Calcified Tissue International

, Volume 81, Issue 4, pp 294–304

Fuzzy Logic Structure Analysis of Trabecular Bone of the Calcaneus to Estimate Proximal Femur Fracture Load and Discriminate Subjects with and without Vertebral Fractures using High-Resolution Magnetic Resonance Imaging at 1.5 T and 3 T

Authors

  • Priyesh V. Patel
    • Department of RadiologyUniversity of California
    • Chicago Medical School
  • Felix Eckstein
    • Musculoskeletal Research Group, Institute of AnatomyLudwig-Maximilians-Universität
    • Institute of Anatomy and Musculoskeletal ResearchParacelsus Medical Private University
  • Julio Carballido-Gamio
    • Department of RadiologyUniversity of California
  • Catherine Phan
    • Department of RadiologyUniversity of California
  • Maiko Matsuura
    • Musculoskeletal Research Group, Institute of AnatomyLudwig-Maximilians-Universität
  • Eva-Maria Lochmüller
    • 1st Gynecology HospitalLudwig-Maximilians-Universität
  • Sharmila Majumdar
    • Department of RadiologyUniversity of California
    • Department of RadiologyUniversity of California
Article

DOI: 10.1007/s00223-007-9058-5

Cite this article as:
Patel, P.V., Eckstein, F., Carballido-Gamio, J. et al. Calcif Tissue Int (2007) 81: 294. doi:10.1007/s00223-007-9058-5

Abstract

Newly developed fuzzy logic-derived structural parameters were used to characterize trabecular bone architecture in high-resolution magnetic resonance imaging (HR-MRI) of human cadaver calcaneus specimens. These parameters were compared to standard histomorphological structural measures and analyzed concerning performance in discriminating vertebral fracture status and estimating proximal femur fracture load. Sets of 60 sagittal 1.5 T and 3.0 T HR-MRI images of the calcaneus were obtained in 39 cadavers using a fast gradient recalled echo sequence. Structural parameters equivalent to bone histomorphometry and fuzzy logic-derived parameters were calculated using two chosen regions of interest. Calcaneal, spine, and hip bone mineral density (BMD) measurements were also obtained. Fracture status of the thoracic and lumbar spine was assessed on lateral radiographs. Finally, mechanical strength testing of the proximal femur was performed. Diagnostic performance in discriminating vertebral fracture status and estimating femoral fracture load was calculated using regression analyses, two-tailed t-tests of significance, and receiver operating characteristic (ROC) analyses. Significant correlations were obtained at both field strengths between all structural and fuzzy logic parameters (r up to 0.92). Correlations between histomorphological or fuzzy logic parameters and calcaneal BMD were mostly significant (r up to 0.78). ROC analyses demonstrated that standard structural parameters were able to differentiate persons with and without vertebral fractures (area under the curve [AZ] up to 0.73). However, none of the parameters obtained in the 1.5-T images and none of the fuzzy logic parameters discriminated persons with and without vertebral fractures. Significant correlations were found between fuzzy or structural parameters and femoral fracture load. Using multiple regression analysis, none of the structural or fuzzy parameters were found to add discriminative value to BMD alone. In summary significant correlations were obtained at both field strengths between all structural and fuzzy logic parameters. However, fuzzy logic-based calcaneal parameters were not well suited for vertebral fracture discrimination. Although significant correlations were found between fuzzy or structural parameters and femoral fracture load, multiple regression analysis showed limited improvement for estimating femoral failure load in addition to femoral BMD alone. Local femoral measurements are still needed to estimate femoral bone strength. Overall, parameters obtained at 3.0 T performed better than those at 1.5 T.

Keywords

BoneCalcaneusOsteoporosisFuzzy logicTrabecular

During the last decade, the role of trabecular bone structure imaging in the assessment of osteoporosis has substantially gained in importance. Evaluation of bone mineral density (BMD) remains the current standard for the diagnosis of osteoporosis and assessment of osteoporotic fracture risk. However, an increasing number of studies have found that alterations in bone architecture can explain bone fragility independent of bone mass [15]. Recent studies have also shown that interpreting BMD in conjunction with trabecular structural parameters may yield additional information [610]. Therefore, analysis of bone microarchitecture is a promising method for gaining insight into the metabolic and structural effects of osteoporosis, as a potential prognostic tool for osteoporotic fractures, and to study the effects of pharmacotherapy on trabecular bone.

High-resolution magnetic resonance imaging (HR-MRI) has taken a prominent role in trabecular structure analysis. Improvements in spatial resolution, field strength, and signal-to-noise ratio have allowed for improved depiction of trabecular structure [11]. Additionally, multiple studies have reported significant correlations between MRI-derived measures of bone structure obtained at 1.5 T and 3.0 T with the trabecular bone structure derived from contact radiographs and microcomputed tomography (micro-CT) [1115].

