Abstract
Prostate cancer bone metastasis poses significant health challenges, affecting countless individuals. While treatment with the radioactive isotope radium-223 ($ ^{223} $Ra) has shown promising results, there remains room for therapy optimization. In vivo studies are crucial for optimizing radium therapy; however, they face several roadblocks that limit their effectiveness. By integrating in vivo studies with in silico models, these obstacles can be potentially overcome. Existing computational models of tumor response to $ ^{223} $Ra are often computationally intensive. Accordingly, we here present a versatile and computationally efficient alternative solution. We developed a PDE mathematical model to simulate the effects of $ ^{223} $Ra on prostate cancer bone metastasis, analyzing mitosis and apoptosis rates based on experimental data from both control and treated groups. To build a robust and validated model, our research explored three therapeutic scenarios: no treatment, constant $ ^{223} $Ra exposure, and decay-accounting therapy, with tumor growth simulations for each case. Our findings align well with experimental evidence, demonstrating that our model effectively captures the therapeutic potential of $ ^{223} $Ra, yielding promising results that support our model as a powerful infrastructure to optimize bone metastasis treatment.