- Open Access
A novel technique for fetal heart rate estimation from Doppler ultrasound signal
© Jezewski et al; licensee BioMed Central Ltd. 2011
- Received: 12 July 2011
- Accepted: 14 October 2011
- Published: 14 October 2011
The currently used fetal monitoring instrumentation that is based on Doppler ultrasound technique provides the fetal heart rate (FHR) signal with limited accuracy. It is particularly noticeable as significant decrease of clinically important feature - the variability of FHR signal. The aim of our work was to develop a novel efficient technique for processing of the ultrasound signal, which could estimate the cardiac cycle duration with accuracy comparable to a direct electrocardiography.
We have proposed a new technique which provides the true beat-to-beat values of the FHR signal through multiple measurement of a given cardiac cycle in the ultrasound signal. The method consists in three steps: the dynamic adjustment of autocorrelation window, the adaptive autocorrelation peak detection and determination of beat-to-beat intervals. The estimated fetal heart rate values and calculated indices describing variability of FHR, were compared to the reference data obtained from the direct fetal electrocardiogram, as well as to another method for FHR estimation.
The results revealed that our method increases the accuracy in comparison to currently used fetal monitoring instrumentation, and thus enables to calculate reliable parameters describing the variability of FHR. Relating these results to the other method for FHR estimation we showed that in our approach a much lower number of measured cardiac cycles was rejected as being invalid.
The proposed method for fetal heart rate determination on a beat-to-beat basis offers a high accuracy of the heart interval measurement enabling reliable quantitative assessment of the FHR variability, at the same time reducing the number of invalid cardiac cycle measurements.
- Cardiac Cycle
- Autocorrelation Function
- Fetal Heart Rate
- Periodicity Measurement
- Triangular Window
The main task of fetal monitoring is to ensure that all vital organs are properly supplied with oxygenated blood. Direct measurement of oxygen saturation during pregnancy is not possible, but the risk symptoms can be identified through the fetal heart rhythm analysis. The most accurate measurement of the periodicity in fetal heart activity is limited to the labour, when the acquisition of electrical signals using direct fetal electrocardiography (FECG) is possible . The duration of each cardiac cycle (Ti) is estimated on the basis of measurement of time interval between successive R-waves in electrocardiogram. As a result the sequence of consecutive interval values is obtained in a form of time event series. Instantaneous fetal heart rate (FHRi) values (expressed in beats per minute - bpm) are calculated for each cardiac cycle according to formula: FHRi [bpm] = 60000/Ti [ms].
In fetal electrocardiogram recorded directly, the shape of QRS complexes does not change significantly from beat to beat, and thus each beat can be easily identified by detecting the evident R-waves . In case of mechanical activity of a fetal heart, both the shape of signal and locations of prominent peaks are varying even between consecutive beats. Hence, in processing of the ultrasound Doppler signal an autocorrelation function (AF) considering a full shape of the analyzed signal is mostly used . In such approach, a graph of similarity between the input signal and its time-shifted version is analyzed. The instantaneous signal periodicity is determined by detection of the AF maximum, whose position indicates the dominant periodicity of signal contained in the window applied. It was confirmed that the AF improves the noise immunity [7, 8], although the obtained FHR signal shows a significant decrease of beat-to-beat variability.
The short-term variability describing fluctuations of beat-to-beat intervals is considered to be the most important FHR signal feature indicating appropriate fetal development. The indices describing this variability have been originated from the FECG signal recorded during labour via a direct electrode, and they have been applied without any adaptation to the ultrasound technique. It was shown that the FHR values calculated with the AF are characterized by significant inaccuracy , affecting the variability being estimated . It is caused by an averaging nature of the autocorrelation function, which provides a single representative periodicity value but calculated on the basis of all heart beats enclosed in the AF window. The second issue, also affecting the variability measurement, is that autocorrelation technique does not detect events - individual heart beats, which is a standard in FECG signal processing. Therefore, to calculate variability indices consistent with those derived from electrocardiogram, it is necessary to provide the FHR signal in a form of time event series. Such approach was proposed by Tuck  and Peters . However, they focused only on accuracy of interval measurement, while from a clinical point of view more important is whether the method improves the reliability of the FHR variability indices.
The aim of our work was to develop a novel processing method for the Doppler ultrasound signal in order to measure periodicity of fetal heart activity with a beat-to-beat accuracy comparable to direct electrocardiography. A special effort was made to reduce the number of incorrectly measured heart intervals, which was achieved by multiple measurement of each cardiac cycle and application of triangular window function for prediction of periodicity in AF. We particularly would like to answer the question if the modern instrumentation together with signal processing technique are able to provide the cardiac cycle measurements with accuracy enough for reliable determination of clinically important signal features. For that purpose, the signals of mechanical heart activity were analyzed using our algorithm for extraction of true time event series representing the consecutive heart beats. The estimated fetal heart rate values were compared to the reference data simultaneously obtained from direct FECG. The final evaluation was based on parameters describing the beat-to-beat variability of the FHR as a signal feature being the most sensitive to any periodicity inaccuracy.
