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Fourier Analysis Reveals Increased Trabecular Spacing in Sickle Cell Anemia

Section of Oral and Maxillofacial Radiology, UCLA School of Dentistry, 10833 Le Conte Ave., Los Angeles, CA 90095-1668, USA;

*corresponding author, swhite{at}dent.ucla.edu

	ABSTRACT

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Sickle cell anemia may expand marrow spaces in the jaws. Fourier analysis is well-suited to the analysis of trabecular spacing in radiographs. We hypothesize that individuals with sickle cell anemia demonstrate increased intertrabecular spacing. Periapical radiographs of 18 African Americans with sickle cell disease and 18 controls were examined by one-dimensional discrete Fourier analyses in both jaws for measurement of the spatial frequency distribution of repeating trabecular structures. A strut analysis of trabeculae was also performed and the results compared. Trabecular structures in individuals with sickle cell anemia revealed increased intertrabecular distance compared with controls. Strut analysis revealed significant reductions in trabecular complexity. Fourier analysis allows for the classification of subjects with 94% sensitivity and specificity. Fourier analysis of dental radiographs is a more effective method of identifying individuals with sickle cell anemia than strut analysis.

KEY WORDS: Fourier analysis • computer-assisted radiographic image interpretation • dental digital radiography • sickle cell anemia • jaw

	INTRODUCTION

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The recent availability of digital radiography offers means for the quantitative analysis of patterns in trabecular bone structure in dental radiographs for the detection of early or subtle manifestations of systemic disease. A standard means for detecting pattern changes in imagery is Fourier analysis. This technique mathematically decomposes an image into a unique sum of sine waves of different wavelengths (Cooley and Tukey, 1965). In a radiographic image of trabecular bone, intertrabecular spacing will determine the predominant wavelengths. This method has been used to characterize bone patterns in radiographs (Southard and Southard, 1992a, b; Caligiuri et al., 1993; Oxnard, 1993; Wigderowitz et al., 1997; Chinander et al., 1999, 2000; Gregory et al., 1999). Sickle cell anemia is an inherited hemoglobin disorder in which the life span of red blood cells is reduced from the normal 120 days to 10-30 days (Sickle Cell Information Center, 1997; Schlichtmann and Graber, 1999). This premature loss of red cells results in a systemic compensatory hyperplasia of bone marrow which leads to trabecular changes and bony expansion of the jaws (Mourshed and Tuckson, 1974; White et al., 2000). We hypothesize that Fourier analysis of the trabecular bone in dental radiographs can detect significant alterations of the trabecular spacing of individuals with sickle cell anemia. Detecting such changes could lead to the development of automated tools for screening dental radiographs for evidence of sickle cell anemia and potentially other systemic diseases that alter bone.

	MATERIALS & METHODS

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Study Design
We analyzed radiographs of subjects with sickle cell anemia and controls by both Fourier analysis and strut analysis to determine if trabecular structure differed between these groups. Further, we evaluated the comparative efficacy of these two analytic methods for subject classification.

Radiographs
Eighteen sets of periapical radiographs were obtained from ten African American females and eight African American males (mean age, 20.8 yrs) proven by electrophoresis to have sickle cell anemia (SCA). Eighteen additional sets of radiographs were obtained from a comparable control group matched by ethnicity and age. IRB informed consent approval was granted for this study. From these data, we selected 18 radiographs of the anterior maxilla and mandible of controls, 18 of the anterior mandible from SCA subjects, and 16 from the anterior maxilla of SCA subjects. All radiographs were digitized at 600 dpi and 256 levels of grayscale. From each radiograph, we selected for analysis square images of trabecular bone (256 x 256 pixels) in the anterior maxilla and mandible apical to the incisors.

Spatial Analysis
One of us (TDF) wrote a computer program using Matlab (The Mathworks, Natik, MA, USA) software to measure the spatial frequency distribution of the trabecular pattern found in the selected images. The analysis used the one-dimensional fast Fourier transform (Cooley and Tukey, 1965), a numerical implementation of the discrete Fourier transform optimized for computers. Pre-processing of the images consisted of subtracting a blurred version of the image (for each pixel, the mean of surrounding ± 10 pixels square) from the original to remove regional variations in the average image intensity (Russ, 1995). We first performed a linear contrast stretch of the image (removing the upper and lower 5% of pixels) to make full use of the intensity range. We applied the one-dimensional Fourier transform separately to each row and column of the processed image to obtain their respective spatial frequency distributions. Each of the frequencies in a distribution corresponds to the number of trabeculae per mm. For each individual, we averaged the distributions from all rows (or columns) in the image to obtain a composite distribution for the whole image. High- and low-frequency bands (corresponding to short and long intertrabecular spacings, respectively) were selected from the overall frequency distribution. We derived a comparison statistic, here called a ratio metric, by forming the ratio of the average magnitude of low to high frequency contributions. The logarithm base 10 was taken of each ratio for better approximation of a Gaussian distribution for this statistic. An example of the spatial frequency distribution, and the ratio metric calculation for an individual, are shown in Fig. 1. A bandwidth of 5 adjacent frequency bins was chosen for both the low- and high-frequency contributions. The location of the high- and low-frequency bands was systematically varied to optimize the t value between sickle cell anemia and control individuals. We examined all combinations of locations where the low-frequency band was to the left of the crossover frequency and the high-frequency band to the right (Fig. 2). By using ratios of low- to high-frequency components, we could perform a test of the study hypothesis by analyzing this single parameter. These ratios were determined for each location (maxilla and mandible), each direction (apico-coronal and mesio-distal), and for each subject group (sickle cell anemia and control).

