Mathematics Helps Predict Facial Surgery Results

The first step is to use medical imaging data of the patient to construct a three-dimensional (3D) computer model, called the "virtual patient.” The surgeons can then use the model in a virtual lab to predict the effects of surgical procedures and options, and patients can get a picture of approximately how they will look after the surgery.

The paradigm requires modeling and solving partial differential equations (PDEs), equations that represent changing physical systems. This involves identifying PDEs that are appropriate for biomechanical modeling of soft facial tissue and bone and that formulate ways to represent the interface and interaction between tissue and bone. Since such PDEs generally cannot be solved exactly in closed form, mathematics is used to provide numerical techniques for producing approximate solutions.

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, finding a mean prediction error of 1-1.5 mm for the soft tissue between a post-operative model of the patient and the predicted outcome. The study appears in the October 2006 issue of Notices of the American Mathematical Society (AMS).

"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,” concluded Professor Peter Deuflhard, Ph.D., and colleagues. "For the surgeon, our computer-assisted planning permits an improved preparation before the actual operation.”



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