The Math Behind Medical Imaging Technology

The ability to diagnose and treat diseases has come a long way. By combining the principles and concepts of mathematics and medical imaging techniques, we can uncover new insights into diagnosis and treatment, enabling practitioners to make better decisions more accurately. So, put your lab coats on and join us as we explore how mathematics can be used to unlock the secrets of medical imaging!

 

Introduction to Math and Medical Imaging

Medical imaging is a field of medicine that uses images to diagnose diseases. Images can be created using,

• X-rays
• Computed Tomography (CT)
• Magnetic Resonance Imaging (MRI), 
• Ultrasound

Using math can improve the quality of medical images. For example, mathematical algorithms such as calculus, basic arithmetic and geometry can remove noise from an image or enhance important features for diagnosis. In addition, medical images can be processed and analysed using Statistics and Machine Learning (ML) tools, which can help extract relevant information.

The Benefits of Combining Math and Medical Imaging

Medical imaging is a rapidly growing field that uses mathematical techniques to diagnose diseases. The benefits of combining math and medical imaging include,

• Increased Accuracy
• Improved Treatment
• More Efficient Workflows
• Improved Safety

Increased Accuracy

Using mathematical techniques like histogram equalisation, Fourier transforms, probability and statistics, medical images can be more accurately analysed and interpreted. This can lead to earlier and more accurate diagnoses of diseases.

Improved Treatment

By understanding the underlying cause of diseases, better treatments can be developed. This can be done using mathematical modelling, which deals with the body's system, disease mechanism and chemical reactions. This can lead to improved patient outcomes and nullify the side effects.

More Efficient Workflows

Mathematics can help streamline medical imaging processes, making them more efficient and allowing doctors to focus on the patient, such as using fractions and percentages to know the amount of medication for a patient according to their body weight. 

Improved Safety

Mathematical algorithms such as pre-algebra and linear algebra can increase safety in medical imaging results by interpreting the graphs. This can help to prevent misdiagnosis and other medical mistakes, leading to better patient outcomes. 

Mathematical techniques in CT Scan and X-rays

Depending on the density of the body's tissue, different grayscales represent the body in CT scans and X-rays. This imaging relies on mathematical functions.

CT scan machines translate raw X-ray data into reconstructed images by solving multiple linear equations. Projections and inversion algorithms are the major math used in the results. CT scans also have Fourier-based algorithms for accuracy. Good reconstructions from the interlaced lattice can also be obtained using the direct algebraic reconstruction algorithm or by increasing the amount of data through interpolation according to the sampling theorem and also describing the convergence properties of iterative algorithms.

The interpolation step can introduce significant errors in certain cases. It has also been shown that the interpolation can be avoided by choosing the points x where the reconstruction is computed on a polar grid rather than on a square Cartesian grid and interchanging the order of the two summations. Combining all these mathematical techniques makes medical imaging a much easier procedure.

Common Applications of Math and Medical Imaging

Math and medical imaging are often used together to help diagnose diseases. 

• MRI, X-ray and CT scans use mathematical algorithms to create images of the body, which doctors can then analyse to look for signs of disease. 
• Math and medical imaging are used in research.
• Doctors can use mathematical models to predict a drug's effectiveness or determine the best dosage. 
• They are also used in the field of bioinformatics.
• Bioinformatics combines mathematics, computer science, and biology to analyse biological data, such as DNA sequences.

Other math applications in medicine include calculating dosages of medications, designing clinical trials, creating personalised medicines and analysing data from patient records.

1. Brain tumour size estimation for better surgical aspiration
2. Breast lump size location and estimation for mastectomy
3. For differentiation of malignant and benign tumours

Challenges Faced with Using Math and Medical Imaging

Several challenges must be considered when using math and medical imaging to diagnose diseases.

• Diseases may have similar symptoms, making it difficult to diagnose the disease accurately.
• Medical images can be hard to interpret, as they can be blurry or contain a lot of noise.
• Determining how to mathematically model diseases, as there is often a lot of complex data involved.
• Medical images are often taken from different angles and perspectives, making it difficult to interpret the data accurately.

As new technologies and techniques are developed, the mathematics used in medical imaging must be updated and refined to keep up with the changing landscape.

Conclusion

Numerical algorithms are being developed to speed up the scanning process, and newer machines are being designed to implement them and produce more efficient and better images. Mathematics is proving its worth in this field and will continue for years. Want to learn more about medical imaging?

We at Skill-Lync offer several courses, including a PG program in Bioengineering & Medical Devices.

Join Skill-Lync and set yourself up for success! Do enrol for Skill-Lync’s free demo sessions to talk with our experts to know more.