Saturday, March 14, 2015

Examining Fractal Geometry to Combat Cancer Cells

The first time I heard about fractals was four years ago in my Calculus class. I remembered how fascinated I was by a pattern that is so common yet overlooked. Fractal patterns can be seen everywhere in nature--clouds, lightning, seashells, ferns, broccoli, river systems, blood vessels, and the list continues. This demonstrates how nature has specific designs with which it builds its beings and structures. And this amazes me because it shows that nature can be random and spontaneous (based on thermodynamics), but at the same time, highly systematic and organized. Fractals are simple in terms of their attributes but are varied and complex in the ideas and applications that accompany them. Salient attributes of fractals include: self-similarity, iteration and shape irregularity (Baish & Jain, 2000; Dokukin, Guz, Woodworth, & Sokolov, 2015; Losa, 2014). Self-similarity means that when one fragment of an object is examined on various scales, that fragment is similar to and "reproduce the whole object from which it is derived (Losa, 2014). Recently, fractals and the concepts related to them, which first arose in mathematics, are used to examine cell and tissue morphologies (Baish & Jain, 2000; Dokukin et al., 2015; Losa, 2014). Using fractals as an approach to studying structures in biological systems may provide new perspectives and insights on structures, and thus functions, of cells and tissues.

Fractal pattern seen in Romenesco broccoli. Image retrieved from McNally (2010). Cancer is a complex disease that many researchers are trying to address and fractals have been observed in cancerous cells (Baish & Jain, 2000; Dokukin et al., 2015). Cancer is often characterized as a "chaotic, poorly regulated growth" and cancer cells have "irregular shapes" (Baish & Jain, 2000). Fractal geometry is a "vocabulary of irregular shapes" (Baish & Jain, 2000). Because structure is closely related to function, examining the fractality in cancer cells provides a new perspective on combating cancer. However, Dokukin et al. (2015) recently published their research of fractals on human cervical epithelial cells and found that, contrary to most studies of fractals and cancer, fractals was only observed at a limited time frame. True fractal patterns develop at the "precise point in which precancerous cells transform into cancer cells" (Dokukin et al., 2015). This suggests that fractals may play a role in the transformation of nonmalignant cells into malignant tumors, however, the authors have not confirmed this. There is a fairly new perspective and there is more progress to be made. And according to Losa (2014), the fractal approach is valuable in that it prevents oversimplification or approximation in analyzing structures and therefore, functional behaviors of cellular components and tissues.

1. Baish, J.W. & Jain, R.K. (2000). Fractals and Cancer. Perspectives in Cancer Research, 60, 3683-3688. 
2. Dokukin, M.E., Guz, N.V., Woodworth, C.D., & Sokolov, I. (2015). Emergence of fractal geometry on the surface of human cervical epithelial cells during progression towards cancer. New Journal of Physics, 17, 1-12. doi:10.1088/1367-2630/17/3/033019 
3. Losa, G.A. (2014). The fractal geometry of life. Rivista di biologia, 102, 29-59. 
4. McNally, J. (2010, 09 10). Earth's most stunning nature fractal patterns. Wired, Retrieved from


  1. If the fractal growth pattern occurs when noncancerous cells turn into cancerous cells, it would be cool if a cancer screening technique could be developed that would identify when cells change their growth patterns based on this switch.

  2. Building on these findings in a more activist way, I wonder if there is something unique about the process of fractal growth that could give clinicians a way to target the progression of noncancerous cells to cancerous cells. If fractal growth is not seen elsewhere in the body, it might depend on some environmental condition whose disruption could serve as a prevention tactic.

  3. I'm intrigued by the idea that cancer cells change shape, when compared to noncancerous cells. Cancer is the result of uncontrolled cell division, but how does dividing rapidly result in a change in shape? Additionally, I always wondered how cancer causes death, but if function follows form and cancer cells change shape, than they would not be able to perform their designated function. Overall a very interesting topic, which really approached the concept of cancer from a different perspective.

  4. I've been intrigued by fractals as well, and it's astounding that the transition from non-cancerous to cancerous cell has such a recognizable point. This seems to be in the very early stages of translational research, and I hope to hear more about this in the future. As interesting as the connection is, the vagueness of the importance of the connection between cancer cells and fractality makes me think this will not be terribly helpful in fighting cancer, or it may just be a while before it becomes part of a treatment. I wish I knew more about math so I could understand the relevance better, but this is still really fascinating.

  5. I think it is fascinating that so many things that appear to have no order can actually be arranged in fractals at a microscopic level. Any and all new information on cancer is a step in the right direction so this new research is great. Especially in the regard that it focuses on the first step of cancer forming, a period of time which is crucial for successful treatment in humans.