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In this paper, a three-layered (maternal, amniotic fluid and fetal) tissue model is described where photon migration is simulated using Monte-Carlo techniques. This model is utilized to estimate the trans-abdominal optical power and optimum source-detector (S-D) separation. Results based on launching of 2 million photons with 1 mW optical power show that the expected optical power output is in range of 10-6-10-10 W/cm2 depending on S-D separation. Considering the limit of the signal processing methods (such as adaptive noise canceling) and the used of silicon photodetector, an S-D separation of 4 cm has been selected as a practical compromise between signal level and percentage of optical power (70%) coming from the fetal layer. Based on these findings, an optical fetal heart rate detection system has been developed and tested.
Key words: trans-abdominal, fetal heart rate, Monte-Carlo simulation, tissue model
I.Â Â INTRODUCTION
Recently, optical technique has received a considerable attention in biomedical diagnostic and monitoring of biological tissues such as brain imaging, breast imaging and for fetal heart rate detection and oxygen saturation measurement due to its theoretical advantages in comparison with other modalities [1,2]. Near infra-red (NIR) light ranged between 650-950 nm  is only moderately absorbed by water, hemoglobin and other body substances therefore can penetrate the human tissues and propagate while in the tissue. The behavior of the photon migration process in turbid media is a fundamental research in many practical applications in biological tissue. Monte-Carlo algorithms of light propagation through turbid media have been utilized extensively in biomedical optics. It has been used to solve the radiative transport equation within the turbid medium as the analytical solution to it is complicated.
More recently, continuous wave near infrared (NIR) spectroscopy has been applied to non-invasive trans-abdominal fetal pulse oximetry [4-9]. Trans-abdominal NIR spectroscopy was first proposed by Ramanujam et al  using four 20 Watt halogen lamps (10 cm separation from the pair of silicon photodetectors) and two 0.575-Watt tungsten lamps (4 or 2.5 cm separation on either side of the pair of silicon photodetectors) as light sources and a pair of photodiodes as detectors. In this work, the generated heat justified using cooling fans for the halogen lamps. NIR measurements were made from the maternal abdomen and laboratory tissue phantom to study photon migration through the fetal head in utero. Feasibility of trans-abdominal NIR spectroscopy has also been demonstrated to detect and quantify fetal hypoxia in utero in a pregnant ewe model [5-6] using three laser diodes with a total power of 15 mW and an avalanche photodiode  and source-detector separation ranging from 1.8 to 4 cm. Chance  had proposed to use nine laser diodes and four photomultipliers (10 cm S-D separation) for in vivo, non-invasive examination of internal tissue of a subject. Furthermore, trans-abdominal fetal oxygen saturation have been successfully obtained using NIR spectroscopy  (light-emitting diodes (735, 805, and 850 nm) as light source and a photomultiplier tube as a detector) (7 to 11 cm source-detector separation). The choice of wavelengths (675-700 and 850-900 nm) in the NIR instrument is based on minimizing the error in saturation for trans-abdominal measurement . At large detector separation (7 cm), the photons are expected to migrate through both fetal and maternal tissues before reaching the photo-detector and the error in the measurement caused by shunting is therefore reduced .
In trans-abdominal spectroscopy, the optical radiation from the source (on the maternal abdomen) has to travel through maternal tissues and amniotic fluid before reaching fetal layers, then travel back to the detector located on the mother abdomen. Due to the modulation of the incoming light by both maternal and fetal blood pulsations, the detected signal contains a mixture of maternal and fetal signals. In , a three layered model (consisting of maternal, amniotic fluid and fetal layers) is proposed where the maternal and fetal blood pulsations were emulated with typical SNR (ratio of fetal to maternal) values of -25 dB. Results from this study showed that while decreasing with thicker maternal tissue, the SNR increases with fetal skin thickness, and that adaptive noise cancelling (ANC) using the recursive least square (RLS) algorithm is still capable to extract fetal PPG peaks even at SNR of -34 dB .
To improve the signal to noise ratio of the detected signal, some approached can be adopted such as varying the S-D separation, synchronous detection and the digital signal processing techniques. In trans-abdominal fetal heart rate (FHR) detection system which utilized a low optical power light emitting diode (LED), the S-D separation play an important role as it affects the detectivity of the photo-detector. Previous study  shows that adaptive noise canceling (ANC) algorithm is still capable of extracting the peaks of fetal signal for SNR = -34.7 dB. In order to estimate the fetal signal from the mixed signal using adaptive noise canceling , the fetal signal has to be greater than or equal to photo-detector's noise otherwise only noise is estimated.
