Repositioning the knee joint in human body.pdf

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Repositioning the Knee Joint in Human Body FE Models Using a Graphics-Based Technique a

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Dhaval Jani , Anoop Chawla , Sudipto Mukherjee , Rahul Goyal , Nataraju Vusirikala & Suresh Jayaraman

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A. D. Patel Institute of Technology, Gujarat, India

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Department of Mechanical Engineering, Indian Institute of Technology, Delhi, India

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Department of Computer Science, Indian Institute of Technology, Delhi, India

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VS &S Group, India Science Lab, General Motors Tech Centre India Pvt. Ltd., New Delhi, India Accepted author version posted online: 03 Apr 2012.

To cite this article: Dhaval Jani, Anoop Chawla, Sudipto Mukherjee, Rahul Goyal, Nataraju Vusirikala & Suresh Jayaraman (2012): Repositioning the Knee Joint in Human Body FE Models Using a Graphics-Based Technique, Traffic Injury Prevention, 13:6, 640-649 To link to this article: http://dx.doi.org/10.1080/15389588.2012.664669

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Traffic Injury Prevention, 13:640–649, 2012 C 2012 Taylor & Francis Group, LLC Copyright ISSN: 1538-9588 print / 1538-957X online DOI: 10.1080/15389588.2012.664669

Repositioning the Knee Joint in Human Body FE Models Using a Graphics-Based Technique DHAVAL JANI,1 ANOOP CHAWLA,2 SUDIPTO MUKHERJEE,2 RAHUL GOYAL,3 NATARAJU VUSIRIKALA,4 and SURESH JAYARAMAN4 1

A. D. Patel Institute of Technology, Gujarat, India Department of Mechanical Engineering, Indian Institute of Technology, Delhi, India 3 Department of Computer Science, Indian Institute of Technology, Delhi, India 4 VS &S Group, India Science Lab, General Motors Tech Centre India Pvt. Ltd., New Delhi, India

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Objective: Human body finite element models (FE-HBMs) are available in standard occupant or pedestrian postures. There is a need to have FE-HBMs in the same posture as a crash victim or to be configured in varying postures. Developing FE models for all possible positions is not practically viable. The current work aims at obtaining a posture-specific human lower extremity model by reconfiguring an existing one. Methodology: A graphics-based technique was developed to reposition the lower extremity of an FE-HBM by specifying the flexion–extension angle. Elements of the model were segregated into rigid (bones) and deformable components (soft tissues). The bones were rotated about the flexion–extension axis followed by rotation about the longitudinal axis to capture the twisting of the tibia. The desired knee joint movement was thus achieved. Geometric heuristics were then used to reposition the skin. A mapping defined over the space between bones and the skin was used to regenerate the soft tissues. Mesh smoothing was then done to augment mesh quality. Results: The developed method permits control over the kinematics of the joint and maintains the initial mesh quality of the model. For some critical areas (in the joint vicinity) where element distortion is large, mesh smoothing is done to improve mesh quality. Conclusions: A method to reposition the knee joint of a human body FE model was developed. Repositions of a model from 9 degrees of flexion to 90 degrees of flexion in just a few seconds without subjective interventions was demonstrated. Because the mesh quality of the repositioned model was maintained to a predefined level (typically to the level of a well-made model in the initial configuration), the model was suitable for subsequent simulations. Keywords Human body FE model; Posture; Repositioning; Mesh morphing

INTRODUCTION In the last decade, many human body finite element models (FE-HBMs; for instance, the Total Human Model for Safety [THUMS; Maeno and Hasegawa 2001], HUman Model for Safety 2 [HUMOS2; Vezin and Verriest 2005], Japan Automotive Manufacturing Association and Japan Automotive Research Institute models [JAMA/JARI models; Sugimoto and Yamazaki 2005], and Global Human Body Models Consortium model [GHBMC model; Gayzik et al. 2011] have been reported. The existing FE-HBMs are developed in a few standard postures only. It is known that precrash posture of the victim influences the injuries sustained. For instance, Yang et al. (2005) observed Received 27 September 2011; accepted 3 February 2012. Address correspondence to: Anoop Chawla, Department of Mechanical Engineering, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India. E-mail: [email protected]

that, for a pedestrian, the impact responses and injury outcomes are significantly affected by the initial postures and the orientation of victim. Meissner et al. (2004) used a computational model to demonstrate that the resulting post-impact kinematics of the pedestrian is sensitive to pre-impact motion and posture of the victim. The variation in stance changes the severity of an injury incurred during an impact by altering the region impacted and the subsequent upper body kinematics. Ramamurthy et al. (2011) also observed the influence of pedestrian pre-impact characteristics on post-impact kinematics and the severity of injury sustained during the pedestrian–vehicle contact stage. Elliot et al. (2011) reported the influence of pedestrian speed and stance on kinematic parameters such as transverse offset, amount of head rotation between first contact between the vehicle and the legs, and the time of head contact with the vehicle. There exists a high level of uncertainty in the initial conditions of the pedestrian and the vehicle prior the impact (Untaroiu et al. 2010). The pre-impact parameters such as

