Distance to healthy cardiovascular dynamics from fetal heart rate scale-dependent features in pregnant sheep model of human labor predicts cardiovascular decompensation
Stéphane G. Roux, Nicolas B. Garnier, Patrice Abry, Nathan Gold, Martin G. Frasch
DDistance to healthy cardiovascular dynamics from fetalheart rate scale-dependent features in pregnant sheepmodel of human labor predicts cardiovasculardecompensation
S.G. Roux , N.B. Garnier , ∗ , P. Abry , N. Gold and M.G. Frasch Laboratoire de Physique, Univ Lyon, Ens de Lyon, Univ Claude Bernard, CNRS,F-69342 Lyon, France; Department of Mathematics and Statistics, York University, Canada;Centre for Quantitative Analysis and Modelling, Fields Institute, Toronto, USA. Dept. of OBGYN and the Center on Human Development and Disability,University of Washington, Seattle, USA
Abstract
The overarching goal of the present work is to contribute to the understandingof the relations between fetal heart rate (FHR) temporal dynamics and the well-being of the fetus, notably in terms of predicting cardiovascular decompensation(CVD). It makes uses of an established animal model of human labor, wherefourteen near-term ovine fetuses subjected to umbilical cord occlusions (UCO)were instrumented to permit regular intermittent measurements of metabolites,pH, and continuous recording of electrocardiogram (ECG) and systemic arterialblood pressure (to identify CVD) during UCO. ECG-derived FHR was digitizedat the sampling rate of 1000 Hz and resampled to 4Hz, as used in clinicalroutine. We focused on four FHR variability features which are tunable totemporal scales of FHR dynamics, robustly computable from FHR sampled at4Hz and within short-time sliding windows, hence permitting a time-dependent,or local, analysis of FHR which helps dealing with signal noise. Results showthe sensitivity of the proposed features for early detection of CVD, correlationto metabolites and pH, useful for early acidosis detection and the importanceof coarse time scales (2.5 to 8 seconds) which are not disturbed by the low FHRsampling rate. Further, we introduce the performance of an individualized self-referencing metric of the distance to healthy state, based on a combination ofthe four features. We demonstrate that this novel metric, applied to clinicallyavailable FHR temporal dynamics alone, accurately predicts the time occurrenceof CVD which heralds a clinically significant degradation of the fetal healthreserve to tolerate the trial of labor.
Keywords: fetal heart rate, animal model of human labor, cardiovasculardecompensation, distance to healthy, time-scales dependent features, entropyrate, sliding-window analysis 1 a r X i v : . [ phy s i c s . m e d - ph ] F e b . IntroductionContext. Monitoring fetal heart rate (FHR) during labor is a common clinicalroutine worldwide, aiming to asses fetal well-being and ensure safe delivery. Themain objective is to decide on timely operative delivery or uterine relaxationto prevent brain injury and adverse outcomes [9]. In clinical practice, fetalwell-being is assessed by obstetricians principally by visual inspection of car-diotocograms (CTG, bivariate time series of beat-per-minute FHR and uterineactivity). The interpretation is guided by a set of rules combining a collectionof features, aiming to probe various aspects of the CTG, such as baseline FHR,FHR variability and deceleration shape and timing as well as the relation of thevarious FHR features to the patterns of uterine activity. One such set of featuresand rules was defined by the International Federation of Gynecoloy and Obstet-rics [19, 6]. Applying such procedure has however been documented as yieldingsignificant inter-and intra-observer variability [40], triggering significant effortsto develop computerized and automated assessment of FHR patterns during la-bor. Beyond the direct computation of the FIGO features themselves (cf., e.g.,[47, 58, 46]), from digitized CTG usually sampled at 4Hz in clinical practice, alarge variety of features stemming from advanced signal processing and infor-mation theory tools has been computed for FHR assessment. These advancedfeatures, however, have not reached performance benchmarks to lead to a con-sensus in the research and medical communities. Additionally, performanceassessment has mostly been based on immediate post-birth umbilical cord pHmeasurements, as the ground truth metrics for fetal well-being. However, ithas been documented that fetal brain injury poorly correlates with measures ofacidemia at birth such as pH [8]. These observations leave open a significantnumber of issues ranging from the choice of relevant FHR features and the con-struction of decision rules for such features to the assessment of the relationshipsbetween FHR time series and fetal well-being. Interested readers are referred to[29] (and references therein) for a recent (lack of) consensus overview and theinterdisciplinary discussions.
Related works.
Following achievements in adults and the seminal contributionin [3], frequency-based features were used to model linear temporal dynamicsin FHR [57, 35, 63, 45, 56]. To permit richer descriptions of the non-linear dy-namics of FHR, information theoretic quantities were used such as entropy rates[12, 18, 50, 61, 37], as well as several nonlinear transforms [44, 45, 10, 30], andscale-free or (multi)fractal paradigms [20, 15, 1, 16]. For overviews, interestedreaders are referred e.g. [25, 27, 58, 32, 38, 59, 2, 39, 29]. An important limi-tation in the use of these features lies in their dependence on high quality fetalelectrocardiogram (ECG) or magnetocardiogram (MCG) data as input. Suchdata are not readily available in the majority of clinical settings, with over 90 percent of North American hospitals, for example, still relying on CTG monitorsduring labor. CTG however provides FHR at a 4 Hz sampling rate, to be com-pared to 1000 Hz sampling rate golden standard available with ECG or MCG,while vagally mediated HRV is found on a time scale that goes beyond what iscaptured at 4 Hz sampling rate. This results in information loss [17, 43, 34, 21].2eyond the mere design of features and their standalone use, numerous effortswere devoted to devise multiple-feature decision rules, often based on supervisedlearning and machine learning (cf., e.g.,[7, 11, 64, 31, 58, 13, 64, 65, 28, 60, 2]).Besides the need for large labelled databases to make machine learning effective[28], a recurrent issue is associated with the ground truth being based on pH.This is regularly questioned [29] as, first, pH is only available after deliveryhence when FHR is no longer available, and second, brain compromise due tohypoxia-ischemia can ensue when the fetal cerebral blood flow is persistently re-duced, e.g. due to precipitous drop in cerebral perfusion pressure resulting fromcardiovascular decompensation (CVD) [5, 23]. To better asses the relationsbetween FHR, systemic arterial blood pressure (ABP) and fetal health statesheep were surgically instrumented and subjected to an umbilical cord occlu-sion (UCO) protocol in [22], in a well-established animal model of human labor.It was observed that the Bezold-Jarisch reflex, a vagal depressor reflex observedin fetal sheep, with worsening acidemia, leads to CVD [24]. This animal modelpermits to assess relations between FHR and the Bezold-Jarisch reflex mediatedvagal sensing of acidemia, a contribution towards the understanding of the linksbetween FHR temporal dynamics and fetal well-being and the central questionaddressed in the present work.
Goals, contributions and outline.
The goal of the present work is to askwhether FHR monitoring can capture the Bezold-Jarisch reflex mediated vagalsensing of acidemia. More particularly, it aims to assess the sensitivity of FHRtemporal dynamics, probed by four scale-dependent features, to CVD, metabo-lites and pH measurements. To that end, it makes uses of the animal model ofhuman labor proposed in [22], where fourteen near-term ovine fetuses subjectedto a UCO protocol were instrumented to permit measurements of metabolites,pH and ABP during the UCO mimicking human labor process. Experiments, in-strumentation and measurements are described in Section 2. Four features werechosen here essentially because of their being tunable to temporal scales of FHRdynamics preserved at low sampling rate of 4 Hz. This feature choice is alsodesigned to allow computation within short-time time windows, thus permittingto achieve a sliding-window, time-dependent analysis of FHR, which may even-tually be exploited to perform real-time and on-line FHR monitoring on noisyFHR data. These features, together with sliding-window analysis are describedin Section 3. Results, reported in Section 4, show the sensitivity of the proposedfeatures to UCO strength (cf. Section 4.1), their correlation to metabolites andpH, which may allow for an early acidosis detection (cf. Section 4.2), and theimportance of coarse time scales (2 .
2. Materials: sheep animal model and umbilical cord occlusionsFetal sheep model of labor and surgical preparation.
The anestheticand surgical procedures, postoperative care of the animals and the UCO model3f labor have been previously described [22]. Briefly, fourteen near-term ovinefetuses (123 ± ± Umbilical cord occlusion protocol.