From the previous study [4-9], the S-D separations were varied depending on the type of sources and the photo-detectors used in their studies. As our approach  is different from the previous study, low-noise photo-detector and an appropriate S-D separation should be considered in this work. In this paper, a practical consideration for the trans-abdominal fetal heart rate detection was studied using Monte-Carlo simulation and three-layered tissue model which consists of maternal, amniotic fluid and fetal layer . By using Monte-Carlo technique, optical power that reached photo-detector is estimated at various S-D separations. Then, an appropriate S-D separation can be determined for trans-abdominal fetal heart rate detection.
II.Â MATERIAL AND METHODS
A. Monte-Carlo Algorithm
Monte-Carlo simulation is a computational method for calculating the movement of photons within a tissue by launching millions of photons and enables one to map the fluence rate distribution of photons. It is a flexible and accurate approach to simulate photon transport in tissues and produce multiple physical quantities. Monte Carlo technique has been utilized to estimate optical properties of tissues, which may be used to differentiate cancerous tissues from normal tissues [3, 11]. Besides that, light dosage for photodynamic therapy may be simulated using Monte-Carlo method.
An excellent work has been done by Wang & Jacques  for Monte-Carlo modeling of photon transport in multi-layered tissues. In this section, a brief discussion of the Monte Carlo simulation is given for the benefit of the readers. Instead of numerical method, Monte Carlo approached solves the radiation transport problems  in a more realistic way. This method describes local rules of photon propagation which expressed as probability distribution that describe the step-size of photon movement between photon-tissue interaction and the angles of deflection in a photon's trajectory when a scattering occurs [3, 11]. When the number of photons grows, the net distribution of all photons path gives an accurate approximation to the radiation transport problem.
Beer's law as expressed in Equation 1 describes the exponential decrease in intensity with depth.
It can be interpreted in Monte Carlo as the probability, that a photon will propagate a distance L without being scattered or absorbed. Equation 2 expressed L in terms of the probability where the probability is a random number.
For each step, an L is calculated randomly by a number p from a uniform distribution as in Equation 3.
The expectation value of loge(p) over distribution is -1. As the number of random sampling grows, the mean free path will converge to .
There are commercial software namely TracePro and ASAP can be used to perform the Monte Carlo simulation in the layered model. Wang and Jacques  had written a program in ANSI C for Monte-Carlo modeling of photon transport in multi-layered tissues . The simulation software used in this work (Tracepro version 3.0.0, Lambda Research Corporation) is a ray-tracing program for illumination, optical, radiometry, and photometry analysis. This software combines solid modeling, optical analysis features, strong data exchange capabilities, and is user friendly .
B. LED and Detector Model
The proposed IR LED (SFH-484-2, OSRAM Opto Semiconductors, Inc) used by trans-abdominal fetal heart rate (FHR) detection system is modeled. The proposed IR LED has wavelength closest to the low noise photo-detector where the peak responsivity occurred at 900 nm. The optical characteristic of the LED is given in Figure 1. The detector model is an object where the surface property is a perfect absorber. Any incident light is absorbed and produces the output signal.
Figure 1 Radiation pattern of selected LED (SFH-484-2, OSRAM Opto Semiconductors, Inc.).
C. Three-layered Tissue Model
The anatomical model  showed the female abdominal area which includes components simulating the layers of tissue in the abdominal area, the female reproductive organs and the bladder. Previous work has outlined the use of the perturbation method to model photon transport through an 8 cm diameter fetal brain located at a constant 2.5 cm below a curved maternal abdominal surface with an air/tissue boundary . In order to study the photo migration process, the anatomical model has been simplified into three-layered tissue model which has been reported in the literature [4, 9-10]. In , a three-layered tissue model which consists of maternal, amniotic fluid and fetal layers has been proposed (Figure 2). Maternal layer thickness (dM) and amniotic fluid layer thickness (dam) in this model are obtained from the literature.
In this work, the fetal layer thickness (dF) is given infinite thickness so that it is close to the realistic condition. As in realistic condition, light impinged on the fetal tissue will penetrate and travel into an unknown depth. Therefore, a finite fetal layer thickness which is given in  is not an appropriate boundary condition to perform the simulation. In order to obtained the optical power at various S-D separation, detectors, D1, D2, D3, D4 and D5 are placed at 2 cm, 4 cm, 6 cm, 8 cm and 10 cm respectively from the source, S (Figure 2).
