A comparison of methods for quantitating fetal heart rate variability RUSSELL
K.
WILSON
S. WONG,
DAVID
C.
JULIAN SOL
M.
PARER,
M.Sc.
B.S.
PH.D. M.D.,
SHNIDER,
M.D.
NAYLOR,
M.A.
BUTLER,
San Francisco,
JR., M.D.,
HEILBRON,
T.
HILARY JANE
LAROS,
PH.D.
R.N.
Cal$ornia
Fetal heart rate (FHR) variability is thought to be an important index of fetal he&h. In the presence of normal variability, the fetus is vigorous, but Iadc of beattobeat variability may be associated with fetal compromise. A distinction between shortterm variability (STV) (beattobeat changes between successive beats) and longterm variability (LTV) (rhythmic fluctuations in FHR) has not been made to date. We have utilized computer programs to compare three pairs of mathematical indices and one visual index of FHR variability. Among the three pairs of indices designed for detection of STV and LTV, de Haan’s shortterm and longterm indices exhibited the least interdependence, and the longterm index was completely insensitive to artificially generated pure STV. Yeh’s shortterm and longterm indices exhibited substantial positive interdependence. lion’s visual index appears to detect LTV primarily rather than STV. When the effect of progression of labor on FHR variability was examined, no conclusions were possible because of inconsistencies between patients. Ultimately, the clinical value of any one of these indices awaits testing of their ability to define fetal wellbeing or fetal distress. (AM. J. OBSTET. GYNECOL: 128: 381, 1977.)
intrinsic pacemaker activity. This intrinsic rate is modified by the autonomic nervous system.’ It has been proposed that, in addition to a constant vagal tone, there is an oscillatory vagal tone which acts on the intrinsic rate, giving a slightly variable time between adjacent cardiac contractions.3 This interpretation is supported clinically by the observed disappearance of the variability of FHR upon administration of a vagolytic drug such as atropine and preservation of the variability on administration of a sympatholytic drug such as propranolol.4 Responses of the fetal autonomic system to intrauterine stress also contribute to the variability of the FHR as shown by the diminution of the pattern during uterine contractions.’ CaldeyroBarciaS noted that the FHR pattern consists of two phenomena: (1) very rapid fluctuations, socalled shortterm irregularity or variability (STV); and (2) slow fluctuations, socalled longterm irregularity or variability (LTV), seen as dips, decelerations, and accelerations. Recent evidence suggests that the beattobeat vari
FETAL HEART RATE (FHR) monitoring has been widely accepted as a valuable clinical tool for intraparturn management, especially in the case of highrisk patients. Empiric clinical findings have shown that certain FHR patterns, particularly certain transient decelerations associated with uterine contractions, are frequently associated with fetal hypoxia.’ Moreover, FHR baseline deviations from the normai range of 110 to 160 beats per minute are sometimes related to fetal distress. The basic rhythm of the fetal heart is provided by From the Department of Obstetks, Gynecology, and Reproductive Sciences and the Office of Inform&ion Systems,University of Calijknia, San Francisco. Presented by invitation at the Fortythird Annual of the Pa@ Coast Obstetial and Gynecological Kona, Hawaii, November 713, 1976. Reprint requests: Dr. R. K. Laros, fr., Debartment Obstetrics, Gynecology, and Refiod”wtive .&ewes, University of Califoornia, San Francisco, M 1485, Francisco, California 94143.
Meeting Socieb, of 2 San
381
382
Laros et al.
Table
I. Taxonomy
of indices
FHR patterns relevant to our discussion. Pure STV is defined as alternation between two fixed interval lengths. Pure LTV, meaning variation in interval length with no change between successive intervals, cannot exist but is approximated by periodic variations with extremely long periodicity.
STV indices
1. Scale free ST1 (shortterm indexde Haan) DI (differential indexYeh) 2. Not scale free SH (shortterm varianceIIeilbron) LTV indices 1. Scale free II (interval indexYeh) 2. Not scale free LTI (longterm indexde Haan) LH (longterm varianceHeilbron) VRI (visual range indexHon) Balance
between LTV
and STV
1. Scale free A (autocorrelation
Table
II. Variability
Material and methods
coefficientHeilbron)
indices computed
from test data
Pure STV Indices
No. 1
Sinusoidal
No. 2
No. 1
No. 2
STV
STI* DI SH
0.0637 31.04 12.50
0.2315 116.2 50.00
0.0025 1.200 0.6000
0.0034 1.540 0.7700
0.0000 0.0319 0.0400
0.0000 0.1164 0.0300
185.0 0.1721 68.14
196.7 0.1732 70.10
+l.O 396.3
+1.0 405.6
LTL’
LTI II LH Bahnce STV, LTV A Tmean (msec.)
