In this work we summarize some of our studies on paraconsistent artificial neural networks (PANN) applied to electroencephalography. We give attention to the following applications: probable diagnosis of Alzheimer disease and attention-deficit /hyperactivity disorder (ADHD). PANNs are well suited to tackle problems that human beings are good at solving, like prediction and pattern recognition. PANNs have been applied within several branches and among them, the medical domain for clinical diagnosis, image analysis, and interpretation signal analysis, and interpretation, and drug development. For study of ADHD, we have a result of recognition electroencephalogram standards (delta, theta, alpha, and beta waves) with a median kappa index of 80 %. For study of the Alzheimer disease, we have a result of clinical diagnosis possible with 80 % of sensitivity, 73 % of specificity, and a kappa index of 76 %.
1 Introduction
Generally speaking, artificial neural network (ANN) can be described as a computational system consisting of a set of highly interconnected processing elements, called artificial neurons, which process information as a response to external stimuli. An artificial neuron is a simplistic representation that emulates the signal integration and threshold firing behavior of biological neurons by means of mathematical structures. ANNs are well suited to tackle problems that human beings are good at solving, like prediction and pattern recognition. ANNs have been applied within several branches, among them, in the medical domain for clinical diagnosis, image analysis, and interpretation signal analysis and interpretation, and drug development.
So, ANN constitutes an interesting tool for electroencephalogram (EEG) qualitative analysis. On the other hand, in EEG analysis we are faced with imprecise, inconsistent and paracomplete data.
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The EEG is a brain electric signal activity register, resultant of the space-time representation of synchronic postsynaptic potentials. The graphic registration of the sign of EEG can be interpreted as voltage flotation with mixture of rhythms, being frequently sinusoidal, ranging 1–70 Hz [1]. In the clinical-physiological practice, such frequencies are grouped in frequency bands as can see in Fig. 1.
Fig. 1
Frequency bands clinically established and usually found in EEG
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EEG analysis, as well as any other measurements devices, is limited and subjected to the inherent imprecision of the several sources involved: equipment, movement of the patient, electric registers, and individual variability of physician visual analysis. Such imprecision can often include conflicting information or paracomplete data. The majority of theories and techniques available are based on classical logic and so they cannot handle adequately such set of information, at least directly.
In this paper we employ a new kind of ANN based on paraconsistent annotated evidential logic \(E\tau \), which is capable of manipulating imprecise, inconsistent, and paracomplete data to make a first study of the recognition of EEG standards.
The studies about recognition of EEG standards have application in two clinical areas: attention-deficit/hyperactivity disorder (ADHD) and Alzheimer disease (AD).
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Recent researches reveal that 10 % of the world population in school age suffer of learning and/or behavioral disorders caused by neurological problems, such as ADHD, dyslexia, and dyscalculia, with predictable consequences in those students insufficient performance in the school [2‐7]. EEG alterations seem to be associated those disturbances. Thus, some authors have proposed that there is an increase of the delta activity in EEG in those tasks that demand a larger attention to the internal processes.
Several studies on behavioral and cognitive neurology have been conducted to characterize dementias through biological and functional markers, for instance, the EEG activity, aimed at understanding the evolution of AD, following its progression, as well as leading toward better diagnostic criteria for early detection of cognitive impairment [8, 9]. At present, there is no method able to determine a definitive diagnosis of dementia, where a combination of tests would be necessary to obtain a probable diagnosis [10].
Let us now make some considerations of how to apply paraconsistent artificial neural network (PANN) to analyze probable diagnosis for ADHD and AD.
2 Background
PANN is a new artificial neural network [11]. Its basis leans on paraconsistent annotated logic \(E\tau \) [12]. Let us present it briefly.
The atomic formulas of the logic \(E\tau \) are of the type \(p_{(\mu , \lambda )}\), where (\(\mu , \lambda ) \in [0, 1]^{2}\) and [0, 1] is the real unitary interval (\(p\) denotes a propositional variable). \(p_{(\mu , \lambda )}\) can be intuitively read: “it is assumed that \(p\)’s favorable evidence is \(\mu \) and contrary evidence is \(\lambda \)”. Thus
\(p_{(1.0, 0.0)}\) can be read as a true proposition.