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vehicle speed, point of contact between the victim and vehicle, and orientation of the pedestrian at the time of contact would affect the post-impact kinematics, forces induced in the body of the victim, and thus the injuries sustained. Untaroiu et al. (2009) developed a methodology to identify pre-impact vehicle speed and pedestrian posture using rigid-body simulations (MAthematical DYnamic MOdels [MADYMO] pedestrian model) and genetic algorithms. The work was extended for child pedestrian scenarios and an advanced methodology for reconstructing child pedestrian–vehicle impacts was reported in Untaroiu et al. (2010). The methodology combines the crash data with multibody simulations and optimization techniques for identifying the pedestrian posture and vehicle speed prior to impact. Extension of such techniques for detailed investigation of injuries when using FE-HBMs would require fast and efficient repositioning of the models. The effect of posture on the postcrash kinematics and injuries has been established for vehicle occupants as well and can vary significantly due to age, anthropometry, and driving habits (Zhang et al. 2004). Unlike the case of the pedestrian, the confines of the vehicle interior also place bounds on the initial position of the occupant. Yoganandan et al. (2001) observed an effect of leg prepositioning and orientation of the impacting axis on the trauma to the pelvic region. Bose et al. (2010) reported that occupant posture was the most influential parameter affecting the overall risk of injury in frontal collisions. Though the risk of injuries to the upper body regions increased significantly for postures with the upper body close to the steering column, the risk of lower extremity injuries reduced with the decrease in the excursion distance of the upper body (Bose et al. 2010). Adam and Untariou (2011) also observed a relationship between posture and injuries sustained by occupants. Thus, the estimation of interaction of human body parts with the vehicle would be more accurate if the model being used for the simulation were reoriented to postures representative of the precrash victim. Developing FE models for all possible postures is not viable. Compromises due to nonavailability of FE models for different postures may lead to erroneous conclusions and may limit the use of these models. Therefore, reconfiguration of existing FE models to get posture specific human body models is required. Few studies have reported repositioning techniques for FEHBMs. Vezin and Verriest (2005) and Bidal et al. (2006) discussed posture change techniques adapted for the HUMOS2. In the first approach, a database of precalculated positions is used and intermediate positions are obtained by linear interpolations. The second approach is based on interactive real-time calculations provided by a simplified finite element solver. However, not much information about the technique and the quality of the results obtained is available and it has not been possible to judge the accuracy of the anatomical relation among the body segments, the time required for repositioning, and the quality of the mesh obtained. Parihar (2004) repositioned the lower extremity of the THUMS model from an occupant posture to a standing (pedestrian) posture using a series of dynamic FE simulations. Some

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major drawbacks of the method were a lack of direct control over the body kinematics being generated and the poor quality of the resulting mesh. Jani et al. (2009) investigated the time required, control over bone kinematics, anatomical correctness of the repositioned model (position acquired by bones), and user intervention needed when repositioning FE-HBM using dynamic FE simulations. For the simulations, the bones were defined as rigid to reduce the runtime of simulation. The tibia was fixed and the femur was given an angular velocity of 0.5 rad/s about the flexion–extension (F-E) axis on the femur. The process required large CPU time (approximately 6 h on an Intel Core2Quad, 2.4-GHz processor Q6600, 8 GB DDR2 RAM, assembled in lab) and exhibited a lack of control over the bone kinematics in absence of subjective interventions. In addition, though the anatomical correctness of the final posture was uncertain, the mesh quality of the repositioned model was poor and required subjective mesh editing. It was determined that another more efficient and effective method was necessary. In the present study, a new method to reposition the FE-HBM is proposed. The method is based on graphics techniques such as morphing and affine transformations, which are widely used for animating graphical characters. The technique also provides for incorporating available clinical data on kinematics of bones. METHODS This section describes the methodology developed for the FE-HBM repositioning along with the implementation for the lower extremity (knee joint). Methodology The repositioning process starts with segregation of model components into 2 groups: (1) rigid components (bones) and (2) deformable components (soft tissues). For a model segment (for instance, limb) to be repositioned, joint configuration (rotation or translation) and axes of motion are located based on available information from the literature. The bones are repositioned with affine transformations and the skin is repositioned using graphics-based heuristics. The soft tissues are mapped in the space between the bones and the skin using Delaunay triangulation/tetrahedralization (Preparata and Shamos 1988). The mesh quality is improved (if necessary) through mesh smoothing, which does not alter the element connectivity. Though the methodology is generic, this article addresses its implementation on the lower extremity (knee joint). Model Geometry Because the knee joint was used to demonstrate the repositioning methodology, a lower extremity FE model excluding the pelvis and foot was used. The geometry of the model was extracted from a full human body FE model (The General Motors [GM]/University of Virginia [UVA] 50th percentile male FE model; Untaroiu et al. 2005). The model in the initial configuration is shown in Figure 1a and details of the knee joint of the


