Journal of Medical and Biological Engineering, 30(2): 113-118
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Non-invasive Technique for Human Caries Detection and Monitoring Using Time-resolved Photothermal Imaging Mahmoud E. Gadallah*
Yasser H. El-Sharkawy
Department of Biomedical Engineering, Military Technical College, Kobry Elkobbah, Cairo, Egypt Received 25 May 2009; Accepted 16 Oct 2009
Abstract Photothermal methods are currently being employed in a variety of research areas, ranging from materials science to environmental monitoring. Photothermal imaging is non-invasive, painless and ionizing radiation-free. The techniques and instruments of photothermal phenomenon for dental diagnostics has been developed to enable early detection of lesions which cannot be observed by visual inspection. The use of lasers for this purpose is considered to be promising, mainly through the phenomenon of laser-induced fluorescence of the enamel. In this paper, a high-resolution caries detection of human teeth using photothermal imaging is introduced. In addition to its high accuracy, this technique is suitable for clinical application in caries detection as well as for continuous monitoring during its removal because it enables the physician to easily get a real image. Both in vitro and in vivo tests for the proposed system have been conducted and shown promising results. Keywords: Photothermal imaging, Phase-gradient imaging, Laser-induced, Thermal camera, Caries detection
1. Introduction The photothermal effect produced by light absorption of materials can be monitored via either photoacoustic or photorefractive methods. Photoacoustic methods are based on the detection of the acoustic waves due to the changes of material volume or pressure. The photorefractive methods are based on measuring the change of the refractive index due to the change of the density of the material. Comprehensive analysis of these methods together with some of their applications is presented in [1]. Photothermal methods are usually implemented using laser light sources to obtain stronger signals than with conventional light sources because of their high spectral purity and power as well as the spatial beam profile [1]. Investigation of dental caries using laser and light-induced effects has found great attention in different studies. This interest results from the importance of the early detection of caries, which is difficult when relying on vision or even X-ray imaging. In a review by Moore and Wilson [2], three non-invasive techniques for caries detection are introduced. These techniques are laser autofluorescence, electric conductance measurement and fiber optic transillumination. This study suggested that electric current resistance and laser fluorescence were the leading technologies (at that time). * Corresponding author: Mahmoud E. Gadallah Tel: +20-2-22629585, +20-2-0106779843 E-mail:
[email protected]
Laser-induced spectroscopy has been applied to discriminate between normal and carious teeth [3-5]. Optical spectroscopy offers many ways to detect and characterize biochemical and morphological changes occurring in tooth structures [6-8]. In an investigation by Borisova and colleagues [9], application of laser-induced and light-induced fluorescence spectroscopy technique for detection of different caries stages has been studied. Also, in that work, a comparison between the diode excitation source and the argon-ion laser showed that the diode excitation source was more promising for assessing the severity of early caries lesions than the argon-ion laser. Photothermal radiometry and luminescence imaging techniques have been investigated and applied for human tooth diagnosis as well as for detection of artificial subsurface holes and variations in tooth thickness [10]. The investigations introduced in this reference have been performed with two near-IR source wavelengths (659 and 830 nm) from semiconductor lasers which are used for line scanning of the tooth. Although in this research, impressive results have been reported, clinical application of this method is undesirable for the physician because of the difficulty in the process of line scanning and the need for accurate investigation of the plotted curves during caries detection. Photoacoustic signals produced in the teeth by laser pulse stimulus have been detected and they were able to distinguish between normal and carious parts. In those trials, piezoelectric sensors as well as optical interferometer were used to monitor the photoacoustic signals [11]. In this paper, an imaging technique for early caries detection as well as its monitoring
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during removal is proposed. This technique depends on picking up a thermal image, using thermal camera, for the tooth after its stimulation by a laser pulse.
