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Hepatic epithelioid hemangioendothelioma is a rare neoplasm with a variable malignant potential and a high risk of recurrence. No general treatment guidelines have been established. Fortunately, we were able to minimize immunosuppressant after liver transplantation because of a full HLA‐matched case. There was no recurrence 1 year after treatment.

Hormone therapy is one of the popular therapeutic methods for prostate cancer. Intermittent androgen suppression (IAS) is the method which stops and resumes hormone therapy repeatedly. The efficacy of IAS differs depending on patients; both the cases have been reported where the relapse of cancer happened and did not happen, for the patients who had undergone IAS. For the patients who cannot avoid the relapse of cancer by IAS, we should delay the relapse of cancer as later as possible. Here we compared some practical methods of determining when to stop and restart hormone therapy for IAS using an existing mathematical model of prostate cancer. The method we suggest is to determine the ratio of on-treatment period and off-treatment period sparsely for each cycle, namely the “sparse search.” We also compared the performance of the sparse search with the exhaustive search and the model predictive control. We found that the sparse search can find a good treatment schedule without failure, and the computational cost is not so high compared to the exhaustive method. In addition, we focus on the model predictive control (MPC) method which has been applied to the scheduling of IAS in some existing studies. The MPC is computationary efficient, although it does not always find an optimal schedule in the numerical experiments here. We believe that the MPC method might be also promising because of its reasonable computational costs and its possibility of expanding of the model.

The chromatin conformation capture-related methods such as Hi-C have improved our understanding of nuclear architecture and organization in recent years. However, reconstruction of nuclear architecture from single-cell Hi-C (scHi-C) data is challenging due to limited information of DNA contacts obtained from a single cell. We have previously developed the Recurrence Plot-Based Reconstruction (RPR) method for reconstructing three dimensional (3D) genomic structure from Hi-C data of single haploid cells (1) and diploid cells (2). This algorithm is based on a recurrence plot, a tool of nonlinear time-series analysis for visualizing patterns within a time series (3, 4), and enables the reconstruction of a unique 3D chromosome architecture even from low-coverage DNA contact information. Here we used the RPR method to analyzing published scHi-C data of diploid cells derived from early-stage F1 hybrid embryos (5) as a proof-of-concept for understanding of global developmental changes in chromosomal architecture of early stage embryos. We found that paternal and maternal chromosomes become gradually intermingled from 1 cell to 64 cell stage, and that discrete chromosome territories are largely established between 8 cell and 64 cell stages. We also observed Rabl-like polarization of chromosomes from the 2-to 8-cell stages, but this polarization becomes mostly dissolved by the 64-cell stage. Rabl-like chromosome polarization precedes rod-like extension and parallel alignment of chromosomes, implicating the role of Rabl-like polarization in effective mixing of chromosomes before establishing chromosome territories. We also found cell-to-cell variability in chromatin configuration. A combination of scHi-C and RPR analyses can depict features of the 3D chromatin architecture of individual cells at different developmental stages during early embryogenesis.

Using a dataset of 150 patients treated with intermittent androgen suppression (IAS) through a fixed treatment schedule, we retrospectively designed a personalized treatment schedule mathematically for each patient. We estimated 100 sets of parameter values for each patient by randomly resampling each patient’s time points to take into account the uncertainty for observations of prostate specific antigen (PSA). Then, we identified 3 types and classified patients accordingly: in type (i), the relapse, namely the divergence of PSA, can be prevented by IAS; in type (ii), the relapse can be delayed by IAS later than by continuous androgen suppression (CAS); in type (iii) IAS was not beneficial and therefore CAS would have been more appropriate in the long run. Moreover, we obtained a treatment schedule of hormone therapy by minimizing the PSA of 3 years later in the worst case scenario among the 100 parameter sets by searching exhaustively all over the possible treatment schedules. If the most frequent type among 100 sets was type (i), the maximal PSA tended to be kept less than 100 ng/ml longer in IAS than in CAS, while there was no statistical difference for the other cases. Thus, mathematically personalized IAS should be studied prospectively.