\(p_{(0.0, 1.0)}\) can be read as a false proposition.
\(p_{(1.0, 1.0)}\) can be read as an inconsistent proposition.
\(p_{(0.0, 0.0)}\) can be read as a paracomplete (unknown) proposition.
\(p_{(0.5, 0.5)}\) can be read as an indefinite proposition.
We introduce the following concepts (all considerations are taken with \(0\le \mu , \lambda \le 1\)):
Intuitively, \(G_{\mathrm{un}}(\mu , \lambda )\) show us how close (or far) the annotation constant \((\mu , \lambda )\) is from inconsistent or paracomplete state. Similarly, \(G_{\mathrm{ce}}(\mu , \lambda )\) show us how close (or far) the annotation constant \((\mu , \lambda )\) is from true or false state. In this way we can manipulate the information given by the annotation constant \((\mu , \lambda )\). Note that such degrees are not metrical distance.
An order relation is defined on [0, 1]\({^{2}}\): \((\mu _{1}, \lambda _{1}) \le (\mu _{2}, \lambda _{2}) \Leftrightarrow \mu _{1} \le \mu _{2}\), and \(\lambda _{2} \le \lambda _{1}\), constituting a lattice that will be symbolized by \(\tau \).
With the uncertainty and certainty degrees we can get the following 12 output states (Table 1): extreme states and non-extreme states:
Table 1
Extreme and non-extreme states
Extreme states
Symbol
Non-extreme states
Symbol
True
V
Quasi-true tending to inconsistent
\(\hbox {QV}\rightarrow \hbox {T}\)
False
F
Quasi-true tending to paracomplete
\(\hbox {QV}\rightarrow \bot \)
Inconsistent
T
Quasi-false tending to inconsistent
\(\hbox {QF}\rightarrow \hbox {T}\)
Paracomplete
\(\bot \)
Quasi-false tending to paracomplete
\(\hbox {Qf}\rightarrow \bot \)
Quasi-inconsistent tending to true
\(\hbox {QT}\rightarrow \hbox {V}\)
Quasi-inconsistent tending to false
\(\hbox {QT}\rightarrow \hbox {F}\)
Quasi-paracomplete tending to true
\(\hbox {Q}\bot \rightarrow \hbox {V}\)
Quasi-paracomplete tending to false
\(\hbox {Q}\bot \rightarrow \hbox {F}\)
Some additional control values are:
\(V_{\mathrm{scct}}\) = maximum value of uncertainty control = \(\hbox {Ft}_{\mathrm{un}}\)
\(V_{\mathrm{scc}}\) = maximum value of certainty control = \(\hbox {Ft}_{\mathrm{ce}}\)
\(V_{\mathrm{icct}}\) = minimum value of uncertainty control = \(-\hbox {Ft}_{\mathrm{un}}\)
\(V_{\mathrm{icc}}\) = minimum value of certainty control = \(-\hbox {Ft}_{\mathrm{ce}}\)
Such values are determined by the knowledge engineer, depending on each application, finding the appropriate control values for each of them.
All states are represented in the next figure (Fig. 2).
Fig. 2
Extreme and non-extreme states
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3 The main artificial neural cells
In the PANN, the certainty degree \(G_{\mathrm{ce}}\) indicates the ‘measure’ falsity or truth degree.
The uncertainty degree \(G_{\mathrm{un}}\) indicates the ‘measure’ of the inconsistency or paracompleteness. If the certainty degree in module is low or the uncertainty degree in module is high, it generates a paracompleteness.
The resulting certainty degree \(G_\mathrm{ce}\) is obtained as follows:
A paraconsistent artificial neural cell (PANC) is called basic PANC (Fig. 3) when given a pair \((\mu , \lambda )\) is used as input and resulting as output:
The uncertainty degree \(G_\mathrm{un}\) indicates the ‘measure’ of the inconsistency or paracompleteness. If the certainty degree in module is low or the uncertainty degree in module is high, it generates an indefiniteness.
