Hindawi Publishing Corporation
Journal of Medical Engineering
Volume 2013, Article ID 161090, 9 pages
http://dx.doi.org/10.1155/2013/161090
Research Article
Spectroscopic Detection of Caries Lesions
Mika Ruohonen,1 Katri Palo,2 and Jarmo Alander1
1 Faculty of Technology, University of Vaasa, P.O. Box 700, 65101 Vaasa, Finland
2Dental Services of the City of Vaasa, Social and Health Administration, P.O. Box 241, 65101 Vaasa, Finland
Correspondence should be addressed to Mika Ruohonen; mika.ruohonen�uwasa.�
Received 30 August 2012; Accepted 6 November 2012
Academic Editor: Hengyong Yu
Copyright © 2013 Mika Ruohonen et al. is is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly
cited.
Background. A caries lesion causes changes in the optical properties of the affected tissue. Currently a caries lesion can be detected
only at a relatively late stage of development. Caries diagnosis also suffers from high interobserver variance.Methods. is is a pilot
study to test the suitability of an optical diffuse re�ectance spectroscopy for caries diagnosis. Re�ectance visible/near-infrared
spectroscopy (VIS/NIRS) was used to measure caries lesions and healthy enamel on extracted human teeth. e results were
analysed with a computational algorithm in order to �nd a rule-based classi�cation method to detect caries lesions. Results. e
classi�cation indicated that the measured points of enamel could be assigned to one of three classes: healthy enamel, a caries lesion,
and stained healthy enamel. e features that enabled this were consistent with theory. Conclusions. It seems that spectroscopic
measurements can help to reduce false positives at in vitro setting. However, further research is required to evaluate the strength of
the evidence for the method’s performance.
1. Introduction
Minimally invasive dentistry is an approach that seeks to
maintain the patient’s oral health with preventive measures
and to treat possible disturbances of health as early as possible
and with as little intervention as possible [1]. is requires
that caries is detected at an early stage of development and
that its status can be monitored frequently [2]. However, the
currentmethods for diagnosing caries are able to detect caries
only at a relatively advanced stage. Accordingly, methods for
early detection of caries have been researched for the past
twenty years. Many of these methods still require extensive
research before they can be used in clinical practice. Optical
caries diagnosis methods are based on the fact that caries
cause changes in the tooth’s optical properties at an early stage
of development [3].
is was a pilot study to investigate whether diffuse
re�ectance visible/near-infrared spectroscopy (VIS/NIR-S)
can be used to detect dental caries lesions. Re�ectance spec-
troscopy measures the intensity of light at several different
wavelengths, that is, its spectra, a�er the light has re�ected
from the studied ob�ect. Diffuse re�ectance refers to light that
has been re�ected from the inside of the ob�ect, rather than
from its surface. In this study the intensity was measured
at wavelengths in the visible range and at wavelengths in
the near-infrared range, covering wavelengths in the range
420–1000 nanometers. Within this range, the intensity was
measured at 2305 different wavelengths, so that the differ-
ence between consecutive wavelengths was approximately
0.25 nm. is study was limited to studying natural caries
lesions that could be diagnosed with �ber-optic illumination,
on smooth surfaces of extracted tooth.
A theory of caries diagnosis using near-infrared spec-
troscopy emerges from the previous studies of detecting
caries lesions with near-infrared light [2–7]. According to
this theory, the development of a caries lesion increases
the porosity of the affected tissue, which in turn leads to
an increased scattering of light in the lesion. Wavelengths
in the near-infrared range are considered better than the
wavelengths in the visible range, because the former can
penetrate deeper into the tissue and are less affected by
stains on the tooth. e purpose of this study was to provide
additional evidence in support of this theory. More work on
this topic can be found in [8–15].
2 Journal of Medical Engineering
Probe
Fiber optic
Diffuse reflectance
Spectroscope
Light source
F 1: An illustration of the measurement setup.
2. Methods
2.1. Samples. e dental services of the City of Vaasa pro-
vided extracted human teeth for the study. e teeth were
stored immersed in denatured alcohol in order to disinfect
them and to keep them hydrated. Before inspection and
measurements, the teeth were gently dried with a cue tip.
e teeth were inspected by the �rst author with �ber-optic
illumination, aer the technique was introduced to him by
the second author, in order to detect healthy areas of enamel
and areas of enamel that contained caries lesions.
