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Medicine / mathematics science fair project:
Stochastic Monte Carlo Simulations to Determine Breast Cancer Metastasis Rates

Science Fair Project Information
Title: Stochastic Monte Carlo Simulations to Determine Breast Cancer Metastasis Rates from Patient Survival Data
Subject: Medicine / Mathematics
Subcategory: Breast Cancer
Grade level: High School / College - Grades 10-16
Academic Level: Advanced
Project Type: Experimental
Cost: Low
Awards: Google Science Fair Finalist
Affiliation: Google Science Fair
Year: 2013
Materials: Patient data on lethality and lymph node positivity
Concepts: Tumor metastasis
Description: 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, there was 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. These metastasis rates can then be used to predict the number and size distribution of secondary and tertiary tumors in different vital organs.
Short Background

Metastatic Breast Cancer

Metastatic breast cancer is a stage of breast cancer where the disease has spread to distant sites. It is also referred to as metastases, advanced breast cancer, secondary tumours, secondaries or stage 4 breast cancer.

It is a complication of primary breast cancer, usually occurring several years after the primary breast cancer. But sometimes it is diagnosed at the same time as the primary breast cancer or, rarely, before the primary breast cancer has been diagnosed.

Metastatic breast cancer cells frequently differ from the preceding primary breast cancer in properties such as receptor status, have often developed resistance to several lines of previous treatment and acquired special properties that permit them to metastasize to distant sites, making them especially dangerous. Metastatic breast cancer can be treated, sometimes for many years, but it cannot be cured. Distant metastases are the cause of about 90% of deaths due to breast cancer.

Breast cancer primarily metastasizes to the bone, lungs, regional lymph nodes, liver and brain, with the most common site being the bone. Lymph node metastasis into the sentinel node and few surrounding nodes is regarded as a treatable local event and not metastatic breast cancer, both when occurring at primary presentation or later.

The diagnosis of breast cancer is confirmed by taking a biopsy of the concerning lump. Once the diagnosis is made, further tests are done to determine if the cancer has spread beyond the breast and which treatments it may respond to.

Monte Carlo method

Monte Carlo methods are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results; typically one runs simulations many times over in order to obtain the distribution of an unknown probabilistic entity. The name comes from the resemblance of the technique to the act of playing and recording results in a real gambling casino. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to obtain a closed-form expression, or infeasible to apply a deterministic algorithm. Monte Carlo methods are mainly used in three distinct problem classes: optimization, numerical integration and generation of draws from a probability distribution.

Stochastic simulation is a simulation that operates with variables that can change with certain probability. Stochastic means that particular factors (values) are variable or random.

Monte Carlo is an estimation procedure. The main idea is that if it is necessary to know the average value of some random variable and its distribution can not be stated, and if it is possible to take samples from the distribution, we can estimate it by taking the samples, independently, and averaging them. If there are sufficiently enough samples, then the law of large numbers says the average must be close to the true value. The central limit theorem says that the average has a Gaussian distribution around the true value.

See also:

Source: Wikipedia (All text is available under the terms of the GNU Free Documentation License and Creative Commons Attribution-ShareAlike License.)

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