# The Impact of Intermittent Androgen Suppression Therapy in Prostate Cancer Modeling
###### Abstract  
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. Keywords:prostate cancer modeling; intermittent androgen suppression therapy; data fitting; cell quota models +
Footnote †: journal: Medical  
antigen (PSA--a prostate cancer biomarker) level reaches a desired low threshold, then they are taken off the treatment until the PSA level rises above a predetermined threshold. The process is then repeated until the patients reach hormonal resistance [1]. Various mathematical models have been developed, in the past two decades, to study many aspects of prostate cancer, especially under androgen suppression therapy. The first experimentally-driven model of PCa under continuous androgen suppression therapy (CAS) is credited to [PERSON] in 2004 [4]. This inspired a series of works that study PCa under IAS and compare the effect of CAS versus IAS [5; 6; 7; 8]. Furthermore, theoretical perspectives on population dynamics and spatial structure have also been explored in subsequent works [9; 10; 11]. In addition, a biologically detailed model with a complex biochemical network has also been developed and verified with experimental data [12]. On a more applicable note, optimal scheduling, complex algorithms to predict hormonal resistance, and stochastic models have been used to provide insights into clinical aspects of prostate cancer treatment [13; 14; 15; 16]. For a detailed review of recent work, the authors refer to [17]. In this paper, we focus on a previous approach by [PERSON], which was the first successful attempt at using both PSA and androgen data for fitting and forecasting [8]. A recent work by [PERSON] et al. [18] shows that, with the available types of data (e.g., PSA and androgen data), the model in [PERSON] (BK model) has the optimal population structure to describe and to forecast the dynamics of prostate cancer under IAS. On the other hand, the model fails to completely capture the growth phase of the PSA level when the patient is taken off treatment. Additionally, fitting of the androgen data is done by assuming similar levels of body androgen and intracellular androgen, which may not hold throughout the course of treatment. Thus, we extend the BK model to directly take into account serum androgen separately from intracellular androgen. We carry out numerical comparisons between the two models, in terms of fitting and forecasting.