We adopt three time domain feature parameters: K1, K2 and K, where K1 represents the systolic area, K2 denotes the diastolic area, whereas K holds the entire pulse wave area. In medical sense pulse wave area K represents characteristics of microcirculation in general but does not reflect the correlation of other feature points and areas of the whole pulse wave. We then divide the pulse wave area into 2 parts, where K1 is the systolic area, and K2 is the diastolic area.

We calculate the K1, K2 and K with reference to Figure 1.

K is the ratio of the area S_ABCDE vs. area of rectangular AHFE, denoted as below

K = S A B C D E S A H F E , S A B C D E = ∫ x A x E G ( t ) d t (2.1-1)

where x_A denotes the start of the pulse wave segment, whereas x_E denotes the end of the segment, G(t) is the function over time of the pulse wave.

Consequently, the K1 and K2 can be calculated as follows.

K 1 = S A B C S A H G I , K 2 = S C D E S I G F E S A B C = ∫ x A x C G ( t ) d t , S C D E = ∫ x C x E G ( t ) d t , K = K 1 + K 2 (2.1-2)

where area S_ABC is area starting from the X_A to the dicrotic notch, whereas S_CDE is the area covering dicrotic notch to X_E.

It is well understood that dirty data affects the clustering results with K-MEANS algorithms; while PPG measurement is prone to noise caused by many factors. We propose an improved K-MEANS algorithm by introducing updated sample center and thresholds after each round of clustering calculation in order to achieve more accurate clustering. Such an improved algorithm is less sensitive to noise and dirty data at the expense of more computing. Fortunately in our case we just have small set of data, hence it is more appropriate to land on the algorithm.

Figure 2(a) depicts the improved K-MEANS results whereas Figure 2(b) depicts K-MEANS results.

The confidence level of improved K-MEANS is much higher than that of the standard K-MEANS algorithms.

We calculate the wavelet entropy as follows.

W E = − ∑ j P j ln ( P j )

P j = E j E t o t

E j = ∑ k | C j ( k ) | 2 (3.1-1)

E t o t = ∑ j E j

where j denotes the layers of the signal decomposition (j = 1, 2, 3, ... , 5); k is length of the original signal (k = 1, 2, 3, ..., 512); W_E denotes the wavelet entropy, E_j denotes total energy at each layer, P_j is the probability of layer j’s energy vs. total energy.

• Data Preparation

PPG measurement can be affected by many factors, including pathophysiological condition and environmental condition upon test, among which age and blood pressure are key factors. We picked 23 healthy (coronary artery normal or mild stenosis) participants and 23 unhealthy (severe coronary artery stenosis) participants all at age of 50 - 70.

• Test Results

The Mean, Variance and Standard Deviation of Wavelet Entropy for healthy and unhealthy participants are listed in Table 1.

The fact that mean value of wavelet entropy of healthy people is less than that of unhealthy people implies that healthy people’s PPG pulse wave is more stable than that of unhealthy people.

Probabilistic Neural Networks (PNN) [7] is a simple network which can be implemented using linear algebra computation and applicable to classification. As depicted in Figure 4, five layers are input layer, normalization layer, hidden layer, summation layer, and output layer.

PNN Input

SIX time domain paramters: T, Pab, SI, K1, K, RI

ONE frequency domain parameters: wavelet entropy.

Where,

• T is the cycle of pulse wave; Pab = Tab/T, Tab is diff btw Xa and Xb.

• SI is height(m)/T_bd, T_bd is diff btw Xb and Xd.

• RI is H_d/H_b, H_d is vertical diff between Yd and Ya, H_b is vertical diff between Yb and Ya,

• K1 and K are defined in 2.1-2

Healthy People’s Parameters are listed in Table 2.

Unhealthy People’s Parameters are listed in Table 3.

It is obvious that the time domain parameters listed above for healthy and unhealthy people vary in different degree; hence it is difficult to derive any valuable information alone. As a result, we use all these time domain parameters together with wavelet entropy as inputs to the PNN for classification of PPG pulse wave.

Our test consists of 13 samples as input for training, 10 samples for classification. Results of classification are listed in Table 4.

It clearly demonstrated that classification results in 60% accuracy for healthy people and 80% accuracy for unhealthy ones. The reason for this is that there are clear standard to define unhealthy (stenosis) but not for the healthy ones.

Where, N denotes healthy people, P denotes unhealthy people; “+” denotes coronary artery normal; “-”, denotes severe coronary arterystenosis; “_” denotes misclassification.