The resulting certainty degree \(G_\mathrm{ce}\) is obtained as follows:
Using the concepts of basicPANC, we can obtain the family of PANC considered in this work: analytic connection (PANCac), maximization (PANCmax), and minimization (PANCmin) as described in Table 2 below:
Table 2
Paraconsistent artificial neural cells
PANC
Inputs
Calculations
Output
Analytic connection: PANCac
\(\mu \)
\(\lambda _\mathrm{c} = 1 - \lambda \)
If \({\vert }G_\mathrm{ce}{\vert } > \hbox {Ft}_\mathrm{ce}\) then \({S}_{1}=\mu _\mathrm{r}\) and \({S}_{2} = 0\)
\(\lambda \)
\(G_\mathrm{un} G_\mathrm{ce}\),
If \({\vert }G_\mathrm{un}{\vert } > \hbox {Ft}_\mathrm{ct}\) and \({\vert }G_\mathrm{un}{\vert } > {\vert } G_\mathrm{ce}{\vert }\) then
\(\hbox {Ft}_\mathrm{un}\)
\(\mu _\mathrm{r} = (G_\mathrm{ce} + 1)/2\)
\({S}_{1}=\mu _\mathrm{r}\) and \({S}_{2} = {\vert }G_\mathrm{un}{\vert }\)
\(\hbox {Ft}_\mathrm{un}\)
If not \({S}_{1 }= 1/2\) and \({S}_{2 }= 0\)
Maximization: PANCmax
\(\mu \)
\(G_\mathrm{ce}\)
If \(\mu _\mathrm{r} >\) 0.5, then \({S}_{1}=\mu \)
\(\lambda \)
\(\mu _\mathrm{r} = (G_\mathrm{ce} + 1)/2\)
If not \({S}_{1}=\lambda \)
Minimization: PANCmin
\(\mu \)
\(G_\mathrm{ce}\)
If \(\mu _\mathrm{r} < 0.5\), then \({S}_{1}=\mu \)
\(\lambda \)
\(\mu _\mathrm{r} = (G_\mathrm{ce} + 1)/2\)
If not \({S}_{1}=\lambda \)
To make easier the understanding on the implementation of the algorithms of PANC, we use a programming language Object Pascal, following logic of procedural programming in all samples.
3.1 Paraconsistent artificial neural cell of analytic connection (PANCac)
The PANCac is the principal cell of all PANN, obtaining the certainty degree \((G_\mathrm{ce})\) and the uncertainty degree \((G_\mathrm{un})\) from the inputs and the tolerance factors.
This cell is the link which allows different regions of PANN perform signal processing in distributed and through many parallel connections [11].
The different tolerance factors certainty (or contradiction) acts as inhibitors of signals, controlling the passage of signals to other regions of the PANN, according to the characteristics of the architecture developed (Fig. 4).
Fig. 4
Representation of PANCac
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In Table 3, we have a sample of implementation made in Object Pascal.
Table 3
PANCac implementation
3.2 Paraconsistent artificial neural cell of maximization (PANCmax)
The PANCmax allows selection of the maximum value among the entries.
Such cells operate as logical connectives OR between input signals. For this is made a simple analysis, through the equation of the degree of evidence (Table 4) which thus will tell which of the two input signals is of greater value, thus establishing the output signal [11] (Fig. 5).
Fig. 5
Representation of PANCmax
Table 4
PANCmax implementation
×
In Table 4, we have a sample of implementation made in Object Pascal.
3.3 Paraconsistent artificial neural cell of minimization (PANCmin)
The PANCmin allows selection of the minimum value among the entries.
Such cells operate as logical connectives AND between input signals. For this it is made a simple analysis, through the equation of the degree of evidence (Table 5) which thus will tell which of the two input signals is of smaller value, thus establishing the output signal [11].
Table 5
PANCmin implementation
In Table 5, we have a sample of implementation made in Object Pascal.
3.4 Paraconsistent artificial neural unit
A PANU is characterized by the association ordered PANC, targeting a goal, such as decision making, selection, learning, or some other type of processing.
When creating a PANU, one obtains a data processing component capable of simulating the operation of a biological neuron.
3.5 Paraconsistent artificial neural system
Classical systems based on binary logic are difficult to process data or information from uncertain knowledge. These data are captured or received information from multiple experts usually comes in the form of evidences.
