Fuzzy controller design for predicting the systolic area of photoplethysmogram signal using Persian medicine pulsology

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BACKGROUND

Advancements in science and technology have considerably increased the complexity of decision-making processes, resulting in longer response times and disruptions to subsequent operations. This complexity is further compounded by uncertainty, which can take various forms and influence decision outcomes. Information is frequently incomplete, inaccurate, ambiguous, or even contradictory. Most of this uncertainty can be managed using fuzzy logic, a predictive technique that involves developing systems based on fuzzy rules [1–3]. Studies have shown that fuzzy logic methods are useful in the early diagnosis of diseases and reported that such early diagnosis plays a critical role in developing more effective treatment plans [4, 5].

Persian medicine (PM), one of the most well-established schools of traditional medicine, is currently undergoing a revival and facing academic scrutiny in several countries, including its place of origin, Iran. Among the clinical diagnosis tools used in PM, pulse diagnosis is considered one of the most important and has been practiced for centuries by traditional medicine specialists to evaluate patients’ health and disease status [6, 7]. Given that pulsology accounts for more than a quarter of the semiology content in major PM textbooks, it appears promising as a complementary diagnostic approach to conventional methods [8, 9]. Consequently, in recent years, emerging applications of artificial intelligence, such as fuzzy systems, have been explored to support the development of standard PM pulse detection methods and their integration with conventional diagnostic methods [10–13]. However, challenges remain regarding physicians’ interpretation of pulse results and the training of students in this domain. Photoplethysmography (PPG) is a technique used to measure blood volume changes with each pulse. It is widely applied in healthcare settings to estimate vital physiological parameters [14, 15]. Particular attention is given to the role of PPG in PM pulsology.

PM is one of the most well-established schools of traditional medicine and has contributed substantially to health care over the centuries. Among its core diagnostic methods, pulse diagnosis has been used by PM practitioners for thousands of years to evaluate patients’ health status [5, 16]. In PM, as in modern physiology, a pulse is defined as the rhythmic expansion of the arteries caused by the heart’s contraction and the ejection of blood. Each pulse cycle is understood to consist of two phases of movement—contraction and expansion and two pauses occurring between these movements. An individual’s pulse is analyzed using various parameters to assess their health status. These parameters include three-dimensional pulse expansion, strength, frequency, the condition of overlying skin and tissue, vessel fullness and consistency, speed, uniformity or variation of the pulse, and pulse weight or “music” [17–19].

PPG is a noninvasive method for measuring changes in blood volume with each pulse [14]. It is widely used in healthcare to estimate various physiological parameters. PPG is also employed to assess blood glucose levels, heart rate, blood oxygen saturation, and arterial stiffness [15]. During PPG, a sensor is typically placed on the skin and includes a photodetector that measures changes in light absorption over a set time interval. The PPG signal reflects heart rate and includes nonpulsatile frequency components that are influenced by factors such as respiration and sympathetic nervous system activity [14, 15]. Pulse waveform analysis involves extracting characteristic features from the PPG signal recorded using a single sensor. Advances in data analysis tools and computing have simplified the pre- and postprocessing of physiological signals, including PPG waveforms [14]. The systolic amplitude, defined as the maximum amplitude during the systolic phase of the PPG waveform, is related to the pulsatile component of blood volume [20]. The systolic amplitude is closely associated with stroke volume, which in turn is proportional to vasodilation at the measurement site [21, 22].

