Numerical simulation of the radiofrequency safety of 128-channel hd-EEG nets on a 29-month-old whole-body model in a 3 Tesla MRI

Abstract

This study investigates the radiofrequency (RF) induced heating in a pediatric whole-body voxel model with a high-density electroencephalogram (hd-EEG) net during magnetic resonance imaging (MRI) at 3 Tesla. A total of three cases were studied: no net (NoNet), a resistive hd-EEG (NeoNet), and a copper (CuNet) net. The maximum values of specific absorption rate averaged over 10g-mass (10gSAR) in the head were calculated with the NeoNet was 12.51 W/kg and in the case of the NoNet was 12.40 W/kg. In contrast, the CuNet case was 17.04 W/Kg. Temperature simulations were conducted to determine the RF-induced heating without and with hd-EEG nets (NeoNet and CuNet) during an MRI scan using an age-corrected and thermoregulated perfusion for the child model. The results showed that the maximum temperature estimated in the child’s head was 38.38 °C for the NoNet, 38.43 °C for the NeoNet, and 43.05 °C for the CuNet. In the case of NeoNet, the maximum temperature estimated in the child’s head remained compliant with IEC 60601 for the MRI RF safety limit. However, the case of CuNet estimated to exceed the RF safety limit, which may require an appropriate cooling period or a hardware design to suppress the RF-induced heating.

I. Introduction

THE electroencephalogram (EEG) is a non-invasive method to monitor seizures in children with epilepsy [1], [2]. It is reported that about 470,000 children are affected by epilepsy [3]. One out of three patients develop drug resistance epilepsy (DRE) and may require surgery to control their seizures. The goal of epilepsy surgery is to resect the epileptogenic zone (the area of the brain which is indispensable for the generation of seizures) with preserving the eloquent cortex. High-density EEG (hd-EEG) and/or EEG-fMRI is helpful for the estimation of the epileptogenic zone accurately [4]–[7]. Whereas the EEG acquires brain signals with a high temporal resolution, the spatial resolution is limited by the non-invasive EEG recording on the scalp’s surface. As a result, combining the high temporal resolution of the EEG and spatial resolution of the fMRI is of high significance to improve the estimation of the epileptogenic zone, especially in patients with deep epileptic sources [8], [9]. Thus, the need for the multimodal acquisition of EEG and functional magnetic resonance imaging (fMRI) has arisen in neuroscience, which reaps the benefits of the brain’s high spatial resolution in fMRI and the high temporal sampling rate in EEG. However, simultaneous EEG-fMRI is challenging and potentially unsafe because the MRI creates electromagnetic (EM) fields that induce radiofrequency (RF) current in the EEG trace (also known as ‘antenna effect’) that could cause undesirable Joule heating in the subject’s scalp. Previous studies have shown that the EM field interaction between EEG leads and the human body can vary depending on the main magnetic field strength of MRI, dimension, and type of RF transmitting coil, the number of EEG channels, dielectric properties of the EEG trace, and as well as the subject’s anatomy, posture, and body tissue composition [10]–[14]. EEG-fMRI systems are medical devices that require direct contact with human subjects. EEG could produce safety issues when interacting with the RF fields during an MRI scan. In this paper, we have studied the interaction of the RF field inside a child wearing an EEG net. The MRI RF safety limit for SAR in the international standard, IEC 610601–2-33 [15], suggests that the maximum RF exposure level in the normal mode be limited to 3.2 W/kg averaged in the head in case of the volume transmit coil, and 10 W/kg of the 10g-mass-averaged SAR in the head for the use of local transmit coil. These IEC standard MRI RF safety limits do not differ in children compared to adults. In terms of limits for temperature against RF energy, the maximum local temperature is limited to 39°C in the IEC 60601 [15]. Furthermore, the up-to-date Food and Drug Administration (FDA) guidance suggests that for the medical devices, an increase in local temperature up to 2°C for the SAR does not require any SAR restriction in the labeling [16]. To the best of our knowledge, the RF safety of the EEG-fMRI is only studied in the adult subjects as there were few pediatric voxel models available to date and the EEG MR safety simulation requires complex modeling of EEG electrodes and traces. This study compares RF safety in EEG-fMRI with a new proposed resistive trace compared to a copper-based trace. Compared to adults, children have a thinner skin (i.e., thermal layers), leading to deeper and more severe burn injuries than in adults [17] when exposed to heat sources.

