The effects of asymmetric volume conductor modeling on non-invasive fetal ECG extraction

There are a number of source models available to approximate cardiac electrical activity, ranging from the point dipole to the equivalent double layer (EDL). For an in-depth discussion of these models and their physiological basis, the reader is referred to Malmivuo and Plonsey (1995). The source model used in the fecgsyn toolbox is the point dipole due to its straightforward volume conductor solution and ability to approximate 80%–90% of the power in observed surface potentials (Malmivuo and Plonsey 1995, Van Oosterom 2002). While the true cardiac activity is spatially distributed in 3D space, the point dipole model provides an adequate approximation in the far-field case investigated by this work. The time-varying potential vector $\boldsymbol{\phi}(t)$ produced by a point dipole for a chosen set of sensor positions in the fecgsyn toolbox is given by

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \boldsymbol{\phi}(t) = {\bf H}(t)\cdot {\bf R}(t)\cdot {\bf d}(t) \label{potential_single} \nonumber \end{align} \tag{ 1 }$$

where for n sensor positions, ${\bf d}(t)$ is a $3\times1$ vector representing the point dipole, ${\bf R}(t)$ is a $3\times3$ rotation matrix and ${\bf H}(t)$ is a $n\times3$ lead field matrix. The lead field matrix ${\bf H}(t)$ represents the transformation from source vector to scalar potential at each sensor position as given by the volume conductor model (see section 2.2), whereas the ${\bf R}(t)$ matrix allows for independent rotation of the time-varying point dipole, useful for simulating physiological events such as respiration or fetal movement. Both ${\bf H}(t)$ and ${\bf R}(t)$ may be time-varying when the cardiac source is in motion. Combining the maternal and fetal cardiac sources with noise results in

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \boldsymbol{\phi}(t) = {\bf H}_m(t)\cdot {\bf R}_m(t)\cdot {\bf d}_m(t)+{\bf H}_f(t)\cdot {\bf R}_f(t)\cdot {\bf d}_f(t)+{\bf w}(t) \label{potential_multiple} \nonumber \end{align} \tag{ 2 }$$

where the subscripts m and f indicate the respective maternal and fetal parameters and ${\bf w}(t)$ is noise.

To calculate the potential distribution generated by electrical sources within the human body, a model of its electrical properties must be defined. The volume conductor model used in the fecgsyn toolbox to calculate ${\bf H}(t)$ is summarized as follows with further detail available in Geselowitz (1989) and Sameni et al (2007). Considering the human body as a linear, resistive volume, the quasi-static potential ϕ at a sensor position external to any current source can be described by the Poisson equation:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \nabla\cdot\sigma\nabla\phi = \nabla\cdot {\bf J}^i \label{poisson} \nonumber \end{align} \tag{ 3 }$$

where ${\bf J}^i$ is the impressed current density and σ is the conductivity. Assuming an infinite, homogeneous volume, a solution to (3) is given by

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \phi({\bf r}) - \phi_0 = \frac{1}{4\pi\sigma}\int\!\int\!\int_V \frac{\nabla\cdot{\bf J}^i}{\vert {\bf r}\vert}\,dV \label{poisson_solution} \nonumber \end{align} \tag{ 4 }$$

where ${\bf r}$ is the vector from source to sensor position and $\phi_0$ a chosen reference potential. For a single time-varying source, (4) has a solution:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \boldsymbol{\phi}(t) - \phi_0 = \frac{{\bf d}(t)\cdot{\bf r}(t)}{4\pi\sigma\vert {\bf r}(t)\vert^3} \label{poisson_solution_analytic} \nonumber \end{align} \tag{ 5 }$$

where ${\bf d}(t)$ is the time-varying vector representing the point dipole and ${\bf r}(t)$ is the time-varying vector from source to sensor position. Equation (5) thus expresses the solution for the elements of ${\bf H}(t)$ as used in the fecgsyn toolbox with the rotation matrix ${\bf R}(t)$ used to modify the overall dipole orientation. However, this solution is only valid for a volume conductor comprised of an infinite homogeneous medium. As an inhomogeneous volume conductor affects dipole sources depending on their specific position and orientation, the proposal by Behar et al (2014) to model vernix caseosa by reducing the signal-to-noise ratio (SNR) of the fetal cardiac source will not accurately reflect morphological changes introduced by an asymmetric volume conductor.

