Waterloo graduate student David Qian, under the guidance of the Faculty of Mathematics’ Ricardo Fukasawa and Jochen Koenemann, introduced optimization techniques based on integer and dynamic programming to surgeons at SickKids hospital. By applying mathematical optimization algorithms, Qian and team advised doctors on the best surgical cut points to minimize the volume-difference between the surgically modified skull, and an ideal skull.
Surgeons currently rely on their intuition and experience to repair skull deformities, found at birth, in over 100 infants each year. This surgery requires doctors to remove a section of an infant’s skull, called the bandeau, reshape it into a natural curve and secure it back into the child’s head. There are a limited number of doctors willing to perform this surgery and without it these children may experience further complications to their eyesight and mental development as their skull hardens.
A section of an infant’s skull cut, cut and reshaped into a natural curve
“Prior to our involvement, surgeons were required to eye ball much of their efforts,” said Fukasawa, a faculty member in the Department of Combinatorics & Optimization. “For us, this appeared to be an ideal practical project from an optimization perspective. We used a paradigm known as dynamic programming to design fast methods to assist us in finding a volume minimizing collection of cut points.”
“Using CT scans of patients’ skulls and the bandeau templates, we developed a model to determine where the frontal bone should be cut in order to attain an ideal curvature post-surgery,” said Qian, a Waterloo graduate, with degrees in Combinatorics & Optimization.
The Waterloo team worked hand-and-hand with doctors in September 2014 for the first surgery mapped by optimization. On the walls of the surgical room were pages of algorithm output that determined the exact cut points for the bandeau of an infant’s skull. The surgical team first removed the infant's bandeau, and then installed artificial hinges in the cut locations recommended by the Waterloo team's algorithms.
Mathematical algorithms to minimize the volume-difference between the surgically modified skull, and an ideal skull
“It was a very nerve-wracking experience, but the doctors at SickKids were so amazing,” said Koenemann, also a faculty member in the Department of Combinatorics & Optimization. “They were so open to work with us and there was very little red tape, so we could get access to the information we needed to run our algorithms.”
“It was a real collaboration between teams with two very different sets of expertise,” said Fukasawa. “It was so rewarding to directly impact someone’s life, especially the life of such a small child.”
SickKids surgeons Dr. John Phillips, Dr. James Drake, and Nikoo Saber have been very positive about the process and collaboration with Waterloo. The lead surgeon explicitly expressed how well Waterloo’s cut instructions matched his intuition after years of experience.
With this success, the Waterloo team is passionate about providing further algorithms for surgical procedures. Today they are involved in a broader and more complex procedure that includes surgery and remodeling of the entire skull.
"While our initial collaboration considered optimizing the reshaping of the bandeau portion of the skull, a much more challenging problem presents itself when we consider the entire skull," said Koenemann. "In this case, surgical cuts split the infant skull into a jigsaw puzzle of sorts. The pieces of these puzzles are then reordered, and potentially flipped, and rotated to create a new and more suitable skull shape. The resulting optimization problem to compute the best cuts in this case is significantly more complicated than what we did in the bandeau setting."
An overview of this SickKids project can be found in David Qian’s 3MT presentation.