 1.0 392.5
1.0 430.0
*See Table I for taxonomy. ability in FHR during labor and delivery correlates with the neonatal condition at birth and subsequent infant survival and morbidity. 6g The absence of FHR variability can be associated with fetal asphyxia. Several investigators have described methods for quantifying FHR variability. Han’ described a visual index related to the amplitude of variation. De Haan and associateslo and Yeh and associatesi’ have each derived pairs of indices in which one index is designed to detect STV and the other, LTV. Another pair of indices. similarly intended, is proposed by us. This study assesses these three pairs of indices with respect to their specificity in detecting STV and their statistical interdependence in the presence of actual FHR data. Additionally, all of the abovementioned indices are examined for trends exhibited during progression of labor. Clinically described STV and LTV patterns are not quantitatively defined, a fundamental need in this area of investigation. We use the terms “pure STV” and “pure LTV” for convenience in referring to idealized
The four methods of quantitating FHR variability compared in this study are listed and described below. HO& visual range index (VRI). Han’ has proposed the use of a template containing five pairs of lines at different distances apart. The template is placed on the FHR tracings, and a pair of lines is selected which best encloses the variable pattern. The pattern is classified as “minimal ” “decreased,” “moderate,” “increased,” or “marked” variability, depending upon the separation of the lines. In our study, Nos. 1 through 5 have been assigned to the five pairs of lines with 1 corresponding to “minimal” and 5 corresponding to “marked.” De Haan’s indices. De Haan and associates”. “‘. ” have presented a graphic method with the use of computer analysis of the FHR patterns. Consecutive time intervals between beats are plotted against each othet and two functions are derived. The nrg~rn~r( is the angle formed by the line from the origin to each plotted point with the abscissa. The modulus is the distance of the point from the origin. The argument represents STV of the FHR and the modulus represents LTV; thus, the FHR variability is resolved into two simpler patterns. Histograms of the urgztmmtsand moduli are prepared, and the spread and amplitude of the maxima of the histograms are used as indices in the evaluation of FHR variability. in our study, a shortterm index (STI) and a longterm index (LTI) were derived from the arguments and moduli, respectively, by the interquartile range, a statistic describing the range of values within which the central 50 per cent of’ a distribution falls. The details of calculation are presented in Appendix 2 (A, B, and C, I). Yeh’s indices. Yeh and associate?’ proposed another numerical method consisting of two indices: the dfjffcwntial i,,da (DI) which measures the STV in fetal RR intervals and the intcrzui indm (II) which measures the LTV. The indices are calculated from a statistical treatment of the variance between successive beats. The indices are displayed numerically or in analogue form. The details of calculation are presented in Appendix 2 (A, B, and C. 2). Heiibron’s indices. Heilbron, a coinvestigator in this study, derived three indices from consideration of secondorder interval distributions as defined by de indices involve parriHaan and associates ia Heilbron’s
Volume Number
Quantitating FHR variability
128 4
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Fig.
914 2. Case 5; ST1 and LTI
plotted
against
time
sequence
in labor.
384
Laros
et
al.
June
Am. J. Obstet.
Table
III. Variability
indices
for all patients
15, 1977
Gynecol.
(mean values) No medication
Sample size indices* ST1 DI SH
Cafe I
Case2
Ca5e3
Case 4
Case5
Casc6
Case7
Case 8
15
18
12
11
68
15
23
45
0.0053 18.02
0.0090 26.06
0.0059 20.39
0.0060 27.85
8.150
12.27
8.934
0.0053 11.13 4.642
STV
LTV
0.0139 65.61 44.66
0.0060 12.84 5.331
0.0053 7.225 3.228
16.49
induces
LTI TI LH Balance
33.41 22.84
20.99
38.97 27.66 24.32
+0.6667 427.0
+0.5475 461.5
26.71 20.52 18.09
36.21 68.72 48.01
29.24
15.73
21.72
29.13
16.94 14.92
11.73 10.86
12.23 10.96
38.47 23.33
STV, LTV
A Tmean (msec.)
