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Principle study on the signal connection at transabdominal fetal pulse oximetry

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Current Directions in Biomedical Engineering
From the journal Current Directions in Biomedical Engineering Volume 2 Issue 1

Abstract

Transabdominal fetal pulse oximetry is an approach to measure oxygen saturation of the unborn child non-invasively. The principle of pulse oximetry is applied to the abdomen of a pregnant woman, such that the measured signal includes both, the maternal and the fetal pulse curve. One of the major challenges is to extract the shape of the fetal pulse curve from the mixed signal for computation of the oxygen saturation. In this paper we analyze the principle kind of connection of the fetal and maternal pulse curves in the measured signal. A time varying finite element model is used to rebuild the basic measurement environment, including a bulk tissue and two independently pulsing arteries to model the fetal and maternal blood circuit. The distribution of the light fluence rate in the model is computed by applying diffusion equation. From the detectors we extracted the time dependent fluence rate and analyzed the signal regarding its components. The frequency spectra of the signals show peaks at the fetal and maternal basic frequencies. Additional signal components are visible in the spectra, indicating multiplicative coupling of the fetal and maternal pulse curves. We conclude that the underlying signal model of algorithms for robust extraction of the shape of the fetal pulse curve, have to consider additive and multiplicative signal coupling.

Keywords: diffusion theory; fetal pulse oximetry; finite element model; signal coupling

1 Introduction

Oxygen saturation is seen to be a reliable parameter to assess the wellbeing of human beings as well as unborn children. During late pregnancy and delivery, it happens that the oxygen feed of the fetus is reduced and may lead to hypoxia and severe organ damage [1], [2]. A new approach to detect fetal hypoxia is the transabdominal fetal pulse oximetry. The non-invasive method aims to measure fetal oxygen saturation continuously and to provide a parameter to directly assess the state of health of the fetus. LEDs and photo detectors are placed on the belly of the pregnant woman, such that the photons travel through maternal and fetal tissue before reaching the surface again. The acquired signal consists of both, the fetal and maternal pulse curves. The most important step prior to calculation of the fetal oxygen saturation is the extraction of the fetal pulse curve from the signal mixture [2], [3], [4].

This paper investigates the connection of the fetal and maternal pulse curves in the measured signal. The knowledge of coupling and composition of the signal components is the main precondition for separation of the fetal pulse curve from the signal mix. Former works focused on analyzing the photon distribution in static models of the abdomen [3], [4], [5]. We constructed a time variant finite-element model to rebuild the basic measurement principle of transabdominal fetal pulse oximetry. Diffusion theory is used to compute the light propagation in the model. Utilizing COMSOL Multiphysics® allows us to do time sweeps and analyze the light fluence rate in a time varying model geometry. The light fluence rate computed at the detector side is modulated by pulsations of both, maternal and fetal, arteries. We analyze the resulting mixed signals to conclude about the superposition and coupling of the maternal and fetal signal components.

2 Methods

2.1 Tissue model with pulsing arteries

The tissue model (shown in Figure 1) is kept as simple as possible to reduce computation time and memory consumption for better handling. Basically it consists of a bulk medium with two arteries embedded. The whole model takes 20 cm × 20 cm × 5 cm (width × height × depth). The maternal and fetal arteries are located in depths of 1.5 cm and 3.5 cm, respectively, measured from the surface of the bulk medium. The arteries are parallel to each other, but slightly displaced by 0.2 cm symmetrically around the center of the model. The optical parameters, scattering coefficient (μs), absorption coefficient (μa), anisotropy (g) and refractive index (n), used for light propagation simulation, are listed in Table 1. The surrounding medium of the model is air.

Figure 1 Tissue model with two pulsing arteries embedded. The model consists of a bulk tissue (20 cm × 20 cm × 5 cm) and two artery tubes. The maternal artery and the fetal artery are slightly displaced around the center of the bulk tissue. The light source is placed on top in the middle of the model. Three detectors are on the bottom side.
Figure 1

Tissue model with two pulsing arteries embedded. The model consists of a bulk tissue (20 cm × 20 cm × 5 cm) and two artery tubes. The maternal artery and the fetal artery are slightly displaced around the center of the bulk tissue. The light source is placed on top in the middle of the model. Three detectors are on the bottom side.

Table 1

List of the optical properties of the tissue model.

