Trigonometry in Medical Imaging

Trigonometry in Medical Imaging

Nicole Cruder

CAT Scan

Computerized Axial Tomography

• Technique that combines a series of X-ray images taken from different angles and uses computer processing to create cross-sectional images, or slices, of organs, blood vessels and bones inside the body

What is Medical Imaging?

MRI

How does it work?

Magnetic Resonance Imaging

• Magnetic field aligns protons inside of hydrogen atoms
• Bursts of radio waves are sent from the scanner into body
• Knock protons from their position
• STOP -> protons realign back into place (emit signals)
• Signals are detected by a receiving device in the scanner
• Receiving device transmits the signals to a computer
• Creates a picture based on radio signals

• Technique and process of creating visual representations of the interior of a body
• Variety of imaging technologies
• Ex: MRI, CAT scan and ultrasound
• Depends on symptoms and part of body being examined
• Seeks to...
• Reveal internal structures hidden by the skin and bones
• Monitor medical conditions
• Diagnose and treat diseases
• Non-invasive; painless

• Technique that uses a strong magnetic field and radio waves to create detailed images of bones, organs and tissues within the body

Triangulation

Use of Trigonometry

• MRI scanning process
• Protons oscillate in magnetic field
• Release energy -> return to equilibrium state
• MRI signal
• Produces graph (damped sinusoidal wave)
• Oscillates in same manner as sine waves except...
• Amplitude approaches zero as time increases
• Signal creates MRI image

• Brain tumor removal -> requires careful preparation
• Process of determining the location of a point by measuring angles to it from known points at either end of a fixed baseline, rather than measuring distances to the point directly
• Used to pinpoint exact location of tumor

Use of Trigonometry

• Open fracture
• Ex: leg
• Use trig to determine the exact plate size needed to fix and support it
• Trigonometric function cosine
• Needs to heals properly; regain full movement of leg

What's Wrong???

• A 32-year-old man comes into the ER complaining of severe abdominal and lower back pain. A nurse takes his blood pressure - it is unusually low for his age. Alarmingly, the man looses consciousness for a few seconds every 15 minutes.

Doppler Ultrasound

• Test uses reflected sound waves to see how blood flows through a blood vessel

Use of Trigonometry

Ruptured abdominal aortic aneurysm

• Flow of blood directed toward the probe
• Reflected wave = high frequency (positive shift)
• Flow of blood moving away in relation to the probe
• Low frequency is reflected (negative shift)
• Determines direction the probe needs to be shifted
• Tech must be able to accurately measure blood flow and have a clear view of it on monitor
• Calculated using cosine of the angle between the axis of the ultrasound beam and direction of flow
• Max Doppler shift occurs at 0 degrees (cosine of o = 1)
• Flow is directly towards or away from probe
• Perpendicular flow to ultrasound beam = 90 degrees (cosine of 90 = 0), no shift is detected