Tarsal and Metatarsal Bone Mineral Density Measurement Using Volumetric Quantitative Computed Tomography

Subjects

Volumetric QCT images were collected from eight subjects with diabetes, peripheral neuropathy, and a history of forefoot or mid-foot plantar ulceration. The subject characteristics are shown in Table 1. Subjects were recruited from the Wound and Ostomy Center, Volunteers for Health, and the Diabetes Research Training Center at Washington University School of Medicine and BJC Health System, St. Louis, MO, USA. Prior to testing, informed consent was obtained from each subject according to an approved Washington University School of Medicine Human Research Protection Office protocol. Peripheral neuropathy was confirmed by assessing sensation to light touch (pressure) with Semmes–Weinstein monofilaments using a previously described technique¹³. All subjects were unable to feel the 5.07 (10 gram) monofilament on at least two sites on the plantar surface of the foot and had a history of plantar ulcers which confirmed they had peripheral neuropathy.

Image Acquisition

A Siemens Sensation 16 CT scanner was used to acquire the images from the eight subjects (Somatom Sensation 16, Siemens Medical Systems, Inc, Iselin, NJ, USA). The CT images were acquired using a previously documented procedure^14–16. Briefly, the foot with the history of ulceration was selected for study. The subjects were seated with their foot resting on the table and their toes pointed away from their body. For each subject, their foot was scanned, repositioned, and scanned again. The following VQCT parameters were used to acquire the scans for all subjects: 12-mm table increment per gantry rotation, 16 × 0.75 mm collimation, 220 mAs, 120 kVp, with a pitch of 1, and a 512 × 512 matrix. The Sensation 16 has 16 parallel x-ray sources that were set to a collimation of 0.75 mm. Each subject’s foot was scanned from beyond the toes to above the talus. The acquisition time depended on the size of the subject’s foot. Approximately 200 to 300 mm of data was acquired. The VQCT projection data sets were reconstructed at 0.75-mm reconstruction intervals at the CT scanner to create the VQCT images.

A solid QCT-Bone Mineral™ Phantom (Image Analysis, Inc., Serial No. 4225) was used to determine that the CT scanner had low variability between scans within a session and between scanning sessions. The phantom was constructed of three different calcium hydroxyapatite samples (200, 100, 50 mg/cc calcium hydroxyapatite) incorporated in a water equivalent compound. The phantom was repeatedly scanned on the same day (session) and between days (sessions).

Whole-Bone Semiautomatic Segmentation

VQCT images of the foot was imported into the Analyze^17,18 software program and resampled to 0.7-mm isotropic voxels (Fig. 1a) in preparation for segmentation. Segmentation of an individual region of interest (i.e., bones) from the VQCT images is an important step when measuring BMD. Numerous segmentation techniques are available^19–21. Our approach for segmentation of whole foot bones from the soft tissue was based on edge detection filtering²². The resampled volumetric data was imported into ImageJ (a public domain Java image processing program developed at the National Institutes of Health)²³ for identifying the boundaries (cortical shells) of the bones with an edge detection filter. Filtering allows the grayscale volumetric image to be reduced to a binary representation. All voxels located on edges (boundaries between two different tissue types) are set to a binary 1 and the remaining voxels are set to a binary 0. Since each bone in the foot consists of a cortical shell and trabecular internal region, identifying the cortical shell was sufficient as a means to identify the boundary of each bone.

After the boundaries of the bones were collectively determined using the edge detection filter, we used editing tools and morphology operations to separate the individual bones in the binary image^18,24. The entire boundary of each bone was nearly completely isolated from the surrounding bones by the edge detection filter due to joint spaces between bones, but in locations where the bones were either touching or nearly touching, connections between the bones were manually deleted. After removal of the connections, any place in the cortical boundary where a gap was identified, the operator would manually fill in the gap. The gaps were typically small (i.e., just a few voxels). Occasionally, larger gaps would be created by an extremely thin cortical shell, which required manual filling. Then, internal holes found in the segmented bone resulting from marrow spaces were filled automatically using the fill morphology operator. Binary mathematical morphology is a process used to manipulate an object of interest^18,24. After breaking the connections and filling the holes, the operator utilized auto-trace to define each of the 12 tarsal and metatarsal bones as independent objects (Fig. 1b). The binary representation of the individually segmented bones was multiplied by the original volumetric grayscale data to extract the grayscale values for each tarsal and metatarsal bone.

