730
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING. VOL. 39. NO. 7. JULY 1992
Time-Frequency Transforms: A New Approach to First Heart Sound Frequency Dynamics John C. Wood, Andrew J. Buda, and Daniel T. Barry, Member, IEEE
Abstract-This study employed a new analytical tool, the Binomial joint time-frequency transform, to test the hypothesis that first heart sound frequency rises during the isovolumic contraction period. Cardiac vibrations were recorded from eight open chest dogs using an ultralight accelerometer cemented directly to the epicardium of the anterior left ventricle. The frequency response of the recording system was flat + 3 dB from 0.1 to 400 Hz. Three characteristic time-frequency spectral patterns were evident in the animals investigated: 1) A frequency component that rose from approximately 40-140 Hz in a 30-50 ms interval immediately following the ECG R-wave. 2) A slowly varying or static frequency of 60-100 Hz beginning midway through the isovolumic contraction period. 3) Broadband peaks occurring at the time of the Ia and Ib high frequency components. The presence of rapid frequency dynamics limits the usefulness of stationary analysis techniques for the first heart sound. The Binomial transform provided much better resolution than the spectrograph or spectrogram, the two most common non-stationary signal analysis techniques. By revealing the onset and dynamics of first heart sound frequencies, time-frequency transforms may allow mechanical assessment of individual cardiac structures.
INTRODUCTION
C
LASSICALLY, the first heart sound was thought to result from atrioventricular valve impact. Valvular kinetic energy, however, is insufficient to account for the acoustic energy received at the chest wall [ 13. Stein and others propose that AV valve closure produces sound by restraining the backflow of the ventricular blood masses, establishing simple spring-mass type oscillations [2]-[4]. Alternatively, Rushmer hypothesized that the sudden deceleration of the blood mass during isovolumic systole excites resonances within all of the cardiac structures including the myocardium, valves and great vessels [5]. Manuscript received February 22, 1991; revised October 16, 1991. This work was supported by a Grant-in-aid from the American Heart Association of Michigan, Lathrup Village, MI, and in part by NS01701 from the National Institute of Communication Disorders and Stroke, and HL3469 1 from the National Heart, Lung and Blood Institute of the NIH, Bethesda, Maryland as well as BSC-9000257 from the National Science Foundation. This work was presented, in part, at the 63rd Scientific Sessions of the American Heart Association, November 12-15, 1990, Dallas, TX. J. C. Wood and A. J. Buda are with the Bioengineering Program, the Cardiology Division, Department of Internal Medicine and the Department of Physical Medicine and Rehabilitation, University of Michigan Medical School, Ann Arbor, MI 48109. D. T. Barry was with the Bioengineering Program, the Cardiology Division, Department of Internal Medicine and the Department of Physical Medicine and Rehabilitation, University of Michigan Medical School, Ann Arbor, MI 48109. He is now with NASA, Johnson Space Center Astronaut Office, Mail Code CB Houston, TX 77058. IEEE Log Number 9200701.
Since resonant frequencies are determined by the stiffness and the geometry of the vibrating structure, heart sound frequency analysis may yield information regarding the fundamental material properties of the valves and the myocardium. Indeed, first heart sound frequency changes have been noted in valvular and myocardial pathologies [6]-[8]. However, if heart sounds are produced by cardiac resonance, the rapidly rising left ventricular pressure should cause heart sound frequency to increase during the isovolumic contraction period [3], [7], [ 111. Direct measurement of left ventricular resonant frequency supports this hypothesis; the resonant frequency increases monotonically with increased left ventricular pressure [9]. In addition to the frequency dynamics caused by the rising ventricular pressure, the opening and closing of the cardiac valves may produce sudden perturbations in cardiac vibrations. Consequently, dynamic frequency analysis techniques are necessary to relate cardiac structures to the vibrations they emit. Standard frequency analysis, such as the Fourier transform or autoregressive spectral estimation techniques, are inappropriate because signal frequency is assumed to remain constant during the transform interval. For nonstationary signals, joint timefrequency transforms are more suitable analysis tools. This is illustrated in Fig. 1 which shows a nonstationary signal, its power spectrum, and its time-frequency transform. The signal (upper panel) is the sum of a cosinewindowed slowly rising frequency of duration 64 ms and a decreasing frequency transient of duration 32 ms. The power spectrum demonstrates that signal frequencies are concentrated below 200 Hz but provides no insight into when they occur. In contrast, the time-frequency transform clearly demonstrates the dynamics of the individual components including the high frequencies introduced by the sudden onset of the decreasing frequency component. Previously, heart sound dynamic frequency analysis has primarily relied upon analog bandpass filtration methods such as the sound spectrograph [lo], [ l l ] . Using this technique, heart sounds are recorded on a tape loop and repeatedly filtered to generate the heart sound frequency distribution as a function of time. This method is timeconsuming and requires expensive instrumentation. In addition, the overlapping filter passbands produce poor frequency resolution, particularly in the frequencies below 100 Hz. A second approach, employed by Iwata, is to assume that the first heart sound spectrum is quasistatic over short time intervals and to analyze each signal segment with stationary spectral techniques [ 121. The smaller
0018-9294/92$03.00
0 1992 IEEE
WOOD et al.: TIME-FREQUENCY TRANSFORM OF T H E FIRST HEART SOUND
73 1
i
40
120
80
Time (ms)
00 1
o 120
480
360
240
Frequency (Hz) 240
h
N
zx
E 120 al 3
0-
?!i
LL
0
40
80
120
Time (ms) Fig. 1. The top panel shows a smoothly rising frequency from 0-75 Hz (left lower), a rapidly decreasing frequency 150-0 Hz (left upper), and the sum of the two signals (right). Cosine-squared and ramp windowing were performed on the rising and the falling frequency components respectively. The power spectrum of the compound signal is shown in the middle panel with frequency on the horizontal axis and magnitude squared on the vertical axis normalized to the most powerful frequency band. The time-frequency transform of this signal (lower panel) is displayed with time on the horizontal axis, frequency on the vertical axis, and magnitude is represented by a gray scale with darker areas possessing greater energy.