2. The proposed laser-induced photothermal imaging of teeth The laser-induced absorption spectroscopy addressed in the present paper is schematically represented in Figure 1. The shadowed region represents a human tooth which is subjected to laser heating on the top surface. A laser excitation source was used to obtain the photothermal waves: an Nd:YAG laser “DECA” (Italy) (short pulse, 1069 nm, 3 J, 30 Hz repetition rate). The excitation and transmission signals were delivered via optical fibres. The blackbody radiation from the optically excited sample was focused and detected using 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 USB port. The thermograph were stored using the camera specialized software and were analyzed and graphically represented with our algorithm and computer program. Hard tissue (tooth)
Optical fiber Design of delivery system
Rotary-stage
Digital display Signal conditioning ADA converter
(Ultrasonic sensor) Design of detecting system
Optical sensor (Thermal sensor)
Healthy tooth model
Ultrasonic or reflected or thermal signals
where t0 can be interpreted as the pulse rise time. Heat is generated inside the tissue during the laser exposure. Deposition of heat in tissue is due only to absorbed light in it. The heat generated is defined as [15]: Q(r,z,t) = µaI(r,z,t)
(2)
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:
Q( r , z , t ) =
Q0 (1 − R) µ a r2 exp(− 2 − µ a z ) g (t ) 2 2πa t 0 a
(3)
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. [12-14]
ρc
∂T ( r , t ) − k∇ 2T (r , t ) = Q ( r , t ) ∂t
(4)
whereρ, c and k represent the density, heat capacity and heat conductivity of the sample, respectively. If the heat conductivity k is neglected and heat densityρc is a constant, the transient temperature distribution can be written as a function of the radial distance r, the penetration depth z and the time t as follows:
T (r, z, t ) = Q0 (1 − R) µ a r2 t t exp(− µ a z − 2 )[1 − exp(− )(1 + )] ( 5 ) 2 t0 t0 2πa ρc a
No
The spatial extent of heat transfer is described by the time-dependent thermal penetration depth [15] as:
Processing
Carious tooth model
(6)
Z therm (t) = 4kt
Yes Algorithm design
Figure 1. A schematic representation of the experimental setup.
The bottom surface of the teeth, as shown in the Figure, is assumed to be located within the body core. The studied 3D computational domain was chosen to have widths S1 = S2 = 5 mm and height L = 3 mm.
3. Photothermal imaging Based on the physical layout shown in Figure 1, a mathematical model of heat transfer is subsequently developed. 3.1 Theory and principles of operation A teeth sample is illuminated by a Q-switched laser with a pulse shape g(t) given by
g (t ) =
t t exp(− ) t0 t0
(1)
The term “penetration depth” originates from the argument of exponential function in Eq. (5). Thus, Ztherm(t) is the distance in which the temperature has decreased to 1/e of its peak value. We note that: (i) Heat generation is determined by laser parameters and the optical tissue properties primary irradiance I, exposure time, and the absorption coefficient; (ii) Heat transport is characterized by thermal tissue properties such as heat conductivity and heat capacity; and (iii) Heat effects depend on the type of tissue temperature achieved inside the tissue. 3.2 Phase gradient imaging The method for determining the phase gradient is based on the transport of intensity equation describing a paraxial optical field travelling in the z-direction: ▽┴ • (I(x, y, z) ▽┴ φ (x, y, z)) = -k ∂I (x, y, z)
∂z
(7)
Non-invasive Technique for Human Caries Detection
where k = 2π/λ is the wave number of the optical field, λ is the wavelength, I(x, y, z) is the intensity of the light measured in a transverse plane z, and ▽┴ is the transverse gradient operator; ▽┴ =
∂ ∂ x+ y . In the absence of phase singularities, ∂x ∂y
the previous equation can be written in terms of a Fourier transform since the derivative and the inverse Laplacian operators become multiplicative operators when acting on the Fourier representation of a function, and the phase gradient ▽┴ψ(x, y) can therefore be written
∇ ⊥φ = −
k ik ∂I ( x, y ) Λ -1 k y ∂I ( x, y ) Λ [F -1 ( x2 F ( )) x + F ( 2 F ( )) y ] (8) I ( x, y ) ∂z ∂z kr kr
