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The objective of this work is to perform automatic diagnosis using a non invasive method which consists on the bioimpedance signal processing. Bioimpedance signal (BIS) represents the aorta impedance variation during the heart cycle activity. BIS is detected by mean of two electrodes located at the level of the ascendant aorta. Automatic diagnosis method consists on preparing, first, a data base with a set of cepstral parameters of different BIS according to normal case and different cardiac diseases. This data base is composed from n classes Yk corresponding to n diseases. The classification of anonymous individuals is based on the determination of Fisher distance between anonymous disease and class Yk using Fischer formula. Our method permits to calculate seven relevant cepstral parameters. The application of Fisher method has allowed us to perform the diagnosis of five anonymous cases. The major interest of this method is its especially useful for the exploration of cardiovascular system anomalies for emergency cases, children, elderly and pregnant women who can’t support surgical operations especially at the level of the heart.

Several studies have been performed on medical signal processing with the aim of enriching the table in diagnosis of heart disease [

The method used in this study consists of applying a low level rectangular current and high frequency (1 mA, 30 kHz), through a pair of electrodes placed respectively in the front and above the leading edge of the heart [

The aim of this bioimpedance signal analysis is the diagnosis of cardiac diseases by means of cepstral processing of this signal using Fisher theory [

Cepstral method consists on considering that bioimpedance signal y(t) is the response of left ventricle aorta system to a cardiac excitation signal x(t) and the aorta pulsatile response h(t) (

Then:

(Temporal convolution product)

Cepstral analysis consists on the determination of excitation signal x(t) and pulsatile response h(t), in order to describe, separately, anomalies, respectively, in heart and aorta. Computation is carried out at the minimum phase (Φ = 0).

Let:

where:

Let:

y_{1}(t) is the Cepstre C1

where:

Let:

Let:

Early, a statistical study, using the discriminant method analysis, has been performed [_{1}, r_{2}, r_{3}) and seven cepstrals variables (U, M, N, F, I, G, LF) (

Our idea in this study is to use the seven cepstral parameters for the automatic diagnosis of the heart disease

using Fisher’s test. Cesptres C2 and C3 permit to provide these seven relevant parameters: U, M, N, F, I, G, LF (

The principle of discriminant analysis is based on FISCHER theory and the criteria of “Step by Step”. The relevant plethysmographic parameters represent the set of parameters which allows having the maximum of matrix product T^{−1} E. Where T is whole covariance matrix, E is the interclass covariance matrix. The classification of anonymous individuals is based on the use of the FISHER formula [

_{k}, a is the anonymous individual defined by cepstral parameters, y_{k} is the average of Y_{k} classes, T_{cov} is whole covariance matrix.

Temporal parameters | A | Wave amplitude of the bioimpedance derivate signal |
---|---|---|

C | ||

O | ||

X | ||

S | Bioimpedance signal maximum amplitude | |

Spectral parameters | r_{1} | Spectral parameters |

r_{2} | ||

r_{3} | ||

Cepstral parameters | U | Cepstral parameters (cardiac excitation amplitude: cepstral C2) |

M | ||

N | ||

F | Cepstral parameters (impulsional response amplitude: cepstral C3) | |

I | ||

G | ||

LF | LF is the normalized width of wave F (aortic cepstral): = |

Cepstral parameters | U | M | N | F | I | G | LF |
---|---|---|---|---|---|---|---|

Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 |

Computed algorithms are expressed by a MAHAL 3 program [

P is the total of average cepstral parameters corresponding to 25 classes (

Bioimpedance parameters, proposed for the discrimination between the classes, are in this study 7 cepstral parameters.

After testing the seven parameters during the first step, the program indicates the parameter number 7 which represents the normalized width LF of the aortic cepstral. Therefore, the parameter number 7 is the best discriminant plethismographic parameter. The best classified percentage of individual is then 64.29% (

At steps number 2, 3 and 4, the program choose, respectively, parameters number 7, 5, 6 and 4 corresponding respectively to the parameters: LF, I, G and F. The classified percentage is then 86.01%. At step 5, the percentage of classification reaches 93.66% the parameters are 7, 5, 6, 4, and 3 corresponding to the parameters: LF, I, G, F and N. Finally at step number 6 and 7 the program choose parameters 2 and 1 corresponding to M and U respectively with the percentage 94.1% and 95.4%.