Traditional image processing techniques applied to HR-MRI are based on microstructural parameters and texture analysis [6, 1620]. As spatial resolution of HR-MRI is on the order of trabecular thickness, substantial partial volume effects are inherent in trabecular imaging, rendering MRIs fuzzy. Recently, the experimental use of fuzzy logic as a tool for trabecular bone analysis has been encouraging [21]. Carballido-Gamio et al. [21] studied radii and calcanei and showed high correlations between a fuzzy parameter (fuzzy bone volume fraction [f-BVF]) and bone volume fraction (maximum r = 0.99, P < 0.001) and between measures of fuzziness and trabecular number (r > 0.85, P < 0.001). These results suggested that the level of fuzziness in HR-MRIs could be related to trabecular bone structure.

Furthermore, HR-MRI has been used to examine different anatomic locations with the hope of gaining additional insight into the osteoporotic disease process. Studies have examined the distal radius and calcaneus due to their high proportion of trabecular bone as well as the proximal femur and distal radius due to their propensity to fracture in osteoporosis.

Prior studies examining the calcaneus, in particular, have shown promising results [2228]. Studies have focused on the discrimination of vertebral and hip fractures as these fractures have historically been associated with high rates of morbidity and mortality. Recently, Phan et al. [11] examined the calcaneus at 1.5 T and 3.0 T. They showed that trabecular parameters from the calcaneus can discriminate between subjects with and without osteoporotic vertebral deformities. In addition, Patel et al. [29] and Link et al. [6] have shown that trabecular structure parameters from the calcaneus can discriminate between subjects with and without osteoporotic vertebral and hip fractures, respectively.

In this study, we utilized HR-MRI to investigate trabecular structure in calcaneal specimens obtained from elderly human donors. We compared new fuzzy logic-derived parameters with standard histomorphological parameters in their ability to discriminate subjects with and without vertebral fractures and their ability to estimate experimentally determined fracture loads of the proximal femur. The performance of these parameters was compared at 1.5 T and 3.0 T, and results of fuzzy logic and structural analyses were evaluated relative to BMD measures obtained using dual-energy X-ray absorptiometry (DXA) and quantitative computed tomography (QCT) at the proximal femur and the spine.

Materials and Methods

Specimens

Calcaneal, femoral, and vertebral specimens were obtained from 39 formalin-fixed human cadavers, which included 20 male and 19 female donors (mean age 79.1 ± 11 years). They were obtained from a course of macroscopic anatomy from the Institute of Anatomy at the Ludwig Maximilians University (Munich, Germany). The criterion for inclusion in the course was the dedication of the donor’s body to the institute several years prior to death according to local legislative guidelines. The individuals belonged to a wide range of medical and social backgrounds, but no detailed medical or social history was available. To identify specimens with bone diseases other than osteoporosis or osteopenia, biopsy specimens were evaluated histologically from the left iliac crest for histology. Individuals with bone disease other than osteoporosis or osteopenia were excluded from the study. All specimen procedures were performed in accordance with legislative, institutional guidelines.

Specimens were examined macroscopically and tagged using a numerical and color scheme to ensure anonymity. The left calcaneus from each cadaver was embedded in a paraffin plate with a marker filled with gadodiamide (Gd-DTPA, Omniscan; GE Healthcare, Waukesha, WI) doped saline as a landmark to obtain identical slice positioning. The entire thoracic and lumbar spines from the same human specimens were radiographed for assessment of vertebral fractures. In the left femur, measurements of BMD were obtained with DXA, and biomechanical testing was performed as described below.

Magnetic Resonance Imaging

HR-MRIs of the calcaneus were acquired with a two-element phased-array wrist coil, using clinical 1.5 T and 3.0 T scanners equipped with 44 mT/m gradients (Signa; GE Medical Systems, Milwaukee, WI). At the two field strengths, a series of sagittal, axial, and coronal gradient-echo MR sequences were used as localizers for the calcaneus. A set of 60 sagittal images of the calcaneus was obtained using a three-dimensional (3D) fast gradient recalled echo (FGRE) sequence. At 1.5 T, the repetition time (TR), echo time (TE), and acquisition time were 20.0 milliseconds, 5.1 milliseconds, and 8 minutes and 10 seconds, respectively. At 3.0 T, the corresponding parameters were 18.5 milliseconds, 4.3 milliseconds, and 7 minutes and 34 seconds. At both 1.5 T and 3.0 T, the flip angle was 20°, bandwidth 12.5 kHz, field of view 100 × 75 mm, section thickness 0.5 mm, and the matrix 512 × 384 pixels (in-plane pixel size 156 × 156 μm) with one signal acquired.

