Several studies have recommended the use of hydrogels for localized targeted delivery of chemotherapeutic drugs following tumor removal surgery. This approach aims to both fill the cavity and prevent cancer recurrence. The use of Multiphysics-based simulation emerges as a valuable strategy for minimizing experimental work, providing detailed insights into how drug release occurs in the tissue, and enabling the optimization of the design. In this study, we introduced a mathematical model, utilizing experimental data, to investigate the transport of liposomes carrying MZ1 from a thermosensitive hydrogel and their impact on the viability of breast cancer cells. The proposed comprehensive model considers not just the transport within the interstitial tissue, represented as a porous medium, but also the uptake by cells and its influence on cell viability, along with the potential lymphatic drainage. The six real patient-specific tumor shapes extracted from MRI scans were used to investigate how the size and form of the tumor can modify the transport pattern. The computational results revealed that the concentration of liposomes in the tissue is significantly influenced by their release from the hydrogel, which proved to be the limiting step. Liposome concentrations of approximately 0.1 % weight were found to be sufficient in ensuring minimal cell survival in the vicinity of the tumor.