The study protocol was approved by the Hiroshima University Human Subject Committee, and DPRs were obtained for all the subjects after informed consent was obtained. The study subjects were 100 postmenopausal women recruited at Hiroshima University Hospital; 60 were allocated for system training and 40 for testing. All 100 women underwent dual energy X-ray absorptiometry (DXA) for the measurement of the BMD of the lumbar spine (L2-L4) and femoral neck (DPX-alpha; Lunar Co., Madison, WI). The inclusion criteria were 1) postmenopausal women, 2) aged ≥50 years, and 3) with no previous diagnosis of osteoporosis. The exclusion criteria were the same as per our previous study protocol.9,14-16 The subjects were classified as normal (T-score greater than -1.0), osteopenia (T-score between -1 and -2.5), or osteoporosis (T-score less than -2.5) at each skeletal site according to the World Health Organization (WHO) criteria.17 The Adult Health Study cohort in Japan18 reported that the cutoff BMD value defining osteoporosis in the lumbar spine that was based on the Japanese definition19 (<70%) was similar to that based on the WHO definition (T-score less than -2.5 SD); therefore, we used the WHO definition in this study.

All radiographs were obtained using an AZ-3000 Panoramic Dental X-ray equipment (Asahi Roentgen Co. Ltd., Kyoto, Japan) at 70-80 kVp, 12 mA, and 15 seconds, and a flat-bed scanner (ES-8000; Epson, Tokyo, Japan) was used to digitize the images at a resolution of 300 dpi. Screens of speed group 200 (HG-M; Fuji Photo Film Co., Tokyo, Japan) and film (UR-2; Fuji Photo Film Co., Tokyo, Japan) were used. The 100 original panoramic radiographs for the assessment consisted of one set of duplicate films (MI-Dup; Fuji Photo Film Co., Tokyo, Japan) processed with an automatic film processor (Cepros M; Fuji Photo Film Co., Tokyo, Japan). The appearance of the inferior cortex of the mandible was clear in the radiographs bilaterally.

The measurement system of Kavitha et al13 for MCW measurement between the upper and lower boundaries of the cortical bone in the region of interest involves various image processing algorithms. Briefly, in this approach, the area (300×300 pixels) forming the lower border of the inferior cortex below the mental foramen, cropped manually on the right and left sides was selected as the region of interest (ROI) (Fig. 1). In order to distinguish cortical bone from trabecular tissue and the background, pre-processing of the images is conducted. This included the typical histogram equalization method for a new enhanced image, a thresholding algorithm for classifying image pixels into objects and background,9 and high-pass filtering20 for sharpening the boundary along the cortical bone. In this approach, the cortical margin segmentation is considered a challenging task because x-ray images of the skeleton are complex in nature. We attempted to overcome this problem using the eight neighbourhood distance function (ENDF) and dynamic programming. The former technique estimates the diameter of the cortical bone and the latter produces the optimal path, thereby estimating the pixel locations of the central axis.13 The cortical margins were finally obtained as the envelope of the disc, which was outlined by each pixel on the trace whose radius equalled the pixel value. Finally, we measured the distance between the boundaries of the cortex using a second-order polynomial function (Fig. 2).

The cortical bone image is sometimes affected by irremovable noises or objects that can arise inside the cortical bone between the upper and lower boundaries, as shown in Figure 3. It is difficult to predict the location of noise. Places in which noise occurs make the cortical bone region appear thinner than its normal or original structure. This kind of variation in thickness of the cortical bone could decrease or affect the continuous measurement results and accuracy of the diagnostic system. In order to improve the precision of MCW measurement in the presence of noise, we developed a cluster number optimization method in which the ratio of element numbers between the largest and the second-largest cluster is adopted as the criterion. Despite the fact that conventional cluster number optimization methods that consider variance or the Akaike Information Criterion (AIC) value between clusters21,22 work well on the majority of noise-free images, they did not work well in this application. With regard to this problem, a method based on the k-means clustering algorithm23 was adopted. We assumed that the cluster with the most elements in the histogram would be regarded as the most desirable cluster for accurate MCW measurement. In this algorithm, the optimum number of clusters k is required to be decided automatically. The aim of this application was to preserve the cluster with the most elements and remove the cluster with fewer elements instead of making clusters with less variance, as shown in Figure 4C (right side) and in Figure 5C (left side). To avoid the border effect, eight measures were removed from both the left and right sides before the clustering procedure, as shown in Figure 4B (right side) and in Figure 5B (left side).

