Ultra-Low Dose Hip CT-based Automated Measurement of Volumetric Bone Mineral Density at Proximal Femoral Subregions

Abstract

Background:

Forty to fifty percent of women and 13 to 22% of men experience an osteoporosis-related fragility fracture in their lifetimes. After the age of 50 years, the risk of hip fracture doubles in every ten years. X-ray based DXA is currently clinically used to diagnose osteoporosis and predict fracture risk. However, it provides only 2-D representation of bone and is associated with other technical limitations. Thus, alternative methods are needed.

Purpose:

To develop and evaluate an ultra-low dose (ULD) hip CT-based automated method for assessment of volumetric bone mineral density (vBMD) at proximal femoral subregions.

Methods:

An automated method was developed to segment the proximal femur in ULD hip CT images and delineate femoral subregions. The computational pipeline consists of deep learning (DL)-based computation of femur likelihood map followed by shape model-based femur segmentation and finite element analysis-based warping of a reference subregion labelling onto individual femur shapes. Finally, vBMD is computed over each subregion in the target image using a calibration phantom scan. A total of 100 participants (50 females) were recruited from the Genetic Epidemiology of COPD (COPDGene) study, and ULD hip CT imaging, equivalent to 18 days of background radiation received by U.S. residents, was performed on each participant. Additional hip CT imaging using a clinical protocol was performed on 12 participants and repeat ULD hip CT was acquired on another 5 participants. ULD CT images from 80 participants were used to train the DL network; ULD CT images of the remaining 20 participants as well as clinical and repeat ULD CT images were used to evaluate the accuracy, generalizability, and reproducibility of segmentation of femoral subregions. Finally, clinical CT and repeat ULD CT images were used to evaluate accuracy and reproducibility of ULD CT-based automated measurements of femoral vBMD.

Results:

Dice scores of accuracy (n = 20), reproducibility (n = 5), and generalizability (n = 12) of ULD CT-based automated subregion segmentation were 0.990, 0.982, and 0.977, respectively, for the femoral head and 0.941, 0.970, and 0.960, respectively, for the femoral neck. ULD CT-based regional vBMD showed Pearson and concordance correlation coefficients of 0.994 and 0.977, respectively, and a root-mean-square coefficient of variation (RMSCV) (%) of 1.39% with the clinical CT-derived reference measure. After 3-digit approximation, each of Pearson and concordance correlation coefficients as well as ICC between baseline and repeat scans were 0.996 with RMSCV of 0.72%. Results of ULD CT-based bone analysis on 100 participants (age (mean±SD) 73.6±6.6 years) show that males have significantly greater (p < 0.01) vBMD at the femoral head and trochanteric regions than females, while females have moderately greater vBMD (p = 0.05) at the medial half of the femoral neck than males.

Conclusion:

Deep learning, combined with shape model and finite element analysis, offers an accurate, reproducible, and generalizable algorithm for automated segmentation of the proximal femur and anatomic femoral subregions using ULD hip CT images. ULD CT-based regional measures of femoral vBMD are accurate and reproducible and demonstrate regional differences between males and females.

1. INTRODUCTION

Osteoporosis, characterized by reduced bone mineral density (BMD), greatly increases the risk of fragility fractures.^1–4 Nearly, 40 to 50% women and 13 to 22% men suffer a fragility fracture in their lifetimes.⁵ Skeletal degeneration with aging is common,^6–9 and the process is accelerated in bone metabolic disorders.^10,11 For each decade after the age of 50 years, the risk of hip fracture doubles.¹² A woman who lives to the age of 90 years has a one in three chance of sustaining a hip fracture.¹³ The increased fracture-risk with age combined with a rapidly expanding older adult population translates to a projected increase in worldwide hip fracture incidence from 1.7 million in 1990 to 6.3 million in 2050.¹⁴ Osteoporotic fractures are one of the most common causes of disability, and a major contributor to medical care costs.¹⁵ Hip fractures are especially devastating, reducing life expectancy by 10–20%,¹⁶ and more than three-quarters of all hip fractures occur in women.¹⁵

Dual-energy X-ray absorptiometry (DXA) measured areal BMD is clinically used to diagnose and quantify osteopenia and osteoporosis. Being a two-dimensional (2-D) measure, DXA has several technical limitations including sensitivity to bone size, thus overestimating fracture-risk in individuals with small body size and lack of accuracy in the setting of degenerative changes in the hip and spine. It is known that the majority of individuals who suffer fragility fractures have their DXA T-scores greater than ‘-2.5,’ i.e., they are misclassified by DXA as not having osteoporosis.^17,18 Lack of volumetric information in DXA limits its accuracy to assess bone health and fracture-risk. Magnetic resonance imaging (MRI)^19–23 and high-resolution peripheral quantitative CT (HR-pQCT),^24–28 have been popularly used to derive volumetric bone measures including microarchitectural metrics. Despite considerable efforts and successes with these techniques, HR-pQCT imaging is limited to peripheral sites, while it is known that hip BMD has the strongest association with overall fracture risk.²⁹ MRI fails to quantify BMD.²²

Hip CT imaging has been applied to measure volumetric BMD (vBMD) at the proximal femur. In a cadaveric study, Cheng et al.³⁰ showed that quantitative CT-derived femoral vBMD metrics correlate with its strength measured using mechanical testing (n = 64). In another cadaveric study, Lang et al.³¹ observed that quantitative CT-based trabecular vBMD measures are reproducible and correlate with experimentally determined femoral strength. Huber et al.³² developed a semi-automated CT-based method to segment the femur surface and detect geometrically modelled regions of interest (ROIs) at the femoral head, neck, and trochanter and applied the method on cadaveric proximal femur specimens (n = 178). They observed that regional CT vBMD measures correlate with femur failure load determined by mechanical testing. Several algorithms are available in the literature to segment different bones and joint structures in hip CT imaging. For example, Chu et al.³³ fused multi-atlas mesh modelling with a constrained graph-cut approach to segment the pelvis and femur joint structure in hip CT images, while others have adopted variations of the statistical shape modelling approach to accomplish the same task.^34–36 Recently, deep learning (DL) has been adopted to segment the femur in hip CT imaging. Deng et al.³⁷ developed a three-dimensional (3-D) end-to-end fully convolutional neural network (CNN) to segment the periosteal and endosteal femur surfaces from hip CT images. Zhao et al.³⁸ adopted a spatial transformation V-Net (ST-V-Net) combining a V-Net³⁹ and a spatial transformer network (STN)⁴⁰ to extract the proximal femur from CT images. Cheng et al.⁴¹ presented a 3-D feature-enhanced network to segment the femur surface from CT images. Also, a few DL-based algorithms have been presented to segment the femur surface from MR images.^42,43 However, an ultra-low dose (ULD) quantitative CT-based automated hip bone imaging method is yet to be established that may be useful as a screening tool for osteoporosis.

