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Year : 2015  |  Volume : 9  |  Issue : 2  |  Page : 80-88

Design and implementation of noninvasive laser imaging system for human teeth carious detection and removal

Department of Biomedical Engineering, Military Technical College, Cairo, Egypt

Date of Web Publication26-Nov-2015

Correspondence Address:
Yasser H El-Sharkawy
Department of Biomedical Engineering, Military Technical College, Cairo
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Source of Support: None, Conflict of Interest: None

DOI: 10.4103/0976-2868.170563

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Background: Knowledge of heat transfer in biological bodies has many diagnostic and therapeutic applications involving either raising or lowering of temperature, and often requires precise monitoring of the spatial distribution of thermal histories that are produced during a treatment protocol. Aim: This paper, therefore, aims to design and implementation a laser therapeutic and imaging system used for carious tracking and drilling by developing a mathematical algorithm using Hilbert transform for edge detection of photothermal imaging. Photothermal imaging has the ability to penetrate and yield information about an opaque medium well beyond the range of conventional optical imaging. Method: Owing to this ability, Q-switching neodymium-doped yttrium aluminium garnet laser at wavelength 1064 nm has been extensively used in human teeth to study the subsurface deposition of laser radiation. Results: The high absorption coefficient of the carious as compared to the normal region contributes to a greater increase in temperature generating infrared thermal radiation captured by the high resolution thermal camera. Changing the pulse repetition frequency of the laser pulses affects the penetration depth of the laser, which can provide three-dimensional images in arbitrary planes and allow imaging deep within a solid tissue. Conclusions: Photothermal imaging with 2-D Hilbert transform algorithm is a powerful tool for human carious detection

Keywords: Human teeth diagnosis, optical and thermal properties of hard tissue, photothermal techniques

How to cite this article:
El-Sharkawy YH. Design and implementation of noninvasive laser imaging system for human teeth carious detection and removal. J Dent Lasers 2015;9:80-8

How to cite this URL:
El-Sharkawy YH. Design and implementation of noninvasive laser imaging system for human teeth carious detection and removal. J Dent Lasers [serial online] 2015 [cited 2023 Jun 10];9:80-8. Available from:

  Introduction Top

It is of interest to characterize hard tissue for two reasons. First, in the treatment of narrowed carious using noninvasive techniques such as laser, which remove or displace abnormal material, and second, it is necessary to acquire information about the composition and thickness of the human teeth.

Optical characteristics of the hard tissues of human teeth are of significant importance in modern dentistry.[1],[2],[3],[4],[5] Optical properties are native properties that characterize biological tissues, which do not depend on the geometry of the structure.

Low-intensity laser light can be used for diagnostic applications. The optical properties of dental tissue components resolve the nature and degree of the tissue reaction through the processes of absorption, transmission, reflection, and scattering of the light. To make progress in employing optical techniques especially laser methods in dentistry, basic knowledge of the optical characteristics of dental hard tissues is necessary.[6]

Enamel is an ordered array of hydroxyapatite crystals surrounded by protein/lipid/water matrix. Comparatively, well-oriented hexagonal hydroxyapatite crystals of ~30–40 nm in diameter and up to 10 μm in length, are packed into an organic matrix to form enamel rods or prisms with an overall cross section of 4–6 μm. [Figure 1] shows the absorption spectra of enamel. The absorption peaks were seen at 200, 600, 700, 1064, 9320, and 9900 nm. The specificity of the dentin is known by the dental tubules that communicate with the enamel, pulpal surface, and cementum.
Figure 1: Absorption spectra of enamel from 150 to 11000 nm (Modified from Arcoria C and Miserendino LJ. in Laser in Dentistry, Eds. L. J. Miserendino and R. M. Pick (Quintessence Publ. Co, Inc., Chicago, et al.), 1995;76

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Enamel and dentin are considered to be optical systems with wave guiding, absorption, and scattering components. The absorption and transmission of light in teeth is generally dependent on the wavelength of the excitation light.

A technique that has the potential to provide both composition and thickness information is that of time resolved photothermal imaging. The principle effect of laser energy is photothermal (i.e., the conversion of light energy into heat). This thermal effect of laser energy on tissue depends on the degree of temperature rise and the corresponding reaction of the normal and carious teeth. The rate of temperature rise plays an important role in this effect. In this technique, sub-ablation threshold nanosecond laser pulses are absorbed in the tissue, producing thermal waves.[7],[8],[9],[10]

The amplitude and temporal characteristics of the thermal waves depend strongly upon the optical properties of the tissue and it has been suggested that, by exploiting the preferential optical attenuation in carious in the wavelength 1064 nm, the photothermal signature could be used to identify carious position.

