This article is a work in progress (not submitted yet) . It has not been edited to a final form as a journal article.
Transcutaneous electrical nerve stimulation (TENS) is used to relieve lower back pain associated with pregnancy. However, little has been reported on the safety of the resulting electric field inside the fetus. This paper uses the computational phantom of a 30 weeks pregnant female to compute the electric field inside the fetus and assess the safety based on the guidelines of the International Commission for Non-Ionizing Radiation Protection (ICNIRP). Two electrode types, a symmetric biphasic electrode current waveform, and a range of stimulation parameters used in standard TENS devices were considered. For waveform of pulse duration less than 260 μs, an electrode current of 30 mA ensures the electric field inside the fetus's brain is below the ICNIRP basic restriction. This implies a risk of stimulating the fetus's brain if a wide pulsed high strength TENS is used.
Transcutaneous electrical nerve stimulation (TENS) is a noninvasive technique to relieve pain. TENS uses pulsed electrical currents that are applied across the surface of the skin to inhibit the onward transmission of pain-related information in the central nervous system. This is considered a safe therapy for lower back and/or pelvic girdle pain during pregnancy since other options, such as, drug treatment and exercise, are usually limited due to pregnancy [1, 2]. However, there is little knowledge about the level and safety of the electric field inside the fetus. Perhaps the only study on the safety of TENS during pregnancy, Bundsen and Ericson  suggested the current density on the fetal heart should not exceed 0.5 μA/mm^2 based on clinical experience and experimental measurements. However, it is difficult to relate this current density value to measurable parameters, such as, the amplitude of the electrode current.
Here, the electric field produced inside the fetus was computed by utilizing the computational phantom of a 30 weeks pregnant female. The computed electric field was compared to the basic restrictions of the International Commission for Non-Ionizing Radiation Protection (ICNIRP) to determine whether TENS stimulates the fetus's central nervous system. A range of stimulation parameters, a symmetrical biphasic current, and two type of electrodes were considered to establish a linear relationship between the maximum electric field in the foetus's brain and the electrode current.
The pregnant female computational phantom was built by merging the mesh model of a non-pregnant female (obtained from http://www.nevaelectromagnetics.com ) and a foetus (obtained from http://femonum.telecom-paristech.fr/ ). The non-pregnant female mesh model (VHP Base 3.0), which has 26 individual anatomical structures, was constructed from a cryosection image dataset of a female cadaver of height 162 cm. The VHP Base 3.0 was modified by stretching the skin, fat and muscle tissues at the abdomen by referring to the anatomical atlas of a pregnant female. Also, other body parts, such as the intestine, liver, stomach, and blood vessels were deformed to place the uterus. The triangular surface meshes were made not to have non-manifold edges, non-manifold vertices and self-intersected faces to make them compatible for finite-element-method (FEM) computations. The development of the foetus phantom is discussed in . The model consists of brain, lungs, skeleton, soft tissues, uterus and uterus content. The uterus content consists of uterus wall, placenta and amniotic fluid. The placenta was modeled with location and shape similar to that of the anatomical atlas used. Figure 1 shows the computational phantom of the pregnant female and the foetus.
For the frequency spectrum of TENS current, the instantaneous electric potential distribution inside the body can be computed by solving the charge continuity equation. And, the electric field strength can be computed from the potential distribution using the its gradient. We solved the charge continuity equation using the stationary current solver of CST Studio (CST, Darmstadt, Germany), which allows the use of a uniform electrode current density (or the electrode current) as the initial condition.
The conductivity of the mother's tissue were obtained from the online ITIS database (https://itis.swiss/virtual-population/tissue-properties/database/ ). Since the fetal tissue has higher water content than that of the mother's, its conductivity is higher. For a 30 weeks fetus, the conductivity of the fetal tissue are 1.84 times more than the mother's tissue according to the formula proposed in . Consequently, the conductivity of the foetal brain was related to the average of the conductivities of the mother's isotropic grey matter and white matter, the fetal lungs to the mother's deflated lungs, the fetal skeleton to the mother's cortical bone, and the foetal soft tissues to the mother's muscle. The conductivity of the amniotic fluid was taken as 1.27 S/m  and the conductivity of the placenta was assumed to be equal to the conductivity of blood.