the segment, the better the temporal resolution. Since frequency resolution deteriorates with short signals, there is a tradeoff between temporal and spectral resolution. The short-time method and the bandpass filter method perform well for signals with time-frequency components that are well separated. Biological signals in general, and heart sounds in particular, do not respond well to these techniques because of their short duration and small bandwidth. For these signals, newer digital methods, particularly the class of joint time-frequency transforms, offer significant improvements in resolution [ 131. For example,
the Wigner time-frequency transform has been used to successfully estimate the rising resonant frequency produced by contracting skeletal muscle in vitro [14]. The Wigner transform may be thought of as a generalization of the Wiener-Khinchin autocorrelation theorem to symmetric, time-dependent autocorrelation functions. That is, instead of s(w) =
j
m r(7)e’WT
d7
-W
S(w) = Power Spectrum off(t)
(1)
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 39, NO. 7 , JULY 1992
132
characterize first heart sound frequency dynamics using time-frequency transforms; and to compare the time-frequency resolution of the spectrograph, short-time methods, and the Binominal time-frequency transform. we have METHODS
J
r ( t , 7)ejw‘ dt
Experimental procedures complied with the ‘‘Guiding ~ ( tw,) = -m Principles in the Use and Care of Animals” approved by W(t, U) = Wigner transform of f ( t ) (3) the Council of the American Physiological Society as well as with state and federal law. r ( t , 7) = f ( t 7/2)f(t - 7/21 Anesthesia was induced with triamylal (20 mg/kg) and r(t, 7 ) = Symmetric time-varying autocorrelation of f ( t ) . maintained with pentobarbital (30 mg/kg) in eight adult male mongrel dogs. The dogs were intubated and venti(4) lated with room air via a Harvard respirator. The right Although the Wigner transform performs well with mono- femoral artery was dissected free and cannulated for arcomponent signals, multicomponent signals produce un- terial pressure measurement. Left atrial pressure was desirable cross-terms that obscure signal dynamics. Re- monitored through a line placed through the tip of the left atrial appendage. Static pressures were amplified and reduced Interference Distributions, such as the Choi-Williams and Binomial transforms, suppress cross-term corded on an Electronics for Medicine VR-12 strip chart formation providing more interpretable results of multi- recorder. A left lateral thoracotomy was performed in the component signals [ 151, [ 181, [ 191. These transforms may fifth intercostal space, the pericardium incised, and the be expressed in a similar manner to the Wigner transform, heart suspended in a pericardial cradle. Heart sounds were but a smoothed estimate of the time-dependent autocor- recorded directly from the anterior left ventricular epicardium to eliminate chest wall filtering and resonance efrelation, r(t, T), is employed. That is, fects. Ultralight ( < 1 g) accelerometers (Entran EGA-125om 50-D) were used to reduce inertial ventricular loading. The techniques employed were similar to those used by Ozawa et al. in their studies of a third heart sound genesis R(t, 7) = r ( t , ~ ) * ‘ h ( t7) , (6) [16]. The transducers were cemented to a 64 mm2 square where WRID(a,t ) represents a reduced interference distri- patch of 0.2 mm thick aluminum which, in turn, was atbution instead of the Wigner distribution, and *‘ signifies tached to the myocardial wall using cynoacrylate glue. The transducer was placed 3 cm lateral of the left anterior convolution with respect to time. For the Choi-Williams descending artery between the first two marginal branches and binomial transforms the windowing functions are the (Fig. 2). The left ventricular anterior wall was chosen for following: study because of its accessibility, its relatively small balh,,(t, 7) = (4X2/a)’/2e-‘2/(4~‘2/u) (7) listic movement, and its proximity to the chest wall. In addition, using the epicardial coronary arterial anatomy as a reference allowed more reproducible placement of the transducer from animal to animal. The signal was amplified using a Grass P-522 AC amplifier and stored on a where m and k are the discrete-time counterparts of t and Neurodata model DR-484 VHS tape recorder. The frequency response of the accelerometer, amplifier, data re7, respectively. The Choi-Williams transform employs an exponential corder system was flat k 3 d b from 0.1 Hz to 400 Hz. Left weighting function that emphasizes temporally close in- ventricular pressure was monitored via a Millar 5-F mastantaneous autocorrelation values but incorporates greater nometer-tipped catheter inserted through the left atrial apaveraging as the lag variable, 7, increases. Cross-term pendage. Heart sounds recorded prior to and following suppression is achieved because cross-terms oscillate more catheter insertion were identical. ECG lead I1 was colrapidly than signal autocomponents. The Binomial trans- lected as a timing signal. Following instrumentation, heart rate, mean left atrial form uses a binomial approximation to the exponential, and is particularly efficient because the convolution in (6) pressure, mean arterial pressure and peak left ventricular may be implemented using shift and add operations alone, pressure were recorded on a chart recorder. ECG, left avoiding floating point multiplication [ 181, [20]. Concep- ventricular pressure, and epicardial acceleration were tually, the algorithm uses ‘‘Pascal’s triangle” to generate subsequently recorded on VHS tape for 3 min. The sigthe binominal coefficients. As a result, the algorithm is nals were later digitized at 1920 Hz and stored on floppy efficient and compact as illustrated by the C-language Bi- disk. Ten beat averages of the first heart sound were formed; proper waveform alignment was assured by crossnomial transform subroutine shown in Appendix A. The purpose of this study was two-fold: to identify and correlation techniques. Adjacent beats with cross-corre-
+
WOOD et a l . : TIME-FREQUENCY TRANSFORM OF T H E FIRST HEART SOUND
Left Ventricular Instrumentation and Orientation Left Ventricular Catheter
-----+-Left Atrial Catheter
A
733
output was calculated by taking the magnitude of the analytic signal. The frequency steps were 1.87 Hz, equal to those from the spectrogram and time-frequency transform.
I
Fig. 2. The placement of the accelerometer, left atrial, and left ventricular catheters are illustrated.
lation coefficients less than 0.9 were rejected. A 260 ms analysis window beginning 34 ms prior to the ECG R-wave was time-frequency transformed using a 256 point Binomial transform. The time-varying autocorrelation sequence was Hanning windowed prior to Fourier transformation. Epicardial heart sound reproducibility was assessed in both the time and time-frequency domains by comparing the magnitude of cross-correlation between ten individual beats and their average. The time-frequency spectral mean and coefficient of variation were formed to establish whether interbeat variation produced a characteristic timefrequency signature. The two-dimensional coefficient of variation matrix was then used to calculate the coefficient of variation as functions of time and frequency alone. To compare the time-frequency spectra from short-time techniques, bandpass filtration, and Binomial time-frequency transforms, time-frequency spectra for each of the three methods were calculated from ten beat averages of the epicardial first heart sound. The spectrogram, a timefrequency spectrum calculated from Fourier transformation of a sliding data window, was used to represent shorttime techniques because it is widely used in speech analysis and its properties are well characterized. The sliding data window was 33 ms (64 points) in duration. Following Hanning windowing, the data window was zeropadded to 512 points to produce a frequency step of 1.87 Hz. The first 128 positive frequencies were retained from each data window to form the time-frequency spectrum. The spectrographic time-frequency spectra were calculated from a digital simulation of the Bell spectrograph used by McKusick [lo]. The magnitude response of the digital bandpass filter was matched to that of McKusick’s filter choice; the phase response was set uniformly to zero. The passband was centered at 1000 Hz and the heart sound was modulated with 1000-1240 Hz sinewave prior to filtration in the frequency domain. The envelope of the filter
RESULTS First heart sounds recorded from the epicardium and from the overlying pericardium and chest wall are demonstrated in Fig. 3 . The epicardial and pericardial recordings are nearly identical with all the high frequency peaks aligned. Chest wall recordings are attenuated %fold, consist of lower frequencies, and are slightly delayed relative to the epicardial signals. Representative epicardial first heart sounds, their power spectra, and their Binomial time-frequency spectra are shown in Figs. 4 and 5. In Fig. 4 , the first heart sound [Fig. 4(a)] had between 6-8 oscillations with periods ranging from 8 to 24 ms in duration. The time signal suggested two components, labeled I and 11. Oscillations of component I became more closely spaced as the heart sound progressed, suggesting a frequency that rose in time. Fourier power spectral analysis [Fig. 4(b)] indicated that first heart sound frequencies are concentrated below 150 Hz. Since the transducer response was flat up to 400 Hz, the sharp cutoff at 150 Hz resulted from properties of the heart itself. Following the rapid cutoff the spectrum attenuated at roughly 20 dB per decade. The spectrum demonstrated a sawtooth appearance without a dominant component that would suggest a stationary resonant frequency. Notice that the power spectrum did not provide insight into the dynamics implied by inspection of the time signal. In contrast, the time-frequency spectrum [Fig. 4(c)] revealed a striking rising frequency occurring shortly after the ECG R-wave. Component I frequency rose from approximately 50-120 Hz in 30 ms. The second component was less dynamic, having slowly varying frequencies near 60 and 90 Hz. In Fig. 5(a), no clear distinction into early and late components is evident. The most dominant feature again appears to be a rapidly rising frequency as indicated by decreased zero-crossing interval in time. Signal inflections and envelope variation, however, suggest the presence of additional components. The power spectrum [Fig. 5(b)] again fails to provide insight into the frequency dynamics, although a stationary peak near 10 Hz is suggested. The Binominal transform [Fig. 5(c)] reveals a powerful rising frequency beginning at or slightly preceding the ECG-R wave that continues for approximately 60 ms. Three additional components are evident in the time-frequency domain. Two of these run vertically in the time-frequency plane and are located 20 and 40 ms following the R-wave. The third, a 10-20 Hz stationary frequency, spans isovolumic systole. The heart sounds recorded from the epicardium varied little from beat-to-beat. With the respirator stopped at end expiration, correlation coefficients greater than 0.99 were consistently observed. Fig. 6 shows ten consecutive beats
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 39. NO. 7, JULY 1992
134
*
II n
4
II
4 -
50
0
I
I
0
IO0
120
80
40
Time (ms)
I50
Tirne(ms)
A
I 0
200
400
io00
800
600
Frequency (Hz) 100
150
Tirne(ms)
240
-
180
N
3 =-
53
II
c )
120
8!