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Figure 1 (a) Lower extremity model and (b) details of the knee joint (lateral view) (Color figure available online).

model are shown in Figure 1b. Bones (femur, tibia, fibula, and patella) were modeled in multiple layers with shell and hexahedral elements. The model also includes ligaments (hexahedral elements) of the knee joint, menisci (hexahedral elements), patellar tendon (shell elements), knee capsule (shell elements), and flesh (hexahedral elements). In order to ensure postural accuracy of the model, it is essential to derive accurate information of the kinematics of bones of the joint under consideration. In the present study, the focus is on the knee joint, which involves 2 distinct motions: tibiofemoral motion and patellofemoral motion. These motions are discussed in subsequent sections. Tibiofemoral Motion The kinematics of tibiofemoral motion has been discussed extensively in various literature. Different techniques such as computed tomography scans with biplanar image matching (Asano et al. 2001, 2005) and magnetic resonance imaging scans (Freeman and Pinskerova 2005; Hill et al. 2000; Johal et al. 2005; Martelli and Pinskerova 2002; Pinskerova et al. 2001) have been used to study the tibiofemoral kinematics. In addition to these techniques, the use of fluoroscopy, X-ray radiographs, and radio-stereometric analysis (RSA) have been reported. Studies on tibiofemoral kinematics have been either in vivo (Asano et al. 2001, 2005; Hill et al. 2000; Johal et al. 2005; Li et al. 2007) or with the cadaveric knee (Churchill et al. 1998; Elias et al. 1990; Hollister et al. 1993; Iwaki et al. 2000; McPherson et al. 2005; Most et al. 2004). These studies have investigated relative movement between the proximal tibial plateau and distal femoral condyles considering different anatomical references. Even though a broad qualitative agreement is observed among data reported with regard to type of motion, a quantitative comparison on knee joint kinematics between studies

is difficult. This is due to variation in activities and population studied, variations in the references used for measurements, and differences in the way data are reported (whether the data are reported as rotations about axes identified or translations along coordinates). However, the results led to a conclusion that the tibiofemoral movement is a combination of 2 motions: (1) rotation of the femur with respect to the tibia (or vice versa) about a flexion–extension axis (referred to hereafter as pure flexion–extension rotation) and (2) sliding/translation of femoral condyles over the tibial plateau. There is agreement that the tibiofemoral rotation (pure flexion–extension) has “no fixed” axis; that is, flexion–extension rotation occurs around an instantaneous axis that sweeps a ruled surface (known as an axode; Mow et al. 2000). Thus, it difficult to describe or reproduce anatomically correct pure flexion–extension rotation using mathematical models. However, studies have shown that the motion can be described better if the F-E axis is considered as a fixed axis (Churchill et al. 1998; Hollister et al. 1993; Stiehl and Abbott 1995). Recently, Eckhoff et al. (2003) suggested that the knee F-E axis can be approximated as a single cylindrical axis in posterior femoral condyles. Based on the understanding developed from the cited studies, it was decided to locate a fixed (single) F-E axis in the knee joint of the model to define the pure (flexion–extension) rotation in the present study. There are different views about the definition of the F-E axis in the posterior femoral condyles. Two definitions of fixed F-E axes are widely used: 1. The transepicondylar axis (TEA) is defined as the axis connecting the most prominent points on the lateral and medial femoral condyles or the axis connecting the femoral origins of collateral ligaments (Blankevoort et al. 1990; Churchill et al. 1998; Hollister et al. 1993; Miller et al. 2001). Berger et al. (1993, 1998) reported the use of TEA in total knee arthroplasty. 2. The geometric center axis (GCA) is defined as the axis passing through the medial and lateral centers of the circular profiles of the posterior condyles (Asano et al. 2001, 2005; Eckhoff et al. 2001; Pinskerova et al. 2001). The circularity of posterior femoral condyles and its application to study knee kinematics has also been reported by Kurosawa et al. (1985), Iwaki et al. (2000), Elias et al. (1990), Hollister et al. (1993), and Churchill et al. (1998). The GCA has also been used to represent the posterior geometry of the femoral condyle (Eckhoff et al. 2001) and kinematic data (Blankevoort et al. 1990; Freeman and Pinskerova 2003; Hill et al. 2000; Iwaki et al. 2000). Most et al. (2004) analyzed the sensitivity of the knee joint kinematics calculation to selection of the flexion axes (TEA or GCA) and established that, as long as a clear definition of the flexion axis is given, any of the axes can be used to describe knee joint kinematics. The circles fitted on posterior femoral condyles to locate GCA on the model being used is shown in Figure 2. The GCA is chosen as the line passing through the centers of these circles.


