Multinuclear MR and Multilevel Data Processing

Rationale and Objectives

Quantitative assessment of knee articular cartilage (AC) morphology using magnetic resonance (MR) imaging requires an accurate segmentation and 3D reconstruction. However, automatic AC segmentation and 3D reconstruction from hydrogen-based MR images alone is challenging because of inhomogeneous intensities, shape irregularity, and low contrast existing in the cartilage region. Thus, the objective of this research was to provide an insight into morphologic assessment of AC using multilevel data processing of multinuclear ( 23 Na and 1 H) MR knee images.

Materials and Methods

A dual-tuned ( 23 Na and 1 H) radio-frequency coil with 1.5-T MR scanner is used to scan four human subjects using two separate MR pulse sequences for the respective sodium and proton imaging of the knee. Postprocessing is performed using customized routines written in MATLAB. MR data were fused to improve contrast of the cartilage region that is further used for automatic segmentation. Marching cubes algorithm is applied on the segmented AC slices for 3D volume rendering and volume is then calculated using the divergence theorem.

Results

Fusion of multinuclear MR images results in an improved contrast (factor >3) in the cartilage region. Sensitivity (80.21%) and specificity (99.64%) analysis performed by comparing manually segmented AC shows a good performance of the automated AC segmentation. The average cartilage volume (23.19 ± 1.38 cm 3 ; coefficient of variation [COV] −0.059) measured from 3D AC models of four data sets shows a marked improvement over average cartilage volume (23.24 cm 3 ; COV −0.19) reported earlier.

Conclusions

This study confirms the use of multinuclear MR data for cartilage morphology (volume) assessment that can be used in clinical settings.

Osteoarthritis (OA) is one of the most common joint disorders in the knee that affects a large population around the world . Incidences of OA onset have been found in patients with age as early as 25 years . Research in OA assessment involves detection of prediseased to early diseases conditions followed by its monitoring at severe grades. The onset and progression of OA has been associated with the degradation of knee articular cartilage (AC). Changes in physiology and morphology of AC in early stages of diseases progression can be measured by quantitative measurement of selective features that are associated with OA using magnetic resonance (MR) imaging (MRI) .

Morphologic assessment of AC involves measurement of changes in thickness, volume, and curvature . In particular, a decrease in cartilage volume at the rate of ∼5% per year is observed in a longitudinal study of 123 OA patients . In another study, a decrease in volume at ∼2.8% annually is observed in a healthy cartilage . Quantitative measurement of AC morphology (volume and thickness) using MRI is becoming the standard due to its noninvasive nature, nonionizing, and in vivo imaging capabilities. It has been reported that MRI data can be postprocessed for reliable morphologic measurement of the AC in three dimensions (3D). Most of the studies involving morphologic measurement use pre-installed software tools such as Argus, OCTANE Duo, and similar software that are available in most of the MR scanners . These software tools require AC segmentation from MR image slices before 3D rendering and quantitative morphologic assessment. Although the previously described software tools provide regional (by selecting the region of interest manually) assessment of the cartilage morphology, manual segmentation of AC before reconstruct 3D models and manual selection of different cartilage regions are tedious and can result in inter–intra observer issues in the morphologic assessment.

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Materials and methods

MRI Data Acquistion

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Data Preprocessing

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Fusion of Sodium and Proton MR Image

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C|AC−BG|=1n∣∣∑ni=1IACi−∑nj=1IBGj∣∣ C

−

∑

−

∑

where, I__AC and I__BG represent the intensities in the AC and background regions of fused images, respectively; n is the number of pixels selected in the cartilage and background regions of merged images. Using the same approach, the measured contrast values from fused images are compared to contrast values from original proton slices. In the measurement, five random pixels are selected from the cartilage (yellow dots) and background (red dots) regions of each slice in the data set as shown in Figure 3 , followed by the calculation of mean signal intensities in both regions.

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CIF=CfusedCproton C

where, C fused is the contrast difference between the cartilage and background regions of the fused image extracted from sodium and original proton MR images, and C proton is the contrast difference between the cartilage and background regions of original proton images.

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AC Segmentation

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Sensitivity=TPTP+FN Sensitivity

Specificity=TNTN+FP Specificity

where, true positive (TP) is the number of pixels correctly labeled as the cartilage region, true negative (TN) is the number of pixels correctly labeled as the noncartilage region, false positive (FP) is the number of pixels incorrectly labeled as the cartilage region, and false negative (FN) is the number of pixels incorrectly labeled as noncartilage region.

