Determination of early bone metastasis on Bone Scans Using the Gray Levels Histogram

The aim of this paper is to show a technique to speed up the interpretation of bone scans in order to determine the presence of early bone metastasis. This is done using the gray levels histogram of the region of interest. The technique is intended to assist in the bone scans interpretation in order to provide a successful diagnosis. During the analysis, three types of histograms were observed on the regions of interest. If the histogram is narrow and shifted toward the origin, the bone scan is free of metastasis. If it is shifted to the right and slightly broadened, indicates the presence of a bone anomaly different from a metastasis. On the other hand, if the histogram is more broadened and shifted to the right, is suggests the presence of metastasis. This histogram is characterized by displaying small curls on the right side providing information about the metastatic disease stage, which could be low-amplitude peaks and have a short length, if the metastasis is in early stage, or high-amplitude peaks and a long length, if is advanced. Finally, the analyzed region is displayed in false color considering the minimum gray levels observed in the histogram.


INTRODUCTION
Among malignant neoplasms, prostate cancer has a considerably high incidence rate in 65-year-old men and older. For instance, 230000 new cases were diagnosed in the US in 2005 [1] . In 2018, between 21000 and 25000 new cases were diagnosed in Mexico, representing 11.7% of the total cancer-detected cases. From this total approximately 7000 patients died during the course of the year [2] . The main prostate cancer risk factors are age, race, as well as genetics (if a first-grade relative suffers the disease, the probability increases by a factor of 2). Hence, an objective of the health system is the early detection using screening strategies, through the use of specific prostatic antigen, focused in 50-year-old men and above.
The bone is third most common location likely to develop metastatic disease, below the lungs and liver [3] . It is well known that once the patient has been diagnosed with metastatic disease, the prognosis of life expectancy is short, due to the dissemination of the disease to the bones, being unlikely to be cured.
However, in each case, available treatments can be used to retard the disease advance, and increase the life expectancy.
The patients' knowledge of such a treatment is essential for the treatments choice. Thus, the purpose of imaging techniques is to identify the early phases of an ongoing bone disease, in order to determine its extension, and subsequently address the possible complications, such as pain, pathological fractures, hypercalcemia or medullary compression. Also, it is remarkably useful in evaluating the response to a treatment, serving as a guide during a biopsy procedure to obtain a diagnostic confirmation of the disease.
Diagnosis of bone metastases through imaging techniques basically consists of direct visualization of tumor infiltration or detection of bone reaction to the tumor process.
Bone scintigraphy is the most common imaging modality used to evaluate cancer-to-bone dispersion.
In most cancer centers their interpretation is performed visually, however, to give successful diagnoses a vast experience is required due to the difficulties associated with the recognition of hot spots (areas with high marker content). Hence, a quantitative rather than a qualitative interpretation would be more useful in the bone scans interpretation to improve and standardize diagnoses [4] .

Background
Several computer-assisted methods have been developed to find metastasis. Some techniques use the bone scan index [5] , neural networks [6] and false color [7] . All of them require a large number of bone scans datasets to calibrate the system, resulting in time-consuming procedures.
In this work we introduce a method based on the patients' bone scans analysis, intended to determine the presence of metastatic disease. To this aim a segmentation procedure is required, which is the first step.
Subsequently, the gray levels histogram of the region of interest (ROI) is displayed and observed. The image segmentation is required for performing the analysis by region due to the diverse bone densities and their probability to develop a metastatic disease. The diagnosis of bone metastasis using image processing techniques is based on the direct visualization of tumor infiltration or bone reaction to metastatic disease.
Bone scans images are often stored in an archive, where a pixel can contain up to 1024 values (210 umbers, bit depth). In the case of a healthy skull, free of bone diseases, we observed that its gray tones did not reach values above 60. The same behavior holds for healthy bones [8] . There are only two regions where the gray levels could reach the value 1024: the zone where the radiotracer is injected and the bladder, which is where the unsorted marker is stored.
However, these regions do not matter for diagnosis, given their high values, being inconclusive to detect metastasis. Throughout the whole analysis and visualization data is always used in DICOM format ("raw" DICOM images).
In the case of a bone free of metastasis, the image gray levels interval is small, of the order of 60 tones. This interval is larger in the presence of a bone anomaly.