+0.6093
415.9
+0.2931 941.7
+0.7020 434.1
to.7991 419.1
+0.6553 396.5
+0.4127 462.8
*See Table I for taxonomy.
Fig. 3. Case 5; Tmean and DI plotted against time sequence in labor. tioning the variance of a sequence of fetal RR intervals into shortterm variance (SH) and longterm variance (LH). A third index (A) was also derived to represent the intraclass autocorrelation coefficient relating SH and LH. A value of  1.0 for A indicates that the FHR data contain pure STV; a value of + 1 .O indicates pure
LTV. The details of derivation of Heilbron’s indices are noted in Appendix 2 (C, 3). Table I summarizes the taxonomy of the various indices used in this study. Because uterine contractions are known to produce specific forms of LTV (early. late, and variable deceler
Volume Number
Quantitating FHR variability
128 4
Alphaprod& hydrochloride Case 9
15 0.0072 13.51
Chloroprocaine hydrochloride Case 10
Case 11
Case 12
Care 13
43 0.005 1
15
13.92
55.67
19.70
7.057
20.78
10.18
3.006
0.0053
22 0.0100
22 0.0049
7.145
5.831
39.09
12.77
73.49
46.22
33.76
23.40
11.86
40.63
38.77
18.10
34.22
36.13
17.63
21.76
9.042
+0.7952 488.6
+0.4610
+0.4529
391.3
371.1
+0.7883 519.4
+0.9127 432.4
ations and accelerations), we have chosen to examine the FHR only during the intercontractile period. We programmed the computer to select out only those intervals of FHR data between uterine contractions with the use of the formulas and algorithms detailed in Appendix 1. A contraction was defined as an increase in intrauterine pressure (IUP) of >lO mm. Hg above baseline tonus lasting greater than 10 seconds and occurring at least 10 seconds after return to baseline of the preceding event considered to be a contraction. Only human subjects with normal antepartum and intrapartum courses already undergoing FHR monitoring were used in this study. Electrical activity of the fetal heart and intrauterine pressure (IUP) were obtained with standard monitoring techniques and were processed by and recorded on a twochannel stripchart monitor (Corometrics FMSI 11). This monitor generated four voltages which were recorded on a fourchannel analogue tape recorder (HewlettPackard 3960). The voltages were recorded on 1.0 ml. mylar recording tape at a speed of 15/ 16 inches per second and represented: (1) unedited fetal electrocardiogram (RFECG), (2) FHR (computed by the monitor from the intervals between RFECG peaks [Rwaves] by a peaktopeak sensing cardiotachometer), (3) IUP, and (4) a squarewave voltage generated coincident with each detected Rwave by the monitor. Channel 3 and 4 of the analogue tape were transcribed by an analoguedigital computer (PDP 7) into digital form. The time interval between heartbeats was calculated by the computer from the squarewave information. The computer’s interval clock was set so as to measure the RR interval to the nearest l/4 msec. and then to record the digital data to the nearest millisecond. The digital data were stored on a seventrack
385
tape for processing by an IBM 370 computer. The IBM 370 was programmed to recognize contractions, to select intervals of FHR data between contractions, and to calculate indices of FHR variability with the algorithms described above. Fig. 1 is an example of digitized data graphically displayed by the computer. Periodic samples of data were displayed and visually examined from each patient following the analoguetodigital conversion and prior to calculation of indices. This step was necessary both to obtain visual reassurante as to the quality of the data and to choose a pressure parameter value for contraction detection. Dependence between indices and time trends were assessed with the Kendall rankorder correlation coefficient tau. Statistical analysis was performed with the Statistical Package for the Social Sciences (SPSS).‘3
Results Analysis of artificial heart rate data. Before analyzing FHR data from patients, we examined artificially generated FHR data. These data were created by computer and consisted of two sets of FHR records with pure STV and two sets with sinusoidally varying beattobeat intervals. The two sets of pure shortterm data were alternating rates, with the second set having a larger time interval difference between beats than the first set. The two sets of sinusoidal data were of moderately long periods, the second set having a shorter period than the first. Variability indices were computed from these artificial data, and the results are shown in Table Il. With the pure STV data, the three shortterm indices (STI, Dl, and SH) increase 3.63 to 4fold from the first to the second set of data. However, differences are apparent between the various longterm indices. De Haan’s LTI is zero for both sets of data while Yeh’s II has residual positive value and increases in approximately the same proportion as the Dl (3.65fold versus 3.63fold) from the first to the second set of data. Heilbron’s LH also has a small positive value which decreases slightly from the first to the second set of data. The autocorrelation coefficient (A) of Heilbron has a value of 1.0 which is indicative of pure STV for both sets of shortterm data. With the sinusoidal FHR data, all three pairs of shortterm and longterm indices behave similarly. The shortterm indices increase 1.28 to 1.36fold, and the longterm indices increase 1 .Ol to 1.06fold. Actual FHR data. Thirteen patients were monitored, and the FHR’s were recorded and analyzed. Six patients received no medications during labor, five received ‘20 mg. of alphaprodine hydrochlo
