Fuzzy controller design for Estimation of Systolic area in PPG signal by Persian medicine

Resumo

Introduction: Photoplethysmogram (PPG) is a method for measuring blood volume changes per pulse and is widely used in healthcare. On the other hand, Persian medicine (PM) pulsology is one of the most important methods of clinical diagnosis. In this research, by using the potential of fuzzy systems, it has tried to establish a relationship between PPG signal indicators in the systolic area and PM pulsology.

Methods: The theory of fuzzy sets is a very applicable basis for the development of knowledge-based systems in medical studies . To design the fuzzy controller, the pulse information as well as the PPG signal was simultaneously recorded using 55 individuals by a PM specialist. First, the rules were created using input-output variables. Also, by keeping the rules to the highest degree and removing the rest of the rules, 35 rules remained which was shown in the form of a lookup table in two-input-one-output mode.

Results: The fuzzy system with 35 rules, triangular and trapezoidal membership functions, singleton fuzzifier, product inference engine, and center average defuzzifier was designed by MATLAB software. This system with two inputs of pulse frequency and pulse strength, as well as an output of systolic area, has an acceptable efficiency in the defined range of inputs.

conclusion: This fuzzy controller system provides a reasonable estimate of the systolic area of the PPG signal using PM pulse parameters, and it was observed that increasing the pulse frequency decreases the systolic area and also increasing the pulse power increases the systolic area, which is consistent with the results of previous studies. Therefore, it can be used to help increase the clinical skills of PM students and practitioners. This can also be promising to be applied in the diagnosis and prediction of diseases, as well as to establish communication between PM and mainstream medicine.

Texto integral

1.  

Currently, due to the progress of science and technology, the complexity of the decision-making process is very high, and it causes the time to make the right decision to increase and therefore affects the subsequent processes. Uncertainty appears in various forms and affects decisions. Often, information may be incomplete, inaccurate, ambiguous, contradictory, or incomplete, and most of this uncertainty can be controlled using fuzzy logic, one of the prediction and estimation techniques is the technique of developing a system based on fuzzy rules [1-3]. Research has shown that fuzzy logic methods can be used in the early diagnosis of diseases and it has been proven that early diagnosis is very valuable in creating a more effective treatment plan [4,5].

On the other hand, one of the most rooted schools of traditional medicine is Persian medicine (PM) which is currently revival and undergoing academic criticism in many countries, including its motherland i.e. Iran. Pulse diagnosis is one of the most important methods of clinical diagnosis in PM, which has been used for many centuries by traditional medicine specialists to assess the disease and health status of clients [6,7]. As pulsology includes more than a quarter of the pages written about semiology in major PM textbooks, the use of its capacities seems fruitful and usable for diagnosing and identifying diseases aside from conventional methods of diagnosis [8, 9]. Therefore, recently, wider and newer dimensions of artificial intelligence applications such as fuzzy systems have been shown, which help to develop standard PM pulse detection and integrate it with conventional detection methods [10-13]. In addition, there are problems and considerations related to the experience and analysis of pulse results by doctors and the training of students in this field. Also, Photoplethysmogram (PPG) is a method to measure blood volume changes per pulse, moreover, PPG is widely used in healthcare where it is used to predict vital health-related parameters [14, 15]. This research aimed to evaluate the usability of PM pulsology to estimate the systolic area in PPG signal with the help of a fuzzy controller design. Therefore, for the design of the fuzzy controller, concepts related to PM and PPG signal as well as the fuzzy systems have been mentioned, and then the stages of designing and analyzing the results of the fuzzy system have been described.

Persian Medicine

Persian Medicine (PM) is one of the rich schools of traditional medicine that has provided many services to humanity and pulse diagnosis is one of the most important clinical diagnostic methods in PM that has been used by PM physicians for thousands of years to assess patients' health‎ [5,‎16]. In PM school - same as in modern physiology - the regular periodic expansion of an artery due to the ejection of blood into the arterials by heart contractions is known as the pulse. Each pulse is considered to include two movement periods of contraction and expansion, and two pauses, lying in between every two movements. The pulse of each individual is analyzed by different parameters to judge the health status. These parameters include pulse expansion in three spatial dimensions, strength, frequency, quality of the overlying skin and tissue, vessel fullness and consistency, speed, pulse uniformity or diversity, and pulse weight or music [17-19].

