IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-26, NO. 7, JULY 1979
405
search interests include electromagnetic biological effects and biomedical applications of microwaves. Dr. Gandhi is a member of Sigma Xi, Phi Kappa Phi, and Eta Kappa Nu.
During 1968-1975, he worked in the research and development of explosives for IRECO Chemicals, West Jordan, UT. Since 1978 he has been a Research Associate at the Department of Electrical Engineering and the Department of Bioengineering, University of Utah. His main research interests are electromagnetics and microwave biological effects.
Mark J. Hagmann (S'75-M'79) was born in Philadelphia, PA, on February 14, 1939. He received the B.S. degree in physics from Brigham Young University, Provo, UT, in 1960, and the M.Sci.Ed. and Ph.D. degrees in electrical engineering from the University of Utah, Salt Lake City, in 1966 and 1978, respectively. From 1961 to 1964 he worked as a Physics and Mathematics Teacher. He did additional graduate studies in physics at Brigham Young University, Provo, UT, during 1965-1967.
Indira Chatterjee (S'78) was born in Bangalore, India, on April 2, 1954. She received the B.Sc. Honors and M.Sc. degrees in physics from Bangalore University, Bangalore, India, in 1973 and 1975, respectively, and the M.S. degree in physics from Case Western Reserve University, Cleveland, OH, in 1977. She is currently working towards the Ph.D. degree in the Department of Electrical Engineering, University of Utah, Salt Lake City. The emphasis of her degree is on the interaction of electromagnetic radiation with biological systems.
Autoregressive Analysis Applied to Surface and Serosal Measurements of the Human Stomach HARRY H. L. KWOK
ful applications of the electroencephalogram (EEG) and the electrocardiogram (ECG) are two examples where such research work has led to clinical usage. Other parts of the human body also exhibit electrical activity and one such area has been the gastrointestinal tract. The human gastrointestinal tract is rich in electrical activity that ranges from a few cycles per minute in the stomach to more than 10 c/min in the duodenum. The activity is present continually and is believed to be associated with the muscular movements of the gut [1]. This paper reports the use of the autoregressive technique in a comparative study of surface and serosal measurements from the human stomach. The main objective has been to identify the difI. INTRODUCTION ferences in the two methods of recording. The autoregressive electrical activity from the human body technique stands out uniquely in such a comparative study of the THE study has long been recognized to be of significant value in the because it assumes in its application that the signal informaunderstanding of the different organs and tissues. The success- tion has arisen from the action of a linear filter, and as a consequence, the comparison can be made in the characteristic Manuscript received May 15, 1978; revised November 24, 1978. This equations of the filters. It is observed that for most surface work was supported in part by the Commonwealth Scholarship Com- recordings, it is possible to identify the main sources of intermission. The author is with the Department of Electronics, The Chinese Uni- ference, and in the human stomach they correspond to respiration artifacts and some 9-10 c/min activity. versity of Hong Kong, Shatin, New Territories, Hong Kong.
Abstract-A comparative study has been made on the surface and serosal data recorded from the human stomach. Autoregressive technique has been used for frequency analyses. It is observed that slow waves in both the surface and the serosal data can be detected with reasonable success using a moderate model order. An examination of the frequency spectra reveals that while the serosal signals have a welldefined harmonic pattern, the surface signals are noiselike. Some 9-10 c/min spike activity seems to be present in both kinds of recordings. Attempts have been made to single out the "surface effects" making use of the linear properties of the autoregressive filters and our results indicate that the main surface interferences seem to be related to respiration artifacts and the 9-10 c/min spike activity.
T
0018-9294/79/0700-0405$00.75 C 1979 IEEE
406
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-26, NO. 7, JULY 1979
II. THEORY
SEROSAL SIGNAL
The theory of the autoregressive technique is well established in the literature [21-[5] and we shall mainly outline those features relevant to frequency analysis work. The technique or its model assumes that the signal has arisen from a random white noise source passing through a linear filter. If the signal has been stationary, or at least weakly so, it is then possible to write an equation relating the signal to the noise and its past history. Equation (1) represents a pth order process for a signal Y occurring at time k:
NOI SE
Fl LTER
I
[.z ...... * ap
P1ii
FILTER 11 I*~ +
SURFACE SIGNAL
-
apz
la'zI+ .....I1~ ....I ll+alz~| Fig. 1. Model of two autoregressive filters giving rise to the serosal and surface signals. ) -t.