Image Analysis

In the 20 central slices of the MRIs, an anterior, rectangular region of interest (ROI-A) was manually chosen, starting with the posterior facet of the talocalcaneal joint and extending inferiorly to the calcaneal base. This region was shown to contain a relatively dense trabecular pattern in the calcaneus, which may represent an area of increased weight-bearing [30]. This ROI was chosen to investigate the specific properties of this region. A circular region of interest (ROI-P) was placed in the posterior region of the calcaneus, given that this region has the highest amount of trabecular bone [6]. ROIs were carefully chosen to include trabecular bone and marrow, avoiding cortical bone and any air artifacts. Fig. 1 shows representative images from a donor with and a donor without vertebral fractures at 1.5 T and 3.0 T with ROI placement. The investigator who chose the ROIs was blinded to BMD and MRI structural data, as well as fracture status of the spine and fracture load of the proximal femur.
https://static-content.springer.com/image/art%3A10.1007%2Fs00223-007-9058-5/MediaObjects/223_2007_9058_Fig1_HTML.jpg
Fig. 1

Sagittal MRIs at 1.5 T (A, C) and 3.0 T (B, D) from calcaneus specimens acquired with an FGRE sequence. (A, B) A specimen with dense (BMD calcaneus = 0.66 g/cm2) calcaneal trabeculae (donor had no osteoporotic vertebral deformities). (C, D) A specimen with diminished (BMD calcaneus = 0.17 g/cm2) calcaneal trabecular bone (donor had multiple osteoporotic vertebral fractures). The ROI-A (rectangle) begins at the posterior facet of the talocalcaneal joint and extends inferiorly to the calcaneal base. The ROI-P (circle) was placed in the posterior region of the calcaneus, similar to the ROI for BMD measurements. Images also demonstrate the enhanced depiction of individual trabeculae at higher field strength

Structural Parameters

The first step of the structural analysis was the binarization of the ROI based on a dual reference model, assuming a biphasic distribution as previously described by Majumdar et al. [31]. This model requires user input in choosing cortical bone as a reference threshold value for binarization. Using the binarized ROIs, 2D morphological structural parameters equivalent to bone histomorphometry were then calculated. They included (1) bone volume/total volume (BV/TV), (2) trabecular number (Tb.N, 1/mm), (3) Tb thickness (Tb.Th, mm), and (4) Tb separation (Tb.Sp, mm). In the MRIs, these parameters were defined as apparent (App.) since the spatial resolution is lower than that required for standard bone histomorphometry [32]. MRI parameters were calculated using the mean intercept length (MIL) method based on the plate model with software developed in-house using IDL (version 6.0; Research Systems, Boulder, CO, USA) [33].

Fuzzy Logic

The application of fuzzy logic techniques to characterize trabecular bone structure from HR-MRIs has been described in detail by Carballido-Gamio et al. [21]. In brief, using the chosen ROIs, individual slices were stacked to create a 3D volume and multiplied by themselves to increase contrast. This is a common linguistic hedge in fuzzy logic known as “concentration.” To reduce computational time for future image processing, a threshold [mean + (0.25 × the standard deviation [SD] of the brightness of the whole volume of interest)] was applied. Voxels above this value were discarded, and voxels below this value were classified into bone and marrow phases using soft fuzzy c-means (FCM) clustering segmentation. This model differs from the model above in that user input for binarization is not required, saving time and reducing potential user errors.

In the iterative clustering process, partial memberships of voxels to bone and to marrow are allowed. The final membership value for each voxel in the bone fuzzy subset was then considered as the degree of membership of each voxel to the category of bone. Furthermore, the final bone fuzzy subset could be considered as an f-BVF map since the range of values for each voxel is from 0 to 1, where 0 represents a marrow voxel, 1 represents a bone voxel, and any value in between represents the corresponding bone fraction of that voxel. Fig. 2 shows representative calcaneal ROI magnification views with their corresponding f-BVF maps of a donor with and a donor without osteoporotic vertebral fractures.
https://static-content.springer.com/image/art%3A10.1007%2Fs00223-007-9058-5/MediaObjects/223_2007_9058_Fig2_HTML.jpg
Fig. 2

ROI magnification of the ROI-A ( rectangle) acquired with an FGRE sequence at 3.0 T (A, E) and 1.5 T (C, G) and their corresponding f-BVF maps to the right (B, D, F, H). (A,C) A specimen with diminished (BMD calcaneus = 0.17 g/cm2) calcaneal trabecular bone (donor had multiple osteoporotic vertebral fractures). (E, G) A specimen with dense (BMD calcaneus = 0.66 g/cm2) calcaneal trabeculae (donor had no osteoporotic vertebral deformities)

f-BVF values were compared to the corresponding bone volume fraction (App.BV/TV) parameters. Then, 3D linear and quadratic indices of fuzziness and 3D logarithmic and exponential fuzzy entropies were calculated based on the f-BVF maps and statistically compared to the standard trabecular bone index of App.Tb.N.