MATERIALS AND METHODS
An observational, retrospective, and analytic study was conducted in the Nuclear Medicine Department of the National Medical Center "La Raza" at IMSS [7] . The The local image segmentation is the main scope of this research. Such procedure is considered as part of the developed software along with the previously mentioned techniques. Image segmentation using the histogram-based thresholding procedure is probably the most common approach, since it is easy to implement and requires less computational resources to be executed. These methods generally employ the maximization or minimization of a criterion function based on the image histogram. The optimal threshold is the gray level intensity at which the criterion function reaches its maximum or minimum values. In our case we use the minimum value.
Several methods for image segmentation are available in the literature. We used the variance between classes method (VBC), in this work, to find the minimum value between two Gaussian distributions. Such a method uses a discriminant function to determine the optimal threshold of an image histogram, in order to perform the image segmentation in near uniform regions [9] .
In some cases, it is required to perform the segmentation procedure in tri-modal histograms, hence two thresholds are required. An iterative algorithm based on the maximization of the VBC was proposed in Reddi, Rudin and Keshavan [10] . We will refer to these images as tri-modal images.
The algorithms used in this work were developed in Matlab. These algorithms determine one or two thresholds, depending on each case, similar to the procedures in the algorithms developed by Demirkaya et al [11] . For the two-thresholds case, an iterative implementation for the VBC method was used.
We display the segmented ROI in color, and we regard the region edges as level contours or curves since pixels with equal gray tones form a contour.

Development
Our proposed software splits the bone scan in six ROIs: skull, shoulders, thorax, vertebral spine, scapula and pelvis. Such a segmentation is performed considering the higher probabilities of the bones in these regions to develop a metastatic disease.
Subsequently, the split image histogram is displayed, showing its bi-modality. The first global histogram minimum indicates the gray tone separating the ROI image background, which will refer to as min. When the ROI is constituted by a metastasis-free bone, the right end of the histogram drops to zero quickly. We will refer to this minimum as "max". However, if the ROI contains a metastasis-free bone, with another pathology or disease, the histogram will broaden in the presence of a degenerative disease, such as osteoporosis, osteopenia, etc.
On the other hand, if the ROI shows signs of metastatic disease, the right end of the histogram will approach zero slowly and monotonically, showing small lobes (local maxima with low amplitude). The lobes extension will depend on the metastatic disease stage. Early metastatic disease is characterized by small-amplitude and short-extension lobes.
In order to illustrate this method, we show the analysis of the skull and pelvis ROIs (the segmentation procedure was performed in the whole-body scan using the previously mentioned techniques). We show only two regions since the rest of the regions show a similar behavior. If the region is embedded in a dark background, as in the skull case, the histogram will be similar to the one shown in Figure 1.a. The minimum gray tone is shown by a red line in the left of the plot, separating the dark background from the ROI. In the case of healthy skull, the maximum gray tone value will be below 50.
Moreover, the histogram will quickly approach to zero.
In the presence of a degenerative disease the max value will be above 50 and the plot width will increase, as in Figure 1d. The histogram end will approach to zero in descending form, shifted to the right regarding the healthy body histogram.  Such a knowledge can be obtained by the specialist from training devoted to study the bone scans histograms. On the other hand, the software includes a visualization tool to display the analyzed ROI's using false color. Such a tool adds color from a list of seven colors assigned to gray levels intervals, setting as a reference the min and max observed values obtained from the histogram analysis. The color assignation scheme is summarized in Table 1.   Table 1 can be arbitrarily chosen based on the specialist requirements. Tones closer to yellow in the resulting image will indicate a more advanced stage of the metastatic disease in the ROI. Regions with metastatic disease as well as those with gray tones above 255, corresponding to the bladder case or to cases where radiotracer was injected, will be displayed in white in the visualization tool.

RESULTS AND DISCUSSION
The previously shown Table 1 was obtained from the histogram analysis, considering its minimun and maximun values.
We apply the scheme in the table to three healthy skulls free of metastasis and we show the results in false color in Figure 3. In this case, the three images colors should be royal blue for the background and blue for the ROI. It should be noticed that as in the case of Figure 2d and 2f, the max values for both ROIs were not suitable since the three ROIs are free of metastasis.
However, in this case, it did not alter the diagnosis.
The tones problem could be corrected using the min and max values for each age, considering that the ranges in the table for each ROI as well as the corresponding analysis are dynamical, leaving room for a manual correction.
In Figure 4 we show the results for three skulls with degenerative diseases. Figure 4e and 4f show and increase in the radiotracer absorption, with the extension and geometry of non-malignant diseases.  In Figure 5 we show the results for the pelvis case. We observe a region with high gray tone values, and two regions in black. The bladder tones were set to zero to ease the visualization of the ROI. In the case of a ROI free of metastasis but with a broadened histogram (Figures 1.c and 1.d), it is proposed to split the interval 2 of Table 1   f(x, y)= cte corresponding to a ROI [12] . This technique is particularly useful in oncology centers with large patients flow, or with limited resource due to its efficiency and execution times, allowing the specialists to diagnose more patients faster.
On the other hand, considering that a LUT the input values are assigned without following any specific criterion, which is not the case of the LUT tables in Nuclear Medicine [13] .

ETHICAL STATEMENT
Ethical Research Committee of IMSS approved and supervised the study complied with all applicable research and ethical standards and laws.