In this work, we extend the fecgsyn toolbox by replacing ${\bf H}(t)$ with a lead field matrix computed using the finite element method (FEM). The FEM operates by discretizing the volume conductor into smaller elements with defined electromagnetic properties, enabling the computation of electric potential and magnetic field distribution in complex geometric structures. This technique has been used previously in the field of electroencephalography (EEG) where inhomogeneities such as the highly non-conductive skull have a significant effect on EEG measurements (Chauveau et al 2004). Several open-source EEG toolboxes with volume conductor modeling capability have been released to study these effects including the Neuroelectromagnetic Forward Head Modeling Toolbox (NFT) (Acar and Makeig 2010), Brainstorm (Tadel et al 2011) and FieldTrip (Oostenveld et al 2011). In this work, we utilize the FieldTrip-Simbio FEM pipeline developed by Vorwerk et al (2018). This pipeline has been chosen due to its numerical accuracy (Vorwerk et al 2012) and straightforward integration into the MATLAB environment. For further reference on its implementation, the reader is referred to Vorwerk (2016).

To describe the maternal–fetal anatomy, we use a model containing four tissue types consisting of fetus, vernix caseosa, amniotic fluid and maternal abdomen as proposed by Stinstra and Peters (2002). We assume the maternal–fetal anatomy Ω can be decomposed into a finite number of compartments $\Omega_1, \Omega_2, \ldots, \Omega_n$ each containing a tissue type of a single resistive conductivity $\sigma_i$. Adjacent compartments must share a common boundary and there may be disjoint compartments containing the same tissue type within the overall domain. The electrical conductivities used for each tissue type in our model are taken from Stinstra and Peters (2002) and are given in table 1.

To generate a finite element model based on realistic maternal–fetal geometry, we utilize the publically available Fetus and Mother Numerical Models (FEMONUM) as described in Bibin et al (2010) and Dahdouh et al (2014). These models were created using a combination of 3D ultrasound and magnetic resonance imaging (MRI) data from women with pregnancies ranging from eight to 34 weeks GA. Specifically we use the Victoria-TiGroFetus-32weeks model composed of the maternal body model Victoria (provided by DAZ 3D Studio, www.daz3d.com) and 32 weeks GA model which discretizes the fetus, amniotic fluid and maternal body into three triangulated compartments of 24 901, 382 and 11 149 nodes respectively as shown in figure 3. All units in this model are given in millimetres where the x-z plane represents the anatomic coronal view and the y-z plane represents the anatomic sagittal view.

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Before use, all models were processed using the open-source MeshLab toolbox developed by Cignoni et al (2008) to achieve the following: (1) remove self-intersections, (2) smooth and resample each compartment to create a single closed surface and (3) compute the constrained Delaunay triangulation (CDT) of the resulting surface.

To describe the asymmetric distribution of vernix caseosa we propose a model that delineates the fetal body into seven regions as defined by the fetal body maps in figure 4(a). The physiological basis for this model comes from (1) observations of vernix caseosa asymmetry in these regions as presented by Akiba (1955) and Visscher et al (2005) and (2) results from Archana (2008) which classify vernix caseosa thickness in these regions into five ranges (0 mm, 0–1 mm, 1–2 mm, 2–3 mm, >3 mm) as shown in figure 4(b). The correlation between vernix caseosa thickness in each region and breakdown by gestational age was not reported by Archana, therefore these results should not be interpreted as the typical vernix caseosa distribution for an individual but instead serve as an indicative range of values to be studied.

