Mathematics in modeling cancer cell mechanics

The article “An Increasing Role for Mechanics in Cancer Modeling” dated 21 October 2007 (http://www. siam. org/news/news. php? id=1216) was truly a revelation on the diversity of roles in which we cast applied mathematics as well as the vitality of these applications. The article, appearing in the fortieth volume of the Society for Industrial and Applied Mechanics, details how the internal organization and growth kinetics of malignant tumor cells are being analyzed with mathematical models.

The biologists at the heart of this field envision that such simulations shall enable them to not only understand the mechanics of cancer cells and their propagation, but also suggest hitherto unknown methods for their prevention. Written by Luigi Preziosi, the article begins by commenting on the increasing attention that tumor related talks garner at conferences and how they have changed over the years. It is stated that there was a six fold increase in the number of talks in the SIAM conferences themselves and that the trend is equally visible in many other forums.

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Earlier models restricted themselves to a single cell type tumor, which is hardly representative of the actual situation, where many phases coexist – be it cells of different types or a matrix of living and dead cells. This had definitely made modeling challenging but the results are correspondingly more illuminating. It is currently understood that mechanics play a vital role in cell propagation. This can be governed not only by chemical stimulus but also by mechanical characteristics of a cell’s immediate surroundings.

Further, the cell as well as its environment change as the cell grows, necessitating a dynamic approach to programming and modeling. As an example, cells do not duplicate if there is no space for them to grow – implying that tumors can grow only if their immediate surroundings is congenial to their growth and propagation. Therefore any model that ignores the cell environment is essentially doomed to failure. These models are required to account for as well as to predict the micro stresses that arise from abnormal cell growth.

An important factor governing cell division is the pressure exerted by the external tissue. An encapsulated tumor will be deformed and its membrane chemically damaged often causing rupture. Thus the fundamental challenge before all such researchers is to describe the mechanical behavior of continuously remodeling tissues. Tumor cells are bound to other cells and to the matrix outside them by ‘adhesion molecules of limited strength’.

Thus, the tumor grows in an environment of continuous deformation and cell reorganization. If any group of cells is subject to sufficiently high tension or shear, some links will break and new ones may form. This occurs in particular during growth, when a duplicating cell needs to displace its neighbors to make room for its daughter cells. “This qualitative description highlights the need for a quantitative description of interaction forces involving the extracellular matrix, including viscoplastic phenomena.

A similar description is needed for the adhesions between cells, which provide a mechanism for the release of excessive stresses. ” The highlights of the article are that it clearly outlines the need for a mathematical model to describe a biological phenomena and to an extent is successful in justifying why the underlying process is a suitable candidate for mathematical modeling. The qualitative processes that govern the basic functions are easily understood and are linked to each other in a simple fashion, yet the final outcome is uncertain.

This as well as the sheer relevance of the article justifies it being selected here for review. However, it should be noted that the author does not give any details of the models that are currently being considered or even the slightest suggestion of what transpired in the talks on mathematical biology. Their inclusion would not only have been germane to the topic but also helped in drawing the attention of a pure mathematician who is unlikely to read it elsewhere.

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