In total 21 teeth were used in the study. A total of 109
points of enamel were measured on the teeth, consisting of
69 points which were thought to represent healthy enamel
and 40 points which were thought to represent caries lesions.
Eachmeasurement point produced a spectra, a sample for the
rest of the analysis. In pattern recognition terminology the
diagnosis of a given sample, as either healthy or carious, is
called the label of the sample.e analysis of the samples tries
to create a method which estimates the diagnosis, the label,
of the sample based only on the measurements.e resulting
estimates are called predictions.
2.2. Measurements. e measurement setup is presented in
Figure 1. An optical �ber, placed in contact with the sample,
conveys light from a light source to the sample. e light
enters the sample and scatters to all directions inside of it.
Another optical �ber is placed in contact with the sample
at a small distance from the �rst �ber. Some fraction of the
light which scatters inside the sample will eventually exit the
sample so that it enters the second optical �ber. It then gets
conveyed to a spectrometer, which measures the spectra of
the re�ected light. Properties of the sample material affect
the measured spectra. Photonics describes the key properties
with the absorption coefficient and the scattering coefficient
of the material. e measured spectra is analyzed in order to
deduce information about the sample material.
e measurements were made with a spectrometer
HR4000 (Ocean Optics Inc., Dunedin, FL, USA) and with
a general purpose transmission dip probe model T300-RT-
VIS/NIR (Ocean Optics Inc., Dunedin, FL, USA). e probe
contains two optical �bers, both with a diameter of 300𝜇𝜇m,
housed in a stainless steel assembly with a diameter of
3.175mm. e assembly is surrounded by a ferrule with a
diameter of 6.35mm. One of the �bers is connected to a light
source and brings light to the sample. e light source used
in this study was a tungsten halogen lamp HL-2000 (Ocean
Optics Inc., Dunedin, FL, USA).e other �ber is connected
to the spectrometer. It collects and transmits the diffusely
re�ected light. Construction of a custom probe for this study
was deemed unfeasible. us, the study had to be carried out
with a probe that was readily available in our laboratory. e
selected probe is designed for measuring the transmission
spectra of liquid samples. However, it was considered to be
suitable for this study when the ferrule enclosing the inner
assembly was removed, exposing the stainless steel assembly
that houses the �ber optics.
e period of time for which the spectrometer collects
light when it is making one measurement is called the
integration time. In this study integration time was set to
20milliseconds. A longer integration time produces better
measurement results than a short one, because the intensity
of the collected light increases at all wavelengths, yielding a
better signal-to-noise ratio (SNR). erefore, the integration
time is typically set as long as possible. However, if the
intensity of the collected light at a given wavelength exceeds
themeasurement range of the spectrometer, the spectrometer
saturates. In that case the intensity cannot be measured, and
we know only that it exceeded the maximum measurable
value.
In order to make the measurement results comparable
to results that would have been obtained with the same
spectroscope using another light source or another integra-
tion time, the spectroscope has to be calibrated for these
factors. is is done by measuring the smallest and the
greatest intensity value that a measurement can produce
with the given integration time for each wavelength and
by scaling all other measurements to that range. is gives
values between zero and one for all wavelengths.ese scaled
results are called normalized intensities. e lowest possible
intensity values are obtained by measuring the so-called dark
current, which is caused by thermal noise. Measuring a white
reference sample produces the greatest possible intensity
values. In this study, the integration time was set so that
the white reference sample (a white reference tile WS-2,
Avantes Inc., Eerbeek, e Netherlands) did not saturate at
any wavelength. A spectrometer must also be calibrated for
its detector, so that its measurement results are comparable
to those obtained by other spectroscopes. is is done by
measuring the spectra of a sample whose spectra is known. In
this study the used spectroscopewas calibrated for its detector
by the manufacturer as part of its construction.
A spectroscopicmeasurement result containsmany small
random errors, which are collectively called (thermal) noise.
ese errors are caused by heat, or thermal energy, in the
spectroscope. ey follow a normal distribution with a given
mean value. e dark current presents the mean value of
the noise for each wavelength. When the dark current is
subtracted from the spectra, the mean value of the effect
caused by the noise is shied to zero, and thus the effect of
noise is observed as errors which have a normal distribution
with a zero mean. In order to minimize the effect of noise
in the samples, each point was measured one hundred times
Journal of Medical Engineering 3
consecutively, and the resulting spectra were averaged. is
meant that the probe needed to stay as motionless as possible
for two seconds. However, a far shorter time period would
have probably been sufficient.
