Combined cryosurgery and cold-responsive drug-loaded nanoparticles to enhance deep-lying tumor therapy: A mathematical model

•Novel chemo-cryo treatment to enhance the treatment of deep-lying tumor is developed.•Macroscopic mathematical model is firstly established for cryosurgery, drug release and transport.•Therapeutic efficacy is evaluated in term of the effective killing volumes of tumor and normal tissue.•Compared with cryosurgery, chemo-cryo treatment reduces the killing volume of normal tissue by 89.36%.•Adjusting the holding time and the properties of nanoparticles and drug can augment the effective killing of tumor. Minimally-invasive cryosurgery is incapable of killing the tumor at the outer periphery of iceball, resulting in the inefficiency of tumor treatment. In this paper, we develop a new combined treatment of chemotherapy and cryotherapy (chemo-cryo) by injecting cold-responsive drug-loaded nanoparticles around the tumor before cryosurgery to enhance the treatment of deep-lying tumor. A macroscopic mathematical model is established for the first time, covering the cryosurgery, the release of anti-tumor drug (doxorubicin) from cold-responsive nanoparticles, and the drug transport in biological tissues. Therapeutic efficacy is evaluated in terms of the effective killing volumes of tumor and normal tissue, including cryosurgery killing and drug killing. Simulation results show that comparisons with cryosurgery alone demonstrate the advantage of chemo-cryo treatment in enhancing the therapeutic efficacy, given that the killing volume of normal tissue is lessened by 89.36% for the single-probe and 72.57% for the multi-probe in the case of complete tumor killing. The amount of doxorubicin released is determined by the holding time of cryoprobe, the sensitive temperature and initial concentration of drug-loaded nanoparticles, independent of doxorubicin diffusivity. Adjusting the holding time and the properties of nanoparticles and doxorubicin can augment the effective killing volume of tumor, but it is also accompanied by side effect on normal tissue, mainly manifested as drug killing. Results obtained can serve as the guideline to optimize chemo-cryo treatment regimens for deep-lying tumor.