X-ray radiation exposure from CT imaging is considered one of the most important safety concerns,⁴⁴ and the biologic effect, including the risk of cancer, decreases with reduction in the radiation dose.⁴⁵ The goal of achieving ULD CT imaging has been advocated by several federal agencies and national institutes^46,47 Several studies have applied ULD CT to different imaging applications including kidney, ureters, and bladder imaging for acute renal colic,⁴⁸ thoracic imaging for detection of chest pathology,⁴⁹ and pelvic imaging for assessing bone anatomy and osseous pathologies⁵⁰ and evaluated their accuracies as compared to standard CT. To the best of our knowledge, no in vivo study has been reported evaluating the accuracy of an ULD CT method for assessment of regional volumetric bone measures at the hip. Such methods will be useful for assessment of fracture risks in patients. The ULD feature of such tools is particularly important when it is considered as a screening tool that may be applicable to a general population beyond an age threshold.

In this paper, we present and evaluate an ULD hip CT-based automated quantitative method for assessment of regional vBMD at the proximal femur. Specifically, we develop an ULD hip CT imaging protocol using tin (Sn) filtration to measure vBMD at femoral subregions that is equivalent to 18 days of environmental radiation. An important advancement presented in this paper includes synthesis of different approaches that makes it feasible to automate segmentation of the proximal femur using ULD hip CT imaging and delineation of anatomically consistent femoral subregions for individual participants. Specifically, our hybrid approach of femur surface segmentation combining deep learning and active shape modeling is novel. Accuracy, reproducibility, and generalizability of these methods are examined. Also, accuracy and reproducibility of ULD hip CT-based regional vBMD measures are evaluated. Finally, differences in femoral regional vBMD between males and females are assessed.

2. MATERIALS AND METHODS

Overall goals of this work are to develop an ULD hip CT-based automated method for in vivo assessment of regional vBMD metrics at the proximal femur, examine its accuracy and reproducibility, and compare regional vBMD among males and females. Also, accuracy, reproducibility, and generalizability of ULD CT-based automated segmentation of femoral subregions are examined. Our computational framework includes: (i) segmentation of the proximal femur at ULD hip CT imaging; (ii) delineation of anatomically consistent femoral subregions; and (iii) computation of regional vBMD metrics. This research involves: (i) acquisition of in vivo hip CT imaging of human participants; (ii) development of new algorithms for segmentation of proximal femur and delineation of femoral subregions and computation of regional vBMD metrics; and (iii) application of the new method to ULD hip CT data to evaluate its performance.

2.A. Human Subjects and Hip CT Imaging

A total of 100 participants (50 females) were randomly selected from an ongoing research project related to CT-based modelling of bone microarchitecture and fracture-risk in chronic obstructive pulmonary disease (COPD), an ancillary study under the multi-center Genetic Epidemiology of COPD (COPDGene) study.⁵¹ ULD hip CT imaging, equivalent to 18 days of environmental radiation, was performed on all participants. Among these participants, 12 participants (5 females) consented to an additional hip CT scan using a clinical protocol (detailed below), and another 5 participants (5 females) consented to a repeat ULD hip CT scan. The data from human participants were divided into two subsets. The first subset included hip CT data from 20 participants (10 females), which also included clinical hip CT scans of 12 participants and repeat hip ULD CT scans of 5 participants. This dataset was used to evaluate different performance metrics. The second subset included data from the remaining 80 participants (40 females), which was used for DL training. Fifty participants were selected from the second subset of 80 participants to train a femur shape model. This strategy was adopted to ensure that the dataset for performance evaluation does overlap with the datasets used for DL and shape model training.

All additional clinical CT and repeat ULD hip CT scans were performed after repositioning the participant on the scanner table immediately following the initial or baseline ULD scan. All CT imaging was performed on a Siemens SOMATOM Force (Forchheim, Germany) scanner located at the University of Iowa Comprehensive Lung Imaging Center (I-CLIC) research CT facility. Every scan was performed in the feet-first supine position. For both ULD and clinical CT imaging, the field of view (FOV) was defined on an anterior-posterior (AP) scout as follows: scan length was selected starting at 3 mm superior to the femoral head extending 15 cm inferiorly, and the transverse field of view was defined to just barely contain the complete lateral cutaneous surface bilaterally. This study was approved by the University of Iowa Institutional Review Board (IRB ID # 201802724), and written informed consent was obtained from each participant.

Ultra-Low Dose Hip CT Imaging:

ULD CT imaging was performed using single X-ray source spiral acquisition mode with tin (Sn) filtration and following parameters: Sn100 kV, 200 effective mAs, pitch factor: 1.0, scan length: 15 cm, collimation: 192 × 0.6 mm, CTDI_Vol: 0.69 mGy; DLP: 10.35 mGy*cm; effective dose: 0.155 mSv equivalent to 18 days of environmental radiation based on 3.1 mSv of average annual background radiation exposure received by U.S. residents.⁵² Images were reconstructed at 500 μm slice spacing and thickness using Siemens Br40 kernel; mean ± standard deviation (SD) of in-plane resolution observed in our study was 0.88 ± 0.07 mm. See Figure 1(a,c) for a typical ULD hip CT image.

Figure 1.