Y(k)=-0cxY(k- 1) -
:2 Y(k- 2)-
. -
pY(k - p) +
§p(k)
(1)
where the cc's are the weighing coefficients and §p(k) is the white noise at time k. One can also rewrite (1) using the time-shift operator Z as {l + Ocz-Z + aC2Z-2 + . . . + CcpZ-P} . Y(k) = § p(k), (2)
where Y(k)=Z {Y(k- 1)}. Thus, the signal and the noise are related by a simple polynomial of the time-shift operator Z. The procedure for solving the frequency components is similar to that normally used in the root solving of filters. The basic idea is to find the weighing coefficients by minimizing the sum of the residuals squared of the noise terms and then to determine the roots of the polynomial in Z. The roots are directly related to the signal frequencies and the level of significance of any particular pair of roots is dependent on the proximity of the magnitude of Z to the unit circle in its complex plane. The most significant frequencies appear nearest to the unit circle. The fact that this technique assumes that the signal information is contained mainly in a polynomial of the time-shift operator makes it extremely attractive for comparing signals with similar harmonic contents. In this paper we shall assume that the surface signals have arisen from two successive filters, one giving rise to the serosal data and the other giving added features to the surface recordings. Fig. 1 shows the model for such a representation. As long as the filters are linear, it should be possible in principle to single out the added features in the surface recordings through the simple division of the characteristic equations representing the two filters. Such a division process can be easily implemented in the standard computer program for the autoregressive model.
Fig. 2. Positions of the electrodes used to obtain the surface data of the stomach.
of the respiration pneumograph were also made. The analog data were first taped on a four-channel thermionic recorder (Racal) and subsequently digitized at 2 Hz for use in the analysis work. An autoregressive program based on the YuleWalker algorithm was developed to compute the signal frequencies and their significance. Twentieth-order autoregressive models were used. This model order was selected after a preliminary study indicated that analyses using this model order were sufficient to cover all the significant frequencies appearIII. EXPERIMENTAL PROCEDURES ing in similar fast Fourier transform (FFT) analyses. A lower The surface and serosal measurements have been made by model order may be used if only the serosal data is analyzed. the Departments of Surgery and Medical Physics at the Uni- The computing was done in single precision arithmetic using versity of Sheffield. The details of the recording procedures a Nova II 16-k bit minicomputer. were similar to those reported [61, [7]. The serosal measureIV. RESULTS ments were made using internal suction stainless steel electrodes while the surface measurements used Ag/Ag Cl electrodes Fig. 3(a) and (b) show some typical surface and serosal data (Elma-Schonander type ES 202). Bipolar recordings were used measured simultaneously from the human stomach. Apart throughout. The surface electrodes were placed at two neigh- from the approximately 3 c/min slow wave activity present, boring positions on the skin surface immediately above the there appeared to be a certain amount of 9-10 c/min spiky stomach. Their locations were such that the time of observation activity in the two sets of data. Fig. 4(a) and (b) show the of the gastric signals had been maximized. The exact positions signal frequencies computed from autoregressive analyses of of the electrodes are shown in Fig. 2. Simultaneous recordings the surface and serosal data recorded simultaneously. Twentieth-
KWOK: AUTOREGRESSIVE ANALYSIS
407
:t L-m L. 4
Iu
Cl-
X:
0
100
50 TIMEw sec
50 TIME ,sec.
0
100
(b)
(a)
Fig. 3. (a) Typical stretch of serosal gastric signal. Time duration is 100 s. (b) Surface gastric signal recorded simultaneously with the serosal gastric signal in Fig. 3(a). I
I
I
I
I
I
I
0
0
18
0
0
0
0
0
0
0
0
18
0~~~~~~ o
0
0
0
0
0
N, * _
Li
0
0
0
0
0
0
0
12 t
0
0 0
0
0
V) N
0
0~~~~~~~~~ 0 0~~~~~ 0
i 12
0
LI-I ,.j
0
~~0
,,
0
0
~~~0
0
0 0
00
6F
0
0
00 0
0
0~~~~~~~ 0
0
U-
0
0
0
0
0
0
0
6
0
0
1
0
0
~~0
-
0
0
0
0
i
I
I
0
0 0
0~~~~~~ 0 0
0
0
I
0
0~~~~~~
0 0
0
0
0~~~
0
0
0
~
0
06
00
0
0
CY)U
0
0
0 CU
LU
0
0
0 0~~~~~~~~ 0
o
0
.u VIJ
0 0
c
E l-~
0
F
II
I
2 3 4 5 6 7 8 9 10 10 STRETCHES OF DATA
2 3 4 5 6 7 8 9 10 10 STRETCHES OF DATA
(a)
(b)
Fig. 4. (a) Frequencies generated from a 20th-order autoregressive model for 10 stretches of 4 min serosal gastric signal. Data sampling rate was 2 Hz. (b) Frequencies generated from a 20th-order autoregressive model for 10 stretches of 4 min surface gastric signal. Data were measured simultaneously with the serosal gastric signal in Fig. 4(a). Data sampling rate was 2 Hz.