Photoplethysmogram

A photoplethysmogram (PPG) is a non-invasive method to measure blood volume changes per pulse [14]. PPG is widely used in healthcare where it is used to predict vital health-related parameters. Also, PPG is used for determining blood glucose levels, heart rate, blood oxygen saturation, and atrial stiffness [15]. The PPG sensor displays the surface of the skin and is a photodetector for measuring changes in light absorption over a set time interval. The PPG signal contains information about heart rate and is over a large non-pulsatile frequency range that is affected by factors such as respiration and sympathetic nervous system activity. [14, 15]. Pulse waveform analysis deals with the extraction of specific characteristic features and signal processing from the PPG wave, which requires only one measuring sensor, PPG. Developments in data analysis tools and computing have simplified the pre-and post-processing of physiological signals such as PPG [14]. The maximum amplitude of the systolic phase of the PPG is called the systolic amplitude that related to the pulsatile component of blood volume [20]. Systolic amplitude is largely directly related to stroke volume, which is directly proportional to the vasodilatation of the local body site where PPG is measured [21, 22].

In recent years, given that PPG is a simple and low-cost optical technique, renewed attention to this technique has increased due to the demand for a low-cost, simple, and portable technology for primary care and community-based applications. PPG-based technology is available in a large number of current commercial medical devices for measuring oxygen saturation, cardiac output, and blood pressure, evaluating autonomic function, as well as diagnosing peripheral vascular disease. Some of them can be mentioned: John Allen 2007 introduced and illustrated the technique of PPG in general and it has shown great potential for its use in a wide range of clinical measurements [23]. Hay Lee et al. in 2015 a method for PTT estimation that uses two opposite cameras and receives PPGi signals simultaneously, one from the camera at the tip of the index finger and the other from the surface of the skin in the forehead temple [24]. In another study, Mojam Hossein Chowdhury et al. In 2020, with the help of PPG signal features and machine learning, they presented a method to estimate blood pressure. [25]. Junyung Park et al. in 2022 did a study on PPG signal. Their purpose was to examine PPG from an engineering viewpoint through the previous research and review the current status and vision of PPG, including its measurement principle and mechanism, waveform characteristics, pre-processing technology, and post-processing technology [22]. Also, in recent years, the use of artificial intelligence and fuzzy systems in PM is increasing. Some of them are mentioned: In 2016, Dehghandar et al. used fuzzy logic to determine the retentive causes of the pulse by the pulse parameters of PM. They presented their proposed model assuming 10 input variables, 3 output variables, and 25 rules [11]. Vahid R. Nafisi and Roshanak Ghods 2021 investigated the possibility of implementing a remote care system based on PM which Uses a thermal camera to measure temperature/humidity and a custom device for measuring pulse characteristics in the wrist [12]. In 2022 Vahid Reza Nafisi et al. used the information of 34 participants to achieve a user-independent and reproducible method for measurement and evaluated the characteristics of the wrist pulse [10]. Also, Dehghandar et al. in another study in 2022 estimated the gradient of brachial blood pressure in men with 11 input variables and one output variable, and 36 rules, and explained how to estimate the gradient of brachial blood pressure in men using pulse parameters of PM [6]. In the following, the method of designing and analyzing the results of the fuzzy system is explained.

1. Materials and methods

In this section, in general, the necessary fuzzy concepts were discussed first, and then the indicators of the PPG signal and its relationship with the pulse variables of PM were presented, and then the design steps of the fuzzy system were explained using the recorded data.

Fuzzy systems

Fuzzy logic is currently used in various branches of science. In artificial intelligence, which is designed based on non-deterministic data, fuzzy logic and rules of this logic are widely used. The fuzzy set A in the global space U is defined as  Equation (1) that takes values ​​in the interval [0, 1].

