Translator Disclaimer
1 September 2008 Absolute transmitted light plethysmography for assessment of dental pulp vitality through quantification of pulp chamber hematocrit by a three-layer model
Author Affiliations +
Abstract
After confirming that the gingival circulation had little effect on transmitted light plethysmography measurement in the upper central incisor in both in vivo experiments and numerical Monte Carlo simulation studies, a three-layer model comprising of a pulp chamber sandwiched between two dentin layers has been introduced to quantify the pulp chamber hematocrit (Hctp) from the measured optical density. Two-flux theory was utilized to derive a mathematical equation for transmitted intensity in terms of tooth dimensions, Hctp, and light-source wavelength. Each layer was assumed homogeneous so as to represent its optical properties by the bulk absorption and scattering constants. The mean error between the Hctp estimate based on the three-layer-model equation and the Hctp actual in the extracted model tooth was -0.00115 with standard deviation (SD) of 0.00733 at 522 nm wavelength, while for 810 nm +0.09157 and 0.02493. The Hctp estimate of the upper central incisor in 10 young volunteers at 522 nm using the three-layer model ranged from 0.002 to 0.061 with the mean of 0.032. The Hctp change reflects blood volume shift in the pulp microcirculation to possibly indicate dental pulp vitality.

1.

Introduction

The vitality or wellness of the dental pulp is determined by the electric pulp testing (EPT) or thermal sensitivity test, where the sensitivity of the pulp sensory nerves to an electrical or thermal stimulus is given a score according to the patient’s responses. These methods, however, may not reveal real vitality or wellness of the pulp tissue because of the indirectness and subjectivity of the modality. In addition, because the EPT relies on the patient’s responses and might induce as unpleasant sensation, it could result in a false-positive outcome, particularly in young patients. In some cases, such as traumatized or young permanent teeth, false-negative outcomes have also been reported due to elevated threshold levels in the pulp nerves.1, 2

Following the earlier works by Upthegrove 3 and Beer, 4 durings 1980 to 1990s Laser Doppler flowmetry5, 6 pulse oximetry,7, 8, 9 and transmitted light plethysmography 10, 11 (TLP) were investigated to noninvasively assess “pulp vitality.” Among them, the TLP was found to be promising to provide information related to circulatory changes occurring inside the pulp chamber by measuring the transmitted light through a whole tooth. Toward quantitative assessment of pulp vitality, Diaz-Arnold, 12, 13 utilizing the extracted model tooth whose pulp chamber had been filled with the bovine blood, reported that the hemoglobin content and oxygen saturation of the blood in the pulp chamber could be quantified by measuring the optical transmission at the 576, 660, and 830nm wavelengths. It was speculated that the TLP could be used to assess pulp vitality reflected in the blood volume changes occurring in the pulp chamber synchronized with the heart beat. Contrary to the report of Diaz-Arnod, Fein emphasized that in the middle-aged and older patients the TLP pulsation was caused by the blood volume changes in the gingiva not in the pulp chamber.14 It was reported that the optical signal transmitted through the gingiva and then the tooth appeared to have topped over the signal changes occurring in the pulp chamber. The controversy of the TLP signal cause was previously addressed by our group, where the effects of the periodontal blood flow on the TLP signal amplitude were investigated by blocking the background light propagation through the periodontal tissue with an opaque rubber material placed over the gingiva.15 The results, however, were not conclusive because of the constrictive force of the rubber material altering the blood flow through the gingiva. Thereafter, a series of studies had been designed (i) to verify optical propagation paths through a tooth, (ii) to develop a model in quantifying the pulp hematocrit in human upper central incisors based on the TLP measurement, and (iii) to validate the applicability of the TLP for assessing pulp vitality. To attain the goal, a multiwavelength TLP system was constructed to obtain a tooth’s optical transmission spectrum in the visible and near-infrared regions sampled at 467, 506, 522, and 810nm wavelengths using light-emitting diodes (LEDs).16 It was demonstrated in the extracted model tooth as well as in the human volunteer studies that the pulsed LED signals of 560Hz minimized the background light noise to enhance the signal-to-noise ratio and to obtain cleaner TLP signal.

In this study, preliminary studies, both experimental and theoretical, were conducted first to verify optical propagation paths in an upper central incisor. First, the effects of the light signal traveling on the palatal surface of the tooth, entering the gingiva, and then propagating through the tooth toward the detector placed on the labial surface were examined experimentally by blocking the transmission between the light source and gingiva with a silicone material injected around the gingival sulcus. Second, the amount of the light that had reflected off the gingiva, and periodontal ligaments inside the tooth and that had propagated toward the detector was estimated numerically by the Monte Carlo simulation.17 After confirming that the gingival circulation had little affect on TLP measurement, a three-layer model comprising of a pulp chamber sandwiched between two dentin layers was then developed to quantify the transmitted light intensity in terms of (i) pulp chamber hematocrit Hctp , (ii) tooth dimensions, and (iii) light-source wavelength. By assuming a diffuse radiation incident upon the tooth and by employing the two-flux model proposed by Kubelka,18, 19 a mathematical equation was developed. The accuracy of the model for estimating the Hctp was then examined in the extracted model tooth by varying the pulp chamber size, Hctp , and light-source wavelength. Finally, the model was applied to quantify the hematocrit of the blood in the upper central incisors of the human volunteers from which the volume fraction of the pulp vascular system was estimated to evaluate pulp vitality.

2.

Studies to Verify Optical Paths in a Tooth

Referring to the anatomical structure of the upper central incisor and possible light propagation paths depicted in Fig. 1 , the preliminary studies composed of (i) measurements in human volunteers to verify the effects of the light wave external to the tooth propagating to the gingiva on the TLP signal change (black broken lines in Fig. 1) and (ii) Monte Carlo simulation to quantify the effects of the light that had scattered off the gingiva and periodontal ligaments inside the tooth on the TLP signal change (red solid lines in Fig. 1).

Fig. 1

Vertically cut cross section of the upper central incisor showing its anatomical structure and possible optical paths.

054023_1_008805jbo1.jpg

2.1.

Effects of Light Wave External to the Tooth Propagating Directly to Gingiva on TLP Signal

The effects of the light wave external to the tooth traveling through the gingiva on the TLP signal were examined in the human volunteers. After the protocol for human study was approved by the Institutional Review Board of the Tokyo Medical and Dental University, the optical measurements in the upper central incisor of human volunteers were conducted using the multiwavelength TLP system (Fig. 2 ).16 Preceding the study, a resin adaptor (as shown in Fig. 3 ) for each subject was fabricated to fix the optical fibers against a tooth. As a light source, we used the 522nm wavelength LED pulsed at 560Hz . The transmitted light through the tooth at 560Hz was sampled to minimize the background light. At first, the dc component (absolute level of the transmitted light signal) and the ac component (periodically varying signal amplitude synchronized to heart beat) of the TLP signals at 522nm wavelength were recorded in each subject for 2min . Then, the silicone impression material, Exafine Regular Type (GC Dental Products Corp., Tokyo Japan) was injected into the gingival sulcus around the resin cap and proximal surface of the tooth to block the light propagation between the optical fiber and the gingiva, followed by the recording of the dc and ac signals again. The significance in the difference between the two measurements with and without the silicone material was evaluated with p<0.01 .