We previously proposed, on theoretical grounds, that the cerebellum must regulate the dimensionality of its neuronal activity during motor learning and control to cope with the low firing frequency of inferior olive neurons, which form one of two major inputs to the cerebellar cortex. Such dimensionality regulation is possible via modulation of electrical coupling through the gap junctions between inferior olive neurons by inhibitory GABAergic synapses. In addition, we previously showed in simulations that intermediate coupling strengths induce chaotic firing of inferior olive neurons and increase their information carrying capacity. However, there is no in vivo experimental data supporting these two theoretical predictions. Here, we computed the levels of synchrony, dimensionality, and chaos of the inferior olive code by analyzing in vivo recordings of Purkinje cell complex spike activity in three different coupling conditions: carbenoxolone (gap junctions blocker), control, and picrotoxin (GABA-A receptor antagonist). To examine the effect of electrical coupling on dimensionality and chaotic dynamics, we first determined the physiological range of effective coupling strengths between inferior olive neurons in the three conditions using a combination of a biophysical network model of the inferior olive and a novel Bayesian model averaging approach. We found that effective coupling co-varied with synchrony and was inversely related to the dimensionality of inferior olive firing dynamics, as measured via a principal component analysis of the spike trains in each condition. Furthermore, for both the model and the data, we found an inverted U-shaped relationship between coupling strengths and complexity entropy, a measure of chaos for spiking neural data. These results are consistent with our hypothesis according to which electrical coupling regulates the dimensionality and the complexity in the inferior olive neurons in order to optimize both motor learning and control of high dimensional motor systems by the cerebellum., Author summary Computational theory suggests that the cerebellum must decrease the dimensionality of its neuronal activity to learn and control high dimensional motor systems effectively, while being constrained by the low firing frequency of inferior olive neurons, one of the two major source of input signals to the cerebellum. We previously proposed that the cerebellum adaptively controls the dimensionality of inferior olive firing by adjusting the level of synchrony and that such control is made possible by modulating the electrical coupling strength between inferior olive neurons. Here, we developed a novel method that uses a biophysical model of the inferior olive to accurately estimate the effective coupling strengths between inferior olive neurons from in vivo recordings of spike activity in three different coupling conditions. We found that high coupling strengths induce synchronous firing and decrease the dimensionality of inferior olive firing dynamics. In contrast, intermediate coupling strengths lead to chaotic firing and increase the dimensionality of the firing dynamics. Thus, electrical coupling is a feasible mechanism to control dimensionality and chaotic firing of inferior olive neurons. In sum, our results provide insights into possible mechanisms underlying cerebellar function and, in general, a biologically plausible framework to control the dimensionality of neural coding.

We review our studies on how to identify the most appropriate models of diseases, and how to determine their parameters in a quantitative manner given a short time series of biomarkers, using intermittent androgen deprivation therapy of prostate cancer as an example. Recently, it has become possible to estimate the specific parameters of individual patients within a reasonable time by employing the information concerning other previous patients as a prior.We discuss the importance of using multiple mathematical methods simultaneously to achieve a solid diagnosis and prognosis in the future practice of personalized medicine. Open image in new window

A 46-year-old man with severe back pain visited our hospital. Magnetic resonance imaging revealed extensive bone metastasis and rectal wall thickness. Colonoscopy revealed circumferential stenosis with edematous mucosa, suggesting colon cancer. However, histological findings of biopsy specimens revealed inflammatory cells but no malignant cells. The patient underwent endoscopic ultrasound, which demonstrated edematous wall thickness without destruction of the normal layer structure. After unsuccessful detection of neoplastic cells by boring biopsies, we performed endoscopic mucosal resection followed by boring biopsies that finally revealed signet ring cell carcinoma. Herein, we present a case and provide a review of the literature.

Intermittent androgen suppression (IAS) therapy is a class of hormonal treatment for prostate cancer, in which a drug-induced androgen deprivation can reduce the population of prostate cancer cells. In IAS therapy, drugs are administrated only in on-treatment periods that are separated intermittently by off-treatment periods. The presence of off-treatment periods may be beneficial for maintaining the sensitivity of the tumor cells to androgen deprivation. Thus, IAS can be superior to continuous androgen suppression (CAS) for delaying or possibly preventing relapse of a tumor. IAS therapy usually monitors the level of serum prostate-specific antigen (PSA), which is related to the population of tumor cells. Each on-treatment period begins when the PSA level is greater than an upper threshold; treatment results in a decrease in the PSA level. The on-treatment period is suspended when the PSA level falls below a lower threshold; the PSA level then rises again until the beginning of the next on-treatment period. To determine the transitions between on- and off-treatment periods, we propose a new IAS protocol that uses a model-based estimate of the state point in the phase space of the tumor dynamics. We show that the proposed protocol is effective if, in each of the on- and off-treatment periods, the tumor dynamics exhibits a saddle-point instability accompanied by a stable manifold. Mathematical analysis reveals that tumor dynamics can be controlled in a more effective and robust manner with the proposed protocol than with conventional IAS. We also discuss the clinical feasibility of the proposed protocol as an alternative to conventional IAS therapy.