where F and F-1 denote the Fourier transformation and inverse Fourier transformation, respectively, kx and ky are the variables conjugate to x and y, and k r2 = k x2 + k y2 . Once (∂I ( x, y ) ∂z ) has been estimated by obtaining defocused images, Eq. (8) forms the basis of an algorithm based on fast Fourier transforms to determine the phase gradients introduced into the wave field by the specimen which, in the case of a cylindrically symmetric object, is sufficient to reconstruct the index profile of that specimen. Note that four Fourier transforms and inverse transforms are required to determine the phase gradient. The phase can be written as a Fourier cosine series: ∞
φ (x, y) = a 0 (y) + ∑ am ( y ) cos( m =1
mπx ) R
(9)
where the am(y) are Fourier coefficients, and the inverse Abel transform is applied to each Fourier component. Using this same notation, the transverse gradient is given by:
(
∂φ ( x, y) π ∞ mπx ) = − ∑ mam ( y ) sin( ) ∂z R m=1 R
(10)
Hence, by decomposing the transverse phase gradient (∂φ ( x, y) ∂z ) as a Fourier sine series, it is possible to determine the coefficients am(y) for m ≥ 1. Note that a0(y) cannot be determined and corresponds to an irrelevant constant phase offset. Hence, once the transverse phase gradient has been determined using an algorithm derived from Eq. (8), it is possible to reconstruct the index profile at any point along the fibre using the technique of reference [12] or other inverse Abel transform algorithm. Referring to Eq. (2), which describes the relation between heat generation and the light intensity, we can write:
I (r , z, t ) =
1
µa
[Q(r , z, t )]
(11)
Also, taking into consideration that the heat waves are the consequence of the light waves, we can assume that the behaviours of the heat waves are similar to that of the light waves. By replacing I in Eqs. (7) and (8) by T, the change of the temperature phase with respect to the depth, z, (∂φ ( x, y) ∂z ) can be calculated using the same algorithm of Fourier and inverse Fourier transforms. This algorithm has been applied to obtain phase gradient images.
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4. Experimental tests and discussions 4.1 In-vitro tests In this experiment, many human teeth samples, some normal and some with different levels of caries, were used to evaluate the performance of the proposed laser-induced imaging system. Figure 2(a) shows a photo of one of the tested samples that comprises 3 teeth which are installed on a jaw-like platform. The three teeth contain one normal and the other two infected with different levels of caries. Figure 2(b) shows their thermal image depicted by the thermal camera. As shown in this image, there is a clear distinction between the normal (the tooth on the left) and the two infected teeth. In addition, this result shows the clear dependence of the image of the tooth on the level of caries (the middle tooth is highly infected while the rightmost is moderately infected). This image ensures the fact that the amount of the absorbed light by the carious parts of the tooth depends on the level of the caries. Figures 2(c) and (d) show the temperature distribution of the depicted image (b), as defined in Eq. (4), plotted in 3-D and 2-D, respectively, to indicate the correspondence between the status of the three teeth and the temperature intensity of their images. From this result, the coincidence between the locations of the detected caries and the peaks of the thermal distribution is clear because the emitted heat from the carious parts is higher than that from the normal parts. Also, this result reflects the effect of both optical properties (Qo, R, µa) and thermal properties (ρc) of the tissue, which is clear in the amplitude of T in Eq. (4). In other words, for normal teeth, the reflection coefficient, R, is higher than that of the carious parts, but the opposite is the case for the absorption coefficient, µa. This is the reason for the direct proportionality between the amplitude of the peak at the caries position with the level of the caries as shown in Figure 2(d). For more confirmation, Figure 2(e) is a contour plot of the depicted thermal