A double channel TENS with four electrodes attached on the lower back was simulated as shown in fig 2. The standard electrode sizes of 5x5 cm and 5x9 cm were considered. The electrodes of one channel were placed symmetrically in paravertebral location at the level of L3 and L2; and the electrodes of the other channel in the distal and lateral aspect of the sacroiliac joint. A symmetric biphasic waveform electrode current with pulse duration of 30 μs - 260 μs and frequency 2 Hz - 150 Hz was considered.
For constant-current TENS devices, a linear relationship between the electrode current I (A) and the maximum electric field strength in the fetus's brain E_a (V/m) can be derived as E_a= kI, where k is the proportionality constant. From the computations, we found that k = 12.25 for 5x5 cm electrodes and k = 11.75 for 5x9 cm electrodes. Figure 3 shows the electric field and the corresponding current density for 80 mA electrode current using the 5x9 cm electrodes.
The safety of TENS was assessed by comparing the maximum electric field in the fetus's brain to the basic restriction set by the ICNIRP. The basic restrictions of ICNIRP in the frequency range of 1 Hz - 100 kHz were defined based on the well-known effects of the low frequency electric fields, which are, the stimulation of electrically excitable nerve and muscle tissues, the perception of surface charges, and the induction of retinal phosphenes . The ICNIRP guideline states that the evidences for the neurobehavioural, developmental or reproductive effects due to low frequency electromagnetic field exposure are much less clear or very weak. ICNIRP recommends basic restrictions of an internal electric field less than 0.4 V/m for 1 Hz - 3 kHz and 1.35x10^-4 f V/m for 3 kHz - 10 MHz, where f is frequency in Hz. For frequencies lower than 1 kHz, additional restriction conditions apply for the central nervous system (CNS) tissues in the head, which sets 0.1/f V/m for 1 Hz - 10 Hz, 0.01 V/m for 10 Hz - 25 Hz, and 4x10^-4 f V/m for 25 Hz - 1000 Hz.
The maximum electric field inside the fetus's brain was compared to the ICNIRP basic restriction by converting it to the frequency domain via Fourier Transform and applying the spectral method outlined in . For the electric field in the foetus's brain to be below the ICNIRP basic restriction, the equation shown in fig 4 (or equation 7 in page 829 of the ICNIRP guideline) should be satisfied, where t is time and EL_i is the exposure limit at the ith harmonic frequency f_i, where E_i, theta_i, phi_i, are the amplitude of the electric field spectrum, its phase angles and phase angles of the filter given in the ICNIRP guideline at the harmonic frequencies. The values of E_i and theta_i were generated from the spectrum of the symmetric biphasic waveforms obtained by varying the pulse rate within 2 Hz - 150 Hz, the pulse duration 30 μs - 260 μs and the matching the amplitude with E_a as shown in Fig 5.
Figure 6 shows the maximum value of M(t) for the electric field of 0.94 V/m versus the pulse frequency of waveform of different pulse duration. The 0.94 V/m corresponds to the maximum electric field on the fetus's brain due to 80 mA electrode current for 5x9 cm electrodes or 77 mA for 5x5 cm electrodes. A further analysis showed that a maximum electrode current of 30 mA ensures the electric field inside the fetus's brain is below the ICNIRP basic restriction for waveform with pulse duration less then 260 μs. This indicates that when using the standard TENS devices at high stimulation strength of wide pulses, there might be a risk of stimulating the fetus's brain.
It should be noted that the electric field was computed using a computational model that represents a 30 weeks fetus in head-down and bottom-up position and a slightly obese mother. The numerical values presented might not be representative for other fetal positions, different stages of fetal development, and the anatomical variations of the mother. Thus, caution should be taken when using the results.
The electric field inside a 30 weeks fetus was computed by utilizing the computational phantom of a pregnant female. Two types of electrodes, a symmetrical biphasic waveform, and a range of stimulation parameters were considered to assess the safety of the electric field inside the fetus's brain. For waveform of pulse width less than 260 μs, it was found that a maximum of 30 mA electrode current ensures the electric field inside the fetus's brain is below the ICNIRP basic restrictions. This implies that when wide pulses are administrated at high stimulation intensity, there is a risk of stimulating the fetus's brain.