In vivo hip CT imaging using ultra-low dose (ULD) and vendor- recommended clinical protocols. (a-d) Matching axial (a,b) and coronal (c,d) image slices using ULD (a,c) and clinical (b,d) protocols. Zoomed in regions on coronal images are shown on the right. Relatively low signal-to-noise-ratio in ULD CT images (a,c) are visually apparent. CT contrast setting for all images: level = 500 Hounsfield units (HU); window = 1800 HU.

Clinical Hip CT Imaging:

The vendor-recommended clinical hip CT imaging protocol was implemented to acquire reference hip CT data. Specifically, clinical hip CT imaging was performed using single X-ray source spiral acquisition mode with the following parameters: 120 kV, 100 effective mAs, pitch factor: 0.8, scan length: 15 cm, collimation: 192 × 0.6 mm; dose modulation: ON; CTDI_Vol: 8.71 mGy; DLP: 130.65 mGy*cm; effective dose: 1.960 mSv equivalent to 238 days of environmental radiation (dose metrics were computed without dose modulation). Images were reconstructed at 500 μm slice spacing and thickness using Siemens Br40 kernel; mean ± SD of in-plane resolution observed in clinical CT images was 0.84 ± 0.06 mm. Figure 1(b,d) shows a typical clinical hip CT image.

Each hip CT scan was followed by a CT imaging of a Gammex RMI 467 Tissue Characterization Phantom (Gammex RMI, Middleton, WI, USA) using the matching protocol to calibrate CT intensity values (Hounsfield unit (HU)) into bone mineral density (mg/cc). All hip CT images were interpolated at an isotropic resolution of 500 μm to reduce computational complexities related to the correspondence between image and physical spaces.

2.B. Image Processing and Computation of Regional Bone Metrics at the Proximal Femur

Our computational pipeline was designed to segment the proximal femur in a CT image, delineate anatomically consistent femur subregions, and derive regional bone metrics. The computational pipeline consists of five sequential steps (Figure 2). First, a trained U-Net^53,54 based DL network module is used to generate a spatial probability likelihood map of the proximal femur from a hip CT scan. The output probability map is then fed into a custom-designed segmentation module to delineate the proximal femur. The segmentation module includes proximal femur statistical shape modelling⁵⁵ and an optimizer that determines the pose and shape parameters to delineate the proximal femur volume on the DL-derived likelihood map. It may be noted that this module generates a structured representation of the delineated proximal femur surface using surface mesh of landmarks, which we will refer to as a surface shape representation of a proximal femur. Once the surface shape of a given proximal femur is obtained, a finite element analysis (FEA) method is applied to deform a reference volumetric landmark mesh on to a target femur volume using the correspondence of surface landmarks; the reference volumetric landmark mesh is defined on the mean femur shape. After establishing the volumetric correspondence between the mean and the given target femur shapes, the predefined anatomic subregion labelling is warped from the mean femur shape on to target femur. Finally, regional bone metrics are derived from different labelled regions in the target image. Figure 2 illustrates intermediate results. These steps are described in the following.

Figure 2.

Workflow diagram of our computational pipeline for segmentation of proximal femur using ultra-low dose (ULD) hip CT imaging and delineation of femoral subregions. A deep learning (DL) network was trained to compute voxel-level femur likelihood map. Output of the DL module is fed to a custom-designed segmentation module to delineate the proximal femur and generate its surface landmark mesh representation. It is followed by an elastic deformation module that deforms the reference volume mesh of the mean femur shape on the target shape using surface landmark correspondence and finite element analysis. In the final module, the volume mesh correspondence is applied to warp reference subregion labeling of the mean shape on to the target femur volume.

2.B.1. Estimation of Femur Likelihood Map using Deep Learning

A 3-D U-Net model^53,54 was implemented, trained, and applied to generate a voxel-level proximal femur likelihood map from a hip CT image. The network was implemented using three levels of pooling that provide four different layers of feature resolutions or scales (Figure 3). At a specific scale, each convolutional layer was designed using a 3×3×3 kernel, except for the final layer, where it was implemented using a 1×1×1 kernel.⁵⁶ At the highest resolution, 32 kernels or feature maps were used. Along a contracting path, the number of features maps was doubled at each pooling step leading to 64, 128, and 256 feature maps at three lower resolutions. Expansive paths were designed symmetrically, and the number of feature maps was halved after each deconvolution step.

Figure 3.

Block diagram of the U-Net used to derive voxel-level femur likelihood map from hip CT imaging. The network was implemented for 96×96×96 input patches of CT images to generate same size output patches representing voxel-level femur likelihood map. The network was trained using matching patches from ultra-low dose hip CT images and manual segmentation of the proximal femur on those images.

The DL network was trained using image subregions of size 96×96×96 voxels; subregion size was determined so that it captures local geometric contexts of the femur boundary, while being computationally compatible for available resources in our laboratory. A space-variant sampling density strategy was adopted for different subregions in hip CT images to generate a diverse training set including samples with different regional characteristics. Specifically, the image-space was divided into four characteristic regions as follows:

• $R_1$: the region within a predefined distance threshold $t_{\text{dist}}$ from both femur and pelvic boundaries;

• $R_2$: the region within the distance threshold $t_{\text{dist}}$ from either femur or pelvic boundary, but excluding $R_1$;

• $R_3$: the region inside the femur or pelvic bone excluding $R_1\cup R_2$;

• $R_4$: the region outside the femur and pelvic bones and excluding $R_1\cup R_2$.

Figure 4 presents an illustration of the four regions on a coronal image slice. A fixed distance threshold $t_{\text{dist}}$ of 5 mm was used to define these regions. Twenty-five percent samples were randomly selected from each of the regions $R_1$ to $R_4$. Note that, although the training samples were selected from femur and pelvic regions, the network was trained only for the femur. Weighted binary cross-entropy loss function was applied. The output femur probability map, denoted by $P_{\text{Fem}}$, was computed using a sliding window approach where adjacent subregions overlapped by 48 voxels in each direction. The femur probability at a given voxel $p$ was computed by averaging the probability values at $p$ derived from all 96×96×96 sample-regions containing the voxel.

Figure 4.