Paraconsistent artificial neural system (PANS) modules are configured and built exclusively by PANU, whose function is to provide the signal processing ‘similar’ to processing that occurs in the human brain.
4 PANN for morphological analysis
The process of morphological analysis of a wave is performed by comparing with a certain set of wave patterns (stored in the control database). A wave is associated with a vector (finite sequence of natural numbers) through digital sampling. This vector characterizes a wave pattern and is registered by PANN. Thus, new waves are compared, allowing their recognition or otherwise.
Each wave of the survey examined the EEG corresponds to a portion of 1 s examination. Every second of the exam contains 256 positions.
The wave that has the highest favorable evidence and lowest contrary evidence is chosen as the more similar wave to the analyzed wave.
A control database is composed by waves presenting 256 positions with perfect sinusoidal morphology, with 0.5 Hz of variance, so taking into account delta, theta, alpha, and beta (of 0.5–30.0 Hz) wave groups.
In other words, morphological analysis checks the similarity of the passage of the examination of EEG in a reference database that represents a wave pattern.
4.1 Data preparation
The process of wave analysis by PANN consists previously of data capturing, adaptation of the values for screen examination, elimination of the negative cycle, and normalization of the values for PANN analysis.
As the actual EEG examination values can vary highly, in module, something 10–1,500 \(\upmu \)V, we make a normalization of the values between 100 and \(-\)100 \(\upmu \)V by a simple linear conversion, to facilitate the manipulation the data:
where \(m\) is the maximum value of the exam; \(a\) is the current value of the exam; \(x\) is the current normalized value.
The minimum value of the examination is taken as zero value and the remaining values are translated proportionally.
It is worth observing that the process above does not allow the loss of any wave essential characteristics for our analysis.
4.2 The PANN architecture
The architecture of the PANN used in decision making is based on the architecture of PANS for treatment of contradictions.
Such a system performs a treatment of the contradictions continuously if presented by the three information signal inputs, presenting as an output a resulting signal that represents a consensus among the three information. This is made by analyzing the contradiction between two signals, and by adding a third one; the output is chosen by dominant majority. The analysis is instantly carrying all processing in real time, similar to the functioning of biological neurons.
This method is used primarily for PANN (Fig. 8) to balance the data received from expert systems. After this the process uses a decision-making lattice to determine the soundness of the recognition (Table 6; Fig. 6).
Fig. 6
Lattice for decision-making used in morphological analysis used after making PANN; \(F\) logical state false (it is interpreted as wave not similar); \(V\) logical state true (it is interpreted as wave similar)
Table 6
Lattice for decision-making used in the morphological analysis (Fig. 7)
Ce contrary evidence, Fe favorable evidence, \(G_\mathrm{ce}\) certainty degree
Fig. 7
Representation of PANCmin
×
×
A sample of morphological analysis implementation using Object Pascal is showed in Table 7.
Table 7
The architecture for morphological analysis implementation (Fig. 8)
Fig. 8
The architecture for morphological analysis. Three expert systems operate: PA for check the number of wave peaks; PB for checking similar points, and PC for checking different points The 1st layer of the architecture: C1–PANC which processes input data of PA and PB; C2–PANC which processes input data of PB and PC; C3–PANC which processes input data of PC and PA. The 2nd layer of the architecture: C4–PANC which calculates the maximum evidence value between cells C1 and C2; C5–PANC which calculates the minimum evidence value between cells C2 and C3; The 3rd layer of the architecture: C6–PANC which calculates the maximum evidence value between cells C4 and C3; C7–PANC which calculates the minimum evidence value between cells C1 and C5. The 4th layer of the architecture: C8 analyzes the experts PA, PB, and PC and gives the resulting decision value. PANC A \(=\) paraconsistent artificial neural cell of analytic connection. \(\hbox {PANCLs}_\mathrm{Max} =\) paraconsistent artificial neural cell of simple logic connection of maximization. \(\hbox {PANCLs}_\mathrm{Min} =\) paraconsistent artificial neural cell of simple logic connection of minimization. \(\hbox {Ft}_\mathrm{ce} =\) certainty tolerance factor; \(\hbox {Ft}_\mathrm{un} =\) uncertainty tolerance factor. \({S}_\mathrm{a} =\) output of C1 cell; \({S}_\mathrm{b} =\) output of C2 cell; \({S}_\mathrm{c} =\) output of C3 cell; \({S}_\mathrm{d} =\) output of C4 cell; \(S_\mathrm{e} =\) output of C5 cell; \(S_\mathrm{f} =\) output of C6 cell; \(S_\mathrm{g} =\) output of C7 cell. C = complemented value of input; \(\mu _\mathrm{r} =\) value of output of PANN; \(\lambda _\mathrm{r} =\) value of output of PANN
×
The definition of regions of the lattice decision-making was done through double-blind trials, i.e., for each battery of tests, a validator checked the results and returned only the percentage of correct answers. After testing several different configurations, set the configuration of the lattice regions whose decision-making had a better percentage of success.