Computational simulation has been used to estimate the EM field interaction between EEG traces and the human body. The Finite-Element-Method (FEM) was used to model for the thin EEG traces accurately [11]. FEM-based method discretizes well the geometry of the thin electrodes and wire. However, FEM relies on the surface-based model without any geometric errors (over- connections, self-intersections, etc.), and the total number of faces in the model is limited. Thus, very complex and anatomically accurate models like MARTIN [18] are currently not appropriate for FEM solvers [19]. Therefore, the finite-difference time-domain (FDTD) method has been used to estimate the EM field interaction between EEG traces and the human body in MRI [20] and GHz in Cell phone frequency [13], [14], [21]. Although the high-resolution anatomical human model can be used in the FDTD method, accurate EEG trace modeling is challenging due to the stair-case effect on the FDTD cubic grid. This caveat has been addressed in this study by implementing the FDTD solver with a non-uniform grid to generate a local grid resolution region to model the 128-channel hd-EEG traces, higher than a uniform 1 mm³ voxel in the EEG traces.

This study conducted a set of electromagnetic and thermal simulations with three different conditions: a resistive hd-EEG net (NeoNet), a copper hd-EEG net (CuNet), and without a net (NoNet). The NeoNet is the novel resistive trace design proposed in this study to mitigate RF-induced heating with thin-film technology. The CuNet is a commonly studied case [22] since commercial EEG traces/wires are composed of copper. A whole-body child model was used to assess the RF-induced heating at 3 Tesla MRI (i.e., 128 MHz Larmor frequency). The proposed study was built upon our previous work [23], which reported the numerical results of EM simulations, whereas, in this paper, we added a set of comprehensive thermal simulations and a complete uncertainty analysis.

The paper consists of the following sections. The methods utilized in the numerical simulation are described in Section II. The results of EM and thermal simulation are described in Section III. The discussion and conclusion are presented in Sections IV and V.

II. Methods

A. The Geometry and Physical Properties.

A 29-month-old whole-body voxel model, MARTIN [18], was used in the numerical simulations to compare the EM field interaction in the three cases (NeoNet, CuNet, and NoNet) in a 3 Tesla MRI. The numerical model of the hd-EEG net was composed of electrodes (i.e., sponges), pedestals (not included in the model), and traces. The EEG trace in the NeoNet was resistive to minimize the RF heating during MRI [22]. To build the hd-EEG traces, we followed the steps below:

• The EEG electrodes’ position was determined from the 3D scanned hd-EEG net on the MARTIN’s 3D printed head (Fig. 1a). Each electrode (diameter: 5 mm, length: 8 mm) was positioned perpendicularly to the model’s skin, and to avoid gaps between the model and the electrodes, these were inserted slightly into the skin. Afterward, the head’s partial electrode volume was removed during the voxelization process by assigning a higher priority for the grid on the MARTIN model than the electrodes.

• Fifteen reference trajectories were routed through adjacent rows of the electrodes that were lined up from temporal, frontal, or occipital to the parietal at the distance of 10mm on top of the skin. (Fig. 1b) The initial starting point for each reference trajectory was located at the first electrode of the respective row.

• Each reference trajectory had a length of 510 mm and ran perpendicular to the head on top of the reference electrode, where it was spaced at least 15 mm apart from every other reference trajectory. This routing trajectory is typical of a type of commercial (Brain Products GmbH, Gilching, Germany) EEG nets designed to escape the wires through the head coil (Fig. 1c).

• Up to nine traces were grouped in 3 × 3 arrays routed 1mm apart, running parallel to the reference trajectories shown in Fig. 1d.

• The voxel view of the single electrode and trace is presented (Fig. 1e)

• The 128 traces were following the reference trajectory with a width of 1 mm in diameter. (Fig. 1f)

Fig. 1.

The simulation set-up for the EEG traces and electrodes: (a) the 3D scanned hd-EEG net put on the 29-month-old head mockup, (b) the position of the electrodes which is chosen from (a) and used as the reference points for the EEG trace allocation, (c) fifteen reference trajectories routed to the parietal of the head, (d) illustration of the trace routing, (e) 3D voxel view of the single electrode and trace (f) the final drawing of 128 channel EEG traces connected on electrodes on the head of the child voxel model.

The child’s head with the hd-EEG net was positioned at the center of a body transmit coil (i.e., internal diameter: 610 mm, leg length: 570 mm, endring width: 25 mm).

The dielectric properties of the hd-EEG traces for the NeoNet were chosen as σ = 46.30 S/m, and relative permittivity of 4.2, while σ = 5.7 ∙ 10⁷ S/m, and relative permittivity of ε_r = 4.2 for the CuNet. The properties of electrodes (i.e., sponges) soaked in saline solution [11] were chosen for σ = 2.14 S/m, ε_r = 84.7, respectively. The dielectric properties of tissues were selected from the MARTIN model [18].

