Cancer Research Applies a Markov Chain Monte Carlo Approach


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The Markov Chain Model Found Complex Cancer Seeding Patterns

3D CT Scan of Thorax with Lung Cancer at Arrow : image by via Lange123

One key and surprising result from this research, however, was that the Markov Chain model was only feasible for a more complex “seeding” process. The previous model assumed that cancer would spread from a tumour site to a new, non-cancerous site. The research found, in addition, that:

  • The primary tumour may “seed” itself. For example, a tumour in the lung could start a second lung cancer tumour.
  • A metastatic tumour could also “seed” itself.
  • A metastatic tumour could even “re-seed” the site of the primary tumour.

The Markov Chain model only worked with this complex seeding, and not for one-directional seeding.

Complications Highlighted by the Markov Chain Model

Dr. Newton’s team found that one metastatic site could act as either a spreader or a sponge, depending on the primary tumour.

For example, “for lung cancer, adrenal is a key spreader; whereas for bone and prostate cancer, bone is the key spreader” as Dr. Newton explained to Decoded Science.

Dr. Newton further clarified that “Adrenal…is a sponge for prostate cancer. Bone is a sponge for lung cancer, but it is a spreader for breast and prostate cancer“.

Monte Carlo Simulation to Support the Markov Chain Model

The researchers then ran a Monte Carlo simulation on the data from the Markov Chain model to examine the likely metastatic tumour sites, and how quickly cancer would spread to those sites.

In part, this process verified the accuracy of their Markov Chain data. It also provided insight into the effectiveness of different cancer treatment options, depending on the stage the cancer had reached.

It also supported the conclusion that the model is quite accurate with only the knowledge of the primary and first metastatic tumour site.

Microscope Slide Image of Lung Cancer : picture by GreenFlames09

Math: A Valuable Addition to Cancer Research

Dr. Newton’s research suggests the value of clinical trials for cancer treatment that takes into account the primary and first metastatic tumour sites. This research also demonstrates the value of math by testing autopsy statistics using a Monte Carlo simulation of a Markov Chain model.


Newton, Dr. Paul K. et alSpreaders and sponges define metastasis in lung cancer: A Markov chain mathematical model. (2013). Journal of Cancer Research. Accessed March 28, 2013.

Weisstein, Eric W. Markov Chain and Monte Carlo Method. MathWorld-A Wolfram Web Resource. (1999-2013). Referenced March 27, 2013.

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