Mathematical modelling of prostate cancer growth and its application to hormone therapy

Tanaka, Gouhei; Hirata, Yoshito; Goldenberg, S. Larry; Bruchovsky, Nicholas; Aihara, Kazuyuki

doi:10.1098/rsta.2010.0221

Cited by 92 publications

(92 citation statements)

References 38 publications

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“…[14][15][16][17][18][19] The model of Hirata et al 17 reproduces the actual quantitative changes in the tumor marker, prostate specific antigen ͑PSA͒. With this model, we were able to approximate conditions for both averting and delaying relapse, but we did not obtain the optimal scheduling of the on-and off-treatment periods of IAS.…”

Section: Introductionmentioning

confidence: 95%

Hybrid optimal scheduling for intermittent androgen suppression of prostate cancer

Hirata¹,

Bernardo²,

Bruchovsky³

et al. 2010

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We propose a method for achieving an optimal protocol of intermittent androgen suppression for the treatment of prostate cancer. Since the model that reproduces the dynamical behavior of the surrogate tumor marker, prostate specific antigen, is piecewise linear, we can obtain an analytical solution for the model. Based on this, we derive conditions for either stopping or delaying recurrent disease. The solution also provides a design principle for the most favorable schedule of treatment that minimizes the rate of expansion of the malignant cell population. © 2010 American Institute of Physics. ͓doi:10.1063/1.3526968͔ Drug resistance is a critical factor in limiting the success of treating various types of malignancy. In the case of prostate cancer, hormonal therapy results in a significant response in about 95% of patients at the initiation of treatment. Despite impressive responses, such treatment, when applied on a continuous basis is not curative and eventually culminates in life-threatening androgenindependent disease. In contrast, intermittent hormone therapy with alternating on-and off-treatment periods is a possible clinical strategy to delay progression to a hormone refractory state. Despite extensive clinical experience with this approach, little or no information is available to guide decisions concerning the ideal protocol for any given patient. In this paper, we employ the mathematical model recently described by Hirata et al.17 to design and validate a protocol that optimizes the on-and off-scheduling of intermittent androgen suppression in the treatment of prostate cancer. We show that an optimal schedule can be obtained in terms of an on-off feedback control action that aims to minimize the expanding rate of tumor growth. Our formula is based on a retrospective analysis, and accordingly, its utility will have to be confirmed in a prospective clinical trial.

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Section: Introductionmentioning

confidence: 95%

Hybrid optimal scheduling for intermittent androgen suppression of prostate cancer

Hirata¹,

Bernardo²,

Bruchovsky³

et al. 2010

Chaos: An Interdisciplinary Journal of Nonlinear Science

Self Cite

View full text Add to dashboard Cite

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“…To avoid this separation of models and to be able to describe the effects of treatments on a long period of time, hybrid models using switches have been developed. The model by Tanaka et al (2010) [35] integrates in this way the alternation of on and off treatment phases on a continuous model of tumour growth dynamics involving different cell types. The model gives insights to specifically treat prostate cancer.…”

Section: Intricate Modelsmentioning

confidence: 99%

Hybrid Modelling in Biology: a Classification Review

Stéphanou

Volpert

2015

Math. Model. Nat. Phenom.

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Abstract. This paper presents a general review on hybrid modelling which is about to become ubiquitous in biological and medical modelling. Hybrid modelling is classically defined as the coupling of a continuous approach with a discrete one, in order to model a complex phenomenon that cannot be described in a standard homogeneous way mainly due to its inherent multiscale nature. In fact, hybrid modelling can be more than that since any types of coupled formalisms qualify as being hybrid. This review first presents the evolution and current context of this modelling approach. It then proposes a classification of the models through three different types that relate to the nature and level of coupling of the formalisms used.

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“…At present, there are no effective therapies available for curing or controlling the androgen-independent stage of prostate cancer, due to the high rate of apoptosis resistance. The primary therapeutic modalities used to treat prostate cancer are surgery, radiation and hormone therapy (3,4). These modalities have been demonstrated to have certain curative effects on early-stage prostate cancer; however, they have various limitations, including injury to the surrounding normal tissues, drug resistance and tumor recurrence (4)(5)(6).…”

Section: Introductionmentioning

confidence: 99%

Liposome-mediated transfection of wild-type P53 DNA into human prostate cancer cells is improved by low-frequency ultrasound combined with microbubbles

Bai

Zhang

et al. 2016

Oncology Letters

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Abstract. Prostate cancer is a common type of cancer in elderly men. The aim of the present study was to evaluate the effects of ultrasound exposure in combination with SonoVue microbubbles on liposome-mediated transfection of wild-type P53 genes into human prostate cancer cells. PC-3 human prostate cancer cells were exposed to ultrasound; duty cycle was controlled at 20% (2 sec on, 8 sec off) for 5 min with and without SonoVue microbubble echo-contrast agent using a digital sonifier (frequency, 21 kHz; intensity, 46 mW/cm 2 ). The cells were divided into eight groups, as follows: Group A (SonoVue + wild-type P53), group B (ultrasound + wild-type P53), group C (SonoVue + ultrasound + wild-type P53), group D (liposome + wild-type P53), group E (liposome + SonoVue + wild-type P53), group F (liposome + wild-type P53 + ultrasound), group G (liposome + wild-type P53 + ultrasound + SonoVue) and the control group (wild-type P53). Following treatment, a hemocytometer was used to measure cell lysis, reverse transcription-quantitative polymerase chain reaction and western blotting were performed to detect P53 gene transfection efficiency, Cell Counting Kit-8 was employed to reveal cell proliferation and Annexin V/propidium iodide staining was used to determine cell apoptosis. Cell lysis was minimal in each group. Wild-type P53 gene and protein expression were significantly increased in the PC-3 cells in group G compared with the control and all other groups (P<0.01). Cell proliferation was significantly suppressed in group G compared with the control group and all other groups (P<0.01). Cell apoptosis levels in group G were significantly improved compared with the control group and all other groups (P<0.01). Thus, the results of the present study indicate that the use of low-frequency and low-energy ultrasound in combination with SonoVue microbubbles may be a potent physical method for increasing liposome gene delivery efficiency.

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Mathematical modelling of prostate cancer growth and its application to hormone therapy

Cited by 92 publications

References 38 publications

Hybrid optimal scheduling for intermittent androgen suppression of prostate cancer

Hybrid optimal scheduling for intermittent androgen suppression of prostate cancer

Hybrid Modelling in Biology: a Classification Review

Liposome-mediated transfection of wild-type P53 DNA into human prostate cancer cells is improved by low-frequency ultrasound combined with microbubbles

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