1. Grade Sheet – 600.145 HW #2 Name 1: __________________ Email/Phone: ______________ Role/contribution: ___________ __________________________ Name 2: __________________ Email/Phone: ______________ Role/contribution: ___________ __________________________ I/we have adhered to the rules on this homework assignment: ___________________________ (signature)(date)(signature)(date) Problem 130 Problem 25 Problem 35 Problem 420 Problem 520 Problem 630 Totals110

2. Homework groundrules Work in groups of at most 2 people Do not work with other groups on homework Do not refer to previous years’ homework Include the cover sheet on the homework Both students should sign the honor pledge You should state what each of you did NOTE: Although this is called a homework assignment, it is effectively a take home exam. I do not hesitate to let the Ethics Board investigate cases where I have reason to believe that students have broken my trust.

3. Computer-Assisted Craniofacial Osteotomies Consider the problem of navigation-assisted craniofacial surgery, as discussed in class. In this case, assume that the desired facial transformation is from an existing skull shown on the left to the elongated version shown on the right. Further, the surgeon will use the optical tracking system discussed in class Desired change

4. Computer-Assisted Craniofacial Osteotomies Further, suppose that the surgeon eventually wants to perform this procedure by means of a four segment osteotomy, illustrated below Desired change

5. Computer-Assisted Craniofacial Osteotomies Further, we will suppose that the procedure is being planned in CT coordinates and that the planning system will eventually associate the following coordinate systems with the four bone fragments, all expressed as transformations with respect to CT image coordinates: Desired change

6. Computer-Assisted Craniofacial Osteotomies 1.(30 points) Develop a “surgical CAD/CAM” information flow diagram similar to the diagrams shown in class for this application. The diagrams and accompanying description should identify the major system components, identify what each component does, what information is needed as input, what information is provided as output and to which components this information is provided and why it is needed. 2.(5 points) Provide an expression for computing the relationship between the skull base and bone fragment A before the osteotomy is perfomed. I.e., give an expression for computing F SA such that F A =F Skull ● F SA 3.(5 points) If the rotation and translation parts of F A are [R A,p A ], etc. Give expressions for determining the rotation and translation components of F Bf with respect to F Af.

7. Computer-Assisted Craniofacial Osteotomies 4.(20 points) Identify the key coordinate systems associated with the application (e.g., CT image coordinates, planned initial bone fragment positions, planned final bone fragment positions, navigational tracker makers, navigational tracker device, actual bone fragment positions at different times). Draw diagrams illustrating the relationship between these different coordinates at the following times: during planning, during registration, and after the bone fragments have been placed in their final positions. Hint: The introductory material has part of the answer, in so far as the planning system is concerned. 5.(20 points) In the work discussed in class we used matching point anatomical landmarks (specifically, points on the patient’s teeth) to perform the registration between CT plans and reality. Two other alternatives would be implanted fiducials such as the pins of Robodoc or a point-to-surface based method such as used in “pinless” Robodoc. –Discuss in a few short sentences advantages and disadvantages of these methods relative to each other. –To whom are these factors important & why? –Where & when (on the skull) would you collect points for a point-to-surface method? –Of the pinless methods discussed in class, which would you select & why?

8. Computer-Assisted Craniofacial Osteotomies 6.(30 points) The method used in class used an Optotrak navigational tracker with active markers. Within the context of the craniofacial surgery application, discuss the relative strengths and drawbacks of at least two non-optical tracking technologies with respect to each other and with respect to optical marker-based tracker methods.