View larger version (59K): [in this window] [in a new window]   Figure 1. Intertrabecular spacing. (A) Fourier frequency distribution for an individual with sickle cell anemia. The peak frequency (large arrow) is 1.28 trabeculae per mm, corresponding to an intertrabecular spacing of 0.78 mm. The widths (stippled) and means (horizontal bar) of the low- and high-frequency bands used to compute the ratio metric. (B) Processed image where trabeculae are white, showing a 0.78-mm line in white in comparison with intertrabecular spaces.

View larger version (27K): [in this window] [in a new window]   Figure 2. Distribution of trabeculae per mm, comparing sickle cell anemia (SCA) individuals (dashed line) and controls (solid line) for the mesio-distal analysis direction in the mandible. Individuals with sickle cell anemia have more low-frequency components (large intertrabecular spacing) and fewer high-frequency components (small intertrabecular spacing) than control individuals. Note crossover in frequency distributions at 2 trabeculae per mm.

Statistical Analysis
The differences between the ratio metrics and strut variables for sickle cell anemia and control subjects were tested by a two-sample unpaired t test. We also tested the predictive power of the ratio metric and strut analysis to classify individuals as being in the sickle cell anemia or control group by using a classification and regression tree method (CART). This multivariate approach, an alternative to linear regression techniques, can be used to predict categorical (classification) or continuous (regression) outcomes (Breiman et al., 1984; Clark and Pregibon, 1992).

	RESULTS

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Individuals with sickle cell anemia have a significantly higher ratio metric than control individuals (p < 0.001), in both the maxilla and the mandible, and for both directions of analysis (apico-coronal and mesio-distal; Table 1). To determine the source of the change in the ratio metric, we plotted the average spatial frequency distributions (Fig. 2). In both jaws and in both directions of analysis, individuals with sickle cell anemia have both an increase in low-frequency features and a decrease of high-frequency features. Using the strut analysis, we found significant differences between the trabecular structure of subjects with sickle cell anemia and that of controls. Subjects with sickle cell anemia have decreased numbers of branch and terminal points per unit area in both the maxilla and mandible (Table 2).

	DISCUSSION

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The anticipated increased use of digital imaging in dentistry provides the opportunity for innovative uses of such images. It may become possible to improve diagnosis by improving the display of images for professional assessment and by quantitative analysis of features in an image. Expected benefits include more precise estimates of extent of disease and rates of disease progression, as well as the earlier detection of disease (White et al., 1999). This study addresses the possibility of the detection of systemic disease, sickle cell anemia in this instance, through analysis of the trabecular pattern shown on dental radiographs.

Fourier analysis revealed a significant shift from higher- to lower-frequency features in patients with sickle cell anemia. This implies a shift from shorter to longer intertrabecular spacing of the trabecular pattern. This finding is consistent with the erythroblastic marrow hyperplasia associated with sickle cell anemia. It is also consistent with the strut analysis that found reduced numbers of branch and terminal points per unit area (White et al., 2000). This work extends the strut analysis findings by demonstrating a significant increase in the intertrabecular spacing of individuals with sickle cell anemia. Both methods had high sensitivity and specificity for identifying affected individuals. Because the Fourier analysis is independent of the strut methods used here and in previous work, we evaluated whether combining both approaches would achieve a more accurate means for identifying individuals with sickle cell anemia. We found that the optimum CART classification of subjects required only consideration of the apico-coronal intertrabecular spacing in the maxilla. This finding shows that, for evaluation of the trabecular structure of individuals with sickle cell anemia, the use of intertrabecular spacing as measured with Fourier analysis offers more discriminating capability than strut analysis.