B. The Numerical estimation of the EM field

The complete set of harmonic Maxwell’s equations were solved at 128 MHz using a finite difference time domain (FDTD) solver using a non-uniform Yee cell grid in Sim4Life (Zurich, Switzerland). A high-performance GPU card (Tesla V100 32GB, NVIDIA, Medford, MA) was used to sample the traces with a grid fine enough to accurately model the geometry of the traces with a resolution of a maximum grid step of 0.7 mm × 0.7 mm × 1.0 mm and a minimum grid step of 0.3 mm × 0.3 mm × 0.4 mm to ensure the connection between electrodes and traces. The trace electrical continuity can be compromised by inaccurate trace modeling. After each simulation, we carefully inspected the current density on each trace and trace-electrode to verify electrical continuity or J>0. The total grid size, including the RF coils, EEG traces, and anatomical model simulated in Sim4Life, consisted of 255.8·10⁶ Yee cells. A 16-channel high-pass birdcage coil was used to generate B₁ transmit field with circularly polarized (CP) mode with an RF shield tuned to 3 Tesla Larmor’s frequency of 128 MHz [24] (Fig. 2). The electric field strength was normalized to produce a specific absorption rate (SAR) of 3.2 W/kg averaged over the child’s head in the NoNet case, which is the maximum allowed RF exposure level in a normal operation mode in the IEC guidelines [15]. In each of the three cases, the simulations’ magic time step was 0.65 ps, and the total number of steps was 596,645.

Fig. 2.

The simulation overviews. (a) the relative position of the child voxel model inside of 3T body transmit coil with RF-shield without an hd-EEG net, (b) the position of the child model in sagittal view, and (c) the child voxel model with an hd-EEG net positioned on the child’s head.

C. Temperature Estimations

The temperature of each tissue (T) over time was estimated using Pennes’ bio-heat partial differential equation [25]:

$$\mathit{\rho }·\mathit{c}\frac{\partial T}{\partial t}=\nabla ·\left(\mathit{k}·\nabla \mathit{T}\right)+\mathit{\rho }·\mathit{Q}-\mathit{\rho }·\mathit{W}\left(\mathit{T}\right){\rho }_b{c}_b\left(\mathit{T}-T_b\right)+\mathit{\rho }·\mathit{S}\mathit{A}\mathit{R}$$ (1)

where ρ is the tissue mass density matrix (kg/m³), ρ_b is the blood mass density (k/m³), c is the heat capacity matrix (J/kg/°C), c_b is the blood heat capacity (J/kg/°C), T is the temperature matrix (°C), T_b is the basal blood temperature (°C), k is the thermal conductivity matrix (W/m/°C), Q is the metabolic heat generation rate matrix (W/kg), W(T) is the thermoregulated blood perfusion rate matrix (ml/min/kg), and SAR is the specific absorption rate matrix (W/kg). The SAR is the peak spatial SAR, which was computed in section II.B.

The thermoregulated perfusion rate (W(T)) is patient dependent [26], [27]. The following thermoregulated perfusion rate was initially proposed by Laakso and Hirata [27], and modified by Murbach et al. [26], [28]. In the case of a young child, reduced systemic thermoregulation (i.e., impaired model) must be followed when modeling W(T) [28]–[30].

$$\mathit{W}\left(\mathit{T}\right)={\mathit{W}}_{\mathbf{0}}·{\mathit{L}}_{\mathit{b}}\left(\mathit{T}\right)$$ (2)

where:

$$L_b\left(x,y,z,t\right)=\left\{\begin{array}{cc}1& T(x,y,z,t)<T_0\\ 1+\left(2^{\frac{T\left(x,y,z,t\right)-T_0}{\Delta B}}\right)·0.3& T_M(x,y,z)>T(x,y,z,t)\ge T_0\\ 1+\left(2^{\frac{T_M\left(x,y,z,t\right)-T_0}{\Delta B}}\right)·0.3& T(x,y,z,t)\ge T_M(x,y,z)\end{array}\right.,{\mathit{T}}_{\mathit{M}}=\left\{\begin{array}{cc}45\mathrm{°}C& if\left(x,y,z\right)\in skin\\ 43.4\mathrm{°}C& otherwise\end{array}\right.$$

where T₀ is the initial temperature of the basal perfusion rate (T₀ = 37°C), and T_M is the maximum thermoregulated perfusion temperature matrix (°C) (Fig. 3). W₀ (ml/min/kg) is the basal perfusion rate matrix at below T₀, L_b (T) is the local temperature dependent multiplier, and ΔB (°C) is the local vasodilation parameter to match the desired perfusion increase over temperature change above T₀ (ΔB = 1.6°C).