BMD Measurements

BMD was determined at the posterior body of the calcaneus and the proximal femur using a GE/Lunar (Milwaukee, WI) Prodigy scanner. The calcaneus was placed on the scanner in a lateral position and covered by saline-filled bags simulating soft tissue. The heel region was scanned with a forearm algorithm using a pencil-beam X-ray mode. BMD (g/cm2) was measured in a circular ROI in the posterior region of the calcaneus, similar to that used for MRIs.

The femoral specimen from each donor was positioned similar to in vivo conditions, mildly internally rotated, in a container filled with tap water up to 15 cm to simulate soft tissue. BMD was evaluated in four different ROIs: femoral neck, upper neck, trochanteric region, and intertrochanteric region.

To determine spinal BMD the T11 to L1 segments were degassed within a vacuum pump for 12 h prior to imaging and sealed within fluid in polyethylene bags. CT was performed using a clinical Somatom Plus 4 scanner (Siemens, Erlangen, Germany) and an osteodensitometry phantom provided by the manufacturer. One-cm thick sections of each T12 vertebra were obtained at midvertebral level with 80 kilovoltage peak (kVp) and 146 milliampere-seconds (mAs), and bone mineral density (BMD in g/ml) was determined for a peeled, trabecular ROI using the manufacturer's software.

Radiographic Assessment of Fracture

Fracture status of the thoracic and lumbar spine was assessed on lateral radiographs by a musculoskeletal radiologist (T. M. L) and categorized using semiquantitative grading according to the spinal fracture index (SFI) method, previously described by Genant et al. [34]. Briefly, deformities with height reductions greater than 20% were defined and graded as fractures: grade I was defined as a deformity with a height reduction of 20–25%, grade II as deformity with height reduction of 25–40%, and grade III as height reductions larger than 40%. The spinal fracture status of each cadaver was defined as the maximum grade of deformity observed in any vertebra within the spine.

Mechanical Testing of the Proximal Femur

A side impact configuration was employed to test the femora, simulating a lateral fall onto the greater trochanter, as previously described [3538]. This test has been shown to display good reproducibility in previous tests on paired femora, the upper limit of the precision error being estimated to amount to 15% or less [36].

After the mechanical test, the fracture patterns were classified from the fractured bones as cervical or trochanteric by one observer, according to the standard arbeitsgemeinschaft fuer osteosynthesefragen (AO) classification. Subcapital and transcervical (basicervical and midcervical) fractures were classified as cervical fractures and pertrochanteric, intertrochanteric, and subtrochanteric fractures as trochanteric fractures. Femoral shaft failures were excluded from the analysis.

Statistical Analysis

The means and SDs of femoral spinal and calcaneal BMD and the calcaneal fuzzy and structural parameters derived from HR-MRI using fuzzy logic and histomorphological techniques were calculated. Differences between parameters were evaluated using the two-tailed t-test of significance. Correlations (r) between the individual fuzzy and structural parameters, calcaneal and femoral BMD, and femoral fracture load were assessed using linear regression analysis. To analyze if structural and fuzzy logic parameters in addition to BMD values can better estimate femoral fracture load than BMD alone, a multiple regression analysis was performed. Subgroups of calcaneal and femoral BMD, structural, and fuzzy parameters were first analyzed; and the best parameters from each subgroup were selected. These parameters were then tested individually and as a group with BMD. Receiver-operator characteristic (ROC) analyses were performed for fuzzy and structural measures and BMD, and the area under the curve (Az) values were used to estimate their power for differentiating participants with and without vertebral fractures. All statistical computations were processed using SPSS 11 (Chicago, IL).