Tissueμsμagn
Bulk5.0 cm−10.08 cm−10.801.300
Artery12.0 cm−14.70 cm−10.991.400

The scattering coefficient (μs), absorption coefficient (μa), anisotropy (g) and refractive index (n) describe the optical characteristics of the tissues.

The diameter of the arteries depends on the time parameter. We implemented a cosine function following Equation 1 as a simple approximation of the pulse curve.

(1)d=3⋅A+A⋅c⁢o⁢s⁢(2⁢π⋅H⁢R/60⋅t+P⁢h⁢a⁢s⁢e)

A is the amplitude of the oscillation, HR the simulated heart rate in bpm and Phase the phase shift between the fetal and maternal pulsation. The parameters for the pulsation are listed in Table 2.

Table 2

List of the geometrical parameters of the fetal and maternal arteries.

ArteryAHRPhase
Maternal0.1 cm61 bpmπ/3 s
Fetal0.1 cm113 bpm0.0 s

A is the amplitude of the oscillation, HR the heart rate and Phase the phase shift of the cosine function.

The light source and detectors are approximated by points. The source point is placed in the center on top of the model, as can be seen in Figure 1. Detector 1 is located on the bottom plane of the model below the source. Detectors 2 and 3, also on the bottom of the model, are slightly displaced from the center, 5 cm following and orthogonally to the direction of the arteries.

2.2 Diffusion theory

The diffusion equation as approximation of the radiative transfer equation is used to compute the light propagation in the tissue model. In comparison to the widely used Monte Carlo method, the diffusion equation allows faster computation of the light fluence distribution in complex geometric models, at similar accuracy [6]. The distribution of the light fluence rate Φ is described by Equation 2 [7], [8].

(2)−∇⋅D⁢∇ Φ+μa⁢Φ=q

D denotes the diffusion coefficient, μa the absorption coefficient and q the source term. The diffusion coefficient is computed by Equation 3. It can be seen that, beneath the absorption coefficient μa, D also depends on the scattering coefficient μs and the anisotropy g.

(3)D=13⋅(μa+μs⁢(1−g))=13⋅(μa+μs′)

Similar to the anatomy, the model represents several types of tissue with different optical properties. To consider a mismatch of refractive indices between two media, a Robin-type boundary condition is applied. At boundaries, i.e. tissue and air or bulk tissue and blood, the light fluence rate is computed by Equation 4.

(4)Φ+2⁢A⁢D⁢n→•∇ Φ=0

A is computed by Equation 5 with R0=(n−1)2/(n+1)2 and n=ni⁢n/no⁢u⁢t. The refractive indices are denoted by nin and nout and the critical angle of total reflection by θc [7], [8].

(5)A=2(1−R0)−1+|c⁢o⁢s⁢θc|31−|c⁢o⁢s⁢θc|2

In COMSOL Multiphsyics® we use the Helmholtz equation as basic physic to implement these equations and solve for the fluence rate. The time parameter t is sweeped from 0 to 60 s with an interval of 1/60 s, representing a sampling rate of 60 sps. The power of the light source was set to 100 mW.

3 Results

The simulation results show the spatial distribution of the fluence rate in the time varying tissue model. Some examples are shown in Figure 2, with timestamps t = 0.2 s, 0.5 s and 0.8 s. Depicted are slices of the model in its y-z-plane, showing the profile of the arteries. It can be seen that the diameters of the fetal and maternal artery model changes over time, while the light’s intensity of the point source is constant. Further, the spatial distribution of the fluence rate slightly varies depending on the current model geometry.

Figure 2 Images of the spatial distribution of the fluence rate for timestamps t = 0.2 s, 0.5 s and 0.8 s. It can be seen that the diameter of the fetal and maternal arteries changes over time, while the source intensity is constant. The fluence distribution slightly changes in dependence on the current geometry of the arteries. For visualization, logarithmic scale is used.
Figure 2

Images of the spatial distribution of the fluence rate for timestamps t = 0.2 s, 0.5 s and 0.8 s. It can be seen that the diameter of the fetal and maternal arteries changes over time, while the source intensity is constant. The fluence distribution slightly changes in dependence on the current geometry of the arteries. For visualization, logarithmic scale is used.

We extracted the fluence rate computed at the bottom side of the model where the two detectors are located. Figure 3 shows the resulting time dependent signal. Depicted is the fluence rate at the detectors relative to the fluence rate at the light source. Basically the two signals show a very similar progress, but differ in their offsets. Detector 1 has a larger offset due to the shortest distance to the light source. It may be assumed that these mixed signals look like two superimposed harmonic oscillations.

