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How Geometry Is Used In The Medical Field

By: Hayden and Alice

Math in Medicine

Math for a long time has been a contributing factor to the medical field. Math applies to probability and statistics in new drugs or procedures, estimating survival rates, and many others. However, the types of applications discussed today are ones that are less notable but just as important

CT Scans

CT Scans also known as a computed tomography is one of the many medical devices that have the use of geometry.

CT Scans

CT Scans: How do they work?

CT Scans

CT Scans allow doctors to see inside the human body. With a combination of X-rays and a computer, it creates pictures of your organs, bones, and other various tissues. CT Scans use a narrow X-Ray beam that circles around one part of your body. This procedure creates a series of images from many different angles that resemble a cross-sectional picture

Use of Mathematics

Use in Medicine

The black and white digital image is denoted by two coordinates that gradually has a changing light intensity known as a gray level.The actual black and white picture is a function that assigns to each pixel a certain number corresponding to its gray level. Gray levels have an integer power of two.

How it works

The functions used can integrate along straight lines and in a sense can measure a weighted average of the function along the line. When an X-ray beam passes through an object perpendicular to the beam path, the detector records the data from the tissue's absorption of the X-rays.

MRI Scans

Magnetic Resonance Imaging (MRI) is another technology used in medical imaging to do different tasks, such as dynamic heart imaging.

MRI Scans

How they work

MRI Scans

MRI scans use the interaction of a strong magnetic field with the hydrogen nuclei contained in the body’s water molecules. It uses strong magnetic fields and radio waves to construct an image of the body from signals that are detected by sensors.

Mathematics in MRI scans

Use in medicine

Math has helped speed up the scanning process by using compressed sensing and high-dimensional geometry.

Suppose we have an image or an audio signal represented by measured numerical data. These data can be arranged in a row or a column consisting of n entries, which in mathematics is called a vector with n components, where n is usually a large number.

Compressed Sensing

Compressed Sensing

Compressed Sensing is a part of the MRI process. It can be defined as a new framework for sampling and reconstructing sparse signals using small enough measures. This new strategy has been applied to synthetic aperture radar (SAR) and it links two principles: sparsity, which is linked to the signal we are interested in, and incoherence, which refers to methods of sensing.

Prescriptions

Regularly, doctors write prescriptions to their patients for various ailments. Prescriptions indicate a specific medication and dosage amount.

Prescription

Mathematics in prescriptions

Mathematics of prescriptions

Most medications have guidelines for dosage amounts in milligrams (mg) per kilogram (kg). Doctors need to figure out how many milligrams of medication each patient will need, depending on their weight. Then they have to factor in how long the medication will be in the patients body which will determine how often the patient needs to take their medication in order to keep a sufficient amount of the medicine in the body.

Conclusion

Conclusion

From prescriptions to medical imaging, the usage of math is highly needed. Geometry used by CT scans make precise cross sectional imaging of the human body. Geometry in MRI scans help speed up the scanning process for the imaging. Prescription dosage require math as well so patients do not receive too little or too much a certain prescription. Math goes hand in hand in the medical field to help those in need.

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