All animals were studied over a ∼ Sat morethan 55 percent before UCOs) (n=9, N/UCO). As reported, after a 1-2 hourbaseline control period, the animals underwent mild, moderate, and severe se-ries of repetitive UCOs by graduated inflation of the occluder cuff with a salinesolution [22].During the first hour following the baseline period, mild variable FHR de-celerations were performed with a partial UCO for 1 minute duration every 2.5minutes, with the goal of decreasing FHR by ∼
30 bpm, corresponding to a ∼ ∼
60 bpm, corresponding to a ∼
75 percent reduction in umbilical blood flow.Animals underwent severe variable FHR decelerations with complete UCO for1 minute duration every 2.5 minutes until the targeted fetal arterial pH of less4han 7.0 was detected or 2 hours of severe UCO had been carried out, at whichpoint the repetitive UCO were terminated. These animals were then allowed torecover for 48 hours following the last UCO. Fetal arterial blood samples weredrawn at baseline, at the end of the first UCO of each series (mild, moderate,severe), and at 20 minute intervals (between UCO) throughout each of the se-ries, as well as at 1, 24, and 48 hours of recovery. For each UCO series, bloodgas sample and the 24h recovery sample of 0.7 ml of fetal blood were drawn,while 4 ml of fetal blood were drawn at baseline, at pH nadir < o C. Plasma from the 4 ml blood samples was frozen and stored for cytokineanalysis, reported elsewhere. After the 48 hours recovery blood sample, the eweand the fetus were killed by an overdose of barbiturate (30 mg sodium pento-barbital IV, MTC Pharmaceuticals, Cambridge, Canada). A post mortem wascarried out during which fetal sex and weight were determined and the loca-tion and function of the umbilical occluder were confirmed. The fetal brain wasperfusion-fixed and subsequently dissected and processed for later immunohis-tochemical study [51].
Data acquisition and pre-processing.
A computerized data acquisitionsystem was used to record fetal systemic arterial and amniotic pressures andthe ECG signal [17]. All signals were monitored continuously throughout theexperiment. Arterial and amniotic pressures were measured using Statham pres-sure transducers (P23 ID; Gould Inc., Oxnard, CA). Fetal systemic ABP wasdetermined as the difference between instantaneous values of arterial and amni-otic pressures. A PowerLab system was used for data acquisition and analysis(Chart 5 For Windows, ADInstruments Pty Ltd, Castile Hill, Australia). Pres-sures, ECOG and ECG were recorded and digitized at 1000 Hz for further study.For ECG, a 60 Hz notch filter was applied. R peaks of ECG were used to de-rive the heart rate variability (HRV) times series [17]. The time series of R-Rpeak intervals were then uniformly resampled at 4 Hz [17]. A representativeFHR signal is shown in Fig. 1a: FHR variability increases with the rising UCOstrength.
Fetal cardiovascular decompensation.
During UCO, by visual inspection,we noted the individual time point at which three successive hypotensive ABPresponses to UCO-triggered FHR decelerations occurred. We refer to this timepoint as the ABP sentinel corresponding to the timing of CVD. We also com-puted the difference delta between the ABP sentinel and the time when pH nadir (below 7.00) is reached in each fetus. For illustration, the ABP sentinel is de-picted using a black vertical line in Figure 1.Metabolites data (pH, lactate and BE) is obtained by blood sampling per-formed at specific times during the experiment (vertical lines in 1). In order tohave metabolites data at any time, we assume a linear drift between two suc-cessive measurements and consequently interpolate between two measurements5 igure 1: Typical data recorded in the experiment. Up: FHR resampled at 4Hz. The colorindicates the intensity of UCO during the experiment: blue and black for no UCO (baselineand recovery), green for mild UCO, magenta for moderate UCO and red for severe UCO.Down: Fetal arterial pH values during the experiment. The pH (as well as the other bloodmeasurements) is obtained at specific time points, indicated by the vertical lines; the openblack circles correspond to the actual measurements from blood sampling and the black linescorrespond to a linear interpolation. times. We thus obtain a piece-wise linear time series sampled at 4Hz, depictedin Figure 1b as a black curve.
3. Methods: time scale-dependent features
Analysis of FHR and metabolites data are performed in sliding time-windowsof size T = 20 minutes. The time-windows are shifted by dT = 5 minutes, thusimplying a T − dT = 15 minutes (75%) overlap. The k -th time-window thuscorresponds to time ranging in [ kdT, kdT + T ].This sliding window analysispermits the assessment of the temporal evolution of cardiovascular responses tochanges in UCO intensity. Using FHR, x t , four quantities, whose definitions rely on the choice of a timescale τ , are computed, for each time-window k : increment mean m k ( τ ),incrementstandard deviation σ k ( τ ), the corresponding Student ratio R k ( τ ), and the en-tropy rate h k ( τ ). The time evolution of (three of) these four features, alongwith FHR is shown for illustration purposes in Figure 2 for arbitrarily chosen20-minute window, time scale τ and animal.6 .2.1. Mean variation (or local trend) at time-scale τ For all t in window k , the average increment over a time scale τ is computedas: m t ( τ ) = 1 τ t (cid:88) i = t − τ +1 ( x i − x t − τ ) = 1 τ t (cid:88) i = t − τ +1 x i − x t − τ . (1)These m t ( τ ) are then averaged across window k , for all non-overlapping time-intervals [( j − τ ; jτ ]: m k ( τ ) = 1 (cid:98) T /τ (cid:99) (cid:98)
T/τ (cid:99) (cid:88) j =1 m kT + jτ ( τ ) , (2)where (cid:98) T /τ (cid:99) , the floor of the fraction
T /τ , indicates the number of time-intervalsof size τ available in the time-window of size T . An illustration of the method-ology is given in Figure 2b for the window k = 0: values of m t ( τ ) are depictedin black, and the single value m k ( τ ) is represented in red.
234 -0.6-0.4-0.200.20 5 10 15 2000.10.2 0 5 10 15 20-4-2024
Figure 2: Illustration of the methodology in the first time-window [0; T ] of size T = 20minutes, using the fixed time scale τ = 25s. (a): raw FHR. (b): m t ( τ ). (c): σ t ( τ ). (d): R t ( τ ). The black circles in (b),(c),(d) correspond each to a value obtained in a time-intervalof size τ = 25s, according to eqs (1),(3),(5). The horizontal red lines in (b), (c), (d) indicatethe values m k =1 ( τ ), σ k =1 ( τ ) and R k =1 ( τ ) obtained after averaging all the black circles, i.e.,over all available time-intervals of size τ , according to eqs (2),(4),(6). The quantity m k ( τ ) measures the average variation — either an increase ora decrease — of FHR on the time scale τ , the average being computed over the k th time-window of size T according to (2). τ Given a time-interval [ t − τ ; t ], we define the variance of the set of increments { ( x t − i − x t − τ ), t − τ < i ≤ t } . This indeed is nothing but the variance of x t ,computed over the set of values in the time-interval [ t − τ ; t ]: σ t ( τ ) = 1 τ t (cid:88) i = t − τ +1 x i − (cid:32) τ t (cid:88) i = t − τ +1 x i (cid:33) . (3)7e then average its square root over the (cid:98) T /τ (cid:99) non-overlapping time intervalsof size τ available in the k th time-window of size T : σ k ( τ ) = 1 (cid:98) T /τ (cid:99) (cid:98)
T/τ (cid:99) (cid:88) j =1 σ kT + jτ ( τ ) . (4)This quantity measures the average — in the k th time-window of size T —amplitude of the fluctuations of x t over τ consecutive points. The methodologyis illustrated in Figure 2c. τ The Student ratio, or normalized local trend, at time-scale τ , is defined foreach time interval [ t − τ ; t ], as: R t ( τ ) = m t ( τ ) σ t ( τ ) . (5)It is averaged across all available non-overlapping intervals in the k th time-window: R k ( τ ) = 1 (cid:98) T /τ (cid:99) (cid:98)
T/τ (cid:99) (cid:88) j =1 R kT + jτ ( τ ) . (6)This quantity, up to a factor √ τ , would correspond to a random variable drawnfrom the distribution of the t -value if the data x t were independently drawn froma Gaussian distribution. It can be interpreted as the average variation over atime step τ , normalized by the local standard deviation; as such, it provides anormalized measure of the trend of the signal x t to depart from its expectedvalue when observed across a duration τ . τ One commonly used feature in heart rate analysis, both for adults and fe-tuses, is sample entropy (SampEn) [53, 54, 42], an elaboration on approximateentropy (ApEn) [49, 48]. It was shown recently that the entropy rate providesa related tool to probe FHR with better performance than ApEn or SampEnto detect acidosis [62, 37, 36].The entropy rate of order 1 in the k th time-window at time-scale τ is definedas: h k ( τ ) = H ( x t , x t − τ ) − H ( x t ) , (7)where H ( (cid:126)x ) = − (cid:90) p ( (cid:126)x ) ln p ( (cid:126)x ) d(cid:126)x , (8)denotes the Shannon entropy [55] of either a vector (cid:126)x = ( x t , x t − τ ) or a scalar (cid:126)x = x t . h k ( τ ) is computed using all the pairs of points ( x t , x t − τ ) available inthe k -th time-window, and following Theiler’s prescription [37] to avoid spuriouscorrelation. 8 k ( τ ) measures the extra information conveyed by the vector ( x t , x t − τ ) when( x t ) is known, or in other words, the extra information given by the knowledgeof the signal at an earlier time t − τ . The entropy rate probes the dynamicsof the signal, and to better focus on this dynamical aspect, we compute it onthe normalized signal ( x t − (cid:104) x t (cid:105) ) / (cid:112) (cid:104) ( x t − (cid:104) x t (cid:105) ) (cid:105) , where (cid:104) . (cid:105) stands for the timeaverage on the window of size T .