Figure 3 Time series of the light fluence computed at the Detectors 1 (blue), 2 (red) and 3 (black), denoted as mixed signals.
Figure 3

Time series of the light fluence computed at the Detectors 1 (blue), 2 (red) and 3 (black), denoted as mixed signals.

Finally, spectral analysis is done to identify the components of the acquired signals. The magnitude spectra in Figure 4 are generated by using the Fast Fourier Transformation (FFT) and a Blackman window function. The whole signal consists of 3601 samples, so that a frequency resolution of 0.0167 Hz is reached.

Figure 4 Frequency spectra of the mixed signals, computed from the signals shown in Figure 3. The spectra are computed by using a Blackman window function and the Fast Fourier Transformation (FFT). Beneath the basic oscillations of the arteries (at 1.0167 Hz and 1.883 Hz), two more components exist at frequencies of 0.8664 Hz and 2.899 Hz, respectively.
Figure 4

Frequency spectra of the mixed signals, computed from the signals shown in Figure 3. The spectra are computed by using a Blackman window function and the Fast Fourier Transformation (FFT). Beneath the basic oscillations of the arteries (at 1.0167 Hz and 1.883 Hz), two more components exist at frequencies of 0.8664 Hz and 2.899 Hz, respectively.

The spectra of the three detectors slightly differ in their magnitudes. The main components in the spectrum of the mixed signals are two spectral peaks caused by the arteries, at their basic frequencies of 1.0167 Hz and 1.883 Hz. The weak first harmonic of the maternal artery oscillation is remarkable at 2.0334 Hz. Two additional peaks are at 0.8664 Hz and 2.899 Hz, respectively. The magnitudes of these peaks are about two decades below the magnitude of the main peaks. Due to the simulation, the signals are free of noise.

4 Discussion

The spectra in Figure 4 indicate an additive overlaying of the maternal and fetal pulse curves. A substitution of x and y in Equation 6 by the frequencies of the artery oscillations results in two more components. They are evident in the spectrum at frequencies of 1.883 Hz–1.0167 Hz = 0.8664 Hz and 1.0167 Hz + 1.883 Hz = 2.899 Hz. Thus, these additional peaks result from the multiplicative connection of the maternal and the fetal pulse curves.

(6)c⁢o⁢s⁢(x)⋅c⁢o⁢s⁢(y)=12⁢(c⁢o⁢s⁢(x−y)+c⁢o⁢s⁢(x+y))

In the consequence, the signal model has to consider a multiplicative connection of the fetal and the maternal pulse curves, following Equation 7.

(7)Sm⁢i⁢x⁢e⁢d=a⋅P⁢Cm⁢a⁢t+b⋅P⁢Cf⁢e⁢t+c⋅P⁢Cm⁢a⁢t⋅P⁢Cf⁢e⁢t

Smixed represents the mixed signal captured by the detector, PCmat and PCfet the maternal and fetal pulse curves weighted by a, b and c, respectively.

The magnitude of the multiplicative connected signal components in the simulation is weak. This indicates that in our simulation setup the amount of light modulated by both arteries before reaching the detector is weak compared to the amount of light modulated by either the maternal or the fetal artery. For Detector 1 and 3 the ratio between the maternal peak and the peak of the multiplicative component is 0.018 and 0.017, respectively, indicating a slightly stronger multiplicative component at Detector 1. In conclusion the ratios among the signal components may change in dependence on the model geometry, i.e. on the position of the arteries, their motion and the position of the light source and detectors. In this study we showed that the fetal and maternal pulse curves are multiplicatively coupled to several extend. Further studies will analyze these components in dependence on the detection quality. A more complex and realistic model of the optical ways in the abdomen will be useful to compare our generated signals to real measurements.

5 Conclusion

This paper analyzes the connection of maternal and fetal signals as they are acquired by non-invasive transabdominal fetal pulse oximetry. Finite element modeling and diffusion equation are conducted to compute spatial distributions of the fluence rate in a tissue model. Two pulsating arteries (maternal and fetal) are embedded in the model, varying their diameter over the time. The light fluence rate is computed for several points at the surface of the model over a time range from 0 to 60 s. A time dependent fluence signal can be extracted and analyzed in frequency domain. Our results show that there is an additive and a multiplicative connection of the fetal and the maternal artery pulsation in the acquired signals. The component resulting from the multiplicative connection in our model geometry is weak. However, following signal processing methods for any separation of the maternal and the fetal pulse curves will consider a signal model with a multiplicative component.