In recent years, PPG has garnered renewed interest owing to the growing demand for simple, low-cost, and portable technologies suitable for primary care and community-based applications. Technologies based on PPG have been integrated into many commercial medical devices used to measure oxygen saturation, cardiac output, and blood pressure; evaluate autonomic function; and diagnose peripheral vascular disease. For example, Allen introduced and illustrated the general principles of PPG, demonstrating its potential for a wide range of clinical measurements [23]. Lee et al. proposed a method for pulse transit time estimation using two cameras positioned opposite each other to simultaneously acquire imaging PPG signals—one from the tip of the index finger and the other from the forehead temple region [24]. In 2020, Chowdhury et al. developed a method to estimate blood pressure using PPG signal features and machine learning algorithms [25]. Park et al. examined PPG from an engineering perspective, summarizing previous research and discussing its measurement principles, mechanisms, waveform characteristics, and associated pre- and postprocessing technologies, as well as the current status and future vision for PPG development [22]. Moreover, in recent years, the use of artificial intelligence and fuzzy systems in PM has been increasing. For instance, Dehghandar et al. applied fuzzy logic to the retentive causes of of the pulse using PM pulse parameters. Their model was based on 10 input variables, three output variables, and 25 rules [12]. Nafisi and Ghods [13] investigated the implementation of a remote care system based on PM. Their system used a thermal camera to measure temperature and humidity, along with a custom device to capture pulse characteristics at the wrist. In 2022, Nafisi et al. used data from 34 participants to develop a user-independent and reproducible method. They used this method to evaluate the characteristics of the wrist pulse [10]. In another study, Dehghandar et al. [6] estimated the gradient of brachial blood pressure in men using 11 input variables, one-output variable, and 36 rules. They also described how this gradient could be derived from PM pulse parameters [6].

AIM

This study aimed to estimate and predict the systolic area of PPG signals using PM pulsology, by leveraging the potential of fuzzy systems.

METHODS

Study design

Given the lack of similar prior studies, this research was conducted as a observational, single-center, cross-sectional pilot study.

Study setting

The study was conducted in collaboration with the Ahmadieh PM Clinic at Tehran University of Medical Sciences. To support the fuzzy controller design, relevant concepts related to PM, PPG signals, and fuzzy systems have been introduced.

Eligibility criteria

The volunteers were aged between 7–69 years and were all healthy; individuals with known cardiovascular conditions were excluded from the study.

Fuzzy systems

Fuzzy logic is widely applied across various branches of science. In artificial intelligence, which involves nondeterministic data, fuzzy logic and its associated rules are extensively used. A fuzzy set A within a universal set U is defined by Equation (1), with values ranging from [0, 1].

$A = \left\{\left(x,{\mu }_A\left(x\right)\right)\left| x\in U\right.\right\}, {\mu }_A\left(x\right)\in \left[\mathrm{0,1}\right]$, (1)

A fuzzy set is therefore a generalization of a classical set. While a classical set allows only two values—0 or 1—the fuzzy membership function is continuous over the interval [0, 1]. A fuzzy expert system typically consists of four components: input fuzzification, rule base, inference engine, and output defuzzification. One key focus of this study is the construction of the fuzzy rule table for fuzzy system design. The following five steps outline the process of designing a fuzzy system using a lookup table:

Step 1: Define appropriate fuzzy sets to cover the input and output spaces

Step 2: Generate fuzzy rules based on input–output variables

Step 3: Assign a degree to each established rule

Step 4: Construct a fuzzy rule base and develop the fuzzy system according to it

Step 5: Construct a fuzzy system based on the fuzzy rule base

If the fuzzy system is designed according to the steps above, with a singleton fuzzifier, a product inference engine, and a center-average defuzzifier, the resulting fuzzy controller will take the form shown in Equation (2). This controller is continuous, bounded, and piecewise linear:

$u = -f\left(x\right) = \frac{{\displaystyle {\sum }_{l = 1}^{2N + 1}{\overline{y}}^l ({\prod }_{i = 1}^n {\mu }_{A_i^l}\left(x\right))}}{{\displaystyle {\sum }_{l = 1}^{2N + 1} ({\prod }_{i = 1}^n {\mu }_{A_i^l}\left(x\right))}}$, (2)

where $x \in U\subset R^n$ represents the input variable, and ${\overline{y}}^l$ denotes the center of the output fuzzy set. The terms $A_i^1,A_i^2,\dots ,A_i^N,A_i^{N + 1},A_i^{N + 2},\dots ,A_i^{2N + 1}$ represent the input fuzzy sets, with $A_i^{N + 1}$ being the center of symmetry of these sets. The parameter $n$ denotes the number of input variables, and $2N + 1$ represents the number of fuzzy rules in the system. To ensure symmetry in the membership function definitions, $N$ fuzzy sets are placed to the left of the central point, $N$ fuzzy sets to the right, and one fuzzy set centered at the midpoint. Notably, the fuzzy system defined by Equation (2) can approximate any continuous function to a desired level of accuracy [26].

