# Maths and facial surgery

People who suffer from malformations of their jaws or problems with their facial skeleton after an accident need special facial surgery to help rebuild their faces. And patients want to know what will they look after the operation. Now German researchers have built mathematical tools for predicting facial surgery results. Read more...

Some people want to get a better look and they ask a plastic surgeon to remodel their nose. But other ones have more serious problems, such as malformations of the upper or lower jaw or problems with their facial skeleton after an accident. These people need cranio-maxillofacial surgery to help rebuild their faces. This is a very difficult process which needs to be planned in advance. And patients want to know what will they look after the operation. Now, German researchers have built mathematical tools for predicting facial surgery results. But read more...

The mathematical and computing tools used to assist cranio-maxillofacial surgeons have been developed by researchers from the Konrad Zuse Zentrum, Berlin (ZIB), Peter Deuflhard, Martin Weiser and Stefan Zachow.

The methodology for planning such a difficult operation requires three distinct steps described by the American Mathematical Society news release linked above.

The first step in the planning paradigm for such surgery is to use medical imaging data of the patient to construct a 3-dimensional computer model, called the "virtual patient". The second step, which is the one the article focuses on, uses the data to create a "virtual lab" in which various operative strategies can be tested. The last step is to play back to the patient the outcomes of the various strategies.

You can read the news release for some more details about the methods used. But you can see below the results for virtual and real facial surgery for four patients: "3D reconstruction from preoperative CT data (left), simulation after surgery planning (center left), reconstruction from postoperative CT data (center right), and postoperative photograph (right)." (Credit: ZIB and American Mathematical Society)

And do these mathematical techniques work well? Apparently yes.

The [research paper] states that qualitative comparisons between the outcomes predicted by the model, and the actual surgical outcomes, have been surprisingly good. The authors have also made quantitative comparisons, by creating a post-operative model of the patient and comparing it quantitatively to the predicted outcome. They found a mean prediction error of between 1 and 1.5mm for the soft tissue, which they write "seems to be a fully acceptable result."

For more information, this research work has been published by the American Mathematical Society in its Notices of the AMS under the title "Mathematics in Facial Surgery" (Volume 53, Number 9, October 2006). Here is a link to this paper (PDF format, 5 pages, 448 KB), from which the above diagram has been extracted. And here are some of the conclusions.

Even though biomechanical tissue modeling turns out to be a tough problem, we are already rather successful in predicting postoperative appearance from preoperative patient data. For the surgeon, our computer assisted planning permits an improved preparation before the actual operation. Different operation variants can be studied in advance and evaluated. For patients, our planning clearly leads to better preoperative information and therefore an improved decision basis.

And patients can even use the system themselves to see how an operation will modify their appearance. Great research!

Sources: American Mathematical Society, via EurekAlert!, September 26, 2006; and various websites

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