LL
J
I
0
t
50
IO0
I50
T 4 0
80
120
0
Time (ms)
Time (ms)
Fig. 3 . First heart sound recorded from the epicardium (top), overlying pericardium (middle), and nearest chest wall location (bottom).
Fig. 4. A typical epicardial first heart sound (top), its power spectrum (middle), and its time frequency transform (bottom).
overlaid upon one another. Time-frequency transformation preserved beat-to-beat reproducibility. Two-dimensional cross-correlation coefficients between ten individual time-frequency spectra and their time-frequency spectral average ranged from 0.93 to 0.97. The time and frequency projections of the two dimensional time-frequency coefficient of variation are shown in Fig. 7. Greater variation is seen at the frequencies above 120 Hz as a result of the decreased signal-to-noise ratio at higher frequencies. Similarly, variability was inversely proportional to signal power, again as a result of improved signal-to-noise ratio. However increased variability was evident for 20 ms following the R-wave, possibly reflecting
the uncertainty in the rising frequency onset or rate of rise. Distinct time-frequency features were absent from the two-dimensional time-frequency coefficient of variation (not shown) suggesting that changes in existing component timing rather than the appearance and disappearance of components is responsible for interbeat timefrequency spectral variation. Heart sound heterogeneity was much larger between animals. Cross-correlation coefficients ranged from 0.25 to 0.7 suggesting that interanimal cardiac physiologic and anatomic differences strongly influence the first heart sound. Despite the lower correlation coefficients, the gross appearance of the heart sounds was similar, with five to
WOOD et a l . : TIME-FREQUENCY TRANSFORM OF THE FIRST HEART SOUND
135
10 Beats, Respirator stopped
40
0
80
120
Ti me(ms)
lo
1 I
I
I
0
40
80
I
120
Time (ms) Fig. 6 . Ten consecutive first heart sounds plotted on top of one another.
.0001 1 0
200
400
600
I
8M)
1000
Frequency(Hz)
0.0
120
60
180
1 240
Frequency (Hz)
Time (ms) Fig. 5. A second epicardial first heart sound (top), its power spectrum (middle), and its time frequency transform (bottom).
seven cycles ranging from 10 to 120 Hz. Fig. 8 demonstrates time-frequency spectra from six additional animals. A rapidly rising frequency was apparent in every animal, increasing from approximately 20 to 100 Hz in 25-35 ms. In six of the animals this component began within 10 ms of the ECG R-wave. Hemodynamic differences did not appear to account for the delay seen in two of the animals (Table I). The time-frequency properties of the remainder of the first heart sound were more variable. Nevertheless two other characteristic elements were identified: 1) A slowly varying frequency between 50 and 70 Hz, beginning slightly after the rapidly rising compo-
0.0'
80
40
120
Time (ms) Fig. 7 . The coefficient of variation (CV) as a function of time (top) and frequency (bottom) for time-frequency transforms of ten consecutive first heart sounds.
nent. 2) One or two impulse-like components occurring at the same time as the Ia, Ib, and IC first heart sound high frequency components. Fig. 9 demonstrates an epicardial first heart sound time-
136
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 39, NO. I , JULY 1992
AD722
240
h
AD715
180
N
I, x
5
120
(T 3
??
LL
60
R
Time (rns)
240
h
180
N
I, x
5
120
U 3
??
LL
60
I
R
80
R
Time (rns) 240
N
-
I
E
6
6 5 120
h
E
180
Time (rns) AD707
AD721
240
120
180
N
120
3
2 (T
i5
??
U-
LL
60
60
R
R
Time (rns)
Time (rns)
Fin. 8 . Time frequency spectra from six additional animals
TABLE I HEMODYNAMICS OF THE EIGHT ANIMALS INVESTIGATED
Dog#
HR (bpm)
LAP (mm Hg)
MAP (mm Hg)
dPdTmax (mm HgT/s)
707 711 712 7 I4 719 72 1 722 724
115 135 131 140 148 128 141 111
13 13 10
160 146 120 122 115 128 NIA 115
1890 2180 2332 1740 2450 3300 NIA 1730
6 2 3 NIA 6
N/A, not available because o f technical malfunction
frequency spectrum generated by a spectrograph simulation, spectrogram and the Binomial time-frequency transform. While all three representatives have similar features, the Binomial representation provides the best resolution of time-frequency detail. The spectrograph has the most smearing; considerable spectral energy is evident when the signal is quiescent because of the long duration impulse response of the high-Q filter. The spectrogram performs slightly better than the spectrograph because Fourier transforms provide higher resolution frequency estimates than bandpass filters. Nevertheless, the spectrogram blurs the two major components sufficiently that other spectral features are obscured.
WOOD et al.: TIME-FREQUENCY TRANSFORM OF THE FIRST HEART SOUND
240
h
N
I, >.
E 120 a
=
F
LL
0
40
80
120
Time (ms)
0
40
80
120
Time (ms) Binomial Transform
240
N
z. x
E 120 0, 3 CT
?
LL
0
40
80
120
Time (ms) Fig. 9. Three different time-frequency representations of the same first heart sound are compared. The top panel shows a digital simulation of McKusick’s spectrograph, the middle panel demonstrates a running window power spectrum or spectrogram, and the bottom panel shows a binomial time frequency transform.