order models
were
used and the
sampling
rate
was
2 Hz.
The
full length of the data was about 45 min and had been divided into 10 stretches, each lasting approximately 4 min and consisting of 512 data points. In the figures, the computed frequencies are shown in the vertical axes and the number of the stretch of data in the horizontal axes. Only the most significant
frequencies (with IZI nearest to the unit circle in the Z plane) shown and the majority of the frequencies (greater than 80 percent) have IZI > 0.85. (The frequencies from the surface data, because of the heavier noise content, have lower significance compared with that of the serosal data.) The approximately 3 c/min activity was found in 100 percent of the are
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-26, NO. 7, JULY 1979
408
o
O
A
18
+~~~~~ A
c
o
0
Ol.
+ , 0
+
0o
+ A0
0
A
-
+~~~~~~~~~ LA
12
A
LLi
'I
If-l
6
0
A
0 A
A0a
LL O LUj U-
0
&
A~~~~~ A 0o
0 %
0
1
X
l
l
l
0~~~~~
0
°
l
2
A
l
I
0
2 3 4 5 6 7 8 9 10 10 STRETCHES OF DATA
Fig. 5. Frequencies generated from the "surface effects." Symbols (o, A) corresponded to frequencies from the surface measurements at two neighboring sites and the symbol (+) was the frequency from the
pneumograph.
B. Gastric Signals and Their Autoregressive Analyses The use of autoregressive techniques in signal analysis work has a number of advantages. Other than that the signals can be weakly stationary, the main advantage has been that the signals are given in a finite number of discrete frequency components with a specified order of significance. This enables one to confine one's analysis to a few major signal frequencies and can greatly simplify the work especially if a large amount of statistical data analyses is required. In this section, we shall attempt to compare the surface and serosal signals with their autoregressive analyses. The serosal signals measured from the human stomach are fairly periodic and have a well-defined shape. The resemblance of these signals to square waves is reflected in the highly regular and significant odd harmonics in the autoregressive analyses. The even harmonics, however, are less regular and have a much larger frequency spread. The implication ofthe even harmonics is that of irregular pulsewidth modulation although sometimes this may not be the case. The gastric signals from the human stomach indeed seem to fall into the latter category. The first even "harmonic," at about 9-10 c/min, coincides with the spiky activity appearing on these slow waves and the second even "harmonic," as we shall see, is very near the respiration frequency. These complications make it extremely difficult to identify the different effects. The surface signals are highly irregular. Other than the 3 c/min (and there may be some 9 c/min) rhythm, there are very little detectable periodic features. The autoregressive analyses show a similar trend. None of the previous harmonic patterns can be observed and it is doubtful if one can extract any information for the waveshape at all. It is, therefore, most likely that the analyses of any such surface signals will be restricted to the detection of the presence or the absence of the activity and no more. Full harmonic analyses using FFT's were also made on these data. Our results show that the 3 c/min slow wave activity from the surface data can also be detected by the FFT although the presence of a substantial amount of low frequency noise makes the identification difficult in some cases. The analyses of serosal data using the FFT show the similar harmonic patterns and give no more useful information than the autoregressive analyses.
serosal results and 70 percent of the surface results. A somewhat well-defined harmonic pattern was also observed in the serosal data. Fig. 5 shows the frequencies computed from the surface data when the effects of the serosal signals were removed. This was achieved by a division of the characteristic equations [see (2)] set up for the two models. This process assumes that the models are linear and that the surface effects can be isolated. Twentieth-order models were used and the frequencies generated from the pneumograph were also shown. It is observed that the "surface effects" have two main frequency components lying around 0.16 Hz (10 c/min) and 0.26 C. Surface Effects Hz (16 c/min), respectively. As we have pointed out previously, the autoregressive technique puts the signal into a linear model consisting of a charV. DiSCUSSION acteristic equation of the time-shift operator. It should, thereA. Technique Applicability fore, be possible in principle to isolate the effects of the surface Our results show that the autoregressive technique can be measurements by the division of the characteristic equations used to analyze surface and serosal data from the human for the surface and serosal data. This process was done for the stomach. The slow wave rhythm is detected in both the sur- 10 stretches of data measured simultaneously from the human face and the serosal recordings, although the occurrence and stomach and the results are shown in Fig. 5. It is observed the resolution are somewhat inferior in the former. The main that the main contribution to the "surface effects" are frereason for this, we believe, lies in the increasing noise content quencies at 9-10 c/min and around 16 c/min. They occur for in the signal as it is measured further away from the generating almost 100 percent of the time and have high significance. These frequencies, as we noticed, are precisely at the first and source.