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.

Intermittent androgen suppression is becoming a standard clinical option for patients who suffer from recurrence after an initial treatment of prostate cancer such as radiation therapy and radical prostatectomy. In the first mathematical model of intermittent androgen suppression (Ideta et al., 2008), the authors tried to control the trajectory of the model to a periodic orbit to enable patients to coexist with prostate cancer, even if it cannot be eradicated. Recently, we proposed a mathematical model capable of improving the quantitative reproduction of the behavior of prostate cancer under intermittent androgen suppression (Hirata et al., 2010a). Here we examine whether such a stable periodic orbit can be created for patients who eventually will have to experience the relapse of cancer at a later stage. By using a mathematical analysis, we found that the above model of Hirata et al. does not contain a non-zero periodic orbit that can be targeted for such patients, namely patients of type (ii) or type (iii) for whom intermittent androgen suppression cannot stabilize the origin where no cancer cells exist. This result might suggest that the patients must seek to delay the relapse as much as possible if the cancer cannot be eradicated. We further classify type (i) into subclasses where such a non-zero periodic orbit can either be stabilized or asymptotically stabilized.

When a physician decides on a treatment and its schedule for a specific patient, information gained from prior patients and experience in the past is taken into account. A more objective way to make such treatment decisions based on actual data would be useful to the clinician. Although there are many mathematical models proposed for various diseases, so far there is no mathematical method that accomplishes optimization of the treatment schedule using the information gained from past patients or “rapid learning” technology. In an attempt to use this approach, we integrate the information gained from patients previously treated with intermittent androgen suppression (IAS) with that from a current patient by first fitting the time courses of clinical data observed from the previously treated patients, then constructing the prior information of the parameter values of the mathematical model, and finally, maximizing the posterior probability for the parameters of the current patient using the prior information. Although we used data from prostate cancer patients, the proposed method is general, and thus can be applied to other diseases once an appropriate mathematical model is established for that disease.

Well-trained clinicians may be able to provide diagnosis and prognosis from very short biomarker series using information and experience gained from previous patients. Although mathematical methods can potentially help clinicians to predict the progression of diseases, there is no method so far that estimates the patient state from very short time-series of a biomarker for making diagnosis and/or prognosis by employing the information of previous patients. Here, we propose a mathematical framework for integrating other patients' datasets to infer and predict the state of the disease in the current patient based on their short history. We extend a machine-learning framework of “prediction with expert advice” to deal with unstable dynamics. We construct this mathematical framework by combining expert advice with a mathematical model of prostate cancer. Our model predicted well the individual biomarker series of patients with prostate cancer that are used as clinical samples.

Mathematical modelling is essential for personalizing intermittent androgen suppression, which was proposed to delay the relapse of prostate cancer by stopping and resuming the hormone therapy repeatedly than adopting the conventional continuous androgen suppression, or normal hormonal therapy. Although there are several mathematical models for intermittent androgen suppression, the performances of these mathematical models have not been compared sufficiently. In this paper, we compare the Hirata–Bruchovsky–Aihara model with the Portz–Kuang–Nagy model, two recently proposed models for intermittent androgen suppression. We fitted these mathematical models to the actual data of 17 patients and examined the dynamical behavior and prediction accuracy of these models. Although we found no significant difference between these models in terms of prediction accuracy, the Portz–Kuang–Nagy model could not reproduce the relapse under the simulation condition assuming the continuous androgen suppression. Thus, the results suggest that the Hirata–Bruchovsky–Aihara model is more useful than the Portz–Kuang–Nagy model when we attempt to compare the therapeutic efficiencies of intermittent suppression and continuous androgen suppression.

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 method's 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.

We review our recent work on chaos in neurons and its application to neural networks from perspective of chaos engineering. Especially, we analyze a dataset of a squid giant axon by newly combining our previous work of identifying Devaney's chaos with surrogate data analysis, and show that an axon can behave chaotically. Based on this knowledge, we use a chaotic neuron model to investigate possible information processing in the brain.