DISCUSSION Time-frequency analysis clearly demonstrates that the first heart sound frequency is dynamic and multicomponent. The prominent rising frequency in early systole seriously compromises the validity of stationary frequency techniques in first heart sound analysis. As demonstrated in Figs. 1, 4, and 5, stationary frequency analysis of a rising frequency produces a smear of frequencies without
737
clear peaks. Furthermore, stationary frequency techniques provide no insight into the timing of the appearance and disappearance of various frequency components. The first heart sound of Fig. 4 and its time-frequency transform suggest two distinct components to the first heart sound; no such information is provided by the power spectrum. In addition to the modulation of first heart sound frequency by the rising left ventricular stiffness and pressure, the opening and closing of the cardiac valves causes discrete changes in the cardiac vibratory properties that will be missed by stationary techniques. Restricting frequency analysis to the isovolumic contraction period, as was done by Adolph et al. and others, does not improve the validity of these techniques because the most rapid frequency dynamics occur during the isovolumic contraction period. It is hypothesized that joint time-frequency methods will achieve greater diagnostic sensitivity by quantifying first heart sound frequency dynamics. The Binomial time-frequency transform used in this study provides higher joint resolution of time and frequency than the spectrograph and spectrogram and better interpretability than other time-frequency transforms such as the Wigner-Ville. The limited resolution of the spectrograph is inherent to the filtering process; narrow filters provide better frequency resolution but the resulting slow decay of the impulse response smears temporal detail [ 101. Thus, even modem spectral analyzers must strike a balance between time and frequency resolution. The short time Fourier Transform (STFT) and its magnitude, the spectrogram, have an analogous time-frequency tradeoff. Shorter analysis windows produce better temporal resolution but degrade spectral resolution. Some time-frequency transforms, such as the Wigner-Ville and ChoiWilliams transforms, do not contain inherent time-frequency resolution tradeoffs and provide higher joint resolution of time and frequency of many nonstationary signals than short-time Fourier transforms or bandpass filtration [ 171, [ 131. The improved resolution, however, has a price; multicomponent signals have undesirable cross-term artifact that often obscures the signal’s frequency dynamics. Reduced interference distributions, including the Choi-Williams and Binomial transforms, trade some auto-term resolution for cross-term inhibition, providing more interpretable results of multicomponent signals. The degree of the resolution/cross-term tradeoff depends upon the convolving kernel, h ( t , T ) , used in the transform [see (6)], 1181, [19]. The more similar h(t, T ) is to 6 ( t ) , the more the resulting time-frequency spectrum will resemble the Wigner spectrum. Although any number of reduced interference distributions would produce qualitatively similar results to those obtained in this paper, the Binomial transform combines a particularly efficient algorithm with outstanding cross-term suppression properties [18], 1201. Previous studies of first heart sound frequency have primarily been limited to the chest wall. Cardiac vibrations propagate as mechanical shear waves; intervening visco-
738
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING. VOL. 39. NO. 7. JULY 1992
elastic thoracic tissue attenuates higher frequencies and introduces a variable propagation delay [21], [22]. Bertrand and Zalter eliminated chest wall filtering by recording heart sounds directly from the epicardium [23], [24]. However, the fidelity of these recordings was compromised by the heaviness and poor frequency response of the microphones. In this study, ultralight, wide-band accelerometers cemented directly to the epicardium eliminated chest wall effects without mechanically loading the myocardium. While epicardial recordings are more focal than chest wall recordings, the strong similarity of the epicardial, pericardial and chest wall recordings indicates common underlying mechanics. The epicardial heart sound signal is generally 10-100 times more powerful than chest wall recordings, having accelerations typically between 1-5 m/s2. Consequently, the signal-to-noise ratio is quite high and little beat-to-beat variation is seen. Since the chest wall is a low pass filter, heart sounds recorded from the epicardium have greater bandwidth than chest wall recordings. The 6 dB/octave rolloff is consistent with chest wall recordings using acceleration transducers and is 12 db/octave less than observed with displacement type transducers [2 I], [22], [25], [26]. The first heart sound demonstrates several characteristic time-frequency components but the most prominent was a rapidly rising frequency during early systole. Other investigators have noted a rising frequency on the intact canine chest wall [ 1 I]. A rising first heart sound frequency is predicted by theoretical models of both myocardial and valvular vibrations. Direct measurements of left ventricular resonant frequency reveal a monotonic dependence with left ventricular pressure; a similar dependence has not yet been demonstrated for mitral valve vibrations [9]. Neither the presence of a rising frequency per se nor the range of frequencies of first heart sound vibrations strongly favor either genesis mechanism. The rapid rate of frequency rise, however, is more consistent with a myocardial origin. Valvular vibrations rise as the cube-root of left ventricular pressure, a relatively weak dependence [3], [ 111. Myocardial vibrations increase in frequency at least as fast as the square-root of left ventricular pressure because both the wall tension and the wall elastic modulus are increasing [ 7 ] . The early onset of the rising frequency also supports a muscular origin. The atrioventricular valves close asyncronously and do not function as a unit until nearly 20-25 ms following ventricular-atrial pressure crossover [27], [28]. The rapid upstroke of left ventricular pressure does not precede the R-wave, thus valve closure would not be expected until 20-25 ms later. In six of the eight animals studied, however, the rising frequency began within 10 ms of the ECG R-wave. Thus, if valvular vibrations are present, they begin at a time when the valves are not coordinated and the papillary muscles dominate the valve assembly stiffness. Table I1 summarizes the arguments for and against resonances of the myocardium and the valves. It must also be noted that rising frequency components do not necessarily
TABLE 11 MYOCARDIAL VERSUS VALVULAR GENESIS Evidence
Valvular
Myocardial
Rising frequency present Range of frequencies Rate of frequency rise Rising frequency timing
++ ++ + +
++ ++ + +++
+ Possible, but unlikely. + + Consistent. + + + Supported. have a resonant origin. Nonresonant phenomena, such as the depolarization wave passing across the ventricle or the gross myocardial rearrangement in response to increased pressure, might also produce a rising frequency; s w h mechanisms are unlikely to produce rapid frequency changes however. High-frequency transients, superimposed upon such a slowly rising frequency, might appear to be a rapidly rising frequency component. While time-frequency analysis historically was timeconsuming and required special instrumentation, timefrequency transforms may be calculated easily and efficiently on ordinary personal and laboratory computers. Advanced new algorithms provide higher resolution and easier interpretation of formerly intractable biological signals. The first heart sound, because of its small bandwidth and short duration, has not responded well to traditional dynamic frequency analyses. Since information about cardiac material properties and vibrational genesis may be contained in first heart sound frequency dynamics, timefrequency transforms may shed light on basic heart sound mechanics and improve diagnostic sensitivity of in vivo heart sound analysis. ACKNOWLEDGMENT We would like to thank M. Gallagher and S. Haarer for their expert technical assistance. We would also like to thank Dr. W. J. Williams for the use of his computer facilities and Dr. P. Stein for his insightful criticism of the manuscript. APPENDIXA /* Bin Transform accepts a complex (the analytic signal is usually used) floating point array “data” of length “length” and produces a time frequency array with frequency resolution ‘ ‘freq-pts” . The algorithm complexity is length*(freq-pts) * 2. This subroutine assumes that the user has access to a Fast Fourier Transform routine “ColFft()” that will calculate the column wise Fourier Transform to a complex matrix as well as complex math subroutines “Caddo”, “Cmul()”, and “Conjg()” for addition, multiplication, and conjugation. Note that no floating point multiplication is required for generation of the binomial coefficients, only for formation of the outer
WOOD er a l . : TIME-FREQUENCY TRANSFORM O F T H E FIRST HEART SOUND
139
products. * I void Bin Transform(data,length,output,freq-pts) fcomplex *data,**output; I* double indirection used here for 2D arrays *I int length ,freq -pts;
fcomplex ACF[256]; / Length =maximum desired freq-pts * I int j,k,n; double power; power= 1.OOOO; for (j=O;j
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING. VOL. 39. NO. 7. JULY 1992
Time-Frequency Transforms: A New Approach to First Heart Sound Frequency Dynamics John C. Wood, Andrew J. Buda, and Daniel T. Barry, Member, IEEE
Abstract-This study employed a new analytical tool, the Binomial joint time-frequency transform, to test the hypothesis that first heart sound frequency rises during the isovolumic contraction period. Cardiac vibrations were recorded from eight open chest dogs using an ultralight accelerometer cemented directly to the epicardium of the anterior left ventricle. The frequency response of the recording system was flat + 3 dB from 0.1 to 400 Hz. Three characteristic time-frequency spectral patterns were evident in the animals investigated: 1) A frequency component that rose from approximately 40-140 Hz in a 30-50 ms interval immediately following the ECG R-wave. 2) A slowly varying or static frequency of 60-100 Hz beginning midway through the isovolumic contraction period. 3) Broadband peaks occurring at the time of the Ia and Ib high frequency components. The presence of rapid frequency dynamics limits the usefulness of stationary analysis techniques for the first heart sound. The Binomial transform provided much better resolution than the spectrograph or spectrogram, the two most common non-stationary signal analysis techniques. By revealing the onset and dynamics of first heart sound frequencies, time-frequency transforms may allow mechanical assessment of individual cardiac structures.