Results

MRI Structural Parameters at 1.5 T and 3.0 T and BMD Measurements

App.BV/TV and App.Tb.N were higher and App.Tb.Sp was lower at 3.0 T compared with 1.5 T, due to susceptibility effects at 3.0 T with amplification of the trabeculae (Table 1). In ROI-P, App.BV/TV and App.Tb.Th were lower, indicating that more gracile trabeculae are found here than anteriorly, which is in accord with trabecular visualization (Fig. 1). The mean BMD (g/cm2) results were as follows: calcaneus 0.32 ± 0.16 (mean ± SD), spine 73.3 ± 35.8 (mg/ml), femoral neck 0.71 ± 0.14, femoral upper neck 0.52 ± 0.12, femoral trochanteric region 0.68 ± 0.14, femoral intertrochanteric region 0.94 ± 0.18, and total femur 0.79 ± 0.15. At 3.0 T, App.BV/TV of ROI-A was significantly correlated with age (r = −0.317, P < 0.05) as well as App.Tb.Sp of ROI-A (r = 0.336, P < 0.05). BMD of the calcaneus did not show a significant correlation with age, while for femoral neck BMD a correlation of r = −0.466 (P < 0.01) was observed.
Table 1

MRI-derived standard histomorphological structural parameters at 1.5 T and 3.0 T in the corresponding ROI (ROI-A/ROI-P): results are expressed as means ± SD

Parameters

ROI-A

ROI-P

MRI 1.5 T

MRI 3.0 T

MRI 1.5 T

MRI 3.0 T

BV/TV (%)

0.32 ± 0.06

0.40 ± 0.05

0.24 ± 0.05

0.38 ± 0.05

Tb.N (mm−1)

1.41 ± 0.12

1.69 ± 0.15

1.37 ± 0.20

1.78 ± 0.14

Tb.Sp (mm)

0.49 ± 0.08

0.37 ± 0.07

0.59 ± 0.16

0.35 ± 0.05

Tb.Th (mm)

0.23 ± 0.04

0.23 ± 0.02

0.18 ± 0.02

0.21 ± 0.02

Structural vs. Fuzzy Logic Parameters

Significant (P < 0.01) correlations were obtained at both field strengths between all structural parameters and parameters derived using fuzzy logic (Table 2). The highest correlation was at 3.0 T in ROI-P between App.BV/TV and f-BVF (r = 0.92). Additionally, at 3 T in ROI-P, exponential fuzzy entropy and logarithmic fuzzy entropy (r = 0.82 and 0.81, respectively) showed a high correlation with App.Tb.N. In ROI-A at 3.0 T, the correlation between App.BV/TV and f-BVF was high (r = 0.86), while linear index of fuzziness and quadratic fuzziness showed similarly high correlations with App.Tb.N (r = 0.81). Correlations at 1.5 T were also significant but lower, with the highest correlation being observed between App.BV/TV and f-BVF in ROI-A (r = 0.74).
Table 2

Correlation (r) between fuzzy logic and histomorphological structural (App.BV/TV and App.Tb.N) parameters at 1.5 T and 3.0 T in the corresponding ROI (ROI-A/ROI-P)

Parameters

ROI-A

ROI-P

MRI 1.5 T

MRI 3.0 T

MRI 1.5 T

MRI 3.0 T

App.BV/TV

    

  f-BVF

0.74**

0.86**

0.52**

0.92**

App.Tb.N

    

  Linear fuzziness

0.48*

0.81*

0.59*

0.80*

  Quad fuzziness

0.41*

0.81*

0.50*

0.66*

  Log entropy

0.49*

0.75*

0.60*

0.81*

  Exp entropy

0.49*

0.78*

0.60*

0.82*

*Correlation is significant at the 0.01 level

Structural Parameters and Fuzzy Logic vs. BMD

Correlations between MR-derived histomorphological and fuzzy logic parameters vs. calcaneal BMD were mostly significant (P < 0.05 and 0.01, respectively) (Table 3). The highest correlations were found for the fuzzy parameter f-BVF in ROI-P, with similar results at both field strengths (r = 0.78). In contrast, most MR-derived histomorphological parameters had higher correlations at 3.0 T than at 1.5 T, with the highest correlations at 3.0 T for App.BV/TV and Tb.Sp. (r = 0.72 and −0.72, respectively). The correlations between BMD at the calcaneus and femoral neck and trochanteric BMD were significant (r = 0.55 and 0.64, P < 0.01, respectively). Correlations for calcaneal structural parameters and femoral BMD values were also significant (P < 0.05 and 0.01, respectively) but only marginally higher than those between BMD at the calcaneus and femur. For instance, femoral trochanteric BMD performed best, with the highest correlations found for App.Tb N (maximum r = 0.71) and for App.Tb.Sp (maximum r = –0.69) with ROI-P at 3.0 T. Higher correlations were found at 3.0 T for all parameters. Correlations between spinal BMD and calcaneal structural parameters were mostly nonsignificant.
Table 3

Correlation (r) of calcaneal BMD vs. f-BVF and trabecular structural parameters at 1.5 T and 3.0 T in the corresponding ROI (ROI-A/ROI-P)

BMD vs. parameters

ROI-A

ROI-P

MRI 1.5 T

MRI 3.0 T

MRI 1.5 T

MRI 3.0 T

f-BVF

0.66**

0.73**

0.78**

0.78**

BV/TV (%)

