Math behind the medicine

Carmen A. Perez, MD, PhD, Department of Radiation Oncology

Carmen A. Perez, MD, PhD, a clinician in the St. Jude Department of Radiation Oncology, understands the importance of timely treatments and appropriate doses when patients undergo radiation therapy. However, sometimes patients experience unintended interruptions in therapy, such as during the COVID-19 pandemic. Interruptions can lead to a phenomenon called repopulation, wherein the cancer cells regrow, requiring more treatment.

To account for this, Perez and other radiation oncologists calculate the biological equivalent dose (BED), which measures how strong a punch is needed to kill a cancer cell.

This equation accounts for the number of treatments, n, the radiation dose per treatment, d, and the α/β ratio, which measures how sensitive a cell is to radiation. To compensate for the break in treatment, a correction factor is added, which includes a tumor repopulation factor, K, to account for the extent to which the biological effect of the daily dose is reduced by repopulation, and considers total treatment time, T, and repopulation time, TR.

Using this equation, even patients who experience gaps in their treatment can have optimal clinical outcomes.

Kenny Kellon, Biomedical Engineering

Kenny Kellon is a biomedical engineer at St. Jude, contributing to the research and clinical enterprise through equipment maintenance and construction. While the tools used at St. Jude continue to increase in complexity and functionality, the fundamental principles behind them still hold true. Ohm’s Law, first described in 1827, defines the relationship between voltage, V, current, I, and resistance, R, in an electrical circuit, and is routinely used by biomedical engineers including Kellon by means of a multimeter.

While the equipment that Kellon and the team of biomedical engineers at St. Jude help maintain involves cutting-edge technology, fundamental mathematic concepts like Ohm’s Law never change, and understanding and using them helps Kellon keep the research and clinical enterprise in top shape.

Marcie Davis, St. Jude Imagine Academy by Chili’s

Marcie Davis is a teacher for the visually impaired within the St. Jude Imagine Academy by Chili’s. When children come to St. Jude for treatment, it is vital that they receive top-level care, but also that they are supported as they continue their education. The Imagine Academy plays a key role in maintaining a child’s sense of community and routine in addition to learning.

Davis helps children who come to St. Jude with visual impairments or develop them through their treatment regimen to continue their schoolwork using Braille. Braille allows for any letter to be represented as a series of dots within a six-dot matrix. This is not limited to letters, however. A special form of Braille called Nemeth code was developed specifically for mathematics.

Distinct symbols can be used by Davis in her lessons to inform students whether they are reading numbers or letters. Unique representations for mathematical symbols like plus and minus allow basic equations to be formed.

By incorporating literary Braille, trigonometry functions and calculus terms such as differentiation and integration can also be represented. The Braille system that Davis uses to teach her students ensures that every child at St. Jude has what they need to continue learning and developing.

Subodh Selukar, PhD

Subodh Selukar, PhD, is an assistant member in the Department of Biostatistics. The impact of math on the research and healthcare enterprises at St. Jude places biostatistics in a central role in St. Jude operations. As clinical research grows in complexity, investigators need to study if certain treatments can maintain long-term cures or not. Increasingly sophisticated statistical analyses can be deployed to ensure high-quality care.

Biostatistical models are vital in clinical trials. They allow clinicians to answer research questions by utilizing available information to design the appropriate study setup and analysis upfront. Selukar’s research investigates how to use cure models, a type of biostatistical model, to study whether therapies in clinical trials maintain long-term cures and limit short-term toxicity.

One equation for cure models represents the population survival probability S(t), using the probability of being cured, p, and the survival probability among the uncured population, S*(t).

A large part of Selukar’s job is fitting such models to data and estimating parameters. Another major part is knowing when to use and not use these models.

Darcie Miller, PhD, Biomolecular X-Ray Crystallography Center

Darcie Miller, PhD, is the St. Jude Biomolecular X-Ray Crystallography Center director in the Department of Structural Biology. X-ray crystallography is a mainstay technique used to decipher the structure of biomolecules and biomolecular complexes involving proteins, DNA, RNA and small molecules, like drugs. Further, drug interactions with target proteins are routinely elucidated in exquisite detail, guiding structure-based improvement of cancer therapeutics.

To get the structure of a biomolecule, X-rays are sent through a crystal made from the biomolecule being studied at different angles. Electrons in the biomolecule bend the X-rays and cast a molecular fingerprint called a diffraction pattern. From these patterns, a 3D representation of all the electrons within the biomolecule can be constructed, within which researchers can build atomic models of the whole biomolecule.

To check that the models created are accurate, Miller and other researchers use an equation called the R-value, which compares simulated diffraction patterns with real diffraction patterns to measure the quality of the atomic model obtained from the crystallographic data.

The R-value is calculated by dividing the sum (∑) of the absolute difference between observed (Fo) and calculated (Fc) diffraction patterns by the sum of the observed pattern. This equation is a good guide for crystallographers like Miller to determine the accuracy of their atomic models in their research. The closer the match, the better the model.