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Research Papers: Design of Mechanisms and Robotic Systems

# Docking Robustness of Patient Specific Surgical Guides for Joint Replacement Surgery

[+] Author and Article Information
Joost Mattheijer

Biomechanics and Imaging Group,
Department of Orthopaedics,
Leiden University Medical Center,
Albinusdreef 2,
Leiden 2333 ZA, The Netherlands
Department of Biomechanical Engineering,
Delft University of Technology,
Mekelweg 2,
Delft 2628 CD, The Netherlands
e-mail: J.Mattheijer@lumc.nl

Just L. Herder

Department of Precision and
Microsystems Engineering,
Delft University of Technology,
Mekelweg 2,
Delft 2628 CD, The Netherlands
e-mail: J.L.Herder@tudelft.nl

Gabriëlle J. M. Tuijthof

Department of Biomechanical Engineering,
Delft University of Technology,
Mekelweg 2,
Delft 2628 CD, The Netherlands
Department of Orthopaedic Surgery,
Meibergdreef 9,
Amsterdam 1105 AZ, The Netherlands
e-mail: G.J.Tuijthof@amc.uva.nl

Edward R. Valstar

Biomechanics and Imaging Group,
Department of Orthopaedics,
Leiden University Medical Center,
Albinusdreef 2,
Leiden 2333 ZA, The Netherlands
Department of Biomechanical Engineering,
Delft University of Technology,
Mekelweg 2,
Delft 2628 CD, The Netherlands
e-mail: E.R.Valstar@lumc.nl

1Corresponding author.

Contributed by the Mechanisms and Robotics Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received May 24, 2014; final manuscript received January 22, 2015; published online March 10, 2015. Assoc. Editor: Matthew B. Parkinson.

J. Mech. Des 137(6), 062301 (Jun 01, 2015) (12 pages) Paper No: MD-14-1298; doi: 10.1115/1.4029665 History: Received May 24, 2014; Revised January 22, 2015; Online March 10, 2015

## Abstract

In joint replacement surgery, patient specific surgical guides (PSSGs) are used for accurate alignment of implant components. PSSGs are designed preoperatively to have a geometric fit with the patient's bone such that the incorporated guidance for drilling and cutting is instantly aligned. The surgeon keeps the PSSG in position with a pushing force, and it is essential that this position is maintained while drilling or cutting. Hence, the influence of the location and direction of the pushing force should be minimal. The extent that the pushing force may vary is what we refer to as docking robustness. In this article, we present a docking robustness framework comprising the following quantitative measures and graphical tool. Contact efficiency $ηc$ is used for the quantification of the selected bone–guide contact. Guide efficiency $ηg$ is used for the quantification of the whole guide including an application surface whereon the surgeon can push. Robustness maps are used to find a robust location for the application surface based on gradient colors. Robustness $R$ is a measure indicating what angular deviation is minimally allowed at the worst point on the application surface. The robustness framework is utilized in an optimization of PSSG dimensions for the distal femur. This optimization shows that 12 contacts already result in a relatively high contact efficiency of 0.74 ± 0.02 (where the maximum of 1.00 is obtained when the guide is designed for full bone–guide contact). Six contacts seem to be insufficient as the obtained contact efficiency is only 0.18 ± 0.02.

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## Figures

Fig. 2

The surgical guide is docked onto the opposing distal femur by a geometric fit and a pushing force of the surgeon. A top view, front view, and right view are, respectively, shown on the knee joint in (a), (b), and (c). The femur and tibia are shown in typical angles for joint replacement surgery. (b) The region of the cartilage which is suitable for contact is the portion that is not interfered by the tibia. (c) and (d) The surgeon applies force fa at an arbitrary point pa on the circular application surface S. The resulting contact reaction forces fc,i act normal to the bony surface. The allowed variation in the application line la depends on the contact locations pc,i and the location of application surface S. (d) For a specified point pa, the direction da of application line la may vary within a convex cone Da. Cone Ca is the largest circular cone inscribed in Da, giving stricter but simpler bounds to the allowed variation of da.

Fig. 1

An artist impression of a surgical guide and its usage in knee replacement is shown. (a) The surgical guide is docked onto the distal femur by a geometric fit and a pushing force of the surgeon. (b) The drill holes are used to drill pins into the bone. (c) The pins and surgical guide are removed, whereupon the pins are repositioned. (d) The pins are used to guide a saw block in place and the saw slot is used to cut the distal femur.

Fig. 3

Robustness maps for a guide with basis contact P'c,full. The contacts are indicated by the small circles. (a) The top view onto the bony geometry shows all the selected contacts. View (b) and (c) show the robustness maps which are, respectively, an yz-slice and an xz-slice of the robustness volume. For a certain application point within the robustness maps, the direction of the application line is bounded by a circular cone Ca (as depicted in Fig. 2(d)). The mean direction va and aperture θa of Ca is indicated, respectively, by vector fields and gradient colors. Two locations for the application surface are shown, namely S1 and S2, whereof S2 is a translation and rotation of S1 in the xz-plane to a better location and orientation.

Fig. 4

Robustness maps for a guide with six optimized contacts. The contacts are indicated by the small circles. (a) The top view onto the bony geometry shows all the selected contacts. View (b) and (c) show the robustness maps which are, respectively, an yz-slice and an xz-slice of the robustness volume. For a certain application point within the robustness maps, the direction of the application line is bounded by a circular cone Ca (as depicted in Fig. 2(d)). The mean direction va and aperture θa of Ca is indicated, respectively, by vector fields and gradient colors. Two locations for the application surface are shown, namely S1 and S2, whereof S2 is a translation and rotation of S1 in the xz-plane to a better location and orientation.

Fig. 5

Robustness maps for a guide with 12 optimized contacts. The contacts are indicated by the small circles. (a) The top view onto the bony geometry shows all the selected contacts. View (b) and (c) show the robustness maps which are, respectively, an yz-slice and an xz-slice of the robustness volume. For a certain application point within the robustness maps, the direction of the application line is bounded by a circular cone Ca (as depicted in Fig. 2(d)). The mean direction va and aperture θa of Ca is indicated, respectively, by vector fields and gradient colors. Two locations for the application surface are shown, namely S1 and S2, whereof S2 is a translation and rotation of S1 in the xz-plane to a better location and orientation.

Fig. 7

Results of the optimization of ηc for even-numbered contact sets ranging from 6 to 18 contacts. The number of contacts is denoted by k. The contacts are optimized one at the time and in three cycles to confirm convergence. The iteration that ends each optimization cycle is denoted by a dot.

Fig. 6

Robustness maps for a guide with 18 optimized contacts. The contacts are indicated by the small circles. (a) The top view onto the bony geometry shows all the selected contacts. View (b) and (c) show the robustness maps which are, respectively, an yz-slice and an xz-slice of the robustness volume. For a certain application point within the robustness maps, the direction of the application line is bounded by a circular cone Ca (as depicted in Fig. 2(d)). The mean direction va and aperture θa of Ca is indicated, respectively, by vector fields and gradient colors. Two locations for the application surface are shown, namely S1 and S2, whereof S2 is a translation and rotation of S1 in the xz-plane to a better location and orientation.

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