4. Results and discussion: Features, time-scales and distance to healthystate
In section 4.1, the four features — computed in overlapping time-windows —evolution in time are firstly presented and studied with respect to their relationsto UCO intensity. Because these features are computed at a given time-scale τ ,they offer a description of the FHR dynamics at this time-scale. We thus explorethe correlation between the features at a given time-scale τ and the measuredvalues of the metabolites — including the pH. This global analysis, presentedin section 4.2, is performed using all available time-windows and all availableanimals. We then reduce the dimensionality of the analysis by averaging re-sults over the long-term time-scales, as defined and presented in section 4.3.This allows us to examine more clearly how the features evolve jointly with theUCO intensity for the entire cohort, while quantifying the variability betweenanimals. We then examine quantitatively in section 4.4 how these long-termfeatures correlate with metabolites. We then combine them in an appropriatelynormalized vector; we are then able to describe the large variability across thesubjects in the population as the variability of this vector in the early stagesof the experiments. This allows us to define a measure of the degradation ofthe health state of an animal as the distance from healthy state. Finally, wepropose in section 4.5 to use this ”individual” distance as a novel indicator — orsentinel — to alert for the degradation of the health status due to CVD. Wealso show that this indicator/sentinel matches very well with pH measurements. We first examine on a single animal how the four FHR features evolvethroughout an experiment, depending on the time-scale τ . The values obtainedin the k -th time-window [ kdT ; kdT + T ] are assigned to the date t k = kdT + T / m k ( τ ), σ k ( τ ), R k ( τ ) and h k ( t, τ ) are depicted in Figure 3 for a large band of time scales τ .Such a time-scale representation reveals qualitatively that when the UCOstrength is increased, m k ( τ ), R k ( τ ) and h k ( τ ) decrease along time, while σ k ( τ )increases along time. This agrees with the previous studies where the decreaseof the entropy rate h k ( τ ) was associated with fetal acidosis [62, 36, 37].Qualitatively, although the four features barely evolve in time for smallervalues of τ (below 2 seconds, bottom of the images in Fig. 3), a noticeable timeevolution can be observed for large values of τ and especially in the severe UCOregime. To better observe the dependence of the four features on the scale τ ,9 -0.1-0.050
100 200 30024681012 -0.8-0.6-0.4-0.200.20.4
100 200 30024681012 -101
Figure 3: Representation of the time evolutions of m k ( τ ), σ k ( τ ), R k ( τ ), h k ( τ ), depending onthe scale τ . The time in abscissa is kdT + T/
2, the location of the k th time-window of size T where the quantity is computed, and the ordinate represents the scale τ . Vertical color linesindicates the times at which blood sampling was performed (same color code as in Fig. 1:green in the mild UCO regime, magenta in the moderate UCO regime, and red in the severeUCO regime). In the severe UCO regime and for larger time scales τ , stronger variations areobserved. we plot in Fig. 4 their evolution with τ for the time points when blood samplingwas performed. Fig. 4 therefore presents the evolution of the four features alongthe vertical color lines indicated in the images of Fig. 3.We observe in Figure 4 that the evolution of m k ( τ ) is rather linear in τ ,but the slope depends on the time, and hence on the UCO level. We observealmost no evolution of R ( τ ) with τ , but the value of R ( τ ) depends on time,so on the UCO level. On the contrary, both σ ( τ ) and the entropy rate h ( τ )present a distinct change of their evolution with τ below and above τ = 2 . < . > . We now examine, for a fixed time-scale τ , how the features relate to thehealth state of the animal, as described by the metabolites and pH. To do so,we use all time-windows of size T on one side, and interpolated metabolitesdata on the other side. We compute the correlation between any of the fourfeatures (for a fixed τ ) and any of the biochemical measurements, by averagingover all time-windows (average over k ) and over all animals. Results are plottedin Fig. 5 as a function of the scale τ .As suggested by Fig. 4 and confirmed by Fig. 5, we can isolate two bandsof time scales: shorter scales τ < .
5s (i.e., high frequency band, above 0.4 Hz,short term time scales, labeled ST) and larger ones τ > .
5s (low frequencyband, below 0.4 Hz, long term time scales, labeled LT).For any of the four features and any of the three biochemical measurements,the correlation in the range [2 . −
8] seconds is not only the largest — in abso-10
Figure 4: Quantitative representation of the evolution of m ( τ ) , σ ( τ ) , R ( τ ) , h ( τ ) over thetime scale τ for a single animal. The data represented here is extracted from Fig.3: eachcurve corresponds to a time-window of size T for which a fetal arterial blood sample wastaken. The color of the curve represents the corresponding UCO level, with the same colorcode as in Figures 1 and 3: blue is the baseline prior to any UCO, green in the mild UCOregime, magenta in the moderate UCO regime, red in the severe UCO regime, and then blackin the recovery regime (after UCO). Vertical black dashed lines indicate the time-scales 2.5sand 8s. lute value — but also the most stable: it fluctuates less and does not dependmuch on τ . Above 8s, all correlations decrease in absolute value, which maybe attributed in part to poorer statistics: the number (cid:98) T /τ (cid:99) of available time-intervals of size τ in a time-window of size T decreases, which impacts theaverages, see, e.g., equation (2)). As a consequence, we choose in the followingto restrict the long term (LT) range to τ ≤
8s in order to have enough statisticalpower.
For the sake of simplicity, we now eliminate the dependencies of our featureson τ and focus on the LT range. To do so, we compute the area under the Figure 5: Correlation coefficient between the biochemical measurements (a: lactate, b: pH,c: BE) and the four FHR features: m k ( τ ) (magenta), σ k ( τ ) (blue), R k ( τ ) (red), and entropyrate h k ( τ ) (black), as function of the scale τ . . < τ < k , we compute: m LT k = τ =8s (cid:88) τ =2 . m k ( τ ) (9)and we define accordingly σ LT k , R LT k and h LT k . These features depend only ontime, via the index k of the time-window in which they are computed.Time evolutions of these four LT features are depicted in Fig. 6 for thecomplete set of 14 animals. Note that for some animals, due to fluctuations inthe experimental conditions, there may be less consecutive time-windows of size T available than expected in a given UCO region, and we have then chosen toassign the dark blue color (arbitrary) for the quantity in that situation — see,e.g., the second line (a hypoxic animal), where no data is available in the mildUCO region, and only 4 windows are available in the severe UCO region. -0.08-0.06-0.04-0.020 0.050.10.15-0.6-0.4-0.200.2 -0.500.51 Figure 6: Long term AUC of the four FHR features m LT , σ LT , R LT and h LT for all 14animals. For a given quantity, each line represents an animal; chronically hypoxic ones areabove and normoxic ones are below. Each column represent a time-window of size T and timeis increasing from left to right. The region of mild UCO starts at the vertical green line andlasts for 4 windows, up to the vertical magenta line, followed by 4 windows in the moderateUCO region, and then up to 6 windows in the severe UCO region, and up to 3 windows inthe recovery region. Using the first column (on the left of the vertical green line) of each subfigureas a reference, we observe that every quantity evolves as the UCO strength isincreased. Although very few changes are observed in the mild UCO region,12uch larger variations are observed in the severe UCO region. After the stop-ping of UCOs (on the right of the vertical black line), we observe that the fourfeatures seem to regain their original value, which we interpret as indicatingthe recovery of the animal, typically after 1 window of size T , so typically 20minutes after the end of UCOs. We now explore how our four FHR features relate to the metabolites’ levels,and especially to the pH value, which is a widely used indicator of the fetalhealth status. We report in Table 1 the correlation coefficient between each ofthe four features m LT , σ LT , R LT and h LT on one hand, and the three biochemicalmeasurements pH, BE and lactate on the other hand. To increase the statisticalpower, we use all available time-windows of size T and so all linearly interpolatedvalues of the three biochemical measurements.We observe that the four FHR features correlate well with the pH and BE,while the correlation with the lactate is smaller. All features but σ LT — theLT amplitude of fluctuations — have a correlation coefficient with pH that isat least 0.50, and a correlation coefficient with BE that is at least 0.43. Thisis interesting, as R LT appears strongly correlated with m LT while relativelyuncorrelated with σ LT . m LT σ LT R LT h LT || (cid:126)u || D pH BE Lactate m LT σ LT -0.51 1.00 -0.19 -0.43 -0.35 0.61 -0.42 -0.36 0.35 R LT h LT || (cid:126)u || D -0.87 0.61 -0.63 -0.76 -0.50 1.00 -0.61 -0.53 0.44pH 0.53 -0.42 0.50 0.50 0.35 -0.61 1.00 0.95 -0.77BE 0.48 -0.36 0.48 0.43 0.29 -0.53 0.95 1.00 -0.72Lactate -0.36 0.35 -0.35 -0.33 -0.21 0.44 -0.77 -0.72 1.00 Table 1: Correlation coefficients between the four individual features, their vectorial combi-nations, and the three measurements pH, Be and Lactate. Data from all 14 animals and allavailable time-windows were used.