Therefore, a fuzzy set is a generalization of a classical set, in other words, a classical set could only have two values ​​1 and 0, while the fuzzy membership function is continuous in the range [0, 1]. The structure of a fuzzy expert system consists of 4 parts, which are: fuzzification of inputs, rules, inference engine, and defuzzification of outputs. One of the issues raised in this article for the design of fuzzy systems is the construction of the fuzzy rules table. The five steps for designing a fuzzy system using a lookup table are introduced as follows:

Step1: Covering input and output spaces by defining appropriate fuzzy sets

Step2: Generate rules using input-output variables

Step3: Assign a degree to each generated rule

Step4: Create a fuzzy rule base and build a fuzzy system based on it

Step5: Fuzzy system design based on fuzzy rules

If the above conditions and steps are included in the fuzzy system design and its fuzzifier is selected as singleton, its engine is product inference, and its defuzzifier is selected center average for the fuzzy system then the designed fuzzy controller will be in the form of equation (2) which is continuous, bounded and piecewise linear:

Where is the input variable, is the center of the output fuzzy set,  are input fuzzy sets and is the center of symmetry of these fuzzy sets,  is the number of input variables and  is the number of rules of the fuzzy system. It is noted that  fuzzy sets on the left side of the equilibrium or medium point and one fuzzy set including the medium point and  fuzzy sets on the right side of the medium point are defined in order to provide symmetry in the definition of the membership functions. It is noted that the fuzzy system in the form of Equation (2) can approximate all continuous functions with the desired accuracy [26]. Therefore, with these fuzzy systems, all continuous functions can be estimated with the desired accuracy.

Fuzzy system design with variables of PM and PPG

The parameters of systolic amplitude, systolic peak, and systolic upstroke time describe the successive phases of the cardiac cycle and have shown significant diagnostic and prognostic value for evaluating the overall function of the heart [22, 23, 27]. Therefore, in this research, the systolic area that has the above-mentioned items has been discussed. Figure 1 shows a PPG signal diagram indicating the point of the systolic peak on the systolic upstroke time. The systolic peak area is also marked.

Figure 1. A PPG signal curve indicating the systolic peak area ( )

Theoretically, it seems that the pulse frequency and pulse strength parameters in PM are most related to the systolic area in the PPG signal [8, 27]. Therefore, in this study, the obtained pulse parameters have been reduced to frequency and Strength parameters. The increase in pulse strength has a direct impact on the increase in blood volume per pulse in the systolic phase, and therefore it is directly related to the increase in the systolic area Also, the increase in pulse frequency has a direct effect on the reduction of blood volume per pulse in the systolic phase, and therefore has an inverse relationship with the increase in systolic area [12, 27].

To design the system first, the pulse information including pulse frequency and pulse strength of 55 individuals was recorded by a PM specialist at the Ahmadiyya PM Clinic of Tehran University of Medical Sciences. Also, the PPG curve data of these 55 individuals were simultaneously recorded by the PO80 pulse oximeter device for 5 seconds for each person. Then ​​the systolic area corresponding to Figure 1 for each PPG signal was approximately calculated using the image processing toolbox in MATLAB R2021b software based on the defined coordinates. Here the variables are named like this: pulse frequency is F, pulse strength is S and systolic area is .The task is to design a controller whose inputs are  and whose output is , so that the inputs can track the output of . For these 55 data, general specifications ​​of pulse frequency(F), pulse strength(S) and systolic area ( ) are given in Table 1.

Table 1. General specifications of pulse frequency(F), pulse strength(S) and systolic area ( ) for 55 individuals

Variables	Max	Min	Mean	Female	Male
N	-	-	-	15	40
pulse frequency(F)	7	1	4.2	3.8	4.4
pulse strength(S)	5	1	3.1	2.9	3.2
systolic area ( )	1210	660	973	940	985

Using Table 1, the limits of the variables are as follows:

Where  is the input space and  is the output space. Due to the lack of previous similar data, limited sampling according to the objectives of this research was done with difficulty and the data was generated. This system is considered as a pilot study and future systems with more data and variables can be used for more efficiency.