Illustration of different regions for space-varying sampling of deep learning training data. Twenty five percent samples were randomly selected from each of the regions $R_1$ to $R_4$. Note that the higher density of samples was applied to $R_1$ that occupies the minimum volume, while posing the greatest challenge due to the vicinity of both femur and pelvic bones.

2.B.2. Femur Surface Shape Modelling

Previously, we developed a shape modelling framework^57,58 using manually drawn fiducial landmarks as well as computer-generated secondary landmarks to efficiently and effectively build a shape model of 3-D anatomic structures. Two types of landmarks are identified in this framework. Several prominent landmark locations and lines are defined on a 3-D anatomic shape by a clinical expert that can be manually located with high confidence and reproducibility on different instances of the same anatomic shape. On the other hand, the large set of secondary landmarks are defined using the reference of fiducial landmarks and are automatically computed by an algorithm. Our 3-D landmark generation consists of (i) manual drawing of fiducial landmark locations and lines on all training shape instances; (ii) computation of fiducial landmark points on fiducial lines using B-spline fitting of manually drawn lines and generation of a predefined number of uniformly spaced landmark points on each B-spline fiducial line; (iii) selection of quasi uniform secondary landmark points on a reference shape and generation of a surface mesh of all fiducial and secondary landmarks; and (iv) warping of secondary landmarks of the reference shape on individual training shapes using the correspondence of fiducial landmarks.

The fiducial lines on the proximal femur are defined as follows and are shown in Figure 5. Long Axis: An oblique coronal plane ($l_1$) is defined to symmetrically divide the femoral head/neck in a plane that also divides the greater trochanter. A perpendicular plane through the femoral head ($l_2$) is next chosen. Short Axis: The point of inflection in the femoral head/neck junction is defined ($l_3$). An additional line is drawn inferiorly at the point of inflection between the femoral neck and intertrocanteric region ($l_4$). A line inferior to the lesser trochanter ($l_5$) serves as the third short axis contour. Other lines: the fovea of the femoral head is identified ($l_6$); a line defining the base of the lesser tuberosity is marked ($l_7$); a line ($l_8$) is drawn along the ridge at the greater trochanter; and two geodesic lines $l_9$ and $l_{10}$, quasi parallel to $l_2$, are drawn from the two ends of $l_8$. The point $p_1$ is located as the geodesic mid-point on the short segment of $l_1$ between its intersections with $l_4$ and $l_9$. Similarly, the point $p_2$ is located as the geodesic mid-point on the short segment of $l_1$ between its intersections with $l_4$ and $l_{10}$. Another point $p_3$ is located at the nadir of the trough between the greater trochanter and femoral neck. Additional geodesic lines connecting the three points $p_1$, $p_2$, and $p_3$ with different fiducial lines of their intersections are drawn to divide the femoral surface into relatively simpler patches. To capture the width of the greater trochanter, lines $l_9$ and $l_{10}$, parallel to $l_2$, were computed. To represent the complex surface geometry at the trough between the greater trochanter and femoral neck using simpler surface patches, additional geodesic lines were added (Figure 5). The proposed compartmentalization of the femoral surface was aimed to represent the surface in simpler patches, while minimizing the number of additional fiducial lines that require manual input.

Figure 5.

Fiducial and secondary landmarks on human proximal femur. Top row from left to right: manually drawn fiducial landmark lines; computer generated fiducial landmarks (green dots) using B-spline representation of each fiducial line and uniform sampling of a predefined number of fiducial landmarks; computer generated secondary landmarks (white dots) and adjacency mesh (light blue). Bottom two rows: Same as the top row at different viewing angles. See the text for numbering of fiducial landmark lines.

Fiducial landmarks were drawn on individual training shapes using a custom-designed graphical user interface (GUI) developed in our laboratory to interactively locate fiducial landmark lines on the femur surface. Conventional GUI systems provide graphical interface functions to manipulate points, lines, and curves on a 2-D plane. Our custom-designed GUI system, referred to as geodesic editor,⁵⁷ enables a user to directly interact on a geodesic surface facilitating landmark location on anatomic shapes. The GUI facilitates landmark generation with proper identification numbers for individual fiducial landmark lines on different training instances. As mentioned earlier, the fiducial landmark points are generated by uniformly sampling a predefined number of points on each fiducial line.

In our shape modelling protocol, fiducial landmark lines are manually drawn for all training shape instances, which takes approximately 30 minutes per femur instance. Secondary landmarks are manually defined only for one reference training shape. The idea is to use the correspondence of fiducial landmarks to warp secondary landmarks from the reference femur shape surface onto the target surface. This warping step is accomplished using a previously published geodesic elastic mesh deformation algorithm^57,58 that simulates elastic spring deformation of a mesh on to and along the surface of the target shape. Piece-wise elastic deformation of individual surface patches, defined by the fiducial lines, are applied. Results of geodesic elastic warping of the reference secondary landmark mesh on to a target femur shape are presented in Figure 6. The initial reference shape for secondary landmark drawing was arbitrarily selected. The iterative method recommended by Cootes et al.⁵⁵ to reduce the effect of this arbitrary selection was applied. Specifically, the reference shape instance together with its fiducial and secondary landmark mesh was iteratively replaced by current mean shape and associated landmark mesh until convergence.

Figure 6.

Warping of secondary landmarks from a reference shape (a,b) on to a target shape (c,d) using the correspondence of fiducial landmarks and a geodesic elastic mesh deformation algorithm.^57,58 The correspondence of fiducial landmarks in (a) and (c) is used to warp the secondary landmark of (b) on the target femur surface to generate the mesh shown in (d).