Fig. 2

Multiwavelength optical plethysmograph.

054023_1_008805jbo2.jpg

Fig. 3

Resin cap placed on the upper central incisor with optical fibers.

054023_1_008805jbo3.jpg

Figure 4 showed the changes in dc and ac/dc signals of the TLP in the upper central incisors before and after injection of the silicone impression material (n=12 , 2531years old with mean 27.3years old). With the silicone injected in the gingival sulcus, the average value of the optical density (OD) changed from 6.55±0.07to6.60±41 , and ac/dc ratio changed from 0.069±0.031to0.064±0.025 . For both OD and ac/dc values, there were no significant differences with and without silicone impression material. This study demonstrated that the light wave traveling on the tooth surface directly from the light source to the gingiva had little affect on TLP measurements.

Fig. 4

OD and ac/dc ratio obtained in human volunteers showing the effects of the silicone material injected around the gingival sulcus.

054023_1_008805jbo4.jpg

2.2.

Monte Carlo Simulation of Light Propagation Inside the Tooth

Figure 5 showed a two dimensional Monte Carlo simulation model of the tooth Fig. 1 showing layers of enamel, dentin, pulp, and gingiva. The dimensions of the model reflect those of the average size tooth as measured using the X-ray machine (refer to Table 1 data). In the microscopic domain of dentin, each dentin layer consisted of a collagen fiber and mineral substance having a 30-μm thickness, each with the differential optical properties between them affecting the light propagation. Table 2 shows the optical properties of the dentin material for the wavelengths of 522 and 810nm .20 The Monte Carlo simulation of the light propagation for the model tooth of Fig. 5 was derived by an iterative calculation using Eqs. 1, 2, 3, 4.17 The photon step size and its angle of scattering at one scattering were determined by Eqs. 1, 2, 3, yielding the maximum step size of photon in the mineral substance to be 37μm for 522 and 810nm . We thus employed the mesh size of 30μm in the Monte Carlo simulation. The iterative equations used for calculation were

Eq. 1

s=ln(RN1)μt

Eq. 2

θ=cos112g[{1+g2(1g21+g2gRN2)2}]

Eq. 3

ϕ=2πRN3

Eq. 4

μt=μa+μs,
where s is the mean free path between the scattering; RN1,2,3 is the random number evenly distributed between 0 and 1 and μt , μa , and μs are the extinction, absorption, and scattering coefficient, respectively. θ , the probability distribution for an arc-cosine of a deflection, obeys the scattering function of Henyey and Greenstein phase function. g is the anisotropicity of scattering that has the value between 1.0 and 1.0, where the value of 0 indicates isotropic scattering and the value near 1.0 indicates highly forward scattering. ϕ is the azimuthal angle.

Fig. 5

Two-dimensional tooth model vertically cut in the plane of the optical fibers for the Monte Carlo simulation.

054023_1_008805jbo5.jpg

Table 1

Dimensions of the selected teeth.

ToothNo.Tooth BLthickness (mm)Pulp BLthickness (mm)
16.10.44
26.10.67
36.60.34
4-16.00.28
4-26.00.40
4-36.00.51
56.60.78

Table 2

Optical properties of dentin and gingiva.

Light wavelength(nm)Optical properties (mm−1) Oxygenatedblood (100%) DentinGingiva
MineralsubstanceFiber(Spinal fluid)
522 μs 0.9528.090.010.10
μa 42.600.440.0024.26
g 0.850.8000.90
810 μs 0.9526.970.010.10
μa 1.460.340.0020.15
g 0.850.8000.90

In order to emphasize the photon paths in the model, the result was shown by the level of absorption intensity. The numbers of photons that had scattered off the gingiva and then traveled through the tooth and those that did not reach gingiva were tracked separately to show the effects of gingiva on the transmitted light intensity. Figure 6 showed the absorbed light intensity for 522 and 810nm wavelengths in the macroscopic scale. In Fig. 7 absorption intensities in the 500×500μm microscopic scale were shown, where the photons scattered in the enamel layer became guided along the dentin tubule toward pulp chamber, the effect similar to that reported by Kiele and Hibst21 Table 3 summarizes the statistical results showing how many photons have traveled to hit the gingiva and scattered off toward the detector. Out of 20 million photons injected inside the model tooth, only 5 photons (0.000025%) traveled to the gingiva, while 497 photons (0.0025%) at 522nm and 876 photons (0.0044%) at 810nm , over 100 times those that hit the gingiva, traveled through pulp to the detector without routing the gingiva. The Monte Carlo simulation has thus indicated the minimal effects of the gingival circulation on the optical transmission measurements in an upper central incisor model.

Fig. 6

Absorption intensity for 522nm and 810nm obtained by the Monte Carlo simulation. Left side are two-dimensional plots and right side three-dimensional plots.

054023_1_008805jbo6.jpg

Fig. 7

Microscopic absorption intensity for 522nm (top) and 810nm (bottom) in the left panel without enamel layer. In the right panel, for 522nm , with the enamel layer, the scattered light in the enamel layer was directed along the dentin tubules with the highest intensity at the center.

054023_1_008805jbo7.jpg

Table 3

Results of the Monte Carlo simulation.

Wavelength Number of transmitted photons(Incident photon number=20,000,000 )
Scattered by the gingivaNo scattering atgingiva
522 [nm]5(0.000025%)497(0.0025%)
810 [nm]17(0.000085%)876(0.0044%)

3.

Theoretical Model for the Human Upper Central Incisors

Because the results in the preliminary studies showed that the transmitted light intensity through an upper central incisor was little affected by the gingival circulation, we proceeded with the development of a theoretical model to quantify pulp hematocrit so as to evaluate pulp vitality.

3.1.

Dentin-Pulp Chamber-Dentin Three-Layer Model

The tooth structure was simplified to a three-layer model comprising of dentin-pulp chamber-dentin layers (Fig. 8 ). Although there are paths around the pulp chamber for the photons to propagate, the tubules in the dentin layer are organized in such a way to guide the light toward the pulp chamber.21 The Monte Carlo simulation presented above supported the light-guiding phenomenon, as illustrated in the microscopic absorption intensity in the dentin model. The scattering property of the dentin layer is so much greater than that of the enamel layer that the tooth appearance is determined mainly by the scattering property of the dentin tubules.22, 23 The exclusion of the enamel layer from the model thus does not affect the relative changes of the model performances in terms of the red blood cell concentration inside the pulp chamber.

Fig. 8

Simplified TLM consisting of dentin, pulp, and dentin layers.

054023_1_008805jbo8.jpg

3.2.

Three-Layer Model (TLM) Equation

In deriving a mathematical equation for the transmitted light intensity through a three-layer model (TLM), we assumed that each layer was homogeneous and also the diffuse radiation was incident upon the medium so as to justify the application of the two-flux model introduced by Kubelka with no reflection at the layer boundary (Fig. 9 ).18 The differential equations for the two fluxes, I in the positive direction and J in the negative direction are written as

Eq. 5

dIdx=(S+K)I+SJ

Eq. 6

dJdx=(S+K)JSI
with boundary conditions at x=0 and x=d
J(x=d)=0
I(x=0)=I0.
In Eqs. 5, 6, S and K are the scattering and absorption constants of the medium in mm1 . The solutions for Eqs. 5, 6 in the form of the transmittance and reflectance, T and R , are given as18

Eq. 7

T=basinh(bP)+bcosh(bP)

Eq. 8

R=1a+bctgh(bP),
where

Eq. 9

a=S+KS,b=(a21)12

Eq. 10

P=Sd,d:thicknessofthelayer.