Computational methods have complemented experimental and clinical neursciences and led to improvements in our understanding of the nervous systems in health and disease. In parallel, neuromodulation in form of electric and magnetic stimulation is gaining increasing acceptance in chronic and intractable diseases. In this paper, we firstly explore the relevant state of the art in fusion of both developments towards translational computational neuroscience. Then, we propose a strategy to employ the new theoretical concept of dynamical network biomarkers (DNB) in episodic manifestations of chronic disorders. In particular, as a first example, we introduce the use of computational models in migraine and illustrate on the basis of this example the potential of DNB as early-warning signals for neuromodulation in episodic migraine., 13 pages, 5 figures

Resting-state study is a useful tool to investigate the brain activity related to cognitive abilities in children because it may be difficult for children to perform some experimental tasks. In the present study, we report a preliminary examination to associate the resting-state neuromagnetic signals from magnetoencephalogram (MEG) with cognitive abilities in children. We applied a non-linear time-series analysis for 90-s resting-state neuromagnetic signals and estimated interdependency of two channels of MEG signals. Then we examined the relation between the magnitudes of interdependency and the cognitive abilities and ages. Although we found some indications of age differences in the lateralization of interdependency, the results highlighted several limiting factors in measuring cognitive abilities and resting-state neuromegnetic signals in children and suggested that further elaboration of devices, procedures, and analysis would be warranted.

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.

In this review, we summarize our recently developed mathematical models that predict the effects of intermittent androgen suppression therapy on prostate cancer (PCa). Although hormone therapy for PCa shows remarkable results at the beginning of treatment, cancer cells frequently acquire the ability to grow without androgens during long-term therapy, resulting in an eventual relapse. To circumvent hormone resistance, intermittent androgen suppression was investigated as an alternative treatment option. However, at the present time, it is not possible to select an optimal schedule of on- and off-treatment cycles for any given patient. In addition, clinical trials have revealed that intermittent androgen suppression is effective for some patients but not for others. To resolve these two problems, we have developed mathematical models for PCa under intermittent androgen suppression. The mathematical models not only explain the mechanisms of intermittent androgen suppression but also provide an optimal treatment schedule for the on- and off-treatment periods.

This talk is to review our recent work on mathematical modeling of prostate cancer and its application to hormonal therapy of intermittent androgen suppression. First, we model the tumor growth of prostate cancer composed of a mixed dynamical assembly of androgen‐dependent and androgen‐independent cancer cells. Then, we introduce the intermittent androgen suppression to the model as feedback control with monitoring the serum prostate‐specific antigen, where the controlled model is described as a hybrid system with continuous and discrete variables. Next, we analyze nonlinear dynamics and bifurcations of the hybrid system. Finally, we discuss a possibility to improve the hormonal therapy.

We propose an algorithm based on cross-entropy to determine parameters of a piecewise linear model, which describes intermittent androgen suppression therapy for prostate cancer. By comparing with clinical data, the parameter estimation for the switched system shows good fitting accuracy and efficiency. We further optimize switching time points for the piecewise linear model to obtain a feasible therapeutic schedule. The simulation results of therapeutic effect are superior to those of previous strategy.

e15201 Background: Recently a phase III trial demonstrated that IAS was non-inferior to continuous AS in men with M0 disease after primary or salvage radiation and quality of life was better in the intermittent arm (Crook ASCO 2011). In that trial, men were treated with 8 months of AS followed by a variable time off AS driven by the absolute PSA value. The Hirata mathematical model describes the dynamics of prostate cancer treated with IAS (Hirata et al, J of Theoretical Biol 2010). In the model, there are three classes of cancer cells: a class of androgen dependent (AD) cells and two classes of androgen independent (AI:X1 and AI:X2) cells. During AS, AD cells will change to the two AI classes, and during the off treatment period, AI:X1 cells will revert to AD cells whereas AI:X2 cells cannot revert to either AD or AI:X1 cells. Methods: After IRB approval, we applied the Hirata model using serial monthly PSAs from men with M0 disease treated with IAS from Japan, Canada, and the United States. The proportions of men from each country who fell into the 3 categories of patients previously defined by the Hirata model were compared. Results: Serial PSAs from 26 men from Japan, 72 from Canada, and 79 from US were put into the model. The 3 categories of patients from the model include: (i) those with disease that will remain androgen sensitive and will respond to IAS without development of castration resistance (CRPC) (ii) those who will benefit from IAS but will develop CRPC sooner than those in group (i), (iii) those for whom continuous AS is superior to IAS. The datasets from each country show a similar distribution among the categories, and overall there were 42%, 51%, and 7% falling into groups i, ii, and iii respectively. Conclusions: This retrospective analysis shows that men with M0 disease treated with IAS fall into the 3 categories predicted by the Hirata model in similar proportions, regardless of country of origin. The ability to apply this model to the individual patient in the clinic is currently under development. The model may ultimately be able to optimize both the on and off treatment durations of IAS and to predict those patients who will most benefit from this approach.

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.

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