Figure 2 Three-layer tissue model for light transport (not to scale) consist of maternal, amniotic fluid and fetal layer. S is denoted as source and D is denoted as detectors.
Table 1 show the optical properties (absorption, scattering and refraction index) of the tissue model which are obtained from the previous study. The aim of this simulation is to estimate the optical power at photo-detector using three-layered tissue model. To calculate the percentage of light at the fetal layer, two different simulation conditions have been performed as listed below;
i. The maternal and amniotic fluid layers have optical properties shown in Table 1. The fetal layer is given with infinite high absorption.
ii. The maternal, amniotic fluid and fetal layers have optical properties shown in Table 1.
The first simulation (i) condition is used to obtain the maternal and amniotic fluid signal (PM+am). All photons that reached the fetal layer are absorbed. The second simulation (ii) condition is used to obtain the maternal, amniotic fluid and fetal signal (PM+am+F). By subtracting PM+am from PM+am+F, fetal signal (PF) is obtained.
Table 1 Optical property of the tissue model proposed
Refractive indices, n
2.4 Â±0.8 cm
Amniotic fluid layer
Assume same as water
Refractive indices, n
Assume same as water
1.3 Â±0.4 cm
Assume same as mother
Assume same as mother
Refractive indices, n
Assume same as mother
Simulations have been performed at 2.5 cm, 3.7 cm and 4.9 cm fetal depth (depth of maternal layer to the fetal layer) respectively to calculate the expected optical power at the photo-detector. The number of photons that have been injected into the maternal abdomen is obtained by trial and error. Five million and two million of photons do not give any significant different in the result. Therefore, two million photons with 3.5 mW/cm2 (1 mW) optical power have been selected to run the simulation. It takes at approximately 9 hour to complete one simulation in Pentium IV 2.8 GHz processor.
D. Photo-detector Noise
When designing an optical instrument, detector is an essential component. Selection of an appropriate detector resulted in better signal quality of the acquired signals. The noise floor of the photo-detector will determine the maximum S-D separation which is useful in the optical instruments.
Currently, the low noise photo-detector can be obtained from Edmond Optics Corporation with noise equivalent power as low as 1.8Â´10-14 W/Hz1/2 (0.051 cm2) (W57-522, Edmund Optics, Inc.) and 8.6Â´10-14 W/Hz1/2 (1.00 cm2) (W57-513, Edmund Optics, Inc.). Noise equivalent power is the incident optical power required to produce a signal on the detector that is equal to the noise when SNR is equal to one. These silicon detectors are then utilized in the following analysis.
The photo-detector can either operate in photovoltaic or photo-conductance condition. Photovoltaic operation offered a low noise system compared to the photo-conductance operation. Shot noise (due to the dark current) is the dominant noise component during photo-conductance operation. Small photo-detector's active area resulted in lower noise level compared to the large photo-detector's active area. Since strong scattering process in the human tissue dispersed the light in random fashion , large photo-detector's active area increases the probability of detecting photon that exit from the maternal layer. Therefore, photo-detector with 1 cm2 area is proposed for the optical fetal heart rate instrument. This value has thus been used in the rest of this work. Table 2 showed the proposed silicon photo-detector's noise, PNoise during photovoltaic operation at various bandwidths. It shows that photo-detector's noise increases with its bandwidth.
Table 2 PNoise during photovoltaic operation at various bandwidths
III.Â RESULTSÂ ANDÂ DISCUSSIONS
A. LED Simulation
The polar candela distribution plot (radiation pattern) produced by the LED model in TracePro is shown in Figure 3. Compared with Figure 1, it can be seen that the simulated IR LED has the optical characteristic close to the actual LED.
Figure 3 LED simulation: polar candela distribution.
B. Expected Optical Power and Source-Detector Separation
The Monte Carlo simulation model is shown in Figure 4. Results show that the expected optical power at the input of the detector is in the range of 10-6 to 10-10 W/cm2 (for 1 mW of launched input optical power) depending on the source-to-detector separation (Figure 5). The optical power from the fetal layer (any part of the fetal body, not necessarily restricted to the fetal head) increases with increased source-to-detector separation (Figure 6). At a source-to-detector separation of 2 cm, only 3% of the received optical power comes from fetal tissues layer. At 6 cm this value increases to 97%. However, the intensity of the collected light becomes too low for the detector compared to noise, a practical compromise is therefore achieved by choosing a source-to-detector separation of 4 cm resulting in 70% of received optical power coming from fetal layer.