Fuzzy system design using PM and PPG variables

Systolic amplitude, systolic peak, and systolic upstroke time represent successive phases of the cardiac cycle and have demonstrated diagnostic and prognostic value in evaluating overall heart function [22, 23, 27]. Accordingly, this study focuses on the systolic area, which encompasses the characteristics described above. Figure 1 illustrates a PPG signal with the systolic peak marked along the systolic upstroke time. The systolic peak area $\left(P_s\right)$ is also indicated.

Theoretically, the pulse frequency and pulse strength parameters in PM appear to be most strongly associated with the systolic area of the PPG signal [8, 27]. Accordingly, this study focused on two key pulse parameters: frequency and strength. An increase in pulse strength directly increases the blood volume per pulse during the systolic phase and is therefore positively associated with the systolic area. In contrast, an increase in pulse frequency reduces the blood volume per pulse during the systolic phase and thus exhibits an inverse relationship with the systolic area [12, 27].

To design the system, a PM specialist recorded the pulse frequency and pulse strength data. These parameters were evaluated and classified using two scales: Pulse frequency was rated on a seven-level scale (extremely low, very low, low, medium, high, very high, extremely high), corresponding to values one through seven; pulse strength was rated on a five-level scale (very low, low, medium, high, very high), corresponding to values one through five. Simultaneously, PPG signals were recorded for each participant using the PO80 pulse oximeter for a duration of 5 s. The systolic area corresponding to each PPG signal (as illustrated in Figure 1) was approximately calculated using the Image Processing Toolbox in MATLAB R2021b. Based on the defined coordinates, the resulting values ranged from 660 to 1210. For the purposes of this study, pulse frequency is denoted as F, pulse strength as S, and systolic area as . The objective is to design a fuzzy controller that takes $\left(F,S\right)$ as inputs and generates $P_s$ as the output. The general specifications for pulse frequency (F), pulse strength (S), and systolic area (P_s) across the 55 participants are summarized in Table 1.

 

Fig. 1. PPG signal indicating the systolic peak area (P_s).

 

Table 1. General specifications of pulse frequency (F), pulse strength (S), and systolic area (Ps) for the 55 healthy volunteers
Variables	Max	Min	Mean	Female	Male
n	—	—	—	15	40
Age	69	7	25.9	43.3	19.4
Pulse frequency (F)	7	1	4.2	3.8	4.4
Pulse strength (S)	5	1	3.1	2.9	3.2
Systolic area (Ps)	1210	660	973	940	985

 

Based on Table 1, the variable limits are defined as follows:

$U = \left[\mathrm{0,8}\right] \times \left[\mathrm{0,6}\right]\subset R^2, \text{V }=\left[\mathrm{650,1220}\right]\subset R$,

where $U$ represents the input space, and $V$  denotes the output space. Given the lack of similar existing data, sampling according to the objectives of this study was considerably difficult and hence limited. The developed system represents a pilot framework; future systems incorporating additional data and variables may offer improved performance.

The steps involved in fuzzy controller design are as follows:

Step 1: Define fuzzy sets to cover the input and output spaces

Specifically, for each interval $\left[{\alpha }_i,{\beta }_i\right], \text{where} i = \mathrm{1,2,}\dots n,$ fuzzy sets $A_i$ are defined as $A_i^l, \text{where} l = \mathrm{1,2}\dots 55$. These sets are complete over $\left[{\alpha }_i,{\beta }_i\right]$, implying that for every $x_i\in \left[{\alpha }_i,{\beta }_i\right]$, there exists $A_i^l$ such that ${\mu }_{A_i^l}\left(x_i\right)\ne 0$. For instance, in this study, the following fuzzy sets were used:

$A_1^1 = H_2,A_2^1 = L_2,B^1 = L_3$.