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Figure 2 Circles fitted on posterior femoral condyles in the sagittal plane to locate the GCA (lateral view).

It has also been reported that the sliding of the medial femoral condyle is minimal (typically in the range of ±1.5 mm; Iwaki et al. 2000) while the lateral femoral sliding is large (could be as large as 24 mm; Iwaki et al. 2000). Unequal movement of lateral and medial femoral condyles can also be observed when movement of the GCA is traced from hyperextension to 120 degrees of flexion. Hence, Churchill et al. (1998), Asano et al. (2001, 2005), Pinskerova et al. (2001), Wretenberg et al. (2002), and Johal et al. (2005) suggested that such uneven femoral sliding can be approximated as an external rotation of the femur about a longitudinal rotation axis (L-R axis) fixed on the medial part of the tibia. From the above discussion about knee kinematics, the following information can be concluded: 1. Tibiofemoral motion can be approximated by 2 rotations: flexion about the F-E axis followed by rotation about the L-R axis. 2. Flexion–extension motion can be approximated by a rotation about a single stationary axis in the posterior femoral condyles. Implementation of Tibiofemoral Kinematics In the present work, tibiofemoral motion data from Asano et al. (2001) were used. The F-E axis (GCA) was located on the posterior femoral condyles, passing through the centers of the circles approximating the lateral and medial posterior femoral condyles. The circles were fitted using nodes on the posterior femoral condyles of the FE model such that when nodes on the posterior condyle surface are projected on the sagittal plane, circles approximate the boundary nodes. The radii of these circles were 20.52 mm on the lateral side and 23.31 mm on the medial side. The values obtained were within the range of 18 to 23 mm and 20 to 25 mm, respectively, as reported by Pinskerova et al. (2001). The lateral and medial ends of this axis were found to be within the area of the femoral origins of the lateral and

Figure 3 (a) Flexion extension axis and longitudinal rotation axis (anterior view) and (b) mechanical and anatomical axes of tibia and femur (anterior view; Jani et al. 2009) (Color figure available online).

medial collateral ligaments, respectively. However, sensitivity of the axes location could not be analyzed further because only one femur model was available. The L-R axis was located between a point on the medial tibial plateau (approximate center of the contact path) and the center of the tibio-talar joint (just below the point of intersection of the distal end of the tibia and the anatomical axis of the tibia). The F-E and L-R axes are shown in Figure 3a. The knee motion was approximated as rotation of the femur about the F-E axis followed by a rotation about the L-R axis (using the relationship between the 2 rotations reported in Asano et al. 2001). Mechanical and anatomical axes (as described in Luo 2004) of the femur and tibia were also located as shown in Figure 3b. Tibiofemoral flexion was measured as an angle between the long axes (anatomical axes) of the tibia and the femur, projected on the sagittal plane as suggested by Li et al. (2007). Because the bones were rotated as per available kinematic information, and flexion angles were tracked using anatomical references (anatomical axes of tibia and femur), complete control over the bone kinematics was achieved. Patellofemoral Motion Numerous studies have investigated the patellofemoral motion. Some studies have focused on analysis of patellofemoral forces (contact areas/pressure; Singerman et al. 1995; Zavatsky et al. 2004), and a few others investigated patellofemoral kinematics (Asano et al. 2003; Heegard et al. 1995; Li et al. 2007; Zavatsky et al. 2004). The kinematics data were presented either as translations (anterior–posterior, medial–lateral, superior–inferior) of

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affine transformations (rotation about F-E and L-R axes) and the skin was transformed through a set of geometric heuristics (discussed in the next section), the volume coordinates were used to regenerate new position of the nodes of the deformable components.


