The problem of constructing a mathematical model of the electrophysiological properties of the tissues of a patient's surgical wound around the thyroid gland is discussed in this article. This problem occurs during surgery on the thyroid gland. The technology and means of identification of the reverse laryngeal nerve in the process of surgical intervention are briefly considered. It is shown that the model of distribution of electrophysiological characteristics of woven surgical wounds increases efficiency of detection of recurrent laryngeal nerve. The model is constructed in a differential form on the basis of trial irritation of surgical wound tissues pulsed current with an root mean square (RMS) of current strength value of up to 2 mA. However, this model requires customization for a specific patient, which reduces the effectiveness of the technology of detection of recurrent laryngeal nerve. It is proposed to classify all types of pathologies in the thyroid gland and to develop an ontological model that will serve as a model for managing the selection processes of previously developed difference equations for operated patients. This approach makes it possible to increase the efficiency of existing technology.
Surgical interventions on various human organs often require classification and recognition of
surgical wound tissue types. Most often, the surgeon has to identify nerve tissue on the background of
muscle and connective tissue in order to avoid damage. Nerve tissue damage can be fatal to the
functioning of other human organs. One such tissue is the Recurrent laryngeal nerve (RLN). Its
detection and localization is carried out during surgery on the neck or during the removal of thyroid
tumors [
All these neuromonitors work on the principle of stimulation of tissues by pulsed current at different
frequencies and processing of the signal-reaction to stimulation by means of spectral analysis methods,
or simple check of conductivity of electric current by nervous tissues [
However, tissue classification to some extent makes it possible to detect the location of the RLN,
but does not help the surgeon to predict the distance from the site of surgery to the nerve tissue. The
technology for solving this problem is given in [
Similar studies are given in [
It should be noted that such models are built in the form of an algebraic equation, or difference [
Preliminary observations of patients in the course of a number of thyroid surgeries have shown that the electrophysiological properties of the tissues of the surgical wound of patients largely depend on the pathology of the thyroid gland. Therefore, it was decided to improve the existing technology through the use of an ontological model that contains all the acquired knowledge about the pathologies of patients who have been operated on to remove a thyroid tumor.
Consider the features of the construction of the above model in the form of an interval difference equation.
Suppose you performed a series of tissue irritations on a surgical wound with current strength of up to 2 mA. Also, let the results of those stimuli received the characteristics of the information signal in the interval form. Then the results of these stimuli are presented as follows:
[ , ] = [ −, , +, ], = 1, . . . , , = 1, . . . , , [ 0( , )] ∈ [ −, ; +, ], (1) where [ 0( , )] is the value of the signal which obtained after processing the data of the reaction to surgical wound stimulation = 1, . . . , , = 1, . . . , ; −, , +, are the min and max values of the corridor for the amplitude signal; = 1, . . . , , = 1, . . . , are a discrete coordinate of the spatial distribution of tissue characteristics of the surgical wound;
In expression (1) takes into account the main errors of technical or other tools.
A model for RLN identification is considered as a discrete equation, that is, the main difference
equation in such form [
= + 1, . . . , , = + 1, . . . , , (2) where ⃗ is a vector of unknown parameters of discrete difference equation; is order of difference equation; ⃗ (•)is a vector of is a vector of special functions, can be linear, that define the structure of discrete equation; ̑ , is a predicted value of main amplitude in the mark with specified discrete coordinates , . Further, the mathematical model (2) will be called an interval difference equation (IDE).
+, ] ⊂ [ −, ; +, ],∀ = 1, . . . , , ∀ = 1, . . . , .
By substituting in the formula (3), the other recurrent formula (2) instead of the interval evaluations [ ̑−, ; ̑
+, ], we obtain the interval system of non-linear algebraic equations (ISNAE) with the defined values of the interval: ⋮ ⋮ { [ ̑0−,0; ̑0+,0] ⊆ [ 0−,0; 0+,0];
− [ ̑ , ; ̑
+, ] ⊆ [ −, ; +, ]; −+1, +1 ≤ ⃗ ([ ̑0,0], . . . , [ ̑0, ], . . . , [ ̑ ,0]. . . . . . , [ ̑ , ], ⃗⃗0, … ⃗⃗ ) ⋅ ⃗̑ ≤ −+1, +1; −, ≤ ⃗ ([ ̑0,0], . . . , [ ̑0, ], . . . , [ ̑ ,0]. . . . . . , [ ̑ , −1], ⃗⃗0, … ⃗⃗ ) ⋅ ⃗̑ ≤ −, ; = + 1 … , = + 1 … , = 0 … . (3) (4)
In contrast to the linear case [
The application of this model identification method involves the execution of activity phases of all
types of bees in the colony: employed bees, scout bees and onlooker bees [
Thus, using the parametric and structural identification [
For example, take the model built in [
Fragment of the Set of Values of the Amplitude of the Spectral Components 0 0 0 4 4 …
Coordinates 0 1 2 … 3 4
Interval values
[ , ] [0,58;0,92] [0,45;0,54] [0,39;0,44]
… [0,025;0,034] [0,016;0,025] [ ̑−, ; ̑ +, ] = −0.0161 + 0.503 ⋅ [ ̑ , −2; ̑ , −2]
− + +0.6344 ⋅ [ ̑ −1, −1; ̑+−1, −1] ⋅
− − + − + ⋅ [ ̑ , −1; ̑ , −1] ⋅ [ ̑ , −1; ̑ , −1],
i=1…4, j=2…4, +0.2145 ⋅ [ ̑ −1, ; ̑+−1, ] + 0.7969 ⋅ [ ̑ , −1; ̑ , −1] ⋅ [ ̑ , −1; ̑ , −1] − − + − + (5) where[ ̑−, ; ̑
+, ] ⊂ [ −, ; +, ] = [ , − , 0,02; , + , 0,02] and {i=0, j=0,…,4} {i=0,…,4, j=0,1} are the initial conditions.