INTRODUCTION
C
LASSICALLY, the first heart sound was thought to result from atrioventricular valve impact. Valvular kinetic energy, however, is insufficient to account for the acoustic energy received at the chest wall [ 13. Stein and others propose that AV valve closure produces sound by restraining the backflow of the ventricular blood masses, establishing simple spring-mass type oscillations [2]-[4]. Alternatively, Rushmer hypothesized that the sudden deceleration of the blood mass during isovolumic systole excites resonances within all of the cardiac structures including the myocardium, valves and great vessels [5]. Manuscript received February 22, 1991; revised October 16, 1991. This work was supported by a Grant-in-aid from the American Heart Association of Michigan, Lathrup Village, MI, and in part by NS01701 from the National Institute of Communication Disorders and Stroke, and HL3469 1 from the National Heart, Lung and Blood Institute of the NIH, Bethesda, Maryland as well as BSC-9000257 from the National Science Foundation. This work was presented, in part, at the 63rd Scientific Sessions of the American Heart Association, November 12-15, 1990, Dallas, TX. J. C. Wood and A. J. Buda are with the Bioengineering Program, the Cardiology Division, Department of Internal Medicine and the Department of Physical Medicine and Rehabilitation, University of Michigan Medical School, Ann Arbor, MI 48109. D. T. Barry was with the Bioengineering Program, the Cardiology Division, Department of Internal Medicine and the Department of Physical Medicine and Rehabilitation, University of Michigan Medical School, Ann Arbor, MI 48109. He is now with NASA, Johnson Space Center Astronaut Office, Mail Code CB Houston, TX 77058. IEEE Log Number 9200701.
Since resonant frequencies are determined by the stiffness and the geometry of the vibrating structure, heart sound frequency analysis may yield information regarding the fundamental material properties of the valves and the myocardium. Indeed, first heart sound frequency changes have been noted in valvular and myocardial pathologies [6]-[8]. However, if heart sounds are produced by cardiac resonance, the rapidly rising left ventricular pressure should cause heart sound frequency to increase during the isovolumic contraction period [3], [7], [ 111. Direct measurement of left ventricular resonant frequency supports this hypothesis; the resonant frequency increases monotonically with increased left ventricular pressure [9]. In addition to the frequency dynamics caused by the rising ventricular pressure, the opening and closing of the cardiac valves may produce sudden perturbations in cardiac vibrations. Consequently, dynamic frequency analysis techniques are necessary to relate cardiac structures to the vibrations they emit. Standard frequency analysis, such as the Fourier transform or autoregressive spectral estimation techniques, are inappropriate because signal frequency is assumed to remain constant during the transform interval. For nonstationary signals, joint timefrequency transforms are more suitable analysis tools. This is illustrated in Fig. 1 which shows a nonstationary signal, its power spectrum, and its time-frequency transform. The signal (upper panel) is the sum of a cosinewindowed slowly rising frequency of duration 64 ms and a decreasing frequency transient of duration 32 ms. The power spectrum demonstrates that signal frequencies are concentrated below 200 Hz but provides no insight into when they occur. In contrast, the time-frequency transform clearly demonstrates the dynamics of the individual components including the high frequencies introduced by the sudden onset of the decreasing frequency component. Previously, heart sound dynamic frequency analysis has primarily relied upon analog bandpass filtration methods such as the sound spectrograph [lo], [ l l ] . Using this technique, heart sounds are recorded on a tape loop and repeatedly filtered to generate the heart sound frequency distribution as a function of time. This method is timeconsuming and requires expensive instrumentation. In addition, the overlapping filter passbands produce poor frequency resolution, particularly in the frequencies below 100 Hz. A second approach, employed by Iwata, is to assume that the first heart sound spectrum is quasistatic over short time intervals and to analyze each signal segment with stationary spectral techniques [ 121. The smaller
0018-9294/92$03.00
0 1992 IEEE
WOOD et al.: TIME-FREQUENCY TRANSFORM OF T H E FIRST HEART SOUND
73 1
i
40
120
80
Time (ms)
00 1
o 120
480
360
240
Frequency (Hz) 240
h
N
zx
E 120 al 3
0-
?!i
LL
0
40
80
120
Time (ms) Fig. 1. The top panel shows a smoothly rising frequency from 0-75 Hz (left lower), a rapidly decreasing frequency 150-0 Hz (left upper), and the sum of the two signals (right). Cosine-squared and ramp windowing were performed on the rising and the falling frequency components respectively. The power spectrum of the compound signal is shown in the middle panel with frequency on the horizontal axis and magnitude squared on the vertical axis normalized to the most powerful frequency band. The time-frequency transform of this signal (lower panel) is displayed with time on the horizontal axis, frequency on the vertical axis, and magnitude is represented by a gray scale with darker areas possessing greater energy.
