Mechanistic modelling of prostate-specific antigen dynamics shows potential for personalized prediction of radiation therapy outcome

Abstract

<jats:p>External beam radiation therapy is a widespread treatment for prostate cancer. The ensuing patient follow-up is based on the evolution of the prostate-specific antigen (PSA). Serum levels of PSA decay due to the radiation-induced death of tumour cells and cancer recurrence usually manifest as a rising PSA. The current definition of biochemical relapse requires that PSA reaches nadir and starts increasing, which delays the use of further treatments. Also, these methods do not account for the post-radiation tumour dynamics that may contain early information on cancer recurrence. Here, we develop three mechanistic models of post-radiation PSA evolution. Our models render superior fits of PSA data in a patient cohort and provide a biological justification for the most common empirical formulation of PSA dynamics. We also found three model-based prognostic variables: the proliferation rate of the survival fraction, the ratio of radiation-induced cell death rate to the survival proliferation rate, and the time to PSA nadir since treatment termination. We argue that these markers may enable the early identification of biochemical relapse, which would permit physicians to subsequently adapt patient monitoring to optimize the detection and treatment of cancer recurrence.</jats:p>

Review: Mathematical Modeling of Prostate Cancer and Clinical Application

“…Aside from the aforementioned work that focuses on hormonal therapy, there are other works that utilize mathematical models to study other aspects of prostate cancer. For instance, Lorenzo et al [80] use mathematical models to study personalized treatment with radiation therapy, where they suggest several potential prognostic measurements that can be obtained from the model. A recent study by Farhat et al [81] formulates a mathematical model of metastatic prostate cancer while taking into account the bone micro-environment to investigate several possible therapeutic strategies.…”

Optimization of Dose Fractionation for Radiotherapy of a Solid Tumor with Account of Oxygen Effect and Proliferative Heterogeneity

“…Optimized RT fractionation schemes did not contain days-off, unlike standard clinical schemes. It should be noted that the current model neglected the change of radiosensitivity during the cell cycle for the proliferating cells, as well as the fact that cells do not die immediately due to irradiation [58]. The introduction of these aspects into the model may somehow alter the appearance of the optimized schemes, found by the used algorithm.…”

Integrating Quantitative Assays with Biologically Based Mathematical Modeling for Predictive Oncology

“…Continuous formulations feature ordinary (ODE) or partial (PDE) differential equations that describe the population-averaged or spatially resolved dynamics of tumor cells, respectively. ODE models are limited to temporal dynamics, but this enables their use in a wide range of cellular and tissue-scale settings that can leverage multiple types of time-resolved data ( Benzekry et al., 2014 ; Jarrett et al., 2019 ; Johnson et al, 2020 ; Lorenzo et al., 2019b ; Mendoza-Juez et al., 2012 ; Morken et al., 2014 ). PDE models further include spatial dynamics and constitute the standard approach for clinical, tissue-scale applications, which usually rely on longitudinal in vivo imaging data ( Hormuth et al., 2020 ; Jarrett et al., 2018 ; Lorenzo et al., 2019a ; Mang et al., 2020 ; Rockne et al., 2015 ; Wong et al., 2017 ).…”

“…Biology-based models enable the transformation of measured data samples into mechanistically interpretable parameters and variables, which help to quantitatively analyze the investigated cancer mechanisms and further guide new research directions ( Ayuso et al., 2017 ; Jarrett et al., 2020b ; Johnson et al., 2019 , Johnson et al, 2020 ; Lorenzo et al, 2019b , 2020 ; Merkher et al., 2020 ; Morken et al., 2014 ; Pérez-García et al., 2019 ; Wang et al., 2006 ). Moreover, mathematical models parameterized by biological data need not be comprehensive to make to gain insight into underlying tumor dynamics and make valid predictions.…”