# Health Physics, Math, and the Monte Carlo Simulation Connection

In this post, I would like to discuss a little bit about my background and how it relates to math.  Currently, I am a distance-learning student at the Illinois Institute of Technology (IIT) in Chicago (but live in Cleveland, Ohio), in the Professional Master’s program in Health Physics.  This master’s program is a part-time program geared toward students who are already in the health physics or medical physics fields and would like to advance/further their careers/career opportunities by gaining deeper understanding of these fascinating fields.  I actually do not work in the health physics field–I have worked in the chemistry field in chemistry patents for a short period, but have turned my focus and attention to health physics as it is very interesting and challenging.

So, one might ask what is health physics?It is not a very commonly heard of field of study, granted.  Well, health physics is a field of study that concerns itself with the interaction of different forms of radiation with matter, in particular, the environment and life–humans, animals, plants, etc.  The reason why this field is important is because besides the cosmic and terrestrial forms of radiation present, human civilization has developed many applications in medicine (nuclear medicine) and nuclear physics that utilize radiation for diagnostic/therapeutic or energy purposes, respectively.  With the increasing use of radiation, there exists the potential for accidents/disasters, such as happened in Chernobyl, Ukraine on April 26, 1986.  In that case, a unit of the nuclear reactors at the nuclear power plant in Chernobyl exploded while a test was being conducted by workers, which led to the release of a great deal of radiation in the form of radionuclides, such as strontium-90, iodine-131, and cesium-137 being the predominant ones that affected the surrounding population on both a short- and long-term basis.

Accordingly, with accidents that happen at nuclear reactors and in medical facilities where a staff member or patient may be irradiated in the process of performing a routine procedure, it is necessary to establish radiation safety guidelines and radiation dose limits for radiation workers and for the public.  These radiation safety guidelines and radiation dose limits are established by regulatory agencies such as the Nuclear Regulatory Commission (NRC), Department of Energy (DOE), Department of Transportation (DOT), Environmental Protection Agency (EPA), National Council on Radiation Protection & Measurements (NCRP) in the US, and the International Atomic Energy Agency (IAEA), and the International Commission on Radiation Protection (ICRP) in the world (some guidelines and limits are different between US and international standards).

In order for radiation safety guidelines and limits to be established and adopted, the physical (and chemical) processes for the interaction of radiation in the form of photons (light particles/waves), neutrons (neutral subatomic particle that is one of the two components of the nucleus of an atom), protons (subatomic particle with positive charge that is the other component that comprises the nucleus of an atom), and beta particles (electrons that negatively charged and are found in a cloud of different shapes in orbitals surrounding the nucleus of an atom) with matter must be understood with great accuracy.  The dynamics of the plethora of interactions of radiation with a certain material, such as lead or concrete that is used as a shielding material for a building so that it could shield workers from the radiation coming from various devices/instruments and the public outside the building, are very complex and so cannot be solved analytically.  Consequently, this scenario must be solved numerically, and the preferred method is the Monte Carlo method, which has been increasingly growing in use since the 1960s with the advent of digital computers becoming accessible, but was even used by Comte de Buffon in 1777 to estimate the value of  $\pi$ in what is famously known as Buffon’s needle problem.

The Monte Carlo method seeks to represent nature through direct simulation of the essential dynamics of the system in question.  So, the Monte Carlo method is simple in its approach–a solution to a macroscopic system through simulation of its microscopic interactions.  The way in which a solution is obtained is through random sampling of the relationships, or the microscopic interactions, until the result converges, which constitutes repetitive action or calculation, usually involving a computer (but is not necessary as the method predates the computer) making the computation faster.  Many examples of the use of the Monte Carlo method exist, including in social science, traffic flow, population growth, finance, genetics, quantum chemistry, radiation physics, including radiotherapy and radiation dosimetry.  In the next installment of this series, I will deal more closely with the mathematics of photon transport in condensed materials using the Monte Carlo method.