FOSTER: A Comprehensive Pipeline for Transabdominal Fetal Pulse Oximetry Validated in a Large Animal Model of Pregnancy

Abstract

Objective:

Transabdominal fetal pulse oximetry (TFO) has the potential to supplement present intrapartum fetal monitoring approaches, which cannot accurately detect fetuses at risk of birth asphyxia. However, non-invasive measurement of fetal oxygen saturation (fSpO₂) is challenging due to dominant maternal tissue signals. We present methods to overcome such challenges, enabling robust and continuous fSpO₂ measurement.

Methods:

We introduce FOSTER (Fetal Oxygen SaTuration EstimatoR), a comprehensive pipeline that combines novel signal processing and machine learning techniques to process photoplethysmogram (PPG) signals and estimate continuous fSpO₂. Using controlled desaturation experiments in pregnant ewes, we evaluate FOSTER’s performance with both mixed maternal-fetal signals and isolated fetal components.

Results:

Processing isolated fetal signals improves estimation accuracy with respect to arterial blood oxygen saturation (SaO₂), showing improvements of 13.7% in mean absolute error (MAE) and 10.5% in Pearson correlation coefficient relative to using mixed TFO signals alone. A dual-branch neural network, processing mixed and isolated PPG signals simultaneously, achieves additional improvements of 6.3% in MAE and 4.1% in Pearson correlation compared to using isolated fetal signals alone.

Conclusion:

The FOSTER pipeline demonstrates significant improvements in continuous fSpO₂ estimation accuracy through advanced signal processing and a dual-branch architecture, establishing a foundation for reliable fSpO₂ monitoring.

Significance:

This work represents an important innovative step toward accurate, continuous, and non-invasive monitoring of fetal oxygenation. The validated methods in animal studies establish a foundation for advancing the development of fetal monitoring systems, offering new possibilities for improved maternal-fetal care.

I. Introduction

Assessment of fetal well-being during labor presently relies on cardiotocography (CTG), through which fetal status is evaluated via interpretation of fetal heart rate tracings and uterine activity [1]. While this technology aims to identify fetuses at risk of hypoxic distress, it has significant limitations. Most critically, CTG alone leads to frequent misidentification of healthy fetuses as hypoxic, contributing to unnecessary C-sections without improving neonatal outcomes [2], [3].

The lack of direct measurement of fetal oxygenation represents a fundamental limitation in current monitoring approaches [4]. An invasive transvaginal fetal pulse oximeter, evaluated in multicenter trials [5], [6], positioned a sensor against the fetal face during labor after membrane rupture, to measure fetal blood oxygen saturation (fSpO₂). A 2014 Cochrane Systematic Review found that the combination of transvaginal fetal pulse oximetry and CTG did not significantly impact the overall rate of cesarean sections [7]. However, a more recent review found a reduction in cesarean deliveries specifically for non-reassuring fetal status when fetal pulse oximetry is used in cases with existing fetal concerns [8]. Despite an FDA approval in 2000, transvaginal fetal pulse oximetry was later commercially discontinued.

Transabdominal fetal pulse oximetry (TFO) is a non-invasive approach with potential for integration into existing monitoring systems [9]. Continuous-wave near-infrared spectroscopy (CW-NIRS) for transabdominal monitoring has been investigated since the early 2000s [10], [11], with feasibility explored through computational modeling [12], [13], phantom studies [14], [15], and limited clinical trials [16]–[18]. Recognizing the potential of this technology, the FDA has granted “Breakthrough Device” designation to Raydiant Oximetry’s Lumerah, an investigational non-invasive fetal pulse oximeter, though technical details and validation results remain publicly unavailable [19]. A comparative table of fetal pulse oximetry approaches can be found in supplementary materials.

The TFO system places near-infrared (NIR) light sources and an array of photodetectors on the maternal abdomen to acquire photoplethysmogram (PPG) signals containing a mixture of maternal and fetal components [20]. While similar in principle to conventional pulse oximetry, TFO must detect signals that traverse substantial depths of tissue to reach the fetus. Consequently, the measured mixed signals contain strong maternal physiological components from cardiac activity, respiration, and Mayer waves, while the fetal components are significantly attenuated [10], [18].

Several key challenges must be addressed before TFO can achieve clinical viability [21], [22]. Traditional pulse oximetry calibration methods prove inadequate for transabdominal measurements due to complex optical properties of deep tissue. Signal processing poses another major hurdle, as fetal components represent a tiny fraction of the overall measured signal, making reliable extraction particularly demanding [17].

Recent innovations in signal separation, particularly the development of Deep Harmonic Finesse (DHF), present new opportunities to advance TFO technology [23]. This novel approach uses deep image priors and in-painting of data in time-frequency space to extract fetal components from mixed physiological signals [23], [24]. DHF can effectively separate quasi-periodic signals even with limited data, making it particularly suitable for fetal monitoring applications where high-quality data is scarce [23].