2.3. Analysis. As a furthermeasure against noise, the samples
were smoothed by using the Savitzky-Golay method with
a window length of 61 and sixth degree polynomials. is
method selects the coefficients of a sixth degree polynomial
so that the polynomial is the best possible approximation
for the measurement result, that is, the spectra, for the
30 wavelengths before a given wavelength and for the 30
wavelengths aer it. e value of the polynomial at the
given wavelength replaces the measured intensity at that
wavelength. is removes, or smoothens, fast and small
changes in the spectra, which are mainly caused by noise.
A simple computational algorithm, based on exhaustive
search, was then used to �nd a set of rules that could be
used for detecting caries lesions. At this point, the goal
was to classify the samples into two classes: points on
healthy enamel (healthy samples) and points on caries lesions
(carious samples). For this, a set of rules was searched for,
so that every rule had the following format: if the sample’s
normalized intensity at a given wavelength 𝜆𝜆 is greater than
(or smaller than) a given threshold 𝐼𝐼⋆, the sample is classi�ed
as carious� otherwise, the sample is classi�ed as healthy.
us, each rule had three parameters: the wavelength 𝜆𝜆, the
intensity threshold 𝐼𝐼⋆, and whether or not the threshold is an
upper or lower limit for the intensity. If, and only if, one or
more of the rules classi�ed the sample as carious, the sample
was classi�ed as carious. If none of the rules considered the
sample as carious, it was classi�ed as healthy. A pseudocode
for this step is given in Pseudocode 1. It was hoped that the
algorithm would select a set of rules which resembles the
results found in earlier studies on this subject.
A number of wavelengths were selected from the range
of available wavelengths (≈420–1000 nm) as options for
parameter 𝜆𝜆 in the search, so that the intervals between
the wavelengths were equal and the �rst and the last wave-
length were always selected as options. A pseudo-code for
this is given in Pseudocode 2. e search was done with
different numbers of wavelengths. For each of the selected
wavelengths, the algorithm sorted the samples’ intensities at
that wavelength and considered the midpoint between each
two consecutive intensities as a possible threshold 𝐼𝐼⋆ in a rule.
A pseudo-code for this is given in Pseudocode 3.
e algorithm calculated the classi�cation accuracy on
the training set for each of the pairs 𝜆𝜆 and 𝐼𝐼⋆ described above,
using the threshold 𝐼𝐼⋆ �rst as an upper limit for classifying
the sample as carious and then using it as a lower limit,
and chose the values of 𝜆𝜆 and 𝐼𝐼⋆ and the type of threshold,
which gave the best accuracy (see pseudo-code at Pseudocode
4). Aer a rule had been selected this way, the algorithm
selected another rule with the same method, so that the
new rule gave the best possible accuracy when used together
with the previously selected rule(s). is was continued until
the maximum allowed number of rules, here �ve rules, was
reached, or until the classi�er was unable to �nd a new rule
which would improve the classi�cation accuracy. A pseudo-
code for this logic is given in Pseudocode 5.
is algorithm, like every machine learning method,
requires a set of samples which is used for searching for
the rules and a separate set of samples which is used for
evaluating the accuracy that is achieved with the resulting
rules. e former set of samples is called the training set
and the latter set is called the validation set. e number of
samples available for this study was rather limited. is may
cause problems for the machine learning method when the
samples are divided into a training set and a validation set,
because some types of samples may become overrepresented
in the training set, misleading the learning method as it tries
to recognize what discerns the two classes from each other.
In this study, this risk was alleviated by using a 4-fold
cross-validation. In this method, the samples are divided into
four groups, and one of them is used as the validation set
while the other three groups form the training set. Each group
in turn is used as the validation set, and the results from these
four “folders” are averaged. is way each sample is a part of
the training set in three folders and a part of the validation
set in one folder. It is unlikely that the same types of samples
would be overrepresented in all four training sets, unless the
entire set of available samples has this problem. A single
training set which has this problem would stand out from
the others, and the skewed learning results from it would be
corrected by the results from the other training sets. While
the small set of samplesmay still give a skewed representation
of the kinds of samples which are being studied, the cross-
validation seeks to minimize this problem.