386 Lam et al.
June Am. J. Obstet.
15, 1977 Gynecol.
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ride,* and two patients were given the epidural anesthetic agent chloroprocaine hydroch1oride.t The mean values of the various indices for each patient are detailed in Table III. Case 4 was remarkable in that the fetus evidenced sustained bradycardia which proved to be due to congenital heart block. The fetus was otherwise normal and had Apgar scores of 8 and 9 at one and five months of life and normal umbilical cord blood gas levels at delivery. To determine the amount of interdependency between the various indices, Kendall rank correlations were computed and are summarized in Table IV. Hon’s VRI was computed in only five cases (Nos. 7, 8, 9, 10, and 12). Of the three sets of indices, de Haan’s ST1 and LTI are least dependent (median tau 0.27; p > 0.05) and Yeh’s indices DI and II are most dependent (median tau 0.58; p = 0.001). Among the STV *Nisentil, Roche Labs., Div. HoffmannLa ley, New Jersey. tNesacaine, Strasenburgh, Div. Pennwalt New Yovk.
Roche Corp.,
Inc.,
Nut
Rochester,
against
time
.
:
sequence
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in labor.
indices, DI and SH are very strongly correlated (median tau 0.94; p = 0.001) while ST1 in general appears to be only weakly related to the other two shortterm indices. The VRI of Hon is best correlated with LTI and LH. However, these correlations are weak and the correlation was highly inconsistent from patient to patient. Figs. 2 to 5 depict the graphic display of the various indices plotted against time sequence for Case No. 5, and Table V summarizes the dependency of the various indices on time sequence for the four patients who received no medications during labor. In Cases 1 and 3, a significant negative trend in several indices of both STV and LTV was exhibited, i.e., variability decreased as labor progressed. In Case 5, there was a significant positive trend in STI, LTI, II, and LH as labor progressed. comlmmt Variability of FHR may be influenced by many factors such as hypoxia, vagai tone, gestational age, uterine blood flow, various drugs, and others. A welldefined index of FHR variability that is predictive of
Volume Number
Quantitating FHR variability
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fetal distress or wellbeing would be a useful adjunct to the management of highrisk pregnancies. In this study we have compared four methods of quantifying FHR variability. Because the clinically described STV and LTV patterns are not quantitatively defined, there is no criterion for accuracy of STV and LTV indices for which clinical relevance can be claimed. We have examined the sensitivity of these indices with respect to artificial FHR patterns which have some features of clinical STV and LTV. Also we have examined the interdependence between indices, partly to assess the relatedness of the different methods. The interdependence between the shortterm and longterm indices is also of concern on the grounds that two indices are most informative if they are sensitive to different kinds of variation. The studies on artificial FHR show that, of the three LTV indices, only de Haan’s LTI is totally insensitive to pure STV. The small values of Heilbron’s LH (small relative to the values on the sinusoidal data) may be attributed to “end effects” which would vanish in very long sequences. However, Yeh’s II undergoes the same
against
time
sequence
in labor.
relative increase between STV sequences Nos. 1 and 2 as does DI, and these II values are substantial relative to their values for the sinusoidal data. The sensitivity of II to shortterm variability is apparent. The ST1 and DI are based on closely related quantities. ST1 is the interquartile range of the quantities @i = arctan (Ti+ lITi), the polar coordinate angles of the points (Ti, Ti + i). DI is essentially the standard deviation of the quantities di = (Ti  Ti+ i)/(Tr + Ti+ 1). It follows that di = (COS 2 @r)/( 1 + sin 2 Qr). The transformation from @i to dj has slope 5  1 everywhere, equalling  1 at @r = 45” and decreasing monotonically to 2 at @i = 0” and 90”. Thus, d, is essentially the same as @i when T, and Ti+ 1 are close but has larger magnitude than Cpi when Ti and Ti +i are relatively far apart. The use of the standard deviation for DI instead of the interquartile range will also tend to make DI more sensitive to large relative changes between successive interval lengths. Yeh’s II is the sample coefficient of variation of the interval lengths. As such it should reflect both STV and LTV, and thus DI and II are expected to be somewhat
388
Lam
et
al.