The steps of fuzzy controller design are as follows:

Step1: Define fuzzy sets for covering input and output spaces

Specifically, For each  fuzzy sets  are defined as  which are complete in ; That is, for every , there exists : such that . For example, in this study, some fuzzy sets are used as follows:

The input variables the pulse frequency and pulse strength were determined with triangular membership functions as shown in Figure 2,3.

Figure 2. Membership function of pulse frequency input variable

Figure 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.

Figure 4. Membership function of systolic area output variable

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

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 ,  corresponding membership values in fuzzy sets  were determined. Then, for each input-output pair , 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 ( ) for 3 individuals

n	pulse frequency(F)	pulse strength(S)	systolic area ( )
1	6	1	660
2	1	5	1209
3	1.5	5	1171

Using the data in Table 2, the first input-output pair  =  is considered and according to the membership functions in Figures 2 and 5, it can be seen that:  has a membership value of 1 in the fuzzy set  and in other fuzzy sets has a membership value of 0   in other words .

     Figure 5. Membership value of                                  Figure 6. Membership value of  

So according to the membership functions in Figures 3 and 6, it can be seen that:  has value of 1 in the fuzzy set in other words .

Also according to the membership functions in Figures 4 and 7, it can be seen that:  has a membership value of 0.95 in the fuzzy set in other words

                  Figure 7. Membership value of                                             Figure 8. Membership value of

Therefore, the first rule is obtained as follows: IF  is  and  is  , THEN  is .Using the data in Table 1, the second input-output pair  =  is considered and according to the membership functions in Figures 2 and 8, it can be seen that:  in the fuzzy set  has a membership value of 1 and in other fuzzy sets has a membership value of 0 in other words .

Therefore, according to the membership functions in Figures 3 and 9, it can be seen that: .

                Figure 9. Membership value of                                  Figure 10. Membership value of

Also according to the membership functions in Figures 4 and 10, it can be seen that: Therefore, the second rule is obtained as follows: IF  is  and  is  , THEN  is . Using the data in Table 1, the Third input-output pair  =  is considered and according to the membership functions in Figures 2 and 11, it can be seen that:  has a value of 0.5 in the fuzzy set  and  and in other fuzzy sets has a membership value of 0. Since both  and  have the same membership values,  can be selected, in other words . Also according to the membership functions in Figures 3 and 12, it can be seen that: .

                                      Figure 11. Membership value of                Figure12. Membership value of

Also according to the membership functions in Figures 4 and 13, it can be seen that: .

Figure 13. Membership value of

Therefore, the 13th rule is obtained as follows: IF  is  and  is  , THEN  is .

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 conflict, each rule generated in step 2 is assigned a degree, and only one rule of conflicting rules remains. The group with the maximum degree. In this way, it is not only a problem of conflict solved, but the number of rules is also drastically reduced. The degree of a rule is defined as follows:

Now the degree of the first, second, and thirteenth rules is calculated. For first rule, is as follows:

Therefore  

For second rule, is as follows:

Therefore   

For 13th rule, it is as follows:

Therefore 

Considering that rules 2 and 13 are in the same group and the degree of rule 2 (0.89) is greater than rule 13 (0.255), therefore rule 13 is removed.

Step4: Create a fuzzy rule base and build a fuzzy system based on it

At this step, a fuzzy rule base can be represented as a lookup table in two input cases. Table 3 shows a representation of the lookup table based on the fuzzy rules corresponding to the fuzzy sets in Figures 2, 3, and 4. Each box is a combination of fuzzy sets in  and  and shows a possible rule. As seen in Table 2, the rule base consists of 35 rules.