In this study the averaging was done so, that a median
rule set was constructed from the rules which the algorithm
selected for the folders, and all of the samples were then
classi�ed with the median rule set. Median of the numbers
of rules in the folders determined the number of rules in the
median rule set. Some manual deliberation was used when
constructing the rules of the set. For each rule in the �nal set,
a temporary rule set was composed by selecting one rule from
each folder’s rule set, so that the rules in the temporary set
resembled each other, if that was possible given the available
rules. e median of the wavelengths used in the rules in the
temporary rule set determined the wavelength for the rule in
the median rule set. e intensity threshold and the type of
threshold were selected similarly for the rule in the median
rule set. A pseudo-code for this is given in Pseudocode 6.
Each samplewas diagnosed as either healthy or carious by
the �rst author, and the selected rules estimated each sample
to be either healthy or carious. Based on these two properties,
the samples can be divided into four classes. Samples which
were diagnosed as healthy and which were estimated to be
healthy by the rules are called true negatives (TNs). Similarly,
carious samples which were correctly estimated are called
true positives (TPs). A healthy sample which was estimated
to be carious is called false positive (FP) and a carious
sample which was estimated to be healthy is called a false
negative (FN).e sizes of these classes comprise a confusion
matrix, or a contingency table. ese four values can be
used to calculate the following �ve values which describe the
accuracy of the selected rules.
4 Journal of Medical Engineering
C(𝑅𝑅, 󵱁󵱁𝑥𝑥)
(1) // Classify sample 󵱁󵱁𝑥𝑥 using the set of rules 𝑅𝑅
(2) for 𝑖𝑖 𝑖 1 to 𝑅𝑅.length
(3) 𝑡𝑡 𝑖 𝑅𝑅𝑡𝑖𝑖𝑡.limitreshold // reshold intensity 𝐼𝐼⋆
(4) 𝑗𝑗 𝑖 𝑅𝑅𝑡𝑖𝑖𝑡.limitIndex // Index of wavelength 𝜆𝜆𝑖𝑖
(5) if 𝑅𝑅𝑡𝑖𝑖𝑡.limitType 𝑖𝑖 U and 𝑥𝑥𝑗𝑗 > 𝑡𝑡
(6) return (+1)
(7) elseif 𝑅𝑅𝑡𝑖𝑖𝑡.limitType 𝑖𝑖 L and 𝑥𝑥𝑗𝑗 < 𝑡𝑡
(8) return (+1)
(9) return (−1) // No rule indicated sample as positive
P 1: Pseudocode for classifying a sample. Samples in the positive class are carious, and samples in the negative class are healthy.
A sample 󵱁󵱁𝑥𝑥 is a vector, where each component 𝑥𝑥𝑖𝑖 equals the normalized intensity at a given wavelength 𝜆𝜆𝑖𝑖.
G-W-I(𝑋𝑋, 𝑖𝑖)
(1) // Get the 𝑖𝑖th wavelength option for a rule, given a set of samples𝑋𝑋
(2) // For �rst wavelength, 𝑖𝑖 𝑖 1
(3) 𝑠𝑠 = (X.maxWavelength − X.minWavelength)/WOC
(4) 𝜆𝜆 = X.minWavelength + 𝑠𝑠(𝑖𝑖− 1)
(5) // Get the index of the measured wavelength 𝜆𝜆𝑖𝑖, which is closest to 𝜆𝜆
(6) 𝑗𝑗 = C-I(𝜆𝜆)
(7) return 𝑗𝑗
P 2: Pseudocode for computing the 𝑖𝑖th wavelength option for a rule.
(i) Positive predictive value (PPV) is the probability that
the classi�er, that is, the set of rules, is correct when it
estimates a sample to be carious.
(ii) Negative predictive value (NPV) is the probability
that a healthy estimate is correct.
(iii) Sensitivity is the fraction of all carious samples that
were classi�ed as carious.
(iv) Speci�city is the fraction of healthy samples that were
classi�ed as healthy.
(v) Accuracy is the fraction of the samples which were
correctly estimated, that is, where the rules gave the
correct answer.
2.4. Two Hypotheses of Misdiagnosis. A�er the classi�cation
rules had been selected and the samples had been classi�ed
according to them, there were ��een samples which the
author had diagnosed as carious but which were classi�ed as
healthy (false negatives). e spectra of these samples were
virtually indistinguishable from the spectra of the healthy
samples (see Figure 3(a)), at least for the analysis methods
used in this study. us, a hypothesis was made that these
samples, the false negative cases, had been misdiagnosed by
the author and subsequently mislabeled.
e rules that were selected by the algorithm suggested
that a short wavelength, namely, 420 nm, was relatively useful
in the diagnosis of caries. is was inconsistent with the
theory on the optical diagnosis of caries. erefore, another
hypothesis was made, according to which a number of
samples had been diagnosed by the author as carious while
in fact the measured points were only stained and were
thus false positive cases of the diagnosis, even if they had
been classi�ed correctly by the classi�er. A pair of rules was
manually selected in order to detect such stained samples.
ese rules were 𝐼𝐼(𝜆𝜆 𝐼 42𝐼) 𝐼 𝐼𝐼2𝐼6 𝐼 𝐼𝐼(𝜆𝜆 𝐼 815) 𝐼 𝐼𝐼313.