The signals are preliminary filtered in dsPIC microcontroller to suppress unwanted sources of Doppler signal. Cutting the lower frequencies removes components usually related to fetal movements, whereas the upper limit reduces maternal blood vessel interferences . For this purpose the bandwidth was limited to 100÷600 Hz using FIR filter structure of 120-th order. In the next step, the procedure for depth selection determines the signal (or depth range) in which the fetal heart movements are the most visible. In the obtained Doppler signal sampled with 3 kHz, the mechanical activity of heart is represented as temporary increases of signal amplitude, while its frequency is proportional to a valve/wall movement speed . The signal of the best quality is selected and transmitted via USB interface to personal computer, where processing is carried out using algorithms implemented in Matlab environment.
where s a (n) is an analytic signal and ŝ(n) is a Hilbert transform of s(n) signal.
Since the calculation of the envelope is a continuous process, we applied Hilbert transform filter to ensure constant 90° phase shift of the Doppler signal. Finally, the envelope is fed to 120-th order FIR low-pass filter (fc = 50 Hz) to remove high frequency components.
Estimation of the FHR signal consists of three steps. The first is responsible for adjustment of window parameters and calculation of the AF, the second determines the instantaneous periodicity of signal by means of improved peak detection algorithm, and the last one calculates the time event series representation of FHR signal using our algorithm for segmentation of instantaneous measurement series.
where s is the analyzed signal, n is the number of first sample in the autocorrelation window and N is the AF window length expressed in signal samples. The R(i) function expresses the similarity of the analyzed signal and its version shifted in time by i samples. As we assumed that the measurable range of fetal heart rate is between 50 and 240 bpm, the periodicity measurement relies on searching the maximal value R max of the function R(i) in a range between 250 and 1200 ms.
where W stands for the parameter controlling triangular window shape, which was being changed between 0 (no windowing) and 6 (the narrowest window). Any instantaneous periodicity values Fk for which the peak is lower than the minimal acceptable peak PTH = 0.15 are rejected.
Time event series
The autocorrelation function enables estimation of cardiac cycle duration within a given time window. However, no information on the exact position of heart beats in time is given. Thus, using the AF we obtain a series of values, where each cardiac cycle is represented by a set of periodicity measurements Fk. This representation has to be converted into time event series using an additional algorithm for segmentation of measurement series Fk. Then, on the basis of Fk values contained in each segment, a true value of Ti which represents successive cardiac cycles is calculated .
In details the algorithm for segments shift and matching is as follows:
Starting conditions: i = 1, beginning of the first interval τ 1 = 0 and T 0 = F 1 (zero interval equal to the first periodicity measurement).
Step 2 Calculate the mean difference between values of instantaneous periodicity Fk measured within segment from τi-2 to τi+Ti and the values Ti, Ti-1, Ti-2 corresponding to segments: τi-2÷τi-1, τi-1÷τi, τi÷τi+Ti respectively (Figure 7b).
Step 3 Repeat the same calculations for cardiac cycle markers τi-2, τi-1, τi shifted in time by γ = ±Shift, where Shift stands for temporary shift increment, defining time interval between periodicity measurements Fk (Figure 7c and 7d).
Step 4 If the least mean difference is obtained in case of markers displacement, set the correction factor ε to 1/4·γ, otherwise to 0 (Figure 7e).
Step 5 Calculate the time of the next interval beginning τi+1 = τi + Ti + ε.
Step 6 Update i = i+ 1 and repeat the calculations for subsequent intervals (return to 1).
Steps 2÷4 are skipped during calculation of first two intervals.
The Ti is accepted if it belonged to the group of three consecutive intervals fulfilling the (4). The validation is carried out bidirectionally, which means that in the next step intervals are accepted according to their successors. A given interval is considered as incorrect only if it does not meet the criteria in both directions.
Reference data statistics
Signal loss [%]
Number of heart beats
Mean FHR [bpm]
STI Mean ± SD
9.17 ± 2.40
7.37 ± 0.75
6.54 ± 0.65
Comparison with reference signal
As the research material consisted of three recordings, the results were describing the cumulative data (a set of ΔTi values obtained from all three recordings).
where φ i = arctg(T i /T i -1), IQR - interquartile range.
where j indicates the j-th minute of a record being analyzed.
Triangular window adjustment
A significant decrease of invalid measurements ratio (from 4.7 to 1.7%) was observed for W values being changed from 0 to 2.5. However, at the same time the interval measurement error slightly increased (from 1.83 to 1.91 ms). It can be explained by the fact that the fragments of signal, in which the correct measurement was only possible with application of the triangular window, usually contained strong interferences.
Further increase of W values (from 3 to 6) did not affect the invalid measurements ratio, while the interval error ΔTi increased up to 2.20 ms, because the window was too narrow to follow the beat-to-beat changes of FHR. Finally the W = 2.5 as an optimal value was established for further signal processing.
