Towards personalized prostate cancer therapy using delta-reachability analysis

Abstract

Recent clinical studies suggest that the efficacy of hormone therapy for prostate cancer depends on the characteristics of individual patients. In this paper, we develop a computational framework for identifying patient-specific androgen ablation therapy schedules for postponing the potential cancer relapse. We model the population dynamics of heterogeneous prostate cancer cells in response to androgen suppression as a nonlinear hybrid automaton. We estimate personalized kinetic parameters to characterize patients and employ δ-reachability analysis to predict patient-specific therapeutic strategies. The results show that our methods are promising and may lead to a prognostic tool for prostate cancer therapy.

An evolutionary–type model for tumor immunotherapy

“…Note that the model discussed in this paper is not specific to a type of cancer, nevertheless the employed analysis tools can be enhanced if specific cancer information is available through the model parameters. An example of such a model, whose parameters are clinical data validated, was derived in Liu et al (2015) for prostate cancer.…”

Infinitesimal Perturbation Analysis for Personalized Cancer Therapy Design**The authors’ work is supported in part by NSF under Grants CNS1239021 and IIP-1430145, by AFOSR under grant FA9550-12-1-0113,and by ONR under grant N00014-09-1-1051.

“…Moreover, previous work focusing on classifying patients into groups in order to infer optimal treatment schemes have been based on more manageable, albeit less accurate, approaches to nonlinear hybrid dynamical systems. In contrast, a nonlinear hybrid automaton model was recently proposed by Liu et al (2015) to identify patient-specific therapy schemes without accounting for noise and fluctutations that are inherently associated with cell population dynamics and monitoring of clinical data. Stochastic effects were incorporated into a hybrid model of tumor growth under IAS therapy by Tanaka et al (2010), but the ensuing analysis was performed considering a pre-determined therapy scheme, i.e., no design of personalized therapy was carried out.…”

“…In this paper, we draw upon the deterministic hybrid automaton model from Liu et al (2015) to which we incorporate stochastic effects. We propose a cost metric in terms of the desired outcome of IAS therapy that is parameterized by a controllable vector, and formulate the problem of optimal personalized therapy design as the search for the parameter values which minimize our cost metric.…”

ProbReach: A Tool for Guaranteed Reachability Analysis of Stochastic Hybrid Systems

“…We conducted the experiment with one continuous random initial parameter (x 3 (0), normally distributed) which took about 100 hours to compute ( = 0.0001) and returned the numerically guaranteed interval Personalized prostate cancer therapy. We consider a model of personalised prostate cancer therapy introduced by Ideta et al [11] and improved by Liu et al [15]. The patient's prostatespecific antigen (PSA) level is monitored throughout the therapy.…”

“…The main aim of the therapy is to delay cancer relapse for as long as possible. The model of the therapy is given in Figure 1 (a full explanation of the model and its parameters can be found in [15]). Mode 1 is the on-therapy stage, and it continues until the PSA level (measured by x + y in Fig.…”