The input variables—pulse frequency and pulse strength were analyzed using triangular membership functions, as shown in Figures 2 and 3.

 

Fig. 2. Membership function for pulse frequency (input variable).

 

Fig. 3. Membership function of pulse Strength input variable.

 

Also, the output variable systolic area was determined with triangular membership functions as shown in Figure 4.

 

Fig. 4. Membership function of systolic area output variable.

 

As can be seen, normal fuzzy sets are designed so that

$\forall A_i^l:\exists x_i\left| {\mu }_{A_i^l}\left(x_i\right)=1,\right.$(3)

In Step 1, a number of 7 fuzzy sets were defined in  where the membership functions are shown in Figure 2, a number of 5 fuzzy sets were defined in  where are shown in Figure 3 and a number of 7 fuzzy sets were defined in , where the membership functions are shown in Figure 4.

Step2: Generate rules using input-output variables

In this step, for each input-output pair $\left(F^l,S^l;{P_s}^l\right)$, $l=\mathrm{1,2}\dots 55$ corresponding membership values in fuzzy sets $A_i^l$ were determined. Then, for each input-output pair $\left(F^l,S^l;{P_s}^l\right)$, the fuzzy set in which it has the largest membership value is determined. For example, the first, second, and third data in Table 2 are examined to generate rules.

 

Table 2. The values of pulse frequency (F), pulse strength (S) and systolic area (Ps) for 3 volunteers
n	Variables
	pulse frequency (F)	pulse strength (S)	systolic area (Ps)
1	6	1	660
2	1	5	1209
3	1,5	5	1171

 

Using the data in Table 2, the first input-output pair $\left(F^1,S^1;{P_s}^1\right)$ = $\left(\mathrm{6,1};660\right)$ is considered and according to the membership functions in Figures 2 and 5, it can be seen that: $F^1=6$ has a membership value of 1 in the fuzzy set  and in other fuzzy sets has a membership value of 0 in other words ${\mu }_{H_2}\left(F^1\right)=1$.

 

Fig. 5. Membership value of F¹.

 

So according to the membership functions in Figures 3 and 6, it can be seen that: $S^1=1$ has the value of 1 in the fuzzy set in other words ${\mu }_{L_2}\left(S^1\right)=1$.

 

Fig. 6. Membership value of S¹.

 

Also according to the membership functions in Figures 4 and 7, it can be seen that: ${P_s}^1=660$ has a membership value of 0.95 in the fuzzy set $L_2$ in other words ${\mu }_{L_3}\left({P_s}^1\right)=0.95$

 

Fig. 7. Membership value of P_s¹.

 

Therefore, the first rule is obtained as follows: IF $F^1$ is $H_2$ and $S^1$ is  $L_2$, THEN ${P_s}^1$ is $L_3$ .Using the data in Table 1, the second input-output pair $\left(F^2,S^2;{P_s}^2\right)$ = $\left(\mathrm{1,5};1209\right)$ is considered and according to the membership functions in Figures 2 and 8, it can be seen that: $F^2$ in the fuzzy set $L_3$ has a membership value of 1 and in other fuzzy sets has a membership value of 0 in other words ${\mu }_{L_3}\left(F^2\right)=1$.

 

Fig. 8. Membership value of F².

 

Therefore, according to the membership functions in Figures 3 and 9, it can be seen that: ${\mu }_{H_2}\left(S^2\right)=1$.

 

Fig. 9. Membership value of S².