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To investigate the range of observed vernix caseosa thicknesses, we manually divide the processed 32 weeks GA fetal model into the seven regions as defined in figure 4(a). Compartments of vernix caseosa are generated by selecting a group of connected triangles S₁ representing a desired region and translating its inner nodes along the vertex normals to create a new surface S₂. Following this, a triangulated surface S₃ is created joining the exterior nodes of S₁ and S₂ to define the vernix caseosa compartment bounded by $S_1 \cup S_2 \cup S_3$. This process is repeated until all desired vernix caseosa compartments have been created. It is important to note the true distribution of vernix caseosa may be more granular than these seven regions, however this model will help identify regions which have a significant effect on NI-FECG extraction accuracy.

To facilitate finite element model generation from the defined surfaces, the compartments of fetus, vernix caseosa, amniotic fluid and maternal body are combined to form a triangulated piecewise linear complex (PLC) (Miller 1998). From the triangular PLC, a tetrahedral finite element model can be generated via constrained Delaunay tetrahedralization. In this work, this process is achieved using the open-source TetGen tool (v1.5.1) developed by Si (2015) invoked through the iso2mesh MATLAB toolbox (v1.8.0) developed by Fang and Boas (2009). TetGen allows the user to set a maximum element volume for the discretization of each compartment, important for the thin layer of vernix caseosa to ensure an accurate FEM solution. An example tetrahedral finite element model generated using this process is shown in figure 5.

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Each cardiac source within this model must be assigned three parameters: (1) position of the source, (2) orientation of the source representing the electrical axis of the heart and (3) source vector loop, otherwise known as the vectorcardiogram, representing the 3D path traced by the source model. For the maternal heart these parameters are affected by inter-individual variations and physiological changes in the heart during pregnancy as well as fetal presentation and fetal size due to the displacement of internal organs (Fowler and Braunstein 1951, Bacharova and Ugander 2014, Gultekin et al 2016). As the scope of investigating these parameters is beyond this work, the default position and orientation of the maternal source in our model are determined based on the mean values for a normal adult heart as reported by Nousiainen et al (1986) with the ability to select from nine different vectorcardiograms as provided in the fecgsyn toolbox.

For the fetal source, in addition to inter-individual variations, the ratio of right ventricular to left ventricular weight varies throughout gestation resulting in a shift in electrical axis due to the increased thickness of muscle fibre (Emery and Macdonald 1960). While a recent study by Verdurmen et al (2016) recorded preliminary results for the normal fetal electrical axis, they are not suitable for use in this work due to their small sample size. Instead, the default position of the fetal source in our model is based on the normal position for a healthy fetus (13–40 weeks GA) as reported in Comstock (1987) with the same anatomic orientation as the maternal source adjusted for right ventricular deviation as observed in early neonates (DePasquale and Burgh 1963). A summary of the relevant fecgsyn parameters utilized in our model are shown in table 2 with visualisation of the maternal and fetal source position and orientation shown in figure 6(a).

Table 2. Source model parameters.

Parameter	Description	Value
fectb	Fetal ectopic beats	0
fheart	Fetal source position ($x, y, z$)	($772, 125, 1087$)
fhr	Fetal heart rate	150
ftraj	Fetal movement trajectory	None
ftypeacc	Fetal heart rate acceleration	None
fvcg	Fetal vectorcardiogram	1
mectb	Maternal ectopic beats	0
mheart	Maternal source position ($x, y, z$)	($814, 165, 1315$)
mhr	Maternal heart rate	80
mtraj	Maternal movement trajectory	None
mtypeacc	Maternal heart rate acceleration	None
mvcg	Maternal vectorcardiogram	1
posdev	Heart position deviation	0
Rf	Fetal source rotation ($\theta_x, \theta_y, \theta_z$)	(2.8, 1.6, 3)
Rm	Maternal source rotation ($\theta_x, \theta_y, \theta_z$)	(1.5, 0, 0)