Fig. 3.

The thermal properties map of the child tissue (a) Coronal and sagittal view of the specific heat capacity of the child tissue, (b) shows the coronal and sagittal view of the thermal conductivity of the child’s tissue, (c) shows the coronal and sagittal view of the basal perfusion rate at 37 °C of the child tissue, (d) shows the coronal and sagittal view of the perfusion rate at 38.5 °C of the child’s tissue.

To the best of our knowledge, there is no database for children’s thermal properties. The perfusion rates are both age-dependent and tissue-dependent, whereas specific heat capacity and thermal conductivity were assumed in this work to be only tissue-dependent. All the thermal properties were reported in the IT’IS database [31], but were referred only to adults. The perfusion ratio (c_p) in eight organs was estimated by comparing the blood flow rate [mL/min/100g] in each organ of a 29-month-old vs. a 20-year-old adult using the data reported by Chang et al. [32]. Following the cardiac output vs. age equation [32], the perfusion ratio was set to 1.87 for all the tissues not included in Chang’s original data set, assuming that the organ blood flow rate and cardiac output ratio are similar between children and adults [33] (See Table I). Furthermore, the perfusion ratio of liquid tissues, such as CSF and Urine, were set to 1. In contrast, the specific heat capacity and the thermal conductivity were considered the same as in adults.

TABLE I.

Dielectric and thermal properties of 29-month-old tissue at 128 MHz

Tissue	Permittivity ratio a	29-month-old tissue Permittivity [-]	Conductivity ratio a	29-month-old tissue Conductivity [S/m]	Perfusion ratiob	Basal perfusion rate of 29-month-old [mL/min/kg)]
Adrenal Gland	1.15	73.36	1.4	0.90	1.87	2.73E+03
Air	1.00	1.00	1.0	0	1.00	0
Bile	1.00	88.9	1.0	1.58	1.00	0
Blood	1.00	73.16	1.0	1.25	1.00	1.00E+04
Bone (Cortical)	1.99	29.29	2.4	0.16	1.87	1.88E+01
Bone Marrow (Red)	1.22	16.52	1.4	0.23	1.87	2.53E+02
Brain (Grey Matter)	1.33	97.78	1.6	0.94	2.00	1.53E+03
Brain (White Matter)	1.33	69.87	1.6	0.55	2.00	4.25E+02
Cartilage	1.22	64.57	1.4	0.68	1.87	6.56E+01
Cerebellum	1.33	1.06E+02	1.6	1.33	2.00	1.54E+03
Cerebrospinal Fluid	1.00	84.04	1.0	2.14	1.00	0
Connective Tissue	1.22	63.27	1.4	0.70	1.87	6.98E+01
Dura	1.33	74.44	1.6	1.20	2.00	7.60E+02
Eye (Cornea)	1.22	87.18	1.4	1.48	1.00	0
Eye (Lens)	1.22	52.21	1.4	0.44	1.00	0
Eye (Sclera)	1.22	79.3	1.4	1.28	2.00	7.60E+02
Eye (Vitreous Humor)	1.22	84.26	1.4	2.11	1.00	0
Fat	1.22	15.09	1.4	0.10	1.87	6.13E+01
Gallbladder	1.00	74.14	1.0	1.04	1.87	5.63E+01
Heart Muscle	1.18	99.42	1.4	1.07	1.13	1.16E+03
Intervertebral Disc	1.22	60.63	1.4	1.20	1.87	6.66E+01
Kidney	1.22	1.09E+02	1.4	1.19	1.02	7.23E+03
Large Intestine	1.22	93.42	1.4	0.99	1.37	1.46E+03
Liver	1.22	78.39	1.2	0.61	1.15	1.64.E+03
Lung	1.22	35.95	1.4	0.44	1.87	7.63E+02
Muscle	1.18	74.92	1.4	1.01	1.13	7.00E+01
Nerve	1.22	53.76	1.4	0.50	1.87	3.01E+02
Salivary Gland	1.15	91.38	1.4	0.96	1.87	7.18E+02
Skin	1.29	84.41	1.5	0.78	1.61	1.71E+02
Small Intestine	1.22	1.07E+02	1.4	2.37	1.37	1.41E+03
Spleen	1.22	1.01E+02	1.4	1.17	1.37	2.13E+03
Stomach	1.22	91.37	1.4	1.28	1.37	6.31E+02
Tendon\Ligament	1.22	63.27	1.4	0.70	1.87	5.44E+01
Testis	1.22	88	1.4	1.30	1.87	3.75E+02
Thymus	1.22	66.95	1.4	0.90	1.87	4.63E+02
Thyroid Gland	1.15	76.8	1.4	1.13	1.87	1.05E+04
Tongue	1.22	79.3	1.4	0.96	1.13	8.83E+01
Trachea	1.22	61.7	1.4	0.78	1.87	6.56E+01
Ureter\Urethra	1.22	68.31	1.4	0.67	1.87	3.53E+02
Urinary Bladder Wall	1.22	26.67	1.4	0.42	1.87	1.46E+02
Urine	1.00	49.95	1.0	1.75	1.00	0

Dielectric and thermal properties of 29-month-old at 3T.

