Individual anatomical features of the paranasal sinuses and dentoalveolar system, the complexity of physiological and pathophysiological processes in this area, and the absence of actual standards of the norm and typical pathologies lead to the fact that differential diagnosis and assessment of the severity of the course of odontogenic sinusitis significantly depend on the measurement methods of significant indicators and have significant variability. Therefore, an urgent task is to expand the diagnostic capabilities of existing research methods, study the significance of the measured indicators, and substantiate the expediency of their use in the diagnosis of specific pathologies in an automated mode. This approach is especially relevant with the widespread introduction of objective instrumental diagnostic methods according to the criteria of evidence-based medicine. It is also necessary when developing new diagnostic methods, planning tools for surgical operations, and comparing the discriminant characteristics of the proposed method with existing ones. An important task in this case is the choice of informative parameters of diagnostics and control, as well as criteria by which the discriminant capabilities of the methods will be compared. When developing systems for automated analysis of medical data, it is advisable to introduce a two-level system for assessing diagnostic indicators: preliminary, which allows preliminary diagnostics (control, or differential diagnosis), and final, which allows, according to selected diagnostic indicators, obtaining the most reliable information about the state of the research object.
Modification of the method for diagnosis: It is necessary to carry out studies using spiral or cone-beam tomography and rhinomanometry. Without a rhinomanometric study, the reliability of the diagnosis is slightly reduced. Nevertheless, functional diagnostics of nasal breathing makes it possible to clarify morphological changes in the intranasal structures and paranasal sinuses, obtained from computed tomography data.
Particular attention should be paid to unilateral nasal breathing difficulties (from the side of the compromised paranasal sinus).
3.1. Possibilities of Preliminary Diagnosis of Odontogenic Sinusitis Based on Densitometric Analysis
To determine the radiological signs of odontogenic sinusitis, it is advisable to perform densitometric analysis in an automated mode, which is based on the fact that image intensity is determined by studying the value of image intensity (density) at each point along a certain trajectory, usually along a straight line. Intensity values in relative units (taking into account the choice of tomographic imaging window when displaying the range of the Hu scale of soft tissues in this case) are plotted on the ordinate axis, along the abscissa, indicating the coordinates of the points to be analyzed. This graph of intensity distribution along a certain direction is also called the brightness profile, or densitogram. The densitogram is used for densitographic analysis (analysis of the intensity distribution of the image along a certain direction), which is effective in the study of the density distribution of anatomical structures.
The construction of the densitogram is based on the choice of the initial Ts (x
s, y
s, k) and end Te (x
e, y
e, k) points of the trajectory on the corresponding tomographic section (k)-direct, or obtained by means of multiplanar reconstruction. Given that the measurements take place in the plane of one slice with a fixed number k, it is possible to consider only up to two dimensional coordinates of the start and end points Ts (x
s, y
s) and Te (x
e, y
e), respectively. The parametric equation of the line passing through these points is given as follows:
where
the choice of the step Δt of the change of the parameter t is determined, taking into account the distance d between the points Ts (x
s, y
s) and Te (x
e, y
e)
Thus, to determine the signs of odontogenic sinusitis in an automated mode, the patient undergoes a spiral computed tomography examination to diagnose the condition of the upper respiratory tract and paranasal sinuses. Images of axial spiral computed tomography sections of the upper jaw and maxillary sinus are obtained. In addition, multiplane and three-dimensional surface reconstructions of the studied area in the mode of reflection of bone structures are performed, the anatomical structure of the upper respiratory tract, the presence of deformations, displacements of bone formations, parameters of cranial defects, assessment of soft tissues and bone and bone sinuses are studied, and diagnostic decisions are made. Further, according to tomographic examination on tomographic images of the maxillary sinuses, the procedure of determining the center of the maxillary sinus involves construction of densitograms from the center of the maxillary sinus along radial trajectories in the lower hemisphere and analysis of the shape of densitometric data with characteristic features corresponding to typical pathologies. Normally (see
Figure 1a), a typical densitogram appears with a minimum of intensity throughout the air cavity of the sinus and a pronounced peak of intensity at the bone border. In the presence of a cyst of odontogenic origin (see
Figure 1b), the tissue content of the sinus and the additional border of the cyst are clearly visualized on the densitogram. In the presence of perforation of odontogenic origin in the maxillary sinus (see
Figure 2a), the densitogram clearly visualizes the tissue content of the sinus and the absence of peak intensity at the missing border of the sinus. In the presence of a foreign body in the maxillary sinus (see
Figure 2b), the densitogram on the background of the tissue content of the sinus clearly visualizes an additional area of high intensity, which corresponds to the high intensity of the foreign body.