Figure 4 Coordinate system for patellar motion showing axes for patellar flexion, external–internal rotation of patella, and lateral–medial tilt (Zavatsky et al. 2004).

the patella (with respect to either a tibial reference [Li et al. 2007] or a femoral reference [Asano et al. 2003] or as rotations [Li et al. 2007; Zavatsky et al. 2004]). However, accurate patellar tracking and a definition of normal tracking are not available from experimental or clinical conditions (Katchburian et al. 2003). Furthermore, universal agreement on the definition of normal patellar tracking has not been reached (Grelsamer and Weinstein 2001). Data from Zavatsky et al. (2004) were used to generate patellar motion in the present work. Zavatsky et al. (2004) reported patellar flexion, internal–external rotation, and medial–lateral tilt against the tibiofemoral flexion. The coordinate system used for the patella is shown in Figure 4. The patellar flexion axis was chosen to be the same as the femoral F-E axis and the medial lateral tilt axis was chosen as the line that passes through the centroid of the patella and is contained in frontal plane. Because internal–external rotation was less than 2 percent of the flexural rotation, it was neglected. Flesh Mapping and Delaunay Tetrahedralization Only graphics, without reference to physics, have been used to represent deformation of structures (characters as well as entities), muscles, modeling human characters, and the behavior of musculoskeletal systems (Aubel and Thalmann 2001; Blemker and Delp 2005; Dong and Clapworthy 2002; Sheepers et al. 1997; Sun et al. 1999). These techniques use surface definitions or simplified structures defined by ellipsoids. The current model is a finite element model inclusive of a mesh of bones, flesh, and soft tissues with boundary interaction through contact definitions and multiple element types. It was not viable to adapt techniques used by graphic designers directly for manipulating such a model. Delaunay tetrahedralization (Preparatta and Shamos 1988) is a method to partition the space formed by point cloud data into a set of tetrahedrons. The method developed is based on mapping of nodes of the deformable components using Delaunay tetrahedralization. The space between the skin and the bones was partitioned into a set of tetrahedrons, and nodes of the deformable entities (flesh, ligaments, patellar tendon, and minisci) were then mapped using volume coordinates of enveloping tetrahedron. After the bone was repositioned through

Implementation of the Methodology on Lower Extremity (Knee Joint) A code was developed using VC++ (programming language and Graphical User Interface [GUI] Microsoft Visual C++) and OpenGL (graphics platform) to implement affine transformations of the bones, transformations of skin contours, and mapping of the soft tissues. The repositioning was initiated with identification of contours on the skin of the model. A total of 86 skin contours were identified in the initial configuration of the given model. The soft tissue (hexahedral elements) nodes are contained in the space between the skin contours and outer surface of the bones. Delaunay tetrahedralization was then carried out using nodes on the outer surface of the bones and skin nodes. The process partitions the space of the soft tissues into tetrahedrons and does not alter the existing mesh. Each soft tissue node was then related to the tetrahedron it lies in. The information was later used for reverse mapping to compute position of soft tissues after the bones and skin contours were repositioned. The algorithm of skin contour transformations is based on a technique developed for surface models (Jianhua et al. 1994). A schematic diagram of the model with skin contours and bones (body 1: region above the knee joint; body 2: region below the knee joint) is shown in Figure 5a. If the skin contours were given the same affine transformations as the bones, the skin contours would penetrate into each other as shown in Figure 5b. These penetrations were removed by rotating each contour about an axis lying in the plane of contour along the medial–lateral direction. This rotation is termed parallelizing rotation because it orients the contours in the joint vicinity to become almost parallel to each other. One such typical contour in the region above the knee joint, along with its axis of rotation and direc-

Figure 5 Skin contours: (a) initial configuration and (b) after flexion (Color figure available online).