Fig. 9

Two flux model for diffuse radiation incident on a homogeneous medium.

054023_1_008805jbo9.jpg

Now we consider when three homogeneous layers with different optical properties were next to each other as shown in Fig. 10. The solution can be given in a closed form as a function of the transmittance and reflectance of each layer as follows:19

Eq. 11

T123=T1T2T31R1R2R2R3+R1R22R3R2T2R3,
where T123 is the transmittance through the layers 1, 2, and 3, T1 , T2 , T3 the transmittance and R1 , R2 , R3 the reflectance of the layer 1, 2, and 3, respectively, computed using Eqs. 7, 8, 9, 10 with appropriate S and K values and the thickness of each layer.

Fig. 10

TLM with the transmitted and reflected light fluxes.

054023_1_008805jbo10.jpg

3.3.

Optical Constants of Dentin and Pulp Chamber

The scattering and absorption properties of the medium are wavelength dependent, particularly of hemoglobin contained inside the red blood cells. In this study, the transmission through three layers T123 was computed for the isosbestic wavelengths of the oxy- and deoxy-hemoglobin, in the green region at 522nm and the near-infrared region at 810nm [Fig. 11].24

For the absorption and scattering constants of the dentin layer, Kd and Sd , though its properties are dependent on the density of tubules, in this study we adopted Kd=0.40mm1 , Sd=28.09mm1 for 522nm , and Kd=0.344mm1 , Sd=26.97mm1 for 810nm , as reported by Fried 25

As for the optical constants of the pulp chamber, we assumed that the chamber was a homogeneous medium comprising of the whole blood. The scattering and absorption constants of the pulp chamber, Sb , Kb , were thus derived from the optical constants of the whole blood. According to Twersky,26 Sb can be derived from the scattering and absorption cross sections of a red blood cell, σs and the red blood cell concentration given by HctpVrbc , where Hctp and Vrbc the hematocrit of the blood in the pulp chamber and the mean corpuscular volume of red blood cells, respectively, as follows:

Eq. 12

Sb=σsHctpVrbc(1.0Hctp).
Because the scattering in the whole blood occurs at the plasma and red blood cell interface and the scattering does not take place when Hctp=0.0 or 1.0, Eq. 12 contains the factor Hctp (1.0Hctp) to express nonlinear dependency of scattering on the Hctp . Although Eq. 12 indicates that the maximum value of Sb occurs when Hctp=0.50 , usually the Sb maxima is shifted toward lower Hctp value at 0.10 .27 Thus, in the calculation, the fifth-order regression equation was used to obtain a more practical value of Sb in the pulp chamber, denoted as Sp ,

Eq. 13

Sp=σsVrbc(1002.7Hctp51501.6Hctp4+846.2Hctp3218.0Hctp2+22.8Hctp+0.033).
The σs value of the red blood cell is dependent on the relative ratio of the red blood cell size Vrbc to the wavelength. The Mie theory, which treats a red blood cell as a sphere, gives the scattering cross sections of 56.8 and 31.4μm2 for the wavelength of 522 and 810nm , respectively.28

As for Kb value, σa is usually expressed as a linear sum of the absorption cross section of the oxygenated and deoxygenated red blood cell, σao , σar , and oxygen saturation SO2 and red blood cell concentration HctpVrbc as follows;28

Eq. 14

Kb=HctpVrbc[σaoSO2+σar(1.0SO2)].
At the isosbestic wavelengths of 522 and 810nm used in this study, the absorption does not depend on SO2 and Eq. 14 reduces to

Eq. 15

Kp,iso=HctpVrbcσiso,
where Kp,iso , σiso are the absorption coefficient of the blood in pulp chamber (in mm1 ) and absorption cross section of the red blood cells (in microns squared) at the isosbestic wavelength, respectively. Figure 11 showed the absorption spectra of oxygenated and deoxygenated hemoglobin in the visible and near-infrared wavelengths.24

Fig. 11

Absorption coefficients of the human oxygenated and deoxygenated hemoglobin in the visible and near-infrared regions.

054023_1_008805jbo11.jpg

3.4.

Experimental Verification of the Three-Layer Model

The experiments consisted of (i) selection of the human upper central incisors for optical measurements, (ii) transmitted optical intensity measurements in the selected sample tooth to obtain relationship between the tooth’s OD versus pulp chamber hematocrit Hctp , and to verify the accuracy of the TLM for estimation of Hctp , (iii) microscope examination of the light propagation through a tooth to provide the basis for OD versus Hctp relationships obtained in (ii), and (iv) optical measurements in human volunteers to quantify the hematocrit of the tooth using the TLM.

3.4.1.

Selection of the sample teeth

In selecting the tooth for optical measurements, the mesiodistal (MD) width and buccolingual (BL) thickness of the 25 extracted human upper central incisors free of caries, restoration, attrition, and discoloration were measured at 3mm from the cervical line (Fig. 1) using X-ray equipment, Compuray (Yoshida Dental Mfg., Co. Ltd., Tokyo, Japan). Figure 12 showed the scatter plots of the BL thickness of the pulp chamber (BLp) vs. BL thickness of the tooth (BLT) with a linear regression line BLp(mm)=0.223×BLT(mm)0.996(r=0.568,p<0.01) . Out of 25 samples, five teeth (Nos. 1–5) were selected for optical measurements. Table 1 summarized BLT and BLp of the selected five teeth. As for tooth 4, the pulp chamber was enlarged twice during the optical measurements denoted as Nos.4-1, 4-2, and 4-3, each having different pulp chamber size to see the effects of the pulp chamber size on the OD.

Fig. 12

Scatter plot between the BL thickness of the pulp chamber (BLp) versus BL thickness of the whole tooth BLT .

054023_1_008805jbo12.jpg

In order to introduce the blood into the pulp chamber, the root of all the sample teeth was cut off approximately 3.0mm from the root apex. The root canal was enlarged to 1.5mm diam, and the remnant pulp tissues were removed.

3.4.2.

Optical measurements in the selected teeth

A resin cap was prepared for each tooth to support the tooth as well as to fix the optical fibers as shown in Fig. 13 . Two plastic optical fibers ( 2.0mm diam and 1.0m length each), one for transmitting the light signal from the LED to the tooth and the other for carrying the transmitted light signal from the tooth to a photodiode located in the multiwavelength optical plethysmograph,16 were aligned perpendicular to the longitudinal axis of the tooth illuminating from the palatal surface and collecting the transmitted light from the labial surface.

Fig. 13

Experimental setup for the optical transmission measurements in a extracted model tooth.

