THE INTERNATIONAL JOURNAL OF MEDICAL ROBOTICS AND COMPUTER ASSISTED SURGERY
Int J Med Robotics Comput Assist Surg 2011; 7: 318–326. ORIGINAL ARTICLE
Published online 18 June 2011 in Wiley Online Library (wileyonlinelibrary.com) DOI: 10.1002/rcs.401
A pre-operative approach of range of motion
simulation and verification for femoroacetabular
impingement
Ta-Cheng Chang1,2
Hyosig Kang2
Louis Arata2
Weizhao Zhao1*
1Department of Biomedical
Engineering, University of Miami,
1251 Memorial Drive, Coral Gables,
FL, 33146 USA
2MAKO Surgical Corp., 2555 Davie
Road, Ft. Lauderdale, FL, 33317 USA
*Correspondence to: Weizhao Zhao,
Department of Biomedical
Engineering, McArthur-Annex Bldg.
219A, 1251 Memorial Drive, Coral
Gables, FL 33146, USA.
E-mail: w.zhao1@miami.edu
Accepted: 7 April 2011
Abstract
Background Femoroacetabular impingement (FAI) is increasingly recog-
nized as a potential cause of hip osteoarthritis. A system capable of
pre-operatively simulating hip range of motion (ROM) by given surface
models from either healthy or FAI diseased bone is desirable.
Methods An impingement detection system using bounding sphere hierar-
chies was first developed. Both precision and accuracy of the impingement
detection system were verified by a custom-designed phantom to imitate
ball-and-socket hip movement. The impingement detection system was then
implemented into the hip ROM simulation system to simulate the ROM of
(1) healthy pelvis and femur, and (2) healthy pelvis and pathologic femur.
The ROM simulation system was also verified by manipulating sawbones
under the navigation of an optical tracking system.
Results The impingement detection system achieved a distance error of
0.53 ± 0.06 mm and an angular error of 0.28 ± 0.03◦. The impingement
detection accuracies were 100%, 100%, and 96% in three different phantom
orientations, respectively. The mean errors between simulated and veri-
fied ROM were 0.10 ± 1.39◦ for the ‘healthy pelvis and femur’ group, and
−2.38 ± 3.49◦ for the ‘healthy pelvis and pathologic femur’ group.
Conclusion The present study demonstrates a pre-operative approach to
virtually simulate and predict the functional hip ROM based on the given
bone models. The impingement detection and ROM simulation systems devel-
oped may also be used for other orthopedic applications. Copyright  2011
John Wiley & Sons, Ltd.
Keywords range of motion; simulation; verification; femoroacetabular
impingement
Introduction
Femoroacetabular impingement (FAI) is increasingly recognized as a poten-
tial cause of hip osteoarthritis, particularly in active young adults and athletes
(1–4). The estimated prevalence of FAI in the general population is about
10–15% while the latest study indicates that the prevalence may be even
higher (5–7). The number of scientific studies on FAI has also grown almost
exponentially (8).
FAI is described as an abnormal impingement caused by bony deformities,
between the proximal femur and acetabular rim during hip movement. Two
Copyright  2011 John Wiley & Sons, Ltd.

Range of motion simulation for femoroacetabular impingement 319
distinct types of FAI have been classified. Pincer impinge-
ment, characterized by acetabular deformities, involves
over coverage of the acetabulum, resulting in contact
between the acetabular rim and the femoral head-
neck junction. Cam impingement, characterized by
femoral deformities, involves a non-spherical femoral
head and insufficient head-neck offset, causing impinge-
ment against the acetabular rim (1,9,10).
FAI reduces hip range of motion (ROM) and produces
pain in patients during daily activities. Surgical inter-
vention for FAI includes soft tissue and bony repair in
order to restore hip ROM. Commonly used surgical tech-
niques involve open surgery and hip dislocation (11,12).
A less invasive alternative with minimum exposure is the
hip arthroscopic surgery (13,14). Recently, surgical robot
technology has been proven an approach that yields accu-
rate bone resurfacing following a pre-defined resection
plan in orthopedics (15,16). In order to evaluate virtually
the surgical outcome of the pre-operative plan, a system
capable of simulating hip ROM by given bone models with
FAI is desirable.