Thus, due to the introduction of densitometric analysis of tomographic images of the maxillary sinuses at the previous level, it is possible to determine the characteristic densitometric features of various forms of odontogenic maxillary sinusitis and increase the efficiency of diagnosing pathologies of the paranasal sinuses, which is implemented in an automated mode.
3.2. Selection and Analysis of Diagnostic Indicators for Automated Diagnosis of Various Forms of Odontogenic Sinusitis
The effectiveness of solving problems of monitoring the states of objects with random properties, as a rule, depends on the correct choice of the most informative system of parameters (features) that are sensitive to changes in the characteristics of the object. Any control formally implements a testing procedure, the effectiveness of the result of which is determined by reliability—the probability of making the right decision [
33]. This approach is complicated by the fact that when the properties of the research object are uncertain, the problem of selecting informative parameters becomes problematic. Especially if the metrological support of information transformations in the structure of the control system is difficult, which is often the case when considering the problems of medical diagnostics.
The choice of the optimal (according to the criterion of maximum reliability) system of information signs is a classical problem of statistical synthesis in conditions of a priori uncertainty [
33]. The ranking of the signs in terms of information content is carried out in this case according to the value of the control reliability indicator or the probability of errors.
Let us consider the assessment of the possibility of using criteria and models of parametric recognition (discrimination) when comparing the diagnostic capabilities of X-ray cone-beam computed tomography in the diagnosis of various forms of odontogenic sinusitis.
Consider a linear discrimination model. The informative parameter X, used to obtain information about the a priori undefined properties of the control object, can be considered as a random variable. The latter, in the case of two states of an object (
-norm,
-deviation from the norm), is characterized by conditional probability distribution densities
If
are the means and variances of X for the conditions
, and
, accordingly, for normal (Gaussian) distributions
,
the probability of a decision error in the form of object states is determined for variances
through the probability integral
[
33]
where
The mean and standard deviation values included in Equation (6), respectively, are determined by the formulas below
where n is the number of measurements of the indicator under study.
If
, then the boundary for
can be estimated by the inequality
In case of multiparameter control, when the number of informative parameters
is more than one (
), the variable
in expression (5) is described by the equation
where
is the standard deviation of the i-th indicator, which is determined by the formula
The square
of this quantity from Equation (8)
is called the quadratic normalized Euclidean distance between the controlled states (between the vectors of the state averages
and
) [
33].
The control object in this case is a vector-column of measured values
with conditional n-dimensional normal distribution density
Expression (10) assumes the mutual independence of the components of the vector with a linear model of discrimination [
33,
35,
36,
37].
The higher the error probability, the smaller, that is, the larger the square of the distance between the mean vectors normalized by variance.
Thus, the variables (or ) according to Equations (8) and (10) make it possible to quantitatively compare in terms of discriminating ability (in fact, in terms of information content) not only single informative diagnostic indicators, but also subsets (systems) of indicators.
At the same time, for each group of patients, statistical indicators were found: mean values and and standard deviations of the corresponding indicators, and for the calculation by Formula (8), the maximum standard deviation was selected according to Formula (9).
In calculations to determine the diagnostic significance of the parameters of X-ray cone-beam computed tomography in the diagnosis of various forms of odontogenic sinusitis, five informative parameters () were involved, which are displayed in ascending order of numbering:
—the density of the fluid content of the sinus, Hu;
—the relative indicator of the area of the opening of the anastomosis,%;
—the relative indicator of the volume of the mucous membrane of the sinus,%;
—the relative indicator of the volume of the fluid content of the sinus,%,
—coefficient of aerodynamic nose resistance A, kPa/(L/s).