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-26, NO. 7, JULY 1979
second even harmonics of the 3 c/min slow wave activity and could easily be taken as the harmonics in the straightforward harmonic analysis. The 9-10 c/min rhythm, appearing as the irregular first even "harmonic" in the autoregressive analyses, can be identified with the spiky activity in the serosal data. It is not surprising that the spiky activity with the high-frequency characteristics are more readily transmitted to the skin surface. The detection of such signals (10-11 c/min) from the abdominal surface have previously been reported [1], although the authors suggested that they might be related to duodenal activity. The 16 c/min rhythm compares favorably with the respiration artifacts and can be so explained. It thus appears that this method of extraction of the "surface effects," if it is to be taken seriously, is capable of identifying the major sources of interference from the signal harmonics. In our case of the gastric signals, the main interferences are the respiration artifacts and some 9-1 0 c/min activity from either the stomach or the environment. VI. CONCLUSIONS We have made analyses of the surface and serosal data from the human stomach using the autoregressive technique. We have identified the 3 c/min slow wave activity in both the serosal and surface data and have related the signal waveshape to the harmonic pattern. It is observed that the first even harmonic in the serosal data at 9-10 c/min is not necessarily a consequence of pulsewidth modulation, but may well be some genuine spike activity. The second even harmonic at 16 c/min lies near the respiration frequency and may well be affected by it. An effort has been made to extract the effects of the surface measurements making use of the linear behavior of the autoregressive model. The results again indicate that the main sources of interference are respiration and some 9-10 c/min activity possibly originated from the upper gastrointestinal region.
409 ACKNOWLEDGMENT
The author wishes to thank the members of the Departments of Medical Physics, Surgery, and Control Engineering, University of Sheffield, Sheffield, England, for their technical support and the helpful discussions in this work. The author also wishes to thank the referees for their suggestions and
comments.
REFERENCES [11 B. H. Brown, "Electrophysiological measurements from the smooth muscle of the human gastrointestinal tract," IEE Medical Electronics Monograph, vol. 18, D. W. Hill and B. W. Watson, Ed. London, England: Peregrinus, 1976. G. E. P. Box and G. M. Jenkins, Time Series Analysis, Forecasting [21 and Control. San Francisco, CA: Holden-Day, 1970. [3] J. P. Burg, "Maximum entropy spectral analysis," presented at the 37th Soc. Explorat. Geophysicists, Oklahoma City, OK, 1967. 141 R. H. Jones, "Fitting autoregressions," J. Amer. Stat. Ass., vol. 70, no. 351, pp. 590-592, 1975. [51 T. J. Ulrych, "Maximum entropy power spectrum of truncated sinusoids," J. Geophys. Res., vol. II, pp. 1396-1400, 1972. (61 1. Taylor, H. L. Duthie, R. H. Smallwood, and D. Linkins, "Large bowel myoelectrical activity in man," GUT, vol. 16, p. 808, 1975. 171 B. H. Brown, R. H. Smallwood, H. L. Duthie, and C. J. Stoddard, "Intestinal smooth muscle electrical potentials recorded from surface electrodes," Med. Bio. Eng., p. 67, Jan. 1975.
Harry H. L. Kwok received the B.S. degree from the University of California, Los Angeles, in 1968 and the Ph.D. degree from Stanford University, Stanford, CA, in 1972. Since 1972, he has been with the Department of Electronics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong. His research interests have been in biomedical en-
&
gineering and solid-state circuits and devices. Dr. Kwok is a member of Tau Beta Pi.
New Concepts for PVC Detection IVATURI S. N. MURTHY
AND
MANDAYAM R. RANGARAJ,
Abstract-A new scheme is proposed for the detection of premature ventricular beats, which is a vital function in rhythm monitoring of cardiac patients. A transformation based on the first difference of the digitized electrocardiogram (ECG) signal is developed for the detection and delineation of QRS complexes. The method for classifying the abnormal complexes from the normal ones is based on the concepts of Manuscript received September 3, 1978; revised January 1979.
The authors are with the Department of Electrical Engineering, Indian Institute of Science, Bangalore, India.
STUDENT MEMBER, IEEE
minimum phase and signal length. The parameters of a linear discriminant function obtained from a training feature vector set are used to classify the complexes. Results of application of the scheme to ECG of two arrhythmia patients are presented.
I. INTRODUCTION
R HYTHM monitoring of cardiac patients is one of the vital functions of a modern coronary care unit. It is well known that disastrous ventricular fibrillation is preceded by
0018-9294/79/0700-0409$00.75
© 1979 IEEE
405
search interests include electromagnetic biological effects and biomedical applications of microwaves. Dr. Gandhi is a member of Sigma Xi, Phi Kappa Phi, and Eta Kappa Nu.