Author’s Statement

Research funding: The author state no funding involved. Conflict of interest: Authors state no conflict of interest. Material and Methods: Informed consent: Informed consent is not applicable. Ethical approval: The conducted research is not related to either human or animals use.

References

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Published Online: 2016-9-30
Published in Print: 2016-9-1

©2016 Marcel Böttrich et al., licensee De Gruyter.

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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https://doi.org/10.1515/cdbme-2016-0144
Keywords for this article
diffusion theory; fetal pulse oximetry; finite element model; signal coupling
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  55. Preprocessing of unipolar signals acquired by a novel intracardiac mapping system
  56. In-vitro experiments to characterize ventricular electromechanics
  57. Continuous non-invasive monitoring of blood pressure in the operating room: a cuffless optical technology at the fingertip
  58. Application of microwave sensor technology in cardiovascular disease for plaque detection
  59. Artificial blood circulatory and special Ultrasound Doppler probes for detecting and sizing gaseous embolism
  60. Detection of microsleep events in a car driving simulation study using electrocardiographic features
  61. A method to determine the kink resistance of stents and stent delivery systems according to international standards
  62. Comparison of stented bifurcation and straight vessel 3D-simulation with a prior simulated velocity profile inlet
  63. Transient Euler-Lagrange/DEM simulation of stent thrombosis
  64. Automated control of the laser welding process of heart valve scaffolds
  65. Automation of a test bench for accessing the bendability of electrospun vascular grafts
  66. Influence of storage conditions on the release of growth factors in platelet-rich blood derivatives
  67. Cryopreservation of cells using defined serum-free cryoprotective agents
  68. New bioreactor vessel for tissue engineering of human nasal septal chondrocytes
  69. Determination of the membrane hydraulic permeability of MSCs
  70. Climate retainment in carbon dioxide incubators
  71. Multiple factors influencing OR ventilation system effectiveness
  72. Evaluation of an app-based stress protocol
  73. Medication process in Styrian hospitals
  74. Control tower to surgical theater
  75. Development of a skull phantom for the assessment of implant X-ray visibility
  76. Surgical navigation with QR codes
  77. Investigation of the pressure gradient of embolic protection devices
  78. Computer assistance in femoral derotation osteotomy: a bottom-up approach
  79. Automatic depth scanning system for 3D infrared thermography
  80. A service for monitoring the quality of intraoperative cone beam CT images
  81. Resectoscope with an easy to use twist mechanism for improved handling
  82. In vitro simulation of distribution processes following intramuscular injection
  83. Adjusting inkjet printhead parameters to deposit drugs into micro-sized reservoirs
  84. A flexible standalone system with integrated sensor feedback for multi-pad electrode FES of the hand
  85. Smart control for functional electrical stimulation with optimal pulse intensity
  86. Tactile display on the remaining hand for unilateral hand amputees
  87. Effects of sustained electrical stimulation on spasticity assessed by the pendulum test
  88. An improved tracking framework for ultrasound probe localization in image-guided radiosurgery
  89. Improvement of a subviral particle tracker by the use of a LAP-Kalman-algorithm
  90. Learning discriminative classification models for grading anal intraepithelial neoplasia
  91. Regularization of EIT reconstruction based on multi-scales wavelet transforms
  92. Assessing MRI susceptibility artefact through an indicator of image distortion
  93. EyeGuidance – a computer controlled system to guide eye movements
  94. A framework for feedback-based segmentation of 3D image stacks
  95. Doppler optical coherence tomography as a promising tool for detecting fluid in the human middle ear
  96. 3D Local in vivo Environment (LivE) imaging for single cell protein analysis of bone tissue
  97. Inside-Out access strategy using new trans-vascular catheter approach
  98. US/MRI fusion with new optical tracking and marker approach for interventional procedures inside the MRI suite
  99. Impact of different registration methods in MEG source analysis
  100. 3D segmentation of thyroid ultrasound images using active contours
  101. Designing a compact MRI motion phantom
  102. Cerebral cortex classification by conditional random fields applied to intraoperative thermal imaging
  103. Classification of indirect immunofluorescence images using thresholded local binary count features
  104. Analysis of muscle fatigue conditions using time-frequency images and GLCM features