After generating fiducial and secondary landmarks for all training shape instances, the method by Cootes et al.⁵⁵ was applied to generate a mean shape vector $\overline{\mathbf{x}}$ and a matrix $\mathbf{P}$ of orthogonal eigenvectors representing the hyperspace containing major variations within the shape family. A total of 995 landmarks including 302 fiducial and 693 secondary landmarks were used for our femur shape representation. Fiducial landmarks were generated from 69 manually drawn fiducial lines and uniform sampling on fitted B-splines. Both fiducial and secondary landmarks are uniformly treated for statistical shape modelling. A total of 50 femur shape instances were used for training, and 23 eigenvectors associated with the 23 largest eigenvalues capturing 90% of shape variability were selected to construct the matrix $\mathbf{P}$. Finally, a new femur shape model instance $\mathbf{x}$ is generated using the following equation:

$$\mathbf{x}=\overline{\mathbf{x}}+\mathbf{P}\mathbf{b},$$

where $\overline{\mathbf{x}}$ is a point in the 2985 (3×995) dimensional shape space representing the mean shape, $\mathbf{P}$ represents a 23-dimensional hyperspace defined by the 23 selected eigenvectors, and $\mathbf{b}$ is a control vector characterizing deviations of the model shape instance from the mean shape along the 23 eigenvectors. We will refer to $\mathbf{x}$ as a shape model instance or model instance in short. A few examples of femur shape model instances are shown in Figure 7. It may be noted that the femoral head deviates from a partial sphere in several shape instances generated by shifting along one mode of shape variation at a time. However, this deviation is less obvious on the actual shape instances observed in our experiment at both positive and negative extreme deviations along the modes of our shape model; see the last row in Figure 7. It may be clarified that the shape examples of the first three rows in Figure 7 were created applying shape variations along one mode at a time, where the flexibility of the mathematical shape representation allowed the femoral head to deviate from partial sphericality. However, when the femur shape was allowed to simultaneously vary along different modes to fit with an actual femur instance, the deviation is less obvious.

Figure 7.

Femur instances generated using our femur shape model. Top row from left: Shape instances at −3, −1, 0, 1, and 3 standard deviations away from the mean shape along the first mode of variations. The central panel represents the mean shape. Second and third rows: Same as the top row but for the second and third modes of variations. Last row: Observed shape instances in our experiment using the shape model with extreme negative and positive deviations along the first three shape modes; from left: extreme negative and positive deviations along each of the first three shape modes.

2.B.3. Femur Surface Segmentation Using Shape Model

A model instance $\mathbf{x}$ is reconstructed in an image as $T\left(\mathbf{x}\right)$ after applying an affine transformation $T$ on $\mathbf{x}$; we will refer to $T\left(\mathbf{x}\right)$ as an image shape instance or a shape instance in an image. Finding a shape instance in an image involves optimization of both the shape parameter $\mathbf{b}$ as well as the affine transformation $T$. The method starts with initial values for $\mathbf{b}$ and $T$ and alternatively update these parameters, one at a time, until convergence. The shape parameter is initialized as ${\mathbf{b}}_0=0$; thus, the model instance is initiated as the mean shape, which is the most likely model instance. Following that, hip CT images are acquired under similar patient positioning and the mean affine transformation of shape instances in the set of training images is computed and applied as the initial affine transformation $T_0$.

During the iterative optimization of the shape and affine transformation parameters, each landmark location on the current image shape instance is repositioned along the line orthogonal to the femur surface at the landmark location to locally maximize DL-derived femur likelihood at the interior and minimize the likelihood at the exterior (Figure 8). After repositioning landmarks, the shape and affine transformation parameters are revised following the algorithm by Cootes et al.⁵⁵ to update the model instance as well as the shape instance in the image. Let $T\left(\mathbf{x}\right)$ denote the current image shape instance, $l$ be a landmark on $T\left(\mathbf{x}\right)$, and $s_1,s_2,\cdots ,s_n$ be uniform sample points along the profile line through $l$ locally orthogonal to $T\left(\mathbf{x}\right)$; the sample points are selected such that one of these points coincides with $l$. A boundary cost function $\gamma \left(s_i\right)$ is defined for each sample point $s_i$ as follows:

$$\gamma \left(s_i\right)=\frac{1}{2h+1}\left(\sum _{j=i-h}^{i-1}1-P_{\text{Fem}}\left(s_j\right)+\left|P_{\text{Fem}}\left(s_i\right)-0.5\right|+\sum _{j=i+1}^{i+h}{P}_{\text{Fem}}\left(s_j\right)\right).$$

Figure 8.

2-D illustrations of iterative repositioning of landmarks to locally maximize deep learning computed femur likelihood at the interior and minimize the likelihood at the exterior. The magenta polygon represents the current femur shape instance on the femur likelihood image. Each landmark is repositioned along the profile line locally orthogonal to the current femur boundary. Two landmarks are shown in (a) and the boundary cost function for the two landmarks along the two profile lines are shown in (b). Each landmark is repositioned at the minimum boundary cost location along its profile. The actual algorithm is implemented in 3-D.

In the above equation, the sample points $s_j|j<i$ fall inside and $s_j|j>i$ fall outside of the hypothetical femur boundary, while computing the boundary cost $\gamma \left(s_i\right)$; at the hypothetical boundary location $s_i$, the expected likelihood map is 0.5 with maximum uncertainty. Finally, the landmark location is repositioned at the sample location with the minimum boundary cost (Figure 8b). For our experiments, $h=7$ and the sample interval of 250 μm were applied.

3.B.4. Volumetric Correspondence of Femur Shapes

The overall idea of this step is to use the correspondence of femur surface landmark. A reference volumetric landmark mesh is warped on to a target femur volume. For this purpose, a reference volume mesh is first defined inside a mean femur shape. This step is accomplished using an open-source code software TetGen⁵⁹ that generates tetrahedral mesh representation of a 3-D polyhedral object, while optimizing the mesh quality. Optimization of the tetrahedral mesh quality in TetGen is achieved by minimizing the upper bound of the ratio of circumscribed sphere radius to shortest edge of all tetrahedra under the constraint of a predefined lower bound of tetrahedral angles. The number of tetrahedra was determined by the upper bound of tetrahedral volumes. Figure 9 a and b demonstrate tetrahedral volume mesh generated by TetGen using the 3-D polyhedral representation of the mean femur shape.

Figure 9.

Volumetric correspondence of femur shapes. Top row: Surface (a) and volume mesh representations of the mean femur shape. Surface shape is shown in cyan, while the inner volume landmark mesh is shown in magenta. Middle row: (c) Surface landmark mesh of a participant’s proximal femur. (d) Deformation vector field warping the mean femur shape on to the specific participant’s femur. (e) Generated inner volume landmark mesh together with the surface mesh for the specific participant. Bottom row: Same as the middle row but for a different participant.