image, Figure 2(b), i.e., the lines of equal temperatures. This plot shows the relative concentration of the contours at the infected regions depending on the amount of caries which is directly proportional to the amount of the absorbed light. Also, this contour illustrates the diffusion of the thermal wave around the centre of caries as a source of heat. To study the dependency of the level of light absorption on the tissue depth, z, the natural logarithm of Eq. (5) is taken and plotted as -ln(T) in Figure 2(f) to show the distribution of the absorbed laser energy. Also, 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 these parts. To investigate the dependency of the heat distribution on the penetration depth (z in Eq. (5)), the algorithm of gradient phase imaging, introduced in section 3, is applied to calculate the gradient phase of the temperature. To study the behaviour of the absorbed laser energy by the carious parts, thermal images for the stimulated samples using laser pulse were depicted from the same position at
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3-D plot for the temperature intensity
Temp intensity (Relative units)
Photo thermal image of the teeth sample shown in (a)
Temp intensity (Relative units)
(a)
y
y
x
(b)
2-D plot for the temperature intensity
(c)
Line contour of the temperature distribution
–ln(Temp distribution)
x (e) (f) (d) Figure 2. 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) 3-D plot of the temperature intensity to show the caries position in 2-D (x,y); (d) 2-D plot of (c) illustrating the caries position in X-direction; (e) line contour of the temperature distribution; (f) –ln(Temp) showing the absorption coefficient of normal and abnormal tissues.
Att1=2 sec
Att2=4 sec
Att1=2 sec
Att2=4 sec
Att3=6 sec Att4=8 sec (a) Time-dependent thermal relaxation
Att3=6 sec
(b) -ln(temp)
Att4=8 sec
Att5=10 sec
Att6=12 sec
Att5=10 sec
Att6=12 sec
Figure 3. (a) Time-dependent thermal relaxation of group of thermal images taken at 2-second intervals, and (b) their natural logarithm.
2-second intervals. The temperature distribution of these images and their natural logarithm are shown in Figures 3(a) and (b), respectively. Figure 3(a) shows the time-dependent thermal relaxation. It is obtained by equating the optical penetration depth L to the thermal penetration depth Ztherm, i.e.,
L = 4kτ therm
(12)
where τtherm is the thermal relaxation time. From Figure 3(a), the diffusion of the heat energy absorbed by the carious parts to the surrounding region as the time increases is remarkable. This behaviour 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 the caries. Figures 4(a) and (b) show the variations of amplitude and phase of radiated infrared emission (heat) from the severely infected tooth (middle tooth of Figure (3) with position, at 3 instants separated by 4-second intervals, after stimulation by a laser pulse. Figure 4(a) illustrates the amplitude of the 1-D infrared emission wave peaks for human teeth with respect to x-position, which confirms the diffusion of the emitted heat in the surrounding volume. Figure 4(b) illustrates the
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Non-invasive Technique for Human Caries Detection
(a)
(b)
4 sec
0 sec
8 sec 4 sec
0 sec
0
0
8 sec
0
(c)
Infrared emission from decayed teeth (no 2)
Phase shift (relative units) 5 10 15 20 25 30
Amplitude (relative units) 5 10 15 20 25 30 35 40
Infrared emission from decayed teeth (no 2)
100
Position
200
300
0
(d)
100
Position
200
300
Figure 4. Variation of (a) amplitude and (b) phase of radiated heat from the severe infected tooth (middle tooth above) with position; variation of (c) intensity and (d) position of its peaks of radiated heat from the same tooth.
Figure 5. In-vivo examinations of volunteer teeth.
corresponding phase shift of infrared emission waves due to the thermal relaxation time variation of the tooth. Figure 4(c) describes the variation of infrared intensity (radiated heat) of the tooth (due to thermal conductivity as discussed in Eq. (6) function of time). Figure 4(d) shows the dependence of the position shift of thermal infrared intensity peaks (due to thermal relaxation) on time.