Despite these advances, research gaps remain in achieving reliable continuous monitoring of fetal oxygen levels [9]. First, existing approaches typically rely on either unprocessed mixed signals or focus exclusively on signal separation techniques without addressing the subsequent conversion to fSpO₂ values. Second, there is a lack of comprehensive methodologies that combine advanced signal enhancement with sophisticated estimation algorithms (such as neural network approaches) for continuous fetal oxygen monitoring. Third, current systems rarely leverage the complementary information present in both mixed and isolated signal components.

Our work addresses these gaps through FOSTER (Fetal Oxygen SaTuration EstimatoR), a comprehensive fSpO₂ estimation pipeline with several key contributions:

• Integration of deep learning based fetal signal separation methods, namely DHF, with a custom multilayer perceptron (MLP) architecture that integrates multiple channels of data streams to enhance estimation accuracy.

• Comparative evaluation of different signal processing approaches, demonstrating significant improvements in fSpO₂ estimation when using DHF-isolated fetal PPG signals over unprocessed mixed-PPG measurements.

• A dual-branch MLP that processes both isolated and mixed-PPG signals to leverage their complementary information, achieving additional performance gains.

• Validation against gold-standard arterial blood gas measurements (fSaO₂) using a pregnant ewe model in controlled desaturation experiments.

FOSTER establishes a robust foundation for future development of viable continuous monitoring systems for fSpO₂.

II. Transabdominal Fetal Pulse Oximetry

Transabdominal fetal pulse oximeter (TFO) enables non-invasive fSpO₂ monitoring via CW-NIRS [10], [20]. The TFO system comprises three core components: (1) an optical probe (optode), shown in Fig. 1a, featuring two NIR LEDs (${\lambda }_1=740\text{nm},{\lambda }_2=850\text{nm}$) and five photodetectors, with integrated transimpedance amplifiers, placed at distances of 1.5cm, 3cm, 4.5cm, 7cm and 10cm from the LEDs [26]; (2) an embedded control system that modulates the LEDs at 690Hz-930Hz, adjusts drive currents, and samples photodetector outputs using a high-resolution analog-to-digital converter with programmable gain amplifiers; (3) a custom software interface for data acquisition and management [14]. An illustration of TFO is presented in Fig. 1b. Detected photons are spatially distributed in a banana-shaped pattern, with deeper-penetrating photons more prominently captured by detectors that are more distant from the light source. Signal strength diminishes exponentially as detection distance increases [20]. The resulting PPG signals contain strong components of maternal systemic physiology (cardiac, respiratory, Mayer waves) mixed with substantially weaker signals due to fetal cardiac cycle, necessitating extensive data processing to isolate key features of the fetal PPG for fSpO₂ estimation [25], [27].

Fig. 1:

(a) Picture of Optical Probe (Optode) [25].(b) Illustration of the TFO concept and light path as envisioned for human application. The current study presents preclinical validation in ewes.

Deriving fSpO₂ from TFO’s PPG measurements builds on conventional pulse oximetry principles and the differential modified Beer-Lambert law (dMBLL) [28]. Per dMBLL, changes in light absorbance ($\Delta A$) during arterial pulsation are proportional to changes in concentrations of oxygenated and deoxygenated hemoglobin [28]. $\Delta A$ can be measured by taking the ratio between diastolic light intensity ($I_{\mathit{\text{diastole}}}$, representing $DC+AC$ amplitude) and baseline light intensity at systole ($I_{\mathit{\text{systole}}}$, representing the $DC$) [29]. For details on derivation of $\Delta A$, please refer to supplementary materials.

In the context of TFO, changes in light absorbance due to fetal pulsation are quite small. To address the numerical issue for downstream tasks in the data processing pipeline, we define Exponential Pulsation Ratio (EPR) as given in (1), which expands the range of empirically-observed values of $\Delta A$. EPR is calculated separately for each of the five photodetectors and both wavelengths over time. $DC$ and $A{C}_{\mathit{\text{fetal}}}$ would need to be estimated from mixed maternal-fetal PPG measurements.

$$EPR=\text{exp}(\Delta A)=\frac{DC+A{C}_{\mathit{\text{fetal}}}}{DC}$$ (1)

The TFO system encounters multiple challenges in achieving reliable deep tissue oxygen saturation measurements. The PPG recordings are dominated by maternal physiological signals, including maternal cardiac activity (1–2Hz), breathing patterns (0.2–0.6Hz), and low-frequency Mayer Waves (≈0.1Hz). While fetal cardiac signals typically occur between 1.8–4Hz, their detection is complicated by harmonic components of maternal signals that overlap with this frequency range, rendering traditional filtering techniques ineffective [17], [30]. Additionally, the substantial tissue penetration required for fetal monitoring results in significant light attenuation and very low signal-to-noise ratio (SNR) [22]. System performance is further impacted by physiological variations among subjects, temporal changes within individuals, and environmental factors that can lead to signal degradation [14]. Spectral analysis of a 16-minute TFO recording, shown in Fig. 2, highlights these challenges. The fetal heart rate (FHR), contoured in black, exhibits considerable frequency variability and fluctuating signal strength, with a notable amplitude decrease between minutes 32–34. The spectral data also reveals the prominent maternal heart rate (MHR) harmonics that frequently overlap with fetal signals, compromising the accuracy of fetal AC amplitude essential for fSpO₂ calculations. Furthermore, motion artifacts can saturate the detector and elevate the noise floor, substantially altering the amplitude characteristics of physiological signals. These observations underscore the dynamic nature of the confronted challenges.