We believe that each of the four FHR features contributes a particular pieceof information about FHR and we therefore aggregate them as follows. For a13ingle animal and a single time-window indexed by k , we consider the vector (cid:126)u k = (cid:18) m LT k m LTRMS , σ LT k σ LTRMS , R LT k R LTRMS , h LT k h LTRMS (cid:19) , (10)where each component is normalized by its standard deviation computed overall animals and over all available time-windows of size T . The four values( m RMSLT , σ
RMSLT , R
RMSLT , h
RMSLT ) used for this normalization are hence the same forall animals and all time-windows; they are reproduced in the third line of Ta-ble 2.For a given animal and for a given time-window indexed by k , we use the L norm in R to project any vector (cid:126)u k into a positive real number (cid:107) (cid:126)u k (cid:107) as follows.For each animal, we assume it is in a healthy condition when the experimentis started (so the FHR is fluctuating around the baseline) and we use the firsttime window of size T as a reference. We thus define the distance between (cid:126)u k which describes the state in the k -th time-window and (cid:126)u which describes thestate in the first time-window [0; T ]: D k = (cid:107) (cid:126)u k − (cid:126)u (cid:107) . (11)We interpret this distance D k for a single animal as a measure of the deviationfrom the animal’s ”healthy” state during the experiment.We report in Table 2 global statistics — obtained by considering all ani-mals — of the four FHR features used as the four components of the vector (cid:126)u t . m LT σ LT R LT h LT mean, over animals and over k -0.0067 0.0688 -0.0262 0.5957mean, over animals, fixed k = 0 -0.0009 0.0579 0.0128 0.8811std, over animals and over k k = 0 0,0040 0.0221 0.1082 0.1970 Table 2: Means and standard deviations (std) of the four FHR features over the population of14 animals. First and third lines: averages over animals and over time-windows ( k ). Secondand fourth lines: averages over animals, using the first ( k = 0) time-window [0; T ] only. The third line of Table 2 reports the values m LTRMS , σ
LTRMS , R
LTRMS and h LTRMS used to normalize the vector (cid:126)u k . Their amplitude is notably different, and thenormalization is necessary to ensure that each component of (cid:126)u k contributesequally to its norm || (cid:126)u k || . Whereas this normalization uses all available data(using all times and all animals at once), it is important to stress that we haveaccounted for the large variability from one animal to another by defining D k with a reference relative to the very animal under consideration. The variabilityof the reference point can be seen in the fourth line of Table 2: it accounts for a14arge part of the RMS values used in the normalization. Comparing the first twolines of table 2 brings an additional observation leading to the same conclusion:the position of the healthy state (cid:126)u is on average over the animals (second lineof the table) sensibly different from the position of (cid:126)u k averaged over all animalsand all times (first line of table). Using D k instead of || (cid:126)u k || removes a largepart of the inter-animal variability and definitely improves the relevance of thedistance, as measured by the correlation with the metabolites, see table 1.We present in Figure 7 the 14 trajectories of the vector (cid:126)u ( k ) for the completecohort. Although the trajectories wander in a large region of the phase space,their color-coding seem to only depend on the distance from the origin. During Figure 7: Trajectories of the vector (cid:126)u k − (cid:126)u for all 14 animals in the phase space; the 6subplots correspond to the 6 possible projections onto planes (using 2 coordinates of thevector). Each trajectory corresponds to an animal and is colored to indicate the pH valueat the time k : in this way, we observe the joint temporal evolution of (cid:126)u k and of the pHthroughout the experiment. Trajectories have been centered by subtracting (cid:126)u , accordingto eq.(11) to account for the variability between animals: the thick black dot at the origin,therefore, represents the starting point of all trajectories. The black circle corresponds to D = 1 and the red circle to D = 2. an experiment, the UCO’s strength increases and, as a consequence, the pHdecreases. We observe that the distance D k appears to increase concomitantly,and more precisely we observe its correlation with the pH value. The corre-lation coefficients between the distance D and the biochemical measurements,computed over all animals, are reported in Table 1 (grey-colored cells). We15bserve that among all FHR features we have computed, the distance D is theone that is the most correlated with pH, as well as with the other metabolites.This confirms that using all four FHR features simultaneously — by consideringthe vector (cid:126)u — not only mitigates the various evolutions of single features withthe metabolite value but also aggregates their correlations. To better illustrate the relation between the dynamical features — especiallythe distance D k — on one hand, and the health status as assessed by themetabolites — especially the pH — and blood pressure responses to UCOson the other hand, we examine in detail how these are co-evolving for eachindividual animal.Figure 8 presents the evolutions of (cid:126)u k for two typical normoxic animals.From now on, we discard any indication of the UCO level, and only focus onthe trajectory of D k which we color-code using the pH value, as in Figure 7. S.G. Roux et al.
FHR and cardiovascular dynamics
Figure 8.
Two examples of normoxic animals (right and left). Upper part: BPM signal, together with thedistance D computed along time. Lower part: Projections of the trajectory of the vector ~u in left: the plane ( m LT , h LT ) (the two features that individually better correlate with the pH) and right: the plane ( LT , R LT ) (the other two components of ~u ). The distance D and the trajectories are color-coded with the pH values ineach time-window of size T . For clarity, only the part of the trajectory where D increases up to its maximalvalue is represented. The red vertical line in the time-trace of the distance D indicates the ABP sentinel.We now examine quantitatively the time-evolution of the distance from the reference healthy state. In each time-window [ kdT, kdT + T ] of size T indexed by k , we have a value D k which we assign to time t = kdT + T/ ; we plot the time-evolution of the distance in the upper panels of Figures 8 and 9 with a color that indicates the pH value. This allows for the following interesting observations. First, before the occurrence of UCO, the distance fluctuates with a typical standard deviation of 1. This confirms that the normalization step is valid, albeit it uses values averaged over all animals and all available time-windows. Second, we see that the distance D is substantially larger when UCOs are performed, and more precisely, we see that D increases as the UCO strength is increased or are being applied to the animal with the same intensity but for a longer period of time. As such, the distance D seems to be a good representation of the health condition of the animal. More interestingly, we showed (table 1) that D is highly correlated with the pH value along the complete experiment, but we now observe that a large value of D , above 2, proves to be a very good indicator of a low pH value signaling an acid blood, pH < To further test the ability of the distance D to alert on the fetus condition, we now try to relate the large values of the distance D to the onset of the fetal cardiovascular decompensation, i.e., failure of the fetus to mount a hypertensive arterial blood pressure response to UCOs and the UCO-induced FHR decelerations. Recently, a computerized sentinel approach based on change point detection, referred to as the delta, was proposed which alerts on the cardiovascular compromise (Gold et al., 2018, 2019). This approach was tested against the so-called ABP sentinel. The latter, as also used in this study, is defined visually as the
Frontiers 15
Figure 8: Two examples of normoxic animals (right and left). Upper part: FHR, together withthe distance D computed over time. Lower part: Projections of the trajectory of the vector (cid:126)u in left: the plane ( m LT , h LT ) (the two features that individually better correlate with thepH) and right: the plane ( σ LT , R LT ) (the other two components of (cid:126)u ). The distance D andthe trajectories are color-coded with the pH values in each time-window of size T . For clarity,only the part of the trajectory where D increases up to its maximal value is represented. Thered vertical line in the time-trace of the distance D indicates the ABP sentinel, i.e., the timepoint when we visually confirm the onset of CVD. Because the vector (cid:126)u k has been carefully normalized, and appropriately cen-tered to define the distance D k , this last quantity has no dimension and can becompared to absolute values. The particular value D = 1 defines the standarddeviation range in a healthy situation and the value D = 2 corresponds to vari-ations with an amplitude of 2 standard deviations. Looking at the trajectory16rojections, we see that during the early stages of the experiments the distanceremains small, albeit fluctuating, as long as the pH value remains close to itsnormal value (bluish color, indicating a pH close to 7.4). More interestingly,we see that when the pH decreases down to 7.2 (greenish color), the distanceusually increases up to 2. Finally, we observe that when D >
2, the pH is alwayspathologically low, which signals that the fetus is in an acidemic condition.The very same observations can be made for hypoxic animals, see Figure 9for two examples.