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3D Reconstruction of AC

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Volume Computation of AC

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V=16∑fi∈F∣∣∣∣∣xi1yi1zi1xi2yi2zi2xi3yi3zi3∣∣∣∣∣where⎧⎩⎨⎪⎪⎪⎪vi1=(xi1,yi1,zi1)vi2=(xi2,yi2,zi2)vi3=(xi3,yi3,zi3) V

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where

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∫A∇⋅f→dv=∮∂An→⋅f→dS. ∫

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∇⋅f→=a ∇

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where, a a is constant, then the equation can be expressed as

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Volume(A)=∫Adv=∮∂An→⋅f→dsa V

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∇⋅f→=∂fx∂x+∂fy∂y+∂fz∂z ∇

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where, f→=(fx,fy,fz)T f

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∫A∂x∂x+∂y∂y+∂z∂zdv=∮∂An→⋅f→dS ∫

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Volume(A)=∫Adv=∮∂An→⋅f→dS3 V

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Results

Data Acquisition and Preprocessing

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Fusion of Proton and Sodium Extracted Slices

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Table 1

Mean Signal Intensity Values Obtained From Background and the Cartilage Region of Original Proton and Fused Slices

Data Set Proton Data Set Fused Data Set Average MSI BG Average MSI AC C Proton Average MSI BG Average MSI AC C Fused Data set 1 117.74 148.05 30.32 66.62 166.19 99.56 Data set 2 146.84 182.78 35.94 61.29 174.44 113.15 Data set 3 130.14 161.07 30.93 67.65 161.24 93.58 Data set 4 145.79 178.76 32.97 65.30 169.18 103.88

AC, articular cartilage; C Fused , contrast difference between articular cartilage and background of fused images; C Proton , contrast difference between articular cartilage and background of proton images; MSI AC , mean signal intensities in articular cartilage region; MSI BG , mean signal intensities in background region.

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Automatic Segmentation of AC

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Table 2

Sensitivity and Specificity Analysis Through a Comparison Between Automatically Segmented Slices and Manually Segmented Slices by Two Observers

Data Sets Observer 1 Observer 2 Sensitivity Specificity Sensitivity Specificity Data set 1 80.27 99.65 79.53 99.68 Data set 2 79.13 99.46 80.77 99.57 Data set 3 89.34 99.72 90.17 99.69 Data set 4 72.08 99.74 74.79 99.78 SD 7.082 0.12 6.44 0.08 Average 80.20 99.64 81.31 99.68 COV 0.088 0.0012 0.079 0.0008

COV, coefficient of variation; SD, standard deviation.

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3D Reconstruction and Volume Computation

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Table 3

Average, Standard Deviation, and Coefficient of Variation Values for Total Cartilage Volume Calculation in Different Data Sets

Data Sets TCV 3Dautomatic (mm 3 ) TCV 3Dmanualfirst (mm 3 ) TCV 3Dmanualsecond (mm 3 ) Error (%) Data set 1 22,430 16,585 18,329 −28.48 Data set 2 22,425 18,756 18,736 −19.62 Data set 3 25,268 22,539 24,000 −8.58 Data set 4 22,667 23,504 23,297 3.13 SD 1384 3238 2972 Average 23,197 20,346 21,091 COV 0.0596 0.1591 0.1409

COV, coefficient of variation; SD, standard deviation; TCV 3Dautomatic , total cartilage volume in 3D model reconstructed from automatically segmented cartilage; TCV 3Dmanualfirst , total cartilage volume in 3D model reconstructed from segmented cartilage by first observer; TCV 3Dmanualsecond , total cartilage volume in 3D model reconstructed from segmented cartilage by second observer.

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Discussion

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Acknowledgment

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References

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Multinuclear MR and Multilevel Data Processing

Rationale and Objectives

Materials and Methods

Results

Conclusions

Materials and methods

MRI Data Acquistion

Data Preprocessing

Fusion of Sodium and Proton MR Image

AC Segmentation

3D Reconstruction of AC

Volume Computation of AC

Results

Data Acquisition and Preprocessing

Fusion of Proton and Sodium Extracted Slices

Automatic Segmentation of AC

3D Reconstruction and Volume Computation

Discussion

Acknowledgment

References

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