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Research Papers

New Distraction Osteogenesis Device With Only Two Patient-Controlled Joints by Applying the Axis-Angle Representation on Three-Dimensional Bone Deformation

[+] Author and Article Information
Ying Ying Wu

Department of Biomedical Engineering,
Carnegie Mellon University,
Pittsburgh, PA 15213
e-mail: yingyingwu@cmu.edu

Ryan Lucking

e-mail: ryan.lucking@gmail.com

Robert Oberreuter

e-mail: oberreuter@gmail.com

Kenji Shimada

e-mail: shimada@cmu.edu
Department of Mechanical Engineering,
Carnegie Mellon University,
Pittsburgh, PA 15213

1Corresponding author.

Manuscript received October 29, 2012; final manuscript received July 10, 2013; published online September 24, 2013. Assoc. Editor: Carl A. Nelson.

J. Med. Devices 7(4), 041010 (Sep 24, 2013) (9 pages) Paper No: MED-12-1135; doi: 10.1115/1.4025186 History: Received October 29, 2012; Revised July 10, 2013

Distraction osteogenesis is a procedure to correct bone deformity by breaking the bone and slowly pulling the fragments apart to stimulate bone growth. General bone deformities are three-dimensional in nature, requiring correcting of bone angles in 3D space and also bone length. However, commercially available external fixators are either unable to simultaneously correct for both angular and length deformity or are bulky and require as many as six joints that are adjusted by patients. In this paper, we propose a novel concept of correcting a 3D bone deformity using only two active degrees of freedom (2DOF), or two patient controlled joints, by expressing the orientation deformity of the bone using the axis-angle representation and the length discrepancy as a translation in 3D space. This requires a new device design with two patient-controlled joints, a revolute joint and a prismatic joint, that can be placed in any orientation and position to allow multiple configurations of the device. This in turn allows it to correct for all typical 3D deformities. The aim of our project is to develop the 2DOF axial external fixator and an algorithm for a planner to find the optimal fixator configuration and the correction schedule for a given deformity. An algorithm for the placement of the two patient-controlled joints relative to the osteotomy site was developed. A set of test data extracted from a deformed sawbone was used to check the performance of the proposed computational method. The desired bone trajectory was defined as a straight line from initial to target position, and the optimal position of the revolute joint gives an error of only 0.8 mm. We conclude that the proposed 2DOF device and the computational planner can correct typical bone deformity and works well for the test case in simulation.

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Figures

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Fig. 1

Illustration of the hierarchical free-form deformation technique. Images taken from Ref. [25] with permission. (a) X-ray images of tibia in coronal and sagittal planes. (b) Reconstructed 3D model of tibia compared to the actual tibia model.

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Fig. 2

Simplified 2D illustration of the assignment of frames to bone fragments. (a) Deformed bone with assigned frames. (b) Desired position of bone and associated frames. (c) Magnified osteotomy site showing transformation (vertical downwards arrow) from frame B to frame D during distraction osteotomy.

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Fig. 3

Illustration of fixator as 2DOF kinematic chain with translation joint fixed to the ceiling

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Fig. 4

Illustration of elliptical cylinder workspace when joint axes are not parallel. Circular path in the plane perpendicular to ω¯ and defines the circular coordinate frame, frame J. Projection of the circular path in the plane perpendicular to v¯ and defines the elliptical coordinate frame, frame L.

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Fig. 5

Illustration of circular and elliptical coordinate frames

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Fig. 6

Error is minimized when qi,plane lies along the normal to the ellipse at the point wi,plane

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Fig. 7

Graph of optimal prismatic joint schedule. l refers to the total length extended by the prismatic joint at the end of each day. Day 1 is the first day of the distraction phase.

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Fig. 8

Graph of optimal revolute joint schedule. θ refers to the total angle rotated by the revolute joint at the end of each day. Day 1 is the first day of the distraction phase.

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Fig. 9

Matlab plot of axes of frame B at each rotation step. (a) Plot of solution. Crosses: points on search plane. Dot: optimal rotation point. Dotted line: rotation axis. The x, y, and z axes of Frame B is shown to illustrate the initial and final frame orientations. (b) Close up of trajectory. Straight line down: desired path. The x, y, and z axes of Frame B is shown at each distraction step.

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Fig. 10

VRML conceptual visualization of DO. (a) The original deformed bone. (b) The final shape of the bone. Dotted line: fitted trajectory overlaps with desired trajectory of the bone. Region about the fitted trajectory: regenerated bone.

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Fig. 11

Rapid prototype models of bone distracted via different distraction paths. From left to right: linear, cubic, negative twist, positive twist, rotational correction completed first before starting translational correction.

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Fig. 12

Photos of manufactured 2DOF device laid out to show revolute joint (circled) and prismatic joint (boxed) linked to bone fragments and each other via six hinges

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Fig. 13

Photo showing DENSO manipulator adjusting the configuration of the device

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Fig. 14

Photos showing how device corrects bone deformity over time by adjusting only the revolute and prismatic joints. Order: top left to right, then bottom left to right. Proximal bone fragment is approximately 20 cm long.

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