Whole-Bone Semiautomatic Measurement

Volume and BMD of each whole tarsal and metatarsal bone was measured from the two acquired scans for each subject with the measurement for scan one separated by approximately 1 month from scan 2. The volume and mean Hounsfield units (HU) were computed (measured) for each bone from the extracted grayscale data. HU is a quantitative measure of the x-ray attenuation coefficients (radiodensity) of tissues in computed tomography. In this paper, BMD is given in HU. Typically, HU is converted to BMD because a direct linear relationship exists between HU and BMD^10,25, but this is true when trabecular BMD values fall in a range where the CT scanner has been calibrated. The solid QCT-Bone Mineral^TM Phantom only has BMD values ranging from 0 to 0.200 g/cc and is used to calibrate the CT scanner in the trabecular BMD range. The cortical bone in many of the foot bones ranges from approximately 500 HU to 2000 HU. To our knowledge, we have not been able to find any papers or phantoms that calibrate a CT scanner in the 500 HU to 2000 HU range for making cortical BMD measurements. We are in the process of developing our own CT calibration phantom(s) and methods to convert HU to BMD (g/cc) over a wide range of values from 0 to 2000 HU. The error between measurements from the repeated CT scans for the eight subjects was determined for the foot. The mean time required to segment and measure the 12 foot bones (five metatarsals and seven tarsals) for a single subject was approximately 2.4 (±0.67) h.

Subdivision Atlas Measurement of the Second Metatarsal

While the semiautomatic segmentation method allows for measurement of volumes and BMD of whole individual bones, we were further interested in developing methods for obtaining measures within subregions of a bone. The second metatarsal was utilized to demonstrate our subregion (proximal end, distal end, and the shaft) measurement capability within and between subjects. The second metatarsal is often associated with deformity (hammer toe), stress fractures, and fracture dislocations^26,27. In addition, the length of the second metatarsal allowed us to create subregions along its length. These subregions allow inherent differences in BMD between the proximal end, shaft, and distal end to be measured. Note that the semiautomatic segmentation method discussed above could not have been utilized for partitioning these three subregions due to the poor contrast ratio between subregions in a bone (e.g., between the proximal end and shaft of a metatarsal). To overcome such difficulty, we extended the atlas-based 2D subregion partitioning approach reported by Ju et al.¹¹ to a 3D VQCT volume.

We utilized a volumetric subdivision atlas to model the partitioning of a bone into subregions. Subdivision is a fractal-like process that models a smooth shape by iterative refinement of an initial, coarse shape. Figure 2a,d shows an example atlas of a second metatarsal modeled as a tetrahedral subdivision mesh. Applying subdivision rules²⁸, this coarse atlas is refined in successive subdivision levels into smaller tetrahedral and octahedral elements with a smoother appearance. Figure 2b,e and c, f show the atlases after one and two rounds of subdivision. This atlas was constructed from one metatarsal semiautomatically segmented from a VQCT scan by applying standard surface simplification²⁹ and tetrahedral meshing³⁰ to the segmented bone surface. To further define the subregions, we labeled the interior elements of the atlas at a chosen subdivision level (we used 2) that belong to each subregion. Specifically, we computed an axis of the shaft of the atlas and partitioned all atlas elements using two planes, one located at a distance of 20% from the proximal end and the other at a distance of 20% from the distal end, as shown in Figure 3. These two planes partitioned the metatarsal into three subregions denoted as follows: (1) proximal end, (2) shaft, and (3) distal end (metatarsal head).

After the atlas construction and element labeling, we partitioned the subregions in a new scan by registering the atlas onto the scan. Subdivision was useful because the geometry of the refined atlas was completely determined by the geometry of the initial, base-level atlas, which offered easy control for registering the atlas onto a second structure. Similar to the methods described by Ju et al.¹¹, we registered the atlas with a segmented bone surface in two steps. First, the atlas was aligned to the bone surface using global transformations (e.g., translation, scaling and rotation) obtained by Principle Component Analysis. Next, the location of each individual vertex in the base-level atlas was locally perturbed. The local alignment step was performed in an iterative process that minimized the distance between the outer boundary of the refined atlas to the target as well as the amount of distortion introduced to the interior elements. We adopted the same process described by Ju et al.¹¹ while extending the distortion term designed for 2D triangular elements onto 3D tetrahedral elements. Specifically, we let F be the set of interior triangular faces shared by two tetrahedrons in the initial atlas, v_i and the location of the i-th vertex in the atlas before and after alignment, p, q the indices of the other two vertices in the two tetrahedra sharing the face {v_i, v_j, v_k}, and A_ijkp the unsigned volume of the tetrahedron formed by vertices {v_i, v_j, v_k, v_p}. The distortion of the atlas interior after alignment is measured as the deviation of the alignment from an affine transformation:

1

Following registration, the volume and BMD for each subregion was computed by summing the volume and BMD within each tetrahedral and octahedral element belonging to that subregion in the registered atlas at the chosen subdivision level (linear interpolation is used when the vertices of the elements do not fall on integer coordinates).