the segment, the better the temporal resolution. Since frequency resolution deteriorates with short signals, there is a tradeoff between temporal and spectral resolution. The short-time method and the bandpass filter method perform well for signals with time-frequency components that are well separated. Biological signals in general, and heart sounds in particular, do not respond well to these techniques because of their short duration and small bandwidth. For these signals, newer digital methods, particularly the class of joint time-frequency transforms, offer significant improvements in resolution [ 131. For example,
the Wigner time-frequency transform has been used to successfully estimate the rising resonant frequency produced by contracting skeletal muscle in vitro [14]. The Wigner transform may be thought of as a generalization of the Wiener-Khinchin autocorrelation theorem to symmetric, time-dependent autocorrelation functions. That is, instead of s(w) =
j
m r(7)e’WT
d7
-W
S(w) = Power Spectrum off(t)
(1)
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 39, NO. 7 , JULY 1992
132
characterize first heart sound frequency dynamics using time-frequency transforms; and to compare the time-frequency resolution of the spectrograph, short-time methods, and the Binominal time-frequency transform. we have METHODS
J
r ( t , 7)ejw‘ dt
Experimental procedures complied with the ‘‘Guiding ~ ( tw,) = -m Principles in the Use and Care of Animals” approved by W(t, U) = Wigner transform of f ( t ) (3) the Council of the American Physiological Society as well as with state and federal law. r ( t , 7) = f ( t 7/2)f(t - 7/21 Anesthesia was induced with triamylal (20 mg/kg) and r(t, 7 ) = Symmetric time-varying autocorrelation of f ( t ) . maintained with pentobarbital (30 mg/kg) in eight adult male mongrel dogs. The dogs were intubated and venti(4) lated with room air via a Harvard respirator. The right Although the Wigner transform performs well with mono- femoral artery was dissected free and cannulated for arcomponent signals, multicomponent signals produce un- terial pressure measurement. Left atrial pressure was desirable cross-terms that obscure signal dynamics. Re- monitored through a line placed through the tip of the left atrial appendage. Static pressures were amplified and reduced Interference Distributions, such as the Choi-Williams and Binomial transforms, suppress cross-term corded on an Electronics for Medicine VR-12 strip chart formation providing more interpretable results of multi- recorder. A left lateral thoracotomy was performed in the component signals [ 151, [ 181, [ 191. These transforms may fifth intercostal space, the pericardium incised, and the be expressed in a similar manner to the Wigner transform, heart suspended in a pericardial cradle. Heart sounds were but a smoothed estimate of the time-dependent autocor- recorded directly from the anterior left ventricular epicardium to eliminate chest wall filtering and resonance efrelation, r(t, T), is employed. That is, fects. Ultralight ( < 1 g) accelerometers (Entran EGA-125om 50-D) were used to reduce inertial ventricular loading. The techniques employed were similar to those used by Ozawa et al. in their studies of a third heart sound genesis R(t, 7) = r ( t , ~ ) * ‘ h ( t7) , (6) [16]. The transducers were cemented to a 64 mm2 square where WRID(a,t ) represents a reduced interference distri- patch of 0.2 mm thick aluminum which, in turn, was atbution instead of the Wigner distribution, and *‘ signifies tached to the myocardial wall using cynoacrylate glue. The transducer was placed 3 cm lateral of the left anterior convolution with respect to time. For the Choi-Williams descending artery between the first two marginal branches and binomial transforms the windowing functions are the (Fig. 2). The left ventricular anterior wall was chosen for following: study because of its accessibility, its relatively small balh,,(t, 7) = (4X2/a)’/2e-‘2/(4~‘2/u) (7) listic movement, and its proximity to the chest wall. In addition, using the epicardial coronary arterial anatomy as a reference allowed more reproducible placement of the transducer from animal to animal. The signal was amplified using a Grass P-522 AC amplifier and stored on a where m and k are the discrete-time counterparts of t and Neurodata model DR-484 VHS tape recorder. The frequency response of the accelerometer, amplifier, data re7, respectively. The Choi-Williams transform employs an exponential corder system was flat k 3 d b from 0.1 Hz to 400 Hz. Left weighting function that emphasizes temporally close in- ventricular pressure was monitored via a Millar 5-F mastantaneous autocorrelation values but incorporates greater nometer-tipped catheter inserted through the left atrial apaveraging as the lag variable, 7, increases. Cross-term pendage. Heart sounds recorded prior to and following suppression is achieved because cross-terms oscillate more catheter insertion were identical. ECG lead I1 was colrapidly than signal autocomponents. The Binomial trans- lected as a timing signal. Following instrumentation, heart rate, mean left atrial form uses a binomial approximation to the exponential, and is particularly efficient because the convolution in (6) pressure, mean arterial pressure and peak left ventricular may be implemented using shift and add operations alone, pressure were recorded on a chart recorder. ECG, left avoiding floating point multiplication [ 181, [20]. Concep- ventricular pressure, and epicardial acceleration were tually, the algorithm uses ‘‘Pascal’s triangle” to generate subsequently recorded on VHS tape for 3 min. The sigthe binominal coefficients. As a result, the algorithm is nals were later digitized at 1920 Hz and stored on floppy efficient and compact as illustrated by the C-language Bi- disk. Ten beat averages of the first heart sound were formed; proper waveform alignment was assured by crossnomial transform subroutine shown in Appendix A. The purpose of this study was two-fold: to identify and correlation techniques. Adjacent beats with cross-corre-
+
WOOD et a l . : TIME-FREQUENCY TRANSFORM OF T H E FIRST HEART SOUND
Left Ventricular Instrumentation and Orientation Left Ventricular Catheter
-----+-Left Atrial Catheter
A
733
output was calculated by taking the magnitude of the analytic signal. The frequency steps were 1.87 Hz, equal to those from the spectrogram and time-frequency transform.
I
Fig. 2. The placement of the accelerometer, left atrial, and left ventricular catheters are illustrated.
lation coefficients less than 0.9 were rejected. A 260 ms analysis window beginning 34 ms prior to the ECG R-wave was time-frequency transformed using a 256 point Binomial transform. The time-varying autocorrelation sequence was Hanning windowed prior to Fourier transformation. Epicardial heart sound reproducibility was assessed in both the time and time-frequency domains by comparing the magnitude of cross-correlation between ten individual beats and their average. The time-frequency spectral mean and coefficient of variation were formed to establish whether interbeat variation produced a characteristic timefrequency signature. The two-dimensional coefficient of variation matrix was then used to calculate the coefficient of variation as functions of time and frequency alone. To compare the time-frequency spectra from short-time techniques, bandpass filtration, and Binomial time-frequency transforms, time-frequency spectra for each of the three methods were calculated from ten beat averages of the epicardial first heart sound. The spectrogram, a timefrequency spectrum calculated from Fourier transformation of a sliding data window, was used to represent shorttime techniques because it is widely used in speech analysis and its properties are well characterized. The sliding data window was 33 ms (64 points) in duration. Following Hanning windowing, the data window was zeropadded to 512 points to produce a frequency step of 1.87 Hz. The first 128 positive frequencies were retained from each data window to form the time-frequency spectrum. The spectrographic time-frequency spectra were calculated from a digital simulation of the Bell spectrograph used by McKusick [lo]. The magnitude response of the digital bandpass filter was matched to that of McKusick’s filter choice; the phase response was set uniformly to zero. The passband was centered at 1000 Hz and the heart sound was modulated with 1000-1240 Hz sinewave prior to filtration in the frequency domain. The envelope of the filter
RESULTS First heart sounds recorded from the epicardium and from the overlying pericardium and chest wall are demonstrated in Fig. 3 . The epicardial and pericardial recordings are nearly identical with all the high frequency peaks aligned. Chest wall recordings are attenuated %fold, consist of lower frequencies, and are slightly delayed relative to the epicardial signals. Representative epicardial first heart sounds, their power spectra, and their Binomial time-frequency spectra are shown in Figs. 4 and 5. In Fig. 4 , the first heart sound [Fig. 4(a)] had between 6-8 oscillations with periods ranging from 8 to 24 ms in duration. The time signal suggested two components, labeled I and 11. Oscillations of component I became more closely spaced as the heart sound progressed, suggesting a frequency that rose in time. Fourier power spectral analysis [Fig. 4(b)] indicated that first heart sound frequencies are concentrated below 150 Hz. Since the transducer response was flat up to 400 Hz, the sharp cutoff at 150 Hz resulted from properties of the heart itself. Following the rapid cutoff the spectrum attenuated at roughly 20 dB per decade. The spectrum demonstrated a sawtooth appearance without a dominant component that would suggest a stationary resonant frequency. Notice that the power spectrum did not provide insight into the dynamics implied by inspection of the time signal. In contrast, the time-frequency spectrum [Fig. 4(c)] revealed a striking rising frequency occurring shortly after the ECG R-wave. Component I frequency rose from approximately 50-120 Hz in 30 ms. The second component was less dynamic, having slowly varying frequencies near 60 and 90 Hz. In Fig. 5(a), no clear distinction into early and late components is evident. The most dominant feature again appears to be a rapidly rising frequency as indicated by decreased zero-crossing interval in time. Signal inflections and envelope variation, however, suggest the presence of additional components. The power spectrum [Fig. 5(b)] again fails to provide insight into the frequency dynamics, although a stationary peak near 10 Hz is suggested. The Binominal transform [Fig. 5(c)] reveals a powerful rising frequency beginning at or slightly preceding the ECG-R wave that continues for approximately 60 ms. Three additional components are evident in the time-frequency domain. Two of these run vertically in the time-frequency plane and are located 20 and 40 ms following the R-wave. The third, a 10-20 Hz stationary frequency, spans isovolumic systole. The heart sounds recorded from the epicardium varied little from beat-to-beat. With the respirator stopped at end expiration, correlation coefficients greater than 0.99 were consistently observed. Fig. 6 shows ten consecutive beats
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 39. NO. 7, JULY 1992
134
*
II n
4
II
4 -
50
0
I
I
0
IO0
120
80
40
Time (ms)
I50
Tirne(ms)
A
I 0
200
400
io00
800
600
Frequency (Hz) 100
150
Tirne(ms)
240
-
180
N
3 =-
53
II
c )
120
8!