0.38*

0.57**

0.44**

0.72**

Tb.N (mm−1)

0.60*

0.45**

0.60**

0.65**

Tb.Sp (mm)

−0.57**

−0.55**

−0.49**

−0.72**

Tb.Th (mm)

0.16

0.40*

0.13

0.51**

*Correlation is significant at the 0.05 level

**Correlation is significant at the 0.01 level

Performance in Discriminating Vertebral Fracture Status

In this study, vertebral deformities were found on radiographs in 20 of the 39 cadavers examined: eight grade I fractures, eight grade II fractures, and four grade III fractures, of which 11 were observed in female and nine in male donors. Nineteen donors did not have vertebral deformities by the SFI standards described above, of whom seven were female and 12 were male.

ROC analyses (Table 4) demonstrated that App.Tb.N and App.Tb.Sp obtained at 3.0 T were superior to other parameters in differentiating donors with and without vertebral fractures (AZ up to 0.73). Interestingly, both ROIs showed similar diagnostic performance. None of the parameters obtained in the 1.5-T images showed significant results, and none of the fuzzy logic parameters discriminated persons with and without vertebral fractures. Among BMD values, femoral trochanteric BMD was most discriminative (AZ = 0.88), while femoral neck, upper neck, intertrochanteric, total, and spinal BMD were also able to provide vertebral fracture discrimination (A= 0.75, 0.73, 0.72, 0.82, and 0.71, respectively). BMD of the calcaneus was unable to differentiate donors with and without fractures.
Table 4

ROC analysis (area under curve, AZ) to quantify diagnostic performance of fuzzy and trabecular structural parameters and BMD in differentiating donors with and without vertebral fractures

Parameters

ROI-A

ROI-P

MRI 1.5 T

MRI 3.0 T

MRI 1.5 T

MRI 3.0 T

BV/TV (%)

0.51

0.56

0.50

0.66

Tb.N (mm−1)

0.67

0.73*

0.57

0.73*

Tb.Sp (mm)

0.62

0.70*

0.51

0.71*

Tb.Th (mm)

0.48

0.45

0.44

0.57

f-BVF

0.60

0.65

0.62

0.69

Linear fuzziness

0.64

0.64

0.65

0.65

Quad fuzziness

0.66

0.58

0.63

0.60

Log entropy

0.62

0.66

0.63

0.67

Exp entropy

0.63

0.65

0.63

0.68

 

BMD

Spine

0.71*

Calcaneus

0.68

Femur trochanter

0.88*

Femur neck

0.75*

Femur upper neck

0.73*

Femur intertrochanter

0.72*

Femur total

0.82*

*Significant difference in differentiating donors with and without fractures

Performance in Estimating Femoral Fracture Load

Significant correlations were found between fuzzy and structural parameters derived from MR vs. femoral fracture load (P < 0.05 and 0.01, respectively) (Table 5). Overall, parameters obtained from 3.0-T MRI performed better than those at 1.5 T, and there was no substantial difference in performance between the two ROIs. The highest correlations were found using the fuzzy logic-derived parameters: linear index of fuzziness, logarithmic fuzzy entropy, and exponential fuzzy entropy at 3.0 T (r = 0.47). f-BVF also showed significant correlations at 3.0 T (maximum r = 0.43). App.Tb.Sp was the best histomorphological parameter with the highest significant correlation (maximum r = −0.44). App.Tb.N and App.BV/TV also showed significant correlations (maximum r = 0.41). The correlation of calcaneal and spinal BMD with femoral failure loads (r = 0.44 and 0.33, respectively) was in the same range as that of the structural parameters at the calcaneus, while BMD at the proximal femur (r = 0.74, 0.77, 0.69, 0.70, and 0.73 for femoral neck, upper neck, trochanteric, intertrochanteric, and total BMD values, respectively) showed substantially higher correlations. Using multiple regression analysis and focusing on the parameters that performed best from their respective subgroups, combinations of BMD, histomorphometric, and fuzzy parameters were tested. None of the structural or fuzzy parameters, however, were found to add value to femoral, spinal, or calcaneal BMD alone.
Table 5

Correlation (r) of femoral fracture load vs. fuzzy and trabecular structural parameters and BMD at 1.5 T and 3.0 T with the corresponding ROI (ROI-A/ROI-P)

Parameters

ROI-A

ROI-P

MRI 1.5 T

MRI 3.0 T

MRI 1.5 T

MRI 3.0 T

BV/TV (%)

0.10

0.41*

0.36*

0.40*

Tb.N (mm−1)

0.17

0.32

0.40*

0.41*

Tb.Sp (mm)

