Bone trabecular pattern analysis in Down’s syndrome with the use of computed panoramic tomography with a laser scan system Quantitative analysis with the power spectrum method

Isamu Kashima, D.D.S., Ph.D., Masanori Kanno, MS., Toshiki Oguro, D.D.S., Tomomitu Higashi, M.D., Ph.D., Nobuaki Sakai, D.D.S., Ph.D.,* Kiyoshi Hideshima. D.D.S., * Mario Higaki, D.D.S., Ph.D.,* Kumeo Miyake, D.D.S., Ph.D.,** Masato Mnabe, D.D.S.,*** and Masao Takano, M.S.,**** Kanagawa. Japan

KANAGAWA DENTAL COLLEGE

A quantitative analysis of the mandibular bone trabeculae of 44 patients with Down’s syndrome and 68

normal persons by means of panoramic tomography was performed with a laser scan system. The results

showed that the normal persons exhibited a correlation between the trabecular pattern and aging, whereas

the patients with Down’s syndrome showed no such correlation. These findings were consistent with

geromorphism. which is one of the systemic features of Down’s syndrome.

(ORAL SURG ORAL MED ORAL PATHOL 1988;65:366-70)

T here have recently been many reports on peri- odontal diseases, which are frequently observed in Down’s syndrome.‘-5 Local causes, such as insuffi- cient oral cleanliness, have been suggested to be the reason that patients with Down’s syndrome are likely to suffer from periodontal diseases. There have also been reports indicating systemic causes (e.g., gingi- val abnormalities, abnormalities of salivary compo- nents, immunologic abnormalities). These etiologic factors are derived from the chromosome trisomy 21.6-‘o It is interesting to consider whether such systemic disorders resulting from trisomy 21 occur in bones. However, there is only one report, by Johnson and Young,’ on the mandibular trabecular bone in Down’s syndrome. Thus, the mandibular trabecular bone has never been studied sufficiently. Kashima and coworkers” performed a visual pattern compari- son of patients with Down’s syndrome and normal persons by means of panoramic tomography with the use of a laser scan system. Despite this study, there

*Department of Pedodontics, Kanagawa Dental College. **Department of Anesthesiology, Kanagawa Dental College. ***Department of Periodontology, Kanagawa Dental College. ****Technology Development Center, Fuji Photo Film Company, Miyanodai, Japan.

366

have been no reports on this physical quantitative analysis of the bone trabecular pattern in Down’s syndrome.

Therefore, a quantitative analysis of the bone trabecular pattern in Down’s syndrome was per- formed with high accuracy with the use of a model expression; this model employed a numerical formu- la of this power spectrum by panoramic tomography with the use of a laser scan system that has already been reported by Kashima and coworkers.12 Analysis of the bone trabecular pattern with the use of power spectra has also been reported by Kashima and coworkers.‘3

METHODS

Regions of interest (ROI) for the analysis of bone trabecular pattern were decided on the basis of computed panoramic radiographs. Each ROI involved the body of the mandible of a premolar tooth or a molar tooth on either the right or the left side of the mandible. Sites that appeared to represent modified bone trabecular patterns (e.g., apical lesions, osteosclerotic sites, sites of sclerosing osteitis, edentulous sites) were excluded from the ROI. The subjects were five normal persons and five patients

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Bone trabecular pattern analysis in Down’s syndrome 367

Fig. 1. Block diagram illustrating analysis of bone tra- becular patterns. The digitalized imaging data of the ROI that were read from a memory tape (the distribution of x-ray energy obtained from the imaging plate) were quantified as a power spectrum by means of a general- purpose computer.

with Down’s syndrome with ages ranging from 20 to 40 years of age. There were only two patients in their 40s with Down’s syndrome.

The ROI was a square measuring 1.5 X 1.5 cm. Digital information corresponding to the ROI (150 X 150 picture elements; 100~ X lOOk/picture element) was read from memory tape. The image data from the ROI that were read and digitalized (distribution of x-ray energy from an imaging plate) were subjected to Fourier analysis, and the distribu- tion of the bone trabecular pattern was determined as a power spectrum. A block diagram summarizing the analysis is shown in Fig. 1.

In the present study, the power spectrum was enciphered in order to further quantify its features with high precision.