Junr Am. J. Obstet.
Table IV. Kendall rank correlationsinterdependence of indices Kendall Indices STI, LTI” STI, DI STI, SH LTI, II LTI, LH DI, II DI, SH II, LH SH, LH VRI, ST1 VRI, LTI VRI, DI VRI, II VRI, SH VRI, LH
Table V. Kendall rank correlationsvarious versus time sequence tau
Kerwhll
Minimum
Maximum
Median
0.24 0.56 0.58 0.35 0.46 0.29 0.90 0.56 0.03 0.22 0.35 0.13 0.02 0.12 0.03
0.43 0.44 0.48 0.76 0.77 0.85 1.00 0.96 0.82 0.58 0.54 0.44 0.64 0.47 0.61
0.27 0.16 0.18 0.56 0.62 0.58 0.94 0.83 0.44 0.36 0.48 0.24 0.32 0.25 0.44
STV indices* ST1 DI SH LTV indices LTI II LH Balance STV. A
Tmean (msec.)
correlated. This anticipated interdependency is confirmed in the above patient data where the median tau for DI, II is 0.58. Heilbron’s indices SH and LH are essentially functions of the sample variance and sample firstorder autocorrelation of the interval lengths. As such, they are most appropriately applied to interval sequences which exhibit secondorder stationarity. The superiority of the de Haan statistics in our patient material (median tau for STI, LTI of 0.27) may reflect the nonstationar
REFERENCES
H.: An Atlas of Fetal Heart Rate Patterns, New Haven, 1968, Harty Press, Inc. E.
2. Warner, H. R., and Cox, A.: A mathematical model of heart rate control by sympathetic and vagus efferent information, J. Appl. Physiol. 17: 349, 1962. 3. de Haan, J., van Bemmell, J. H., Stolte, L. A. M., et al.: Quantitative evaluation of fetal heart rate patterns. II. The significance,of the fixed heart rate during pregnancy and labor, Eur. J. Obstet. Gynecol. 3: 103, 1971. 4. de Haan, J., Stolte, L. A. M., Veth, A. F. L., et a!.: The significance of shortterm irregularity in the fetal heart rate pattern, in Dudenhausen, J. W., and Saling, E., editors: Perinatal Medicine, Stuttgart, 1973, Georg Thieme Verlag. 5. CaldeyroBarcia, R.: Control of human fetal heart rate during labour, in Cassels, D. E., editor: The Heart and Circulation in the Newborn and Infant, New York, 1966, Grune & Stratton, Inc. 6. Beard, R. W., Filshie, G. M., Knight, C. A., et al.: The significance of the changes in the continuous fetal heart rate in the first stage of labor, Br. J. Obstet. Gynaecol. 78: 865, 1971. 7. Hammacher, K., Hinter, K. A., Bokelmann, J., et al.:
AQpendlX
of uterine contractions. Recognition Y, = sequence of IUP’s with i = 1,2, . ... N where 1.
indices
tuu
Case I
Case.2
Case3
Case4
0.11 0.47t 0.49t
0.14 0.16 0.16
0.12 0.39$ 0.33
0.24 0.34 0.35
0.21t 0.007 0.08
0.36t 0.20 0.28 LTV 0.20 0.52.f
0.14 0.01 0.06
0.391 0.49.t 0.36$
0.16 0.35 0.31
0.301: 0.21$ 0.29t
0.28 0.29$
0.24 0.09
0.35 0.38
Cwej
0.13 0.08
Case6
0.20 0.11 0.14 0.26 0.05 0.07 0.20 0.26
*See Table I for taxonomy of indices. tP s 0.01. $P = 0.05.
*See Table I for taxonomy of indices.
1. Hon,
15, 1977
Gynerol.
Let N =
ity of the data and the fact that the de Haan statistics depend entirely on local characteristics of the interval sequence. The reason for the strong association of DI and SH is not readily apparent, aside from the fact that both indices use summations based on deviations from means. From the correlation between Hon’s VRI and LTI and LH, it appears that visual evaluation of variability presently used clinically primarily results in detection of LTV and not STV.