Surface landmark representation of a target femur shape is computed using the method described in Section 2.B.3 prior to establishing volume correspondence with the reference femur volume mesh. This module maps volume landmarks of the mean femur shape on to the target femur volume using the correspondence of surface landmarks in both shapes and a FEA-based elastic deformation. Specifically, it is accomplished in the following steps: (i) apply Procrustes analysis to eliminate translation, rotation, and scale differences between mean and target femur surface shapes; (ii) determine the stress vector from each mean surface landmark to the corresponding landmark on the target femur surface; (iii) apply FEA on the mean femur volume mesh to deform the mean femur surface landmark mesh on to the target femur surface mesh. It may be clarified that, at this step, the FEA-based elastic deformation model was preferred, compared to a thin-plate spine deformation model, because the corresponding landmarks are distributed only on the femur surface but not over the femur volume. The FEA algorithm was implemented using the computational platform and facilities provided within the ABAQUS: Finite Element Analysis for Mechanical Engineering and Civil Engineering software (ABAQUS 2021, Dassault Systèmes Simulia Corp, Providence, RI, USA). A uniform isotropic material property with Young’s Modulus of 2 GPa and Poisson ratio of 0.3 was assigned to volume mesh elements. A linear FEA algorithm was applied using the automatic time incrementation method in ABAQUS with the default values for time increment and convergence tolerance parameters for force. It may be noted that, in our application, the objective of the FEA algorithm was not to measure a mechanical property of an object; rather the purpose was to compute a nonlinear deformation field between two femur shapes that is governed by an elastic process. Therefore, default parameters were applied, and a relatively stiffer material property as compared to bone^60–62 was assigned to assure smooth and stable deformation of inner volume mesh elements. Figure 9(c–h) show the results of volumetric femur warping using surface landmark correspondence and FEA.

2.B.5. Subregion Mapping and Regional Bone Metrics

Three femoral subregions, namely, femoral head (FH), femoral neck (FN), and trochanteric region (TR) were identified in the proximal femur. Femoral neck was further divided into lateral and medial halves denoted by FN_L and FN_M, respectively. On the mean femur, these subregions were manually drawn by a clinical expert. After establishing the volume landmark correspondence between the mean and target shapes, a thin-plate-spline (TPS) registration method^63–65 using volume landmark correspondence was applied to establish a voxel-level mapping between the mean and target femur volumes. Finally, a given voxel in the target femur volume was mapped onto the mean shape using the TPS deformation field, and the voxel-level anatomic subregion label in the target shape is determined from the subregion label in the mean shape after TPS mapping. The vBMD (mg/cc) metric was computed for each subregion after converting CT values in Hounsfield unit into vBMD using the matching Gammex phantom CT scan and an automated algorithm developed in our laboratory generating the calibration function from CT Hounsfield numbers to vBMD values.⁶⁶

3. EXPERIMENTS AND RESULTS

The following experiments were performed: (i) training and validation of the DL network; (ii) testing for accuracy, reproducibility, and generalizability of ULD CT-based femur segmentation and regional labelling; (iii) testing for accuracy of ULD CT-based bone measures; (iv) testing for reproducibility of ULD CT-based bone measures; and (v) comparison of regional bone measures between males and females. Based on our study design, all CT image datasets used to examine different performance metrics of the method were separate from the datasets used for DL and shape model training. These experiments and results are described in the following.

3.A. Training and Validation of the DL Network

The DL network for computation of the femur likelihood map was trained using ULD hip CT images from 80 participants, which was randomly partitioned into learning (n = 60) and validation (n = 20) data sets. Five hundred 96×96×96 subregions were randomly sampled from each CT image and its corresponding femur segmentation based on the sampling strategy described in Section 2.B.1. Post processing-based data augmentation was skipped to avoid systematic feature perturbation. Instead, a large number of subregions were randomly sampled to augment the training data size.⁶⁷ Specifically, 500⊆60 = 30,000 subregion samples were used for learning and 500⊆20 = 10,000 subregion samples were used for validation. All DL computations were performed on a server computer with Intel Xeon^® Gold 6420 CPU and a 32 GB NVIDIA Tesla V100 graphics card. The DL network required approximately 36 hours (4 hours/epoch and 9 epochs to converge) to complete the training phase. During the application phase, the network took approximately 1 minute to compute the likelihood map for a hip CT image. On an average, the subsequent step of shape model-based femur segmentation required 10 minutes, while the FEA-based volume-mesh deformation, TPS-based volume warping, and computation of regional bone measures, together, required 45 minutes.

3.B. Accuracy, Reproducibility, and Generalizability of Femur Segmentation and Regional Labelling

Experiments were designed to evaluate the accuracy, reproducibility, generalizability of segmentation of femur subregions in ULD hip CT images. Manual segmentation was used to examine the accuracy of femur subregion segmentation, while repeat CT scans were used for reproducibility. Finally, the accuracy of segmentation of femur subregions in clinical CT images using the DL network trained for ULD CT images was computed to evaluate the generalizability of our method. Actual dose values of the clinical CT scans with modulation observed in our experiments were CTDI_vol: (mean ± SD) 6.65 ± 2.68, [min, max] [4.10, 13.96] mGy; DLP: 99.74 ± 40.19, [61.49, 209.45] mGy*cm; effective dose: 1.50 ± 0.60, [0.92, 3.14] mSv; body mass index (BMI) values of the participants for this experiment were: 27.63 ± 5.11, [23.28, 40.48] kg/m². The CTDI_vol for a participant was computed as the mean CTDI_vol over all slices.

Results of automated segmentation for different subregions for three male and three female participants are illustrated in Figure 10. The Dice scores for accuracy (n = 20) of FH, FN, and TR subregion segmentation were 0.990, 0.941, and 0.981, respectively. To evaluate the generalizability of the method, Dice scores between manual and automated segmentation of corresponding femoral subregions were computed for CT images obtained using the clinical scan protocol. It is worth mentioning that the DL network and other parametric setup were trained for ULD CT images only, and clinical CT images were unseen to the DL network or other image processing modules. Observed Dice scores of the generalizability experiment (n = 12) were 0.977, 0.960, and 0.984 for FH, FN, and TR subregions, respectively.