As you can see, to customize this model for a particular patient, you need to set 14 points for the initial conditions. This means that in the process of surgery, the surgeon must make at least 14 irritations of the tissues of the surgical wound at certain points. However, if you create a repository of models that were built during the operated patients and use it for subsequent patients, it is possible to significantly reduce the time of the operation at the preparatory stage, when the surgeon identifies RLN.
The paper proposes an ontological approach to present the concepts, methods and means of mathematical modeling on the basis of interval data, namely the declarative and procedural parts, mathematical knowledge is separated. The declarative part of ontology consists of the information needed to build the model, the information derived from the mathematical model and the corresponding mathematical expressions that represent the model. The procedural part consists of detailed parts of the mathematical model, appropriate methods and algorithms for their implementation, procedures for initializing.
The ontology of a mathematical model consists of an operating class, the subclasses of which are various operations that occur during the implementation of the model, and also contain the conditions for the implementation of each of the operations. This ontological description also consists of a class of results, which stores the results of the solution of the model, as well as the results of experiments.
The procedural part of the approach consists of a mechanism of construction based on methods of
data relationship analysis, which analyzes equations in the ontological interpretation of mathematical
models and translates them into expressions that can be interpreted in other external software
environments [
Based on the analysis of the structure of mathematical models based on interval data, the modeling process and the features of experiments, the mathematical model in terms of ontological approach can be formalized using the following structures:
= ⟨ , , , , , , ⟩, (6) where is the subject area within which the mathematical model is built or used; - descriptions of the mathematical model; - the set of objects of use of the model; - set of parameters; is a set that describes the result of building object models; - set of characteristics of the experiments; - set of methods for identifying model parameters.
= ⟨ , ⟩, (7) where - subject area.
= ⟨ , , ⟩, (8)
- formalized description of the equations of the - subject area identifier;
where - equation identifier; mathematical model;
= ⟨ where - is the object identifier; model's use object.
, , , ⟩, (9) is the information that describes the structure of the = ⟨ , , , , , ⟩, (10) where - parameter identifier; - parameter type; - values of model parameters; = ⟨ , , , , ⟩, (11) where - result identifier; - statements that describe the result.
= ⟨ , , , , , , , ⟩ (12)
ℎ = ⟨ , ⟩, (13) where ℎ - method of identification of model parameters; - identifier of features that affect the conditions of the experiments; - main characteristics; - alternative characteristics, с - a statement that describes the conditions of use of the mathematical model.
= ⟨ , ℎ, , , , ⟩ (14)
ℎ = ⟨ ℎ, ℎ, ⟩, (15) where ℎ - is the method identifier; ℎ - method of identification of model parameters; - is the set of statements that defines the method.
Figure 1 shows an example of the implementation of the ontological approach for the tasks of
visualization of the RLN in the process of complex surgery on the thyroid gland, the features of the
implementation of some described in detail in [
Methods, means and information technology for predicting the placement of nerve tissues during surgery on the neck or removal of a tumor on the thyroid gland are considered. The technology is based on the construction of an interval difference operator, which describes a surgical wound with its electrophysiological properties as an object with distributed parameters.
Application of the ontological approach in the above-mentioned RLN identification technology. Provides significant time savings for thyroid surgery. Because, instead of completely building an interval model in the form of a difference equation, the surgeon enters the results of the patient's examinations before the operation (history).
Then, using the ontological model and the repository of interval models for the operated patients, the most adequate model is selected. If necessary, the surgeon can make additional adjustments to the model. However, this will not require a large number of irritations in the area of surgery.
It should be noted that the proposed ontology approach is currently being tested during surgery on the thyroid gland. Additional results can be published after the completion of the tests, ie if there is a sufficient sample of statistics.