The aim of the work described in this paper was to design and implement a noninvasive therapeutic and imaging system used for carious tracking at a depth approximately 3 mm with high resolution. The system consists of photothermal imaging system, Hilbert transform algorithm (HLT) for tracking and edge detection, and the use of lasers for cavity preparation, and caries removal is based on the ablation mechanism, in which dental hard tissue can be removed by thermal and/or mechanical effect during laser irradiation.[11],[12],[13]

  Experimental Technique Top

The laser-induced photothermal imaging addressed in this paper is schematically represented in [Figure 2]. The human tooth samples are subjected to laser heating on the top surface. A laser excitation source was used to obtain the photothermal waves: An neodymium-doped yttrium aluminium garnet (Nd: YAG) laser "DECA" (Italy) (short pulse, 1069 nm, 3 J, 5-100 Hz repetition rate). The excitation and transmission signals were delivered via optical fibers. The blackbody radiation from the optically excited sample was focused and detected using infrared (IR) digital camera "fluke IR FlexCam". The camera resolution is approximately 8.5 nm per pixel. A computer was used to store and display data through the USB port. The thermograph was stored using the camera specialized software and was analyzed and graphically represented with our algorithm.
Figure 2: A schematic representation of the problem domain

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Two kinds of experiment were performed. The first group of experiments was conducted to measure pulsed photothermal radiometry (PPTR) images along a spatial coordinate on the tooth surface at a fixed frequency. Because each tooth had an irregular surface, the focal length of the laser beam had to be adjusted accordingly at each measurement position. In this spatial scan, 2–3 min per position was needed to adjust the focal point and do the measurement. As with the frequency scan, a measurement at a new position was performed 15 s after moving the laser beam to that position.

The second group of experiments was conducted to study the effect of the pulse repetition frequency (PRF) on PPTR signals in the range of 1–100 Hz. The PRF range was divided into 5 equal intervals on a logarithmic scale using the computer program. The frequency was automatically increased after each measurement. There was a 15 s delay between the measurements at each frequency, which was necessary for stabilizing the captured thermal images when the frequency was changed. The total measurement time for one frequency scan was about 20 min.

Data analysis

A teeth sample is illuminated by a Q-switched laser with a pulse shape g(t). Deposition of heat in tissue is due only to absorbed light in it. The heat generated is defined as:[14],[15],[16]

Q(r, z, t) = µaI (r, z, t) (1)

Thus, the heat source Q(r, z, t) inside the exposed tissue is a function of the absorption coefficient µa and the local intensity I(r, z, t). If the laser pulse is a Gaussian beam with radius a, then the heating source Q(r, z, t) can be expressed as:

where Q0 is the incident laser energy, a is the laser spot radius, R and μa are the reflective and absorptive coefficients of the sample, respectively. The value r depends on the spatial dimensions x and y of the area facing the laser beam.

The transient temperature distribution satisfies the thermal diffusion Eq.

where ρ, c, and k represent the density, heat capacity, and heat conductivity of the sample, respectively. If the heat conductivity k is neglected and heat density ρc is a constant.

We note that:

  • Heat generation is determined by laser parameters and the optical tissue properties primary irradiance I, exposure time, and the absorption coefficient
  • Heat transport is characterized by thermal tissue properties such as heat conductivity and heat capacity; and
  • Heat effects depend on the type of tissue temperature achieved inside the tissue.