 

Also according to the membership functions in Figures 4 and 10, it can be seen that: ${\mu }_{H_3}\left({P_s}^2\right)=\mathrm{0.89.}$ Therefore, the second rule is obtained as follows: IF $F^2$ is $L_3$ and $S^2$ is $H_2$ , THEN ${P_s}^2$ is $H_3$. Using the data in Table 1, the Third input-output pair $\left(F^{13},S^{13};{P_s}^{13}\right)$ = $\left(\mathrm{1.5,5};1171\right)$ is considered and according to the membership functions in Figures 2 and 11, it can be seen that: $F^{13}$ has a value of 0.5 in the fuzzy set $L_3$ and $L_2$ and in other fuzzy sets has a membership value of 0. Since both $L_3$ and $L_2$ have the same membership values, $L_3$ can be selected, in other words ${\mu }_{L_3}\left(F^3\right)=0.5$. Also according to the membership functions in Figures 3 and 12, it can be seen that: ${\mu }_{H_2}\left(S^{13}\right)=1$.

 

Fig. 10. Membership value of P_s².

 

Fig. 11. Membership value of F¹³.

 

Fig. 12. Membership value of S¹³.

 

Also according to the membership functions in Figures 4 and 13, it can be seen that: ${\mu }_{H_3}\left({P_s}^{13}\right)=0.51$.

 

Fig. 13. Membership value of P_s¹³.

 

Therefore, the 13th rule is obtained as follows: IF $F^{13}$ is $L_3$ and $S^{13}$ is $H_2$ , THEN ${P_s}^{13}$ is $H_3$.

Step3: Assign a degree to each generated rule

Since the number of input-output pairs may be large and each pair generates a rule, there are likely to be conflicting rules, i.e. rules with Same IF parts but different THEN parts. To resolve this conflictsuch conflicts, each rule generated in Step 2 is assigned a degree. Among conflicting rules, only the one with the highest degree is then retained. This approach not only resolves rule conflicts but also substantially reduces the total number of rules. The degree of a rule is defined as

$\text{D}\left(\text{rule }p\right)={\prod }_{i=1}^n{\mu }_{A_i^l}\left(x_{oi}^p\right){\mu }_{B_{}^l}\left(y_o^p\right)$, (4)

We now calculate the degrees of the first, second, and thirteenth rules. For the first rule, we have

$A_1^1 = H_2,A_2^1 = L_2,B^1 = L_3,$ $x_{o1}^1 = F^1,x_{o2}^1 = S^1,y_o^1 = {P_s}^1.$

Thus, $D\left(rule1\right) = {\mu }_{H_2}\left(F^1\right) \times {\mu }_{L_2}\left(S^1\right) \times {\mu }_{L_3}\left({P_s}^1\right) = 0.95$.

For the first rule, we have

$A_1^2 = L_3,A_2^2 = H_2,B^2 = H_3,$ $x_{o1}^2 = F^2,x_{o2}^2 = S^2,y_o^2 = {P_s}^2.$

Thus, $D\left(rule2\right) = {\mu }_{L_3}\left(F^2\right) \times {\mu }_{H_2}\left(S^2\right) \times {\mu }_{H_3}\left({P_s}^2\right) = 0.89$.

For 13th rule, we have

$A_1^{13} = L_3,A_2^{13} = H_2,B^{13} = H_3,$ $x_{o1}^{13} = F^{13},x_{o2}^{13} = S^{13},y_o^{13} = {P_s}^{13}.$

Thus, $D\left(rule13\right) = {\mu }_{L_3}\left(F^{13}\right) \times {\mu }_{H_2}\left(S^{13}\right) \times {\mu }_{H_3}\left({P_s}^{13}\right) = \mathrm{0.255.}$.

Given that rules 2 and 13 belong to the same group and D(rule 2) = 0.89 is greater than D(rule 13) = 0.255, rule 13 is excluded from the rule base.

Step 4: Construct a fuzzy rule base and develop the fuzzy system according to it

At this stage, the fuzzy rule base is represented as a lookup table for the two-input variables. Table 3 presents the lookup table derived based on the fuzzy rules corresponding to the fuzzy sets in Figures 2, 3, and 4. Each cell in the table corresponds to a combination of fuzzy sets within $\left[{\alpha }_1,{\beta }_1\right]$ and $\left[{\alpha }_2,{\beta }_2\right]$, representing a potential rule. As shown in Table 3, the final rule base consists of 35 rules.