The proposed algorithm for MCW measurement was described by the following procedure:

The average value estimated from the optimum number of clusters is considered to be an estimate of the cortical width.

In this study, we treated osteoporosis detection as a two-class pattern classification problem. We applied a SVM classifier to refer to women with low BMD or osteoporosis and normal BMD as the two classes. SVM is based on the idea of minimizing the generalization error when the classifier is applied to test samples that do not exactly match any training sample used to train the classifier (cf., details on the algorithm24 and details on its implementation, optimization, training and testing25). A typical two class problem as the one illustrated in Figure 6 shows the simplest case in which the data vectors (marked by 'X's and 'O's) can be separated by a hyperplane. In such a case, there may exist many separating hyperplanes. Among them, the SVM classifier seeks the separating hyperplane that produces the largest separation margin.

In the more general case in which the sets are linearly non-separable in the input space, a nonlinear transformation is used to map the original space into a high-dimensional space (called feature space), presumably making the separation easier in that space. In brief, both positive and negative examples in a dataset were represented by feature vectors X_i (i=1, 2, ..., N) with corresponding binary labels y_iε{+1, -1}. The SVM algorithm classifies the positive and negative examples by training a classifier that uses a kernel function to map the input samples onto a high-dimensional space that best differentiates the two classes with a maximal margin and a minimal error.26,27 The data that lie on the hyperplane margins are support vectors. The discrimination function for SVM classification of unseen examples is given as:

where 'K(x,x_i)' is the kernel function,'b' is the intercept constant, 'sgn' is the sign indicator (+ or -), 'm' is the number of support vectors and 'α_i' are constants determined by maximization

under the conditions

In this study, we mainly used a non-linear SVM with a radial basis kernel as a classifier.

Two parameters are required to optimize the RBF kernel of the SVM classifier γ that determines the capacity of the RBF kernel and C, the regularization parameter. The moment-based features are used as inputs in the SVM classifier for distinguishing women with low BMD or osteoporosis from those with normal BMD.

Neural networks have been successfully used in many applications.28,29 These highly interconnected structures consist of many simple processing elements or neurons, capable of performing experimental knowledge for data representation.30 In this study we applied the most commonly used feed forward network BP algorithm. It has been widely used in approximating a complicated nonlinear function. The network model in this study is trained with one hidden layer and one output layer by giving four inputs. Figure 7 shows the typical configuration of a BP used in this study for modeling the diagnostic process. The network transfer function log-sigmoid was used. The mathematical equation of each layer can be written as

where Y_O is the output of the neuron o, W_iO indicates the weight increments between i and o, X_i is the input signal, θ_O is the bias term and Φ is the non-linear activation function, which is assumed to be a sigmoid function, specifically,

for the continuous and differential process.

The mean values of the MCW, variance, skewness and kurtosis of both sides of the jaw were used in this study. Receiver operating curve (ROC) analysis was used to measure the diagnostic accuracy of the MCW measurement system in identifying women with low skeletal BMD (R statistical software version 2.15.2, The R Foundation for Statistical Computing). The 100 DPRs (75 healthy and 25 ill, based on lumbar spine BMD, 76 healthy and 24 ill based on femoral neck BMD) were randomly divided into five groups. We set the first group as a testing group and the remaining four groups to train the SVM classifier. Then we set the second group as a testing group and the remaining four groups to train the classifier. This procedure was repeated until each of the five groups had been set as the testing group. The average results of these five classification performances were considered to be the overall performance of the SVM classifier model. Quadratic programming was used to optimize the combination of parameters. The parameters were set to γ=2 and C=1. The RBF parameter and weighting factors were determined by experimentation on the training samples. To compare the performance of our proposed method, we used a BP neural network classifier. The parameters were set to its learning rate η at 0.01, the maximum number of iterations at 1000, and the epochs between showing the process at 50. We employed a data analysis framework written in MATLAB, which incorporates freely available SVM tools and neural network tools for MATLAB that were implemented by31,32 to perform classification. The risk-index range that corresponded to a sensitivity of approximately 90% was chosen to determine the optimal cut-off threshold. The sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), accuracy and likelihood ratio for the positive (LR+) results were calculated.