In this section, experimental results for hematocrit estimation are evaluated. The distribution of reference (true) hematocrit values measured by centrifugation method is shown in Fig. 8.1 with mean 36.02 and deviation 6.39. This distribution is fairly representing the general trend of hematocrit values for human.
In neural network and SVR approaches, the input features were normalized into the range [0 1]. In finding parameters for SVR approach, we tried on different combination of cost parameters C and parameters v: C=[211, 210, …, 2-1, 2-2] and
v=[20, 2-1, …, 2-10]. The average results of 50 trials for each combination of (C, v)
were computed and the best performance was obtained when C=29 and v=2-2. The number of hidden units of neural networks was gradually increased from 2 and the nearly optimal number of units was chosen based on cross-validation method. The number of hidden units was 12 for the original ELM and 5 for LS-ELM, RLS-ELM and ELS-ELM. At this point, we do not concentrate on effective methods for reducing the number of current points used in the LRCP (linear model with reduced current points) approach. Reducing it in the LRCP approach from d to M is done by a trivial search routine called exhaustive search.
The data set was divided into the training set (40%) and the test set (60%). The algorithms were implemented in Matlab 7.0 environment. The root mean square error (RMSE) was computed by
2 1
1 (
n
i i
i
RMSE R E
n =
= ∑ − ) , (8.1)
where R is the reference value and E is the estimated value. The mean percentage
error (MPE) was determined by subtracting the measured hematocrit from the reference hematocrit
i x100
i
i i
MPE R
E R
= −
. (8.2)
Table 8.1 Root mean square errors (RMSE) compared to the reference hematocrit
measurements.
Training Testing Method
RMSE Mean RMSE Mean
LWCP 2.03 -3.2x10-9 2.68 -1.8x10-9
LRCP 2.49 5x10-9 2.74 -1.6x10-9
SVM 3.74 0.25 4.59 -0.09
ELS-ELM 4.25 10-5 4.63 -0.17
RLS-ELM 4.30 10-7 4.90 -0.05
ELM 4.27 10-4 4.90 -0.26
The RMSE values for methods (linear model with whole current points – LWCP (linear model with whole current points), linear model with reduced current points - LRCP, single layer feed-forward neural network – SLFN, and SVM) are shown in Table 8.1. The ELS-ELM can obtain RMSE of 4.63, which is lower than RMSE of other ELM training algorithms. Especially, in comparison with the original ELM, it can obtain a significantly improved performance with small number of hidden units. The RMSE of SVM was 4.59, which is slightly lower than that of neural networks. However, training SVM was slow and hardware implementation is more complex than that of the RLS-ELM or ELS-ELM. We also see that linear
models can obtain the best RMSEs, which were 2.68 for LWCP and 2.74 for LRCP.
Although the LRCP method produced RMSE little higher than that of LWCP method, the number of current points used in the LRCP method is M=44 which is relatively small in comparison with that used in the LWCP method (d=59). The measurement results with the LRCP method can be obtained in 4.5 seconds of the second period while 6 seconds for the LWCP method. This fact can claim that LRCP method can provide faster measurement and save the battery of the hand-held meters.
Note that the computation for two parameters α and β is quite simple, and thus their computational cost is trivial and ignorable. In our study, the neural networks and SVM with the input features as combination of the current curves and their two extracted features are also investigated. They can offer the RMSE of 3.72, which is still significantly higher than that of linear models.
The mean percentage errors for the methods are shown in Table 8.2. As shown in Table 8.2, linear models are better than both SLFNs and SVM by always showing a larger value for the same MPE value. We can see that, for the linear model approaches, more or less than 80% of the blood samples are having relative percentage error (MPE) less than 10%, and 90% of the samples are having MPE less than 15%. We should note that the correlation coefficient between the estimated hematocrit and the reference hematocrit is found with 0.91 and 0.90 for LWCP and LRCP methods, respectively.
Two features αj and βj are extracted from the transduced current curve pattern
x%j=[xj1, xj2, …, xjM]T by an exponential model. Note that x%jis a vector which is
composed of the subset of elements in x. Theoretically, this means that [αj βj] covers the information of x%jor x%j covers the information of [αj βj]. However, our studies have shown that using the combination of features x%j and [αj βj] for the LRCP
method offers better performance than using individual features x%j or [αj βj]. This
result may claim that two extracted features αj and βj does not represent perfectly the characteristics of current curve and using these two features reduce effects of noise which may exist inx%j.
Table 8.2 Mean percentage error (MPE) compared to the reference hematocrit
measurement
Methods MPE (%)
SLFN SVM LRCP LWCP
<10 53.78 52.94 79.13 81.51
<11 59.66 60.50 82.61 84.87
<12 62.18 61.34 86.96 88.24
<13 67.23 66.39 87.83 88.24
<14 71.42 70.59 91.30 89.08
<15 78.15 78.99 91.30 90.76
<16 79.83 81.51 94.78 93.28
<17 83.19 81.51 94.78 95.80
<18 84.87 84.03 94.78 96.64
<19 85.71 84.87 97.39 97.48
<20 90.76 90.76 97.39 100
It is worth mentioning that other methods can also be investigated to measure the hematocrit value, such as centrifugation methods, dielectric spectroscopy, and impedance. However, most of them are quite complicated or require dedicated
devices. The major goal of our study intended to develop a simple approach, which is economically beneficial and does not require complicated and expensive chemical work. Our experimental results shown in Table 8.1 and 8.2 experimentally shows that our approaches to estimate the hematocrit value based on transduced current curve provide acceptable performance with fast measurement time. One significant fact of our approaches is that handheld meter device with electrochemical glucose biosensor can be used to measure the hematocrit density in the whole blood.