−0.16

−0.40*

−0.41*

−0.44*

Tb.Th (mm)

0.02

0.27

0.26

0.26

f-BVF

0.30

0.42*

0.26

0.43*

Linear fuzziness

0.33

0.40*

0.29

0.47**

Quad fuzziness

0.28

0.24

0.25

0.36*

Log entropy

0.33

0.43*

0.29

0.47**

Exp entropy

0.33

0.42*

0.29

0.47**

 

BMD

Spine

0.33

DXA calcaneus

0.44*

Femur neck

0.74**

Femur upper neck

0.77**

Femur trochanter

0.69**

Femur intertrochanter

0.70**

Femur total

0.73**

*Correlation is significant at the 0.05 level

**Correlation is significant at the 0.01 level

Discussion

The results of this study showed that fuzzy logic parameters derived from MRIs of the calcaneus correlate with fracture load of proximal femur specimens, in particular at 3.0 T, but were unable to differentiate subjects with and without vertebral fractures. Overall, no significant improvement of these parameters vs. standard histomorphological parameters was found. Interestingly, fuzzy and structural parameters obtained at 3.0 T performed consistently better than those obtained at 1.5 T. Also, some of the structural parameters at the calcaneus performed better than BMD of the calcaneus in differentiating donors with and without osteoporotic vertebral fractures, while results for femoral BMD were in the same range as those for structural parameters, at 3.0 T.

Traditionally, standard histomorphological bone parameters (i.e., App.BV/TV, Tb.N, Tb.Sp, and Tb.Th) have been used to quantitatively describe trabecular bone structure in high-resolution radiological studies, such as MRI. These measures have been repeatedly shown to not only provide valuable insight into the micro- and macrostructural effects of the osteoporotic disease process but also to be valuable prognostic markers for osseous fractures. Nonetheless, new techniques for the analysis of trabecular bone are being developed to circumvent the spatial resolution limitations of MRI-derived standard histomorphological bone parameters. Our employment of fuzzy logic to examine trabecular bone is in line with this. Fuzzy logic image processing techniques allow voxels to belong to different tissue categories. Using a technique described by Carballido-Gamio et al. [21], fuzzy soft FCM was used as a clustering technique to segment HR-MRIs into bone and marrow phases. This segmenting technique requires less user interaction than the dual reference model described by Majumdar et al. [31] because no cortical bone reference is needed for binarization, an advantage of fuzzy logic. However, the suggested approach was different from the typical use of FCM. Instead of applying the final crisp segmentation based on maximum levels of membership to create binary images representing bone, we used the final bone membership values and created f-BVF maps. In these maps, the voxel values represented the fraction of the voxels corresponding to bone. The remaining fraction was assigned to marrow. Using 3D fuzzy logic analysis of the f-BVF maps, indices of fuzziness and fuzzy entropies were computed.

In the study by Carballido-Gamio et al. [21], human radii were examined ex vivo at 1.5 T and calcanei in vivo at 3.0 T, to characterize trabecular bone from HR-MRI and micro-CT. Highly significant correlations were found between App.BV/TV measurements and f-BVF values obtained from micro-CT data sets of the human radii (r = 0.92, P < 0.001) and for App.BV/TV and f-BVF values from 1.5-T images (r = 0.99, P < 0.001). Indices of fuzziness showed high correlations with App.Tb.N, with r values from micro-CT >0.85 (P < 0.001) and standard histomorphological App.Tb.N >0.90 (P < 0.001). For calcanei, highly significant correlation values were found for the indices of fuzziness and fuzzy entropies (r > 0.92, P < 0.001).

Our current study found slightly lower but significant values of r up to 0.82 (P < 0.01) for the parameter exponential fuzzy entropy. Significant correlations between App.BV/TV measurements and f-BVF values obtained from the calcanei MR data sets were higher than in that study (r up to 0.92, P < 0.01). Both studies utilized similar spatial resolution and field strengths; therefore, a possible explanation for this may be that in the previous study in vivo imaging of the calcaneus was performed, as opposed to the ex vivo imaging in the current study.

