Page 33 - programme book

AM-006
Adaptive Therapy in Two-phase Model of Tumor

Nor Farah Wahidah Nor Khalid 1, a) and Mohd Almie Alias 2, b)

1,2 Jabatan Sains Matematik, Fakulti Sains dan Teknologi, Universiti Kebangsaan Malaysia,
43600 UKM Bangi, Selangor, Malaysia.

a) Corresponding author: p102587@siswa.ukm.edu.my
b) mohdalmie@ukm.edu.my

Abstract. Adaptive therapy is an alternative treatment for standard of care in cancer treatment called
continuous therapy where adaptive therapy is an on and off treatment where this treatment schedule
depends on the size of tumor. Adaptive therapy aims to delay the emergence of resistance in cancer
treatment by allowing a significant number of sensitive cells to remain alive during treatment break
in order to suppress the growth of resistant cells population. Resistant cells often come with fitness
costs where for example resistant cells proliferate slower than sensitive cells. It is important to
understand whether the cost of resistance will play a deterministic criterion in knowing whether the
cancer will respond well to adaptive therapy. We will use a two-phase model consisting of tumor
cells and water where the tumor cells phase is divided into two species: drug-sensitive cells and fully
resistant cells. We use the conservation of mass and momentum equations coupled with oxygen-
dependent cell growth and death terms to model the avascular tumor. For both high and low initial
fraction of resistant cells, a cost in growth rate or competitive rate is required to see meaningful
gains while a cost in death rate does not show that it will get significant benefit from adaptive
therapy. The cell death rate by drug and drug decay rate does affect the response of sensitive cells
towards the drug where low drug decay rate shows that there will be no difference in both adaptive
therapy and the standard of care and low drug effect rate makes both treatments less effective in
killing sensitive cells. High cell death rate by drug results in positive correlation between the cost of
resistance and the time gained by adaptive therapy while this correlation cannot be seen when the
rate of cell death by drug is low.

Keywords: Adaptive therapy, two-phase model, tumor growth, drug resistance, cost of resistance