The amplitude and temporal characteristics of the temperature distribution on tissue depend upon the effective attenuation coefficient μeff of the tissue, which in turn is a function of the absorption coefficient μa. Since the ratio of optical absorption in carious to normal tissues at 1064 nm is approximately a factor of 2 as shown in [Figure 3]d, there will be significant differences between the photothermal signatures of the two tissue types, thus providing a means of discriminating between normal and carious teeth. We can localize the carious areas by calculating the photothermal response peaks using edge-detection method using generalized radial Hilbert transform (GRHLT), which is the generalization of the separable two-dimensional (2D) HLT. Then, we illustrate how to use the GRHLT for 2D edge detection and its advantage.
Figure 3: In vitro examination of a sample of human teeth, (a) a photo of 3 human teeth (test sample), (b) photo thermal image of the test sample, (c) three-dimensional plot for the temperature intensity to show the carious position in two-dimensional (x,y), (d) two-dimensional plot of (c) illustration the carious position in X-direction, (e) line contour of the temperature distribution, (f) –ln(Temp) showing the absorption coefficient of normal and abnormal tissues

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Generalized radial Hilbert transforms

We define the GRHLT as follows:

gH (x, y) = IFT2D (H (ω, s) FT2D [g[x, y]) (4)

where the transfer function H (ω, s) is rotational symmetric:

H (ω, s) = ϕ(θ) when (ω, s) #0, H (0,0) =0, (5)

where θ = cos −1 (ω/r) = sin −1(s/r),

r = sqr (ω2+ S 2) ϕ (θ), is any function. (6)

When doing the edge detection, we usually use the discrete counterpart of the GRHLT, that is, the discrete GRHLT:

gH [m, n] = IDFT2D (H [q, p] DFT2D [g[m n]) (7)

where p and q are the discrete independent variables in the frequency domain, and H(p, q) is rotational symmetric. Due to the discrete fourier transform (DFT) and inverse discrete fourier transform (IDFT), the discrete GRHLT has fast algorithm. Its complexity is MN.lag2MN.

Using the generalized radial Hilbert transform for edge detection

The simplest way for 2D edge detection is doing the difference operation. That is,


(Horizontal) | g[mo, no]−g[mo, no+1]| >threshold

(Vertical) |g[mo, no] − g[mo +1, no]|| >threshold.

We can conclude that the pixel (mo, no) is on the edge. Besides, there are also some edge detection methods based on the convolution with 3 × 3 matrix, e.g., the compass gradient mask, Laplacian mask, and statistical mask methods.

  Experimental Results Top

In the following subsections, the photothermal images generated in the normal human teeth and carious are discussed. The z-axis scale of these waveforms represents the temperature at the surface of the target. The salient features of PPTR signals from dental tissues can be summarized as follows. Since enamel (and generally the whole tooth) is a turbid medium, optical penetration is controlled by the effective optical coefficient, µeff (a combination of optical absorption and scattering coefficients) at a given excitation wavelength. For an estimate of the effective coefficient under irradiation at the wavelength used in this study, Fried et al.[17],[18] reported a scattering coefficient, µs, for enamel of between 15 ± 5 cm −1 at 1053 nm, while the absorption coefficient, µa, was less than 1 cm −1. For dentin, the scattering coefficient was between 260 ± 78 cm −1 at 1053 nm, while the absorption coefficient was 3 to 4 cm −1. Therefore, infrared photothermal radiometry (PTR) is capable of "seeing through" the turbid optical field. The laser source can deposit energy as deep as the optical absorption depth.

The sample consists of three teeth, normal, moderately decayed, and severely decayed, the carious absorber at 1064 nm are infected teeth with varying thickness and carious rate and position. The photothermal imaging represented by [Figure 3] shows the temperature relative to depth in teeth. The variation in absorption coefficient, however, is implicit. In media where scattering is negligible, Beer's law can represent the attenuation of light in the teeth optics we calculate the optical absorption function in depth as shown in [Figure 3]f.{Figure 3}

To study the dependency of the level of light absorption on the tissue depth, z, the natural logarithm is taken and plotted as −ln(T) in [Figure 3]f to show the distribution of the absorbed laser energy. Moreover in this plot, the carious parts are clear as more white areas than the normal parts because of the larger amount of light absorbed by infected area.

The behavior of the absorbed laser energy by the carious area, shown in thermal images for the excited teeth samples using laser pulse were depicted from the same position at 2 s intervals. The resulting temperature distribution of the tooth sample images and their natural logarithm in [Figure 4]a and [Figure 4]b, respectively. [Figure 4]a shows the time-dependent thermal relaxation. It is obtained by equating the optical penetration depth L to the thermal penetration depth Ztherm, From [Figure 4]a, the diffusion of the heat energy absorbed by the carious parts to the surrounding region as the time increases is remarkable. This behavior results in a decay of the temperature in the carious regions (as a heat source) with the time. This phenomenon can be used to estimate the penetration depth and consequently the depth of caries.
Figure 4: (a) Time-dependent thermal relaxation of group of thermal images taken at 2 s intervals, and (b) their natural logarithm

