Data Acquisition
This study and experimental protocol were approved by the North Denmark Region Committee on Health Research Ethics, Denmark. Our experiment was conducted in accordance with the guidelines of the committee. Also, experimental protocol was explained to all participants and written informed consent was obtained. MRI (Signa HDxt 3.0T, GE Healthcare, USA) scans were performed on 11 healthy participants with no history of knee disease or surgery. Since the damaged structures, such as bone and cartilage by disease, deviate from the unique characteristics of the structures to be analyzed. The participants were, on average, 40.56 ± 16.32 years old, weighed 74.84 ± 11.81 kg, and were 178.00 ± 7.31 cm tall. Three MRI sequences were scanned at the same location on the knee, including the femur and tibia (Fig. 1). In order to obtain the same anatomical structure image in the three sequence images, preliminary practice was conducted to prevent positional changes due to the participants' movement, and then the scan was performed. The three sequences used in this study are T1-weighted (T1), proton density-weighted (PD), and fat-suppressed 3D spoiled gradient-echo (SPGR), which are known to have high signal strength in the bone and cartilage structures (Table 1). T1 sequence is mainly used to evaluate bone marrow and bone tumors because they have excellent contrast for cortical, marrow, and surrounding tissues [19]. The PD sequence has good contrast for the cartilage surface, so it is useful for measuring cartilage thickness or examining cartilage abnormalities [20]. Finally, the SPGR is known to have good contrast between cartilage and surrounding bone marrow through fat suppression and has a high contrast-to-noise ratio [21]. Generally, since the segmentation task usually uses already acquired images for clinical purposes, we did not separately set MRI scan parameters for this study. We used MRI scan parameters set for clinical purposes in the hospital without any changes. For quantitative analysis, images with the same anatomical location were manually selected from three sequences, and 12 images per participant (4 images from each sequence) were extracted. The four selected images consisted of two that showed bone structures well and two that showed cartilage structures.
Table 1
Scan protocol and image description
Sequence | TR (msec) | TE (msec) | ETL | FA (°) | Image |
Matrix (pixel) | Slice thickness (mm) | Slice spacing (mm) | Pixel size (mm) |
T1 | 818 | 12.5 | 4 | 90 | 512 × 512 | 3 | 3.5 | 0.3125 × 0.3125 |
PD* | 3928 | 21.16 | 8 | 110 | 512 × 512 | 3 | 3.5 | 0.3125 × 0.3125 |
SPGR† | 9.884 | 4.16 | 1 | 25 | 512 × 512 | 1 | 0.5 | 0.3125 × 0.3125 |
Note.-The images used for analysis were reconstructed in the sagittal plane. TR = repetition time, TE = echo time, ETL = echo train length, FA = flip angle, T1 = T1-weighted, PD = proton density-weighted, SPGR = spoiled gradient-echo. |
*Fat-suppressed 2D proton density |
†Fat-suppressed 3D SPGR |
Manual drawing of edge
The first step of the quantitative edge analysis was extracting the edges of the bone and cartilage. In the three sequence images, the edges of cortical bone, cancellous bone, and cartilage were manually drawn, respectively (Fig. 2). In order to classify the edges according to material, manually drawn edges were defined according to the materials on both sides of the edge (EBB: the edge between the cancellous bone and cortical bone, EBC: the edge between cortical bone and cartilage, ECF: the edge between cartilage and fat, ECM: the edge between cartilage and meniscus, EBT: the edge between cortical bone and tissue, Fig. 3). In EBT, the tissue mainly contains fat or muscle. Tibia's ECF was not included because there was no fat material or only a small area in contact with the tibia cartilage. The manually drawn edges become the target edge for evaluating the characteristics of edges according to the sequence. For this purpose, the manual edges were drawn in the three sequence images.
Quantitative analysis of edge using virtual ray
Unit normal vectors (\(\widehat{n}\)) were calculated in the orthogonal direction from all edge points of the cancellous bone obtained from the manual drawings (Eq. 1, Fig. 2(c)).
$$\widehat{n}=\frac{1}{\sqrt{{dx}^{2}+{dy}^{2}}}\left[\begin{array}{c}-dy\\ dx\end{array}\right] \left(1\right)$$
Here, dx and dy mean derivatives in the x and y directions of the image pixels, respectively. At all edge points of the cancellous bone, virtual rays (\(\overrightarrow{l}=\widehat{n}\alpha\)) with a length of 10 mm or more (\(\left|\alpha \right|>10 \text{m}\text{m}\)) were created in the direction of the computed unit normal vector. The points where the virtual ray and the manual edges meet become EBB, EBC, ECF, ECM, and EBT, respectively (Fig. 3). This virtual ray terminates when a depth of 2 mm is reached in the inside bone of cancellous bone fat, meniscus, and tissue regions. Each virtual ray stores the pixel value of the image through which the ray passes, and a one-pixel value is extracted from one image pixel (Fig. 4). This profile curve with pixel information is interpolated by the cubic spline method [22] with a point interval of 1/10 of a pixel. The sharpness and contrast of the edges are computed through analysis of this profile. First, the sharpness value of EXX (i.e., EBB, EBC, ECF, ECM, and EBT) becomes the differential coefficient value at the point of EXX. Then, the contrast value of EXX is computed as the ratio of the average pixel values in both materials (S1 and S2) in EXX (Eq. 2), where \({S}_{j}\) represents the average pixel values of a single material (Eq. 3).
$$\text{C}\text{o}\text{n}\text{t}\text{r}\text{a}\text{s}\text{t}= \left\{\begin{array}{c}\frac{{S}_{1}}{{S}_{2}}, if {(S}_{1}> {S}_{2})\\ \frac{{S}_{2}}{{S}_{1}}, if {(S}_{2}> {S}_{1})\end{array}\right. \left(2\right)$$
$${S}_{j}=\sum _{i=0}^{n}{P}_{i}/ \varDelta l \left(3\right)$$
Here, Pi represents the pixel value of a material, \(\varDelta l\) means the thickness of the material appearing in the image, and n is the number of interpolated pixels in the jth material.
Inter-subject variability
The inter-subject variability (ISV) was calculated to determine the difference in measured values among the participants. The average (ISVAVE) and maximum (ISVMAX) of ISV were calculated as Equations 4 and 5. The average (SAVE or CAVE) and standard deviation (SSD or CSD) of sharpness (or contrast) were obtained from 11 participants. The σMAX is the largest difference from the mean among the 11 measured values.
$${ISV}_{AVE}= \left(\frac{{S}_{SD}}{{S}_{AVE}}\right) \bullet 100 \left(4\right)$$
$${ISV}_{MAX}= \left(\frac{\left|{\sigma }_{MAX}-{S}_{AVE}\right|}{{S}_{AVE}}\right) \bullet 100 \left(5\right)$$
Data Analysis
The quantitative analysis method of edge, including the image processing algorithm proposed in this study, was implemented using a software development tool (MATLAB, 2019a, MathWorks, USA) and an image analysis software (ImageJ, 1.53k, National Institutes of Health, USA) was used for manual drawing. One-way repeated measures ANOVA was used to compare the three MRI sequences at each edge (EBB, EBC, ECF, ECM, and EBT). In addition, post hoc comparisons were performed with Bonferroni correction. All statistical analyzes were performed using statistical software (SPSS, version 28.0.1.1, IBM Corp., USA), and a P-value of less than .05 was considered statistically significant.