Using mathematics to understand cancer growth

Melanoma schematic

Dr. Roccabianca is currently seeking highly motivated graduate and undergraduate students to join her laboratory and collaborate on this project. Particularly, those with prior experiences and interest in continuum mechanics, solid mechanics, and both numerical and analytical solutions of deformable solids subjected to large deformations are encouraged to apply. Interested students should contact Dr. Roccabianca by email and include a brief personal statement and CV (resume).

 

In the Soft Tissue Mechanics Lab, my students and I are interested in understanding the mechanisms that relate the mechanical environment to the biological process of growth associated with melanoma. The development of a solid body tumor, such as melanoma, can be divided in two phases: an early stage, called avascular growth, where the tumor remains in a regular, axisymmetric configuration of a few millimeters in diameter, and a later phase, called vascular evolution, which is a more aggressive stage where invasion and metastasis may take place. In the first stage of growth, cells in the center of the lesion start dying as a result of the deprivation of nutrients and oxygen and turn into a necrotic core, while the cells in the outer three to five cell layers continue to proliferate. From an engineering perspective this can be described as confined growth: the external ring of cells continues growing, compressing the central core. This phenomenon can give rise to an instability of equilibrium and therefore a shape bifurcation. It is interesting to recall that asymmetry and border irregularity are two of the five points in the short list of clinical symptoms that can be used for the early recognition of this cancer, the so-called ABCDE (Asymmetry, Border irregularity, Color variegation, Diameter and Evolution). The purpose of the research of the Soft Tissue Mechanics Lab is to investigate the effect that the stress field surrounding a growing tumor has on the developmental process of the tumor itself. Specifically, we want to detect and analyze instabilities that might rise from this complex stress state.

Graph

Another project that we are interested in is the development of a model of healthy skin and its adaptive remodeling (i.e. pregnancy, weight loss, muscle growing due to exercise). Skin is a thin multilayered membrane that acts as the body’s main barrier, both biologically and mechanically, against the external environment by fulfilling multiple biological purposes (i.e. regulation of heat and water exchange with the surroundings and protection from mechanical, bacterial or viral insults). Its structure can be subdivided into three principal layers: the epidermis, the dermis and the hypodermis. From an engineering perspective, skin is an orthotropic, highly non-linear material subjected to large deformations. In my lab, my students and I will develop a model able to describe the mechanical behavior of skin by employing the so-called constrained mixture theory. Briefly, every component present in skin, such as collagen, elastin, and cells, will be endowed with different material properties (i.e. the collagen is stiffer than all the rest, the cells has the ability to change their mechanical properties) but they will all be constrained to move together when deformed.