Foetal heart frequency and perinatal condition of the foetus and newborn, Gynaecolagia 166~ 349, 1963. 8. Rochard, F., Schifrin, B. S., Goupil, F., Legrand, H., Blottiere, J., and Sureau, C.: Nonstressed fetalheart rate monitoring in the antepartum period, AM. J. OBSTET. GYNECOL. 146: 699, 1976. 9. Paul, R. H., Suidan, A. K., Yeh, S. Y., et al.: Clinical fetal monitoring. VII. The evaluation and significance of intrapartum baseline FHR variability, AM. J. OBSTET. GYNECOL. 123: 206, 1975. 10. De Haan, J., van Bemmel, J. H., Veth, A. F. L., et al.: Quantitative evaluation of fetal heart rate patterns: I. Processing methods, Eur. J. Obstet. Gynecol. 3: 95, 1971. Il. Yeh, S. Y., Forsythe, A., and Ron, E. H.: Quantification of fetal heart beatt&eat interval differences, Obstet. Gynecol. 41: 355, 1973. 12. De Haan, J., van Bemmel, J. H., Stdte, L. A. M., et al.: Quantitative evaluation of fetal heart rate patterns: III. Beattobeat arrhythmia, Eur. J. Obstet. Gynecol. 4: 137. 1971. 13. Nie, N. H., Hull, C. H., Jenkins, J. G., et al.: Statistical Package for the Social Sciences, New York, 1975, McGrawHill Book Company, Inc.
number of patients. Let Ci = sequence of cumulative times with i = 1, 2, . .. . N: C, = T1, C = Tr + T,; .. where T’s are the time intervals between heartbeats.
Volume Number
Quantitating FHR variabillty
128 4
1
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A&A T
it6
389
T
it8
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msec
msec
’ il Fig. 6. Pure
longterm
Let L = the number of points around a selectedpoint for calculationsof slopeand deviation. Let K = integer value of L/2. For j = k + 1, .... N  k; calculate: A, = ,siekY,+i.
(1)
E, = *jekG+ I.
(2)
Slope: B, = (! EkY, + t C, + I)  A&/L)@.
(3)
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FHR
variability.
If last preceding contraction times were C,,‘, C,,‘), then we require C, > C,,’ + C. (3) Where TP, n, d, h, and C are adjustableparameters: TP = critical value for t, (6.0); n = number of successive points for which onset and termination criteria must be satisfied(10); d = minimum duration of contraction (10 seconds);h = minimum “height” of contraction (adjusted between 5 and 15); C = minimum duration between contractions (10 seconds). 2. Variability indices. Computations on a single uninterrupted sequenceof RR intervals (between contractions and other breaksin continuity and containing >70 points but 62,000 points). Let T, = the RR interval values where i = 1, .... N. A. Computation
of scalars.
T = (&)/N. v
where St =, tC, + 12 Cf/L. OifSbZs 0 “= i IB,/mI ifS,2>0
1
 T)?(N  1) : z‘z p = 0.25 (N + 1). J = [p] = lqar=gepsfi;teger in p. ST =
(5)
,@i
t
where tl is the noise tolerance index. Potential onset time:
B. Computation
j. such that tJo i > TP for i = 1, .... n and B,, +, > 0 for i = 1, .... n.
dt = (Ti+ I  Ti)/(T,+
1 + TI).
@i = arctan (Tt+ ,/T,) where i = 1, .... N  1. rI = (Ti2 +T1+ 12)*. {@)t~}:;/ = {@3:;,’ sorted in increasing order. {r&;ll = {r#Pll sorted in increasing order.
Potential termination time: jIsuchthatB1,I TP for i = 1, .... n.
C. Computer scalars. (1) DE HAAN STATISTICS (INTERQUARTILE RANGES).
Contraction criteria: C,,  C,, > d.
of arrays.
(1)
For somej, j, < j < jI, A, > (A,, + A,,)/2 + L*h. (2)
u1
= q(%LTI
=
qh
J,@‘cJ J)r(J
+ 1)) + (1  q)(%+ + 1))
+
(1

q)h
I+ 1J)
J)  @‘t.,,). r(Jh
390 Lam et al.
June 15, 1977 Am. J. Obstet. Gynecol.