054023_1_008805jbo13.jpg

The pulp chamber was filled with saline first to obtain the reference signal, followed by the measurement with the human blood having different Hctp . After obtaining the informed consent, 10ml of fresh human blood was withdrawn from one of the volunteers, anticoagulated with heparin ( 5000units5ml , Mochida Pharmaceutical Co., Ltd., Tokyo, Japan), centrifuged, and rinsed by phosphate buffer solution (PBS). The hematocrit of the blood was adjusted by adding PBS from 0.35, 0.30, 0.20, 0.10, 0.05, 0.03 to as low as 0.01. The optical measurements were made at 522 and 810nm wavelengths. For each wavelength, the incident light intensity V0 in voltage was derived from the LED current level, while the transmitted light intensity Vt in voltage was recorded to derive the optical density defined as OD=ln(vovc) . The OD measurements were repeated seven times for each wavelength with different LED current levels and the data were expressed as mean ± SD.

3.4.3.

Examination of the optical propagation through a tooth

Following the OD measurement, the optical propagation through a tooth was examined under a microscope to verify the experimental results obtained in Sec. 3.4.2. One of the extracted human upper central incisors was cut horizontally at the plane of the incident light Io , placed under a surgical microscope with the cut surface upward and illuminated from the palatal side with the 522nm wavelength light using an optical fiber, as shown in Fig. 14 to observe the optical propagation process in the tooth close to the cut surface. The microscope pictures of the pulp chamber being filled with (a) saline, whole blood having hematocrit of (b) 0.03, or (c) 0.30 were obtained to elucidate the causes for the OD versus Hctp curves. In addition, the blood was hemolyzed to reduce scattering and the hemoglobin solution equivalent to the cases of (b) or (c) were introduced into the pulp chamber to examine the effect of red blood cell scattering on the OD versus Hctp curves obtained in Sec. 3.4.2.

Fig. 14

Experimental setup for examining optical propagation patterns in an extracted model tooth under a microscope.

054023_1_008805jbo14.jpg

3.4.4.

Hctp estimation in the extracted model tooth

Calibration procedure

From the preliminary study we confirmed qualitative agreement between the TLM and the experimental results, but there was a discrepancy in the absolute levels. To utilize the TLM for quantification of the Hctp , the discrepancy in the absolute signal levels between the TLM and the experimental data was compensated for by using the experimental data. The OD vesus Hctp data of the reference tooth 4-2 ( 6.0mm BLT and 0.40mm BLp ), which was closest to the regression line of Fig. 12 was used to adjust the absolute OD level derived by the TLM. The gain constants for the saline and blood samples, denoted as G(0) and G(Hctp) , were both defined as follows:

Eq. 16

G(0)=ODEX4-2(Hctp=0)ODTLM4-2(Hctp=0)

Eq. 17

G(Hctp)=ODEX4-2(Hctp)ODEX4-2(Hctp=0)ODTLM4-2(Hctp)ODTLM4-2(Hctp=0).
Here, ODEX-4-2(Hctp) , ODEX-4-2(Hctp=0) corresponded to the OD measurements in tooth 4-2 as a function of Hctp and saline, respectively, while ODTLM-4-2(Hctp) , ODTLM-4-2(Hctp=0) the OD calculated by the TLM for reference tooth 4-2 as a function of Hctp and saline, respectively.

Hctp Estimation.

In obtaining Hctp estimate from the OD data measured in the selected teeth (1, 2, 3, 4-1, 4-3, and 5), the ODTLM(T,Hctp) was first calculated for each tooth (where T is the tooth number) as a function of Hctp , then its absolute level was adjusted using the gain constants as follows;

Eq. 18

ODTLM(T,Hctp)=[ODTLM(T,Hctp)ODTLM(T,Hctp=0)]G(Hctp)+ODTLM(T,Hctp=0)G(0).
In Eq. 18, ODTLM(T,Hctp) is the adjusted absolute OD level by the TLM, G(Hctp) , G(0) the gain constants defined by Eqs. 16, 17. The estimation of the Hctp was carried out graphically as shown by Fig. 15 to determine the Hctp value, where the adjusted OD curve by the TLM crossed the measured OD line. The accuracy of the method was quantified for both 522 and 810nm wavelengths for the Hctp values below 0.10.

Fig. 15

Graphical representation of how to determine Hctp estimate from the TLM calculation and experimental OD measured in a tooth.

054023_1_008805jbo15.jpg

3.4.5.

Optical measurements in human volunteers

After the protocol for human study was approved by the Institutional Review Board of the Tokyo Medical and Dental University, the optical measurements in the upper central incisor in a total of 10 volunteers were conducted using the multiwavelength TLP system (Fig. 2). Prior to the study, the purpose of the study was clearly explained and the informed consent form was signed by each volunteer. Preceding the study, a resin adaptor for each subject was fabricated to fix the optical fibers against the upper central incisor as shown in Fig. 3. The measurements were made at 522 and 810nm . The finger-tip optical plethysmogram was also recorded to obtain the heartbeat signal. The venous blood sample of 10ml was acquired from each volunteer to measure the systemic hematocrit.

The dimensions of each tooth, BL thickness, and MD width, were measured from the plaster model made prior to the study. As for the BLp , we used the linear regression equation between the BLT and BLp obtained earlier (Fig. 12). From the measured OD values in each subject, the Hctp was estimated using the methodology defined in Sec. 3.4.4. The gain constants G(0) and G(Hctp) (Eqs. 16, 17) obtained using the reference tooth data were used first to adjust the absolute levels of the OD computed by the TLM for the BLT and the estimated BLp in each subject.

4.

Results

4.1.

Experimental Verification of the Three-Layer Model

4.1.1.

OD versus Hctp in the extracted model tooth

The OD changes of tooth 4 versus Hctp were shown in Fig. 16 when the BLp was varied from 0.28, 0.40, to 0.51mm . The OD at 522nm increased greatly as the Hctp increased from 0.0 to around 7.0–8.0% with a small increase beyond that. The OD change of 810nm , on the other hand, was much milder than that of 522nm wavelength for the entire range of Hctp . As for the effects of the BLp size on the OD level, the OD increased at both 522 and 810nm wavelengths due to increased light loss when the pulp chamber was enlarged.

Fig. 16

OD versus Hctp in tooth 4 for 522 and 810nm wavelengths showing the effects of the pulp canal enlargement on the measured OD.

054023_1_008805jbo16.jpg

Figure 17 showed the OD changes versus Hctp for two different tooth samples, tooth 1 with smaller pulp chamber, while tooth 5 with a larger chamber from Fig. 12. Similar patterns were observed at both 522 and 810nm wavelengths, although the OD level of saline did not agree between the two samples due to differences in the optical characteristics of the tooth material. For a smaller pulp chamber like in tooth 1, the absolute level of the OD was smaller with less light attenuation in the pulp chamber.

Fig. 17

OD versus Hctp of two different extracted teeth showing the discrepancy in the OD level with saline in the pulp chamber.

054023_1_008805jbo17.jpg

4.1.2.

Optical propagation in a tooth

Figure 18 showed the microscope pictures of the light propagation through the tooth seen from the top as the pulp chamber was filled with (a) saline, and the blood having the Hctp of (b) 0.03 and (c) 0.30, or hemoglobin solution with hemoglobin content of (d) 1.2gdL or (e) 10.0gdL . The corresponding OD versus Hctp curves was shown in Fig. 19 to connect the external measurement to the internal optical process.