The total 7 independent parameters (

Automatic diagnosis method consists on preparing, first, a data base with a set of the seven cepstral parameters

F | LF | U | M | N | I | G | |
---|---|---|---|---|---|---|---|

Normal | 1 | 0.49 | 0.19 | 0.21 | 0.17 | 0.05 | 0.32 |

M.D. | 1.4 | 2.11 | 0.44 | 0.02 | 0.01 | 0 | 0 |

AO.I. | 0.78 | 0.54 | 0.18 | 0.20 | 0.17 | 0.05 | 0.49 |

AO.S. | 0.17 | 0.88 | 0.17 | 0.21 | 0.17 | 0.05 | 0.30 |

AO.D. | 1.16 | 0.89 | 0.19 | 0.21 | 0.16 | 0 | 0.30 |

M.I. | 1.4 | 1.57 | 0.15 | 0.05 | 0.05 | 0 | 0.30 |

M.S. | 1.11 | 0.79 | 0.10 | 0.03 | 0.02 | 0.19 | 0.11 |

M.D.++ | 1.44 | 2.21 | 0.54 | 0.12 | 0.11 | 0.1 | 0.1 |

AO.I.++ | 0.88 | 0.64 | 0.28 | 0.30 | 0.27 | 015 | 0.59 |

AO.S.++ | 0.27 | 0.98 | 0.27 | 0.31 | 0.27 | 0.15 | 0.40 |

AO.D.++ | 1.26 | 0.99 | 0.29 | 0.31 | 0.26 | 0.1 | 0.40 |

M.I.++ | 1.5 | 1.67 | 0.25 | 0.15 | 0.15 | 0.1 | 0.40 |

M.S.++ | 1.21 | 0.89 | 0.20 | 0.13 | 0.12 | 0.29 | 0.21 |

M.D.+++ | 1.60 | 2.31 | 0.64 | 0.22 | 0.21 | 0.2 | 0.2 |

AO.I.+++ | 0.98 | 0.74 | 0.38 | 0.40 | 0.37 | 0.25 | 0.69 |

AO.S.+++ | 0.37 | 0.1 | 0.37 | 0.41 | 0.37 | 0.25 | 0.50 |

AO.D.+++ | 1.36 | 0.11 | 0.39 | 0.41 | 0.36 | 0.2 | 0.50 |

M.I.+++ | 1.6 | 1.77 | 0.35 | 0.25 | 0.25 | 0.2 | 0.50 |

M.S.+++ | 1.31 | 0.99 | 0.30 | 0.23 | 0.22 | 0.39 | 0.31 |

P.S. | 1.4 | 2.11 | 0.44 | 0.02 | 0.01 | 0 | 0 |

PS++ | 0.78 | 0.54 | 0.18 | 0.20 | 0.17 | 0.05 | 0.49 |

P.S+++ | 0.12 | 0.88 | 0.17 | 0.21 | 0.17 | 0.05 | 0.30 |

IVC | 1.16 | 0.89 | 0.19 | 0.21 | 0.16 | 0 | 0.30 |

IAC | 1.4 | 1.57 | 0.15 | 0.05 | 0.05 | 0 | 0.30 |

CMP. | 1.11 | 0.79 | 0.10 | 0.03 | 0.02 | 0.19 | 0.11 |

(AO.I: aortic insufficiency; AO.S: aortic stenosis; AO.D: aortic diseases; M.I: Mitral Insufficiency; M.S: Mitral stenosis; M.D: Mitral diseases; PS: pulmonary stenosis; IVC: Inter-ventricle communication; IAC: inter-atrium communication; CMP: Cardio-myopathie).

of different bioimpedance signal according to different cardiac diseases and the formula (18). This data base is composed from n classes Yk corresponding to 25 cases (normal and cardiac disease).