 

Table 3. Fuzzy-rule-based lookup table for systolic area estimation
Frequency	Strength
	L2	L1	M	H1	H2
L3	L1	M	H1	H2	H3
L2	L1	M	M	H2	H3
L1	L1	M	M	M	H2
M	L2	L2	L1	L1	M
H1	L2	L1	L1	L1	L1
H2	L3	L2	L1	L1	M
H3	L3	L2	L2	L1	L1

 

For instance, as shown in Steps 2 and 3, the first rule is as follows: IF $F^1$ is $H_2$ and $S^1$ is $L_2$, THEN ${P_s}^1$ is $L_3$. In other words, IF the pulse frequency is $H_2$ and the pulse strength is $L_2$, THEN the systolic area is $L_3$ This is evident from Table 3. Similarly, the second rule is IF $F^2$ is $L_3$ and $S^2$ is $H_2$, THEN ${P_s}^2$ is $H_3$. In other words, IF the pulse frequency is $L_3$ and the pulse strength is $H_2$, THEN the systolic area is $H_3$ as evident from Table 3.

Step 5: Construct the fuzzy system based on the fuzzy rule base

In this step, a fuzzy system was designed in MATLAB using the rule base constructed in Step 4. The system employed a product inference engine, singleton fuzzifier, and center-average defuzzifier.

Ethical approval

This study was approved by the Ethics Committee of Payame Noor University (Tehran) on March 8, 2025, with protocol No. IR.PNU.REC.1403.685.

RESULTS

Participants

In this study, the pulse frequency, pulse strength, and PPG signal data of 55 volunteers were simultaneously recorded using a PO80 Beurer pulse oximeter, with assistance from the Ahmadieh PM Clinic at Tehran University of Medical Sciences. The volunteer group consisted of 15 females and 40 males.

Primary results

$\left(F^l,S^l;{P_s}^l\right)$ $l = \mathrm{1,2}\dots 55.$ The fuzzy-rule-based system was presented as a two-input, one-output lookup table, as shown in Table 3. This table presents the following rules:

• IF $F$ is $H_2$ and $S$ is $L_2$, THEN $P_s$ is $L_3,$
• IF $F$ is $L_3$ and $S$ is $H_2$, THEN $P_s$ is $H_3$.

In general, increasing the membership value of pulse frequency and decreasing the membership value of pulse strength leads to a lower systolic area membership value. Conversely, decreasing the membership value of pulse frequency and increasing that of pulse strength results in a higher systolic area membership value.

Figure 14 presents a two-dimensional representation of the systolic area, where arrows indicate the gradient values computed using the quiver function. Therefore, considering that an increase in the gradient indicates maximum values of the function, the direction of the arrows shows where these maximum values occur. In two-dimensional functions, regions where arrows from both input dimensions converge represent areas of maximum output, while regions where arrows diverge represent areas of minimum output.

 

Fig. 14. Fuzzy system designed to predict systolic area using 35 rules.

 

As shown in the figure, the highest systolic area values appear in the red region, while the lowest values appear in the yellow region. As highlighted in the red circle in Figure 14, rules associated with pulse strength increases around 4–5 and pulse frequency increases approximately 1–2 result in increased systolic area. In contrast, the yellow circle in Figure 14 highlights rules where pulse strength reductions around 1–2 and pulse frequency reductions approximately 6–7 lead to a decrease in systolic area.

DISCUSSION

Summary of primary results

The fuzzy system, developed based on the final rules, it is possible to Predict the output of the systolic area up to an acceptable value by applying the pulse strength and Persian medical pulse frequency inputs close to the existing rules.