Whole-Bone Semiautomatic Segmentation Measures

The volume of the seven tarsal and five metatarsal bones was computed for the eight subjects’ initial foot scans and for their repeated foot scans to determine the volume measurements error in the semiautomatic segmentation method.

The BMDs for each of the seven tarsal and five metatarsal bones (cortical and trabecular regions combined for each bone) were computed for the eight subjects’ initial foot scans and for their repeated foot scans (Table 2). Since no previously published data exist for the tarsal and metatarsal bones, the individual BMD measurements for each bone were reported to demonstrate the variation in BMD for the individual bones within a subject’s foot and between the feet for each of the subjects. The BMD variation can be seen for the individual bones within a subject’s foot and between the feet for the subjects. For the eight subjects, the 2nd metatarsal had the highest mean density (mean 577 HU) and the cuboid had the lowest mean density (mean 314 HU) (Table 2, rightmost two columns). The BMD for each subject’s five metatarsals were typically higher (mean 494 HU) than the tarsal bones (mean 414 HU). The higher BMD values for the metatarsals likely are due to the large volume of cortical bone, especially in the shafts, whereas the tarsal bones are comprised predominately of trabecular bone. The sesmoids were not measured and were not included in the first metatarsal BMD measurements.

Subdivision Atlas Segmentation Measures

The volume and BMD for the whole second metatarsal was computed from the eight subject’s initial scans and for their repeated foot scans using the subdivision atlas method. The volume and BMD for the whole second metatarsal were measured for comparing the accuracy of the subdivision atlas segmentation method to the semiautomatic segmentation method of measuring.

The BMDs for the second metatarsal’s three subregions (proximal end, shaft, and distal end) were computed from the subdivision’s results for the eight subject’s initial scans (Table 3) and for their repeated foot scans. The mean BMD from the eight subjects for the second metatarsal shaft was approximately 160% more dense (782.4 HU compared to 298.8 HU) compared to the distal end (metatarsal head) and approximately 63% more dense (782.4 HU compared to 480.5 HU) compared to the proximal end (metatarsal base).

Error in the Semiautomatic Segmentation Measures

The error in the semiautomatic segmentation measurements was computed for each bone by subtracting the first scan from the second scan for each of the eight subjects. For absolute errors, the error was computed as the bias (mean) and root mean square standard deviation (SD_RMS) of the difference measures for the seven tarsal and the five metatarsal bones (Table 4)³¹. The bias was small for both the volume and BMD measurements. The mean volume and BMD reliability (SD_RMS) for the 12 bones was 0.12 cc and 4.2 HU, respectively.

For relative errors, the root mean square coefficient of variation (CV_RMS) was computed using the methods described by Gluer et. al. (Table 4)³¹. We computed the CV_RMS to allow interpretation of the standard deviation in relationship to the size of the mean for each bone. The CV_RMS allows for comparison of the errors between the bones. The mean CV_RMS for measuring the volume and BMD for the 12 bones was 0.8% and 0.9%, respectively. The metatarsals had the largest BMD CV_RMS ranging from 0.9% for 2nd metatarsal to 1.6% for the 5th metatarsal. The talus and calcaneus had the smallest BMD CV_RMS of 0.2% and 0.3%, respectively, but these two bones had the largest volume out of the 12 bones. The volume CV_RMS for the five metatarsals and seven tarsal bones was 0.5% and 1.0%, respectively. The BMD CV_RMS for the five metatarsals and seven tarsal bones was 1.3% and 0.6%, respectively.

Error in the Subdivision Atlas Segmentation Measures

To evaluate the quality of the atlas-based subregion segmentation, we registered the bone atlas onto the eight subjects’ repeated CT scans. The whole-bone volume and BMD bias (mean), root mean square standard deviation (SD_RMS), and the root mean square coefficient of variation (CV_RMS) of the difference measures between the repeated CT scans are reported in Table 5³¹ as well as for each subregion. Note that the volume and BMD of any subregion differed by approximately 1% or less between the two scans, demonstrating the small error in segmentation with respect to orientation and position differences between bones. In addition, the volume and BMD of the whole-bone atlas measurement differed from the whole bone measured by the semiautomatic segmentation method on average −0.01% (0.05%) and −0.02% (0.11%), respectively, demonstrating the accuracy of the atlas registration method.