^a.The permittivity (conductivity) ratio is the permittivity of the child tissue/permittivity of adult tissue [31], [50], [51]. Dielectric parameters were based on Gabriel dispersion relationship [52] and the IT’IS database [31].

^b.Perfusion ratio is the perfusion of the child tissue versus the adult. Age-dependent perfusion corrections were set to 1.87 for tissues that were not reported in the study by Chang et al. [32] by assuming that the ratio of organs blood flow rate and cardiac output remains similar between pediatrics and adults (*Eye sclera was treated same as the brain).

The thermal simulation was conducted in a two-step process to estimate the child model’s relative temperature rise with and without the two hd-EEG nets during an MRI scan with the clinically maximum allowed RF power.

i). Estimating the thermal equilibrium in biological tissues:

The steady-state temperature of each tissue T_Eq=T(x,y,z,t_∞) depends on the boundary conditions, the different metabolic heat generation rates, and the thermal properties of each tissue. In order to find the equilibrium temperature T_Eq, a thermal solution was computed with a null external EM source [34]. The equilibrium temperature T_Eq was only computed once per condition (NoNet, NeoNet, and CuNet). The Dirichlet thermal boundary condition was set on the blood with a temperature of 37 °C [34], [35]. A convection-dependent (mixed) boundary conditions were set as follows:

$$\mathit{k}\frac{d\mathit{T}}{dt}+h\left(\mathit{T}-T_{Air}\right)={\mathit{F}}_0$$ (4)

where h is the heat transfer rate for air (constant in time), T_Air = 23°C is the environment temperature (i.e., MRI room), and F₀ is the null heat flux matrix [34]. In the case of everyday clothing, the heat transfer rate of external air was set to h=6 W/m²/°C [26]. In normal breathing, the internal air heat transfer rate was set to h=10 W/m²/°C [26]. The evaporative heat loss on the skin surface was not considered in the thermal simulations, as this b.c. has only minimal effect on the final temperature results (see Supplementary Information S3).

ii). Thermal simulation with EM source using pre-calculated equilibrium temperature:

The maximum temperature (worst-case scenario) was estimated by solving Pennes’ bio-heat equation in (1) with perfusion rates in (2) using a structured time-domain thermodynamic solver [26], [36] in Sim4Life [37] with stable time-step [38]. The solution T was computed in the entire geometry and with a stop time of 15 minutes. The same Yee cell grid sampling was used both in the EM and thermal simulations to co-register the two types of simulations. A conformal thermal solver was chosen to minimize the stair-case artifact, and the total number of cells was 255.88·10⁶.

D. Uncertainty Analysis

The uncertainty analysis of the numerical simulation was performed as in Neufeld et al. [36] Each parameter’s sensitivity factor was calculated by running two simulations, which differed only by a single parameter value of a dielectric material property or coil position shift change. The second value (Value 2) was either set with a 10% change in the dielectric material properties or was set with the position of the body transmit coil shifted by 10 mm in three directions as in Neufeld et al. [36].

III. Results

A. Numerical simulation of the EM field

The results of 10 grams averaged SAR (10gSAR) were compared with and without the hd-EEG nets in Fig. 4. The maximum 10gSAR (10gSAR_max) in the head was 12.52 W/kg in the case of the NeoNet, 12.40 W/kg in the case of the NoNet, whereas the CuNet case generated 17.04 W/kg when fields were normalized to the worst-case condition in clinical scan (i.e., SAR_head = 3.2 W/kg). The maximum peak SAR (pSAR) of the NoNet was 137.54 W/kg, 196.73 W/kg for the NeoNet, and 2,155.64 W/kg for the CuNet.

Fig. 4.

EM simulation results. 10gSAR results in the child’s surface of the head (a) with NoNet, (b) with the NeoNet, (c) with the CuNet. (For all simulation, the input powers are normalized to produce 3.2 W/kg in the head of the child voxel model without the hd-EEG nets).