‘i1
1
I
Titl k
I v
Ti
‘it3
Tit5
Tit7
Tit9
k k
k k
k k
A A v r
V
Tit2
Tit4
Tit6
T ii11
A A
Tit8
T it10
Ti+iJ
A+ T
it12 FECG
msec /’ ‘\
‘\
/
(2) STATISTICS
/
7. Pure
/
shortterm
where a = (“i’ di)/(N  1). IQ1 II = ST/T. 3. HelIbron statistics. These indices derive from consideration of secondorder interval distributions as defined by de Haan and associates”’and the idea that it should be possibleto partition the total variation in a sequenceof intervals (Ti, i = 1, .... n) into “shortterm” and “longterm” components. First we give an intuitive derivation without detailed definition of terms. Let v be the variance of the sequence.We wish to define quantities s and 1 on the sequencesuch that (1)
where s and 1 are the short and longterm indices. s and a are squared in (1) so that they are dimensionally like standard deviations, analogousto the de Haan indices. Fig. 6 represents pure longterm variation with all points (T,  I, T,) essentiallylying on a 45” degree line. In this situation it is desired that s* = o and 1* = v,
variability.
where c is the covariance between subsequences.Thus we assumethat the (auto)correlation coefficient r is given by (4) for an appropriate definition of v and c to be given later. Fig. 7, on the other hand, represents pure shortterm variation where interval values alternate between two fixed values. In this situation, it is desired that s* = v and 1’ = o;
(4)
(5)
that is, all variation is shortterm. Further, in this situation essentially r=
1.
(6)
Assuming equations (1) to (6), one comesto the following definition of s and 1 in terms of c and v: s* = (v  c)/Z; 12 = (v + c)/2.
(7)
Condition (1) is satisfied.With pure LTV, r = 1, soc = v and s* = (vv)/2 = 0 asrequired. With pure STV, r =  1, soc = v and t2 = (vv)/2 = 0 asrequired. Thus, s and 1 have the desired properties. To implement (7), we have chosen C = (2:”  ’ Wi* Wi  I)/(n  l),
(8)
i=*
v = (%(W,* + W,*) + (z7Z.j WF))/(n  l), where Wi =Ti  (I;= 1 Tj)/n),
(3)
in this situation of pure LTV. By ignoring the differencesin membershipof the two subsequences, it can be argued that essentially r=$
FHR
(2)
that is, all variation is longterm variation. If r is the ordinary correlation coefficient between subsequences (T,  I,r i = 2, .... n) and (T,, i = 2, .... n), then essentially r=l
92’0 ‘.
(d,  @]/(N  2)}+
s* + I’ = v.
( 2 =v
‘8 ‘.,,
OF YEH AND ASSOCIATES.
DI = {lOOO[;$,
r = 1
900 ,,/ '. / ‘*, ,,’
p.
Ti
Fig.
'8
(9)
so that r = c/v is the intraclass autocorrelation coefficient. We have designated our shortterm index as SH (calculated as s above), our longterm indexas LH (calculated as 1 above), and the autocorrelation coefficient
r as 4.
Volume 128 Number4
Discussion DR. ALFRED J. HELDFOND, Beverly Hills, California.