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Assessment of volume conductor effects is performed by comparing lead field matrix components ($x, y, z$) and surface potentials at selected nodes in each model using the relative difference measure (RDM^*) as proposed by Meijs et al (1989) and the logarithmic magnitude error (lnMAG) as proposed by Güllmar et al (2010):

$$\begin{align*} \newcommand{\e}{{\rm e}} \newcommand{\norm}[1]{\Vert #1 \Vert} \displaystyle RDM^*=\left\Vert{\frac{x_a}{\norm{x_a}_2}-\frac{x_b}{\norm{x_b}_2}}\right\Vert_2\quad lnMAG={\rm ln}\Big(\frac{\norm{x_a}_2}{\norm{x_b}_2}\Big) \nonumber \end{align*}$$

where for n nodes, x_a and x_b are $n\times1$ vectors for inputs a and b respectively. RDM^* indicates the difference in distribution patterns, bounded by 0 for identical inputs and 2 for $x_b = -x_a$, where increasing RDM^* represents greater difference in distribution patterns. Thus, RDM^* provides a simple metric to compare the morphology of two vectors without penalizing for overall changes in magnitude. lnMAG indicates the difference in overall magnitude where a value of 0 indicates an identical norm of the inputs and positive or negative deviation indicates relative change in magnitude. lnMAG is preferable to a direct magnitude ratio as it is symmetric about ${\rm ln}(1)$, enabling one-to-one comparison between positive and negative differences. As we aim to quantify effects for sources of varying orientation, we calculate RDM^* and lnMAG for the lead field matrices as $3\times1$ vectors $[RDM^*_x, \; RDM^*_y, \;RDM^*_z]$ and $[lnMAG_x, \; lnMAG_y, \;lnMAG_z]$ indicating the value along each coordinate axis where $\newcommand{\norm}[1]{\Vert #1 \Vert} \norm{RDM^*}_2$ and $\newcommand{\norm}[1]{\Vert #1 \Vert} \norm{lnMAG^*}_2$ indicate the 2-norm for each $3\times1$ vector. Additionally, as the T/QRS ratio has been proposed for identifying signs of fetal distress based on its absolute value or relative value compared to a chosen baseline, we define the T/QRS ratio error in each asymmetric volume conductor model as

$$\begin{align*} \newcommand{\e}{{\rm e}} \displaystyle e_{TQRS}=\frac{TQRS_{a} - TQRS_{h}}{TQRS_{h}} \nonumber \end{align*}$$

where TQRS_a is the T/QRS ratio in the asymmetric volume conductor model and TQRS_h is the T/QRS ratio in the homogeneous volume conductor model. The sign and magnitude of e_TQRS thus specifies the relative change in T/QRS ratio introduced by asymmetric volume conductor effects where positive e_TQRS indicates an increase in observed T/QRS ratio and negative e_TQRS indicates a decrease in observed T/QRS ratio compared to a homogeneous volume conductor model.

To quantify the effects of volume conductor asymmetry on NI-FECG extraction, we compute the fetal lead matrix (${\bf H}_f$) at all maternal body surface nodes between 750 mm $\leqslant z \leqslant$ 1350 mm (n  =  682) for visualisation purposes and define a subset of nodes between $950~{\rm mm} < z < 1200~{\rm mm}$ (n  =  266) as the abdominal sensors for numerical evaluation as shown in figure 6(b). To ensure minimal numerical error in the chosen finite element discretization, we perform a refinement process using a model with vernix caseosa generated at 1 mm in the Back region to determine the required TetGen parameters. This process involves repeatedly completing the TetGen and SimBio steps as shown in figure 7 and iteratively halving the maximum element volume per compartment until a defined level of convergence is obtained. For this work, refinement was performed until $\newcommand{\norm}[1]{\Vert #1 \Vert} \norm{RDM^*}_2$ of the abdominal sensors lead field matrix compared with the subsequent solution was below 0.02 for two consecutive iterations as shown in figure 8. All finite element models in this work were generated using the parameters identified via this process and compared to a reference solution with halved maximum element volume per compartment showing minimal numerical error in RDM^* and lnMAG (results in appendix table A1).