Fig. 2:

Spectrogram of a TFO PPG recording, showing challenges of isolating fetal signal.

III. Methods

In this paper, we propose a systematic pipeline for estimating fetal oxygen saturation from transabdominal measurements. The pipeline, called FOSTER (Fetal Oxygen SaTuration EstimatoR), consists of four major stages: (1) signal acquisition with TFO using two NIR wavelengths and 5 photodetector channels to produce 10 channels of mixed PPG measurements, (2) extraction of DC and fetal AC components, (3) computation of EPR as defined in (1), and (4) fetal SpO₂ estimation. Fetal EPR computation requires extraction of DC and fetal AC components from TFO-captured mixed PPG signals. This section presents two different methods for extracting fetal AC. The first method uses lock-in detection to extract fetal AC from mixed PPG measurements. The second method isolates fetal PPG with a deep image prior based network, then extracts fetal AC amplitude using a custom time-series peak detection algorithm. We also present two machine learning based fSpO₂ estimation models that process these differently extracted features: a base model that processes EPR features from either mixed PPG or isolated fetal signals, and an enhanced dual-branch architecture that simultaneously processes both types of EPR features. Fig. 3 shows a high-level overview of the proposed FOSTER pipeline.

Fig. 3:

High-level overview of the FOSTER pipeline for fetal oxygen saturation estimation.

A. DC Component Extraction

DC component of the PPG signal, which in TFO represents a complex mixture of maternal and fetal blood volumes, tissue absorption, and scattering properties, is extracted using lower envelope detection. This method tracks minimas over time to capture non-pulsatile components, as shown in Fig. 5. After extraction, we smooth the DC signal using a moving average filter. This step reduces high-frequency noise and artifacts while preserving the underlying baseline trend. The filter window size is selected to balance between noise reduction and maintaining physiologically relevant variations in DC.

Fig. 5:

Diagram of DC and fetal AC extraction from mixed PPG.

Motion Artifact Compensation:

Environmental changes and motion can destabilize the DC component, and cause SNR fluctuations. Accurate motion artifact detection and compensation is crucial for reliable DC component extraction. We use a two-stage approach: (1) identify motion-corrupted segments through manual annotation, and (2) reconstruct the signal using Piecewise Cubic Hermite Interpolating Polynomial (PCHIP).

The annotation process examines consecutive 1-minute windows with 10-second overlap, analyzing both temporal and spectral characteristics. In the time domain, motion artifacts present as sudden amplitude spikes and baseline shifts. In the frequency domain, these artifacts manifest as broadband noise elevation and distinct horizontal streaks in the spectrogram. PCHIP interpolation is selected for signal reconstruction due to its ability to preserve local monotonicity while ensuring C1 continuity at window boundaries. This property is important for maintaining physiologically plausible transitions in the reconstructed DC component. The interpolation algorithm uses the closest clean segments on either side of the corrupted region to estimate the underlying DC trend, effectively bridging gaps in the signal while preserving the natural characteristics of PPG baseline variations. Fig. 4 shows the extracted DC amplitude over time from one channel of TFO, in an example real-world data. The DC amplitude is extracted using the lower envelope method, and a smoothing moving average filter with 1-minute windows is applied to the extracted DC prior to interpolation. Notice the abrupt jumps in the signal amplitude in the noisy time ranges affected by motion, and how they are mitigated upon smoothing and interpolation.

Fig. 4:

Example PPG data captured from one channel TFO, showing labeled motion artifacts and DC interpolation.

B. Fetal AC Extraction

Extracting the fetal AC component is a critical step in the FOSTER pipeline, as it directly impacts the accuracy of the computed EPR values and, consequently, the final fSpO2 estimation. This section presents two distinct approaches for fetal AC extraction: lock-in detection for mixed PPG signals and peak-valley detection for isolated fetal signals obtained through the Deep Harmonic Finesse (DHF) method.

1). Lock-in AC Detection from Mixed PPG:

Lock-in detection is a technique that can extract the fetal AC component directly from the mixed PPG signal. The process involves band-pass filtering the mixed signal between the minimum and maximum FHR, then multiplying the filtered signal with sine and cosine references at the FHR frequency [31]. The resulting signals are then low-pass filtered, and the magnitude of the in-phase (I) and quadrature (Q) components, calculated as $\sqrt{I^2+Q^2}$, yields the fetal AC amplitude. This method effectively acts as a narrow bandpass filter centered at the FHR frequency, making it robust against interferences outside the FHR band while preserving the physiological pulsatile component of interest. This technique requires accurate FHR references, which can be obtained through auxiliary sensing or further processing of the TFO data [25], [32].

