Non-invasive continuous blood pressure measurement based on mean impact value method, BP neural network, and genetic algorithm

2.1Extraction of PWTT and PWPs

After pretreating [12] the synchronously collected pulse wave signal and ECG signal and extracting their feature points [7, 13], the PWTT was obtained by calculating the time from the ECG R wave to feature point c of the pulse wave signal in the same cardiac cycle, as illustrated in Fig. 1.

The PWPs are shown in Fig. 2. When the PWPs were extracted, it was found that the pulse waveform parameters were affected by physiological and other changes, but while the absolute values of the PWPs varied greatly, the relative values changed little. Therefore, in order to reduce the influence of these various changes and compare the parameters among different subjects, this study used a normalization method to process the time domain parameters of the pulse wave [5].

In this study, PWTT and PWPs (a total of 17 parameters) were selected as the object of study, including: PWTT, the relative time (RT) of the ascending branch (tc/T), RT of feature point d (td/T), RT of feature point e (te/T), RT of feature point f (tf/T), RT of feature point g (tg/T), pulse wave cycle (T), the relative height (RH) of feature point d (Hd/Hc), RH of feature point e (He/Hc), RH of feature point f (Hf/Hc), RH of feature point g (Hg/Hc), pulse waveform characteristic quantity (K), main wave ascending slope (V), cardiac output (Z), relative area (RA) of the systolic period (S1/S), RA of the diastolic period (S2/S), and ratio of systolic and diastolic area (S1/S2).

2.2Construction of the BP neural network

The back-propagation (BP) neural network [14] is the basis of MIV-BP neural network construction. This forward neural network has a minimum of three layers, including input, hidden, and output layers.

The artificial neural network accurately describes not only linear, but also nonlinear, relationships. The BP neural network is the most widely used neural network in artificial neural network, which embodies the most essential part of artificial neural network. Thus, this paper establishes blood pressure models based on BP neural networks. A portion of the experimental data was used as the training set. Extracted PWTT and PWPs (a total of 17 parameters) were used as input parameters, and the SBP or DBP value measured by sphygmomanometer was used as the output parameter to train one BP neural network (Nets0) on SBP and another (Netd0) on DBP.

2.3Construction of the MIV-BP neural network

Furthermore, the mean impact value (MIV) method was used as an indicator of the degree of influence of each independent variable on the dependent variable. The process by which it was calculated is as follows:

The MIV of each independent variable was calculated according to the above steps. Finally, the relative contribution rate of the ith independent variable to the dependent variable was calculated according to Eq. (1).

Where ∂i denotes the relative contribution rate of the ith independent variable to the dependent variable, and ∑in∂i∑im∂i denotes the cumulative contribution rate (CCR) of the first n independent variables. When selecting the input parameters of the BP neural network, the CCR should be greater than 85%.

When PWPs, PWTT, and blood pressure values are used to train a model, due to too many input parameters, the input layer of the BP neural network becomes complicated, the load on the system increases, and the performance of the network decreases. Therefore, the MIV method was used to reduce the dimension of the input data in this study. Based on the BP neural networks constructed in Section 2.2, the first few input parameters with CCRs to SBP or DBP of over 85% were selected. The selected parameters were used as input parameters to retrain the Nets0 and Netd0 networks, and then the two MIV-BP neural networks, NETs0 and NETd0, were obtained.

2.4MIV-BP neural network model based on GA

A GA is a global optimization algorithm, developed by simulating a natural evolutionary process, which is simple, robust, and enhances parallel processing. Therefore, it is widely used in the fields of combinatorial optimization, parameter optimization, machine learning, and others.

Figure 3.

Flow chart of the non-invasive continuous blood pressure measurement models based on the GA-MIV-BP neural network.

Because of differences in individual physiological system, the relationship between each individual’s blood pressure and PWTT/PWPs is different. Therefore, a non-invasive continuous blood pressure monitoring model based on a GA-MIV-BP neural network is proposed. In order to improve the accuracy and generality of the blood pressure model and avoid the influence of individual differences in examiners, the NETs0 and NETd0 networks trained in Section 2.3 were selected to construct the SBP and DBP calculation models, respectively. The GA was used to optimize the individual parameters of the models, and SBP and DBP calculation models with good predictive performance were obtained. The flow chart of the non-invasive continuous blood pressure measurement models based on the GA-MIV-BP neural network are shown in Fig. 3.

3.1Experimental data collection and processing

3.1.1Experimental data collection

Using the characteristics of pulse wave and ECG signals, this experiment utilized a radial artery pulse sensor (HK-2000B piezoelectric sensor; Electronic Technology Research Institute of Hefei Huake, China), ECG electrode and cable, and a USB-D1280 data collecting card (VI Service Network Co., Ltd) to achieve pulse wave and ECG signals synchronization acquisition, in which the sampling frequency was set to 400 Hz.