For an adequate PANN wave analysis, it is necessary that each input of PANN is properly calculated. These input variables are called expert systems as they are specific routines for extracting information.
In analyzing EEG signals, one important aspect to take into account is the morphological aspect. To perform such a task, it is convenient to consider an expert system which analyzes the signal behavior verifying which band it belongs to (delta, theta, alpha and beta).
The method of morphological analysis has three expert systems that are responsible for feeding the inputs of PANN with information relevant to the wave being analyzed: number of peaks, similar points, and different points.
4.3 Expert system 1: checking the number of wave peaks
The aim of the expert system 1 is to compare the waves and analyze their differences regarding the number of peaks.
In practical terms, one can say that when we analyzed the wave peaks, we are analyzing the resulting frequency of wave (so well rudimentary).
It is worth remembering that, because it is biological signal, we should not work with absolute quantification due to the variability characteristic of this type of signal. Therefore, one should always take into consideration a tolerance factor.
A sample of checking the number of wave peaks function implementation using Object Pascal is show in Table 8.
where \(vt\) is the number of peaks of the wave, \(bd\) is the number of peaks of the wave stored in the database, \(\mathrm{Se}_{1}\) is the value resulting from the calculation.
Table 8
Checking the number of wave peaks function implementation
4.4 Expert system 2: checking similar points
The aim of the expert system 2 is to compare the waves and analyze their differences regarding to similar points.
When we analyze the similar points, it means that we are analyzing how one approaches the other point.
It is worth remembering that, because it is biological signal, we should not work with absolute quantification due to the variability characteristic of this type of signal. Therefore, one should always take into consideration a tolerance factor.
A sample of checking similar points function implementation using Object Pascal is shown in Table 9.
where \(n\) is the total number of elements, \(x\) is the element of the current position, a\(j\) is the current position, \(\mathrm{Se}_{2}\) is the value resulting from the calculation.
Table 9
Checking similar points function implementation
4.5 Expert system 3: checking different points
The aim of the expert system 3 is to compare the waves and analyze their differences regarding of different points.
When we analyze the different points, it means that we are analyzing how a point more distant from each other, so the factor of tolerance should also be considered.
A sample of checking different points function implementation using Object Pascal is shown in Table 10.
where \(n\) is the total number of elements, \(a\) is the maximum amount allowed, \(j\) is the current position, \(x\) is the value of wave 1, \(y\) is the value of wave 2, \(\mathrm{Se}_{3}\) is the value resulting from the calculation.
Table 10
Checking different points function implementation
5 Experimental procedures: differentiating frequency bands
In our work we have studied two types of waves, specifically delta and theta waves band, where the size of frequency established clinically ranges (Fig. 1).
Seven examinations of different EEG were analyzed, being two examinations belonging to adults without any learning disturbance and five examinations belonging to children with learning disturbance [5, 6, 13].
Each analysis was divided into three rehearsals; each rehearsal consisted of 10 s of the analyzed, free from visual analysis of spikes and artifacts regarding the channels T3 and T4.
In the first battery of tests, a wave recognition filter belonging to the delta band was considered. In the second one, a wave recognition filter belonging to the theta band was considered. In the third one, none of the filters were considered for recognition (Tables 11, 12, 13, 14, 15, 16).