Fig. 18

Microscope pictures showing (a) optical propagation patterns with saline in the pulp chamber, (b) with 3.0% Hctp blood in the pulp chamber, and (c) with 30.0% blood in the pulp chamber. (d) and (e) show the propagation patterns when the blood of (b) and (c) was hemolyzed to reduce scattering effects.

054023_1_008805jbo18.jpg

Fig. 19

OD versus Hctp or hemoglobin content showing the effects of scattering in the extracted model tooth when the pulp chamber was filled with whole blood or hemoglobin solution.

054023_1_008805jbo19.jpg

4.2.

Accuracy of the Three-Layer Model (TLM)

4.2.1.

OD versus Hctp by the TLM

In Fig. 20 , OD versus Hctp obtained by the TLM for the wavelengths of 522 and 810nm were shown to simulate the results of tooth 4 when the BLp varied from 0.28, 0.40 to 0.51mm . The TLM results agreed qualitatively with the experimental results shown in Fig. 16.

Fig. 20

OD versus Hctp of the tooth 4 for varying pulp chamber size generated by the TLM.

054023_1_008805jbo20.jpg

4.2.2.

Hctp estimation in the extracted model tooth

Figures 21a and 21b showed the scatter plot between the Hctp estimates by the TLM versus the actual Hctp measured in the extracted model tooth at 522nm [Fig. 21a] and at 810nm [Fig. 21b]. Although the error bars increased with the increase in Hctp , the mean of the Hctp estimate versus actual Hctp showed an excellent agreement with the correlation coefficient of 0.957 (p<0.0001) for 522nm , while r=0.849 (p<0.0001) for 810nm wavelength. Figures 22a and 22b showed the mean and SD of the errors between the Hctp estimate and the actual Hctp for 522 [Fig. 22a] and 810nm [Fig. 22b] wavelengths. The mean error for 522nm was 0.00115 with SD of 0.00733, while for 810nm they were +0.09157 and 0.02493.

Fig. 21

Scatter plots between the Hctp estimate by the TLM and the Hctp actual in the extracted model tooth for (a) 522nm and (b) 810nm .

054023_1_008805jbo21.jpg

Fig. 22

Bland and Altman plots showing distribution of errors between the Hctp estimate and the Hctp actual in the extracted model teeth for (a) 522nm and (b) 810nm light-source wavelength.

054023_1_008805jbo22.jpg

4.2.3.

Hctp estimation in human volunteers

Table 4 is the summary of the in vivo measurements in a total of 10 volunteers with the mean age of 27.4 (from 25 to 35years old). There were seven males and three females. The mean BLT was 5.5mm with the mean BLp being 0.26mm . The OD of 522nm ranged from 6.163 to 7.889 with the mean of 7.054. The Hctp estimate using the TLM ranged from 0.002 to as high as 0.061 with the mean of 0.032. The estimation of Hctp using 810nm was not quite successful as 522nm , except in a few subjects.

Table 4

Summary of the in vivo optical measurements.

SubjectAgeM/FR/L BLT (nm) BLP (nm) Hsys OD Hctp Estimate BVF
522nm 810nm 522nm 810nm 522nm 810nm
A25MR5.70.280.477.3775.9450.0420.177
L6.10.360.477.4055.9740.0020.010
B25MR5.70.280.487.3455.8660.0400.168
L5.70.280.486.9855.8320.0190.4680.0771.990
C25MR5.10.140.496.3805.4540.0340.143
L5.00.120.496.4015.2960.0610.256
D25MR6.00.340.447.8726.0930.0480.218
L6.00.340.447.6226.0270.0340.156
E25ML5.00.120.486.1635.4140.0220.3670.0931.633
F26FR5.40.210.446.5375.3200.0130.3990.0581.774
G27MR5.50.230.456.6525.3090.0140.060
L5.70.280.457.3065.5240.0390.175
H29FR5.70.280.417.1855.9060.0320.155
L5.70.280.417.3695.9720.0410.200
I32FR5.00.120.426.3805.4510.0580.275
J35MR6.80.520.477.8895.7100.0070.029
Mean5.50.260.467.0545.6930.0320.4110.1411.799
S.D.0.50.110.030.5630.2890.0170.0510.0790.180
BLT : Tooth BL thickness BLP : Pulp BL thickness BVF : Bloodvessel fraction in the pulp chamber

5.

Discussion

Our preliminary experimental and theoretical studies both revealed that the transmitted-light signal changes detected from the labial side of the upper central incisor were not affected by the periodontal tissue blood flow, including gingiva and periodontal ligament. Although previous researchers14 reported that, because the tooth was surrounded by the periodontal tissue, which had abundant blood supply, the changes in the periodontal tissue blood flow might easily affect the TLP signal level, our experimental study where the silicone material was used to block the direct transmission of the light from the optical fiber placed against the palatal surface of the tooth, no statistically significant changes in both dc and ac/dc levels of the TLP signals with or without the silicone material were observed. Because the resin cap made for each volunteer had a close fit against the palatal surface, it might have helped to prevent light traveling toward the gingiva. In addition, because the newly developed TLP system employed the LED pulsed at 560Hz , the background light, including 50Hz noise, was removed to enhance the signal-to-noise ratio.16 All these factors together probably resulted in improving the overall signal-to-noise ratio.

As for the light that had entered the tooth, which had traveled toward the gingiva and periodontal ligaments and that had reflected back toward the pulp and finally toward the detector on the labial side, the Monte Carlo simulation has revealed that its effects were minimal. Of the 2×10 7 photons injected from the palatal side into the tooth, the simulation showed only five photons or 0.000025% at 522nm had reached the gingiva, reflected there, and finally reached the detector on the labial surface, while 497 photons or 0.0025% at 522nm and 876 photons or 0.0044% at 810nm , over 100times the former, traveled straight to the detector through pulp without reaching the gingiva. The Monte Carlo simulation thus demonstrated minimal effects of the gingiva on the optical transmission measurements in the TLP.

On the basis of the experimental and theoretical studies as described above, we proceeded to develop a theoretical model to quantify pulp circulation. By simplifying the tooth structure, a TLM comprising dentin-pulp chamber-dentin layers was developed to analyze optical propagation in an extracted model tooth and to quantify effective hematocrit of the blood in the pulp chamber (Hctp) . The Hctp was successfully quantified in the extracted model tooth using the 522nm OD data in the TLM equation. The TLM equation was then applied to estimate Hctp in the upper central incisors of 10 young human volunteers. The discussion here addresses (i) optical propagation in an extracted model tooth, (ii) TLM, (iii) quantification of Hctp in the model tooth, (iv) estimation of Hctp in human volunteers, and (v) assessment of dental pulp vitality from Hctp .

5.1.

Optical Propagation in an Extracted Model Tooth

The optical process in the extracted model tooth depended on the red blood cell concentration or Hctp , BLp , and the light source wavelength. The wavelength-dependent absorption and scattering by hemoglobin and red blood cells in the pulp chamber and those of dentin layer determined the relation between the tooth’s OD and Hctp . Although the OD for 810nm increased monotonously with its change of <1.0 for Hctp from 0.0 to 0.35 (Figs. 16 and 17), OD versus Hctp curve at 522nm comprised of two regions (Fig. 19), region I with Hctp <0.10 and region II with Hctp > 0.10 . In the region I, OD increased by 1.0–3.0 as Hctp increased from 0.0 to 0.10 with its rate and final level depending on the pulp chamber size, while > 0.10 it was similar to that of 810nm .