Due to the PPG signal shape, the AC amplitude’s energy is divided across multiple harmonics of the heart rate. Lock-in detection only outputs the amplitude at the first harmonic, which is a fraction of the overall fetal AC amplitude. This approximation is commonly used in single-body pulse oximetry [33]. Additionally, while effective against out-of-band interference, lock-in detection is susceptible to maternal signals (MRR, MHR) that spectrally overlap with fetal signal (Fig. 2). These limitations motivate the development of signal isolation techniques for better AC extraction.

2). DHF: Deep Harmonic Priors for Fetal Signal Isolation:

The Deep Harmonic Finesse (DHF) is a deep prior based image in-painting method for isolating fetal PPG signals from the mixed PPG measurements [23], [24]. DHF employs a convolutional neural network architecture called Spectrally Accurate Light U-Net (SpAc LU-Net), to separate the fetal signal from the maternal components in the time-frequency domain, using a single mixed-signal spectrogram [23]. First, we transform the mixed PPG signal using the Short-Time Fourier Transform (STFT). Then, the SpAc LU-Net processes the resulting spectrogram to in-paint the fetal signal spectrogram amplitudes in regions masked by maternal components [23]. Amplitude in-painting with DHF is performed strictly on the target signal harmonics. The noise signals’ amplitudes that do not interfere with target signal harmonics are simply replaced by the average noise floor of the spectrogram.

We propose an iterative separation approach given the relative strengths of signals in mixed TFO PPG. Fig. 6 illustrates this iterative approach. First, DHF isolates maternal respiratiron by masking maternal and fetal heart rate regions and inferring the respiration amplitude. After subtracting maternal respiration, the residual signal contains primarily maternal and fetal cardiac components. DHF then isolates maternal cardiac signals by masking FHR regions and inferring the amplitude of MHR signal. Subtracting this separated maternal component from the residual signal from the first round yields the input to the fetal PPG separation round. In this final round, remaining MHR harmonics are masked and the amplitude of the signal at FHR harmonics are inferred by DHF, yielding the final separated fetal signal spectrogram at the output. The estimated fetal spectrogram is then converted back to the time domain using the inverse STFT, yielding the isolated fetal PPG signal. This approach enables a more accurate extraction of ${\text{AC}}_{\mathit{\text{fetal}}}$ by minimizing the influence of maternal noise. More details on DHF are provided in the supplementary materials.

Fig. 6:

Diagram of multi-round fetal signal isolation with DHF.

3). Peak-Valley AC Detection for Isolated Signals:

Once the fetal PPG is isolated using DHF, we can use peak-valley detection for ${\text{AC}}_{\mathit{\text{fetal}}}$ extraction instead of lock-in AC approximation. The proposed adaptive algorithm, presented in Algorithm 1, first calculates the expected number of samples per cardiac cycle based on the instantaneous FHR. This dynamic window size accommodates heart rate variability. The algorithm then identifies peaks within each window of two cardiac cycles using adaptive thresholds based on local signal characteristics. Adaptive thresholding is beneficial for accommodating signal amplitude variations. Peak identification employs the “find peaks” algorithm, from Python’s SciPy API. Valleys are subsequently identified between consecutive peaks using similar adaptive valley thresholds, ensuring detection of true physiological minima while avoiding dicrotic notches. The AC amplitude is then constructed by creating continuous upper and lower envelopes through linear interpolation between detected peaks and valleys. This ensures the same sampling frequency as the input PPG signal. The final AC amplitude is calculated as the difference between these envelopes, with optional smoothing using moving average to reduce high-frequency artifacts.

Algorithm 1.

Isolated PPG AC Amplitude Extraction

Require: PPG $x(t)$, heart rate $f(t)$, sampling frequency $f_s$

Ensure: AC amplitude

1: function Calculate_AC_Amplitude $\left(x(t),f(t),f_s\right)$

2:  $\text{cardiac}\_\text{cycle}\leftarrow f_s/f(t)$

3:  min_dist ← 0.75 × cardiac_cycle

4:  for each window of length 2 × cardiac_cycle do

5:   local_range ← max(window) – min(window)

6:   local_mean ← Average(window)

7:   peak_thresh ← 0.15 × local_range

8:   // Peak Detection

9:   $\text{peaks}\leftarrow \text{FindPeaks}(x(t)$,

10:    distance = min_dist,

11:    prominence = peak_thresh,

12:    height = local_mean)

13:  end for

14:  // Valley Detection

15:  $\text{valleys}\leftarrow \varnothing$

16:  for each consecutive peak pair $\left(p_i,p_{i+1}\right)$ do

17:   $\text{segment}\leftarrow x(t)\left[p_i:p_{i+1}\right]$

18:   val_thresh ← 0.15 × local_range

19:   $v\leftarrow \text{FindPeaks}(-\text{segment}$,

20:    prominence = val_thresh)

21:   $\text{valleys}\leftarrow \text{valleys}\cup \{\text{arg}\text{min}(v)\}$

22:  end for

23:  // Envelope Creation

24:  upper ← LinearInterpolate(peaks)