We recruited volunteers based on the principles of voluntary and informed consent, and undertook to protect the rights and interests of the subjects. There was no conflict of interest between the content or results of the research and the volunteers. Five healthy male and five healthy female volunteers, aged 21∼28 years, were included. Resting-state data before exercise and data after light exercise at the temperature ranged from 15 to 25 centigrade degree were collected from the volunteers. The data included the pulse wave and ECG signals of the subjects, which were simultaneously recorded for 40 seconds in each state. After data acquisition in each state, SBP and DBP values were measured by an OMRON HEM-6131 blood pressure meter in triplicate. The average of the three results was calculated as the measured sphygmomanometer value. In order to reduce errors, the signal acquisition and blood pressure measurement of each subject in each state was completed within 5 minutes. A total of 120 sets of data were recorded in the experiment, as shown in Table 1.

Table 1

Collected pulse wave and ECG data

Male					Female					Total
Test_1	Test_2	Test_3	Test_4	Test_5	Test_6	Test_7	Test_8	Test_9	Test_10
15	12	12	12	9	15	12	12	12	9	120

Figure 4.

Original ECG and pulse wave signals collected synchronously.

3.2Construction of MIV-BP neural network

MIV-BP neural networks were constructed in MATLAB R2014a software. A comprehensive set of functions and a graphical user interface in the ANN toolbox of MATLAB were used to train and simulate the MIV-BP neural networks; the specific steps were as follows:

3.2.1Training of BP neural network

Data from male (Test_1, Test_2, Test_3, and Test_4) and female (Test_6, Test_7, Test_8, and Test_9) subjects, a total of 102 sets of data, were selected as training sets. Extracted PWTT and PWPs, a total of 17 parameters, were used as input parameters, and the measured sphygmomanometer SBP or DBP value was used as the output parameter to train one BP neural network on SBP and another on DBP (Nets0 and Netd0, respectively), as described below.

Table 2

Determination of the input and output parameters of the two BP neural network

NN	Input parameters	Output parameters
Nets0	PWTT, PWPs	SBP
Netd0	PWTT, PWPs	DBP

Figure 5.

Feature point recognition of the denoised ECG and pulse wave signals.

The principle of the BP neural network is that the single hidden-layer feedforward neural network can approximate arbitrary continuous functions with arbitrary precision [15]. In order to improve the training speed of the network and to simplify the structure of the network, this study adopted a single hidden layer.

• (1) Determine the input and output parameters of the two networks, Nets0 and Netd0, as shown in Table 2.

  The number of input node for Nets0 or Netd0 network was seventeen, and of output node for Nets0 or Netd0 network was one.

• (2) Initialize the parameters of the Nets0 and Netd0 networks, including learning rate, expected error, and activation functions. The learning rate, the expected error, and the activation functions for hidden and output layers were set to 0.1, 0.01, TANSIG and PURELIN, respectively.

• (3) Select the nodal points of the hidden layer of the Nets0 and Netd0 networks. According to the empirical formula shown in Eq. (2) [16], the number of nodes in the hidden layer of the Nets0 and Netd0 networks ranged from 5 to 15. Using trial-and-error method, the definitive number of nodal points in the hidden layer of the two networks was obtained by taking the root mean square error (RMSE) and complexity of the networks as the index.

  (2)

  m=n+l+∂

  Where m denotes the number of hidden-layer nodes of the BP neural network, n denotes the number of input-layer nodes of the BP neural network, l denotes the number of output-layer nodes of the BP neural network, and ∂ is a constant between 1 and 10.

  After repeated experiments, we found the optimal number of hidden-layer nodes by taking the RMSE and complexity of the networks as the index. Finally, the definitive number of hidden-layer nodes for Nets0 and Netd0 were determined to be 12 and 13, respectively.

• (4) Train Nets0 and Netd0 networks using the scaled conjugated gradient algorithm, which has the advantage of good convergence [17]. The training continued until the expected error was achieved.

Table 3

Ordered MIVs for SBP value input parameters

Variable name	MIV	Ordering	CCR
T	-12.1971	1	0.1725
S1/S	-10.1024	2	0.3154
PWTT	-9.0271	3	0.4431
S2/S	-7.2872	4	0.5462
td/T	-6.1129	5	0.6327
tg/T	-4.6608	6	0.6986
tf/T	-3.7106	7	0.7511
Hd/Hc	-3.1529	8	0.7957
Hg/Hc	-2.7224	9	0.8342
Z	2.3060	10	0.8668
S1/S2	2.2786	11	0.8990
He/Hc	1.8326	12	0.9249
V	-1.6578	13	0.9483
K	1.3715	14	0.9677
tc/T	1.1822	15	0.9844
Hf/Hc	0.9430	16	0.9977
te/T	0.1596	17	1.0000

3.2.3Training and evaluation of MIV-BP neural network model

The input parameters selected using the MIV method were used as input to the MIV-BP neural networks. The learning rate, expected error, and activation functions for the hidden and output layers were set to 0.1, 0.01, TANSIG and PURELIN, respectively. Based on the empirical formula in Eq. (2) and trial-and-error, the number of hidden-layer nodes of NETs0 and NETd0 were set to 9 and 10, respectively, by taking the RMSE and complexity of the networks as the index. Finally, the scaled conjugate gradient algorithm was used to train the two neural networks. The training time for those two networks were all less than 10 seconds.