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Using the developed process, this work aims to characterise morphological changes caused by volume conductor asymmetry including spatially variable distributions of vernix caseosa in the seven fetal body regions as defined in figure 4(a). Based on the data shown in figure 4(b), it would be ideal to investigate models where vernix caseosa thickness in each region takes one of four values: 0 mm, 1 mm, 2 mm or 3 mm. However, as this space represents $16\, 384\;(4^{7})$ possible combinations, we must define a subset of this space to make analysis feasible.

3.5.1. Region assessment

3.5.2. Signal morphology

Using the described volume conductor models, pairwise RDM^* and lnMAG were computed for the abdominal sensors lead field matrix as shown in figure 9. Each heat map indicates the relative change in surface potentials between models in terms of distribution patterns (RDM^*) and overall magnitude (lnMAG) as generated by components of the fetal source along each coordinate axis.

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From these results, we observe that the Back models demonstrate the largest change in $RDM^*_x$ compared to the homogeneous model followed by the Head, Arms and Chest models. Differences in $RDM^*_y$ are less pronounced with the Back, Arms and Head models showing marginally greater change, while for $RDM^*_z$ all models show significant change compared to the homogeneous model. For all models with vernix caseosa, it can be observed that varying vernix caseosa thickness from 1 mm to 3 mm in each region has minimal effect on RDM^* along all coordinate axes.

For lnMAG_x, all models show a decrease compared to the homogeneous model with the Back and Chest models demonstrating the greatest change. Interestingly, while lnMAG_x for the Head models is decreased compared to the homogeneous model, it is marginally increased compared to all other models. For lnMAG_y, all models exhibit a large decrease compared to the homogeneous model with the Head model again showing a small increase in lnMAG_y compared to non-homogeneous models. Most models show minimal change in lnMAG_z compared to the homogeneous model except for the Arms and Head models which marginally increase and the Back models which marginally decrease. Similar to RDM^*, varying the thickness of vernix caseosa from 1 mm to 3 mm in each region has minimal effect on lnMAG along all coordinate axes.

To quantify the three regions of greatest impact, we calculate $\newcommand{\norm}[1]{\Vert #1 \Vert} \norm{RDM^*}_2$ and $\newcommand{\norm}[1]{\Vert #1 \Vert} \norm{lnMAG}_2$ rankings for the 3 mm models compared to the No Vernix model as shown in figure 10. Ranking is performed using the 3 mm models as overall they demonstrate marginally greater impact compared to the 1 mm models. From these rankings, the Back 3 mm model shows the greatest change in $\newcommand{\norm}[1]{\Vert #1 \Vert} \norm{RDM^*}_2$ followed by the Head 3 mm and Chest 3 mm models. For $\newcommand{\norm}[1]{\Vert #1 \Vert} \norm{lnMAG}_2$, the Back 3 mm model shows the greatest change, followed by the Chest 3 mm and Arms 3 mm models. As this work is primarily concerned with morphological changes indicated by greater RDM^*, the three models selected for further analysis are the Back 3 mm, Chest 3 mm and Head 3 mm models.

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To visualize the effects of volume conductor asymmetry in the three selected models, surface potentials produced by dipoles along each coordinate axis for the homogeneous, No Vernix, Back 3 mm, Chest 3 mm and Head 3 mm models are shown in figure 11. As indicated by the Region Assessment results, these visualizations show: (1) large change in distribution patterns and greatly reduced magnitude for x axis dipoles in the Back 3 mm model, (2) reduced magnitude for x axis dipoles in the Chest 3 mm model, (3) large change in distribution patterns for z axis dipoles in all non-homogeneous models, and (4) reduced magnitude for y axis dipoles in all non-homogeneous models.