Interpretation

Given that the systolic area of the PPG signal has considerable diagnostic and prognostic value for evaluating the overall function of the heart, and PM pulsology is one of the most important clinical diagnosis methods, therefore, systolic area estimation by PM pulsology using the fuzzy intelligent system is very important and useful. According to [9] and [11] in PM references and documents, with the increase in heart strength, the volume of blood in each pulse increases in the systolic phase, in this research in the red circle of Figure 14 it was observed that the increase in pulse strength increases the systolic area which is consistent with the results obtained in [27] and [23] in common medicine. Also according to [9] and [11] in Persian medical scientific sources, with the increase in pulse frequency, the volume of blood in each pulse decreases in the systolic phase, in this study, as shown in the yellow circle of Figure 14, an increase in pulse frequency was associated with a decrease in systolic area. This observation is consistent with findings from conventional medicine [22, 28, 29]. A recent related study [30] used a fuzzy system to correlate selected systolic features of the PPG signal with PM pulse parameters. The system was designed using 236 rules, and the resulting error was below 0.05, which is considered an acceptable level of accuracy. This study also demonstrated that the systolic area of the PPG signal, which is strongly associated with its systolic features, is closely related to PM pulse parameters. Given the lack of similar studies for reference or validation, the fuzzy system developed in this pilot study serves as a useful model for predicting the systolic area of the PPG signal using PM pulsology. However, its performance could be further improved with additional data and variables.

CONCLUSIONS

Using the proposed fuzzy controller system, the systolic area of a PPG signal could be reasonably predicted by applying PM pulse strength and pulse frequency inputs that align with the established fuzzy rules. Moreover, an increase in pulse frequency was found to reduce the systolic area, while an increase in pulse strength led to an increase in the systolic area, consistent with findings from previous studies. Overall, given the diagnostic and prognostic importance of systolic PPG intervals as non-invasive indicators of heart function and the central role of pulse assessment in PM, the application of artificial intelligence tools—such as the fuzzy controller system developed in this study—may serve as a promising bridge between PM and modern clinical practice, enhancing the effectiveness of both.

ADDITIONAL INFORMATION

Author contribution: M. Dehghandar: conceptualization, methodology, software, writing and editing the manuscript; S.M. Mirhosseini-Alizamini: data curation, original draft preparation; M.A. Vaghasloo: visualization, data curation, validation, investigation; A.K. Najafabadi: software, methodology, supervision. Thereby, all authors provided approval of the version to be published and agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately investigated and resolved.

Ethical approval: This study was approved by the Ethics Committee of Payame Noor University (Tehran) on March 8, 2025, with ethics code IR.PNU.REC.1403.685.

Funding sources: No funding.

Disclosure of interests: The authors have no relationships, activities or interests for the last three years related with for-profit or not-for-profit third parties whose interests may be affected by the content of the article.

Statement of originality: When creating this work, the authors did not use previously published information (text, illustrations, data).

Data availability statement: The data used to support the findings of this study are available from the corresponding author upon request.

Generative AI: Generative AI technologies were not used for this article creation.

Provenance and peer-review: This article was submitted to the journal on an unsolicited basis and reviewed according to the usual procedure. Оne external peer-reviewerand one member of the editorial board were involved in the review process.

About the authors

Mohammad Dehghandar

Payame Noor University

Author for correspondence.
Email: dehghandar@gmail.com
ORCID iD: 0000-0003-4882-3121

PhD, Assistant Professor

Iran, Islamic Republic of, Tehran

Seyed M. Mirhosseini-Alizamini

Payame Noor University

Email: m_mirhosseini@pnu.ac.ir
ORCID iD: 0000-0003-1433-3124

PhD, Assistant Professor

Iran, Islamic Republic of, Tehran

Mahdi A. Vaghasloo

Tehran University of Medical Sciences; Persian Medicine Network; Universal Scientific Education and Research Network

Email: mhdalizadeh@gmail.com
ORCID iD: 0000-0002-2987-4292

MD, PhD

Iran, Islamic Republic of, Tehran; Tehran; Tehran

Asghar K. Najafabadi

Payame Noor University

Email: khosravi.a@lu.ac.ir
ORCID iD: 0009-0003-3897-8215

PhD

Russian Federation, Tehran

References

Supplementary files