During 1968-1975, he worked in the research and development of explosives for IRECO Chemicals, West Jordan, UT. Since 1978 he has been a Research Associate at the Department of Electrical Engineering and the Department of Bioengineering, University of Utah. His main research interests are electromagnetics and microwave biological effects.
Mark J. Hagmann (S'75-M'79) was born in Philadelphia, PA, on February 14, 1939. He received the B.S. degree in physics from Brigham Young University, Provo, UT, in 1960, and the M.Sci.Ed. and Ph.D. degrees in electrical engineering from the University of Utah, Salt Lake City, in 1966 and 1978, respectively. From 1961 to 1964 he worked as a Physics and Mathematics Teacher. He did additional graduate studies in physics at Brigham Young University, Provo, UT, during 1965-1967.
Indira Chatterjee (S'78) was born in Bangalore, India, on April 2, 1954. She received the B.Sc. Honors and M.Sc. degrees in physics from Bangalore University, Bangalore, India, in 1973 and 1975, respectively, and the M.S. degree in physics from Case Western Reserve University, Cleveland, OH, in 1977. She is currently working towards the Ph.D. degree in the Department of Electrical Engineering, University of Utah, Salt Lake City. The emphasis of her degree is on the interaction of electromagnetic radiation with biological systems.
Autoregressive Analysis Applied to Surface and Serosal Measurements of the Human Stomach HARRY H. L. KWOK
ful applications of the electroencephalogram (EEG) and the electrocardiogram (ECG) are two examples where such research work has led to clinical usage. Other parts of the human body also exhibit electrical activity and one such area has been the gastrointestinal tract. The human gastrointestinal tract is rich in electrical activity that ranges from a few cycles per minute in the stomach to more than 10 c/min in the duodenum. The activity is present continually and is believed to be associated with the muscular movements of the gut [1]. This paper reports the use of the autoregressive technique in a comparative study of surface and serosal measurements from the human stomach. The main objective has been to identify the difI. INTRODUCTION ferences in the two methods of recording. The autoregressive electrical activity from the human body technique stands out uniquely in such a comparative study of the THE study has long been recognized to be of significant value in the because it assumes in its application that the signal informaunderstanding of the different organs and tissues. The success- tion has arisen from the action of a linear filter, and as a consequence, the comparison can be made in the characteristic Manuscript received May 15, 1978; revised November 24, 1978. This equations of the filters. It is observed that for most surface work was supported in part by the Commonwealth Scholarship Com- recordings, it is possible to identify the main sources of intermission. The author is with the Department of Electronics, The Chinese Uni- ference, and in the human stomach they correspond to respiration artifacts and some 9-10 c/min activity. versity of Hong Kong, Shatin, New Territories, Hong Kong.
Abstract-A comparative study has been made on the surface and serosal data recorded from the human stomach. Autoregressive technique has been used for frequency analyses. It is observed that slow waves in both the surface and the serosal data can be detected with reasonable success using a moderate model order. An examination of the frequency spectra reveals that while the serosal signals have a welldefined harmonic pattern, the surface signals are noiselike. Some 9-10 c/min spike activity seems to be present in both kinds of recordings. Attempts have been made to single out the "surface effects" making use of the linear properties of the autoregressive filters and our results indicate that the main surface interferences seem to be related to respiration artifacts and the 9-10 c/min spike activity.
T
0018-9294/79/0700-0405$00.75 C 1979 IEEE
406
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-26, NO. 7, JULY 1979
II. THEORY
SEROSAL SIGNAL
The theory of the autoregressive technique is well established in the literature [21-[5] and we shall mainly outline those features relevant to frequency analysis work. The technique or its model assumes that the signal has arisen from a random white noise source passing through a linear filter. If the signal has been stationary, or at least weakly so, it is then possible to write an equation relating the signal to the noise and its past history. Equation (1) represents a pth order process for a signal Y occurring at time k:
NOI SE
Fl LTER
I
[.z ...... * ap
P1ii
FILTER 11 I*~ +
SURFACE SIGNAL
-
apz
la'zI+ .....I1~ ....I ll+alz~| Fig. 1. Model of two autoregressive filters giving rise to the serosal and surface signals. ) -t.