Variability has been shown to be an important commentary of FHR pattern. It hasbeen proved to correlate with fetal Apgar scoresand pH values. Actually, variability is demonstrated as “wiggles” on the FHR record. When it is present, the fetal condition is at least pretty good, despite decelerations; when it is absent, there are many possibleexplanations, of which drugs are the most common. Decreasedvariability by itself is almost never indicative of asphyxia, unlessit is accompaniedby decelerations. Clinically, good variability means good STV, while poor variability meanspoor STV. LTV is independent, and, most of the time, LTV correlates with STV. Where these dissociate,the predictive value is dependent on STV, not LTV, as in the ominous sinusoidal pattern where there is an increase in LTV and a decreasein STV. Artifacts, arrhythtiia, and complex fetal electrocardiogram signalsmay spuriously increaseapparent variability. Perhaps the most common cause of “exaggerated variability” is the useof ultrasonic transducers. I am sure that Dr. Laros agreesthat these calculations should be restricted to direct techniques where the electrocardiogram is used as the trigger for the cardiotachometer. As the sign over Barry Schifrin’s desk states:“All that wigglesis not variability.” Since its value had been shown, it seemedlogical to quantify variability. The initial attempt was an eyeball technique with the use of rather arbitrary criteria for troughtopeak distance. It was this method, we must remember, that wasusedin the correlation with Apgar scores,fetal pH, and the recovery of the newborn infant afflicted wit‘h respiratory distresssyndrome. It seemsto me that if an observer is present visual evaluation appears to be as good asa computer in distinguishing variability. It is only when the monitoring is being performed without an observer, a questionable practice, that a computerized method offers an advantage. I must give credit to Dr. Laros and his coworkers for their detailed study and especially since they are the first group, to my knowledge, who have compared their indices with those of others. The question I submit is, “Is there any benefit clinically of one of theseindicesover the others?” If not, as I suspect,it speaksfor the need of a better understanding of the physiologic basisof variability; if an appropriate end point can be established, quantification should be simple. DR. ROBERT COODLIN, Sacramento, California. A couple of years ago, I attempted to look at all the commercial fetal monitors and seehow accurate wastheir peak detection of the R wave, or amplitude detection of the R wave, and I found a seriousdeficiency in every commercial apparatus. These machines often exag
Quantitating FHR variability
391
gerated or minimized the true variability. I wasunable to convince any of the manufacturers to provide a machine that wasprecise.My first question to Dr. Larosis: “Did he ever look at the raw data, in regard to the relationship of the peak detection to the actual R wave?” “ Garbage in, garbage out” is still part of the ‘problem. Another question, did he ever actually measure (manually) the RR interval variability and compare it with what the computer says?In my opinion, STV is a “figment of imagination” of the computer because, when I have actually measured the beattobeat variability (when the heart rate is relatively constant), STV doesnot exist in the sensethat there is a sudden beattobeat change. The change always occurs (in my experience) over four or five beats. I have never seen an instantaneous change in variability, as would be implied by the term “STV.” A number of years ago, it wasclaimed that, depending upon how the data were processed,there were at leastnine different interpretations of variability in any given recording. Presumably that number hasbeen increased, and it seemsto me that this sort of paper is almost like the ancientsarguing how many angelscan dance on the head of a pin. We must correlate these computations with the clinical outcome. Midwives can tell us pretty well how most newborn infants are going to do, and I submit that that is all most of this type of data from beattobeat variability does. I have yet to seea paper that can take a specific beattobeat variability index, value, or whatever and say that this infant’s pH will be soandso.And until we can do that, it seemsto me that there is no need to describeanother formula for variability. DR. LAROS(Closing). Dr. Goodlin is correct that we did accept the RR detection of the fetal monitor, and we did not correlate it with RR wavesthat would be a worthwhile project. We did not take the FHR per se but simply the coincident threevolt square wave generated by the cardiotachometer with the detection. As far ascorrelating this with measureby hand, yes, we did, in the sensethat we compared real tracings with the computergenerated tracings. I think the timing inherent in the computer mechanismis far more accurate than laying a tape measureor a ruler on the FHR tracing and measuring the RR in milliseconds that way. I think the most important observation is Dr. Goodlin’s point about the clinical validity. However, before you can take a method and jump into clinical validity, you have to have a valid and sensitivemethod. I think eyeballing an FHR tracing and saying that good variability is shownmay be like looking at a test tube full of blood and saying, “That person is not too anemic,” or “That person is very anemic.” There have been steps forward, and the first step wasto devise a reproducible method of quantitating hemoglobin in grams per cent
392
Lam et al.
and then going on to evaluation of clinical conditions. And that is, in fact, the purpose of this study, to develop reproducible methods of quantitating FHR variability. Dr. Heldfond, I thank you for your kind comments. I think you were the only person who fully appreciated the mathematical complexities of all of this, and I am glad that the appendix wasn’ttoo ominous. These were all done by direct techniques,and it iscorrect that indirect techniques with a Doppler device artificially generate variability. However, we are at a point in time, for instance, when the various manufacturers are showing us devices with external electrocardiogram mea
June 15, 1977 Am. J. Obstet. Gynecol.
surementsand suggestingthat this is much truer beattobeat variability. Again, here is a situation where we have a quantitative method and are in a position to compare output generated by an external electrocardiogram and an internal electrocardiogram, and, in fact, look at somenumbersand seeif they are the same, rather than just lay two tracingsdown and wonder, “Do these look the same?” Last, the physiologists tell us that STV is probably quite important in variability measuredin milliseconds and, in fact, thousandths of milliseconds.So this is an area that still doesneed clinical validation, and I hope this will be forthcoming shortly.