Table 11
Contingency table
Visual analysis
Delta
Theta
Alpha
Beta
Unrecognized
Total
PANN Analysis
Delta
31
3
0
0
0
34
Theta
15
88
1
1
0
105
Alpha
0
5
22
0
0
27
Beta
0
0
1
3
0
4
N/D
7
2
1
0
0
10
Total
53
98
25
4
0
180
Index kappa \(=\) 0.80
Table 12
Statistical results—sensitivity and specificity: delta waves
Visual analysis
Delta
Not delta
Total
PANN
True
31
124
155
False
22
3
25
Total
53
127
180
Sensitivity \(=\) 58 %; specificity \(=\) 97 %
Table 13
Statistical results—sensitivity and specificity: theta waves
Visual analysis
Theta
Not theta
Total
PANN
True
88
65
153
False
10
17
27
Total
98
82
180
Sensitivity \(=\) 89 %; specificity \(=\) 79 %
Table 14
Statistical results—sensitivity and specificity: alpha waves
Visual analysis
Alpha
Not alpha
Total
PANN
True
22
150
172
False
3
5
8
Total
25
155
180
Sensitivity \(=\) 88 %; specificity \(=\) 96 %
Table 15
Statistical results—sensitivity and specificity: beta waves
Visual analysis
Beta
Not beta
Total
PANN
True
3
175
178
False
1
1
2
Total
4
176
180
Sensitivity \(=\) 75 %; specificity \(=\) 99 %
Table 16
Statistical results—sensitivity and specificity: unrecognized waves
Visual analysis
Unrecognized
Recognized
Total
PANN
True
0
170
170
False
0
10
10
Total
0
180
180
Sensitivity \(=\) 100 %; specificity \(=\) 94 %
6 Experimental procedures: applying in Alzheimer disease
It is known that the visual analysis of EEG patterns may be useful in aiding the diagnosis of AD and indicated in some clinical protocols for diagnosing the disease [14, 15]. The most common findings on visual analysis of EEG patterns are slowing of brain electrical activity based on predominance of delta and theta rhythms and decrease or absence of alpha rhythm. However, these findings are more common and evident in patients in moderate or advanced stages of disease [8, 16, 17].
In this study we have 67 analyzed EEG records, 34 normal and 33 probable AD (\(p\) value \(=\) 0.8496) during the awake state at rest.
All tests were subjected to morphological analysis methodology for measuring the concentration of waves. Later this information is submitted to a PANN unit responsible for assessing the data and arriving at a classification of the examination in normal or probable AD (Table 17; Fig. 9).
Table 17
Lattice for decision-making (Fig. 9) used in diagnostic analysis used after making PANN analysis (Fig. 10)
Characterization of the lattice
Area 1
\(G_\mathrm{ce }\le 0.1999\) and \(G_\mathrm{ce }\ge 0.5600\) and \({\vert } G_\mathrm{un} {\vert } < 0.3999\) and \({\vert } G_\mathrm{un} {\vert }\ge 0.4501\)
Area 2
\(0.2799 < G_\mathrm{ce} < 0.5600\) and \(0.3099 \le {\vert } G_\mathrm{un} {\vert } < 0.3999\) and Fe \(< 0.5000\)
Area 3
\(0.1999 < G_\mathrm{ce} < 0.5600\) and \(0.3999 \le {\vert } G_\mathrm{un} {\vert } < 0.4501\) and Fe \(> 0.5000\)
Ce contrary evidence, Fe favorable evidence, \(G_\mathrm{ce}\) certainty degree, \(G_\mathrm{un}\) uncertainty degree
Fig. 9
The architecture for diagnosis analysis
Fig. 10
Lattice for decision-making used in diagnostic analysis (Fig. 9). Area 1 state logical false (AD likely below average population), area 2 state logical Quasi-true (AD likely than average population); area 3 state logical Quasi-false (normal below average population); area 4 state logical true (normal above average population); area 5 logical state of uncertainty (not used in the study area)
×
×
6.1 Expert system 1: detecting the diminishing average frequency level
The aim of the expert system 1 is to verify the average frequency level of alpha band waves and compare them with a fixed external parameter wave.