LL
J
I
0
t
50
IO0
I50
T 4 0
80
120
0
Time (ms)
Time (ms)
Fig. 3 . First heart sound recorded from the epicardium (top), overlying pericardium (middle), and nearest chest wall location (bottom).
Fig. 4. A typical epicardial first heart sound (top), its power spectrum (middle), and its time frequency transform (bottom).
overlaid upon one another. Time-frequency transformation preserved beat-to-beat reproducibility. Two-dimensional cross-correlation coefficients between ten individual time-frequency spectra and their time-frequency spectral average ranged from 0.93 to 0.97. The time and frequency projections of the two dimensional time-frequency coefficient of variation are shown in Fig. 7. Greater variation is seen at the frequencies above 120 Hz as a result of the decreased signal-to-noise ratio at higher frequencies. Similarly, variability was inversely proportional to signal power, again as a result of improved signal-to-noise ratio. However increased variability was evident for 20 ms following the R-wave, possibly reflecting
the uncertainty in the rising frequency onset or rate of rise. Distinct time-frequency features were absent from the two-dimensional time-frequency coefficient of variation (not shown) suggesting that changes in existing component timing rather than the appearance and disappearance of components is responsible for interbeat timefrequency spectral variation. Heart sound heterogeneity was much larger between animals. Cross-correlation coefficients ranged from 0.25 to 0.7 suggesting that interanimal cardiac physiologic and anatomic differences strongly influence the first heart sound. Despite the lower correlation coefficients, the gross appearance of the heart sounds was similar, with five to
WOOD et a l . : TIME-FREQUENCY TRANSFORM OF THE FIRST HEART SOUND
135
10 Beats, Respirator stopped
40
0
80
120
Ti me(ms)
lo
1 I
I
I
0
40
80
I
120
Time (ms) Fig. 6 . Ten consecutive first heart sounds plotted on top of one another.
.0001 1 0
200
400
600
I
8M)
1000
Frequency(Hz)
0.0
120
60
180
1 240
Frequency (Hz)
Time (ms) Fig. 5. A second epicardial first heart sound (top), its power spectrum (middle), and its time frequency transform (bottom).
seven cycles ranging from 10 to 120 Hz. Fig. 8 demonstrates time-frequency spectra from six additional animals. A rapidly rising frequency was apparent in every animal, increasing from approximately 20 to 100 Hz in 25-35 ms. In six of the animals this component began within 10 ms of the ECG R-wave. Hemodynamic differences did not appear to account for the delay seen in two of the animals (Table I). The time-frequency properties of the remainder of the first heart sound were more variable. Nevertheless two other characteristic elements were identified: 1) A slowly varying frequency between 50 and 70 Hz, beginning slightly after the rapidly rising compo-
0.0'
80
40
120
Time (ms) Fig. 7 . The coefficient of variation (CV) as a function of time (top) and frequency (bottom) for time-frequency transforms of ten consecutive first heart sounds.
nent. 2) One or two impulse-like components occurring at the same time as the Ia, Ib, and IC first heart sound high frequency components. Fig. 9 demonstrates an epicardial first heart sound time-
136
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING, VOL. 39, NO. I , JULY 1992
AD722
240
h
AD715
180
N
I, x
5
120
(T 3
??
LL
60
R
Time (rns)
240
h
180
N
I, x
5
120
U 3
??
LL
60
I
R
80
R
Time (rns) 240
N
-
I
E
6
6 5 120
h
E
180
Time (rns) AD707
AD721
240
120
180
N
120
3
2 (T
i5
??
U-
LL
60
60
R
R
Time (rns)
Time (rns)
Fin. 8 . Time frequency spectra from six additional animals
TABLE I HEMODYNAMICS OF THE EIGHT ANIMALS INVESTIGATED
Dog#
HR (bpm)
LAP (mm Hg)
MAP (mm Hg)
dPdTmax (mm HgT/s)
707 711 712 7 I4 719 72 1 722 724
115 135 131 140 148 128 141 111
13 13 10
160 146 120 122 115 128 NIA 115
1890 2180 2332 1740 2450 3300 NIA 1730
6 2 3 NIA 6
N/A, not available because o f technical malfunction
frequency spectrum generated by a spectrograph simulation, spectrogram and the Binomial time-frequency transform. While all three representatives have similar features, the Binomial representation provides the best resolution of time-frequency detail. The spectrograph has the most smearing; considerable spectral energy is evident when the signal is quiescent because of the long duration impulse response of the high-Q filter. The spectrogram performs slightly better than the spectrograph because Fourier transforms provide higher resolution frequency estimates than bandpass filters. Nevertheless, the spectrogram blurs the two major components sufficiently that other spectral features are obscured.
WOOD et al.: TIME-FREQUENCY TRANSFORM OF THE FIRST HEART SOUND
240
h
N
I, >.
E 120 a
=
F
LL
0
40
80
120
Time (ms)
0
40
80
120
Time (ms) Binomial Transform
240
N
z. x
E 120 0, 3 CT
?
LL
0
40
80
120
Time (ms) Fig. 9. Three different time-frequency representations of the same first heart sound are compared. The top panel shows a digital simulation of McKusick’s spectrograph, the middle panel demonstrates a running window power spectrum or spectrogram, and the bottom panel shows a binomial time frequency transform.