Notation 𝐼𝐼(𝜆𝜆) refers to the normalized intensity of the spectra
at wavelength 𝜆𝜆. In other words, the sample was thought to
represent a stain if it had a small scattering coefficient at
both a longwavelength (815 nm,which is in the near-infrared
range) and a short wavelength (420 nm). Application of these
rules identi�ed eight samples as being misdiagnosed due to a
stain.
3. Results
e samples, or the spectra of the measured points, are
presented in Figure 2. e number of wavelengths which
were selected as options for the rule’s parameter 𝜆𝜆, that is,
parameter WOC, had only a small
effect on the accuracy of the resulting median rule set. When
only the shortest wavelength (𝐼420 nm) and the longest
wavelength (𝐼1000 nm)were available as options, themedian
rule set had an accuracy of 82%. With three wavelengths to
choose from, the accuracy was 83%. When the number of
optionswas between four and six, the accuracywas 85%.With
greater numbers of wavelengths available, the accuracy was
84%.
e selected rules were very similar in all folders. is
suggested that the rules depicted a phenomenon which was
consistently present in all four folders. When the number of
options for the rules’ wavelengths was 15, the median rule
Journal of Medical Engineering 5
G-T(𝑋𝑋, 𝜆𝜆′)
(1) // Get the threshold options for a rule, given a set of samples𝑋𝑋 and
(2) // an index of wavelength.
(3) // Use local variables, arrays 𝐴𝐴 and𝑀𝑀
(4) for 𝑖𝑖 𝑖 1 to X.sampleCount
(5) 𝐴𝐴𝐴𝑖𝑖𝐴 =𝑋𝑋𝐴𝑖𝑖𝐴𝐴𝜆𝜆′𝐴 // Intensity at 𝜆𝜆𝑖𝑖 for sample 󵱂󵱂𝑥𝑥𝑖𝑖
(6) 𝐴𝐴 = S(𝐴𝐴) // Ascending or descending
(7) for 𝑖𝑖 𝑖 1 to A.length − 1
(8) 𝑀𝑀𝐴𝑖𝑖𝐴 = (𝐴𝐴𝐴𝑖𝑖𝐴 + 𝐴𝐴𝐴𝑖𝑖 𝐴 1𝐴)/2
(9) return 𝑀𝑀
P 3: Pseudocode for computing the threshold options for a rule at a given measured wavelength 𝜆𝜆𝑖𝑖. �e wavelength is de�ned by
its index, 𝜆𝜆′ 𝑖 𝑖𝑖.
F-N-R(𝑅𝑅,𝑋𝑋)
(1) // Select a new rule, given a set of rules 𝑅𝑅 and a set of samples𝑋𝑋
(2) // Use local variables, rules𝑄𝑄 and 𝐵𝐵
(3) 𝑏𝑏 = 0.0 // Best accuracy found so far
(4) for 𝑖𝑖 𝑖 1 to WOC + 1
(5) 𝜆𝜆′ = G-W-I(𝑋𝑋, 𝑖𝑖)
(6) 𝑄𝑄.limitIndex = 𝜆𝜆′ // Rule’s wavelength 𝜆𝜆, by index
(7) 𝑇𝑇 = G-T(𝑋𝑋, 𝜆𝜆′)
(8) for 𝑗𝑗 = 1 to 𝑇𝑇.length
(9) 𝑄𝑄.limitreshold = 𝑇𝑇𝐴𝑗𝑗𝐴 // Rule’s threshold intensity 𝐼𝐼⋆
(10) 𝑄𝑄.limitType = U
(11) 𝑎𝑎 = C-S(𝑅𝑅 +𝑄𝑄,𝑋𝑋) // Classi�cation accuracy
(12) if 𝑎𝑎 𝑎 𝑏𝑏
(13) 𝐵𝐵 𝑖 𝑄𝑄
(14) 𝑏𝑏 𝑖 𝑎𝑎
(15) 𝑄𝑄.limitType = L
(16) 𝑎𝑎 = C-S(𝑅𝑅 +𝑄𝑄,𝑋𝑋) // Classi�cation accuracy
(17) if 𝑎𝑎 𝑎 𝑏𝑏
(18) 𝐵𝐵 𝑖 𝑄𝑄
(19) 𝑏𝑏 𝑖 𝑎𝑎
(20) return𝐵𝐵 // Best new rule found
P 4: Pseudocode for selecting a new rule.
