Deriving a 3D Femur from Multiple Radiographs Gabriel Telles O’Neill* WonSook Lee† The School of Information Technology and Engineering, University of Ottawa diagnostic tool that uses two or more pelvic radiographs as input ABSTRACT and in return provides a 3D approximation of the femur and aceta- A Femoral Acetabular Impingement refers to a pathological bulum. The advantage of this hybrid approach is to combine the condition where deformities of the hip bones deteriorate the specific strengths of the CT and radiographic imaging methods joint’s protective soft tissues. Unfortunately, the two primary without carrying over their disadvantages. imaging methods used to diagnose this condition (CT and X- Related work aimed at achieving the same goal tends to use parametric models to express the variety of femur shapes. One Rays) both have major drawbacks. This paper describes on-going such approach used by Baudoin et al.[2] was to use parameters research towards a hybrid approach to eliminate these drawbacks such as the femoral head radius, neck shaft angle, neck length, etc. by synthesizing CT-like results of the hip-bones by using multiple to describe a 3D femur’s form and orientation. Alternatively, x-ray images as input. To accomplish this, Digitally Reconstru- Kurazumea et al.[3] generated their 3D femur from parameters cted Radiographs are used to create a mapping between the two obtained through Principle Component Analysis (PCA) of imaging methods and Principle Component Analysis is used to polygonized segmentations of CT data. What differentiates our express the variety of shapes for 3D femurs. research from similar work is that (a) our parametric models are generated from CT voxel intensity values and (b) our data set KEYWORDS: Femoral acetabular impingement, digitally includes patients diagnosed with FAIs. reconstructed radiographs, computed tomography, radiographs. 2 METHODOLOGY INDEX TERMS: J.3 [Life and Medical Sciences]: Health; I.4.5 [Image Processing and Computer Vision]: Reconstruction— The following subsections provide a brief overview of the Transform Methods currently implemented and forthcoming steps required to accomplish this research’s goal. To begin with, this research has 1 INTRODUCTION concentrated on recreating the femoral head only as an experiment to validate the intended methodology before recreating CT-like A healthy hip functions much like a ball-and-socket joint results for whole femurs and acetabulums. composed of two contact bones. These bones are the femur and acetabulum, located in leg and hip respectively. Hip motion is 2.1 Segmentation facilitated by layers of soft tissue between these two bones, such as the articular cartilage which covers the contact surfaces and the The data-set used in this research originates from 20 patients, labrum which seals the hip joint. 17 of which were suffering from FAI in at least one hip at the A Femoral Acetabular Impingement (FAI) describes a patholo- data’s time of taking and 3 from a control group. For each patient gical condition where there exists a bony bump-like deformity on there is one pelvic CT scan, one digital radiograph taken from the either the femur’s head (ball) and/or the acetabular rim (socket) patient’s front and another taken from the patient’s right. which causes abnormal contact between the two bones during normal hip flexion. If this condition is left untreated, the joint’s integrity will degrade over time due to increased damage to the soft tissue. FAIs have been associated with the development of cartilage damage, labral tears, early hip arthritis and lower back pain, among other complications. As such, quickly identifying and treating a patient suffering from a FAI reduces the likelihood of irreversible damage being incurred[1]. Physicians typically have two primary sources they can examine for diagnosing FAIs: (1) radiographs (x-rays images), (2) Computed Tomographic (CT) volumes. Unfortunately, both these sources have weaknesses to balance out their strengths. CT scans provide physicians with a 3D view of a patient’s pelvis, thus no Figure 1. Segmented frontal radiograph. Pixels belonging to the details of patient’s hip can be obscured. However the CT patient’s right/left femur are colored in red/green machines themselves are quite large, expensive and can have a waiting period of three or more months for a scan. On the other Before this data can be interpreted, its relevant features had to hand, x-ray machines have a lower cost, higher availability and first be segmented for extraction. Specifically, the pixels in the lower radiation exposure compared to CT machines. Conversely, radiographic images and the voxels from the CT scans were radiographs suffer from having a single view and flattened details. labelled as belonging to the right femur, belonging to the left The goal of this research is to supply physicians with a new femur, belonging to both femurs or belonging to neither. Figure 1 shows an example of the pixels in a frontal radiograph that would be labelled as belonging to femurs. All segmentations were done *e-mail: gtell036@uottawa.ca semi-automatically using an in-house program and then corrected † e-mail: wslee@uottawa.ca manually to eliminate possible machine errors. 