Tomography : Looking Inside With Outside Tools (Student)

What is the BioMath Connection (BMC) Project?

BMC was a pioneering project linking biology and mathematics in the high schools. It provided an opportunity for high school teachers, writers, researchers, and others to get in on the ground floor of developing innovative classroom materials. The materials consist of 20 modules that can be flexibly adapted for use in a variety of courses at a variety of grade levels in both biology and mathematics. The project was run by DIMACS at Rutgers University in collaboration with the Consortium for Mathematics and its Applications (COMAP) and Colorado State University (CSU).



Tomography is a form of imaging using sections. Tomography truly brings together mathematics, biology and technology to solve problems in many areas. The unit starts with an introduction to tomography and then introduces some basic mathematics used in computed tomography (CT scans). The unit looks at the biology of the human body, what anatomical conditions can be observed using various kinds of scans, and the differences between CT scans and positron emission tomography (PET scans). Many of you have heard of (or even have had) an MRI or CT scan, or even a PET scan, thus you may find the topic of tomography very interesting.

This unit provides real-life examples that use skills from algebra II and geometry, including:

modeling using e and exponential functions
solving systems of equations, and
visualization in 3-D,

to understand one of the important tools available to physicians in understanding the status of the human body. In addition to medical imaging, applications of tomography include autopsies, structural soundness, archeology, and others involving imaging that are increasingly important today.
Throughout the unit, there are many activities, worked examples, homework problems, and various assessment tools.

Topics
Biology: Investigate medical imaging, consider tissue properties (attenuation coefficient), and examine applications of imaging methods.
Mathematics: Apply of Beer's law and visualize shapes and surface are.

Prerequisites
Biology: Basic ideas of anatomy, organs and tissues, and a basic understanding of radiography in terms of x-rays.
Mathematics: nderstand function as an input-output model. Understand concept of exponential functions, the concept of a 3-dimensional grid, and be able to determine surface area.

Length
This unit consists of 4 lessons, an optional unit project lesson and an assessment. It will take 5 - 7 class periods (45 minutes each) if the majority of work is done during class.