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Figure 6 (a) Contour with parallelizing axis depicting direction of parallelizing; (b) parallelizing direction of contours; and (c) removed penetrations after parallelizing (Color figure available online).

tion of rotation, is shown in Figure 6a. The axis of parallelizing rotation passes through the center of the contour, is contained in the plane of the contour, and is along the medial–lateral direction. Figure 6b shows the orientation of skin contours in the vicinity of the joint before parallelizing along with the proposed direction of rotation for parallelizing. The position of skin contours after parallelizing is shown in Figure 6c. The amount of rotation of each contour tends to zero as the distance of the contour increases from the joint. As suggested in Jianhua et al. (1994), to calculate the amount of rotation, consider a line P1 P0 (Figure 7) passing through the center of the skin contours of the thigh region and line P2 P0 passing through the center of the skin contours of the calf region (Figure 7). P0 is the knee joint − → − → position. L1 and L2 are the vectors along the inferior–superior direction of the upper leg and lower leg, respectively. The angle − → − → between L1 and L2 (flexion angle) is 2θ . Let a typical contour in region P1 P0 be denoted by i. The contour i is rotated by angle − → θ i about its parallelizing axis, which is parallel to L and passes through the point Qi . The calculations are summarized below:

Thus, the amount of rotation of a plane reduces as its distance from the joint increases and at ends it becomes zero and a kink-free repositioned model with no penetrating contours is obtained. But this operation reduced the distance of skin nodes from the corresponding bone. Consequently, the volume of flesh between bone and skin was also reduced. To prevent this vol-

Figure 7 Amount of contour parallelizing and estimation of volume preservation scaling (Jianhua et al. 1994) (Color figure available online).

ume squashing (in other words, to ensure volume conservation), the skin contours were scaled about their centroids to maintain distances of points on contours from the centroid. For instance, consider a point A on the ith contour situated at a distance r0 from the link P1 P0 (Figure 7). After parallelizing, the point A is transformed to A1 (Figure 7). As can be observed in Figure 7, the distance of A1 from the link P1 P0 is less than r0 . To compensate for this reduction in distance (and the flesh underneath) −−−→ the point A1 is scaled to position point A2 in the direction Qi A1 . The scaling factor is calculated from Eq. (1) and the coordinates of A2 are obtained as shown in Eq. (2). scale factor=

ro Qi A1 , dist(A1 , P0 P1 )

(1)

Hence, A2 = Qi + scale factor x(|A1 − Qi |)

(2)

The amount of scaling increases as one goes away from the axis of the bone in the anterior–posterior direction. This variation helps in preserving soft tissue volume. The effect of the parallelizing and volume preservation operations on the model is shown in Figure 8. As indicated in Figure 8a, flexion caused contours in the vicinity of the joint to penetrate into each other. Figure 8b shows the model after parallelizing of the contours. However, as a consequence of parallelizing, the volume of the soft tissues in the leg decreases (compare calf portions in Figures 8a and 8b). To compensate for this reduction in shape and to regain the shape of the leg, volume preservation scaling is applied, resulting in a model as shown in Figure 8c. This completes repositioning of the nodes of the bones and skin contours. Because these nodes are a part of the tetrahedrons generated earlier (during Delaunay tetrahedralization), these tetrahedrons were transformed. The nodes of the soft tissues were then relocated as per the procedure explained in the earlier sections. There is a significant movement of bones

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RESULTS


Figure 8 Orientation and size of skin contours (a) after flexion; (b) after parallelizing; and (c) after volume preservation scaling (Color figure available online).

relative to tissues such as menisci, tendons, and ligaments in the environs of the knee joint. This results in penetrations between the bones and these tissues. To address this problem, the nodes of ligaments, menisci, and tendon were mapped only to the nodes of skin contours. Thus, these tissues will be transformed to the new position along with the skin contours to which they are mapped (skin contours in the vicinity of joint). Because the soft tissues in the model were mapped with a complete partition (Delaunay tetrahedralization) of the soft tissue space, the model in the new posture was expected to be penetration free unless the initial model had penetrations. Exceptions were observed due to newer interaction regions for bones and soft tissues. For instance, elements of condyles are not exposed to the capsule and flesh initially. They, however, come in contact after flexion or movement of patella. Such penetrations were tackled by local stretching of skin contours. The repositioned model was finally checked for mesh quality parameters such as maximum aspect ratio, maximum warpage, maximum skew, and minimum Jacobian. The model was then subjected to mesh smoothing if mesh quality parameters were found to be of inferior quality compared to their respective values in initial model. Mesh Smoothing During repositioning, the element quality of soft tissues may change to values below acceptable limits. The deterioration is likely to increase with an increase in relative motion (for instance, flexion angle in the knee). To improve the quality of the mesh, a mesh smoothing algorithm (DARSS technique; Jani et al. 2011) was applied. The algorithm can operate on structured as well as unstructured 2D quadrilateral and 3D hexahedral meshes. For a given spatial mesh, the internal nodes were perturbed in 2 stages. The first stage used an algebraic form and the second stage used Nelder-Mead simplex-based optimization. The process preserves element connectivity and the number of elements.