B. Thermal estimation

The thermal simulations estimated that the maximum temperature changes in the head after 15 minutes were 38.38 °C for the NoNet, 38.43 °C for the NeoNet, and 43.05 °C for the CuNet (Fig. 5). The maximum temperature changes’ time-course was exponential as expected by the bio-heat equation (Fig. 5). Local hot spots were shown around the skin surface in contact with EEG electrodes in the occipital and temporal areas. The thermal simulation results of the NoNet, NeoNet, and CuNet are shown in the three-dimensional surface view in Fig. 6.

Fig. 5.

Numerical simulation of the absolute temperature monitored at the position of the electrodes of the maximum (line) and averaged (bar) heating in three cases (worst-case). Thermal elevation shown with the NoNet (red), with the NeoNet (blue), and with the CuNet (green). Exponential temperature increase functions are reported for the maximum heating cases.

Fig. 6.

Thermal simulation results in 3D view after 15 minutes in the in the 3 Tesla MRI. The results of thermal simulation of a child model (a) with NoNet (b) with the NeoNet, (c) with the CuNet.

C. Uncertainties analysis

The results of the uncertainty analysis are shown in Table II in terms of 10gSAR_max and Table III in terms of peak temperature estimation (T_max). The uncertainty analysis showed that a total uncertainty of 9.83 % in 10gSAR_max and 0.42 % in T_max in the head. The highest single uncertainty parameter was the subcutaneous fat conductivity and the head position in the y-direction (i.e., 2.25 %, 2.01 %) in 10gSAR_max and muscle conductivity in thermal estimation (i.e., 0.13%) in T_max.

TABLE II.

Uncertainty Analysis (10gSAR)

Parameter	Quantity Evaluated	Value 1	Value 2	Result 1 (W/kg)	Result 2 (W/kg)	Sensitivity Factor [%/%]	Std. Dev. [36]	|Uncertainty| (%)
Trace conductivity [S/m]	10gSARmax in the head [W/kg]	46.3	50.9	12.52	12.52	0.10E-02	0.04	0.10E-03
		46.3	1.0E+02	12.52	12.52	6.39E-04	0.04	5.66E-05
		46.3	1.0E+03	12.52	14.19	1.34	0.04	0.12
Trace permittivity [-]		4.20	4.62	12.52	12.52	0.10E-03	2.80	0.53E-02
Electrode conductivity [S/m]		2.14	2.35	12.52	12.52	−2.40E-04	0.04	4.59E-04
Electrode permittivity [-]		84.7	93.2	12.52	12.52	0.50E-03	2.80	0.16E-02
Skin conductivity [S/m]		0.78	0.71	12.52	12.38	−0.11	0.04	0.59
Skin permittivity [-]		84.4	76.0	12.52	12.46	−4.69E-02	2.80	0.l6
Subcutaneous fat conductivity [S/m]		0.10	0.09	12.52	12.45	−5.37E-02	0.04	2.25
Subcutaneous fat permittivity [-]		15.1	13.6	12.52	12.43	−7.28E-02	2.80	1.35
Muscle conductivity [S/m]		1.01	0.91	12.52	11.95	−0.46	0.04	1.87
Muscle permittivity [-]		74.9	67.4	12.52	12.39	−0.10	2.80	0.38
Coil position x [mm]		0.0	10.0	12.52	11.72	−0.64	1.15	0.73
Coil position y [mm]		0.0	10.0	12.52	14.71	1.75	1.15	2.01
Coil Position z [mm]		0.0	10.0	12.52	12.91	0.31	1.15	0.36
Total Uncertainties	9.83 %

The methods used were based on the work of Neufeld et al. [36] to evaluate the uncertainty of the quantities derived by simulation, two simulations were assessed for each parameter by assigning two different values (“Value 1” and “Value 2”). The first value (“Value1”) was the one used for the simulation shown in Fig. 6, whereas the second value (“Value2”) was set across 10% changes in dielectric properties (e.g., tissue properties were adjusted towards adults’ tissue properties) and 10 mm shift of the coil position in three directions to gauge their impact on the simulation results of 10gSAR_max [36]. The results obtained for each value (“Result1” and “Result 2”) were used to evaluate the sensitivity factor of the quantity evaluated of 10gSAR_max. The measurement standard deviation (“Std. Dev.”) was derived from literature values [36].

TABLE III.