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Photothermal imaging system results

In photothermal interactions, photons are absorbed by a chromphore (a light-absorbing molecule) and converted into heat energy, which can cause temperature increasing in the sample. In this experiment, heat energy is deposited in the tissue by the absorption of light and its subsequent conversion to heat via vibrational relaxation. This causes a rise in temperature of the human teeth samples. To evaluate the performance of proposed laser-induced imaging system. [Figure 3]a shows a photo for one of the tested samples that comprises 3 teeth which installed on a jaw-like platform. The three teeth are as follows: Normal, moderately decayed, and severely decayed. [Figure 3]b shows their thermal image depicted by the thermal camera. As shown in these results illustrated in [Figure 5], there is a clear distinguished between the normal (the tooth on the left) and the two infected teeth. It is also clear that the dependence of the image of the tooth on the level of caries (the middle tooth is highly infected while the most right is moderately infected). This image ensures the fact that the amount of the absorbed light by the various parts of the tooth depends on the level of caries. Parts (c) and (d) of the Figure shows the temperature distribution of the depicted image (b).
Figure 5: (a) Calculated absorption coefficient of the three samples from transient temperature distribution. (b) Relative one-dimensional signal of transient temperature distribution. (c) Depth profile of transient temperature distribution and (d) the corresponding absorption coefficients

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Frequency-domain infrared photothermal radiometry imaging of tissue phantoms and ex vivo specimens

Photothermoal depth-selective imaging methodology has emerged and will be illustrated in [Figure 6], featuring linear frequency modulated optical excitation and coherent detection of the PTR response to determine the spatial position and optical parameters of subsurface tissue chromospheres (carious). The main features of the frequency-domain-PTR technique are: (a) The thermal wave is generated by periodic modulation of a Nd: YAG laser; (b) depth information on subsurface tissue structures is derived from temperature distribution of the photothermal images.
Figure 6: Magnitude of the thermal image depicted from (a) front direction of the tooth and (b) rear direction of the tooth

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PTR detection in turbid and other nonopaque media is controlled by a combination of harmonic thermal conduction signals from near subsurface regions and is characterized by a thermal diffusion length associated with the particular modulation frequency and thermal IR (Planck) emissions from deeper regions. In the conductive mode, the depth sensitivity of the PTR signal is theoretically limited up to one or two thermal diffusion lengths, µ(f) = ([α/π] × f) 1/2, where α is the material thermal diffusivity (cm 2/s) and f is the laser modulation frequency (Hz). The thermal diffusivity of enamel is 4.69 × 10−3 cm 2/s.[13]

The measurements were made at variable frequencies and fixed locations. The results of the samples illustrated in [Figure 6] the healthy sample (the first teeth from right to left), moderate decay teeth (second teeth at the center), and severed decay teeth (first teeth from left to right).

[Figure 5]a shows the maximum intensity peak of temperature for teeth affected by different stages of caries the second and third teeth samples of this case. This intensity peak decreased further for all carious areas depending on the stage, with deep cavitations display at low frequency.

The one-dimensional PTR signal amplitude curves from 2D-thermal images [Figure 5]b illustrated that the transient temperature amplitude for severed decay tooth peaks appear to be averaged 205.5 relative units at x-position 1.119 mm and y-position 0.34 mm measured at 30 Hz frequency modulation and 174 relative units at x-position 0.96 mm and y-position 0.411 mm for moderate decay teeth at the same frequency compared with 132 relative unit peaks of the healthy tooth amplitudes, although it should be noted that the precision of determining peak position is very high. The transient temperature amplitude for the three teeth is exponential decayed as optically more penetrated then the three teeth have almost the same transient temperature distribution 136 relative units measured at frequency modulation 5 Hz at depth almost 5 mm as shown in [Figure 5]c. This result illustrated by photothermal images contour plot in [Figure 3]. In this figure, the temperature intensity of caries start at the enamel surface at two positions having almost the same amplitude (tooth 2 and tooth 3 at w9) depends on the carious status levels. Bulk phenomena such as direct optical absorption and thermal wave generation in the carious region and optical interferences and scattered laser light or luminescence confinement in the presence of interfaces with subsurface lesions, render PTR signals sensitive to the lesion under modulated detection, despite the turbidity of dental tissue. Therefore, as a result of interface mediated confinement, which affects optical and thermal fluxes, the PTR signals are maximized at around 1.4 mm thickness in healthy teeth, whereas shifts of the maximum to thicker samples because the highly absorbing lesion strongly confines the extent of optical penetration and enhances thermal conversion. In conclusion, direct infrared radiation thermal wave emission and luminescence interferometry appear to be the major depth profilometric mechanisms of PTR in teeth with subsurface carious lesions.{Figure 5}