Figure 10.

A few examples of fully automated segmentation of femoral head (yellow), neck (magenta), and trochanteric (cyan) regions from CT images. Examples of regional segmentation for three female (top row) and three male (bottom row) participants are shown in two rows. CT contrast setting for all images: level = 500 Hounsfield units (HU); window = 1800 HU.

For repeat ULD CT scans, automated segmentation of different femoral subregions was independently computed for baseline and repeat scans. Subsequently, mutual information-based rigid body registration was applied to the CT images from two scans, which was followed by manual fine-tuning using the ITK-SNAP software.⁶⁸ Finally, Dice scores were computed after applying the same spatial transformation matrix to register the segmentation results of different femoral subregions independently derived from baseline and repeat CT scans. Observed Dice scores for repeat scan reproducibility (n = 5) for the femoral subregions FH, FN, and TR were 0.982, 0.970, and 0.986, respectively. For all three evaluative experiments, the performance at the method at FN is lower than FH and TR due to lower volume of FN compared to the other two subregions.

3.C. Accuracy of ULD CT-based Bone Measures

Clinical CT is an established method for quantitative imaging, and it has been applied to measure vBMD.⁶⁹ The purpose of this experiment is to evaluate the accuracy of an ULD CT-based regional vBMD. Toward this aim, the vBMD value at a matching location derived from an established imaging method using a clinical CT protocol was used as a reference. Specifically, for each clinical CT image, one hundred spherical regions-of-interest (ROIs), each of diameter 11.5 mm, equivalently 23 voxels, were randomly selected inside the segmented femur region. Thus, a total of 100⊆12 = 1,200 ROIs were generated. Matching ROIs for an ULD CT image were generated after registering the ULD CT image with the corresponding clinical CT image. Observed means ± SD of vBMD over the spherical ROIs were 1,128.0 ± 71.8 and 1,114.8 ± 70.3 mg/cc for ULD and clinical CT images, respectively. Results of correlation and error analyses stratified by participants’ BMI are presented in Table 1. ULD CT-derived metrics produced concordance correlation coefficient (CCC) of 0.977 and a root-mean-square coefficient of variation (RMSCV) (%) of 1.39% with clinical CT-derived measures at matching locations as the reference; a Pearson correlation coefficient (PCC) of 0.994 was observed between ULD and clinical CT-derived measures. Performance of the method in terms of CCC and RMSCV (%) values was lower for obese participants as compared to non-obese participants. However, the two BMI groups produced similar PCC values of 0.997 and 0.994 for the obese and non-obese groups. Scatter plot and Bland-Altman plot of observed vBMD values at location-matched individual spherical ROIs using ULD and clinical CT imaging are presented in Figure 11(a,b). As observed in the scatter plot, while the vBMD values using the two imaging protocols are correlated, ULD CT-based vBMD measures are higher than clinical CT-based values. This is further confirmed in the Bland-Altman plot, which shows a mean difference between the two measures of 1.18% (p < 0.001). However, the differences or errors are tightly bounded with ±1.96 SD lines at 1.18 ± 1.14%, and no trend in alteration of errors was observed with the actual vBMD values. It may be noted from Figure 11(a,b) that data points obtained from ULD CT image of obese participants with expectedly higher noise have greater positive deviations from their reference values using clinical CT. These results are consistent with the findings of Table 1. Similar results were observed when image noise was increased using a sharper reconstruction kernel. Specifically, the RMSCV (%) was increased to 2.29% and the CCC value was reduced to 0.93 when BMD values were derived from ULD CT with higher noise using the Siemens Br49 kernel and compared with the reference BMD measures using clinical CT. A greater shift of 2.02% (p < 0.001) in ULD CT derived BMD values using the sharper Br49 kernel, compared to reference clinical CT measures, was observed. A high PCC of 0.98 was observed for BMD using the sharper B49 kernel, which was similar to that using Br40. These findings suggest that noise and artifacts introduced in reconstructed CT images due to the low X-ray signal have a positive mean, and it is enhanced as the image noise is increased either due to a participant’s obesity or use of a sharper reconstruction kernel. It is of interest to further investigate how this positive shift in noise depends on scanners and reconstruction protocol and whether a scanner and reconstruction kernel-specific BMI-dependent adjustment in ULD CT-derived vBMD is feasible.

Table 1.

Accuracy and reproducibility of regional volumetric bone mineral density (vBMD) measures for different body mass index (BMI) groups using ultra-low dose (ULD) CT imaging.

	Accuracy				Reproducibility
	n†	BMI (kg/m2) mean ± SD	CCC	RMSCV (%)	n†	BMI (kg/m2) mean ± SD	ICC	RMSCV (%)
Overall	12	27.63 ± 5.11	0.977	1.39	5	29.28 ± 5.71	0.996	0.72
Non-obese (BMI < 30)	9	25.23 ± 1.99	0.986	1.07	3	23.31 ± 1.15	0.998	0.51
Obese (BMI ≥ 30)	3	34.83 ± 4.90	0.947	2.06	2	33.26 ± 2.24	0.995	0.83

^†100 spherical ROIs of diameter 11.5 mm were randomly selected from each subject.

CCC: Concordance correlation coefficient

RMSCV (%): Root-mean-square coefficient of variation (%)

ICC: Intraclass correlation coefficient

Figure 11.

Accuracy and reproducibility of regional volumetric bone mineral density (vBMD) measures for different body mass index (BMI) groups using ultra-low dose (ULD) CT imaging. (a) A scatter of plot of observed vBMD measures at matching regions from CT images using a clinical protocol and our ULD protocol. Each observation represents vBMD measures at a matching spherical region of diameter 1.15 cm in clinical and ULD CT images. (b) Bland-Altman plot of the difference in vBMD measures from clinical and ULD CT images with clinical CT-based vBMD representing the reference measure. (c,d) Same as (a,b) but for reproducibility analysis comparing the vBMD measures from the baseline and repeat CT scans.