The first four indicators were directly measured on tomograms, and the coefficient of aerodynamic nose drag was also determined indirectly from tomographic data according to the methodology given in the literature [
32,
38,
39]. Let us consider in detail the method of their determination.
For the first diagnostic indicator, the density of the liquid content was determined by measuring the average X-ray absorption in tissues, determined by the Hounsfield scale (in units of Hu, respectively). This is an important diagnostic criterion, since air normally has large negative values on the Hounsfield scale; also, the density of serous contents is significantly less than the purulent contents of the sinuses, which is significant in the differential diagnosis of acute forms of odontogenic sinusitis, respectively.
The second diagnostic indicator is the indicator of the opening of the natural anastomosis of the maxillary sinus, which goes into the middle nasal passage, showing (in percentage) how much the anastomosis is free for the process of physiological aeration and ensuring mucociliary clearance.
Figure 3a shows the segmentation of the airways of the nasal cavity 1 according to tomographic data in the axial projection at the level of the middle nasal passage with the designation of the maxillary sinus 2 and natural fistula 3 (designations are given for the left side of the nasal cavity).
Figure 3b shows a schematic designation of the sagittal section of the natural anastomosis of the maxillary sinus, from left to right, with a working (unblocked) anastomosis, 60% free, 30% free, and with a completely blocked anastomosis.
Figure 4 shows schematic illustrations of the maxillary sinus in a sagittal projection to explain the third and fourth diagnostic indicators (the relative indicator of the volume of the sinus mucosa, %, and the relative indicator of the volume of the fluid content of the sinus, %): a—at a conditional rate; b—at 60% filled sinus cavity with polypous contents, characteristic of chronic odontogenic sinusitis; c—when the sinus is filled by 40% with liquid contents, characteristic of a serous or purulent process; d—filling the sinus with polyposis contents (by 30%) and liquid (by 20%), characteristic of exacerbated chronic odontogenic sinusitis. Examples of real tomographic images with different contents of the sinuses are shown earlier in
Figure 1 and
Figure 2.
The index of changes in nasal breathing (aerodynamic nasal drag coefficient) can be determined from a set of sections of the air channel of the nasal cavity obtained from tomographic data, an example of which is shown in
Figure 5 [
38], according to the methodology given in [
32,
38,
39]. The essence of this approach is to calculate the resistance to air flow (during breathing) of the nasal cavity, represented as a channel with a complex configuration [
32,
38] with the construction of segmented geometric models based on tomographic data [
32,
38,
39,
40].
When calculating pressure losses in complex pipelines, which include parallel channels of the nasal passages, the air flow through each of them is equal to the total, based on the continuity equation according to [
32]
The pressure loss in each channel is determined based on the constancy of the pressure difference between the common inlet (atmospheric pressure) and the outlet to the nasopharynx (where the nasal passages exit) according to
therefore, the pressure loss can be expressed as
where
and
are the pressure losses along the length and on local resistances for the corresponding sections of each channel,
—the length of the channel or calculated section, m,
S—the area of the calculated channel section, m,
—hydraulic (equivalent) diameter [
39],
—air density, = 1.205 kg/m3,
—dimensionless coefficient of local hydraulic losses,
—dimensionless coefficient of hydraulic friction (Darcy coefficient), equal
for laminar, and
turbulent air flow modes, respectively [
32],
A
1 and A
2 are constant values for the aerodynamic drag of the nasal passages, determined from Formulas (14) and (15) as
Taking into account the above Formulas (16) and (17), for the laminar and turbulent regime, the pressure drops are determined according to the formulas
Experimental verification of these data can be carried out according to the data of anterior or posterior active rhinomanometry [
32,
38], taking into account the breathing mode and individual physiological variability, which correspond to the pressure drop across the nasal cavity and the corresponding air flow rate.