S-R(𝑋𝑋)
(1) // Select the set of rules for given set of samples𝑋𝑋
(2) // Use local variable, set of rules 𝑅𝑅
(3) 𝑎𝑎 𝑖 0𝑎0 // Accuracy with current set of rules
(4) 𝑅𝑅 𝑖 𝑅 // Current set of rules
(5) for 𝑖𝑖 𝑖 1 to MRC
(6) 𝐵𝐵 = F-N-R(𝑅𝑅,𝑋𝑋)
(7) 𝑏𝑏 = C-S(𝑅𝑅 𝐴 𝐵𝐵,𝑋𝑋) // Classi�cation accuracy
(8) if 𝑎𝑎 𝑎 𝑏𝑏
(9) return 𝑅𝑅 // New rule did not help
(10) 𝑅𝑅 = 𝑅𝑅 + 𝐵𝐵 // Add new rule to set
(11) 𝑎𝑎 𝑖 𝑏𝑏
(12) return 𝑅𝑅
P 5: Pseudocode for selecting the set of rules. Here𝑋𝑋 is the set of training samples and MRC = 5.
6 Journal of Medical Engineering
C-M-R(𝑆𝑆)
(1) // Compose median rule set from given set of rule sets 𝑆𝑆
(2) // 𝑆𝑆 = (𝑅𝑅1, 𝑅𝑅2,…, 𝑅𝑅𝑛𝑛), 𝑛𝑛 = FC
(3) // Use local variables, sets of rules𝑀𝑀 and 𝑇𝑇, and rule𝑄𝑄
(4) 𝑀𝑀 𝑀 𝑀
(5) 𝑁𝑁 = M(𝑅𝑅1.length, 𝑅𝑅2.length,…, 𝑅𝑅𝑛𝑛.length)
(6) for 𝑖𝑖 𝑀 1 to 𝑁𝑁
(7) // Compose temporary rule set, 𝑇𝑇 = (𝑇𝑇1, 𝑇𝑇2,⋯,𝑇𝑇𝑛𝑛)
(8) // If possible, have 𝑇𝑇1 ≈ 𝑇𝑇2 ≈ … ≈ 𝑇𝑇𝑛𝑛
(9) // Each rule in 𝑅𝑅 𝑅 𝑆𝑆 appears in at most one temporary rule set 𝑇𝑇
(10) 𝑇𝑇 = C-T-S(𝑆𝑆)
(11) 𝑄𝑄.limitIndex = M(𝑇𝑇1.limitIndex,…, 𝑇𝑇𝑛𝑛.limitIndex)
(12) 𝑄𝑄.limitreshold = M(𝑇𝑇1.limitreshold,…, 𝑇𝑇𝑛𝑛.limitreshold)
(13) 𝑄𝑄.limitType = M(𝑇𝑇1.limitType,…, 𝑇𝑇𝑛𝑛.limitType)
(14) 𝑀𝑀 𝑀 𝑀𝑀 𝑀 𝑄𝑄
(15) return 𝑀𝑀
P 6: Pseudocode for computing the median rule set. In this study FC = 4.
1
0.8
0.6
0.4
0.2
0
500 600 700 800 900
Wavelength
N
o
rm
al
iz
ed
 i
n
te
n
si
ty
F 2: e samples, that is, the spectra of the measured points.
e blue curves depict samples whichwere diagnosed as healthy and
the red curves depict samples which were diagnosed as carious.
set indicated that a sample is carious if, and only if, 𝐼𝐼(𝐼𝐼 ≈
420) ≤ 0.2642 ∨ 𝐼𝐼(𝐼𝐼 ≈ 750) 𝐼 0.3502. A confusion matrix
of the classi�cation accuracy that is achieved with these rules
is presented in Table 1, showing that these rules reached an
accuracy of 84%.