S.G. Roux et al.
FHR and cardiovascular dynamics
Figure 9.
Two examples of hypoxic animals. Cf. Figure 8.time when a persistent (over three or more UCO cycles) appearance of pathological hypotensive blood pressure response to UCO-induced FHR decelerations is observed (Gold et al., 2018). ABP sentinel is obtained by an expert visual analysis and offers a valuable benchmark for an early detection of hypotensive blood pressure. The time points given by ABP sentinels is reported in Figures 8 as a vertical red line.
ABP sentinel appears on average over the cohort for a pH of 7.20 and 60 minutes prior to pH nadir of less than 7.00, but shows a considerable inter-individual spread. Here we see that the criterion D offers a similar early alert on the deterioration of the animal condition, see phase-space projections in Figures D , we see that this quantity evolves continuously in time: fluctuations seem to occur on typical time-scales larger than 20 minutes, the duration we have chosen to compute our quantity. The distance increases along the experiment and one can easily measure the time t D at which D crosses the value D = 2 (red circle or horizontal line in Figures 8 and 9). Unfortunately, the distance D is very sensitive and it can be seen on the examples that it is possible for D to reach values larger than 2 early in the experiment. We interpret such events as signaling some blood pressure regulation troubles, though we haven’t push the analysis further. To overcome these events — and hence make our sentinel less sensitive —, we arbitrarily adjust our criteria and require D k > . for at least 3 consecutive time-windows, so for a long enough duration of about 40 minutes. Table 3 presents our findings, together with previous ones from Gold et al. (2018) using the ABP sentinel. The agreement between the ABP sentinel time and the distance time is very satisfying, knowing that we have arbitrarily reduced the sensitivity of our measure. For one animal (number 473360, last line in table 3), a large discrepancy is observed. A closer examination of both the data and our measure for this animal is given in Figure 10 and allows us to discuss the sensitivity of our measure. We have used the 4Hz BPM
This is a provisional file, not the final typeset article Figure 9: Two examples of hypoxic animals (right and left). Cf. Figure 8. Upper part: FHR,together with the distance D computed over time. Lower part: Projections of the trajectory ofthe vector (cid:126)u in left: the plane ( m LT , h LT ) (the two features that individually better correlatewith the pH) and right: the plane ( σ LT , R LT ) (the other two components of (cid:126)u ). The distance D and the trajectories are color-coded with the pH values in each time-window of size T . Forclarity, only the part of the trajectory where D increases up to its maximal value is represented.The red vertical line in the time-trace of the distance D indicates the ABP sentinel, i.e., thetime point when we visually confirm the onset of CVD. We now examine quantitatively for each animal the time evolution of thedistance from its own reference healthy state. In every time-window [ kdT, kdT + T ] of size T indexed by k , we have a value D k which we assign to time t = kdT + T /
2; we plot the time-evolution of the distance in the upper panels ofFigures 8 and 9 with a color that indicates the pH value. This allows for thefollowing interesting observations. First, before the occurrence of UCO, thedistance fluctuates with a typical standard deviation of 1. This confirms thatthe normalization step is valid, albeit it uses values averaged over all animals andall available time-windows. Second, we see that the distance D is substantiallylarger when UCOs are performed, and more precisely, we see that D increasesas the UCO strength is increased or UCOs are being applied to the animal withthe same strength but for a longer period of time. As such, the distance D D is highly correlated with the pH valuethroughout the complete experiment, but we now observe that a large value of D , above 2, proves to be a very good indicator of a low pH value signaling anacidemia with pH < D to alert on the fetal condition,we now try to relate the large values of the distance D to the onset of the fetalCVD, i.e., failure of the fetus to mount a hypertensive arterial blood pressureresponse to UCOs and the UCO-induced FHR decelerations, a prerequisite tomaintaining an adequate cerebral perfusion pressure. To do so, we use theso-called ABP sentinel as the reference time when CVD occurs. This sentinelis defined visually as the time when a persistent (over three or more UCOcycles) appearance of pathological hypotensive blood pressure response to UCO-induced FHR decelerations is observed [33]. ABP sentinel is obtained by anexpert visual analysis and offers a valuable benchmark for an early detection ofhypotensive blood pressure response. As an illustration, the time given by theABP sentinel is reported in Figure 1b as a vertical black line, and in Figure 8b,fand Figure 9b,f as a vertical red line.ABP sentinel appears on group average for a pH of 7.20 and 60 minutes priorto pH nadir of less than 7.00, but shows a considerable inter-individual spread.Here we see on phase-space projections in Figures 8c,d and 9c,d that the criterion D ≥ D , we see that this quantity evolves continuouslyin time, on typical time-scales larger than 20 minutes, the duration we havechosen to compute our quantity. The distance increases over the duration ofthe experiment and one can easily measure the time t D at which D crosses thevalue D = 2 (red circle or horizontal line in Figures 8 and 9). Unfortunately, thedistance D is very sensitive and it can be seen on the examples that it is possiblefor D to reach values larger than 2 early in the experiment. We interpret suchevents as signaling some blood pressure regulatory difficulties, though we did notpushed this analysis further. To overcome these events — and, hence, to makeour new sentinel less sensitive —, we arbitrarily adjust our criteria and require D k > . ≤ . t ABP and t D is always smaller than the differ-ence between t pH and t ABP , and also smaller than 20 minutes, the size of thetime-windows we have used.However, for one animal (number 473360, last line in table 4), a large dis-crepancy is observed. A closer examination of both the data and our distancemeasure for this animal is given in Figure 10 and allows us to discuss the sen-18CO start time pH nadir timeanimal mild moderate severe recovery t pH(ID) (hh:mm:ss) (hh:mm:ss) (hh:mm:ss) (hh:mm:ss) (hh:mm:ss)Hypoxic 8003 01:14:14 02:11:11 03:14:14 03:21:21 03:21:21473351 NaN 04:08:08 05:16:16 06:40:40 05:51:51473362 02:08:08 03:09:09 04:02:02 04:37:37 04:38:38473376 02:52:52 03:47:47 04:43:43 05:46:46 05:50:50473726 02:09:09 03:09:09 04:04:04 05:26:26 05:25:25Normoxic 461060 02:58:58 03:52:52 04:57:57 06:29:29 06:29:29473361 01:55:55 02:58:58 04:01:01 06:31:31 05:25:25473352 NaN 03:58:58 04:58:58 05:44:44 05:37:37473377 02:28:28 03:31:31 04:30:30 06:31:31 06:27:27473378 03:17:17 04:15:15 05:10:10 05:47:47 05:44:44473727 01:37:37 02:42:42 03:39:39 05:47:47 05:18:185054 01:30:30 02:27:27 03:30:30 05:22:22 05:22:225060 01:09:09 02:06:06 03:08:08 04:07:07 04:02:02473360 02:11:11 03:16:16 04:13:13 06:10:10 06:10:10 Table 3: The individual onset times for each UCO regime and reaching pH nadir. The UCOregimes mild, moderate, severe and recovery are colored green, magenta and red in Figure 1)pH nadir time t pH (when pH ≤ .
