Piecewise affine systems modelling for optimizing hormone therapy of prostate cancer

Suzuki, Taiji; Bruchovsky, Nicholas; Aihara, Kazuyuki

doi:10.1098/rsta.2010.0220

Cited by 34 publications

(32 citation statements)

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“…We infer that such an approach will be of diagnostic and prognostic benefit in a clinical setting. For this purpose, the optimal control method would help to provide insight into the best scheduling of hormone therapy (Suzuki et al 2010).…”

Section: Discussionmentioning

confidence: 99%

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

Tanaka

Hirata

Goldenberg³

et al. 2010

Phil. Trans. R. Soc. A.

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Hormone therapy in the form of androgen deprivation is a major treatment for advanced prostate cancer. However, if such therapy is overly prolonged, tumour cells may become resistant to this treatment and result in recurrent fatal disease. Long-term hormone deprivation also is associated with side effects poorly tolerated by patients. In contrast, intermittent hormone therapy with alternating on-and off-treatment periods is a possible clinical strategy to delay progression to hormone-refractory disease with the advantage of reduced side effects during the off-treatment periods. In this paper, we first overview previous studies on mathematical modelling of prostate tumour growth under intermittent hormone therapy. The model is categorized into a hybrid dynamical system because switching between on-treatment and off-treatment intervals is treated in addition to continuous dynamics of tumour growth. Next, we present an extended model of stochastic differential equations and examine how well the model is able to capture the characteristics of authentic serum prostate-specific antigen (PSA) data. We also highlight recent advances in time-series analysis and prediction of changes in serum PSA concentrations. Finally, we discuss practical issues to be considered towards establishment of mathematical model-based tailor-made medicine, which defines how to realize personalized hormone therapy for individual patients based on monitored serum PSA levels.

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Section: Discussionmentioning

confidence: 99%

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

Tanaka

Hirata

Goldenberg³

et al. 2010

Phil. Trans. R. Soc. A.

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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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“…The second topic of cancer and its treatment are considered in three articles by Osborne et al (2010), Tanaka et al (2010) and Suzuki et al (2010) Osborne et al (2010) focus on cancer dynamics of a colorectal crypt in colorectal cancer. Since cancer originates from a mutation initially creating a single abnormal cell, there exists a problem of small numbers of cells, which is different from that of small copy numbers of proteins and mRNAs discussed in Singh & Hespanha (2010).…”

Section: Hybrid Dynamical Systems In Biology and Medicinementioning

confidence: 99%

“…Typical examples of such discontinuities are threshold-triggered firing in neurons (Izhikevich 2010), on-off switching of gene expression by a transcription factor (Imura et al 2010;Perkins et al 2010;Singh & Hespanha 2010), division in cells (Chen et al 2004;Battogtokh et al 2006;Osborne et al 2010) and certain types of chronotherapy for prostate cancer (Guo et al 2008;Ideta et al 2008;Shimada & Aihara 2008;Tanaka et al 2008Tanaka et al , 2010Hirata et al 2010;Suzuki et al 2010). Hence, the second aim of this Theme Issue is to discuss recent studies which apply hybrid dynamical systems to the fields of biology and medicine, through the nine articles with a variety of topics; this should stimulate applications of hybrid systems modelling to other research areas as well.…”

Section: Nonlinear Dynamics and Mathematical Modellingmentioning

confidence: 99%

“…Thus, the mathematical modelling of hybrid dynamical systems should also be considered from the perspective of time and space; that is, the continuous and discrete structure of time and space. Tanaka et al (2010) and Suzuki et al (2010) focus on the hybrid systems modelling of prostate cancer and its treatment. Since prostate tumour growth is sensitive to the male sexual hormone or androgen, at least in its early state, hormone therapy is quite effective.…”

Section: Hybrid Dynamical Systems In Biology and Medicinementioning

confidence: 99%

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Theory of hybrid dynamical systems and its applications to biological and medical systems

Aihara

Suzuki

2010

Phil. Trans. R. Soc. A.

Self Cite

106

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In this introductory article, we survey the contents of this Theme Issue. This Theme Issue deals with a fertile region of hybrid dynamical systems that are characterized by the coexistence of continuous and discrete dynamics. It is now well known that there exist many hybrid dynamical systems with discontinuities such as impact, switching, friction and sliding. The first aim of this Issue is to discuss recent developments in understanding nonlinear dynamics of hybrid dynamical systems in the two main theoretical fields of dynamical systems theory and control systems theory. A combined study of the hybrid systems dynamics in the two theoretical fields might contribute to a more comprehensive understanding of hybrid dynamical systems. In addition, mathematical modelling by hybrid dynamical systems is particularly important for understanding the nonlinear dynamics of biological and medical systems as they have many discontinuities such as threshold-triggered firing in neurons, on-off switching of gene expression by a transcription factor, division in cells and certain types of chronotherapy for prostate cancer. Hence, the second aim is to discuss recent applications of hybrid dynamical systems in biology and medicine. Thus, this Issue is not only general to serve as a survey of recent progress in hybrid systems theory but also specific to introduce interesting and stimulating applications of hybrid systems in biology and medicine. As the introduction to the topics in this Theme Issue, we provide a brief history of nonlinear dynamics and mathematical modelling, different mathematical models of hybrid dynamical systems, the relationship between dynamical systems theory and control systems theory, examples of complex behaviour in a simple neuron model and its variants, applications of hybrid dynamical systems in biology and medicine as a road map of articles in this Theme Issue and future directions of hybrid systems modelling.Keywords: hybrid dynamical systems; mathematical modelling; biological systems; medical systems; nonlinear dynamics; control Nonlinear dynamics and mathematical modellingThe history of natural science can be traced back to Isaac Newton in the seventeenth century. He formulated equations relating force and motion and co-invented calculus. This seminal work inaugurated the field of dynamical systems. His laws of force and motion are also the origin of mathematical modelling of dynamical phenomena in this world. Because calculus generally hates discontinuities and instabilities, most classical studies of dynamical systems and mathematical modelling concentrated on solutions that were smooth and stable. The universe was thus conceived of as a precision machine with smoothness and stability; based on the initial conditions, one could accurately predict future behaviour such as that of planets orbiting the Sun or that of a pendulum clock. However, in the 1960s and 1970s, 'catastrophe theory' (Thom 1975) and 'chaos theory' (Li & Yorke 1975;May 1976) were formulated as special branches of dynamical syst...

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Piecewise affine systems modelling for optimizing hormone therapy of prostate cancer

Cited by 34 publications

References 24 publications

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

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

Hybrid optimal scheduling for intermittent androgen suppression of prostate cancer

Theory of hybrid dynamical systems and its applications to biological and medical systems

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