Y(k)=-0cxY(k- 1) -
:2 Y(k- 2)-
. -
pY(k - p) +
§p(k)
(1)
where the cc's are the weighing coefficients and §p(k) is the white noise at time k. One can also rewrite (1) using the time-shift operator Z as {l + Ocz-Z + aC2Z-2 + . . . + CcpZ-P} . Y(k) = § p(k), (2)
where Y(k)=Z {Y(k- 1)}. Thus, the signal and the noise are related by a simple polynomial of the time-shift operator Z. The procedure for solving the frequency components is similar to that normally used in the root solving of filters. The basic idea is to find the weighing coefficients by minimizing the sum of the residuals squared of the noise terms and then to determine the roots of the polynomial in Z. The roots are directly related to the signal frequencies and the level of significance of any particular pair of roots is dependent on the proximity of the magnitude of Z to the unit circle in its complex plane. The most significant frequencies appear nearest to the unit circle. The fact that this technique assumes that the signal information is contained mainly in a polynomial of the time-shift operator makes it extremely attractive for comparing signals with similar harmonic contents. In this paper we shall assume that the surface signals have arisen from two successive filters, one giving rise to the serosal data and the other giving added features to the surface recordings. Fig. 1 shows the model for such a representation. As long as the filters are linear, it should be possible in principle to single out the added features in the surface recordings through the simple division of the characteristic equations representing the two filters. Such a division process can be easily implemented in the standard computer program for the autoregressive model.
Fig. 2. Positions of the electrodes used to obtain the surface data of the stomach.
of the respiration pneumograph were also made. The analog data were first taped on a four-channel thermionic recorder (Racal) and subsequently digitized at 2 Hz for use in the analysis work. An autoregressive program based on the YuleWalker algorithm was developed to compute the signal frequencies and their significance. Twentieth-order autoregressive models were used. This model order was selected after a preliminary study indicated that analyses using this model order were sufficient to cover all the significant frequencies appearIII. EXPERIMENTAL PROCEDURES ing in similar fast Fourier transform (FFT) analyses. A lower The surface and serosal measurements have been made by model order may be used if only the serosal data is analyzed. the Departments of Surgery and Medical Physics at the Uni- The computing was done in single precision arithmetic using versity of Sheffield. The details of the recording procedures a Nova II 16-k bit minicomputer. were similar to those reported [61, [7]. The serosal measureIV. RESULTS ments were made using internal suction stainless steel electrodes while the surface measurements used Ag/Ag Cl electrodes Fig. 3(a) and (b) show some typical surface and serosal data (Elma-Schonander type ES 202). Bipolar recordings were used measured simultaneously from the human stomach. Apart throughout. The surface electrodes were placed at two neigh- from the approximately 3 c/min slow wave activity present, boring positions on the skin surface immediately above the there appeared to be a certain amount of 9-10 c/min spiky stomach. Their locations were such that the time of observation activity in the two sets of data. Fig. 4(a) and (b) show the of the gastric signals had been maximized. The exact positions signal frequencies computed from autoregressive analyses of of the electrodes are shown in Fig. 2. Simultaneous recordings the surface and serosal data recorded simultaneously. Twentieth-
KWOK: AUTOREGRESSIVE ANALYSIS
407
:t L-m L. 4
Iu
Cl-
X:
0
100
50 TIMEw sec
50 TIME ,sec.
0
100
(b)
(a)
Fig. 3. (a) Typical stretch of serosal gastric signal. Time duration is 100 s. (b) Surface gastric signal recorded simultaneously with the serosal gastric signal in Fig. 3(a). I
I
I
I
I
I
I
0
0
18
0
0
0
0
0
0
0
0
18
0~~~~~~ o
0
0
0
0
0
N, * _
Li
0
0
0
0
0
0
0
12 t
0
0 0
0
0
V) N
0
0~~~~~~~~~ 0 0~~~~~ 0
i 12
0
LI-I ,.j
0
~~0
,,
0
0
~~~0
0
0 0
00
6F
0
0
00 0
0
0~~~~~~~ 0
0
U-
0
0
0
0
0
0
0
6
0
0
1
0
0
~~0
-
0
0
0
0
i
I
I
0
0 0
0~~~~~~ 0 0
0
0
I
0
0~~~~~~
0 0
0
0
0~~~
0
0
0
~
0
06
00
0
0
CY)U
0
0
0 CU
LU
0
0
0 0~~~~~~~~ 0
o
0
.u VIJ
0 0
c
E l-~
0
F
II
I
2 3 4 5 6 7 8 9 10 10 STRETCHES OF DATA
2 3 4 5 6 7 8 9 10 10 STRETCHES OF DATA
(a)
(b)
Fig. 4. (a) Frequencies generated from a 20th-order autoregressive model for 10 stretches of 4 min serosal gastric signal. Data sampling rate was 2 Hz. (b) Frequencies generated from a 20th-order autoregressive model for 10 stretches of 4 min surface gastric signal. Data were measured simultaneously with the serosal gastric signal in Fig. 4(a). Data sampling rate was 2 Hz.
