Adv. Cardiol., vol. 19, pp. 167-168 (Karger, Basel 1977)
A New Mathematical Approach to the Analysis of the VCG T. FREy, M. CsATAR, P.
SCHWARCZMANN,
T.
SZABADOS
and P. KENEDI
Technical University of Budapest, Postgraduate Medical School, Budapest
We have constructed two main programs, one for analysis of the arrhythmias, based on a special chest bipolar lead, whereas the second is used for analysis of the depolarization and repolarization phase of the ventricles based on the Frank leads. Both main programs are initiated by an appropriate digital filtering program, which serves for detection of the initial point of the essential waveforms. The special bipolar lead signal is moreover harmonically analyzed by fast Fourier transformation methods to detect atrial fibrillation and flutter. The main programs make use of original data, because the filtering procedure can suppress some essential features of the wave forms. The arrhythmia analyzer main program uses linguistical methods, because this procedure can be based on very simple characteristic features of the wave elements, on their order of succession and on the ratios of the periods separating them. We are using a method, first suggested by SELVESTER to simulate the electric activity of the heart during depolarization, modified by BELLMAN for diagnostics. We have generalized these methods in two directions. BELLMAN used only five segments, each characterized by five parameters: the time and the spatial amplitude vector of the greatest dipole moment of the segment, and the time constant characterizing the increasing and decreasing velocity of the dipole moment, occurring in the characteristic time function:
We are also using five segments (data reductionl), with six parameters: the five used by BELLMAN, and the sixth, characterizing the slope
Downloaded by: University of Cambridge 131.111.164.128 - 1/31/2019 9:05:17 PM
(-~O. So we have
T.
FREY,
Polytechnical University, Budapest (Hungary)
Downloaded by: University of Cambridge 131.111.164.128 - 1/31/2019 9:05:17 PM
30 parameters; this means a 30-dimensional feature space related to the QRS complex. We are choosing the values of these parameters by minimizing the total mean square error for the given QRS complex. In addition, we extend the recognition algorithm to the ST and to the T complex too, by taking the slow and fast repolarization activity into consideration. So we have five free parameters per segment for the latter wave forms too. In addition, we have a global free parameter for the whole ST and T complex, which characterizes the average period of slow and fast repolarization. In this way, the intactness or illness of the muscle segments can be characterized by the change of the parameters of the segments from the QRS to the T complex. We mention that the time translation is not the only possibility to extend the recognition algorithm to the .ST and T wave. Another possibility is fixing the spatial direction of the dipole moments, and let change the other parameters. However, it seems the most favorable possibility to fix neither the time delay nor the spatial directions but to penalize every change of the parameters, except the change of the amplitudes. The penalty function to be minimized is given as a weighted sum. The sums are the penalties caused by the change of the parameters and the resulted total mean square error. However, until now we have not enough experience for the adequate choice of the penalty and of the weighing factors.
A New Mathematical Approach to the Analysis of the VCG T. FREy, M. CsATAR, P.
SCHWARCZMANN,
T.
SZABADOS
and P. KENEDI
Technical University of Budapest, Postgraduate Medical School, Budapest
We have constructed two main programs, one for analysis of the arrhythmias, based on a special chest bipolar lead, whereas the second is used for analysis of the depolarization and repolarization phase of the ventricles based on the Frank leads. Both main programs are initiated by an appropriate digital filtering program, which serves for detection of the initial point of the essential waveforms. The special bipolar lead signal is moreover harmonically analyzed by fast Fourier transformation methods to detect atrial fibrillation and flutter. The main programs make use of original data, because the filtering procedure can suppress some essential features of the wave forms. The arrhythmia analyzer main program uses linguistical methods, because this procedure can be based on very simple characteristic features of the wave elements, on their order of succession and on the ratios of the periods separating them. We are using a method, first suggested by SELVESTER to simulate the electric activity of the heart during depolarization, modified by BELLMAN for diagnostics. We have generalized these methods in two directions. BELLMAN used only five segments, each characterized by five parameters: the time and the spatial amplitude vector of the greatest dipole moment of the segment, and the time constant characterizing the increasing and decreasing velocity of the dipole moment, occurring in the characteristic time function:
We are also using five segments (data reductionl), with six parameters: the five used by BELLMAN, and the sixth, characterizing the slope
Downloaded by: University of Cambridge 131.111.164.128 - 1/31/2019 9:05:17 PM
(-~O. So we have
T.
FREY,
Polytechnical University, Budapest (Hungary)
Downloaded by: University of Cambridge 131.111.164.128 - 1/31/2019 9:05:17 PM
30 parameters; this means a 30-dimensional feature space related to the QRS complex. We are choosing the values of these parameters by minimizing the total mean square error for the given QRS complex. In addition, we extend the recognition algorithm to the ST and to the T complex too, by taking the slow and fast repolarization activity into consideration. So we have five free parameters per segment for the latter wave forms too. In addition, we have a global free parameter for the whole ST and T complex, which characterizes the average period of slow and fast repolarization. In this way, the intactness or illness of the muscle segments can be characterized by the change of the parameters of the segments from the QRS to the T complex. We mention that the time translation is not the only possibility to extend the recognition algorithm to the .ST and T wave. Another possibility is fixing the spatial direction of the dipole moments, and let change the other parameters. However, it seems the most favorable possibility to fix neither the time delay nor the spatial directions but to penalize every change of the parameters, except the change of the amplitudes. The penalty function to be minimized is given as a weighted sum. The sums are the penalties caused by the change of the parameters and the resulted total mean square error. However, until now we have not enough experience for the adequate choice of the penalty and of the weighing factors.