25:  lower ← LinearInterpolate(valleys)

26:  ac_amp ← upper – lower

27:  if smoothing required then

28:   ac_amp ← MovingAverage (ac_amp)

29:  end ifreturn ac_amp

30: end function

C. Need for Accurate Heart Rate Sensing

The extraction of fetal AC using lock-in detection or DHF signal separation requires accurate reference frequencies: FHR, MHR, and MRR. These frequencies can be measured using auxiliary sensing devices, such as finger pulse oximeters for maternal readings and cardiotocography (CTG) for FHR [1], [33]. However, these external devices have inherent inaccuracies that affect reference frequency measurements. Errors in MRR, MHR and FHR degrades DHF’s isolated signal output due to inaccurate mask locations. Similarly, FHR measurement errors can distort the extracted fetal AC magnitude during lock-in or peak-valley detection, compromising EPR values and fetal SpO₂ estimation.

To address these limitations, we propose using TFO’s PPG measurements to correct the noisy reference frequencies. Fig. 7 presents a spectrogram of mixed PPG data collected with TFO, overlaid with maternal and fetal frequency readings from auxiliary devices. The top plot reveals misalignment between the reference frequency readings (MRR, MHR, and FHR) and the actual peak amplitudes in the TFO spectrogram. To correct these discrepancies, we developed a peak detection algorithm that maps each original reference frequency to the nearest peak amplitude in the TFO spectrogram within a defined search span, as described in (2). When the first harmonic coincides with strong MRR interference peaks, higher harmonics of heart rate readings can be utilized instead.

Fig. 7:

Example real-world data showing reference frequency readings from auxiliary devices are noisy and do not match with peak frequencies in spectrogram of TFO data before correction.

$$f_{\mathit{\text{correct}}}(t)=\underset{f\in \left[f_{REF}\pm f_{\mathit{\text{span}}}\right]}{\text{arg}\text{max}}\mathbf{\text{STFT}}\left\{TF{O}_{PPG}(t)\right\}(f,t)$$ (2)

D. Fetal Oxygen Saturation Estimation

The fSpO₂ estimation stage of FOSTER employs a compact MLP architecture that can be configured in three ways:

1. Mixed-PPG Configuration: Processes EPR features computed directly from mixed maternal-fetal signals.

2. Isolated Fetal Configuration: Processes EPR features computed from DHF-isolated fetal signals

3. Dual-branch Configuration: Simultaneously processes both types of EPR features

For processing mixed-PPG signals, traditional lock-in detection and lower envelope methods extract fetal AC and DC components respectively, as previously illustrated in Fig. 5. For DHF-isolated fetal signals, Algorithm 1 performs peak-valley detection to extract the AC. Furthermore, motion artifact compensation is applied through DC interpolation as detailed in Section III-A. In both cases, we generate a set of 10 EPR values over time - 5 TFO measurement channels per wavelength (${\lambda }_1=740nm$ and ${\lambda }_2=850nm$) with different source-detector separations.

The base architecture, illustrated in Fig. 8a, contains 337 trainable parameters, with an input layer accepting 10 EPR channels, two hidden layers (16 and 8 nodes) with batch normalization and ReLU activation, and a linear output layer producing fSpO₂ estimates. This compact design balances computational efficiency with estimation accuracy, considering both the limited availability of labeled TFO data and embedded deployment constraints.

Fig. 8:

Multi-layer perceptron (MLP) architectures developed for fSpO₂ estimation. (a) Base MLP architecture. (b) Dual-branch MLP architecture with shared weights.

The dual-branch variant, illustrated in Fig. 8b, extends the base architecture to 497 parameters, where the input and first hidden layer share weights between the mixed-PPG and DHF-isolated EPR branches, while the second hidden layer maintains independent weights. This shared weight architecture, called a Siamese network, promotes parameter efficiency, encourages consistent feature learning, and provides additional regularization, while allowing each branch to develop specialized processing capabilities for its respective input type.

FOSTER’s architecture is designed to accommodate different signal processing approaches, each with its own strengths and limitations. The mixed-PPG configuration preserves unaltered physiological information despite maternal interference, while the isolated fetal approach provides cleaner signals through DHF separation but may introduce artifacts during the generative separation process. The dual-branch configuration processes both types of signals simultaneously, providing robustness against the limitations of each approach.

Optimization Framework:

For predicting fSpO₂, we propose a range constrained loss function that combines weighted mean squared error with adaptive boundary constraints. Given normalized predictions $\hat{y}$ and ground truth values $y$ that have been standardized to have zero mean ($\mu$) and unit variance ($\sigma$), the loss function is defined as:

$${ℒ}_{\text{total}}={ℒ}_{\text{MSE}}+w_{\text{min}}{ℒ}_{\text{min}}+w_{\text{max}}{ℒ}_{\text{max}}$$ (3)

We incorporate subject-specific weights into the mean squared error ${ℒ}_{\text{MSE}}$ as follows:

$${ℒ}_{\text{MSE}}=\frac{\sum _i{w}_i{\left({\hat{y}}_i-y_i\right)}^2}{\sum _i{w}_i}$$ (4)

where $w_i=1/L_s$ for the $i$-th sample belonging to subject $s$ with length $L_s$. $w_i$ is constant per subject, and differs across subjects. This weighting scheme ensures each subject contributes equally to the loss function regardless of recording duration, preventing bias towards subjects with longer recordings.