Figure 4 Monte Carlo simulation model where red, green and blue traces indicated traces with high, moderate and low optical power respectively at 890 nm.
Figure 5 Illuminance and the source-detector separation at 2.5 cm fetal depth
Figure 6 Percentage power at the fetal layer and the source-detector separation
C. Adaptive Noise Cancelling and Photo-Detector Limit
Since the adaptive noise canceling limit is -34.7 dB, the photo-detector used in the optical fetal heart rate instrument with 4 cm S-D separation must be able to detect fetal signal at this limit. By using Equation 4, the expected fetal optical power, PF at -34.7 dB is estimated and tabulated in Table 3.
where PF is the estimated fetal optical power, PM+am is optical power at detector (case i) in Monte Carlo simulation as mentioned in section ii(b) and -34.7 dB is the limit of the ANC operation.
Table 3 Expected PF signal level (-34.7 dB) at different source to detector separation
Source to detector separation
Expected signal level
Expected PF signal level at -34.7 dB
From Figure 7, when S-D separation larger than 4 cm (6 cm, 8 cm and 10 cm), the expected optical power is under the photo-detector noise level. At 2 cm and 4 cm source to detector separation, the expected fetal optical powers, 2293.99Â´10-12 W/cm2 and 5.94Â´10-12 W/cm2 respectively, are higher than the photo-detector's noise (1.17Â´10-12 W/cm2) level. The photo-detector is assumed to be operated at the photovoltaic condition with 1000 Hz bandwidth and 1 cm2 active area. Therefore, source to detector separation of 4 cm, which results in 70% of optical power from fetal layer, is suitable to use with this low noise photo-detector. At 890 nm and 4 cm source-detector separation, the receiver sensitivity is optimized by considering the limitation of the adaptive filter in FHR detection.
Figure 7 Estimated PF (-34.7 dB) at 2.5 cm fetal depth
D. Proposed Hardware Set-Up for FHR Detection
The above considerations have been reflected in a preliminary design (Figure 8) which shows the proposed laboratory prototype for optical fetal heart rate (OFHR) detection. A modulation frequency is used to modulate the LED in fetal probe (I1) which is separated by 4 cm from the photo-detector, while LED in finger probe (I2) is not modulated as a common practice of pulse oximeter. These signals are amplified and digitized before digital demodulation. After pre-processing and applying the ANC algorithm, the fetal signal as well as the fetal heart rate is displayed. The detailed discussion of the instrument can be found in  and will not further discuss in this paper.
Figure 8 Proposed hardware set-up for optical FHR detection
Table 4 shows a comparison of the OFHR system and system proposed by other researches. The OFHR system is low power, low cost (eliminate the used of expensive and bulky photo-multiplier), wearable and utilized a robust adaptive filtering to enhance the acquired signal compared to other proposed system.
Table 4 Differences in the hardware configuration used in previous study
Source-detector (cm )
Ramanujam et al 
Halogen lamps (4Ã-20W) and tungsten lamp (2Ã-0.575W)
A pair of photodiode
Choe et al 
Three laser diodes with a total power of 15 mW
Nine laser diodes
Vintzileos et al 
Light-emitting diodes (735, 805, and 850 nm)
Proposed system 
The Monte-Carlo simulations using the three-layer tissue model show that the expected optical power output is in the range of 10-6-10-10 W/cm2 (1 mW input power) depending on the source to detector (S-D) separation. The used of silicon photo-detector and adaptive filter have limited the S-D separation to 4 cm which resulted in 70% of optical power from the fetal layer. This is a practical compromise between signal level and percentage of light as indicated by Monte-Carlo simulation. By using this information, an optical fetal heart rate detection system is proposed.
Currently, the optical fetal heart rate detection system has been developed and tested in Universiti Kebangsaan Malaysia Medical Center (UKMMC). The data acquisition results show a very promising result and it is possible to use the optical method to estimate the fetal heart rate via trans-abdominal measurement . Further work is required to enhance the probe with an array of LEDs to automate the selection of position with high signal to noise ratio.