In explaining the OD versus Hctp curve of 522nm , microscope pictures of Fig. 18 and summary graph of Fig. 23 were helpful. When the pulp chamber had non-scattering fluid like saline [Figs. 18a and 23a], the light reaching the dentin-pulp chamber boundary propagated mainly in the forward direction with some photons scattered off along the boundary. The dentintubules guided the light particles toward pulp chamber as well as from pulp chamber toward labial side of the tooth. When the pulp chamber had a tenuous medium with Hctp <0.10 , photons entering the chamber were multiply scattered to propagate in all directions or absorbed by hemoglobin [Figs. 18b and 23b]. The OD level in the region I thus increased to reach a plateau as the Hctp level increased to 0.10 because the photons penetrating the pulp chamber were reduced due to scattering and absorption. The OD level at plateau depends on the amount of photons routing around the pulp chamber to reach labial side. There was a large difference in OD level between the 522 and 810nm wavelengths because of higher absorption at 522nm , 50 times the 810nm , and also larger scattering at 522nm than 810nm .

Fig. 23

Summary of optical propagation patterns in the extracted model tooth, (a) with saline in the pulp chamber, (b) with a tenuous medium in the pulp chamber, and (c) with dense medium in the pulp chamber.

054023_1_008805jbo23.jpg

In region II with Hctp > 0.10 , as shown in Figs. 18c and 23c, the light hitting the pulp chamber was completely blocked from advancing into the second dentin layer due to increased absorption as well as scattering in the pulp chamber. Only those photons that scattered off at the dentin-pulp chamber boundary and that routed around the pulp chamber probably reached the labial side. The light level at 522nm wavelength beyond Hctp of 0.10 is probably equal to the amount of photons routing around the pulp chamber. When the pulp chamber size was increased both in width and thickness, the amount of the light that was blocked by the pulp chamber increased simultaneously reducing the photons routing around the pulp chamber to consequently increase the OD level. When the pulp chamber size was narrowed to decrease the microvessel density, the OD level decreased with less attenuation of the light in the pulp chamber.

Comparison of the OD versus Hctp characteristics of the 522nm wavelength against those of 810nm , where the pulp chamber was filled with whole blood or hemoglobin solution, suggested that in the region I extremely high absorption by hemoglobin determined the characteristics of the OD versus Hctp curve at 522nm wavelength although scattering had some effects, while at 810nm wavelength the scattering was dominant in both regions, but its effect was much smaller in comparison to the absorption effect at 522nm (Fig. 19).

5.2.

TLM

In modeling the optical process in the extracted model tooth, particularly the effect of the blood volume change in the pulp chamber on the tooth’s OD, the tooth structure was simplified to a TLM comprising dentin, pulp chamber, and dentin. The enamel layer had much lower scattering properties in comparison to the dentin tubules, and thus, it was excluded from the analysis.22, 23 The guided scattering by the dentin tubules as suggested by Kiele and Hibst and demonstrated by the Monte Carlo simulation in the preliminary study21 was helpful in simplifying the model to a TLM. Although there were paths around the pulp chamber for the light to propagate, because of the tubule organization the light entering the dentin layer was mainly guided toward the pulp chamber. The microscope examination of optical process in the tooth revealed that some photons propagated along the dentin-pulp chamber boundary to exit in the second dentin layer. The light propagating in the forward direction out of the pulp chamber was then guided along the dentin tubules spreading radially toward labial side.

The two-flux model proposed by Kubelka18, 19 was utilized to obtain an analytical equation relating the OD to tooth’s dimensions, optical constants of each layer, and light-source wavelength. The optical constants of each layer were expressed by the bulk scattering and absorption constant, S and K , by assuming that each medium was optically homogeneous. For the dentin layer, the experimentally derived values were used,25 while for the pulp chamber they were derived from the red blood cell properties and Hctp . Because the scattering properties of the dentin layer depend on the dentin-tubule density, both scattering and absorption constants require adjustment from person to person.29, 30 In addition, optical properties of the model components including enamel, dentin, and pulp tissue vary with time due to growth, aging, pathological conditions, and discoloration due to surface characteristics, which, in turn, all affect the light transport through a tooth and absolute OD level.31

Concerning the boundary conditions for light transport in a complex medium, such as tooth, boundary conditions at the dentin-pulp chamber boundary need careful attention in improving the accuracy of the model, for the photons might be scattered off at the boundary depending on the ratio of the refractive indices between the dentin and pulp chamber. This effect was shown by the microscope examination where the light level at the dentin-pulp chamber boundary varied depending on the Hctp level. If we assumed the index of refraction of the dentin to be 1.50 at 522nm ,32 because that for the pulp chamber takes a value from 1.33 to 1.45 for the Hctp level varying from 0.0 to 0.30, the ratio of the dentin to pulp chamber refractive indices changes from 1.13 to 1.03, the mismatch in index of refraction becoming lesser at higher Hctp level. The ratio becomes closer to 1.0 at higher Hctp , and hence, the absorption becomes a dominant factor for attenuating the light propagation at green wavelength, while for red and near-infrared wavelengths scattering is dominant to mask absorption. Hence there is a steady but small increase in the OD level. The OD versus Hctp curves of 522 and 810nm obtained in the extracted model tooth with its pulp chamber filled with whole blood or hemoglobin solution verified wavelength-dependent effects of scattering depending on the red blood cell concentration (Fig. 19).

Although the model yielded the qualitative description of the changes in the OD as a function of Hctp and tooth dimensions, it required adjustment in the absolute level to quantify Hctp of the dental pulp. In addition to improving the optical constants of the dentin and pulp chamber, the inclusion of the boundary condition, for example, such as p1p2=(n1n2)2 at the boundary between layer 1 and 2 where p1 , p2 the photon densities and n1 , n2 , the index of refraction of the layer 1 and 2, respectively, as reported by Takatani 33 for the two-layer model, could improve the quantitative accuracy of the model.

5.3.

Quantification of Hctp in the Extracted Model Tooth

In connecting the experimental and theoretical studies, a method was developed to quantify Hctp of the extracted model tooth by utilizing the TLM equation. The difference in the absolute level between the experimental and theoretical OD was adjusted by calibrating the theoretical OD by the TLM against the experimental data of a selected reference tooth. After measuring the physical dimensions of the tooth, the tooth 4 with the BLT and BLp dimensions closest to the linear regression line of Fig. 12 was picked to obtain the gain constants required to normalize the theory to the experimental data. Although other teeth having dimensions not close to the regression line of Fig. 12 were tried, they did not yield results as good as tooth 4. For the Hctp level of <0.10 , where OD sensitivity to Hctp change was much higher at 522nm , it was possible to achieve a higher accuracy with mean error of 0.00115 , while the mean error increased to +0.09157 at 810nm because of low sensitivity of OD with respect to Hctp . As evident from the increasing SD values at higher Hctp for both 522 and 810nm wavelengths in Fig. 21, errors in Hctp estimation based on the method described here increased because of the decreased sensitivity in OD versus Hctp at higher Hctp values.