The boundary constraint terms ${ℒ}_{\text{min}},{ℒ}_{\text{max}}$ penalize predictions outside the physically possible range [0,100%] for SpO₂:

$${ℒ}_{\text{min}}=\frac{1}{N}\sum _i\text{max}{\left(0,b_{\text{min}}-{\hat{y}}_i\right)}^2,{ℒ}_{\text{max}}=\frac{1}{N}\sum _i\text{max}{\left(0,{\hat{y}}_i-b_{\text{max}}\right)}^2$$ (5)

$N$ is the sample size. $b_{\text{min}}$ and $b_{\text{max}}$, defined in (6), are the normalized decision boundaries that correspond to non-normalized [0,100%] SpO₂ range. $\mu$ is the mean and $\sigma$ is the variance of the training labels $y$, before standardization.

$$b_{\text{min}}=-\frac{\mu }{\sigma },b_{\text{max}}=\frac{100\%-\mu }{\sigma }$$ (6)

The adaptive weighting coefficients $w_{\text{min}}$ and $w_{\text{max}}$ are calculated using (7), where the subscript ”constraint” refers to either ”min” or ”max” depending on the boundary being enforced, and $\lfloor \cdot \rfloor$ denotes the floor function. Equation (7) automatically scales the boundary penalty weights to similar magnitudes as the MSE loss. This formulation ensures that any physically impossible predictions are strongly penalized, regardless of their frequency in the batch.

$$w_{\text{constraint}}=\left\{\begin{array}{ll}0& \text{if}{ℒ}_{\text{constraint}}=0\\ {10}^{⌊{\text{log}}_{10}\left({ℒ}_{\text{MSE}}/{ℒ}_{\text{constraint}}\right)⌋}& \text{otherwise}\end{array}\right.$$ (7)

In the extended dual-branch architecture, we incorporate an additional alignment loss term, ${ℒ}_{\text{align}}$, to encourage consistency between the feature representations of the mixed-PPG and DHF-isolated fetal EPR branches:

$${ℒ}_{\text{align}}={‖{\mathbf{f}}_{\text{mixed}}-{\mathbf{f}}_{\text{isolated}}‖}_2^2$$ (8)

where ${\mathbf{f}}_{\text{mixed}}$ and ${\mathbf{f}}_{\text{isolated}}$ represent the feature vectors output by each respective branch. This consistency loss term promotes similar internal representations regardless of input signal type, with the total loss becoming:

$${ℒ}_{\text{total-V2}}={ℒ}_{\text{MSE}}+w_{\text{min}}{ℒ}_{\text{min}}+w_{\text{max}}{ℒ}_{\text{max}}+w_{\text{align}}{ℒ}_{\text{align}}$$ (9)

The alignment loss helps ensure that the network learns consistent feature representations from both signal paths despite their different preprocessing methods. The weighting parameter $w_{\text{align}}$ balances the importance of this feature consistency against the primary fSpO₂ prediction task.

IV. Experimental Results

A. In-Vivo Data Collection

Animal studies for TFO validation were conducted on six near-term pregnant ewes (gestational age 136–140 days) following ethics approval from University of California Davis’ Institutional Animal Care and Use Committee (IACUC) [34]. Each ewe was anaesthetized with stable respiration controlled by an external ventilator, and reference MRR values were recorded. Controlled fetal hypoxia was induced using an inflatable balloon catheter in the ewe’s infra-renal aorta, with mean arterial pressure (dMAP) reduced in 5mmHg steps held for 10 minutes each. This stepped protocol was designed to generate a wide range of fSaO₂ values needed to validate the TFO device’s measurement accuracy. Ground truth fSaO₂ was measured via fetal carotid arterial blood gas (ABG) samples at 2.5min, 5min and 10min marks of each dMAP step, while TFO data was continuously collected at 8kHz (later downsampled to 80Hz). Reference FHR was recorded at 1Hz through an arterial line placed in the fetus’ neck, while MHR was monitored using a conventional pulse oximeter.

A desaturation round ended when fSaO₂ dropped below 15%, and the balloon was deflated to allow fetal recovery. A second round was performed only after successful recovery, with four animals completing two rounds and two completing one round, totaling ten rounds of 20 minutes to 1 hour each. Fig. 9b illustrates the experimental setup, while Fig. 9a shows the TFO device in one of the experiments. The sampled fSaO₂ measurements from ten rounds presented in Fig. 10 shows that de-saturation was performed in a controlled fashion.

Fig. 9:

(a) Photo from in − vivo experiment showing different components of TFO System. (b) Illustration of controlled fetal de-saturation experiment in pregnant ewe model [34].

Fig. 10:

Gold standard fSaO₂ labels in ten hypoxic rounds.

