical points in the discussed models rule out the possibility of tumor-load stabilization, which is sometimes observed experimentally [14,32,33]. Admittedly, cancer growth law is still a controversial phenomenon [6,21,26].…”

Section: The Function E(t) Decreases At the Beginning But The Same Imentioning

confidence: 99%

Critical-Point Analysis For Three-Variable Cancer Angiogenesis Models

Foryś

Kheifetz²,

Kogan

2005

Mathematical Biosciences and Engineering

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Abstract. We perform critical-point analysis for three-variable systems that represent essential processes of the growth of the angiogenic tumor, namely, tumor growth, vascularization, and generation of angiogenic factor (protein) as a function of effective vessel density. Two models that describe tumor growth depending on vascular mass and regulation of new vessel formation through a key angiogenic factor are explored. The first model is formulated in terms of ODEs, while the second assumes delays in this regulation, thus leading to a system of DDEs. In both models, the only nontrivial critical point is always unstable, while one of the trivial critical points is always stable. The models predict unlimited growth, if the initial condition is close enough to the nontrivial critical point, and this growth may be characterized by oscillations in tumor and vascular mass. We suggest that angiogenesis per se does not suffice for explaining the observed stabilization of vascular tumor size.

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Rates of growth of human neoplasms: Part II

Cited by 142 publications

References 45 publications

Modelling the spatiotemporal dynamics of chemovirotherapy cancer treatment

Modelling the spatiotemporal dynamics of chemovirotherapy cancer treatment

Importance of Volumetric Measurement Processes in Oncology Imaging Trials for Screening and Evaluation of Tumors as Per Response Evaluation Criteria in Solid Tumors

Critical-Point Analysis For Three-Variable Cancer Angiogenesis Models

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