Such external parameter can be, for instance, the average frequency of a population or the average frequency of the last examination of the patient. This system also generates two outputs: favorable evidence \(\mu \) normalized values ranging from 0 (corresponds to 100 %—or greater frequency loss) to 1 (which corresponds to 0 % of frequency loss) and contrary evidence \(\lambda \) (Eq. 6.1).
The average frequency of population pattern used in this work is 10 Hz.
$$\begin{aligned} \lambda =1-\mu \end{aligned}$$
(6.1)
6.2 Expert system 2: high-frequency band concentration
The role of the expert system 2 is to analyze alpha band concentration. For this, we consider the quotient of the sum of fast alpha and beta waves over slow delta and theta waves (Eq. 6.2) as first output value. For the second output value (contrary evidence \(\lambda )\) is used Eq. 6.1.
where \(A\) is the alpha band concentration; \(B\) is the beta band concentration, \(D\) is the delta band concentration; \(T\) is the theta band concentration; and \(\mu \) is the value resulting from the calculation.
6.3 Expert system 3: low frequency band concentration
The role of the expert system 3 is to analyze theta band concentration. For this, we consider the quotient of the sum of slow delta and theta waves over fast alpha and beta waves (Eq. 6.3) as first output value. For the second output value (contrary evidence \(\lambda \)) is used Eq. 6.1.
where \(A\) is the alpha band concentration; \(B\) is the beta band concentration. \(D \) is the delta band concentration; and \(T\) is the theta band concentration. \(\mu \) is the value resulting from the calculation.
Diagnosis: normal \(\times \) probable AD patients
Gold standard
AD patient (%)
Normal patient (%)
Total (%)
PANN
AD patient
35.82
14.93
50.75
Normal patient
8.96
40.30
49.25
Total
44.78
55.22
100.00
Sensitivity \(=\) 80 %; specificity \(=\) 73 ; index of coincidence (kappa) 76 %
7 Experimental procedures: applying in attention-deficit/hyperactivity disorder (ADHD)
A similar architecture using PANN was built to study some cases in ADHD. Recent researches reveal that 10 % of the world population in school age suffer of learning and/or behavioral disorders caused by neurological problems, such as ADHD, dyslexia, and dyscalculia, with predictable consequences in those students’ insufficient performance in the school [2‐6, 13].
Concisely, a child without intellectual lowering is characterized as bearer of ADHD when it presents signs of
Inattention: difficulty in maintaining attention in tasks or games; the child seems not to hear what is spoken; difficulty in organizing tasks or activities; the child loses things; the child becomes distracted with any incentive, etc.
Hyperactivity: frequently the child leaves the class room; the child is always inconveniencing friends; the child runs and climbs in trees, pieces of furniture, etc; the child speaks a lot, etc.
Impulsiveness: the child interrupts the activities of colleagues; the child does not wait his time; aggressiveness crises, etc.
Dyslexia: the child begins to present difficulties to recognize letters or to read them and to write them although the child has not a disturbed intelligence, that is, a normal IQ;
Dyscalculia: the child presents difficulties to recognize amounts or numbers and/or to figure out arithmetic calculations.
A child can present any combination among the disturbances above. All those disturbances have their origin in a cerebral dysfunction that can have multiple causes, many times showing a hereditary tendency.
Since from the first discoveries, those disturbances have been associated with cortical diffuse lesions and/or more specific, temporal-parietal areas lesions in the case of dyslexia and dyscalculia [2, 5, 13].
The disturbances of ADHD disorder seem to be associated with an alteration of the dopaminergic system, that is, it is involved with mechanisms of attention and they seem to involve a frontal-lobe dysfunction and basal ganglia areas [3, 13].
EEG alterations seem to be associated with those disturbances. Thus, some authors have proposed that there is an increase of the delta activity in EEG in those tasks that demand a larger attention to the internal processes.
Other authors [1] have described alterations of the delta activity in dyslexia and dyscalculia children sufferers. Klimesch [18] has proposed that a phase of the EEG component would be associated with the action of the memory work. More recently, Kwak [19] has showed delta activity is reduced in occipital areas, but not in frontals, when dyslexic children were compared with normal ones.
In this way, the study of the delta and theta bands becomes important in the context of the analysis of learning disturbances.
So, in this paper we have studied two types of waves, specifically delta and theta wave bands, where the size of frequency established clinically ranges 1.0–3.5 and 4.0–7.5 Hz, respectively.