The complete process of repositioning takes approximately 104 s (on an Intel Core2Quad, 2.4-GHz processor Q6600, 8 GB DDR2 RAM) to alter the posture of the FE lower extremity model. This includes repositioning of the bones (tibia/femur and patella) using affine transformations, repositioning the skin (contours), and mapping of soft tissues such as muscles, ligaments, tendon, and flesh using Delaunay triangulation. The model repositioned with the method developed is shown in Figures 9a and 9b. At this stage, flexion up to 90 degrees has been implemented. As can be seen in Figure 9b, the repositioned model is free from uncontrolled distortion of model components. The mesh quality is hence maintained. The mesh quality parameters in the initial model (min. Jacobian: 0.21, max. aspect ratio: 10.76, max. warpage: 166.67, max. skew: 75.3) were the targeted quality values for the repositioned model. The mesh quality parameters were tracked throughout the flexion range; that is, from 0 to 90 degrees. For flexion up to 90 degrees, the minimum Jacobian (0.21) of the repositioned model was maintained at the initial value, and the maximum warpage (158) was improved in the repositioned model. A small degradation of the element’s aspect ratio (maximum 25) and skew (maximum 84) was observed. But elements with a maximum aspect ratio greater than 10.76 were minimal (less than 0.05%). Up to 60 degrees of flexion, only 2 elements were found to have aspect ratio greater than 10.76, whereas at 75 degrees of flexion only 9 elements (out of ≈19,000 solid elements) had an aspect ratio greater than 10.76. A comparison of the quality of the mesh in the initial model, the model repositioned to 90 degrees of flexion using FE simulations, and the model repositioned to 90 degrees of flexion using the proposed method is shown in Table I. From Table I, the minimum Jacobian of the model repositioned using the proposed method is 0.21 (and 0.19 without smoothing) compared to −27 in case of the model repositioned using FE simulations. The negative value of minimum Jacobian in this case indicates the presence of inverted elements. Maximum warpage value of 180 is also evidence of presence of poor quality elements. In

Figure 9 (a) Repositioned model and (b) detailed view of knee joint (Color figure available online).

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Comparison of mesh quality parameters

Mesh quality metric


Initial model 90 Flexion FE sim 90 Flexion FE sim after Smooth 90 Flexion New Method 90 Flexion New Method after Smooth

Worst (X ± σ ) Worst (X ± σ ) Worst (X ± σ ) Worst (X ± σ ) Worst (X ± σ )

Jacobian

Aspect ratio

Warpage

Skew

0.21 (0.76 ± 0.12) −27 (0.73 ± 0.13) −6.14 (0.73 ± 0.12) 0.19 (0.75 ± 0.13) 0.21 (0.77 ± 0.11)

10.76 (2.52 ± 1) 70 (3.5 ± 2) 38.66 (3.3 ± 2) 25.17 (2.6 ± 1) 25.17 (2.6 ± 1)

166.67 (4.92 ± 4.1) 180 (13.7 ± 12.7) 180 (11.3 ± 10.9) 158.46 (10.8 ± 10.4) 158.46 (10 ± 9.6)

75.3 (22.4 ± 5.1) 90 (35.4 ± 19) 90 (30.5 ± 9.8) 83.94 (28.5 ± 9.6) 83.94 (27.9 ± 9)

case of repositioning with FE simulations, distortion of elements resulted in premature termination of simulation, which was not the case with the proposed method. At higher flexion angles, the elements with poor initial quality were distorted more than the other elements because these elements were in zones where the geometry is complex and difficult to mesh. Specifically, the highest distortions were observed in the solid elements of the knee joint region. The mesh smoothing algorithm was especially effective for flexion angles greater than 75 degrees. The effect of mesh smoothing on the mesh quality parameters of the model repositioned to 90 degrees of flexion can be observed from Table I. For instance, the minimum Jacobian improved from 0.19 to 0.21, and the average minimum Jacobian improved from 0.75 to 0.77. Even after mesh smoothing the model repositioned with FE simulation had inferior mesh quality compared to the model repositioned with the method proposed in the present study. Volume conservation was tracked throughout the flexion range. The maximum change in the elemental volume of the model was 3.8 percent (at 90 degrees of flexion) for repositioning with the method proposed, whereas it was 2 percent in the case of repositioning with FE simulations. The increase in volume was mainly in the calf and knee flesh region. In the simulations, the change in volume was also affected due to the presence of distorted and negative volume elements. The deformation of the soft tissues generated during the morphing process was examined visually (Figures 10a–10c) at various flexion angles. It was observed that with the increase in flexion angle, the anterior edges of collateral ligaments were stretched and the length of the posterior edge decreased. This behavior of collateral ligaments was consistent with that reported by Park et al. (2006).