4.2 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 5(a). Figure 5(b) shows a 2-D plot of the temperature distribution of the depicted thermal image. Figure 5(c) shows
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the natural logarithm of the thermal image shown in part (a). Figure 5(d) shows the two-dimensional intensity distributions from each image averaged into a single curve to obtain a one-dimensional distribution of light absorption coefficient on the x-axis. As shown, Figures 5(c) and (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 non-observed carious levels.
[5]
[6]
[7]
5. Conclusions 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 the caries in the z direction. Also, 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.
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[2] [3] [4]
T. Gensch and C. Viappiani, “Time-resolved photothermal methods: accessing time-resolved thermodynamics of photoinduced processes in chemistry and biology,” Photochem. Photobiol. Sci., 2: 699-721, 2003. D. J. Moore and N. H. F. Wilson, “A review of modern non-invasive systems for caries detection,” CPD Density, 2: 86-90, 2001. K. König, G. Flemming and R. Hibst, “Laser-induced autofluorescence spectroscopy of dental caries,” Cell. Mol. Biol., 44: 1293-1300, 1998. V. Angnes, G. Angnes, M. Batisttella, R. H. Grande, A. D.
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Loguercio and A. Reis, “Clinical effectiveness of laser fluorescence, visual inspection and radiography in the detection of occlusal caries,” Caries Res., 39: 490-495, 2005. N. M. Baseren and S. Gokalp, “Validity of a laser fluorescence system (DIAGNOdent) for detection of occlusal caries in third molars: an in vitro study,” J. Oral Rehabil., 30: 1190-1194, 2003. E. H. Verdonschot, B. Angmar-Månsson, J. J. ten Bosch, C. H. Deery, M. C. D. N. J. M. Huysmans, N. B. Pitts and E. Waller, “Developments in caries diagnosis and their relationship to treatment decisions and quality of care,” Caries Res., 33: 32-40, 1999. R. R. Alfano and S. S. Yao, “Human teeth with and without dental caries studied by visible luninescent spectroscopy,” J. Dent. Res., 80: 120-122, 1981. H. Bjelkhagen, F. Sundström, B. Angmar-Månsson and H. Rydén, “Early detection of enamel caries by the luminescence excited by visible laser light,” Swed. Dent. J., 6: 1-7, 1982. E. Borisova, T. Uzunov and L. Avramov, “Investigation of dental caries using laser and light-induced autofluorescence methods,” Bulg. J. Phys., 33: 55-67, 2006. R. J. Jeon, A. Mandelis, V. Sanchez and S. H. Abrams, “Nonintrusive, noncontacting frequency-domain photothermal radiometry and luminescence depth profilometry of carious and artificial subsurface lesions in human teeth,” J. Biomed. Opt., 9: 804-819, 2004. Y. H. El-Sharkawy, Y. Badr, M. Gadallah and A. F. El-Sherif, “Diagnostic of human teeth using photoacoustic response,” Proc. SPIE Int. Soc. Opt. Eng., 6137: 613701, 2006. Y. H. El-Sharkawy, Y. Badr and M. Hassan, “Laser-induced photoacoustic imaging for characterizing biological tissues,” Proc. SPIE Int. Soc. Opt. Eng., 5689: 165-173, 2005. Y. H. El-Sharkawy, “Physical and thermal properties of human teeth determined by photomechanical, photothermal images to rapidly diagnose,” Proc. SPIE Int. Soc. Opt. Eng., 7186: 71860K, 2009. A. F. El-Sherif and Y. H. El-Sharkawy, “Laser-induced photothermal technique used for detection of caries human tooth,” Proc. SPIE Int. Soc. Opt. Eng., 6843: 68430B, 2008. M. H. Niemz, “Thermal interactions,” in: M. H. Niemz (Ed.), Laser-Tissue Interactions: Fundamentals and Applications, Springer: Berlin Heidelberg, Chapter 3, 1996.