B. Training and Validation

The cross-validation scheme for fSpO₂ estimation addresses temporal dependencies in the data by dividing each hypoxic round into five sequential folds, avoiding information leakage among consecutive EPR samples. Four folds are used for training and one for validation. Due to the characteristic decline in fSaO₂ during balloon inflation, validation folds are rotated across different time segments to ensure balanced representation of oxygen saturation levels.

The MLP architectures used for fSpO₂ estimation are trained using Adam optimizer (learning rate: 1e-4, weight decay: 1e-5). The models are trained using their respective loss functions defined in (3) and (9). For the dual-branch MLP, the alignment weight $w_{\text{align}}$ is set to 0.1 to maintain a balance between feature consistency and prediction accuracy. Network weights are initialized from a Kaiming normal distribution with zero biases. Training runs for 300 epochs with a batch size of 32, and model parameters that achieve the best validation performance are retained for deployment.

C. fSpO₂ Estimation Results

From PPG data at 80 Hz, EPR values are computed at 1Hz and smoothed using a 90-second moving average window. Continuous fSpO₂ estimation is performed for each experimental round. We evaluate model performance using EPRs calculated from: (1) mixed TFO measurements with lock-in detection of ${\text{AC}}_{\text{fetal}}$, and (2) DHF-isolated signals with peak-valley detection of ${\text{AC}}_{\text{fetal}}$. The dataset contains 18,933 fSaO₂ labels. Model outputs are downsampled to provide fSpO₂ every 30 seconds for clinically relevant temporal resolution.

Model performance is evaluated using Pearson’s correlation coefficient (r), mean absolute error (MAE) and Bland-Altman analysis on validation data. At each cross-validation fold, estimated fSpO₂ is compared with gold standard fSaO₂ from blood gases, using a 20%−80% validation-training split. To ensure robust performance evaluation and fair comparison between approaches, we conduct five MLP training runs with different random seeds. This multiple-run approach helps capture the general characteristics of estimation performance while accounting for the inherent variability in neural network training. We report both the best and the average performance metrics. The best seed is selected based on highest correlation.

The estimation results demonstrate significant improvements across FOSTER’s data processing approaches. As shown in Table I, using DHF-isolated EPR inputs achieves a best-case Pearson’s r correlation of 0.76 with ground truth fSaO₂ measurements, compared to 0.69 with mixed-PPG EPR inputs, representing a 10.2% improvement. The dual-branch MLP further improves the best-case correlation to 0.80, marking an additional 5.3% improvement. All correlations showed statistical significance (p<0.001). The correlations are reported for the aggregated total validation samples across all folds. The best-case correlation plots for individual folds of cross-validation are included in supplementary materials.

Table I:

Performance comparison of FOSTER with mixed-PPG EPR inputs, DHF-isolated EPR inputs, and dual-branch configuration. Results show both best-case performance and average metrics across five random initializations.

	Pearson’s r Correlation		Mean Absolute Error (%)		Mean Difference (fSpO2−fSaO2) (%)		Limits of Agreement (fSpO2−fSaO2) (%)
	Best	Mean±SD	Best±SD	Mean±SD	Best	Mean	Best	Mean
FOSTER w/ Mixed-PPG EPR	0.69	0.67±0.02	6.47±5.45	6.96±6.37	−0.58	0.16	[−17.18, 16.02]	[−18.50, 18.82]
FOSTER w/ DHF-isolated EPR	0.76	0.74±0.02	6.01±4.96	6.01±5.31	0.34	−0.03	[−14.99, 15.68]	[−15.76, 15.71]
FOSTER w/ dual-branch EPR	0.80	0.77±0.02	5.40±4.40	5.63±4.84	0.06	0.09	[−13.82, 13.94]	[−14.53, 14.71]

For mean absolute error (MAE) in estimating fSpO₂, the best-case performance improves from 6.47% with mixed-PPG inputs to 6.01% with DHF-isolated inputs (7.1% improvement), and the dual-branch approach further reduces the MAE to 5.40% (10.2% improvement over DHF-isolated inputs alone). The best-case standard deviation of absolute fSpO₂ estimation error shows consistent improvement, reducing from 5.45% to 4.96% with DHF-isolated inputs, and further to 4.40% with the dual-branch configuration, indicating increasingly consistent estimation performance.

Bland-Altman analysis of the best-case models also shows progressive improvement in agreement between our fSpO₂ estimates and fSaO₂ gold standard measurements. FOSTER with mixed-PPG EPR inputs shows a mean difference of −0.58% between fSpO₂ and fSaO₂, with 95% limits of agreement from −17.18% to 16.02%. The DHF-isolated EPR approach improves agreement with a mean difference of 0.34% and narrower limits from −14.99% to 15.68% (13% reduction in spread). The dual-branch architecture achieves the best agreement with a near-zero mean difference of 0.06% and limits from −13.82% to 13.94% (additional 11% reduction). Fig. 11 shows consistent performance across the full oxygen saturation range (10–60%) with no obvious trends in differences. Notably, the dual-branch architecture maintains more uniform scatter across all desaturation rounds, suggesting robust performance across different physiological conditions.

