Study of Tumor Growth under Hyperthermia Condition

Abstract

1. Introduction

Cancer is the second major cause of human death in the world, and its mortality rate is growing every year [1]. Treatments include surgery, radiotherapy, chemotherapy, and gene therapy. Thermal therapy has also been intended to locally destroy tumor cells or enhance the body defense against tumor cells. However, recurrent rate of malignant tumor is still high [2], and the efficacy of the existing therapeutic means is yet to be improved. A new concept has been proposed recently that the primary tumor suppresses distal foci [3, 4]. This sheds new light on tumor treatment. Keeping the primary tumor in situ but restricting its size might enable the host to impede the development of distal foci and progression of metastasis.

For tumor growth, there are three distinct stages: avascular, vascular, and metastatic/invade stage. Mathematical models have been developed to perform parametric studies on factors influencing tumor growth or to evaluate the outcome of tumor treatment modalities [5, 6]. Model-based numerical studies would enable one to extrapolate more spatial and temporal information from the experimental findings and to make predictions [7]. Laird [8] first found that the tumor growth data-fitted Gompertz function could be used to simulate the entire growth curve, which was defined as an empirical model. Hu and Ruan [9] studied the suppression effect of immunity system on tumor growth by merging the Gompertz function into a cellular automaton model. Other mathematical models based on certain biological assumptions have also been attempted to predict tumor growth curve using fundamental physics, such as mass/energy conservation. Greenspan [10] introduced surface tension into the diffusion model developed by Burton [11]. Tumor growth/inhibition factors [12, 13], cell adhesions [14, 15], angiogenesis [16, 17] and invasion [18, 19] were further considered to describe tumor growth at different stages.

Models focusing on the avascular stage [20–27] have been well studied and could be easily applied to in vitro experiment. Ward and King [23, 24] and Casciari et al. [28] proposed a continuum mathematical model focusing on how nutrients' concentration affects tumor growth. These models typically consist of reaction-diffusion equations. Forbes [29] further incorporated energy metabolism (ATP production rate) into the growth model. However, most of these models have not taken the Warburg effect into consideration, which fundamentally differentiates the tumor cell metabolism from that of the normal cells.

Read more>>>>>>

References: