Intermittent Androgen Suppression Research Articles

Selection of prostate cancer therapy strategy under early androgen suppression treatment

Intermittent androgen suppression therapy is increasingly employed as an alternative method of advanced prostate cancer. However, it remains controversial whether intermittent therapy is superior to continuous therapy in controlling cancer progression. In this paper, we study the mathematical model for early treatment of prostate cancer that incorporates the individual differences and the pharmacodynamics of drugs. The mathematical criteria for selection of better treatment are established on the basis of stability of periodic solution induced by treatment. Numerical results further explore the optimal design of intermittent treatment. The results provide valuable insights for clinical practice.

Optimization Therapy by Coupling Intermittent Androgen Suppression with Impulsive Chemotherapy for a Prostate Cancer Model.

Intermittent androgen suppression in the prostate cancer is often relapsed by the increasing of prostate specific antigen level during the on-treatment. Historically, chemotherapy has had a limited role in the treatment of prostate cancer. However, new agents are showing promise in patients with advanced disease. Intermittent androgen suppression plus chemotherapy in pulsed pattern has become an indispensable clinical scheme for prostate cancer, which is presented to describe the transformation mechanism for three kinds of cancer cells in this paper. The model is then extended to include the residual effect of chemotherapy which suppresses the cancer cells production, thereby preventing the relapse. The optimal controls represent the efficiencies of both intermittent androgen suppression and chemotherapy in suppressing relapse of prostate cancer. Based on an optimal algorithm, numerical simulations are implemented not only to show the optimal durations of on- and off-treatment and chemotherapy dosages but also to present the effectiveness of different strategies in inhibiting the relapse for three types of patients. Results reveal that the optimal intermittent androgen suppression scheme with alterable treatment cycles is pivotal for type I and II patients, in part because it can greatly reduce the on-treatment time and degrade the level of prostate specific antigen. Furthermore, optimal hybrid schedule even averts the relapse of prostate cancer for type II and III patients. Finally, comparing the prostate specific antigen under intermittent androgen suppression schedule with residual effect of chemotherapy to one without residual effect of chemotherapy demonstrates the validity of both our model and algorithms in lessening the prostate specific antigen and decreasing the chemotherapy dosages.

An adaptive information-theoretic experimental design procedure for high-to-low fidelity calibration of prostate cancer models.

The use of mathematical models to make predictions about tumor growth and response to treatment has become increasingly prevalent in the clinical setting. The level of complexity within these models ranges broadly, and the calibration of more complex models requires detailed clinical data. This raises questions about the type and quantity of data that should be collected and when, in order to maximize the information gain about the model behavior while still minimizing the total amount of data used and the time until a model can be calibrated accurately. To address these questions, we propose a Bayesian information-theoretic procedure, using an adaptive score function to determine the optimal data collection times and measurement types. The novel score function introduced in this work eliminates the need for a penalization parameter used in a previous study, while yielding model predictions that are superior to those obtained using two potential pre-determined data collection protocols for two different prostate cancer model scenarios: one in which we fit a simple ODE system to synthetic data generated from a cellular automaton model using radiotherapy as the imposed treatment, and a second scenario in which a more complex ODE system is fit to clinical patient data for patients undergoing intermittent androgen suppression therapy. We also conduct a robust analysis of the calibration results, using both error and uncertainty metrics in combination to determine when additional data acquisition may be terminated.

Can fractional differentiation improve stability results and data fitting ability of a prostate cancer model under intermittent androgen suppression therapy?

• This work verifys the advantageous side of fractional differentiation from the perspective of data ftting and stability analysis. • A prospective model in the recent prostate cancer literature is handled to be rebuilt in the context of fractional calculus . • Stability analyses of the reconstructed models release stronger outcomes. • Numerical simulations and mean square error values also show better data fitting results. In this paper, we compare the ordinary and fractional versions of a prospective model in the prostate cancer literature to be able to verify the hypothesis that fractional differentiation can improve stability results and data fitting ability of the ordinary version. For that, the mean square error values for androgen and prostate-specific antigen for the first 1.5 cycles of intermittent androgen suppression therapy administered to 62 selected patients from the Vancouver Prostate Center are computed. Stability analyses of the fractional models are also studied and showed how the fractional differentiation contributes to improve the stability results of an ordinary prostate model. Additionally, our findings are supported by PSA and androgen simulations of three different class of patients. Finally, with a conclusion part, which hints for future works should be taken into account are pointed out.

