# Robust estimation of fetal heart rate from US Doppler signals

Iulian Voicu, Jean-Marc Girault, Morgane Fournier-Massigan, Denis Kouamé

► To cite this version:

Iulian Voicu, Jean-Marc Girault, Morgane Fournier-Massigan, Denis Kouamé. Robust estimation of fetal heart rate from US Doppler signals. International Congress on Ultrasonics (ICU 2009), Jan 2009, Santiago, Chile. Elsevier, 3, pp.691 - 699, 2009. [hal-01076350](https://hal.science/hal-01076350)

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https://hal.science/hal-01076350

Submitted on 21 Oct 2014

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<figure><img src="image_1.png" /></figure>
# Robust Estimation of Fetal Heart Rate from US Doppler Signals

I.Voicu¹, J.-M. Girault¹, M. Fournier-Massigan.², D. Kouamé³

¹Université François Rabelais, 2 bis boulevard Tonnellé, BP3223, 37032 Tours Cedex, jmgirault@univ-tours.fr, France

²CHRU Bretonneau, 2 boulevard Tonnellé, BP3223, 37032 Tours, France

³ Université Paul Sabatier, IRIT UMR 5505, 118 Route de Narbonne, 31062 Toulouse Cedex 9, France

<figure><img src="image_2.png" /></figure>

## I. Introduction

In utero, Monitoring of fetal wellbeing or suffering is today an open challenge, due to the high number of clinical parameters to be considered. An automatic monitoring of fetal activity, dedicated for quantifying fetal wellbeing, becomes necessary. For this purpose and in a view to supply an alternative for the Manning test, we used an ultrasound multitransducer multi-gate Doppler system. One important issue (and first step in our investigation) is the accurate estimation of fetal heart rate (FHR). An estimation of the FHR is obtained by evaluating the autocorrelation function of the Doppler signals for ills and healthiness fœtus. By modifying the existing method (autocorrelation method), we reduce to 5% the probability of non-detection of the fetal heart rate. These results are really encouraging and they enable us to plan the use of automatic classification techniques in order to discriminate between healthy and in suffering foetus.

## II. Equipment

<figure><img src="image_3.png" /><figcaption>Figure 1: Actifoetus System</figcaption></figure>

* 3 groups of 4 sensors, each sensor with 5 exploring depths adjustable between 1,88 cm up to 15cm

* Emission Frequency: 2.25 MHz

* Acoustic Driving Power: 1mW/cm²

* Pulse Repetition Frequency: 1kHz

## III. Objectif

* We want to estimate the fetal heart rate in a long term monitoring. The Doppler signal generated by the fetal moving is disturbed by others Doppler sources (mother's moving, pseudo breathing...).

### Part 1: Fetal Heart Rate (FHR) Estimation (sliding window W)

$$ I_i(t, k) = \frac{1}{W} \sum_{n=1}^{W-k-1} x(t, n) \cdot x(t, n+k) $$

1. find the positions $M_0, ..., M_N$ of maximums of the function $I_i$;

2. compute the distances between the positions of two consecutive maximums: $D_n = M_n - M_{n-1}$, $n=1, ..., N-1$

3. verify that the differences between the maximum's positions ensure a true physiological rhythm:

$$ \Delta_n = |D_n - D_{n-1}| < \varepsilon, n = 1, ..., N-1 $$

$$ \Delta = \{\Delta_1, ..., \Delta_{N-2}\} $$

* if $\Delta < \varepsilon$ => the rhythm is: $FHR = mean(\Delta)$

* if not so => no cardiac rhythm detection

<figure><img src="image_4.png" /><figcaption>Figure 2: Fetal Heart Rate Estimation</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>Figure 3: Autocorrelation technique: Fetal Heart Rate: Sensor 2 Depth 3</figcaption></figure>

## Part 2: Fetal Heart Rate Fusion

### Algorithm 1

1. Identify the number $P(t_{n+1})$ of signals with 1Hz<FHR<4Hz at time $t_{n+1}$

2. Find the values of auto-correlation function $I_1(t_{n+1}, S_i, D_j)$

3. Sort the $I_1(t_{n+1}, S_i, D_j)$ in descending order. In case of equals values choose the channel with higher probability $\Omega(t_n, S_i, D_j)$

$$ FHR(t_{n+1}) = \arg \max (I_1(t_{n+1}, S_i, D_j), \Omega(t_n, S_i, D_j)) $$

4. Update the detection probability $\Omega(t_{n+1}, S_i, D_j)$

<figure><img src="image_6.png" /></figure>

### Algorithm 2

1. Find the signals:

$$ \begin{aligned} FHR(t_{n+1}, S_i, D_j) &< |\mu_{FHR}(t_n) - 3\sigma_{FHR}^2(t_n)| \\ FHR(t_{n+1}, S_i, D_j) &< |\mu(t_n, S_i, D_j) - 3\sigma^2(t_n, S_i, D_j)| \end{aligned} \quad \sum_{p=1}^{P(t_{n+1})} k_p(t_{n+1}, S_i, D_j) = 1; $$

3. Find the new heart rate

$$ FHR(t_{n+1}) = \sum_{p=1}^{P(t_{n+1})} k_p(t_{n+1}, S_i, D_j) \cdot FHR(t_{n+1}, S_i, D_j) $$

2. Find the weights $k(t_{n+1}, S_i, D_j)$

$$ k_p(t_{n+1}, S_i, D_j) = \frac{1}{\sigma_p^2(t_n, S_i, D_j) \cdot \sum_{p=1}^{P(t_{n+1})} \left( \frac{1}{\sigma_p^2(t_n, S_i, D_j)} \right)} $$

<figure><img src="image_7.png" /></figure>

## IV. Experimental Results

<figure><img src="image_8.png" /><figcaption>Reference Sonicaid</figcaption></figure>

<figure><img src="image_9.png" /><figcaption>Alg. 1: Sliding window 2s, Overlapping 250ms</figcaption></figure>

<caption>Alg. 2: Sliding window 2s, Overlapping 250ms</caption>

## IV. Conclusions

* auto-correlation is the method which gives the best trade-off in terms of probability detection and number of operation

* the size of the analysing window and the overlapping step are very important

* the second fusion algorithm seems give a better estimation of the fetal heart rate comparing with the first fusion algorithm

## V. Perspectives

* estimate FHR using the other groups of sensors

* estimate the FHR applying the algorithms over sets of grouped signals (i.e. same depth)