Scalpel… forceps… maths

The squishy world of biology has historically kept a discreet distance from the clean, logical world of maths. While physicists and chemists have become accustomed to working with maths, biology and medicine have traditionally taken a more descriptive, rather than numerical, approach. Now mathematicians are getting stuck into biomedical research, with potential life saving benefits.

Testing medicines

Giving complicated simulations with many parameters a test run in their computers lets mathematicians see which parameters the body is most sensitive to. This helps in designing experiments, telling researchers which of the many measurements and conditions are the most important to keep an eye on.

A cell’s behaviour is controlled by cascades of chemical signals. To restore normal functioning, medicines need to intercept or divert these signals at crucial points. Modelling cellular functions as networks or sets of differential equations lets those designing the medicines sift through the possible options for medicines that can intervene, drawing up a shortlist for testing.

X-rayX-ray spex

Imaging techniques are now so advanced that detailed 3D images are available to help with diagnosis and surgery. These clearer results come from combining scans taken in different positions, and using different methods, to get as much data as possible. Algorithms for image processing clean up the pictures and combine them in an intelligent way. Transformations map how soft tissue is distorted and let surgeons see a more realistic image of how the body lies during surgery.

Artificial joints and prostheses are also improving as knowledge of the body’s structure gets better and better. Biomechanical engineers use maths to model the stresses and tensions on original and replacement body parts to make sure that they work together.

Stitching it together

Trials produce huge amounts of patchy and noisy data about the effects of treatments. Statisticians play an important role in determining what conclusions can be drawn, and how strongly, from this sort of information. For example, some treatments are very effective on some people and not for others. Matching information about patients with the results of their treatments can provide clues as to how the therapy works, feeding back into pure biology.

Modern biology and medicine are complex, and new techniques are needed for further progress. Maths has an important role to play in simplifying these daunting tasks. Interdisciplinary research is diverse and stimulating and it produces both pure knowledge about existing biological systems, and practical new technologies to work with them. Applying maths to the challenging problems of biology and medicine saves lives and improves quality of life.

Related Links

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