Bifurcation analysis on a hybrid systems model of intermittent hormonal therapy for prostate cancer

ERATO Aihara Complexity Modelling Project, JST, Tokyo 151-0065, Japan
Physica D Nonlinear Phenomena (Impact Factor: 1.64). 10/2008; 237(20):2616-2627. DOI: 10.1016/j.physd.2008.03.044


Hybrid systems are widely used to model dynamical phenomena that are characterized by interplay between continuous dynamics and discrete events. An example of biomedical application is modeling of disease progression of prostate cancer under intermittent hormonal therapy, where continuous tumor dynamics is switched by interruption and reinstitution of medication. In the present paper, we study a hybrid systems model representing intermittent androgen suppression (IAS) therapy for advanced prostate cancer. Intermittent medication with switching between on-treatment and off-treatment periods is intended to possibly prevent a prostatic tumor from developing into a hormone-refractory state and is anticipated as a possible strategy for delaying or hopefully averting a cancer relapse which most patients undergo as a result of long-term hormonal suppression. Clinical efficacy of IAS therapy for prostate cancer is still under investigation but at least worth considering in terms of reduction of side effects and economic costs during off-treatment periods. In the model of IAS therapy, it depends on some clinically controllable parameters whether a relapse of prostate cancer occurs or not. Therefore, we examine nonlinear dynamics and bifurcation structure of the model by exploiting a numerical method to clarify bifurcation sets in the hybrid system. Our results suggest that adjustment of the normal androgen level in combination with appropriate medication scheduling could enhance the possibility of relapse prevention. Moreover, a two-dimensional piecewise-linear system reduced from the original model highlights the origin of nonlinear phenomena specific to the hybrid system.

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Available from: Gouhei Tanaka,
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    • "In this paper, we used the criterion of Type (i) such that the origin is asymptotically stabilized. We might be able to relax the criterion so that Type (i) can also include stable periodic solutions and chaotic solutions, which are constrained within bounded regions as discussed in Tanaka et al. (2008). Such relaxation is a possible topic of future research. "
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    ABSTRACT: If a mathematical model is to be used in the diagnosis, treatment, or prognosis of a disease, it must describe the inherent quantitative dynamics of the state. An ideal candidate disease is prostate cancer owing to the fact that it is characterized by an excellent biomarker, prostate-specific antigen (PSA), and also by a predictable response to treatment in the form of androgen suppression therapy. Despite a high initial response rate, the cancer will often relapse to a state of androgen independence which no longer responds to manipulations of the hormonal environment. In this paper, we present relevant background information and a quantitative mathematical model that potentially can be used in the optimal management of patients to cope with biochemical relapse as indicated by a rising PSA.
    Journal of Molecular Cell Biology 05/2012; 4(3):127-32. DOI:10.1093/jmcb/mjs020 · 6.77 Impact Factor
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    • "At the same time, it can be used in biomedical area, such as modeling the disease progression of prostate cancer under intermittent hormonal therapy, where continuous tumor dynamics is switched by interruption and reinstitution of medication. In fact, intermittent therapy regimen has already successfully used for prostate cancer [12]–[14]. It can delay or prevent the cancer relapse. "
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    ABSTRACT: This paper studies the dynamics of the Hepatitis B virus (HBV) model with intermittent antiviral therapy. We first propose a mathematical model of HBV and then analyze its qualitative and dynamical properties with a new treatment therapy. Combining with the clinical data and theoretical analysis, we show that the intermittent antiviral therapy regimen is one of optimal strategies to treat this kind of complex disease. There are two mainly advantages on this therapy. Firstly, it can delay the drug resistance. Secondly, it can reduce the duration of treatment time comparing with the long term continuous therapy, thereby reducing the adverse side effect. Our results clear provides a new way to treat the HBV disease.
    Systems Biology (ISB), 2011 IEEE International Conference on; 10/2011
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    • "The model is capable of replicating three different kinds of qualitative behaviours depending on the parameter values, i.e. a relapse without undergoing an off-treatment period like that in CAS, a relapse after several cycles of ontreatment and off-treatment periods and prevention of a relapse repeating the cycles forever. Phase transitions between the regimes of relapse and relapse prevention in the IAS therapy model were revealed from a mathematical viewpoint by numerical bifurcation analyses (Tanaka et al. 2008). It is notable that a grazing bifurcation of a limit cycle and a chaotic attractor, which cannot be observed in ordinary smooth dynamical systems, plays a crucial role in the phase transition (Tanaka et al. 2009). "
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    ABSTRACT: 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.
    Philosophical Transactions of The Royal Society A Mathematical Physical and Engineering Sciences 11/2010; 368(1930):5029-44. DOI:10.1098/rsta.2010.0221 · 2.15 Impact Factor
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