ing anatomical data and graphics-based techniques, the resulting model, in particular its resulting posture, is not influenced by model-specific parameters such as material properties, contacts, and geometry as in the case of repositioning with FE simulations. In addition, because the bone is transformed using affine transformations, the method allows complete control over the kinematics being followed. Moreover, the method presented does not require any precalculated FE models for different postures as needed in the tool reported by Vezin and Verriest (2005). Because the element type, element connectivity, and mesh quality are preserved during the process, the repositioned model can be used for further applications. It should also be noted that because the method operates with geometric transformations that can be defined in any coordinate system, the result is independent of the different coordinate systems used in clinical practice. The method has been implemented on the knee joint and its suitability for extension to other joints has not yet been evaluated. At present, the method fails to maintain the mesh quality

DISCUSSION The prime objective of this study was to develop a methodology to quickly reposition the limbs of FE-HBMs to achieve an anatomically correct position while maintaining mesh quality. Minimization of subjective interventions and ensuring suitability of the repositioned model for simulations in the new posture without remeshing were also considered important requirements of the repositioning process. Unlike repositioning with FE simulations (Jani et al. 2009; Parihar 2004), in which the repositioning takes a considerable amount of time, the method developed in the present study can reposition a given FE model within a few seconds (at present 104 s for the same model on an Intel Core2Quad, 2.4-GHz processor Q6600, 8 GB DDR2 RAM machine). Because the resulting posture is generated us-

Figure 10 (a) Collateral ligament fiber behavior during flexion (Park et al. 2006); (b) lateral collateral ligament; and (c) medial collateral ligament behavior in the model during flexion (Color figure available online).

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at the expected level at higher flexion (at flexion greater than 75 degrees) angles. The obvious reason for this is significant geometrical changes occurring in the model. In addition, because the accuracy of bone positioning is sensitive to the selection of the axes of rotation chosen, it is essential to locate axes using anatomical landmarks as accurately as possible. Because this is a geometry-based approach, ligament/muscle loading (prestressing) in the repositioned state (beyond that available from change in lengths) cannot be generated. In addition, the accuracy of the skin contours generated has not been established in the absence of any published data for the skin contours for different flexion angles.


CONCLUSIONS A methodology to reposition the knee joint of an existing FE-HBM in a given posture (occupant or pedestrian) to a new position has been presented in this study. Though the implementation of the method is demonstrated on the lower extremity of the GM/UVA 50th percentile male model, the method presented is generic and can be extended to knee joint of other FE-HBMs. Though the applicability of the methodology has been demonstrated for the knee joint only, it is expected to be extendable to other joints such as hip and shoulder joints. Post-repositioning limb positions are anatomically consistent and eliminate an observed limitation in dynamic simulationbased approaches using currently available models. The method efficiently controls the shape of deforming soft tissues and prevents bone-to-bone or soft tissue-to-bone penetrations. The mesh quality of the repositioned model is maintained during repositioning by the combination of mapping and the mesh smoothing algorithm applied. The repositioned model was found to be suitable for subsequent simulations. REFERENCES Adam T, Untaroiu CD. Identification of occupant posture using a Bayesian classification methodology to reduce the risk of injury in a collision. Transp Res Part C. 2011;19:1078–1094. Asano T, Akagi M, Nakamura T. The functional flexion–extension axis of the knee corresponds to the surgical epicondylar axis. J Arthroplasty. 2005;20:1060–1067. Asano T, Masao A, Koike K, Nakamura T. In vivo threedimensional patellar tracking on the femur. Clin Orthop Relat Res. 2003;413:222–232. Asano T, Masao A, Tanaka K, Tamura J, Nakamura T. In vivo three dimensional knee kinematics using a biplanar image matching technique. Clin Orthop Relat Res. 2001;388:157–166. Aubel A, Thalmann D. Interactive modelling of the human musculature. In: Ko H, ed. Computer Animation 2001: Proceedings of the Fourteenth Conference on Computer Animation, Seoul, Korea, November 7–8, 2001. Los Alamitos, Calif: IEEE Computer Society Press; 2001:167–255. Berger RA, Crossett, LS, Jacobs JJ, Rubash HE. Malrotation causing patellofemoral complications after total knee arthroplasty. Clin Orthop Relat Res. 1998;356:144–153.

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