order models
were
used and the
sampling
rate
was
2 Hz.
The
full length of the data was about 45 min and had been divided into 10 stretches, each lasting approximately 4 min and consisting of 512 data points. In the figures, the computed frequencies are shown in the vertical axes and the number of the stretch of data in the horizontal axes. Only the most significant
frequencies (with IZI nearest to the unit circle in the Z plane) shown and the majority of the frequencies (greater than 80 percent) have IZI > 0.85. (The frequencies from the surface data, because of the heavier noise content, have lower significance compared with that of the serosal data.) The approximately 3 c/min activity was found in 100 percent of the are
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-26, NO. 7, JULY 1979
408
o
O
A
18
+~~~~~ A
c
o
0
Ol.
+ , 0
+
0o
+ A0
0
A
-
+~~~~~~~~~ LA
12
A
LLi
'I
If-l
6
0
A
0 A
A0a
LL O LUj U-
0
&
A~~~~~ A 0o
0 %
0
1
X
l
l
l
0~~~~~
0
°
l
2
A
l
I
0
2 3 4 5 6 7 8 9 10 10 STRETCHES OF DATA
Fig. 5. Frequencies generated from the "surface effects." Symbols (o, A) corresponded to frequencies from the surface measurements at two neighboring sites and the symbol (+) was the frequency from the
pneumograph.
B. Gastric Signals and Their Autoregressive Analyses The use of autoregressive techniques in signal analysis work has a number of advantages. Other than that the signals can be weakly stationary, the main advantage has been that the signals are given in a finite number of discrete frequency components with a specified order of significance. This enables one to confine one's analysis to a few major signal frequencies and can greatly simplify the work especially if a large amount of statistical data analyses is required. In this section, we shall attempt to compare the surface and serosal signals with their autoregressive analyses. The serosal signals measured from the human stomach are fairly periodic and have a well-defined shape. The resemblance of these signals to square waves is reflected in the highly regular and significant odd harmonics in the autoregressive analyses. The even harmonics, however, are less regular and have a much larger frequency spread. The implication ofthe even harmonics is that of irregular pulsewidth modulation although sometimes this may not be the case. The gastric signals from the human stomach indeed seem to fall into the latter category. The first even "harmonic," at about 9-10 c/min, coincides with the spiky activity appearing on these slow waves and the second even "harmonic," as we shall see, is very near the respiration frequency. These complications make it extremely difficult to identify the different effects. The surface signals are highly irregular. Other than the 3 c/min (and there may be some 9 c/min) rhythm, there are very little detectable periodic features. The autoregressive analyses show a similar trend. None of the previous harmonic patterns can be observed and it is doubtful if one can extract any information for the waveshape at all. It is, therefore, most likely that the analyses of any such surface signals will be restricted to the detection of the presence or the absence of the activity and no more. Full harmonic analyses using FFT's were also made on these data. Our results show that the 3 c/min slow wave activity from the surface data can also be detected by the FFT although the presence of a substantial amount of low frequency noise makes the identification difficult in some cases. The analyses of serosal data using the FFT show the similar harmonic patterns and give no more useful information than the autoregressive analyses.
serosal results and 70 percent of the surface results. A somewhat well-defined harmonic pattern was also observed in the serosal data. Fig. 5 shows the frequencies computed from the surface data when the effects of the serosal signals were removed. This was achieved by a division of the characteristic equations [see (2)] set up for the two models. This process assumes that the models are linear and that the surface effects can be isolated. Twentieth-order models were used and the frequencies generated from the pneumograph were also shown. It is observed that the "surface effects" have two main frequency components lying around 0.16 Hz (10 c/min) and 0.26 C. Surface Effects Hz (16 c/min), respectively. As we have pointed out previously, the autoregressive technique puts the signal into a linear model consisting of a charV. DiSCUSSION acteristic equation of the time-shift operator. It should, thereA. Technique Applicability fore, be possible in principle to isolate the effects of the surface Our results show that the autoregressive technique can be measurements by the division of the characteristic equations used to analyze surface and serosal data from the human for the surface and serosal data. This process was done for the stomach. The slow wave rhythm is detected in both the sur- 10 stretches of data measured simultaneously from the human face and the serosal recordings, although the occurrence and stomach and the results are shown in Fig. 5. It is observed the resolution are somewhat inferior in the former. The main that the main contribution to the "surface effects" are frereason for this, we believe, lies in the increasing noise content quencies at 9-10 c/min and around 16 c/min. They occur for in the signal as it is measured further away from the generating almost 100 percent of the time and have high significance. These frequencies, as we noticed, are precisely at the first and source.