As shown in Fig. 2, it was assumed that the power spectrum is a composite function of two Gaussian functions, that is, low-frequency components and high-frequency components. In other words, the power spectrum (PS) was considered to be a compos- ite of the normal distribution functions, written as follows:

PS(f) = h, exp(- &)+h,expC-$ *I 1=

1 + b,

where h, = peak height of high-frequency components, hz = peak height of low-frequency components, W, = full width at half maximum (FWHM) for

high-frequency components (it denotes the

point at -!- of the peak), fi

(cycle/mm)

Fig. 2. Power spectrum was assumed to be composite function of low-frequency components and high-frequency components. h,, h,, W,, W2, and b are feature parameters of the power spectrum.

W2 = FWHM for low-frequency components, and

b = background. The measured waveform shown in Fig. 1 was

separated into low-frequency components and high- frequency components, according to the model for- mula. Estimates of the feature parameters (h,, hZ, W,, Wz, b) were obtained by means of the nonlinear least squares method with a general-purpose comput- er. The algorithm for the multilines fittings used the Marquardt’s method.14

The measured waveform of the power spectrum (PS), the estimated power spectrum obtained from the model formula (PS’), and feature parameters are shown in Fig. 3. All of the measured waveforms approximated the estimated waveforms. This sug- gests that a quantitative assessment of the bone trabeculae is possible with high precision by means of feature parameters of the power spectrum.

RESULTS

The parameters estimated from the power spectra in normal persons and in patients with Down’s syndrome by the method of least squares are shown in Tables I and II. The values adjusted for back- ground (b) are hi, h2, and b. W, and WZ are the points on the abscissa of the estimated power spectra, indicating a spatial frequency area representing the bone trabecular component. The values h, and hz indicate the extent of the power spectrum at points W, and WZ, which represent the amount of informa- tion on the bone trabeculae; the higher the values of h, and hz, the greater the amount of information on bone trabeculae corresponding to points W, and Wl.

Within the range of spatial frequency from 0.3 1 to 0.5 cycle/mm in normal persons, there was a corre-

366 Kashima et al. Oral Surg March 1988

Fig. 3. Measured waveform of power spectrum, esti- mated power spectrum obtained by model formula, and feature parameters. The measured and estimated spectra are approximately the same.

lation between age and the mean relative amount of information on the bone trabeculae. The values of h, were 324.2 f 5.0, 258.6 -+ 14.0, and 139.2 it- 26.4 for normal subjects in their 2Os, 3Os, and 4Os, respectively. Within the range from 1.0 to 1.4 cycle/mm, however, there was no age-related corre- lation. The values 5.2 + 0.4, 6.1 f 0.6, and 5.5 + 0.3 were recorded for normal subjects in their 2Os, 3Os, and 4Os, respectively. Within the range of spatial frequency from 0.32 to 0.46 cycle/mm in patients with Down’s syndrome, there was no corre- lation between age and the amount of information on bone trabeculae. The values of h, were 115.4 f 8.3, 70.2 f 8.5, and 140.5 + 11.5 for patients in their

Table I. Parameters of h,, W,, h?, W,, and b 111 normal persons

6.0 1.3 330 0.3 !

h t S.D. 5.2 + 0.4 ( I.1 - 1.4 ) 324.2 f 5.0 co.35 n.401

6.5 1.0 26R 0.x-3 I 1 , / 5.5 1.0 23l 0.31

30 5.4 II 1 Es 1 0.34 1

6.7 I 1.2 I ZQ I 0.31 !

6.0 1.4 1% 0.50

ku + S.D. I 5.5 t 0.3 I (1.0 - 1.4 1 i13.2 i 26.4 I al.35 0.50) I

2Os, 3Os, and 4Os, respectively. Also within the range from 1 .O to 1.5 cycle/mm, there was no correlation between age and the amount of information. Figs. 4 and 5 represent graphically the correlation between h, and W, and between hz and W, in each age group of normal persons and patients with Down’s syn- drome with spatial frequency plotted on the abscissa and the amount of information on bone trabeculae plotted on the ordinate. As shown in Fig. 4, the normal persons showed a tendency to have a decreased amount of information on bone trabeculae with aging within the range of spatial frequency from 0.32 to 0.5 cycle/mm. There was no correlation between age and the amount of information on bone trabeculae in patients with Down’s syndrome, and the patients in each age group showed a tendency approximately similar to that of the normal persons in their 40s. As shown in Fig. 5, there was no correlation between age and the amount of informa- tion on bone trabeculae in normal persons or patients with Down’s syndrome within the range from 1.0 to 1.5 cycle/mm. Thus, the normal group and the patient group showed a similar tendency.