As can be seen in Figure 3(a) and in Table 1, there were
��een carious samples which were classi�ed as healthy (false
negatives), and whose spectra was virtually indistinguishable
from the spectra of the healthy samples. As explained in
Section 2.4, this leads to a hypothesis that these samples had
been misdiagnosed and subsequently mislabeled, and that
they therefore represented healthy samples and were in fact
classi�ed correctly.
According to the theory on optical caries diagnosis, an
elevated intensity in the near-infrared range is the best indi-
cation of a dental caries lesion. However, the rules selected
T 1: e confusion matrix, or the contingency table, of the
median rule set.
Carious Healthy
Estimated carious 25 (TP) 2 (FP) 93% (PPV)
Estimated healthy 15 (FN) 67 (TN) 82% (NPV)
63% (Sens.) 97% (Spec.) 84% (Acc.)
by the search algorithm indicated that a short wavelength,
namely, 420 nm, was relatively useful in the diagnosis of
caries. As explained in Section 2.4, another hypothesis was
thusmade, according to which a number of samples had been
diagnosed as carious while in fact they were only stained. A
pair of rules was manually selected in order to detect such
stained samples.
Application of these rules identi�ed eight samples as
being misdiagnosed due to a stain. All samples that were
identi�ed as stained had been diagnosed and classi�ed as
carious, and thus appeared to be true positive cases. ese
suspected misdiagnoses had not lowered the apparent accu-
racy of the classi�cation, but they may have caused the rule
set to erroneously consider stains as caries lesions.
When the search algorithm was run again, giving 15
options for the parameter 𝐼𝐼, a�er �rst relabeling the ��een
false negative cases as healthy samples (�rst hypothesis) and
then relabeling the eight suspected stains as healthy samples
(second hypothesis), the algorithm selected only one rule in
every cross-validation folder. All rules set an upper limit for
the normalized intensity at a wavelength in the near-infrared
range. If the intensity was greater than this, the sample was
classi�ed as carious. e median of those rules was 𝐼𝐼(𝐼𝐼 ≈
791) 𝐼 0.3255, which is consistent with the theory. e
confusionmatrix of this rule is presented in Table 2.is rule
produced an accuracy of 97%.
Journal of Medical Engineering 7
1
0.8
0.6
0.4
0.2
0
500 600 700 800 900
Wavelength
N
o
rm
al
iz
ed
 i
n
te
n
si
ty
(a)
1
0.8
0.6
0.4
0.2
0
500 600 700 800 900
Wavelength
N
o
rm
al
iz
ed
 i
n
te
n
si
ty
(b)
F 3: Samples which were classi�ed (a) as healthy and (b) as
carious by themedian rule set. Blue curves represent healthy samples
and red curves represent carious samples. e samples which were
diagnosed as carious but classi�ed as healthy (false negatives) are
emphasized.
T 2: e confusion matrix, or the contingency table, for the
median rule (set) which was selected aer relabeling the samples
according to the two hypotheses of misdiagnosis.
Carious Healthy
Estimated carious 14 (TP) 0 (FP) 100% (PPV)
Estimated healthy 3 (FN) 92 (TN) 97% (NPV)
82% (Sens.) 100% (Spec.) 97% (Acc.)
4. Discussion
is study suffers from a small number of samples. Although
the study used 109 measurements, they were taken from
only 21 individual teeth. is fact is signi�cant, because it
is probable that samples taken from a single tooth resemble
each other more than samples taken from different teeth or
from different patients. Furthermore, the 109 measurements
contained only 40 measurements from a caries lesion. Fieen
of those measurements were considered to be misdiagnosed
by the �rst hypothesis, and further eight measurements were
considered to be misdiagnosed by the second hypothesis.
erefore, further study is needed to increase the reliability
of the accuracy estimate of this method.
e measurement results together with the theory on the
topic suggest that many of the measurements which were
supposedly made from a caries lesion are in fact made from
healthy enamel, which was in some cases stained. When
we make these suggested corrections to the labeling of the
samples, the samples seem to �t well to the theory and the
samples can easily be accurately classi�ed. ese kinds of
diagnostic mistakes, or false positive diagnoses, are a credible
explanation, because the diagnoses were made by a novice
on the subject. However, such corrections also pose a risk
that the measurement results are relabeled to make them �t
the theory, which would in�ate the accuracy of the method.
Further study of the method might dispel such possibilities.
e composition of the dental tissues varies from tooth
to tooth and between different sites of a given tooth [16].