DISCUSSION Time-frequency analysis clearly demonstrates that the first heart sound frequency is dynamic and multicomponent. The prominent rising frequency in early systole seriously compromises the validity of stationary frequency techniques in first heart sound analysis. As demonstrated in Figs. 1, 4, and 5, stationary frequency analysis of a rising frequency produces a smear of frequencies without
737
clear peaks. Furthermore, stationary frequency techniques provide no insight into the timing of the appearance and disappearance of various frequency components. The first heart sound of Fig. 4 and its time-frequency transform suggest two distinct components to the first heart sound; no such information is provided by the power spectrum. In addition to the modulation of first heart sound frequency by the rising left ventricular stiffness and pressure, the opening and closing of the cardiac valves causes discrete changes in the cardiac vibratory properties that will be missed by stationary techniques. Restricting frequency analysis to the isovolumic contraction period, as was done by Adolph et al. and others, does not improve the validity of these techniques because the most rapid frequency dynamics occur during the isovolumic contraction period. It is hypothesized that joint time-frequency methods will achieve greater diagnostic sensitivity by quantifying first heart sound frequency dynamics. The Binomial time-frequency transform used in this study provides higher joint resolution of time and frequency than the spectrograph and spectrogram and better interpretability than other time-frequency transforms such as the Wigner-Ville. The limited resolution of the spectrograph is inherent to the filtering process; narrow filters provide better frequency resolution but the resulting slow decay of the impulse response smears temporal detail [ 101. Thus, even modem spectral analyzers must strike a balance between time and frequency resolution. The short time Fourier Transform (STFT) and its magnitude, the spectrogram, have an analogous time-frequency tradeoff. Shorter analysis windows produce better temporal resolution but degrade spectral resolution. Some time-frequency transforms, such as the Wigner-Ville and ChoiWilliams transforms, do not contain inherent time-frequency resolution tradeoffs and provide higher joint resolution of time and frequency of many nonstationary signals than short-time Fourier transforms or bandpass filtration [ 171, [ 131. The improved resolution, however, has a price; multicomponent signals have undesirable cross-term artifact that often obscures the signal’s frequency dynamics. Reduced interference distributions, including the Choi-Williams and Binomial transforms, trade some auto-term resolution for cross-term inhibition, providing more interpretable results of multicomponent signals. The degree of the resolution/cross-term tradeoff depends upon the convolving kernel, h ( t , T ) , used in the transform [see (6)], 1181, [19]. The more similar h(t, T ) is to 6 ( t ) , the more the resulting time-frequency spectrum will resemble the Wigner spectrum. Although any number of reduced interference distributions would produce qualitatively similar results to those obtained in this paper, the Binomial transform combines a particularly efficient algorithm with outstanding cross-term suppression properties [18], 1201. Previous studies of first heart sound frequency have primarily been limited to the chest wall. Cardiac vibrations propagate as mechanical shear waves; intervening visco-
738
IEEE TRANSACTIONS ON BIOMEDICAL ENGINEERING. VOL. 39. NO. 7. JULY 1992
elastic thoracic tissue attenuates higher frequencies and introduces a variable propagation delay [21], [22]. Bertrand and Zalter eliminated chest wall filtering by recording heart sounds directly from the epicardium [23], [24]. However, the fidelity of these recordings was compromised by the heaviness and poor frequency response of the microphones. In this study, ultralight, wide-band accelerometers cemented directly to the epicardium eliminated chest wall effects without mechanically loading the myocardium. While epicardial recordings are more focal than chest wall recordings, the strong similarity of the epicardial, pericardial and chest wall recordings indicates common underlying mechanics. The epicardial heart sound signal is generally 10-100 times more powerful than chest wall recordings, having accelerations typically between 1-5 m/s2. Consequently, the signal-to-noise ratio is quite high and little beat-to-beat variation is seen. Since the chest wall is a low pass filter, heart sounds recorded from the epicardium have greater bandwidth than chest wall recordings. The 6 dB/octave rolloff is consistent with chest wall recordings using acceleration transducers and is 12 db/octave less than observed with displacement type transducers [2 I], [22], [25], [26]. The first heart sound demonstrates several characteristic time-frequency components but the most prominent was a rapidly rising frequency during early systole. Other investigators have noted a rising frequency on the intact canine chest wall [ 1 I]. A rising first heart sound frequency is predicted by theoretical models of both myocardial and valvular vibrations. Direct measurements of left ventricular resonant frequency reveal a monotonic dependence with left ventricular pressure; a similar dependence has not yet been demonstrated for mitral valve vibrations [9]. Neither the presence of a rising frequency per se nor the range of frequencies of first heart sound vibrations strongly favor either genesis mechanism. The rapid rate of frequency rise, however, is more consistent with a myocardial origin. Valvular vibrations rise as the cube-root of left ventricular pressure, a relatively weak dependence [3], [ 111. Myocardial vibrations increase in frequency at least as fast as the square-root of left ventricular pressure because both the wall tension and the wall elastic modulus are increasing [ 7 ] . The early onset of the rising frequency also supports a muscular origin. The atrioventricular valves close asyncronously and do not function as a unit until nearly 20-25 ms following ventricular-atrial pressure crossover [27], [28]. The rapid upstroke of left ventricular pressure does not precede the R-wave, thus valve closure would not be expected until 20-25 ms later. In six of the eight animals studied, however, the rising frequency began within 10 ms of the ECG R-wave. Thus, if valvular vibrations are present, they begin at a time when the valves are not coordinated and the papillary muscles dominate the valve assembly stiffness. Table I1 summarizes the arguments for and against resonances of the myocardium and the valves. It must also be noted that rising frequency components do not necessarily
TABLE 11 MYOCARDIAL VERSUS VALVULAR GENESIS Evidence
Valvular
Myocardial
Rising frequency present Range of frequencies Rate of frequency rise Rising frequency timing
++ ++ + +
++ ++ + +++
+ Possible, but unlikely. + + Consistent. + + + Supported. have a resonant origin. Nonresonant phenomena, such as the depolarization wave passing across the ventricle or the gross myocardial rearrangement in response to increased pressure, might also produce a rising frequency; s w h mechanisms are unlikely to produce rapid frequency changes however. High-frequency transients, superimposed upon such a slowly rising frequency, might appear to be a rapidly rising frequency component. While time-frequency analysis historically was timeconsuming and required special instrumentation, timefrequency transforms may be calculated easily and efficiently on ordinary personal and laboratory computers. Advanced new algorithms provide higher resolution and easier interpretation of formerly intractable biological signals. The first heart sound, because of its small bandwidth and short duration, has not responded well to traditional dynamic frequency analyses. Since information about cardiac material properties and vibrational genesis may be contained in first heart sound frequency dynamics, timefrequency transforms may shed light on basic heart sound mechanics and improve diagnostic sensitivity of in vivo heart sound analysis. ACKNOWLEDGMENT We would like to thank M. Gallagher and S. Haarer for their expert technical assistance. We would also like to thank Dr. W. J. Williams for the use of his computer facilities and Dr. P. Stein for his insightful criticism of the manuscript. APPENDIXA /* Bin Transform accepts a complex (the analytic signal is usually used) floating point array “data” of length “length” and produces a time frequency array with frequency resolution ‘ ‘freq-pts” . The algorithm complexity is length*(freq-pts) * 2. This subroutine assumes that the user has access to a Fast Fourier Transform routine “ColFft()” that will calculate the column wise Fourier Transform to a complex matrix as well as complex math subroutines “Caddo”, “Cmul()”, and “Conjg()” for addition, multiplication, and conjugation. Note that no floating point multiplication is required for generation of the binomial coefficients, only for formation of the outer
WOOD er a l . : TIME-FREQUENCY TRANSFORM O F T H E FIRST HEART SOUND
139
products. * I void Bin Transform(data,length,output,freq-pts) fcomplex *data,**output; I* double indirection used here for 2D arrays *I int length ,freq -pts;
fcomplex ACF[256]; / Length =maximum desired freq-pts * I int j,k,n; double power; power= 1.OOOO; for (j=O;j