Various Fourier analyses have been used previously to analyze trabecular bone structure. Caligiuri et al. (1993), Gregory et al. (1999), and Wigderowitz et al. (1997) used two-dimensional Fast Fourier Transforms (FFTs), whereas Southard and Southard (1992b) and this study used one-dimensional FFTs. The one-dimensional approach offers the advantage of better detection of non-coherent or randomly placed local patterns, typical of trabecular bone structure. A two-dimensional analysis responds strongest to patterns that are coherent, that is, that repeat in location throughout the image, and responds less strongly to non-coherent patterns. In addition, we recognized that there might be a directional bias in trabecular bone structure. Thus, analyses in two perpendicular directions were performed independently. Accordingly, we chose to examine the bone structure parallel and perpendicular to the forces of mastication, where any differences due to occlusal forces would be most evident. Wigderowitz et al. also examined bone in two directions and looked for changes in spatial directional content over time (age). They created a ratio of longitudinal vs. transverse indices and found a rise in the ratio over time that also correlated with the risk of osteoporotic fracture. Thus, we believe that where the structure of bone varies by direction, it may be advantageous to make two 1-D FFTs perpendicular to each other.

Various Fourier metrics have been used, including summed component magnitudes (Wigderowitz et al., 1997), root mean square (Caligiuri et al., 1993), and first moment values (Southard and Southard, 1992b; Caligiuri et al., 1993). We decided to use a simple summed frequency component ratio metric as a means of categorizing individuals by the shift in trabecular spatial frequency presumably due to the pathophysiology of the disease. This metric provides an efficient means of measuring an overall frequency shift and avoids the problem of over-determination associated with excessive numbers of parameters and the need to normalize the amplitude data. We selected to use a bandwidth incorporating 5 frequencies to provide a balance between robustness by average multiple values yet allow latitude in location selection.

It has been known for many years that bones with thick trabecular bone and thin cortices provide for the earliest radiographic evidence of demineralization (Lachmann and Whelan, 1936). Fourier analysis has been previously used to study osseous changes associated with osteoporosis in the distal radius (Wigderowitz et al., 1997), lumbar spine (Caligiuri et al., 1993), bone biopsies (Gregory et al., 1999), and dental radiographs (Southard and Southard, 1992b). Wigderowitz et al. and the Southards used their methods to measure differences between groups of patients with osteoporosis and controls rather than attempting to classify individuals. Caligiuri et al. found that their Fourier-based texture analysis of the spine was more effective than bone mineral density in differentiating individuals with fracture elsewhere in the spine from those who did not fracture. This is particularly pertinent to the evaluation of periapical radiographs of the maxilla for indications of systemic diseases that alter bone morphology. It is also noteworthy that periapical radiographs are non-invasive, inexpensive, in widespread use, and provide high-detail images of bone. We plan further studies combining Fourier and morphometric techniques to analyze patient radiographs to find early signs of osteoporosis.

There are several limitations of this study. Since we used a fairly small sample of images from one clinic, it is not known how robust our methods would be in more general practice. This study also considered only radiographic features. Before attempts are made to deploy a screening system for general use, it would be important for clinical features to be integrated into the algorithm. In the case of sickle cell anemia, it would be important to consider the race of the individual, since this condition is far more prevalent among African Americans than among whites, as well as familial history of sickle cell disease. It should also be clear that, in the particular case of sickle cell anemia, it is unlikely that such a radiographic and clinical screening system would identify new cases. Most affected individuals are already aware of their condition when they visit their dentist, since the diagnosis of sickle cell anemia is usually made in early childhood. However, we anticipate that Fourier and strut analytic methods may also be useful for screening for other systemic diseases, such as osteoporosis, where early detection of bone change would be of potentially great benefit. Since dental radiographs are in such widespread use, these analytic tools offer dentists the prospect of screening large numbers of individuals for early signs of systemic disease.

In conclusion, individuals with sickle cell anemia demonstrate increased intertrabecular spacing in both the maxilla and mandible, consistent with the pathophysiology of this condition. Based on these findings, subjects can be classified with 94% sensitivity and specificity. We anticipate that our Fourier method may also be extended to other systemic diseases, such as osteoporosis, where early detection of bone loss would be of potentially great benefit.

	ACKNOWLEDGMENTS

 
We thank Dr. Farouk Mourshed, Professor, Department of Oral Diagnosis and Radiology, Howard University School of Dentistry, for the use of the radiographs of subjects with sickle cell anemia. We thank Dr. Jeff Gornbein and Ms. Susan Service for their statistical support. This investigation was supported in part by UCLA intramural funds and by USPHS Research Grant R01 AR 47529 from the National Institute of Arthritis and Musculoskeletal and Skin Diseases, National Institutes of Health, Bethesda, MD 20892. A preliminary report was presented at the 30th Annual Meeting & Exhibition of the American Association for Dental Research, Chicago, IL, in 2001.

Received July 16, 2001; Last revision December 27, 2001; Accepted January 15, 2002

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