00) measured from linear interpolation of pH data (as seenfor example in Figure 1b). sitivity of our measure. We have used the 4Hz FHR dataset which was alsostudied in earlier literature. This dataset is obtained from the R-R intervalsdata at 4Hz, which is interpolated from the raw ECG-derived R-R intervalsdata recorded at 1000Hz. As can be seen in Figure 10, the genuine 1000 Hzdataset (in red) is missing some values during short intervals and the resamplingprocess, which uses splines interpolation, creates arbitrary values for the 4HzFHR dataset (in black) within such intervals. This results in additional valueswhich exhibit large and fast fluctuations which are non-physiological. Whereasmost of these do not impact the value of the distance D (see Figure 10e,f and10g,h), there is a time interval (at about t = 172s, see Figure 10b,d where D is unexpectedly large, reaching a value around 4. This is concomitant with asharp drop in FHR, as can be seen in Figure 10a,c. This sharp drop is exacer-19ated on the 4Hz signal compared to the 1000Hz signal, and is very localized intime, which leads to a later decrease of D , contrary to the pathological situationreported in Figure 10g,h where D remains at a large value. As a consequence,we obtain a false positive sentinel time t D which corresponds to this event andis hence much earlier than the ABP sentinel time, although in agreement withpreviously reported results using the same 4Hz FHR dataset [34]. We concludethat splines interpolation should be avoided, and we suggest instead not to addor create artificial data points when genuine data is not available. Addition-ally, each of the quantities we propose, and hence the distance D , can still becomputed, as they are all robust with respect to missing data. S.G. Roux et al.
FHR, metabolic and cardiovascular dynamics
Figure 10.
Same as Figure 8 but for two hypoxic animals.smaller, but earlier troubles (e.g., in the first hypoxic case in figure 9). As such, it is a very sensitive measure of the animal condition.
Our analysis relies on the computation of dynamical quantities using BPM signal sampled at 4Hz as is commonly done in the majority of maternity hospitals. That is, our approach developed from a preclinical model can be directly validated in clinical datasets such as the Prague database (cite from https://physionet.org/content/ctu-uhb-ctgdb/1.0.0/). Moreover, we have checked that it is robust with respect to missing data. Our framework is therefore of great interest in practical situations.
We have explored the effect of the time-window size and obtained satisfying —and very similar — results with windows of size T = 10 minutes. Being able to use such small time-windows opens the door to a real-time analysis that may be used for early detection of fetal acidosis. Our quantities, and especially the distance D is a good candidate to build an enhanced monitoring analysis. Such a real-time analysis should incorporate static features, like the baseline and variability of the BPM signal, as well as our new dynamic features derived from entropy rate, which incorporate dynamical quantities, especially the average variation over a short time scale m ( ⌧ ) and the entropy rate h ( ⌧ ) . This is a provisional file, not the final typeset article Figure 10: A representative example of FHR and the corresponding distance D (colored bypH value) for animal 473360. The 4Hz dataset used in the analysis is reproduced in black,and the original 1000 Hz dataset is presented in red. a,b : complete time trace for all availabledata. c,d : zoom in the problematic region, where D is unexpectedly large. e,f : zoom in aregion where D is small, as expected. g,h : zoom in a region where D is large, as expected.See text. A deeper examination of each experiment, using animal’s systemic arterialblood pressure data, should clarify the relationship between the increases of thedistance from healthy condition and the incipient arterial hypotension. Thiswork is out of scope of the present article which focuses on the dynamics of theclinically relevant 4Hz-sampled FHR signal.As such, we propose that the distance D has the potential to serve as anindividual biomarker of the incipient CVD, i.e., an early sentinel of the fetalbrain injury.
5. Conclusions and outlook
In the present work, four FHR features, whose definitions depend on thetimescale, are computed on the FHR dataset derived from an animal model of20uman labor to quantify the evolution of FHR temporal dynamics as a func-tion of the UCO strength. We also correlated the variations of such timescale-dependent quantities to metabolite and pH measurements. We show the rel-evance of timescales ranging in [2 . −
8] seconds (equivalently [0 . − . m LT which may be inter-preted as an increase of baseline [59, 2]), and lower entropy rate h LT , in agree-ment with earlier findings reported in the literature [37]. More importantly,a per-individual distance metric was constructed from these four (population-normalized) features to quantify a self-referencing departure from a healthy statefor each subject independently. Such a definition raises two issues. Firstly, itrequires, as is often the case, that monitoring is started early enough while thefetus is still in a healthy condition, so as to create a self-reference to normalon a per-individual basis. If fetuses are already in distress when monitoring isinitiated, the distance, albeit increasing with distress, may fail to detect CVDcorrectly. Secondly, the definition of the vector, and hence the distance, requiresa normalization, which is performed in the present work at the population level,i.e., using an average across subjects. Although such an average should convergerapidly with the population size, this dependence requires further investigations.However, the constructed distance proved able to detect accurately the oc-currence of acidemia and CVD from the analysis of FHR only, and withoutrecourse to pH. This opens the route to investigating the relevance of such met-rics in clinical practice, as it is non-invasive and based on mechanical processes,which are much faster than the biochemical ones underlying the use of pH.Further, for practical purposes, the present studies show that the computationof features and distance is robust to FHR sampled at 4Hz and, to some ex-tent, to missing data. Also, the FHR features and distance are computed insliding-windows, permitting a on-line and quasi-real time analysis of the evo-lution of the dynamics of FHR, and thus in relation to a local health state ofthe fetus. The extent to which the 20-min sliding-window size, chosen herefor proof-of-concept developments, can be further reduced to 10 or 5-min, isunder investigation. This provides a large therapeutic time window for healthpractitioners managing the delivery.It has been documented that sheep fetuses have an individual cardiovascularphenotype in their responses to increasing acidemia due to repetitive intermit-tent hypoxia [23]. Chronically hypoxic fetuses have diminished cardiovasculardefenses to hypotensive stress [4]. We hypothesized that such phenotype wouldbe reflected in individual FHR variability properties. We could not identify anyinfluence of the phenotype (normoxic / hypoxic) in any of the metrics includingthe distance D . We are currently exploring whether the initial vector (cid:126)u maycontain such information. 21 onflict of Interest Statement M. G. Frasch has an aECG patent (WO2018160890A1). The authors declarethat the research was conducted in the absence of any other commercial orfinancial relationships that could be construed as a potential conflict of interest.
Author Contributions
S. G. Roux designed the signal processing tools, ensured their practical im-plementation, conducted their application to data and the analysis and inter-pretation of the results. He also prepared the figures and tables reported in thearticle.N. B. Garnier contributed to the design of the signal processing tools, to theanalysis and interpretation of the results and to the writing of the paper.P. Abry contributed to the interdisciplinary connections between signal pro-cessing and medical doctor teams, to the interpretation of the results and to thewriting of the paper.N. Gold contributed to the measurements and the manuscript. He also per-formed the changepoint-based detection of the cardiovascular decompensation.M. G. Frasch designed the experiment and conducted the surgeries and mea-surements. He also performed the expert visual detection of the cardiovasculardecompensation used as ground truth here. He contributed to writing the articleand to the interpretation of the results.
Funding
Work supported by Grant ANR-16-CE33-0020 MultiFracs.
Acknowledgments
The authors thank the Signal Processing and Monitoring Workshop (SPaMworkshop) launched under the umbrella of the ANR French Grant
References [1]
Abry, P., Roux, S., Chud´aˇcek, V., Borgnat, P., Gonc¸alves,P., and Doret, M.
Hurst Exponent and Intrapartum Fetal HeartRate: Impact of Decelerations. In 26th International Symposium onComputer-Based Medical Systems (CBMS) (2013), pp. 1–6.222]
Abry, P., Spilka, J., Leonarduzzi, R., Chud´aˇcek, V., Pustelnik,N., and Doret, M.
Sparse learning for intrapartum fetal heart rateanalysis. Biomedical Physics & Engineering Express 4, 3 (2018), 034002.[3]
Akselrod, S., Gordon, D., Ubel, F. A., Shannon, D. C., Berger,A. C., and Cohen, R. J.
Power spectrum analysis of heart rate fluctu-ation: a quantitative probe of beat-to-beat cardiovascular control. Science213, 4504 (1981), 220–222.[4]
Allison, B. J., Brain, K. L., Niu, Y., Kane, A. D., Herrera, E. A.,Thakor, A. S., Botting, K. J., Cross, C. M., Itani, N., Shaw,C. J., Skeffington, K. L., Beck, C., and Giussani, D. A.
Alteredcardiovascular defense to hypotensive stress in the chronically hypoxic fetus.Hypertension 76, 4 (2020), 1195–1207.[5]
Astrup, J.
Energy-requiring cell functions in the ischemic brain. theircritical supply and possible inhibition in protective therapy. J Neurosurg56, 4 (1982), 482–497.[6]
Ayres-de Campos, D., Spong, C. Y., Chandraharan, E., and In-trapartum Fetal Monitoring Expert Consensus Panel, F. I.G. O.