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Following these observations, we simulate NI-FECG waveforms in volume conductor models comprising the following nine scenarios: (1) homogeneous volume conductor model as previously defined and (2–9) finite element volume conductor models with binary combinations of vernix caseosa at 3 mm thickness in the Back, Chest and Head regions where the presence/absence of vernix caseosa in each region is indicated by the model name (e.g. BackChest 3 mm model contains vernix caseosa at 3 mm thickness in the Back and Chest region, but not the Head region). The six sensor positions as shown in figure 12 are chosen to be approximately equally spaced over the abdominal surface above and below the fetal source and aligned to the closest available nodes in the model discretization. Each sensor is measured in respect to a reference node at the center of the maternal back as per the default fecgsyn sensor configuration (see Andreotti et al (2016) for detail). Figure 12 presents simulated NI-FECG waveforms for the nine volume conductor models as described with e_TQRS and RDM^* reported at each sensor position in table 3. To enable simple visual comparison between models, each signal's isoelectric line in figure 12 is aligned to 0 V and the fetal vectorcardiogram amplitude is linearly scaled by a factor of 10⁻⁵ to a peak source strength of approximately 18 μAm.

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Table 3. Signal morphology results indicating e_TQRS and RDM^* at each sensor position per model. Worst case per row in bold.

Model	Metric	Sensor position
		1	2	3	4	5	6
No Vernix	eTQRS	−0.12	0.12	−0.26	0.08	0.37	0.07
	RDM*	0.10	0.25	0.18	0.03	0.18	0.17
Back 3 mm	eTQRS	−0.49	−0.45	−0.35	−0.01	${\bf -0.66}$	−0.20
	RDM*	0.49	0.45	0.27	0.14	0.36	0.13
Chest 3 mm	eTQRS	−0.27	−0.08	${\bf -0.33}$	0.06	−0.23	−0.23
	RDM*	0.22	${\bf 0.26}$	0.24	0.05	0.14	0.16
Head 3 mm	eTQRS	−0.11	0.30	−0.27	0.12	0.51	0.44
	RDM*	0.08	0.23	0.18	0.07	0.25	0.23
BackChest 3 mm	eTQRS	−0.71	−0.52	−0.46	−0.14	${\bf -0.77}$	−0.55
	RDM*	0.80	0.52	0.39	0.20	0.56	0.45
BackHead 3 mm	eTQRS	−0.30	−0.65	−0.25	−0.04	${\bf -0.67}$	0.04
	RDM*	0.23	0.61	0.20	0.13	0.59	0.07
ChestHead 3 mm	eTQRS	−0.27	−0.16	−0.44	0.11	−0.26	0.48
	RDM*	0.21	0.29	0.36	0.15	0.24	0.15
BackChestHead 3 mm	eTQRS	−0.55	${\bf -0.73}$	−0.61	−0.26	−0.52	−0.39
	RDM*	0.51	0.74a	0.51	0.29	0.74a	0.32

^aIndicates multiple columns with equal value.

As shown in table 3, a maximum e_TQRS of  −0.77 is observed in the BackChest 3 mm model for sensor 5, indicating 77% relative error in the observed T/QRS ratio. The next three highest e_TQRS values are present in the BackChestHead 3 mm (−0.73), BackHead 3 mm (−0.67) and Back 3 mm (−0.66) models indicating that volume conductor asymmetry in the Back region has a large effect on the observed T/QRS ratio. Furthermore, in all models with vernix caseosa in the Back region, e_TQRS is negative at all sensor positions except for sensor 6 in the BackHead 3 mm model, indicating a reduced T/QRS ratio compared to a homogeneous model. The No Vernix model also shows large variation in e_TQRS with a minimum of  −0.26 in sensor 3 and maximum of 0.37 in sensor 5 indicating that volume conductor effects have a large influence on signal morphology even in the absence of vernix caseosa.

