Computation of shapes of three-dimensional linkage structures based on optimization techniques

Spinal modeling is based on a concept called spinal energy which assumes that the spine assumes a shape to minimize spinal energy. Spinal energy depends on parameters called stiffness coefficients. These parameters can be determined from human data which, by hypothesis, are universal for a large class of humans. The method adapts Newton's method to the manifold SO(3) to find a solution of model of the human spine. Where basins of attraction are small in Newton's method, homotopy methods are introduced to move from known solutions to unknown solutions. By setting the gradient of the spinal energy to zero, Newton's method is used to solve the inverse problem of finding stiffness coefficients from human data. A new approach to improving deformed spines uses the modeling method based on spinal energy. This approach preserves maximally the range of motion of the spine. The technique used is vertebraplasty; i.e., adding and/or subtracting material surgically from various vertebral bodies without fusing or altering soft tissue. An interactive process is used to determine the surgery to be performed to improve spinal shape.