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. BME-26, NO. 7, JULY 1979
second even harmonics of the 3 c/min slow wave activity and could easily be taken as the harmonics in the straightforward harmonic analysis. The 9-10 c/min rhythm, appearing as the irregular first even "harmonic" in the autoregressive analyses, can be identified with the spiky activity in the serosal data. It is not surprising that the spiky activity with the high-frequency characteristics are more readily transmitted to the skin surface. The detection of such signals (10-11 c/min) from the abdominal surface have previously been reported [1], although the authors suggested that they might be related to duodenal activity. The 16 c/min rhythm compares favorably with the respiration artifacts and can be so explained. It thus appears that this method of extraction of the "surface effects," if it is to be taken seriously, is capable of identifying the major sources of interference from the signal harmonics. In our case of the gastric signals, the main interferences are the respiration artifacts and some 9-1 0 c/min activity from either the stomach or the environment. VI. CONCLUSIONS We have made analyses of the surface and serosal data from the human stomach using the autoregressive technique. We have identified the 3 c/min slow wave activity in both the serosal and surface data and have related the signal waveshape to the harmonic pattern. It is observed that the first even harmonic in the serosal data at 9-10 c/min is not necessarily a consequence of pulsewidth modulation, but may well be some genuine spike activity. The second even harmonic at 16 c/min lies near the respiration frequency and may well be affected by it. An effort has been made to extract the effects of the surface measurements making use of the linear behavior of the autoregressive model. The results again indicate that the main sources of interference are respiration and some 9-10 c/min activity possibly originated from the upper gastrointestinal region.
409 ACKNOWLEDGMENT
The author wishes to thank the members of the Departments of Medical Physics, Surgery, and Control Engineering, University of Sheffield, Sheffield, England, for their technical support and the helpful discussions in this work. The author also wishes to thank the referees for their suggestions and
comments.
REFERENCES [11 B. H. Brown, "Electrophysiological measurements from the smooth muscle of the human gastrointestinal tract," IEE Medical Electronics Monograph, vol. 18, D. W. Hill and B. W. Watson, Ed. London, England: Peregrinus, 1976. G. E. P. Box and G. M. Jenkins, Time Series Analysis, Forecasting [21 and Control. San Francisco, CA: Holden-Day, 1970. [3] J. P. Burg, "Maximum entropy spectral analysis," presented at the 37th Soc. Explorat. Geophysicists, Oklahoma City, OK, 1967. 141 R. H. Jones, "Fitting autoregressions," J. Amer. Stat. Ass., vol. 70, no. 351, pp. 590-592, 1975. [51 T. J. Ulrych, "Maximum entropy power spectrum of truncated sinusoids," J. Geophys. Res., vol. II, pp. 1396-1400, 1972. (61 1. Taylor, H. L. Duthie, R. H. Smallwood, and D. Linkins, "Large bowel myoelectrical activity in man," GUT, vol. 16, p. 808, 1975. 171 B. H. Brown, R. H. Smallwood, H. L. Duthie, and C. J. Stoddard, "Intestinal smooth muscle electrical potentials recorded from surface electrodes," Med. Bio. Eng., p. 67, Jan. 1975.
Harry H. L. Kwok received the B.S. degree from the University of California, Los Angeles, in 1968 and the Ph.D. degree from Stanford University, Stanford, CA, in 1972. Since 1972, he has been with the Department of Electronics, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong. His research interests have been in biomedical en-
&
gineering and solid-state circuits and devices. Dr. Kwok is a member of Tau Beta Pi.
New Concepts for PVC Detection IVATURI S. N. MURTHY
AND
MANDAYAM R. RANGARAJ,
Abstract-A new scheme is proposed for the detection of premature ventricular beats, which is a vital function in rhythm monitoring of cardiac patients. A transformation based on the first difference of the digitized electrocardiogram (ECG) signal is developed for the detection and delineation of QRS complexes. The method for classifying the abnormal complexes from the normal ones is based on the concepts of Manuscript received September 3, 1978; revised January 1979.
The authors are with the Department of Electrical Engineering, Indian Institute of Science, Bangalore, India.
STUDENT MEMBER, IEEE
minimum phase and signal length. The parameters of a linear discriminant function obtained from a training feature vector set are used to classify the complexes. Results of application of the scheme to ECG of two arrhythmia patients are presented.
I. INTRODUCTION
R HYTHM monitoring of cardiac patients is one of the vital functions of a modern coronary care unit. It is well known that disastrous ventricular fibrillation is preceded by
0018-9294/79/0700-0409$00.75
© 1979 IEEE