RDM^* compared to a homogeneous model also demonstrates considerable variation across all models with a maximum RDM^* of 0.80 observed in sensor 1 for the BackChest 3 mm model followed by the BackChestHead 3 mm (0.74), BackHead 3 mm (0.61) and Back 3 mm (0.49) models with all other models having at least one sensor with an RDM^* of 0.25 or greater.

We observed that volume conductor asymmetry in the Back region leads to the greatest changes in terms of both RDM^* and lnMAG, which can be attributed to its large coverage area and close proximity to the fetal source. Additionally, varying the thickness of vernix caseosa isolated in each region from 1 mm to 3 mm did not greatly affect RDM^* or lnMAG values along all coordinate axes. This can be attributed to the fact that as each region in isolation does not fully enclose the fetus, the path of least resistance to the maternal abdomen is only slightly modified by an increase in vernix caseosa thickness. From these studies, the three models of greatest impact were identified as the Back 3 mm, Chest 3 mm and Head 3 mm models.

Visualisation of surface potentials produced by dipoles along each coordinate axis for the identified three models as shown in figure 11 demonstrated large changes in potential distribution and magnitude compared to a homogeneous volume conductor model. Specifically, we observed that volume conductor asymmetry in the Back region resulted in greatly reduced magnitude for x axis dipoles, typically leading to reduced T wave amplitude as shown in figure 12. Following this observation, we note that difficulties in detecting T-waves via NI-FECG have been reported throughout the literature as summarised in Wacker-Gussmann et al (2017). While other causes may likely contribute to this phenomenon, the high level of vernix caseosa asymmetry reported in the back region by Akiba (1955), Visscher et al (2005) and Archana (2008) presents a novel explanation for this effect. In addition, signal morphology and T/QRS ratio error were significantly altered in the No Vernix model, indicating that volume conductor effects play an important role even when vernix caseosa is not present.

Based on these observations, we conclude NI-FECG algorithm benchmarks utilizing a homogeneous volume conductor model do not indicate representative accuracy of T/QRS ratio extraction in real data and volume conductor effects should be considered in future benchmarks using simulated data. Furthermore, it should be noted that even in a homogeneous volume conductor model, the T/QRS ratio will change with sensor location and fetal orientation due to variations in the projected components of the underlying cardiac dipole. As such, without knowledge of the influence of volume conductor effects, clinical evaluation of the T/QRS ratio derived via NI-FECG should be avoided.

In the present study, we considered a single fetal model with a fixed set of source parameters. While these parameters were carefully selected based on clinical measurements, further analysis should be conducted using a range of anatomic and vectorcardiogram models to determine the typical distribution of error within a larger pregnancy cohort. Further clinical studies are also warranted to determine the likelihood of the investigated vernix caseosa distributions across different gestational ages and validate the predictions of our model against observed abdominal potentials. Regardless of these factors, the presented results demonstrate the significant potential for estimation error in real data and confirm that volume conductor effects represent an important topic in the study of NI-FECG extraction accuracy.

In addition to the 32 weeks GA model utilized in this work, the developed process allows for the simulation of NI-FECG waveforms using any triangular PLC, enabling the study of volume conductor effects over a range of gestational ages and fetal positions with the possibility to include additional structures in the modeling process such as the placenta, umbilical cord and internal organs. As part of further studies, the impact of including additional compartments as well as model simplifications, such as finite element models of a constant conductivity could be investigated. Additionally, as the surface potentials in our process are generated according to a linear mixture, it can be utilized to simulate abdominal ECG mixtures for multiple fetuses (e.g. twins) via the inclusion of additional cardiac sources within an appropriate volume conductor model. Further expansion may also investigate alternative cardiac source models such as a set of spatially distributed dipoles.

Finally, our process can be easily extended to the field of fetal magnetocardiography, allowing study of the effects of volume conductor asymmetry on magnetic field distribution. As our process has been developed using MATLAB and a set of open-source tools, a future development goal is to release the developed code under an open-source license to enable rapid NI-FECG benchmarks incorporating volume conductor effects within the research community.