UNcertainty analysis (Temperature)

Parameter	Quantity Evaluated	Value 1	Value 2	Result 1 (°C)	Result 2 (°C)	Sensitivity Factor [%/%]	Std. Dev. [36]	|Uncertainty| (%)
Trace conductivity [S/m]	Tmax in the head [°C]	46.3	50.9	38.43	38.43	8.85E-04	0.04	7.83E-05
		46.3	1.0E+02	38.43	38.46	0.88E-02	0.04	0.80E-03
		46.3	1.0E+03	38.43	40.85	0.63	0.04	5.58E-02
Trace permittivity [-]		4.20	4.62	38.43	38.43	0	2.80	0
Electrode conductivity [S/m]		2.14	2.35	38.43	38.43	0.26E-04	0.04	4.99E-05
Electrode permittivity [-]		84.7	93.2	38.43	38.43	0	2.80	0.10E-03
Skin conductivity [S/m]		0.78	0.71	38.43	38.43	0.50E-03	0.04	0.26E-02
Skin permittivity [-]		84.4	76.0	38.43	38.42	−0.19E-02	2.80	0.63E-02
Subcutaneous fat conductivity [S/m]		0.10	0.09	38.43	38.43	−0.40E-03	0.04	1.86E-02
Subcutaneous fat permittivity [-]		15.1	13.6	38.43	38.42	−0.35E-02	2.80	6.42E-02
Muscle conductivity [S/m]		1.01	0.91	38.43	38.30	−3.19E-02	0.04	0.13
Muscle permittivity [-]		74.9	67.4	38.43	38.42	−0.20E-02	2.80	0.73E-02
Coil position x [mm]		0.0	10.0	38.43	38.22	−0.54	1.15	6.26E-02
Coil position y [mm]		0.0	10.0	38.43	38.60	4.49E-02	1.15	5.16E-02
Coil Position z [mm]		0.0	10.0	38.43	38.51	1.95E-02	1.15	2.25E-02
Total Uncertainties	0.42%

The methods used were based on the work of Neufeld et al. [36] to evaluate the uncertainty of the quantities derived by simulation, two simulations were assessed for each parameter by assigning two different values (“Value 1” and “Value 2”). The first value (“Value1”) was the one used for the simulation shown in Fig. 4, whereas the second value (“Value2”) was set across 10% changes in dielectric properties (e.g., tissue properties were adjusted towards adults’ tissue properties) and 10 mm shift of the coil position in three directions to gauge their impact on the simulation results[36]. The results obtained for each value (“Result1” and “Result 2”) were used to evaluate the sensitivity factor of the quantity evaluated(maximum temperature or T_max). The measurement standard deviation (“Std. Dev.”) was derived from literature values [36].

IV. Discussion

This study reports the numerical estimation of the RF-induced energy absorption on an anatomically accurate 29-month-old child model wearing 128-channel hd-EEG nets while being scanned in a 3 Tesla MRI. The numerical simulations of EM and Pennes’ bioheat equation on the child model were used to estimate SAR and the RF-induced heating of two different hd-EEG nets compared to the NoNet case. Contrary to SAR, temperature is a non-invasive measurement; therefore, SAR is not measured directly in human studies. According to the recent FDA guideline, both SAR and temperature studies are recommended for MRI RF safety assessments with novel medical devices [39].

Previous studies [10], [14] have shown that the presence of EEG traces could alter the RF field, which was also confirmed in this study. The effects of EEG trace conductivity against the RF heating had been reported by Atefi et al. [11] and Angelone et al. [10]. According to these studies, the choice of trace conductivity lower than 100 S/m does not increase the more than 17% of 1g-averaged peak SAR. Our study also produced similar results as the maximum 1gSAR of the NeoNet showed the 2.86% higher peak 1gSAR in the head compared to the NoNet. The peak 1gSAR of the CuNet exhibited a 2.47 times higher maximum1gSAR (64.31 W/kg) than the NoNet. The spatial distribution of the peak of heating for the CuNet was similar to Atefi et al. since we have estimated a peak in the occipital lobe. However, results differed in the parietal and frontal lobe, most likely because of the different trace geometry and the greater spherical symmetry offered by the child’s head. Furthermore, this study was performed with a 128-channels hd-EEG on a child, whereas Atefi et al. was performed with a 256-channels hd-EEG on an adult.

To the best of our knowledge, this is the first thermal study of the heating effects of hd-EEG nets on the child model with thermoregulation and perfusion in a 3T MRI. The previous thermal studies on the hd-EEG net were done on an adult and without perfusion [11]. The maximum temperature rise in 15 minutes with an InkNet on an adult head was reported relatively small (i.e., 1.7°C) when the trace conductivity was set to 40 S/m [11]. This study observed a maximum temperature rise of 1.18 °C in 15-minutes when the trace conductivity was set to 46.30 S/m with the NeoNet (0.13 °C higher than NoNet case). The thermoregulated perfusion rates need to be accordingly adjusted in the simulation [27], [28] in the case of simulations with child models. According to the study by Laakso and Hirata [27], the thermoregulated perfusion rate correction was needed because, in adults, the skin perfusion was up to 32 times higher than the basal perfusion, and all other tissues are up to 16 times higher in the temperature range between 35–45 °C. However, a reduced thermoregulation model was applied to pediatric subjects since, in children, the systemic thermoregulation is reduced [26], [29], [30]. Several studies have reported the increased basal cerebral perfusion at a young age, which was especially two times higher between 2 to 4 years of age compared to that of adults [32], [40], [41]. Similarly, the cardiac output index (mL/min/m²) was reported to decrease by age and body size [32], [41]–[44]. If the perfusion rate was constant or not age-corrected, the thermal solution results in an unrealistic overestimation of the biological tissue temperature [28].