  105. Numerical evaluation of image parameters of ETR-1
  106. Fabrication of a compliant phantom of the human aortic arch for use in Particle Image Velocimetry (PIV) experimentation
  107. Effect of the number of electrodes on the reconstructed lung shape in electrical impedance tomography
  108. Hardware dependencies of GPU-accelerated beamformer performances for microwave breast cancer detection
  109. Computer assisted assessment of progressing osteoradionecrosis of the jaw for clinical diagnosis and treatment
  110. Evaluation of reconstruction parameters of electrical impedance tomography on aorta detection during saline bolus injection
  111. Evaluation of open-source software for the lung segmentation
  112. Automatic determination of lung features of CF patients in CT scans
  113. Image analysis of self-organized multicellular patterns
  114. Effect of key parameters on synthesis of superparamagnetic nanoparticles (SPIONs)
  115. Radiopacity assessment of neurovascular implants
  116. Development of a desiccant based dielectric for monitoring humidity conditions in miniaturized hermetic implantable packages
  117. Development of an artifact-free aneurysm clip
  118. Enhancing the regeneration of bone defects by alkalizing the peri-implant zone – an in vitro approach
  119. Rapid prototyping of replica knee implants for in vitro testing
  120. Protecting ultra- and hyperhydrophilic implant surfaces in dry state from loss of wettability
  121. Advanced wettability analysis of implant surfaces
  122. Patient-specific hip prostheses designed by surgeons
  123. Plasma treatment on novel carbon fiber reinforced PEEK cages to enhance bioactivity
  124. Wear of a total intervertebral disc prosthesis
  125. Digital health and digital biomarkers – enabling value chains on health data
  126. Usability in the lifecycle of medical software development
  127. Influence of different test gases in a non-destructive 100% quality control system for medical devices
  128. Device development guided by user satisfaction survey on auricular vagus nerve stimulation
  129. Empirical assessment of the time course of innovation in biomedical engineering: first results of a comparative approach
  130. Effect of left atrial hypertrophy on P-wave morphology in a computational model
  131. Simulation of intracardiac electrograms around acute ablation lesions
  132. Parametrization of activation based cardiac electrophysiology models using bidomain model simulations
  133. Assessment of nasal resistance using computational fluid dynamics
  134. Resistance in a non-linear autoregressive model of pulmonary mechanics
  135. Inspiratory and expiratory elastance in a non-linear autoregressive model of pulmonary mechanics
  136. Determination of regional lung function in cystic fibrosis using electrical impedance tomography
  137. Development of parietal bone surrogates for parietal graft lift training
  138. Numerical simulation of mechanically stimulated bone remodelling
  139. Conversion of engineering stresses to Cauchy stresses in tensile and compression tests of thermoplastic polymers
  140. Numerical examinations of simplified spondylodesis models concerning energy absorption in magnetic resonance imaging
  141. Principle study on the signal connection at transabdominal fetal pulse oximetry
  142. Influence of Siluron® insertion on model drug distribution in the simulated vitreous body
  143. Evaluating different approaches to identify a three parameter gas exchange model
  144. Effects of fibrosis on the extracellular potential based on 3D reconstructions from histological sections of heart tissue
  145. From imaging to hemodynamics – how reconstruction kernels influence the blood flow predictions in intracranial aneurysms
  146. Flow optimised design of a novel point-of-care diagnostic device for the detection of disease specific biomarkers
  147. Improved FPGA controlled artificial vascular system for plethysmographic measurements
  148. Minimally spaced electrode positions for multi-functional chest sensors: ECG and respiratory signal estimation
  149. Automated detection of alveolar arches for nasoalveolar molding in cleft lip and palate treatment
  150. Control scheme selection in human-machine- interfaces by analysis of activity signals
  151. Event-based sampling for reducing communication load in realtime human motion analysis by wireless inertial sensor networks
  152. Automatic pairing of inertial sensors to lower limb segments – a plug-and-play approach
  153. Contactless respiratory monitoring system for magnetic resonance imaging applications using a laser range sensor
  154. Interactive monitoring system for visual respiratory biofeedback
  155. Development of a low-cost senor based aid for visually impaired people
  156. Patient assistive system for the shoulder joint
  157. A passive beating heart setup for interventional cardiology training
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