The classification of anonymous individuals is based on the use of FISHER formula (8). Minimum dm distance, between a and the Yk, classes provides the kind of cardiac disease. Investigation has concerned a data base of 25 kinds of signal: one normal and 24 pathological cases (

Three cases of anonymous signals are used (a1: AO.S+), (a2: M.S++) and (a3: M.S+++). The diagnosis of these three anonymous cases is confirmed by Echo-Doppler method.

Steps | Parameters | Percentage |
---|---|---|

1 | 7 | 64.29% |

2 | 7, 5 | 81.71% |

3 | 7, 5, 6 | 83.52% |

4 | 7, 5, 6, 4 | 86.01% |

5 | 7, 8, 6, 4, 3 | 93.66% |

6 | 7, 8, 6, 4, 3, 2 | 94.10% |

7 | 7, 8, 6, 4, 3, 2, 1 | 95.40% |

25 classes | d(a1) | d(a2) | d(a3) |
---|---|---|---|

Normal | 100 | 99.70 | 99.50 |

M.D.+ | 55.30 | 66.23 | 62.39 |

AO.I.+ | 22.23 | 77.32 | 88.36 |

AO.S.+ | 0.10 | 55.11 | 55.22 |

AO.D.+ | 12.22 | 53.78 | 45.36 |

M.I.+ | 55.88 | 26.33 | 12.66 |

M.S.+ | 77.23 | 2.22 | 1.33 |

M.D.++ | 88.22 | 44.23 | 23.78 |

AO.I.++ | 55.99 | 88.66 | 88.77 |

AO.S.++ | 2.33 | 55.88 | 77.11 |

AO.D.++ | 4.66 | 69.58 | 88.55 |

M.I.++ | 54.99 | 22.30 | 22.99 |

M.S.++ | 55.21 | 0.10 | 1.59 |

M.D.+++ | 88.22 | 3.44 | 6.33 |

AO.I.+++ | 5.99 | 88.66 | 66.77 |

AO.S.+++ | 3..66 | 55.66 | 44.45 |

AO.D.+++ | 5.55 | 55.77 | 64.23 |

M.I.+++ | 45.66 | 28.99 | 34.54 |

M.S.+++ | 55.22 | 2.99 | 0.02 |

P.S. | 77.32 | 54.88 | 88.52 |

PS++ | 75.41 | 55.66 | 66.25 |

P.S+++ | 88.23 | 74.36 | 67.99 |

IVC | 90.23 | 95.24 | 89.99 |

IAC | 79.99 | 92.32 | 88.99 |

CMP | 55.58 | 88.45 | 96.33 |

From

At step 7 the percentage of well class reaches 95.40%. This result is slightly better than the one we found in previous work using 15 bioimpedance parameters: 94.64% of percentage of correctly classified.

The results found in this work indicate that the seven cepstral parameters defined above are sufficient to perform the automatic diagnosis of the cardiovascular system abnormalities.

The effectiveness of the cepstral parameters classification is confirmed by the exact allocation of 3 anonymous individuals. Indeed our results demonstrate that patients a1, a2, a3 have been allocated respectively to the previous classes: AO.S+ (d = 0.1), M.S.++ (d = 0.1), and D.M.+++ (d = 0.02).

Automatic quantification of cardiac diseases has been carried out using discriminant analysis method based on the processing of bioimpedance signal. The discrimination uses analysis of seven cepstral parameters. Classifi- cation has been performed using e fundamental data base composed of 25 classes (one normal and 24 cases of diseases). “Step by step” method gives an excellent degree of discrimination 954%. The intelligent method performed in this study permits to confirm the classification of three anonymous patients. Quantification results obtained by the bioimpedance signals analysis are confirmed by those obtained with Echo-Doppler method. Researches are actually orientated for the investigation of peripheral cardiovascular system with the use of hemodynamic bioimpedance and ECG parameters.