5.4.

Estimation of Hctp in Human Volunteers

In translating from the theory, to ex vivo study and finally to in vivo application, the TLM as calibrated by the ex vivo data was utilized to estimate Hctp in 10 young volunteers. As summarized in Table 4, the mean Hctp estimate in human volunteers based on the TLM was found to be 0.032 with a SD of 0.017. In our previous study,16 we speculated the Hctp in vivo from the following approximation:

Eq. 19

Hctp=HctsysHctmicroHctsysBVF
where Hctsys is the systemic large vessel hematocrit and Hctmicro is the microvessel hematocrit in the pulp chamber. Because the red blood cell concentration in the microvascular bed ranges from 46 to 53% of the larger vessels with the mean of 50% ,34 we assumed HctmicroHctsys of 0.5. As for BVF , Vongsavan and Mattheus35 reported its value to be 0.144 from the cross-sectional analysis of the cat’s canine tooth. When the BVF of 0.144, HctmicroHctsys of 0.5 and Hctsys value of each subject as determined from the blood sample were inserted in to the above equation, Hctp estimate came to be 0.032, which is very close to the Hctp estimate based on the TLM analysis. On the basis of the Hctp estimate, the mean BVF in 10 subjects came to be 0.141 with a SD of 0.079 (Table 4), showing excellent agreement with the value of 0.144 reported by Vongsavan and Matthews35

5.5.

Assessment of Pulp Vitality by Hctp

The mean Hctp of the upper central incisor of human as estimated by the TLM agreed fairly well with the theoretical speculation assuming the systemic to microvascular hematocrit ratio of 0.50 as reported in the literature.34 In addition, the effective fractional volume of the microvascular system BVF was estimated to be 0.144 and again showed excellent agreement with the value measured from the cross section of the cat’s canine tooth.35 We thus here propose a new quantity “ Hctp or BVF ” of the pulp chamber to assess microcirculatory changes related to dental pulp vitality.

On the basis of the TLP, the dental pulp vitality may be assessed using the light source wavelength in the green region most likely at the isosbestic wavelength of 522nm . The measured signal can be processed in two ways, one in the pulse mode or the other absolute mode as reported in this study. The pulse mode can diagnose rapidly changing characteristics of the vascular system or compliance of the microvascular bed synchronized with the heartbeat, while the absolute mode can uncover accumulation or depletion of the blood in the dental pulp. The clinical diagnosis of circulatory status of dental pulp based on the absolute TLP should be established through accumulation of clinical data. In addition to the measurement of the absolute and time-varying blood volume at the isosbestic wavelength of 522nm , the nonisosbestic wavelength of 467nm , where the optical absorption is dependent on the oxygenation of the blood, can provide the average tissue oxygen level from which oxygen demand of the dental pulp may be assessed.16 The determination of the blood volume shift in the pulp chamber by the isosbestic wavelength of 522nm together with tissue oxygenation possibly determined from the nonisosbestic wavelength of 467nm can provide the circulatory as well as metabolic dynamics reflecting vitality of the dental pulp.

6.

Summary and Conclusion

Following the experimental and theoretical studies to verify that the periodontal circulation had little effect on TLP measurements, a TLM comprising dentin, pulp chamber, and dentin was developed to quantify pulp chamber hematocrit Hctp of the human upper central incisors. The two-flux theory was used to derive a TLM equation in terms of tooth dimensions, pulp chamber Hctp , and light-source wavelength, while its accuracy was tested in the extracted model tooth by varying the Hctp . The optical transmission through the model tooth was measured at the isosbestic wavelengths of 522 and 810nm . Although the TLM required one-point calibration using a reference tooth, the mean error defined as ( Hctp estimate—actual Hctp ) in the model tooth was 0.00115 with SD of 0.00733 at 522nm , while at 810nm they were +0.09157 and 0.02493. The error at 810nm was one order magnitude higher than that at 522nm because of much lower sensitivity to Hctp change at this wavelength. Finally, the TLM was applied to analyze the transmitted light intensity through the upper central incisors in young human volunteers. Although the optical properties of tooth might have varied from one person to the other and with time, one-point calibration in adjusting the TLM to that of a selected extracted tooth yielded the Hctp estimate at 522nm ranging from 0.007 to as high as 0.058 with the mean of 0.032. The analysis at 810nm was not quite successful as 522nm except in a few subjects because of much lower sensitivity of the optical density measurement at this wavelength. The effective fractional microvessel volume in the pulp chamber as derived from the Hctp estimate, systemic blood hematocrit of each subject, and systemic to microvessel hematocrit ratio of 0.50 agreed well with the published result of 0.144. The noninvasive measurement of Hctp or the fractional volume of microvessels occupied in the pulp chamber quantified by the method reported in this study can possibly provide clinically useful new information to assess vitality of dental pulp.

Acknowledgments

The authors acknowledge cooperation and valuable suggestions provided by Dr. Z. Miwa, Dr. A. Kirimoto, and Dr. K. Ohuchi of Tokyo Medical and Dental University, Tokyo, Dr. T. Yasuda of Yamaguchi University, Yamaguchi, and H. Yoshihara and M. Murata of Opt-Techno Inc., Kanagawa, Japan, for their kind support of the project.

References

1. 

H. J. Fulling and J. O. Andreasen, “Influence of maturation status and tooth type of permanent teeth upon electrometric and thermal pulp testing,” Scand. J. Dent. Res., 84 286 –290 (1976). 0029-845X Google Scholar

2. 

H. Klein, “Pulp responses to an electric pulp stimulator in the developing permanent anterior dentition,” ASDC J. Dent. Child, 45 199 –202 (1978). 0022-0353 Google Scholar

3. 

D. D. Upthegrove, J. G. Bishop, and H. L. Dorman, “A method for detecting of blood flow in the dental pulp,” J. Dent. Res., 45 1115 –1119 (1966). 0022-0345 Google Scholar

4. 

G. Beer, H. Negari, and S. Samueloff, “Feline dental pulp photoplehysmography during stimulation of vasomotor nerve supply,” Arch. Oral Biol., 19 81 –86 (1974). 0003-9969 Google Scholar

5. 

B. Gazelius, L. Olgart, B. Edwall, and L. Edwall, “Noninvasive recording of blood flow in human dental pulp,” Endod. Dent. Traumatol., 2 219 –221 (1986). 0109-2502 Google Scholar

6. 

B. Gazelius, L. Olgart, and B. Edwall, “Restored vitality in luxated teeth assessed by Laser Doppler flowmeter,” Endod. Dent. Traumatol., 4 265 –268 (1988). 0109-2502 Google Scholar

7. 

J. M. Schmitt, R. L. Webber, and E. C. Walker, “Optical determination of dental pulp vitality,” IEEE Trans. Biomed. Eng., 38 346 –352 (1991). 0018-9294 Google Scholar

8. 

W. C. Nobletto, L. R. Wilcox, F. Scamman, W. T. Johnson, and A. Diaz-Arnold, “Detection of pulpal circulation in vitro by pulse oximetry,” J. Endod., 22 (1), 1 –5 (1996). 0099-2399 Google Scholar

9. 

