Mechanics-mathematical models of changing of human cells properties under the cancer action

Abstract

Cancer is one of the most common causes of morbidity and mortality in the world. According to the recent estimates, cancer deaths will increase from an estimated 8.2 million annually to 13 million per year [1]. In Belarus every year nearly 43,000 cases of cancer are diagnosed among residents of the Republic and cancer deaths are 17,000 cases per year [2].Nowadays nanoindentation and atomic force microscopy are widely used to study various cancers and some important principal findings have been reported to date. Our research is devoted to the development of high-performance analytical and experimental methods to evaluate the physical and mechanical properties of biomaterials and biological structures based on nanoindentation techniques and atomic force microscopy (AFM). Analysis of some mechanical and mathematical models which are constructed to solve such difficult problems as the choice/design of mechanical-mathematical model, as the definition the moment of embedded indenter into an object and accounting of physical and mechanical properties of biological structures in the represented techniques on nanoscale level. Adequacy of the use of fractional order derivatives to construct mechanics-mathematical models of the estimation physical and mechanical properties of biomaterials is shown in this work [3]. Results of modifications study due to changes in the physico-mechanical properties of human cells under lung cancer (adenocarcinoma) are demonstrated [4]. These changes can be used as biomarker for tumor cells detection and for determination of therapeutic strategies in this occurrence for every concrete patient.