As can be seen in Figure 2, the spectra of the different
healthy samples vary quite a bit, especially at the visible
wavelengths. is suggests that the threshold intensity or
intensities for diagnosing a suspected lesion as carious might
also vary similarly. In order to compensate for the inter-tooth
and intra-tooth variance, we might consider measuring the
average spectra for a given tooth by measuring several points
on the tooth surface, that is, by scanning the surface and
by evaluating how much the spectra of the suspected lesion
differ from the tooth’s average.
Unfortunately, this approach could potentially make this
method less effective for its original purpose. e method is
being developed for the detection of caries lesions at an early
stage of development. us, the dentist does not necessarily
notice all of the lesions which are detected by the device.
If the inspected tooth surface contains several developing
caries lesions, the average spectra of the surface could be
something in between the healthy enamel and the carious
enamel, making the lesions appear too similar to the average
surface to be diagnosed as carious. A set of �xed thresholds
would avoid this problem. e scanning method would also
make it rather awkward to inspect several teeth per patient.
Quantitative Light-induced Fluorescence (QLF) and
Laser-induced Fluorescence (LF) are two optical methods for
the detection of caries lesions.ey are based on�uorescence,
or the phenomenon thatwhen the tooth sample is illuminated
with a light source, some of the light is absorbed in the
sample, aer which the sample emits light at a longer
wavelength. For both methods the emitted wavelength falls
within the range of measured wavelengths [3]. In this study
the sample was considered carious if the measured intensity
was greater than a �xed threshold, 𝐼𝐼𝐼𝐼𝐼 𝐼 𝐼𝐼𝐼𝐼 𝐼 𝐼𝐼𝐼𝐼𝐼𝐼.
e proposed explanation is that the increased scattering due
to caries causes more light to be re�ected to the measuring
�ber optic. QLF expects to �nd a reduced intensity for carious
samples at wavelengths 𝐼𝐼 𝜆 𝐼𝐼𝐼 nm because increased
scattering due to caries interferes with the detection of the
8 Journal of Medical Engineering
�uorescence, and LF expects to �nd increased intensity at
the near-infrared range caused by �uorescence from organic
molecules in the sample [3].
Since the samples in this study were stored in dena-
tured alcohol, they were probably relatively free of organic
molecules. Further study is required to determine whether
the �uorescence from organic molecules, that is, the phe-
nomenon measured by LF, interferes with the detection
method outlined in this study, especially for in vivo mea-
surements. If it does interfere, it probably makes the method
more eager to label a sample as carious, thus increasing its
sensitivity and reducing its speci�city. is e�ect may be
modi�ed, at least in part, by selecting a new set of rules
based on results from in vivo measurements. Incidentally,
low speci�city has been cited as a major weakness of the
LF method [3]. In contrast, authors of this study felt that
the method outlined in this paper helped them to increase
speci�city.
An ability to measure the amount of dental tissue lost
to caries could be pursued by inducing caries in vitro to
a tooth sample (see [6, 17, 18]) so that the amount of
mineral dissolved from the tooth could be measured without
destroying the sample, and by measuring the spectra of the
sample at varying degrees of mineral loss. One possible
method for this would be to cycle the tooth sample in de-
and remineralization solutions and tomeasure the amount of
mineral dissolved to the solutions with a mass spectrometer.
is would have to be repeated with a sufficient number of
samples. Finding a method to calculate the amount of the
mineral loss from the spectra would be a regression problem.
5. Conclusions
It seems that spectroscopic measurements can help to reduce
false positives at in vitro setting, including those caused
by stains. is method may also give objective evidence of
the presence of a caries lesion. However, the work reported
in this paper was a pilot study, and further research is
required to evaluate the strength of the evidence for the
method’s performance at in vitro setting and to extend the
measurements to in vivo setting.
Acknowledgments
e authors would like to acknowledge the Field-NIRce
project for funding this study and Professor Paul Geladi for
his role in organizing the project. e project was funded
by Bothnia-Atlantica, the EuropeanUnion, Regional Council
of Ostrobothnia, Region Västerbotten, and Provincial Gov-
ernment of Västerbotten. e authors would also like to
acknowledge the support that this study has received from
the Dental Services of the City of Vaasa, particularly the
previous Chief Dental Officer Ph.D. Jukka Kentala. is
study has greatly bene�ted from the help and guidance
of Professor Jouni Lampinen, DSc Petri Välisuo, and Dr.
Vladimir Bochko. Finally, the authors wish to thank the
anonymous reviewers, whose comments helped to improve
the quality of this paper.
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