A. K. Munshi, A. M. Hegde, and S. Radhakrishnan, “Pulse Oximetry: a diagnostic instrument in pulpal vitality testing,” J. Clin. Pediatr. Dent., 26 (2), 141 –145 (2002). 1053-4628 Google Scholar

10. 

I. Shoher, Y. Mahler, and S. Samueloff, “Dental pulp photoplethysmography in human being,” J. Oral Surg., 36 915 –921 (1973). 0022-3255 Google Scholar

11. 

M. Ikawa, H. Horiuchi, and K. Ikawa, “Optical characteristics of human extracted teeth and the possible application of photoplethysmography to the human pulp,” Arch. Oral Biol., 39 821 –827 (1994). 0003-9969 Google Scholar

12. 

A. Diaz-Arnold, L. R. Wilcox, and M. Arnold, “Optical detection of pulpal blood,” J. Endod., 20 (4), 164 –168 (1994). 0099-2399 Google Scholar

13. 

A. Diaz-Arnold, M. Arnold, and L. R. Wilcox, “Optical detection of hemoglobin in pulpal blood,” J. Endod., 22 (1), 19 –22 (1996). 0099-2399 Google Scholar

14. 

M. E. Fein, A. H. Gluskin, W. W. Y. Goon, B. B. Chew, W. A. Crone, and H. W. Jones, “Evaluation of optical methods of detecting dental pulp vitality,” J. Biomed. Opt., 2 58 –73 (1997). https://doi.org/10.1117/12.261679 1083-3668 Google Scholar

15. 

Z. Miwa, M. Ikawa, H. Iijima, M. Saito, and Y. Takagi, “Pulpal blood flow in vital and nonvital young permanent teeth measured by transmitted light photoplethysmography: A pilot study,” Pediatr. Dent., 24 (6), 594 –598 (2002). 0164-1263 Google Scholar

16. 

S. Kakino, Z. Miwa, A. Kirimoto, K. Ohuchi, S. Takatani, and Y. Takagi, “A new multi-wavelength optical plethysmograph for quantitative determination of pulpal hemoglobin content and oxygen level using green and near-infrared LEDs,” Proc. SPIE, 6425 642508 (2007). https://doi.org/10.1117/12.699628 0277-786X Google Scholar

17. 

L. Wang, L. S. Jacques, and L. Zheng, “MCML—Monte Carlo modeling of light transport in multi-layered tissues,” Comput. Methods Programs Biomed., 47 131 –146 (1995). https://doi.org/10.1016/0169-2607(95)01640-F 0169-2607 Google Scholar

18. 

P. Kubelka, “New contribution to the optics of intensely light-scattering materials. Part I,” J. Opt. Soc. Am., 38 457 –448 (1948). 0030-3941 Google Scholar

19. 

P. Kubelka, “New contributions to the optics of intensely light-scattering materials. Part II: Nonhomogeneous layers,” J. Opt. Soc. Am., 44 (4), 330 –335 (1954). 0030-3941 Google Scholar

20. 

A. Kienle, R. Michels, and R. Hibst, “Magnification—A new look at a long-known optical property of dentin,” J. Dent. Res., 85 (10), 955 –959 (2006). 0022-0345 Google Scholar

21. 

A. Kiele and R. Hibst, “Light guiding in biological tissue due to scattering,” Phys. Rev. Lett., 97 018104 (2006). https://doi.org/10.1103/PhysRevLett.97.018104 0031-9007 Google Scholar

22. 

D. Spitzer and J. J. T. Bosch, “The absorption and scattering of light in bovine and human dental enamel,” Calcif. Tissue Res., 17 129 –137 (1975). 0008-0594 Google Scholar

23. 

J. R. Zijp and J. J. T. Bosch, “Theoretical model for the scattering of light by dentin and comparison with measurements,” Appl. Opt., 32 (4), 411 –415 (1993). 0003-6935 Google Scholar

24. 

B. L. Horecker, “The absorption spectra of hemoglobin and its derivatives in the visible and near infrared regions,” J. Biol. Chem., 48 173 –183 (1943). 0021-9258 Google Scholar

25. 

D. Fried, R. E. Glena, J. D. B. Featherstone, and W. Seka, “Nature of light scattering in dental enamel and dentin at visible and near-infrared wavelengths,” Appl. Opt., 34 (7), 1278 –1285 (1995). 0003-6935 Google Scholar

26. 

V. Twersky, “Absorption and multiple scattering by biological suspensions,” J. Opt. Soc. Am., 60 (8), 1084 –1093 (1970). 0030-3941 Google Scholar

27. 

J. Bartminn, “Design and evaluation of a hybrid optical reflectance oxygen saturation and haemoglobin content sensor for mechanical total artificial heart control,” Aachen Technical University, (1998). Google Scholar

28. 

S. Takatani, “On the theory and development of a noninvasive tissue reflectance oximeter,” Case Western Reserve University, (1979). Google Scholar

29. 

J. J. ten Bosch and J. R. Ziip, A. Thylstrup, S. A. Leach, and V. Qvist, “Optical properties of dentin,” Dentin and Dentin Reactions in the Oral Cavity, 59 –65 IRL Press, Oxford (1987). Google Scholar

30. 

J. Vaarkamp, J. J. ten Bosch, and E. H. Verdonshot, “Propagation of light through human dental enamel and dentin,” Caries Res., 29 (8), 8 –13 (1995). 0008-6568 Google Scholar

31. 

J. J. ten Bosch and J. C. Coops, “Tooth color and reflectance a related to light scattering and enamelhardness,” J. Dent. Res., 74 (1), 374 –380 (1995). 0022-0345 Google Scholar

32. 

X. J. Wang, T. E. Milner, J. F. deBoer, Y. Zhang, D. H. Pashley, and J. S. Nelson, “Characterization of dentin and enamel by use of optical coherence tomography,” Appl. Opt., 38 (10), 2092 –2096 (1999). 0003-6935 Google Scholar

33. 

S. Takatani and M. D. Graham, “Theoretical analysis of diffuse reflectance from a two-layer tissue model,” IEEE Trans. Biomed. Eng., 216 (12), 656 –664 (1979). 0018-9294 Google Scholar

34. 

B. W. Zweifach and H. H. Lipowsky, E. M. Renkin, C. C. Michel, and S. R. Geiger, “Pressure-flow relations in blood and lymph microcirculation,” Handbook of Physiology: Cardiovascular System, 4 251 –307 American Physiological Society, Bethesda (1984). Google Scholar

35. 

N. Vongsavan and B. Matthews, “The vascularity of dental pulp in cats,” J. Dent. Res., 71 (12), 1913 –1915 (1992). 0022-0345 Google Scholar
©(2008) Society of Photo-Optical Instrumentation Engineers (SPIE)
Satoko Kakino D.D.S., Yuzo Takagi, and Setsuo Takatani "Absolute transmitted light plethysmography for assessment of dental pulp vitality through quantification of pulp chamber hematocrit by a three-layer model," Journal of Biomedical Optics 13(5), 054023 (1 September 2008). https://doi.org/10.1117/1.2976112
Published: 1 September 2008
JOURNAL ARTICLE
18 PAGES


SHARE
Advertisement
Advertisement
Back to Top