Practically scheduling hormone therapy for prostate cancer using a mathematical model

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 Impact of Intermittent Androgen Suppression Therapy in Prostate Cancer Modeling

Previous studies on prostate cancer modeling under hormonal therapy successfully fit clinical serum androgen data, under the assumption that the levels of intracellular and serum androgen are similar. However, such an assumption may not hold throughout the course of treatment. In this paper, we propose a model that directly accounts for serum androgen and its interaction with intracellular androgen. We establish biological links between the model and clinical data, and discuss in detail parameter ranges and the initialization of model variables. We further investigate parameter sensitivity over time, which gauges the maximum effect of varying each parameter and allows us to fix some parameters, to increase the robustness of the parameter fitting process. By relying on the characteristics of intermittent androgen suppression therapy (IAS), we employ a two-part weighted error function for fitting. We also carry out mathematical analyses to study the dynamic aspects of the system with different androgen thresholds. We find that the proposed model shows superior forecasting ability, compared to its predecessor. Furthermore, we demonstrate the impact of androgen on the dynamics of the androgen-dependent and -independent cancer cells, which suggests the discrete description of androgen dependency may not give a realistic characterization of the cancer population. We show that IAS has certain characteristics that need to be considered for parameter estimation. Our results demonstrate that the model and the fitting scheme are viable for similar applications of prostate cancer modeling under hormonal therapy.

Dynamics and implications of models for intermittent androgen suppression therapy.

In this paper, we formulate a three cell population model of intermittent androgen suppression therapy for cancer patients to study the treatment resistance development. We compare it with other models that have different underlying cell population structure using patient prostate specific antigen (PSA) and androgen data sets. Our results show that in the absence of extensive data, a two cell population structure performs slightly better in replicating and forecasting the dynamics observed in clinical PSA data. We also observe that at least one absorbing state should be present in the cell population structure of a plausible model for it to produce treatment resistance under continuous hormonal therapy. This suggests that the heterogeneity of prostate cancer cell population can be represented by two types of cells differentiated by their level of dependence on androgen, where the two types are linked via an irreversible transformation.

Controllability of hybrid PDE‐ODE systems with structural instability and applications to mathematical models on intermittent hormonal therapy for prostate cancer

Several mathematical models on intermittent androgen suppression (IAS) therapy for prostate cancer are classified into hybrid PDE‐ODE system with structural instability. The purpose of this paper is to give a unified strategy to prove the controllability of the mathematical models on the IAS therapy. For this aim, we prove that (1) a generalized hybrid PDE‐ODE system is controllable for any initial data and (2) the result given by (1) is applicable to the mathematical models on the IAS therapy. Finally, we conclude that the mathematical models on the IAS therapy for prostate cancer are controllable for any initial data.

Abstract B014: Simulating prostate cancer stem cell dynamics to predict patient-specific sensitivity or resistance to intermittent androgen-deprivation therapy

Abstract Intermittent androgen suppression is an attractive treatment approach for biochemically recurrent locally advanced prostate cancer to delay evolution of treatment resistance (PMID: 16783817). We developed a mathematical model of prostate cancer stem cell dynamics during therapy as a plausible mechanism of resistance evolution. We simulate division dynamics of cancer stem cells, non-stem cancer cells, and PSA concentration and generate highly accurate model fits to the longitudinal data of 55 patients undergoing 2-4 cycles of intermittent androgen suppression. We analyze model dynamics to identify cancer stem cell proliferation patterns that correlate with patient outcomes, and score model predictive power to accurately forecast evolution of resistance in individual patients. The presented framework may contribute to identifying patients who do and do not develop resistance to intermittent androgen suppression. The obtained predictive power on a retrospective data set warrants prospective evaluation in a clinical setting. Citation Format: Renee Brady, John Nagy, John Nagy, Heiko Enderling. Simulating prostate cancer stem cell dynamics to predict patient-specific sensitivity or resistance to intermittent androgen-deprivation therapy [abstract]. In: Proceedings of the AACR Special Conference: Prostate Cancer: Advances in Basic, Translational, and Clinical Research; 2017 Dec 2-5; Orlando, Florida. Philadelphia (PA): AACR; Cancer Res 2018;78(16 Suppl):Abstract nr B014.

Personalizing Androgen Suppression for Prostate Cancer Using Mathematical Modeling

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.

Case: Testicular oligometastasis from prostate cancer - Report of rare isolated recurrence after radiotherapy and intermittent androgen-deprivation therapy.

Testicular oligometastasis secondary to prostate cancer is rare. We present a case where a patient with locally advanced prostate cancer was treated with high-dose external beam radiotherapy and two years of androgen-deprivation therapy, followed by intermittent androgen suppression. Three and a half years after initial diagnosis, he was found to have a painless testicular mass. Orchiectomy was performed and histopathology demonstrated metastatic prostatic adenocarcinoma. He remains in clinical remission on intermittent androgen suppression eight years following initial treatment, and over four years after presentation with testicular metastasis.

Mathematical modeling of continuous and intermittent androgen suppression for the treatment of advanced prostate cancer.

Prostate cancer is one of the most prevalent types of cancer among men. It is stimulated by the androgens, or male sexual hormones, which circulate in the blood and diffuse into the tissue where they stimulate the prostate tumor to grow. One of the most important treatments for advanced prostate cancer has become androgen deprivation therapy (ADT). In this paper we present three different models of ADT for prostate cancer: continuous androgen suppression (CAS), intermittent androgen suppression (IAS), and periodic androgen suppression. Currently, many patients in the U.S. receive CAS therapy of ADT, but many undergo a relapse after several years and experience adverse side effects while receiving treatment. Some clinical studies have introduced various IAS regimens in order to delay the time to relapse, and/or to reduce the economic costs and adverse side effects. We will compute and analyze parameter sensitivity analysis for CAS and IAS which may give insight to plan effective data collection in a future clinical trial. Moreover, a periodic model for IAS is used to develop an analytical formulation for relapse times which then provides information about the sensitivity of relapse to the parameters in our models.