Fig. 11:

Bland-Altman plots showing the best-performing model among multiple random seed initializations, each evaluated using 5-fold cross-validation. The aggregated results from all folds are plotted. Results are shown for fSpO2 estimates using different FOSTER configurations: (a) mixed-PPG EPR inputs, (b) DHF-isolated EPR inputs, and (c) dual-branch MLP architecture.

Across five random initializations of MLP weights, FOSTER maintains consistent mean performance, as seen in Table I. The average correlation coefficient improves from moderate (0.67) with mixed-PPG inputs to high with DHF-isolated inputs (0.74), representing a 10.5% improvement. The strength of correlation is interpreted using the guideline in [35]. The dual-branch approach achieves the highest average correlation (0.77) and lowest average MAE (5.63%), demonstrating improvements of 4.1% in correlation and 6.3% in MAE compared to using DHF-isolated inputs alone. The average Bland-Altman analysis maintains similar trends, with mean differences of 0.16%, −0.03%, and 0.09% for mixed-PPG, DHF-isolated, and dual-branch approaches respectively. The corresponding average limits of agreement are [−18.50%, 18.82%], [−15.76%, 15.71%], and [−14.53%, 14.71%], demonstrating consistent improvement in measurement agreement. These results establish that the dual-branch model provides reliable estimation by effectively leveraging both inputs.

An analysis of absolute errors across individual desaturation rounds is presented in Fig. 12 through boxplots comparing all configurations. While FOSTER with DHF-isolated fetal EPRs demonstrate marked improvements in estimation accuracy for rounds 1−3, 5, and 7 compared to mixed-PPG EPRs, using both EPR inputs with the dual-branch approach shows consistent improvement in nearly all rounds. The dual-branch architecture maintains lower median errors and smaller interquartile ranges (IQR) even in rounds 4, 6, 8, 9, where DHF-isolated signals showed slight degradation compared to mixed-PPG inputs. These findings suggest that combining both signal types helps maintain robust performance across varying experimental conditions and physiological states.

Fig. 12:

Absolute fSpO₂ estimation errors per desaturation round for different FOSTER input EPR approaches. Boxplots show quartiles, median, mean, and non-outlier ranges across five random seed initializations and all validation samples from five cross-validation folds. Outliers are errors < Q1 – 1.5IQR or > Q3 + 1.5IQR.

V. Discussion

This study represents an essential first step in the translational spectrum of TFO, providing proof-of-concept and preliminary validation in a preclinical setting. The FOSTER pipeline demonstrates significant improvements in fSpO₂ estimation accuracy through advanced signal processing and machine learning techniques. TFO serves as a valuable research tool that could enable scientific study of intrapartum fetal physiology beyond what is possible with current methods. This technology provides a platform for developing a deeper understanding of fetal responses during labor, with potential benefits extending beyond direct impact on C-section rates. Continuous TFO monitoring combined with modern data analytics could conceptually enable more sophisticated and personalized approaches to fetal health assessment. Our validation methodology demonstrates the model’s ability to estimate oxygen saturation at unseen time points through time-separated cross-validation. Each measurement involves a unique maternal-fetal geometry, with our approach assuming similar geometric configurations exist in the training set. With our limited dataset (6 animals, 10 rounds), this cross-validation approach was appropriate, though it does not assess generalizability to completely unseen subjects. This limitation stems from dataset size rather than architectural constraints and would likely be mitigated with larger, more diverse datasets. The consistent improvement observed across mixed-PPG, DHF-isolated, and dual-branch architectures remains valid and provides meaningful evidence that the approach can track dynamic changes in fetal oxygenation once calibrated.

While this study demonstrates effective fetal signal isolation and oxygen saturation estimation in a sheep model, important challenges remain before clinical translation. A key limitation is the thicker maternal tissue in humans versus sheep (4–5+ cm vs 2–3 cm), resulting in more attenuated fetal signals in human applications. Additional translational challenges include managing the effects of uterine contractions, changes in blood flow, and more frequent maternal/fetal movement during labor. Ongoing intrapartum studies aim to validate the feasibility of TFO in humans. However, this animal study provides an important foundation for clinical translation by demonstrating robust fetal signal isolation and oxygen estimation across a wide range of known fetal SaO2 values, establishing a critical proof-of-concept for this promising technology.

VI. Conclusion and Future Work

In this paper, we presented FOSTER, a pipeline for TFO that combines advanced signal processing with deep learning for fetal oxygen saturation estimation. We demonstrated its effectiveness in monitoring a wide range of fetal oxygenation levels using pregnant ewe experiments. Our proposed dual-branch estimation approach, which processes both mixed and DHF-isolated signals, provides a more robust solution than using either signal type alone. TFO has the potential to improve fetal outcomes by providing clinicians continuous fetal SpO₂ during labor. Future work will focus on expanding our dataset to improve generalizability across subjects and investigating the effects of maternal tissue thickness, placental location, and uterine contractions on measurement accuracy.