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Cosmetic Medicine / Plastic Surgery News
Article Date: 28 Sep 2006 - 12:00pm (PDT)
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Cranio-maxillofacial surgery is a medical specialty
focusing on facial and skull reconstruction. This
surgery can help patients with such disorders as cleft
palate, malformations of the upper or lower jaw, and
problems with the facial skeleton due to injury.
Intensive pre-operative planning is needed not only to
ensure that the medical purposes of the surgery are
achieved, but also to give patients a sense of what
their faces will look like after the surgery is
performed.
In their article "Mathematics in Facial Surgery," Peter
Deuflhard, Martin Weiser, and Stefan Zachow (of the
Konrad Zuse Zentrum (ZIB), Berlin) describe the
mathematical techniques they have used to assist cranio-maxillofacial
surgeons to predict the outcomes of surgery. These
techniques have proven to be quite successful in
producing predictions that end up matching well the
post-operative outcomes.
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.
The second step in the paradigm requires modeling and
solving partial differential equations (PDEs), which are
equations that represent changing physical systems. One
must identify which PDEs are appropriate for
biomechanical modeling of soft facial tissue and bone.
Standard methods for handling the equations need to be
adapted for this particular application. One must also
formulate ways to represent the interface between tissue
and bone, as well as their interactions. Generally such
PDEs cannot be solved exactly in closed form, so
mathematics enters the picture once again to provide
numerical techniques for producing approximate
solutions.
With the "virtual patient" data as input, one can use
the approximate solutions to generate an individualized
model for that particular patient. The surgeons can then
use the model as 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 article by Deuflhard et al 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."
"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," the authors write. "For the surgeon, our
computer assisted planning permits an improved
preparation before the actual operation."
###
The article "Mathematics in Facial Surgery" appears in
the October 2006 issue of the Notices of the AMS.
It is available on the web at
http://www.ams.org/notices/200609/fea-surgery.pdf
Founded in 1888 to further mathematical research and
scholarship, the more than 30,000-member American
Mathematical Society fulfills its mission through
programs and services that promote mathematical research
and its uses, strengthen mathematical education, and
foster awareness and appreciation of mathematics and its
connections to other disciplines and to everyday life.
Contact: Dr. Peter Deuflhard
American
Mathematical Society