This paper presents an impingement detection simu-
lation system, which is based on the bounding sphere
collision computer graphics algorithm to predict the func-
tional hip ROM of given surface models from either
healthy or FAI diseased bones pre-operatively. In the
following sections, we describe how bounding sphere col-
lision detection is applied to the impingement detection
system. A verification process to evaluate the precision
and accuracy of impingement detection is described. An
example of hip ROM simulation based on the system
developed is given. The simulated ROM is verified by man-
ual manipulation of the sawbones under optical tracking
system navigation, which provides the ground truth for
calibration.
Materials and Methods
System description
The software was developed on a personal computer (PC)
(Precision T5400, Dell Inc., Round Rock, TX, USA) with
Quadro FX 3700 graphic card (NVIDIA Corp., Santa Clara,
CA, USA), 4 GB RAM, and the Linux operating system,
Red Hat Enterprise Linux 5.3 (Red Hat Inc., Raleigh, NC,
USA). The software was written in C and Tcl/Tk 8.3
using the installed library of the RIO software navigation
platform (MAKO Surgical Corp., Fort Lauderdale, FL,
USA). A commercially available computer-assisted robotic
system designed for knee surgery, RIO Robotic Arm
Interactive Orthopedic System (MAKO Surgical Corp.,
Fort Lauderdale, FL, USA), was utilized for this study.
The robotic system was equipped with a passive three-
dimensional (3D) optical tracking system, Polaris Spectra
(Northern Digital Inc., Waterloo, Ontario, Canada), with
an accuracy of 0.25 mm root mean square (RMS) error.
The tracking system continuously monitored optical
tracking markers (for simplicity, we use ‘markers’ in
the following description) and returned the position and
orientation of the markers in space. Each optical marker
was attached with infrared reflective spheres (11.5 mm
in diameter) arranged in a unique pattern. The tracking
system can therefore distinguish each individual marker
and return the correct orientation and position based on
this specific pattern.
Three 3D Cartesian coordinate spaces were defined
in this study. ‘Camera space’ was the coordinate system
created by the tracking system; ‘anatomic space’ was the
coordinate system of the patient’s (or sawbone’s) surgical
region; ‘image space’ was the coordinate system of the
CT images and bone surface models. The RIO software
navigation platform integrated the spatial information of
the optical tracking markers in camera space, the patient’s
surgical site information in anatomic space, and the virtual
bone model information in image space.
Bone model generation
and registration
The stereolithographic (STL) surface models of both
healthy and pathologic proximal left femora as well as
a healthy pelvis were generated from CT images. Only
cam lesions were considered in this study since cam
impingement reduces pelvic ROM significantly (17) and
has been reported as a fairly common malformation
(18). A pathologic sawbone left femur was built from
the CT data of a patient who was diagnosed with cam
FAI. This pathologic sawbone left femur together with a
healthy sawbone left femur and pelvis (Pacific Research
Labs, Inc., Vashon, WA, USA) were first implanted with
fiducial markers, and then scanned in supine position at
1 mm slice thickness by CT. Eight fiducial markers were
implanted on both sawbone femora and ten markers on
the pelvis. In order to achieve high accuracy, fiducial
markers were placed close to the anatomic landmarks
to minimize registration errors (Figure 1). The CT scan
covered the entire pelvis as well as the proximal parts
(approximately 25 cm) and distal parts (approximately
6 cm) of both femora so that all fiducial markers and
anatomical landmarks were included (Figure 2).
The 3D STL bone surface models were generated from
the segmented CT images using commercial software
(Mimics 13.1, Materialise, Leuven, Belgium). The highest
possible segmentation quality was selected to ensure that
the anatomical features were well preserved. In order to
improve the performance of the impingement detection
for ROM simulation, the standard STL, triangle surface,
bone models were modified and further processed by in-
house developed software. In brief, the STL models were
first remeshed so that the length of all edges of any triangle
from the triangle meshes was less than 4 mm. This step
ensured that all the ‘bounding spheres’ (described later)
were similar in size to avoid expensive impingement
searching of two far away bounding spheres. Next, the
remeshed models were compressed by removing repeated
vertices and by reordering the corresponding indices.
Copyright  2011 John Wiley & Sons, Ltd. Int J Med Robotics Comput Assist Surg 2011; 7: 318–326.
DOI: 10.1002/rcs