Yoshito Hirata

Development of a mathematical model that predicts the outcome of hormone therapy for prostate cancer

We propose a mathematical model that quantitatively reproduces the dynamics of the serum prostate-specific antigen (PSA) level under intermittent androgen suppression (IAS) for prostate cancer. Taking into account the biological knowledge that there are reversible and irreversible changes in a malignant cell, we constructed a piecewise-linear dynamical model where the testosterone dynamics are modelled with rapid shifts between two levels, namely the normal and castrate concentrations of the male hormone. The validity of the model was supported by patient data obtained from a clinical trial of IAS. It accurately reproduced the kinetics of the therapeutic reduction of PSA and predicted the future nadir level correctly. The coexistence of reversible and irreversible changes within the malignant cell provided the best explanation of early progression to androgen independence. Finally, since the model identified patients for whom IAS was effective, it potentially offers a novel approach to individualized therapy requiring the input of time sequence values of PSA only.

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

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.

Forecasting large aftershocks within one day after the main shock

Forecasting the aftershock probability has been performed by the authorities to mitigate hazards in the disaster area after a main shock. However, despite the fact that most of large aftershocks occur within a day from the main shock, the operational forecasting has been very difficult during this time-period due to incomplete recording of early aftershocks. Here we propose a real-time method for efficiently forecasting the occurrence rates of potential aftershocks using systematically incomplete observations that are available in a few hours after the main shocks. We demonstrate the methods utility by retrospective early forecasting of the aftershock activity of the 2011 Tohoku-Oki Earthquake of M9.0 in Japan. Furthermore, we compare the results by the real-time data with the compiled preliminary data to examine robustness of the present method for the aftershocks of a recent inland earthquake in Japan.

Quantifying Collective Attention from Tweet Stream

Online social media are increasingly facilitating our social interactions, thereby making available a massive “digital fossil” of human behavior. Discovering and quantifying distinct patterns using these data is important for studying social behavior, although the rapid time-variant nature and large volumes of these data make this task difficult and challenging. In this study, we focused on the emergence of “collective attention” on Twitter, a popular social networking service. We propose a simple method for detecting and measuring the collective attention evoked by various types of events. This method exploits the fact that tweeting activity exhibits a burst-like increase and an irregular oscillation when a particular real-world event occurs; otherwise, it follows regular circadian rhythms. The difference between regular and irregular states in the tweet stream was measured using the Jensen-Shannon divergence, which corresponds to the intensity of collective attention. We then associated irregular incidents with their corresponding events that attracted the attention and elicited responses from large numbers of people, based on the popularity and the enhancement of key terms in posted messages or “tweets.” Next, we demonstrate the effectiveness of this method using a large dataset that contained approximately 490 million Japanese tweets by over 400,000 users, in which we identified 60 cases of collective attentions, including one related to the Tohoku-oki earthquake. “Retweet” networks were also investigated to understand collective attention in terms of social interactions. This simple method provides a retrospective summary of collective attention, thereby contributing to the fundamental understanding of social behavior in the digital era.

Amoeba-based Chaotic Neurocomputing: Combinatorial Optimization by Coupled Biological Oscillators

We demonstrate a neurocomputing system incorporating an amoeboid unicellular organism, the true slime mold Physarum, known to exhibit rich spatiotemporal oscillatory behavior and sophisticated computational capabilities. Introducing optical feedback applied according to a recurrent neural network model, we induce that the amoeba’s photosensitive branches grow or degenerate in a network-patterned chamber in search of an optimal solution to the traveling salesman problem (TSP), where the solution corresponds to the amoeba’s stably relaxed configuration (shape), in which its body area is maximized while the risk of being illuminated is minimized.Our system is capable of reaching the optimal solution of the four-city TSP with a high probability. Moreover, our system can find more than one solution, because the amoeba can coordinate its branches’ oscillatory movements to perform transitional behavior among multiple stable configurations by spontaneously switching between the stabilizing and destabilizing modes. We show that the optimization capability is attributable to the amoeba’s fluctuating oscillatory movements. Applying several surrogate data analyses, we present results suggesting that the amoeba can be characterized as a set of coupled chaotic oscillators.

Hybrid optimal scheduling for intermittent androgen suppression of prostate cancer

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.

Characterizing global evolutions of complex systems via intermediate network representations

Recent developments in measurement techniques have enabled us to observe the time series of many components simultaneously. Thus, it is important to understand not only the dynamics of individual time series but also their interactions. Although there are many methods for analysing the interaction between two or more time series, there are very few methods that describe global changes of the interactions over time. Here, we propose an approach to visualise time evolution for the global changes of the interactions in complex systems. This approach consists of two steps. In the first step, we construct a meta-time series of networks. In the second step, we analyse and visualise this meta-time series by using distance and recurrence plots. Our two-step approach involving intermediate network representations elucidates the half-a-day periodicity of foreign exchange markets and a singular functional network in the brain related to perceptual alternations.

Quantitative mathematical modeling of PSA dynamics of prostate cancer patients treated with intermittent androgen suppression

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.

Estimating the ETAS model from an early aftershock sequence

Forecasting aftershock probabilities, as early as possible after a main shock, is required to mitigate seismic risks in the disaster area. In general, aftershock activity can be complex, including secondary aftershocks or even triggering larger earthquakes. However, this early forecasting implementation has been difficult because numerous aftershocks are unobserved immediately after the main shock due to dense overlapping of seismic waves. Here we propose a method for estimating parameters of the epidemic type aftershock sequence (ETAS) model from incompletely observed aftershocks shortly after the main shock by modeling an empirical feature of data deficiency. Such an ETAS model can effectively forecast the following aftershock occurrences. For example, the ETAS model estimated from the first 24 h data after the main shock can well forecast secondary aftershocks after strong aftershocks. This method can be useful in early and unbiased assessment of the aftershock hazard.

DEFINITION OF DISTANCE FOR MARKED POINT PROCESS DATA AND ITS APPLICATION TO RECURRENCE PLOT-BASED ANALYSIS OF EXCHANGE TICK DATA OF FOREIGN CURRENCIES

Recurrence plots are effective in analyzing nonstationary time series. Further, it is desirable to make the recurrence plot-based analysis applicable to marked point process data such as foreign exchange tick data. In this paper, we define a distance for marked point process data and establish the basis for further analyses. We also show that foreign exchange tick data have serial dependence using recurrence plots and the random shuffle surrogate method.