Seven exams of different EEG were analyzed, being two exams belonging to adults without any learning disturbance and five exams belonging to children with learning disturbances (exams and respective diagnoses given by ENSCER—Teaching the Brain, EINA—Studies in Natural Intelligence and Artificial Ltda).
Each analysis was divided into three rehearsals, and each rehearsal consisted of 10 s of the analyzed, free from visual analysis of spikes and artifacts regarding the channels T3 and T4. In the first battery of tests, a delta recognition filter wave was considered. For second battery of tests, a theta recognition wave was considered. For the third battery of tests, none of the filters were considered for recognition, i.e., the system worked freely for any wave type recognition. The total number of exams is 180 (Tables 19, 20, 21, 22, 23, 24).
Table 19
Contingency table
Visual analysis
Delta
Theta
Alpha
Beta
Unrecognized
Total
PANN analysis
Delta
31
3
0
0
0
34
Theta
15
88
1
1
0
105
Alpha
0
5
22
0
0
27
Beta
0
0
1
3
0
4
N/D
7
2
1
0
0
0
Total
53
98
25
4
0
180
Index kappa \(=\) 0.80
Table 20
Statistical results—sensitivity and specificity: delta waves
Visual analysis
Delta
Not delta
Total
PANN analysis
True
31
124
155
False
22
3
25
Total
53
127
180
Sensitivity \(=\) 58 %; specificity \(=\) 97 %
Table 21
Statistical results—sensitivity and specificity: theta waves
Visual analysis
Theta
Not theta
Total
PANN analysis
True
88
65
153
False
10
17
27
Total
98
82
180
Sensitivity \(=\) 89 %; specificity \(=\) 79 %
Table 22
Statistical results—sensitivity and specificity: alpha waves
Visual analysis
Alpha
Not alpha
Total
PANN analysis
True
22
150
172
False
3
5
8
Total
25
155
180
Sensitivity \(=\) 88 %; specificity \(=\) 96 %
Table 23
Statistical results—sensitivity and specificity: beta waves
Visual analysis
Beta
Not beta
Total
PANN analysis
True
3
175
178
False
1
1
2
Total
4
176
180
Sensitivity \(=\) 75 %; specificity \(=\) 99 %
Table 24
Statistical results—sensitivity and specificity: unrecognized waves
Visual analysis
Unrecognized
Recognized
Total
PANN analysis
True
0
180
180
False
0
0
0
Total
0
180
180
Sensitivity \(=\) 100 %; specificity \(=\) 100 %
8 Conclusions
We believe that a process of the examination analysis using a PANN attached to EEG findings, such as relations between frequency bandwidth and inter hemispheric coherences, can create computational methodologies that allow the automation of analysis and diagnosis.
These methodologies could be employed as tools to aid in the diagnosis of diseases such as dyslexia or Alzheimer, provided they have defined electroencephalographic findings.
In the case of Alzheimer’s disease, for example, the studies carried out previously have shown satisfactory results [20] (but still far from being a tool to aid clinical) that demonstrated the computational efficiency of the methodology using a simple morphological analysis (only paraconsistent annotated logic \(E\tau \)). These results encouraged us to improve the morphological analysis of the waves and try to apply the method in other diseases besides Alzheimer’s disease.
With the process of morphological analysis using the PANN, it becomes possible to quantify the frequency average of the individual without losing its temporal reference. This feature becomes a differential, compared to traditional analysis of quantification of frequencies, such as fast Fourier transform, aiming at a future application in real-time analysis, i.e., at the time of acquisition of the EEG exams.
Regarding the specificity, the method showed more reliable results. Taking into account an overall assessment in the sense we take the arithmetic mean of sensitivity (75.50 %) and specificity (92.75 %), we find reasonable results that encourage us to seek improvements in this study.
The consideration of morphological analysis of the main brain waves by employing PANN showed be effective, allowing interesting quantitative and qualitative examinations of EEG data. PANN has been applied in other branches: MICR automated recognition [16], computer-aided diagnosis (breast cancer) [17], and many other themes.
This article is published under license to BioMed Central Ltd.Open AccessThis article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