Ti measurement accuracy
The accuracy of interval measurement
Median (|ΔTi|) [ms]
1.48 ± 6.82
0.24 ± 3.35
0.18 ± 3.05
0.08 ± 3.51
0.09 ± 3.59
0.19 ± 3.67
0.33 ± 4.13
0.48 ± 4.54
STI determination accuracy
Comparison with others
In order to evaluate our approach, we compared it with the method of beat-to-beat FHR determination proposed by Peters et al. , as the only one providing the time event series representation and being described in details, which enable its implementation. As opposed to ours, it is based on single measurement of a given cardiac cycle, by means of preliminary detection of heart beat locations in time, for which a signal window is set. Then, an autocorrelation procedure is applied to each of these windows, providing one instantaneous periodicity measurement for each detected heart beat. Implementation of this method, supported by the same validation rules as applied to our method (4), enabled objective comparison of the accuracy of cardiac interval measurement, the STI indices calculation as well as the number of rejected invalid measurements.
Comparison with other method
Invalid measurement ratio [%]
Correl. coeff. r
An alternative approach was presented by Lee et al. , who used a sliding window to obtain multiple estimates for FHR corresponding to each cardiac cycle which, comparing with Peters' method, improved the immunity to noise. However, the resulting FHR values were in form of evenly distributed samples. Thus, as we would like to evaluate the accuracy on a beat-to-beat basis (which is required to calculate variability indices), we could not relate our results to this method.
The investigation of the proposed signal processing technique was carried out for lengths of AF window changing from 1.5 to 4 Ti. For windows shorter than 2 Ti the correct periodicity measurement is possible only if the window includes two corresponding events of the subsequent cardiac cycles. Fortunately, in the Doppler ultrasound signal each cardiac cycle is represented by a number of different events. Thus, even when some of them are missing, the AF peak remains visible. That is why the results for window length of 1.75 Ti do not differ too much from those for 2 Ti window. On the other hand, extending the window from 2 Ti to even 2.25 Ti noticeably increases the negative variability error δSTI. We showed that even relatively small errors of interval measurement, caused by AF period averaging, lead to a significant decrease of the FHR variability index STI.
Comparing our method with the one proposed by Peters et al. we noted very similar accuracy of measured intervals. But slightly better results concerning the variability indices were noted for single measurement method (mean relative error of -5.1%). It confirms that reliable evaluation of FHR signals requires also an assessment of short-term variability, since it does not depend directly on the accuracy of interval measurement. Nevertheless, in case of both methods the mean relative error of short-term variability did not exceed -7%, which could be an acceptable result.
In the work , the accuracy of the fetal heart rate estimation was evaluated for MT-430 fetal monitor (Toitu, Japan) with built-in autocorrelation function. The authors concluded that even the new-generation fetal monitors are not capable of providing the FHR signals with accuracy enough for reliable beat-to-beat variability assessment. Too long AF window causes considerable averaging of measurements, and in consequence a loss of information concerning the true variability. For that fetal monitor the mean absolute error of intervals was equal to 2.98 ms with standard deviation of 4.18 ms. The relative error, while computing the STI variability index, was equal to -39.5%. These results are similar to those obtained in this work but assuming the window length in a range from 3.5 to 4 Ti. Nevertheless, our new processing technique significantly improves the accuracy of the variability index calculation if shorter windows are applied. The values of mean absolute error and its standard deviation (obtained for selected window length of 2 Ti) equal to 1.91 ms and 3.48 ms respectively, are much better than those reported for MT-430 fetal monitor. In consequence, the relative error of the STI calculation was also significantly lowered (-6.9%).
The results show that autocorrelation technique allows us to obtain reliable parameters describing the beat-to-beat FHR variability, but only when the length of the applied window stays close to two periods of a heart activity. Thus, to achieve the highest accuracy of interval measurement, a precise adaptive algorithm for adjustment of window length is necessary. We noticed that even a shorter window enables to correctly determine the signal periodicity. However, lower accuracy of interval measurement and higher number of intervals rejected by validation criteria make such short window useless. The comparison with another known approach to the FHR estimation  revealed that our method offers the same accuracy of interval measurement and slightly higher values of the short-term variability error (slightly higher for our method). However, the biggest advantage of the proposed solution over the other is the three times lower number of invalid measurements.
In a future we are going to record much more Doppler ultrasound signals, especially during pregnancy, where the reference signal will be provided by an indirect electrocardiography, i.e. from electrodes placed on maternal abdomen. Since abdominal signals are much more comfortable for the patients, considerably more recordings should be collected. Therefore, we will be able to test our processing methods with more representative material, as well as to investigate its efficiency during standardized clinical patterns of the Doppler ultrasound signal (e.g. acceleration/deceleration episodes). Another field of interest is to assess the noise immunity of our method, which is a key issue for accurate variability measurement, due to a short autocorrelation windows applied. This research work should help us to develop the optimal signal processing techniques, that could be implemented in a prototype mobile Doppler ultrasound signal recorder developed as an add-on PC card.
This work was in part financed by the Polish Ministry of Science and Higher Education, and by the Polish National Science Centre.
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