Guillermo Lorenzo


Optimal control of therapeutic regimens for advanced prostate cancer


Once prostate cancer reaches an advanced stage, chemotherapies and targeted therapies may become the only viable treatment options. The current standard-of-care consists of multiple cycles of the cytotoxic drug docetaxel. However, prostatic tumors may develop resistance to this treatment and ultimately resume growth. Thus, much research is devoted to find new drugs and treatment strategies to improve tumor control.

Since advanced prostate cancer relies on the tumor-induced generation of new blood vessels (a processed known as angiogenesis), the combination of docetaxel with antiangiogenic drugs has been considered a promising therapeutic option. However, clinical studies have not revealed a clear benefit from this combined regimen so far.

In this work, my colleagues and I propose to leverage a combination of mathematical modeling, computer simulations, and optimal control theory to identify new strategies to combine cytotoxic and antiangiogenic therapies to treat advanced prostate cancer obtaining superior outcomes than with the standard docetaxel regimen.
Figure. Our methods enable the mathematical analysis and simulation study of our models of  prostate cancer growth and treatment response under multiple hypotheses of tumor, serum prostate specific antigen (PSA, a standard biomarker of prostate cancer), and therapeutic control. This figure shows the optimal cytotoxic and antiangiogenic therapies obtained in a simulation test with increasing control on the tumor and serum PSA for larger values of the parameter denoted as k1. Our simulations suggest that cytotoxic therapy suffices to optimally control prostate cancer growth, also achieving better results than with a standard docetaxel therapy. In our work, we further explore how these simulation results might be exploited to guide the design of new delivery schedules and drug compounds.

Publications


Optimal control of cytotoxic and antiangiogenic therapies on prostate cancer growth


Pierluigi Colli, Hector Gomez, Guillermo Lorenzo, Gabriela Marinoschi, Alessandro Reali, Elisabetta Rocca


Mathematical Models and Methods in Applied Sciences, vol. 31(7), 2021, pp. 1419-1468


Mathematical analysis and simulation study of a phase-field model of prostate cancer growth with chemotherapy and antiangiogenic therapy effects


Pierluigi Colli, Hector Gomez, Guillermo Lorenzo, Gabriela Marinoschi, Alessandro Reali, Elisabetta Rocca


Mathematical Models and Methods in Applied Sciences, vol. 30(7), 2020, pp. 1253-1295