DISCUSSION

Abnormalities in the structure of the mandible- the supporting medium of periodontal tissues-were considered to be a possible cause of the tendency toward periodontal disease in patients with Down’s syndrome. There have been many reports on the quantitative evaluation of bone mineral, which is representative of the total amount of bone, the

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Bone trabecular pattern analysis in Down’s syndrome 369

Table Il. Parameters of h,, W1, h2, Wz, and b in patients with Down’s syndrome

( ) : mar. -min.

amount of bone produced, the amount of bone absorbed, and the absorption rate in attempts to evaluate the morbid condition of periodontal disease objectively.

The patterns of mandibular bone trabeculae were distributed into components of frequency, and the correlation between aging and the patterns of bone trabeculae was studied in each frequency. The distri- bution of x-ray energy was evaluated quantitatively in relation to information on the bone trabeculae on the digitalized imaging plate with the use of a physical procedure. This procedure induces fewer errors and shows higher accuracy than the conven- tional one in which information on bone trabeculae on a roentgenograph is read by a microdensitometer and analyzed. This facilitates treatment of a greater amount of information on bone trabeculae. The power spectrum method has already been reported by Kashima and White. l3 This method, in accor- dance with the concept that the bone trabeculae in a fixed ROI are recognized as randomly varying curves, reveals the type of frequency component and the intensity of each component involved in the variation. In addition, the power spectrum represents the relationship between frequency and the intensity of the variation corresponding to the frequency.

In the present study, the bone trabeculae were also quantitatively evaluated at a high accuracy with the use of an expression employing a numerical formula of the power spectra. As shown in Fig. 4, there was a correlation between aging and the amount of infor- mation on bone trabeculae within the range of spatial frequency from 0.31 to 0.50 cycle/mm in normal persons, while there was no marked correlation in

350

300

150

200

150

100

50

h2

00

00 0

Normal 0 20

0 30

d 40

DOWn . 20

. 50

. 40

e w2 0 0.1 0.4 0.6 0.6 1.0

cytb/m m

Fig. 4. Correlations between W, and h, in normal per- sons and in patients with Down’s syndrome in various age groups.

patients with Down’s syndrome. There was no differ- ence in the amount of information on the bone trabeculae between normal persons and patients with Down’s syndrome within the range from 1 .l to 1.5 cycle/mm, as shown in Fig. 5. Generally, the fre- quency area for bone trabeculae likely to be visual- ized on an image is believed to be 0.5 to 2.0 cycle/mm. The fact that age-related changes were observed within the range from 0.31 to 0.50 cycle/ mm in normal persons suggests variation in the trabeculae of relatively large bone. The patients with Down’s syndrome, however, showed a similar amount of information on bone trabeculae, regard- less of age, resembling the pattern observed in normal persons in their 40s. It was quantitatively demonstrated that the morphology of the bone tra- beculae in patients with Down’s syndrome is similar to that of normal persons in their 40s or older. This result was in accordance with the data for visual evaluation of bone trabecular patterns with the use of computed panoramic tomographs by Kashima and coworkers.‘*

Thus, the mandibular bone trabecular pattern

370 Kashima et al.

hl

Normal 0 20

0 50

A 40

Down l 20

. 30

. 40

LLwl 0 0.1 0.4 0.6 0.6 1.0 1.2 L4 1.6 1.8 2.0

r*tl./mm

Fig. 5. Correlations between W, and h, in normal per- sons and in patients with Down’s syndrome in various age groups.

observed in patients with Down’s syndrome was in agreement with the tendency toward presenility, which is one of the somatic features of this condi- tion.

CONCLUSIONS

The mandibular bone trabecular patterns in patients with Down’s syndrome were quantitatively analyzed by expression of the power spectrum in the form of a numerical formula by computed panoramic tomography. The patterns were compared with those of normal persons, and the following results were obtained:

1. There were no differences in changes of the bone trabeculae among patients with Down’s syn- drome at various ages (18 to 40 years) in the low-frequency (0.32 to 0.46 cycle/mm) or high- frequency (1 .O to 1.6 cycle/mm) area.

2. The normal persons showed differences In the bone trabeculae among various age groups ( 2 X to 4~ years) in the low-frequency area (0.31 to 0.50 cycle/mm), but showed no such age-related changes in the high-frequency area (1 .O to ‘I .4 cycle; mmi.

3. The mandibular bone trabecular patterns and the amount of information on bone trabeculae in Down’s syndrome were similar to those in normal persons between the ages of 40 and 49 years.

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Reprint requests to: Dr. Isamu Kashima Department of Oral Radiology Kanagawa Dental College 82, Inaoka-cho Yokosuka, Kanagawa Japan