The temperature elevation estimated for CuNet showed a more significant rise on the skin than the NoNet and the NeoNet, which corresponds to a smaller safety margin for the CuNet. The safety margin can be computed according to CEM43 standard [45]:

$$\mathit{C}\mathit{E}\mathit{M}43=\sum _{i=1}^n{t}_i·R^{\left(43-T_i(x,y,z)\right)}$$ (5)

where

$$R=\left\{\begin{array}{cc}1/4& T<43\mathrm{°}C\\ 1/2& T>43\mathrm{°}C\end{array}\right.$$

CEM43 is the cumulative equivalent minutes at 43°C of, t_i R is the i-th time interval, R is a temperature-dependent skin burn rate, and T_i is the average temperature during time interval t_i. In terms of CEM43, both NoNet and NeoNet were less than 0.01 min, whereas 8.61 min for the CuNet. To avoid thermal damage in different tissues, it was suggested that the thermal dose should be less than 2 minutes CEM43 for the elderly, children, and less than 9 minutes CEM43 for people with an uncompromised thermoregulatory ability (i.e., adults) in the controlled conditions under the supervision of medical or trained person [29], [30]. Thus, the use of CuNet is not desirable in children, while the NoNet and the NeoNet appear to be nonconducive to thermal damage.

The uncertainty analysis revealed the maximum sensitivity for the subcutaneous fat conductivity in the 10gSAR_max, and the muscle conductivity showed the highest uncertainty in thermal simulation. The coil’s shift in the y-direction showed the highest uncertainty in the 10gSAR_max, which is not surprising since any shift in the x-, y- plane brings the traces closer/further to the RF sources thus increasing/decreasing the 10gSAR.

Finally, attention should be paid to the child’s anamnesis to [46], [47], ensure that he/she has no metallic objects. In addition, it is highly likely for pediatric patients to receive sedation for the MRI scan, the guideline for which varies based on the healthcare facility and the special needs of the pediatric patient [48], [49].

Limitations.

Commercial MRI-compatible EEG electrodes have 10 kΩ current limiting resistors between trace and the electrodes that were not modeled in this paper since the NoNet and the CuNet are two extreme control conditions with no intention of comparing with any particular commercial product. The number of electrodes was fewer than in the previous studies in adults (e.g., 128-channel vs. 256-channel) since, for children, the hd-EEG net has fewer electrodes typically. The traces were chosen to escape through the coil’s opening facing the child’s parietal lobe since this is the path of choice for a type of hd-EEG net (Brain Products, Germany) using RF receive coils with a pathway for EEG leads at the top of the coil. We studied the open-ended condition of the traces since we followed Atefi et al. [11]. Our laboratory’s previous experience showed the thermal solution’s excellent accuracy, so we have not included the phantom measurements. We did not study faulty conditions that might occur on one or more traces (i.e., broken or disconnected). Further studies will cover this type of complex case. Finally, the age-relationship of the body-weight normalized cardiac output was applied for the tissues that were not reported in the study of Chang et al. [32] by assuming that the ratio of organ blood flow rate and cardiac output remains similar between children and adults [33].

V. Conclusion

This study shows that the numerical calculation of the peak 10gSAR, and thermal elevation of the 128-channel hd-EEG nets on an anatomically accurate 29-month-old whole-body model in 3T MRI compared to the NoNet case.

This study indicates that the NeoNet does not produce more than 1.2 °C heating in a 3 Tesla MRI for a 15 minutes continuous scan, whereas the CuNet show increases in the skin temperature up to 43.05 °C with a maximum increase of 7.03 °C. This study confirms the result shown previously in adults that traces with a lower conductivity (46.3 S/m) with respect to the copper lead to lower SAR and heating similar to the NoNetccase. As a result, every EEG/fMRI company restricts the use of their EEG net only to a handful of MRI sequences because of RF heating safety. However, we have shown that the heating profile of the NeoNet is very similar to the NoNet case, which potentially could remove any MRI imaging restriction.