3.D. Reproducibility of ULD CT-based Bone Measures

Repeat ULD CT-derived vBMD values from matching locations were used to examine the reproducibility. Similar to the accuracy analysis, one hundred spherical ROIs, each of diameter 11.5 mm, were randomly selected from baseline and repeat scans using image registration leading to a total of 100⊆5 = 500 ROIs. Observed mean ± SD in baseline and repeat scans were 1,088.6 ± 89.4 and 1,088.8 ± 90.8 mg/cc, respectively. After 3-digit approximation, each of Pearson and concordance correlation coefficients as well as intraclass correlation coefficient (ICC) between baseline and repeat scans were 0.996, and the observed RMSCV was 0.72%. Scatter plot and Bland-Altman plot of observed vBMD values at location-matched individual spherical ROIs in baseline and repeat scans are illustrated in Figure 11(c,d). As observed in the scatter plot, the vBMD values at matching locations in baseline and repeat scans are uniformly and tightly scattered around the identity line, which is confirmed in the Bland-Altman plot showing a nominal value of −0.01% for the mean difference between vBMD values from baseline and repeat scans. As observed in Table 1 and Figure 11(c,d), performance difference in reproducibility for data points derived from obese and no-obese participants is limited, although, the RMSCV (%) of 0.83 for ROIs from obese is slightly greater than that of 0.51 for ROIs from non-obese participants.

3.E. Comparison of Regional Bone Measures between Males and Females

Results of application of the method on the 100 participants (age: 73.6 ±6 .6 years) recruited in this study are presented in Table 2. Specifically, the table presents demographic characteristics, COPD severity, and observed vBMD of the male and female participants. Following the COPDGene study design, all participants were current or ex-smokers with a smoking history of at least 10 pack-years. A significant difference in age (p = 0.01) was observed for male (75.4 ± 6.2 years) and female (72.2 ± 6.9 years) participants. Also, height, weight, as well as BMI of male participants were significantly greater than females (p < 0.01 for height and weight and p = 0.02 for BMI). For both male and female groups, the number of participants with preserved lung function were greater than those with mild, moderate, and severe COPD status, which is consistent with the population distribution of the parent COPDGene study. Observed vBMD at the femoral head and trochanteric regions and as well as at the total femur were significantly greater (p < 0.01) for male participants as compared to female participants. By contrast, vBMD at the medial half of femoral neck was marginally greater (p = 0.05) in female participants. No significant or marginal vBMD difference was observed in the lateral half of FN or in the whole FN.

Table 2.

Demographic characteristics, chronic obstructive pulmonary disease (COPD) severity, and volumetric bone mineral density (BMD) of Genetic Epidemiology of COPD (COPDGene) bone study participants included in this retrospective study.

Metrics: mean ± SD	Males (n = 50)	Females (n = 50)	p-value
Age (year)	75.3 ± 5.8	72 ± 7.1	0.01
Height (cm)	174 ± 6.6	161.4 ± 5.8	< 0.01
Weight (kg)	88.6 ± 16.0	69.6 ± 15.0	< 0.01
BMI (kg/m2)	29.2 ± 4.9	26.7 ± 5.4	0.02
COPDa Severity: n (%)
Preserved lung function	29 (58%)	34 (68%)
Mild	11 (22%)	8 (16%)
Moderate	7 (14%)	5 (10%)
Severe	3 (6%)	3 (6%)
Regional BMD (mg/cc): mean ± SD
Femoral head	1,190.5 ± 29.1	1,169.8 ± 25.9	< 0.01
Femoral neck	1,214.5 ± 35.4	1,223.6 ± 44.8	0.26
Femoral neck lateral	1,154.2 ± 35.5	1,152.5 ± 40.4	0.82
Femoral neck medial	1,281.9 ± 38.4	1,301.0 ± 55.5	0.05
Trochanteric region	1,222.0 ± 32.3	1,201.4 ± 38.9	< 0.01
Total hip	1,211.1 ± 28.2	1,193.1 ± 32.9	< 0.01

Note—All participants were ex-smokers with a smoking history of at least 10 pack-years. SD = standard deviation. BMI = body mass index. COPD = chronic obstructive pulmonary disease.

^aCOPD is defined as postbronchodilator pulmonary function tests (spirometry). Preserved lung function consists of participants with Global Initiative for Chronic Obstructive Pulmonary Disease (GOLD) 0, mild COPD consists of participants with GOLD 1 or Preserved Ratio Impaired Spirometry (PRISm), moderate COPD consists of participants with GOLD 2, and severe COPD consists of participants with GOLD 3 or 4.

4. CONCLUSION

Deep learning combined with shape modelling and finite element analysis produces an accurate, reproducible, and generalizable method for automated segmentation of proximal femoral subregions using ULD hip CT imaging. The approach of using a DL network as a low-level tool for generating a spatial likelihood map of the target object and concatenating it with an advanced object segmentation module suitable to the specific problem significantly improves the robustness and generalizability of the overall method. ULD hip CT-based regional vBMD is accurate and reproducible and may be useful as a screening tool for osteoporosis. Results of application of the method on ULD hip CT data of human participants show interesting sex differences in vBMD measures at different femoral subregions. The observation that vBMD values at the femoral head and trochanteric regions as well as at total hip are significantly greater for males as compared to females is consistent with the greater prevalence of hip fractures observed in women as compared to men.⁷⁰ The other finding that vBMD at the medial half of the femoral neck is moderately greater in women as compared to men is supportive to the observations in previous studies that the ratio of intracapsular or femoral neck fractures with extracapsular femoral fractures is smaller in women as compared to men.^70,71 Also, it has been observed in another study that the proportion of femoral neck fractures is significantly reduced in women with aging, while the pattern is reversed in men.^70,72 However, these findings need to be evaluated on a larger dataset after adjusting for different contributing variables, which are beyond the scope of the current paper oriented toward development and validation of an automated method for regional measurement of femoral vBMD using ULD hip CT images. Also, it will be worth investigating whether the ULD CT imaging protocol and computational framework with retrained shape model and segmentation algorithm may be generalizable to vBMD measurements at other anatomies such as vBMD measurements on lumbar spine.