Optimal design of personalized prostate cancer therapy using Infinitesimal Perturbation Analysis

The standard treatment for advanced prostate cancer is hormone therapy in the form of continuous androgen suppression (CAS), which unfortunately frequently leads to resistance and relapse. An alternative scheme is intermittent androgen suppression (IAS), in which patients are submitted to cycles of treatment (in the form of androgen deprivation) and off-treatment periods in an alternating manner. In spite of extensive recent clinical experience with IAS, the design of ideal protocols for any given patient remains a challenge. The level of prostate specific antigen (PSA) is frequently monitored to determine when patients will be taken off therapy and when therapy will resume. In this work, we propose a threshold-based policy for optimal IAS therapy design that is parameterized by lower and upper PSA threshold values and is associated with a cost metric that combines clinically relevant measures of therapy success. We use a Stochastic Hybrid Automaton (SHA) model of prostate cancer evolution under IAS and perform Infinitesimal Perturbation Analysis (IPA) to adaptively adjust PSA threshold values so as to improve therapy outcomes. We also apply this methodology to clinical data from real patients, and obtain promising results and valuable insights for personalized IAS therapy design.

A nonlinear competitive model of the prostate tumor growth under intermittent androgen suppression

Hormone suppression has been the primary modality of treatment for prostate cancer. However long-term androgen deprivation may induce androgen-independent (AI) recurrence. Intermittent androgen suppression (IAS) is a potential way to delay or avoid the AI relapse. Mathematical models of tumor growth and treatment are simple while they are capable of capturing the essence of complicated interactions. Game theory models have analyzed that tumor cells can enhance their fitness by adopting genetically determined survival strategies. In this paper, we consider the survival strategies as the competitive advantage of tumor cells and propose a new model to mimic the prostate tumor growth in IAS therapy. Then we investigate the competition effect in tumor development by numerical simulations. The results indicate that successfully IAS-controlled states can be achieved even though the net growth rate of AI cells is positive for any androgen level. There is crucial difference between the previous models and the new one in the phase diagram of successful and unsuccessful tumor control by IAS administration, which means that the suggestions from the models for medication can be different. Furthermore we introduce quadratic logistic terms to the competition model to simulate the tumor growth in the environment with a finite carrying capacity considering the nutrients or inhibitors. The simulations show that the tumor growth can reach an equilibrium state or an oscillatory state with the net growth rate of AI cells being androgen independent. Our results suggest that the competition and the restraint of a limited environment can enhance the possibility of relapse prevention.

Ability of intermittent androgen suppression to selectively create a non-trivial periodic orbit for a type of prostate cancer patients

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.

Intermittent Androgen Suppression: Estimating Parameters for Individual Patients Based on Initial PSA Data in Response to Androgen Deprivation Therapy

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.

Infinitesimal Perturbation Analysis for Personalized Cancer Therapy Design

We use a Stochastic Hybrid Automaton (SHA) model of prostate cancer evolution under intermittent androgen suppression (IAS) to study a threshold-based policy for therapy design. IAS is currently one of the most widely used treatments for advanced prostate cancer. Patients undergoing IAS are submitted to cycles of treatment (in the form of androgen deprivation) and off-treatment periods in an alternating manner. One of the main challenges in IAS is to optimally design a therapy scheme, i.e., to determine when to discontinue and recommence androgen suppression. The level of prostate specific antigen (PSA) in a patient's serum is frequently monitored to determine when the patient will be taken off therapy and when therapy will resume. The threshold-based policy we propose is parameterized by lower and upper PSA threshold values and is associated with a cost metric that combines clinically relevant measures of therapy success. Using Infinitesimal Perturbation Analysis (IPA), we derive unbiased gradient estimators of this cost metric with respect to the controllable PSA threshold values based on actual data and show how these estimators can be used to adaptively adjust controllable parameters so as to improve therapy outcomes based on the cost metric defined.

Model predictive control for optimally scheduling intermittent androgen suppression of prostate cancer

Mathematical modeling of prostate cancer under intermittent androgen suppression revealed that we may be able to delay relapse by optimally scheduling the hormone therapy for each patient. However, our previous study showed the difficulty of the scheduling by minimizing the maximal tumor growth rate because the transient dynamics is also important and can help to delay the relapse for a finite time. Here, we propose to use model predictive control for scheduling intermittent androgen suppression. We find that model predictive control tends to delay the relapse of prostate specific antigen more than the method with minimizing the maximal tumor growth rate. Therefore, model predictive control is a promising approach for practically applying the mathematical model to optimally schedule intermittent androgen suppression.

A new protocol for intermittent androgen suppression therapy of prostate cancer with unstable saddle-point dynamics

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.

A proposal of a new intermittent androgen suppression therapy method for prostate cancer with saddle type instability

A proposal of a new intermittent androgen suppression therapy method for prostate cancer with saddle type instability