As a frequency modulation Scand from 5 to 100 Hz, it creates a series of planar images at different depth of the sample. At each stop, only IR emission moving to the camera face passes through the collimator lens. As many of these photons originate from various depths in the sample, the result is a data of all tracer emitting organs along the specific path, much in the same manner that a multiple-image radiograph is a superposition of all anatomical structures from three-dimensions into two-dimensions. A study consists of many planar images (frames) acquired at various depth are acquired, they are subdivided by taking all the frames for a single, thin slice of the sample at a time.

Edge detection using Hilbert transform

We can localize the carious areas by calculating the photothermal response packs using edge detection methods. Edge detection is a well-developed field on its own within image processing. Region boundaries and edges are closely related, since there is often a sharp adjustment in intensity at the region boundaries. Edge detection techniques are, therefore, used as the base of another segmentation technique. The edge detection algorithms as below.(first-order derivative edge detection, second-order derivative edge detection, HLT for edge detection, short response HLT for edge detection, and improved Harri's algorithm for corner and edge detection). We can found that different detectors have a different effect on the images. Some detectors can detect few zero-crossings while others can detect many zero-crossings. The condition depends on which detector we choose and which threshold values we set. The experiment result is simulated by MatLab as shown in [Figure 7]. The discrete GRHLT:GRHLT can much reduce the effect of noise because it has longer impulse response. Their lengths are 1 × 2 and 2 × 1. The impulse responses of the methods based on 3 × 3 matrix convolution (such as the Laplacian mask method) are 3 × 3. However, the GRHLT has much longer impulse response, so it can reduce the effect of noise. Window 1 in [Figure 8], we do the GRHLT for these figures, respectively. [Figure 8]b shows that we can use the GRHLT to detect an image successfully. In [Figure 8]a, we show that even if the original image is interfered by noise, the performance of edge detection does not become worse. So using the GRHLT for edge detection is noise immunity. Moreover, we also use orthogonal polynomial expansion and table looking up and define the cornity as the "integration" of the quadratic function to further improve the performance. From simulations, our algorithm is effective both for corner detection and edge detection. The sensitivity to edge orientation and the ability to localize an edge are both important properties of an edge detector. [Figure 8] (Window 3) contains the analysis performed to determine the edge detector's ability of edge localization of carious effect on human teeth by setting the threshold to half or higher of the edge height, edge location can be properly localized. Setting a high threshold could cause the detector to miss the real edge with low amplitude. The input illustrated in [Figure 8] (Window 1) is the image to be processed, and t is a defined edge detection threshold. The function first computes the row and column gradients as shown in equations 1 and 2. Then the spatial gradient amplitude is calculated using GRHLT. Instead of using a differential detector, edge 1 function directly compare the spatial gradient to the defined threshold input by the function user. Through the comparison, a binary indicator map is generated indicating the position of edges detected within the original image. [Figure 8] (Window 2) displays the obtained image which is quite satisfactory considering the edge1 algorithm is only a simple approximation of row and column gradients. A similar function we do to calculate the edge for different image at different layers of the samples as shown in [Figure 8]b and [Figure 8]c.
Figure 7: Using short response hilbert transform (SRHLTs) to detect the sharp edges. Here we choose b = 1, 4, 12, and 30

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Figure 8: In vivo photothermal imaging of human teeth at different layer slice 7 (Window 1). A normalized photothermal image for sample captured by the thermal camera after 2 s radiation from neodymium-doped yttrium aluminium garnet laser. High carious contrast is seen as the peak temperature intensity (Window 2). The edge map produced by using two-dimensional Hilbert transform edge detection (Window 3) phase image of Hilbert transform (2) (Window 4). The carious is detected by comparing the edge gradient to a defined threshold value. (a) Slice 7, (b) slice 5, and (c) slice 3

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One important local structural feature is the phase φ that can be calculated by means of the HLT as shown in [Figure 8]c. Furthermore, exact curvature can be calculated with all the advantages of rotational invariant local phase based approaches (robustness against noise and illumination changes) and without the need of any derivatives.