Figo consensus guidelines on intrapartum fetal monitoring: Car-diotocography. Int J Gynaecol Obstet 131, 1 (Oct 2015), 13–24.[7]
Bernardes, J., Moura, C., de Sa, J. P., and Leite, L. P.
The Portosystem for automated cardiotocographic signal analysis. J Perinat Med 19,1-2 (1991), 61–65.[8]
Cahill, A., Mathur, A., Smyser, C., and et al . Neurologic injury inacidemic term infants. Am J Perinatol 34, 7 (2017), 668–675.[9]
Chandraharan, E., and Arulkumaran, S.
Prevention of birth as-phyxia: responding appropriately to cardiotocograph (CTG) traces. BestPract. Res. Clin. Obstet. Gynaecol. 21, 4 (2007), 609–624.[10]
Chud´aˇcek, V., Anden, J., Mallat, S., Abry, P., and Doret,M.
Scattering transform for intrapartum fetal heart rate variability frac-tal analysis: A case-control study. IEEE Transactions on BiomedicalEngineering 61, 4 (April 2014), 1100–1108.[11]
Costa, A., Ayres-de Campos, D., Costa, F., Santos, C., andBernardes, J.
Prediction of neonatal acidemia by computer analysisof fetal heart rate and ST event signals. Am J Obstet Gynecol 201, 5 (Nov2009), 464.e1–464.e6.[12]
Costa, M., Goldberger, A. L., and Peng, C. K.
Multiscale entropyanalysis of complex physiologic time series. Physical Review Letters 89, 6(Aug. 2002), 068102. 2313]
Czabanski, R., Jezewski, J., Matonia, A., and Jezewski, M.
Com-puterized analysis of fetal heart rate signals as the predictor of neonatalacidemia. Expert Systems with Applications 39, 15 (2012), 11846–11860.[14]
David, M., Hirsch, M., Karin, J., Toledo, E., and Akselrod, S.
An estimate of fetal autonomic state by time-frequency analysis of fetalheart rate variability. Journal of Applied Physiology 102, 3 (2007), 1057–1064. PMID: 17095644.[15]
Doret, M., Helgason, H., Abry, P., Gonc¸alv´es, P., Gharib, C.,and Gaucherand, P.
Multifractal analysis of fetal heart rate variabilityin fetuses with and without severe acidosis during labor. American Journalof Perinatology 28, 4 (2011), 259–266.[16]
Doret, M., Spilka, J., Chud´aˇcek, V., Gonc¸alves, P., and Abry,P.
Fractal Analysis and Hurst Parameter for intrapartum fetal heart ratevariability analysis: A versatile alternative to Frequency bands and LF/HFratio. PLoS ONE 10, 8 (08 2015), e0136661.[17]
Durosier, D., Green, G., Batkin, I., Seely, A. J., Ross, M. G.,Richardson, B. S., and Frasch, M. G.
Sampling rate of heart ratevariability impacts the ability to detect acidemia in ovine fetuses near-term.Front Pediatr. 2 (May 2014), 38.[18]
Echeverria, J. C., Hayes-Gill, B. R., Crowe, J. A., Woolfson,M. S., and Croaker, G. D. H.
Detrended fluctuation analysis: a suitablemethod for studying fetal heart rate variability? Physiol Meas 25, 3 (Jun2004), 763–774.[19]
FIGO . Guidelines for the Use of Fetal Monitoring. Int J Gynaecol Obstet25 (1986), 159–167.[20]
Francis, D. P., Willson, K., Georgiadou, P., Wensel, R., Davies,L., Coats, A., and Piepoli, M.
Physiological basis of fractal complexityproperties of heart rate variability in man. J Physiol 542, Pt 2 (Jul 2002),619–629.[21]
Frasch, M.
Heart rate variability code: Does it exist and can we hackit?, 2020.[22]
Frasch, M., Durosier, L., Gold, N., Cao, M., Matushewski, B.,Keenliside, L., Y., L., Ross, M., and Richardson, B.
Adaptive shut-down of eeg activity predicts critical acidemia in the near-term ovine fetus.Physiological Reports 3, 7 (2015), 129A.[23]
Frasch, M., Keen, A., Gagnon, R., Ross, M., and Richardson,B.
Monitoring fetal electrocortical activity during labour for predictingworsening acidemia: a prospective study in the ovine fetus near term. PLoSOne 6, 7 (2011), e22100. 2424]
Frasch, M., Mansano, R., Ross, M., Gagnon, R., and Richardson,B.
Do repetitive umbilical cord occlusions (uco) with worsening acidemiainduce the bezold-jarisch reflex (bjr) in the ovine fetus near term? ReprodSci 15, 2 (2008), 129A.[25]
Frasch, M., M¨uller, T., Hoyer, D., Weiss, C., Schubert, H.,and Schwab, M.
Nonlinear properties of vagal and sympathetic modula-tions of heart rate variability in ovine fetus near term. American journalof physiology. Regulatory, integrative and comparative physiology 296, 3(2009), R702–R707.[26]
Frasch, M., Zwiener, U., Hoyer, D., and Eiselt, M.
Autonomicorganization of respirocardial function in healthy human neonates in quietand active sleep. Early Human Development 83, 4 (2007), 269 – 277.[27]
Frasch, M. G., Frank, B., Last, M., and M¨uller, T.
Timescales of autonomic information flow in near-term fetal sheep. Frontiersin physiology 3 (2012), 378.[28]
Frasch, M. G., Xu, Y., Stampalija, T., et al.
Correlating multi-dimensional fetal heart rate variability analysis with acid-base balance atbirth. Physiol meas 35, 12 (2014), L1.[29]
Georgieva, A., Abry, P., Chud´aˇcek, V., Djuri´c, P. M., Frasch,M. G., Kok, R., Lear, C. A., Lemmens, S. N., Nunes, I., Papa-georghiou, A. T., et al.
Computer-based intrapartum fetal monitoringand beyond: A review of the 2nd workshop on signal processing and moni-toring in labor (october 2017, oxford, uk). Acta obstetricia et gynecologicaScandinavica 98, 9 (2019), 1207–1217.[30]
Georgieva, A., Papageorghiou, A. T., Payne, S. J., Moulden, M.,and Redman, C. W. G.
Phase-rectified signal averaging for intrapartumelectronic fetal heart rate monitoring is related to acidaemia at birth. BJOG121, 7 (Jun 2014), 889–894.[31]
Georgieva, A., Payne, S. J., Moulden, M., and Redman, C. W. G.
Artificial neural networks applied to fetal monitoring in labour. NeuralComputing and Applications 22, 1 (2013), 85–93.[32]
Giera(cid:32)ltowski, J., Hoyer, D., Tetschke, F., Nowack, S., Schnei-der, U., and Zebrowski, J.
Development of multiscale complexity andmultifractality of fetal heart rate variability. Autonomic neuroscience :basic & clinical 178, (1-2) (2013), 29–36.[33]
Gold, N., Frasch, M. G., Herry, C. L., Richardson, B. S., andWang, X.
A doubly stochastic change point detection algorithm for noisybiological signals. Frontiers in Physiology 8 (2018), 1112.2534]
Gold, N., Herry, C. L., Wang, X., and Frasch, M. G.
Fetal cardio-vascular decompensation during labor predicted from the individual heartrate: a prospective study in fetal sheep near term and the impact of lowsampling rate, 2019.[35]
Gonc¸alves, H., Rocha, A. P., de Campos, D. A., and Bernardes,J.
Linear and nonlinear fetal heart rate analysis of normal and acidemicfetuses in the minutes preceding delivery. Med Biol Eng Comput 44, 10(Oct 2006), 847–855.[36]
Granero-Belinchon, C., Roux, S., Garnier, N., Abry, P., andDoret, M.
Mutual information for intrapartum fetal heart rate analysis.Conf. Proc. of the IEEE Eng. Med. Biol. Soc. (EMBC) (2017), 2014–2017.[37]
Granero-Belinchon, C., Roux, S. G., Abry, P., Doret, M., andGarnier, N. B.
Information theory to probe intrapartum fetal heart ratedynamics. Entropy 19 (2017), 640.[38]
Haritopoulos, M., Illanes, A., and Nandi, A.
Survey onCardiotocography Feature Extraction Algorithms for Fetal WelfareAssessment. Springer International Publishing, Cham, 2016, pp. 1187–1192.[39]
Herry, C., Burns, P., Desrochers, A., Fecteau, G., Durosier,L., Cao, M., Seely, A., and Frasch, M.