10 2.2 Digitally Reconstructed Radiographs 2. Modifying the raycasting algorithm to use orthographic In order to create CT-like shapes from radiographs, a mapping projection along the CT volume’s vertical axis and scheme must be established between the 2D and 3D segmented perspective projection for the other two axes objects. To accomplish this mapping, Digitally Reconstructed An example of a resulting DRR can be seen in Figure 2. Radiographs (DRRs) are used. DRRs describe a number of volume rendering approaches which attempt to generate synthetic 2.3 Statistical Analysis of Femur Shapes radiographs from CT data. In this research, DRRs are used to This step marks the research’s current stage in development. provide a flattened view at various angles of a CT volume. The The objective is to discover the parameters that best describe the femoral contours from these flattened views can be compared to variations in 3D femur shapes- especially those that might suggest those found on the corresponding radiographs. These overlapping the presence of FAIs. This phase will be performed as follows: contours (as well as their interiors) can be used to provide the 1. Region of Interest Selection. The femoral heads found in necessary mapping. each patient’s segmented CT data are fitted with a 3D Of the many approaches available for generating DRRs, bounding box raycasting is considered the standard[4] because it returns the 2. Normalization. The contents of each bounding box are highest fidelity results. As such, a raycasting scheme was adopted converted into a standardized format, dimension, position, for this project and implemented to exploit the latest graphics orientation, etc. hardware in order to offset its associated high computational cost. 3. Vectorization. The contents of the normalized bounding This scheme naturally lends itself to simulating the radiographic boxes are converted into 1D vectors of voxel intensities process inside a 3D graphics environment: 4. PCA. Principle Component Analysis is used to analyze 1. A point in space is chosen to represent the source of x-rays patterns in the set of 1D vectors 2. The location of the radiographic plate is replaced with a 5. Parameterization. The average femur shape is found in similarly sized texture the PCA space along with the most influential parameters 3. For each pixel on the texture, a ray is cast from the point in space to that pixel 2.4 Creating a 3D Femur from Two Radiographs 4. If a ray traverses the CT volume, the pixel associated with the ray accumulates the intensity values of all the voxels Creating the 3D femur shape from the 2D radiographs is the touched by the ray final phase of the proposed procedure. It will be done as follows: 5. The resulting texture is the DRR 1. Starting from the average femur shape, the PCA space is searched until the contours (and contents) of the parame- terized femur’s DRRs match best with those from the segmented radiographs 2. Reverse any normalization of the parameterized femur to obtain the corresponding 3D femur shape 3 CONCLUSION This paper describes a process by which, two or more pelvic radiographs can be used to recreate the 3D shape of a patient’s femur. This work’s aim is supply physicians with an additional tool to diagnose FAIs. Areas of future work include reconstructing 3D acetabulums along with whole femurs using the same radiographs as source material. 4 ACKNOWLEDGEMENT Funding for G. Telles O’Neill’s research was provided from the Natural Sciences and Engineering Research Council (NSERC). REFERENCES [1] M. Hossain, J. Andrew. Current management of femoro-acetabular impingement. Current Orthopaedics, Volume 22, Issue 4, pages 300-310, 2008. [2] A. Baudoin, W. Skalli, J. A. de Guise, D. Mitton. Parametric subject- specific model for in vivo 3D reconstruction using bi-planar X-rays: Figure 2. (a) Radiograph of a patient’s femoral head (b) DRR of the application to the upper femoral extremity. Medical and Biological same patient’s femoral head with soft tissue subtracted Engineering and Computing, Volume 46, Number 8, pages 799-805, An additional complication exists in that CT data is captured 2008. using a different process than radiographs which results in there [3] R. Kurazumea, K. Nakamuraa, T. Okadab, Y. Satoc, N. Suganoc, T. being a registration error between the DRRs and the radiographs Koyamad, Y. Iwashitaa, T. Hasegawa. 3D reconstruction of a along the patient’s vertical axis. This is caused by a CT scan’s femoral shape using a parametric model and two 2D fluoroscopic slice-based approach, which is different from capturing the whole images. Computer Vision and Image Understanding, Volume 113, volume at once from a perspective point like an x-ray machine. Issue 2, pages 202-211, 2009. Thankfully, this registration error can easily be removed by: [4] B. Russakoff, T. Rohlfing, D. Rueckert, R. Shahidi, D. Kim, C. R. 1. Resizing the CT volume along the patient’s vertical axis Maurer Jr. Fast calculation of digitally reconstructed radiographs according to the volume’s distance from the “x-ray source” using light fields. Medical Imaging 2003: Image Processing. Proceedings of the SPIE, volume 5032, pages 684-695, 2003. 11