Carious edge detection boundaries usually generate strong changes in image intensities as shown in [Figure 9]. Edge detection is used to identify these changes. An important property of edges is that they are less sensitive to illumination changes compared to color features. Algorithms that track the boundary of the objects usually use edges as the representative feature. Every tracking method requires an object detection mechanism either in every frame. A common approach for object detection is to use information in a single frame. This temporal information is usually in the form of frame differencing, which highlights changing regions in consecutive frames. Given the object regions in the image, it is then the tracker's task to perform object correspondence from one frame to the next to generate the tracks. Carious location and size was determined function of depth as shown in [Figure 9] then human enamel specimens irradiated with the high power Nd:YAG laser at seven different energy fluencies and an untreated specimen used as control of image tracking system.
Figure 9: Carious edge detection tracking imaging (a) photothermal edge detection images frames function in depth (b) photothermal edge detection contours

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In vivo tests

An experiment was conducted on a volunteer who had no clear caries in his teeth but complained of mild pain in one tooth. Visually, the problem could not be located. The volunteer was examined by the proposed system, as shown in [Figure 10]a. [Figure 10]b shows a 2D plot of the temperature distribution of the depicted thermal image. [Figure 10]c shows the carious detection of the thermal image shown in part (a). As shown, [Figure 10]c and [Figure 10]d determine accurately the location of the carious part in the volunteer's tooth. This result shows the accuracy of caries detection by the proposed system for the visually nonobserved carious levels.
Figure 10: In vivo examinations of volunteer teeth (a) right side photothermal imaging (b) front side (c) left side (d) carious detection using Hilbert transform Algorithm. W1 shows volunteer photothermal imaging captured, w2 shows High carious contrast seen as the peak temperature intensity (Window 2). W3 illustrate The edge map produced by using two-dimensional Hilbert transform edge detection (Window 3). W4 shows The carious is detected by comparing the edge gradient to a defined threshold value. (Window 4)

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  Conclusions Top

In this paper, a laser-independent photothermal imaging system has been proposed for human tooth caries detection. Both amplitude and phase information of the temperature distribution are used to get accurate localization of the carious parts. In addition to its ability to accurately localize the carious parts in the x–y plane, the proposed system enables the physician to estimate the depth of caries in the z direction. Moreover, the system is physician friendly from the clinical point of view because of its simplicity and the obtained images for the teeth that facilitate monitoring during caries removal.

Financial support and sponsorship


Conflicts of interest

There are no conflicts of interest.

  References Top

Bjelkhagen H, Sundström F, Angmar-Månsson B, Rydén H. Early detection of enamel caries by the luminescence excited by visible laser light. Swed Dent J 1982;6:1-7.  Back to cited text no. 1
Borisova E, Uzunov TZ, Avramov L. Investigation of dental caries using laser and light-induced autofluorescence methods. Bulg J Phys 2006;33:55-67.  Back to cited text no. 2
Jeon RJ, Mandelis A, Sanchez V, Abrams SH. Nonintrusive, noncontacting frequency-domain photothermal radiometry and luminescence depth profilometry of carious and artificial subsurface lesions in human teeth. J Biomed Opt 2004;9:804-19.  Back to cited text no. 3
Lagerweij M, van der Veen M, Ando M, Lukantsova L, Stookey G. The validity and repeatability of three light-induced fluorescence systems: An in vitro study. Caries Res 1999;33:220-6.  Back to cited text no. 4
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El-Sharkawy YH. Physical and thermal properties of human teeth determination by photomechanical, photothermal images to rapidly diagnose Optical Diagnostics and Sensing IX. Edited by Elsharkawy, Yasser H. Proceedings of the SPIE, Vol 7186, 2009; p. 71860K-71869K-11.  Back to cited text no. 7
El-Sherif AF, El-Sharkawy YH. Laser-induced photothermal technique used for detection of caries in human tooth. Proc SPIE 2008;6843:6851B.  Back to cited text no. 8
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  [Figure 1], [Figure 2], [Figure 3], [Figure 4], [Figure 5], [Figure 6], [Figure 7], [Figure 8], [Figure 9], [Figure 10]

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