Vagal contributions to fetalheart rate variability: an omics approach. Physiological measurement 40,6 (2019), 065004.[40]
Hruban, L., Spilka, J., Chud´aˇcek, V., Jank˚u, P., Huptych, M.,Burˇsa, M., Hudec, A., Kacerovsk´y, M., Kouck´y, M., Proch´azka,M., Koreˇcko, V., Seget´a, J., ˇSimetka, O., Mˇechurov´a, A., andLhotsk´a, L.
Agreement on intrapartum cardiotocogram recordings be-tween expert obstetricians. Journal of Evaluation in Clinical Practice 21,4 (2015), 694–702.[41]
Itskovitz, J., LaGamma, E., and A.M., R.
Heart rate and bloodpressure responses to umbilical cord compression in fetal lambs with specialreference to the mechanism of variable deceleration. Am J Obstet Gynecol147, 4 (1983), 451–457.[42]
Lake, D. E., Richman, J. S., Griffin, M. P., and Moorman, J. R.
Sample entropy analysis of neonatal heart rate variability. Am J PhysiolRegul Integr Comp Physiol 283, 3 (Sep 2002), R789–R797.[43]
Li, X., Xu, Y., Herry, C., Durosier, L., Casati, D., Stampalija,T., Maisonneuve, E., Seely, A., Audibert, F., Alfirevic, Z., Fer-razzi, E., Wang, X., and Frasch, M.
Sampling frequency of fetalheart rate impacts the ability to predict pH and BE at birth: a retro-spective multi-cohort study. Physiological measurement 36, 5 (apr 2015),L1–L12. 2644]
Magenes, G., Signorini, M. G., and Arduini, D.
Classification ofcardiotocographic records by neural networks. Proc. IEEE-INNS-ENNSInternational Joint Conference on Neural Networks (IJCNN) 3 (2000), 637–641.[45]
Magenes, G., Signorini, M. G., Ferrario, M., Pedrinazzi, L., andArduini, D.
Improving the fetal cardiotocographic monitoring by ad-vanced signal processing. Conf. proc. of the IEEE Eng. Med. Biol. Soc.(EMBC) 3 (2003), 2295–2298.[46]
Nunes, I., de Campos, D. A., Ugwumadu, A., Amin, P., Banfield,P., Nicoll, A., Cunningham, S., Costa-Santos, P. S. P. C., andBernardes, J.
Central fetal monitoring with and without computer anal-ysis: A randomized controlled trial. Obstet Gynecol. 129, 1 (2017), 83–90.[47]
Parer, J. T., King, T., Flanders, S., Fox, M., and Kilpatrick,S. J.
Fetal acidemia and electronic fetal heart rate patterns: is thereevidence of an association? J Matern Fetal Neonatal Med 19, 5 (May2006), 289–294.[48]
Pincus, S.
Approximate entropy (ApEn) as a complexity measure. Chaos5 (1) (1995), 110–117.[49]
Pincus, S. M.
Approximate entropy as a measure of system-complexity.Proc. Natl. Acad. Sci. U.S.A. 88, 6 (Mar. 1991), 2297–2301.[50]
Porta, A., Bari, V., Bassani, T., Marchi, A., Tassin, S., Canesi,M., Barbic, F., and Furlan, R.
Entropy-based complexity of thecardiovascular control in parkinson disease: Comparison between binningand k-nearest-neighbor approaches. Conf Proc IEEE Eng Med Biol Soc(EMBC) (July 2013), 5045–5048.[51]
Prout, A., Frasch, M., Veldhuizen, R., Hammond, R., Ross, M.,and B.S., R.
Systemic and cerebral inflammatory response to umbilicalcord occlusions with worsening acidosis in the ovine fetus. Am J ObstetGynecol 202, 1 (2010), 82.[52]
Richardson, B., Rurak, D., Patrick, J., Homan, J., andCarmichael, L.
Cerebral oxidative metabolism during sustained hypox-aemia in fetal sheep. J Dev Physiol 11, 1 (1989), 37–43.[53]
Richman, J., and Moorman, R.
Time series analysis using approximateentropy and sample entropy. Biophysical Journal 78, 1 (Jan. 2000), 218A–218A.[54]
Richman, J. S., and Moorman, J. R.
Physiological time-series analysisusing approximate entropy and sample entropy. Am J Physiol Heart CircPhysiol 278, 6 (Jun 2000), H2039–H2049.2755]
Shannon, C.
A mathematical theory of communication. The Bell SystemTechnical Journal 27 (1948), 388–427.[56]
Siira, S., Ojala, T. H., Vahlberg, T. J., Ros´en, K. G., andEkholm, E. M.
Do spectral bands of fetal heart rate variability asso-ciate with concomitant fetal scalp pH? Early Hum Dev 89, 9 (Sep 2013),739–742.[57]
Siira, S. M., et al.
Marked fetal acidosis and specific changes in powerspectrum analysis of fetal heart rate variability recorded during the lasthour of labour. BJOG 112, 4 (Apr 2005), 418–423.[58]
Spilka, J., Chud´aˇcek, V., Kouck´y, M., Lhotsk´a, L., Huptych, M.,Jank˚u, P., Georgoulas, G., and Stylios, C.
Using nonlinear featuresfor fetal heart rate classification. Biomedical Signal Processing and Control7, 4 (2012), 350–357.[59]
Spilka, J., Frecon, J., Leonarduzzi, R., Pustelnik, N., Abry, P.,and Doret, M.
Sparse support vector machine for intrapartum fetal heartrate classification. IEEE Journal of Biomedical and Health Informatics PP(2016), 1–1.[60]
Spilka, J., Frecon, J., Leonarduzzi, R., Pustelnik, N., Abry, P.,and Doret, M.
Sparse support vector machine for intrapartum fetal heartrate classification. IEEE J Biomed and Health Inform 21 (2017), 664–671.[61]
Spilka, J., Roux, S., Garnier, N., Abry, P., Goncalves, P., andDoret, M.
Nearest-neighbor based wavelet entropy rate measures forintrapartum fetal heart rate variability. In Engineering in Medicine andBiology Society (EMBC), 2014 36th Annual International Conference ofthe IEEE (Aug 2014), pp. 2813–2816.[62]
Spilka, J., Roux, S., Garnier, N., Abry, P., Goncalves, P., andDoret, M.
Nearest-neighbor based wavelet entropy rate measures forintrapartum fetal heart rate variability. Conf. Proc. of the IEEE Eng.Med. Biol. Soc. (EMBC) (2014), 2813–2816.[63]
Van Laar, J., Porath, M., Peters, C., and Oei, S.
Spectral analysisof fetal heart rate variability for fetal surveillance: Review of the literature.Acta Obstet. Gynecol. Scand. 87, 3 (2008), 300–306.[64]
Warrick, P., Hamilton, E., Precup, D., and Kearney, R.
Clas-sification of normal and hypoxic fetuses from systems modeling of intra-partum cardiotocography. IEEE Transactions on Biomedical Engineering57, 4 (2010), 771–779.[65]
Xu, L., Redman, C. W., Payne, S. J., and Georgieva, A.
Featureselection using genetic algorithms for fetal heart rate analysis. Physiol meas35, 7 (2014), 1357–71. 28VD time D time deltaanimal t CVD t D t CVD − t D (ID) (hh:mm:ss) (hh:mm:ss) (hh:mm:ss)Hypoxic 8003 03:09:07 03:10:10 -00:00:53473351 05:19:01 05:19:19 -00:00:58473362 03:07:04 03:24:24 -00:17:45473376 04:42:44 04:59:59 -00:17:15473726 04:09:56 04:04:04 00:04:56Normoxic 06:29:29 05:02:12 04:49:49 00:12:26473361 05:04:42 04:44:44 00:19:56473352 05:08:02 05:05:05 00:03:01473377 04:42:09 04:49:49 -00:07:35473378 05:23:40 05:15:15 00:08:40473727 03:12:27 03:29:29 -00:17:325054 04:56:16 04:59:59 -00:03:285060 03:43:56 03:29:29 00:14:07473360 05:51:46 02:54:54 02:56:54 Table 4: Cardiovascular decompensation (CVD) times. Comparison of the visually determinedversus computed predictions: t ABP from [33] as reference, and our new distance time t D ,computed by requiring D > . t ABP − t D between thereference ABP time, always earlier than t pH , and the new t D . Positive values indicate adetection earlier than the ABP sentinel. All data are derived from 4 Hz sampled FHR signal.. Positive values indicate adetection earlier than the ABP sentinel. All data are derived from 4 Hz sampled FHR signal.