Table 3. Fuzzy rule-based final lookup table for systolic area estimation

Strength Frequency

For example, as seen in steps 2 and 3, the first rule  is like this: IF  is  and  is  , THEN  is   in other words, IF the pulse frequency is  and pulse strength is  , THEN systolic area is    which can be seen in Table 3, and also second rule is like this: IF  is  and  is  , THEN  is   in other words, IF the pulse frequency is  and pulse strength is  , THEN systolic area is  which can be seen in Table 3. At step 5, Construct the fuzzy system based on the fuzzy rule base. In this step, using the rules base made in step 4, the fuzzy system with the product inference engine, singleton fuzzifier, and center average defuzzifier was designed by MATLAB software.

1. Results

To design the fuzzy system, the pulse information including the frequency and strength of the pulse and the PPG curve were simultaneously recorded by a pulse oximeter PO80 Beurer from 55 people at PM Ahmadiyeh Clinic of Tehran University of Medical Sciences by a PM specialist. First, fuzzy sets were defined to cover the input and output spaces which are complete and normal. In the second step, rules were created using input-output variables. For each input-output pair ,  corresponding membership values in fuzzy sets  were determined. Then, for each input-output pair , the fuzzy set in which it has the largest membership value was determined. In the third step, to remove conflicting rules, each rule produced in the previous step was given a degree, and by having rules with the highest degree and removing the rest of the rules, the problem of conflicting rules was solved in the end, and 35 rules remained.

In the fourth step, a system based on fuzzy rules was shown in the form of a lookup table in two-input-one-output mode according to Table 3. As can be seen in Table 3, in general, like the following two rules:

IF  is  and  is  , THEN  is

IF  is  and  is  , THEN  is

In the generated rules, by increasing the pulse frequency membership function and decreasing the pulse strength membership function, the systolic area membership function decreases, and by decreasing the pulse frequency membership function and increasing the pulse strength membership function, the area systolic membership function increases. In the fifth step, the fuzzy controller consisting of engine type product inference, fuzzifier type singletone, and defuzzifier type center average is designed by MATLAB software, whose overview can be seen in Figure 14.

.

Figure 14. Fuzzy system designed to estimate systolic area with 35 rules

In the two-dimensional figure 14, which is related to the display of the systolic area value, the significance arrows seen in the figure show the gradient values using the quiver function. Therefore, considering that the increase of the gradient determines the maximum values of the function, the direction of the arrows in any direction shows the maximum values. Considering this issue, in two-dimensional functions, the area that points there from both dimensions therefore, the maximum area will be the function, and conversely, the area that moves away from there in both dimensions will be the minimum area of the function.

It can be observed that the maximum values are in the red area and the minimum values are in the yellow area. As can be seen in the red circle in Figure 14, the generated rules in which the increase in pulse strength is about 4-5, and the decrease in pulse frequency is about 1-2, increase the systolic area. As can be seen in the yellow circle in Figure 14, the generated rules in which the reduction of the pulse strength is about 1-2, and the increase of the pulse frequency is about 6-7, cause the reduction of the systolic area.

1. Discussion and Conclusion

Considering that the systolic area parameter in PPG shows a significant 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. As mentioned, the aim of this research was to design a fuzzy system to estimate the systolic area using the pulsology of PM. By using this fuzzy system which was designed from the 35 final remaining rules, it is possible to estimate 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. 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 research in the yellow circle of Figure 14 it was observed that the increasing the pulse frequency decreases the systolic area which is consistent with the results obtained in [22], [28], and [29] in common medicine and confirms them. By using this fuzzy system, it is possible to estimate and predict the systolic area output to an acceptable value by applying pulse strength and pulse frequency inputs of Persian medical close to the existing rules, and this be a good connection between PM and common medicine, and specialists can benefit from it.

Data Availability

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

Ethical approval

In this study, after obtaining informed consent for admission at Ahmadieh PM Clinic of Tehran University of Medical Sciences as a research and training clinic, only routine pulse examination and plethysmography data obtained for health benefits were considered in the analysis; in addition, no confidential personal information or interventions were involved and thus no additional ethical approval was necessary for this work.