After training the NETs0 and NETd0 networks, the data from ten subjects were selected as the test set. The RMSE and mean relative error (MRE) were used to compare the performance of the Nets0 and Netd0 networks trained by the original 17 input parameters and the NETs0 and NETd0 networks trained by the parameters selected using MIVs. The specific results are shown in Table 5. The contrasting results obtained from the BP neural networks trained by the original and MIV-preferred parameters, and the advantages offered by simplifying the structure of the model, led the authors to select the NETs0 and NETd0 networks trained by the MIV-selected parameters to construct the SBP and DBP calculation models, respectively.

Table 4

Ordered MIVs for DBP value input parameters

Variable name	MIV	Ordering	CCR
T	-11.1125	1	0.2769
tg/T	-5.6052	2	0.4165
Hf/Hc	-3.9810	3	0.5157
S2/S	3.7342	4	0.6087
Hg/Hc	2.5612	5	0.6725
te/T	-2.1131	6	0.7251
He/Hc	1.9877	7	0.7746
tf/T	1.9848	8	0.8240
tc/T	-1.4729	9	0.8607
Hd/Hc	-1.3283	10	0.8938
Z	0.9950	11	0.9186
PWTT	0.9101	12	0.9413
td/T	-0.8710	13	0.9630
S1/S	-0.8399	14	0.9839
V	-0.5096	15	0.9966
K	0.0773	16	0.9985
S1/S2	0.0553	17	0.9999

Figure 6.

RMSE curve using the GA

3.3Construction of GA-MIV-BP neural network

The NETs0 and NETd0 networks trained in Section 3.2 were selected to construct SBP and DBP calculation models, respectively, on the MATLAB R2014a platform. The GA was then used to optimize the individual parameters of models based on a GA-MIV-BP neural network.

The first two sets of data from the ten subjects were used as training sets, and the rest were the test set. Using the GA to optimize the parameters ‘a’ and ‘∇s’ of the GA-MIV-BP SBP model and the parameters ‘b’ and ‘∇d’ of the GA-MIV-BP DBP model, the optimal parameters and the RMSE of the first two training sets were obtained for each individual, as shown in Table 6. The optimization time of SBP or DBP model parameters for each individual was less than 2 minutes. Figure 6 shows the RMSE curve of predicted SBP values while optimizing the parameters ‘a’ and ‘∇s’ of the GA-MIV-BP SBP model, and the measured SBP value; and the RMSE curve of the predicted DBP value while optimizing the parameters ‘b’ and ‘∇d’ of the GA-MIV-BP DBP model, and the measured DBP value (taking the Test_5 for example).

Figure 7.

Comparison of predicted and measured values of SBP.

Figure 8.

Comparison of predicted and measured values of DBP.

4.1Comparison with other blood pressure models

The blood pressure values of ten subjects were predicted using the GA-MIV-BP neural network models, regression models [6], and the ANN model based on PWTT [18]. Figures 7 and 8 show the SBP and DBP values, respectively, predicted by these three models. The horizontal axis in Figs 7 and 8 denotes the jth measured data for the ith subject. For example, ‘1-1’ denotes the first measured data for subject Test_1. It can be seen from Figs 7 and 8 that the predictions obtained by the GA-MIV-BP models are closer to the sphygmomanometer measured blood pressure values than those by regression models and the ANN model. Thus, it can be concluded that the GA-MIV-BP models have better predictive performance than regression models and the PWTT-based ANN model.

In order to further analyze the prediction accuracy of the above three models, the RMSE and MRE were used to compare them. The RMSE and MRE of the predicted blood pressure values from the three models and the values as measured by the sphygmomanometer are shown in Table 7. It can be seen that the RMSE and MRE of the SBP and DBP values calculated by GA-MIV-BP models are lower than those of the regression and the ANN models. Therefore, it can be concluded that the GA-MIV-BP models have greater prediction accuracy than the regression and PWTT-based ANN models. The MRE of SBP and DBP values calculated by GA-MIV-BP models is less than 5%.

Figure 9.

Bland-Altman analysis of predicted and measured SBP values (SBP1 and SBP0).

Figure 10.

Bland-Altman analysis of predicted and measured DBP values (DBP1 and DBP0).

4.2Bland-Altman analysis between results predicted by GA-MIV-BP models and blood pressure values measured by sphygmomanometer

The blood pressure values predicted by the GA-MIV-BP neural network model and the blood pressure values measured by the sphygmomanometer underwent Bland-Altman analysis, as shown in Figs 9 and 10. Figure 9 shows that 96.67% of the points are within the 95% consistency range, and the maximum absolute value of all differences within the consistency range is 5.8895 mmHg. Figure 10 shows that 95.83% of the points are within the 95% consistency range, and the maximum absolute values of all differences within the consistency range is 4.8218 mmHg. These differences are adequate for clinical requirements, and as there is good consistency between the results of the GA-MIV-BP neural network model and the actual measurement, they may be considered interchangeable.