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.

Numerous studies in the literature have proposed the use of thermo-responsive hydrogels for filling cavities after tumor resection. However, optimizing the injection process is challenging due to the complex interplay of various multi-physics phenomena, such as the coupling of flow and heat transfer, multi-phase interactions, and phase-change dynamics. Therefore, gaining a fundamental understanding of these processes is crucial. In this study, we introduce a thermo-sensitive hydrogel formulated with poloxamer 407 and Gellan gum as a promising filling agent, offering an ideal phase-transition temperature along with suitable elastic and viscous modulus properties.

We performed multi-physics simulations to predict the flow and temperature distributions during hydrogel injection. The results suggested that the hydrogel should be kept at 4 °C and injected within 90 s to avoid reaching the transition temperature. Cavity filling simulations indicated a symmetric distribution of the hydrogel, with minimal influence from the syringe's position.

The temperature gradient at the cavity edge delays gelation during injection, which is essential to guarantee its administration as a liquid. The hydrogel's viscosity follows a sigmoidal function relative to temperature, taking five minutes to reach its maximum value. In summary, the multi-physics simulations carried out in this study confirm the potential of thermo-responsive hydrogels for use in post-tumor surgery treatment and define the conditions for a proper administration. Furthermore, the proposed model can be widely applied to other thermo-responsive hydrogels or under different conditions.