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  • 1Short Project Description 
  • 2Summary 
  • 3About MeAbout Our Team 
  • 4Question / Proposal 
  • 5Research 
  • 6Method / Testing and Redesign 
  • 7Results 
  • 8Conclusion / Report 
  • 9Bibliography, References and Acknowledgements 

The long-term survival chance of cancer patients critically depends on whether the primary tumor has metastasized to vital organs, Since metastasized tumors smaller than size ~10-15 mm cannot be seen with the current medical imaging techniques, I have developed a stochastic Monte Carlo simulation code with the aim of predicting the size and number distribution of metastasized tumors based just on the size of the primary tumor. In the process I hope to learn about important aspects of cancer spread, and provide doctors with a statistical tool that would help them make important surgery and post-surgery decisions.

Please see my Google Presentation:

It is a 20-slide presentation with: (1) Title and Abstract; (2) Motivation and Scope; (3) Hypothesis; (4) Experimental + Theoretical background; (5) Model development; (6) Derivation of mathematical formulas; (7) Description of Stochastic Monte Carlo procedure; (8) Simulation results on Lethality and Node Positivity; (9) Decomposition of Lethality into contribution from various channels; (10) Interpretation of simulation results on fractal dimension of tumor vasculature; and (11) Future extensions of this work and possible biological and clinical applications.



I live with my parents in San Ramon, CA, in the East Bay, about 25 miles east of Oakland. I am currently a Junior in California High School.

I have an uncle (my mom's brother) who live in San Diego and an aunt (my dad's sister) who lives in Fremont. All my grandparents live in Kolkata, India.

Two years ago my grandma (mom's mother) died of breast cancer. She was mis-diagnozed at first, and when the doctors finally realized, it had metastasized to her lymph nodes, liver, and bones. This tragedy left me initially fuming in frustration. But later it provided me a strong motivation to develop a mathematical model that could possibly predict how fast metastasized tumors grow and spread as a function of time.

From a young age I love Math and Science, perhaps influenced by the fact that my dad is a Physicist and my mom a math teacher. I have heard of many scientists from my dad, but the ones that have captured my imagination the most are Newton, Einstein, and Stephen Hawking. In future I would likely take up a math-oriented job, possibly a statistician trying to tackle complex biological, environmental, and economic problems through large-scale data analysis.

When not studying I like to play the piano, hang out with friends, and run the track. I am an advanced Piano player, have passed the final certificate of merit (CM level 10) two years ago, and have won medals in many competitions.

Please refer to my Google Presentation:


In this project, I have mostly followed the work of two main research groups, i.e., (1) earlier work by Larry Norton (see my slide # 5), emphasizing on using the Gompertz function for tumor growth and showing that there is considerable patient-to-patient variation in tumor growth rates, and (2) more recent work by James Michaelson (see my slide # 4) exphasizing on developing predictive formulas for 15-year Kaplan-Meier lethality as a function of the primary tumor size.

A third piece of work that interested me initially was that by Iwata et al. (see my slide # 6 and # 16) who analyzed the case of a hepatocellular carcinoma (liver cancer) patient and developed partial differential equations (PDEs) to determine the number and size distribution of secondary and tartiary tumors, all formed in the liver itself.

None of this work (or a few other works that I have surveyed) attempted to predict the probabilities of spread to different organs and provide a number and size distribution map of metastatasized tumors as a function of time. Since the process is probabilistic in nature, I thought a natural way to tackle this problem would be through stochastic Monte Carlo simulations, which itself is probabilistic in nature. Such a strategy is not too complicated to implement, and can incorporate many of the real-life complexities that might be difficult to describe in PDEs.

Last year I wrote a Monte Carlo code that accurately reproduce the results of Iwata et al., and provide more detailed information on different aspects of tumor distribution that the Iwata work did not. This work, entitled: "Monte Carlo Simulation-baed Approach to model the size distribution of metastatic tumors" was published in Physical Review E, vol. 85, Pg. 012901. For your reference, you can access it here:

(also see slide #s 16 and 17 of my presentation).

In the present project, I developed a different Monte Carlo code (see slide # 9), aimed at extracting various metastasis parameters from clinical (hospital) data on Lethality and fraction node positivity of breast carcinoma patients. This work, along with my previous Physical Review E work, is expected to provide the groundwork to a more general tumor distribution prediction code.

I am planning to work with Dr. Michaelson (Harvard Medical School) this summer to further this project.

Please see slide #s 4, 5, 6, 7, 8, 9, 10 of my Google Presentation:


Please see slide #s 11, 12, 13, 14, 15, 16, 17 of my Google Presentation:



1.J. S. Michaelson et al., Predicting the survival of patients with breast carcinoma using tumor size, Cancer 95, 713-713 (2002); . J. S. Michaelson and L. L. Chen., How and why primary tumor size, nodal status, and other prognostic factors contribute to the risk of cancer death, Technical Report #8, The Laboratory of Quantitative Medicine, Harvard Medical School, Cambridge, MA (2009).

2.C. L. Carter, C. Allen, and D. E. Hensen, Relation of tumor size, lymph node status, and survival in 24,740 breast cancer cases, Cancer 63, 181-187 (1989).

3.L. Norton, A Gompertzian model of human breast cancer growth, Cancer Research 48, 7067-71 (1988).

4.K. Iwata, K. Kawasaki, and N. Shigesada, A dynamical model for the growth and size distribution of multiple metastatic tumors, J. Theor. Biol. 203, 177-186 (2000).

5.E. Maiti, Monte Carlo simulation-based approach to model the size distribution of metastatic tumors, Phys. Rev. E 85, 012901 (2012).    


Acknowledegments:   I would like to thank Dr. James Michaelson (Harvard Medical School) for his encouragement, and for his helpful comments on whether my mathematical results made biological sense.   

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