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Dr Naleli Matjelo’s complex maths equations will help doctors to only target and then kill cancer cells in your body, leaving healthy cells alive. A lecturer in the Department of Physics and Electronics at the National University of Lesotho (NUL), he is best known for his love for highly technical and mathematically challenging problems.

Although his maths can have many applications, today we look at the specific application in cancer treatment.

One of the most stubborn diseases in the world today is cancer. Even countries with best technologies still struggle with cancer. However, scientists are just as stubborn in their search for solutions.


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Dr Matjelo and his international team of scientists are some of them.

Among several options for cancer treatment is Radiation Therapy (Radiotherapy). Cancer cells normally group together to form what is called a tumour or a lump. So one of the ways to treat cancer is to target these cells in a tumour by blasting it with protons of high energy.

You will recall that protons are those extremely small particles inside an atom. The radiation machine in this case uses protons to send beams of high energy to tumours, killing the cells.

However, this solution brings one very big challenge. How do we bombard the cancer cells with protons without also destroying neighbouring healthy cells which the patient still need to live?

Two steps are often followed.

“First, doctors will take pictures of the inside of your body using such instruments such as a CT Scan,” Dr Matjelo said. The idea is to identify and take the picture of the tumour from a number of angles. This is done in order to have as much details as possible about the nature of the tumour; where is it located, at what depth from each of the locations…etc. This is called the planning stage.

The beauty of using such instruments as CT Scans is that the tumour can be photographed from many angles to allow for a 3D picture. The picture is then analysed to know as much about the size and position of the tumour as possible.

“The second step is the treatment stage, and this often happens way after the first stage was completed,” he added. The time in between will give doctors enough breathing space to analyse the CT Scan images and plan the treatment.

The treatment then begins. Suppose the tumour is in the brain. The patient will now have his head position fixed for photography. This time the image is taken using an X-Ray imaging machine. X-Ray will just produce a 2D picture whose nature will depend on the angle of imaging. “This 2D X-Ray picture is now compared to the CT-Scan images collected in the first step until a point where the X-Ray image matches one of them,” he said.

Remember the CT-Scan has the details that the X-Ray image doesn’t have. So where pictures from both scans match, it means the right angle for treatment has been found because the CT-Scan has details of that angle. Why is all this happening? It is because the doctors have to be sure that during treatment, they are targeting the right tumour, nothing else.

The problem is that the protons will also pass through healthy normal cells. How do you make sure such cells don’t get killed? The good Dr is happy to explain, “in this case, we manipulate the proton beam such that only the peak of its strength is high enough to kill the cells and this peak is positioned to only where the tumour is located,” he said. In fact, the beam is manipulated so well that the high beam strength, which kills the cells, covers the breadth and depth of the tumour.

Now comes an even harder problem.

We’ve just made an example with a tumour in the brain. This kind is easier to target because it doesn’t often change shapes after the first step.

Now suppose the tumour is in the breast or prostrate. The physicians take the first image with a CT-Scan and the patient goes home.

When the patient comes back for treatment, the tumour might have changed shape!

Breasts and prostrates are way more flexible and tumours in them can change shape accordingly. “Now, that is a big problem,” Dr Matjelo said.

If we take the X-Ray image, how do we know we are dealing with the same tumour that we imaged a few weeks ago if no CT- Scan image taken back then matches it?

Dr Matjelo and his team’s work is to solve this problem.

“Our equations are based on the fact that there are limits to the shape that tumour can take in a human body,” he explained. “So our equations help us approximate that the ‘new’ picture we see, is the picture of the same tumour we photographed a few weeks ago, even if the shape changed.”

In this way, the Dr’s work will make it possible for physicians to be even more accurate when bombarding and killing cancer cells.

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