Superiority of 3.0-T imaging in studying trabecular architecture was demonstrated by a prior study by Phan et al. [11]. The authors were able to show that trabecular bone architecture is better visualized at 3.0 T than at 1.5 T, using micro-CT as a standard of reference. In that study, correlations between structural parameters measured with 3.0-T MRI and by micro-CT were significantly (P < 0.05) higher than those measured at 1.5 T and micro-CT. The investigators also observed an artificial amplification of trabecular dimensions at 3.0 T compared with 1.5 T, though correlations between 3.0 T- and micro-CT-derived parameters remained higher. This overestimation of trabecular structure was attributed to an increase in susceptibility effects, particularly seen in gradient-echo sequences. The trend of larger values seen at 3.0 T in our study may also be partially due to susceptibility effects. Differences between field strengths in our study are more pronounced in ROI-P than in ROI-A for structural measures (Table 1), but they are less pronounced when looking at correlations with femoral failure load (Table 5). This may be related to differences in structure and related MR artifacts; while ROI-P has thinner trabeculae, which are more isotropic and denser, trabeculae are larger and more anisotropic in ROI-A. Artifacts due to susceptibility may be therefore more pronounced posteriorly and counteract the benefit of the higher spatial resolution to some extent. On the other hand, this effect was not evident in the ROC analysis analyzing performance in discriminating donors with and without fractures.

Phan et al. [11] also analyzed vertebral fracture discrimination, with slightly higher results found in their study (AZ up to 0.75) than in ours (AZ up to 0.73). A finding not seen in their study, but found in ours, was that two structural parameters were significantly correlated with age at 3.0 T: App.BV/TV with ROI-A (r = −0.317, P < 0.05) and App.Tb.Sp with ROI-A (r = 0.336, P < 0.05). This would be expected given the decrease in BMD that occurs with aging and the corresponding increase in distance between the remaining trabeculae. Age-related changes were not seen in the posterior region with BMD or standard structural measures, though previous publications focusing on structural analysis of MRIs of the calcaneus also found limited correlations between structural measures and age [6]. Due to overlying malleoli and talus, DXA BMD measurements in ROI-A would not be feasible in vivo.

ROI placement in our study was specifically chosen to analyze a traditionally studied region in the posterior calcaneus and a main weight-bearing trabecular region in the anteroinferior calcaneus in order to compare these two regions. It has been shown that weight-bearing forces can increase BMD and bone properties such as elasticity and microstructure [39]. However, in our study, ROI-A did not show significant differences from the more posterior chosen ROI-P, except when correlated with femoral neck BMD. Thus, the spatial heterogeneity of trabeculae in the calcaneus may not be as prominent as thought. This may be due to a tensile force that is exerted in the posterior region of the calcaneus [30], which may cause a similar change in bone properties to that observed in weight-bearing trabeculae. The lack of differences may also suggest that trabeculae being “stressed” may succumb to the same or even an increased rate of metabolic change in osteoporosis as less “stressed” trabeculae.

Thus far, we have discussed bone strength and bone structure, but bone size and bone mass are also important in providing mechanical competence. Our study found significant correlations (P < 0.01) between MR-derived histomorphological and fuzzy logic parameters vs. calcaneal BMD. The highest correlations were found for the fuzzy parameter f-BVF using the more posterior ROI-P, with similar results at both field strengths (r = 0.78). In contrast, most MR-derived histomorphological parameters had higher correlations at 3.0 T than at 1.5 T, with the highest correlations at 3.0 T for App.BV/TV and Tb.Sp (r = 0.72 and −0.72, respectively). The higher correlations seen in the posterior calcaneus are potentially explained by the use of similar anatomic ROIs in both BMD measurements and structural analysis of the MRIs.

Low BMD of the proximal femur has been clearly associated with fractures [40, 41] and low mechanical strength [4245] at this site. The importance of elucidating parameters that may potentially add to the prediction of these fractures is necessary. The results of this study show that, with regard to femoral failure load, while standard structural measures and fuzzy measures showed similar correlations at 3.0 T, in ROI-P standard structural parameters had mildly higher correlations than fuzzy parameters at 1.5 T, yet this was reversed in ROI-A at 1.5 T. This may be related to the differences in structure observed in these two ROIs, being more isotropic in ROI-A with smaller trabeculae and more anisotropic in ROI-P with more anisotropic and more prominent trabeculae. Although the correlations were not high, the finding that data derived from the calcaneus may potentially contribute to information regarding hip stability is encouraging, though more investigation into this technique is warranted. In addition to this, future work will focus on structural analysis of the proximal femur using HR-MRI since this fracture site is most relevant for osteoporosis.

In conclusion, significant correlations were obtained at both field strengths between all standard structural parameters and parameters derived using fuzzy logic. Fuzzy logic parameters derived from MRIs of the calcaneus were unable to differentiate subjects with and without vertebral fractures. Although significant correlations were found between fuzzy or structural parameters and femoral fracture load, multiple regression analysis showed limited improvement for estimating femoral failure load in addition to femoral BMD alone. Future work will have to focus on local femoral measurements to better estimate femoral bone strength. Overall, structural parameters obtained at 3.0 T performed consistently better than those obtained at 1.5 T.

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© Springer Science+Business Media, LLC 2007