A new computer-based method for measuring periaxial rotation of healthy and fractured femurs from preoperative CT during closed femoral fracture reduction surgery is described. The method provides a comparative quantitative measure to align the distal and proximal femur fragments based on periaxial rotation. The periaxial rotation is defined in terms of patient-specific bone features. An algorithm for automatically extracting these features from the CT based on this definition has been developed. The algorithm extracts the condyle landmarks and neck axis of the healthy bone, determines its periaxial rotation, and extrapolates this data, assuming mirror symmetry between the healthy and fractured bones, to measure periaxial rotation between the fractured fragments. Unlike existing techniques, the method requires minimal user intervention. In a feasibility study, the method was applied to five dry femurs and one patient data set, and simulated a reduction based on the periaxial measurements with satisfactory results. The experiments showed the measured angle on the fractured femur to be within 1-4.5 degrees of that of the healthy bone.

We describe a new computer-based method for periaxial rotation measurement of healthy and fractured femurs during closed femoral fracture reduction surgery from CT. The method provides a comparative quantitative measure to align the distal and proximal femur fragments based on periaxial rotation. We define periaxial rotation in terms of patient-specific bone features and describe an algorithm for automatically extracting these features from the CT. The algorthm extracts condyle landmarks and neck axis of the healthy bone, determines its periaxial rotation, and extrapolates this data, assuming mirror symmetry between the healthy and the fractured bone, to measure periaxial rotation between the fractured fragments. Unlike existing techniques, our method requires minimal user intervention. We applied the method to a patient data set and simulated a reduction based on the anteversion measurements with satisfactory results.

We give a self-contained treatment of Le and Habiro's approach to the Jones function of a knot and Habiro's cyclotomic form of the Ohtsuki invariant for manifolds obtained by surgery around a knot. On the way we reproduce a state sum formula of Garoufalidis and Le for the colored Jones function of a knot. As a corollary, we obtain bounds on the growth of coefficients in the Ohtsuki series for manifolds obtained by surgery around a knot, which support the slope conjecture of Jacoby and the first author.

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