Effect of radiofrequency coil and primary magnetic field on radiolucent composite plates

Abstract

Magnetic Resonance Imaging (MRI) systems need a material compatible with the imaging technique with lesser attenuation and provide accurate images without distortion. Carbon fibers are the best-suited materials for x-ray applications because of their radiolucent properties and reduced attenuation characteristics. However, carbon fiber produces images with distortion in the MRI system by absorbing electromagnetic energy because of its conductive nature. In the present study, five different fiber-reinforced radiolucent composite plates are analyzed to predict their suitability for a radio frequency coil and the effect of a primary magnetic field of 1.5 T and 3.0 T on mechanical responses. Simulation models are built to explore the impact of electromagnetic waves and birdcage coil configurations on composite material and quantify the temperature changes caused due to energy absorption. A multiphysics coupling simulation is being used to understand the effect of stacking sequence, ply orientation, and boundary conditions on the response of composite plates under an electro-magneto-mechanical environment.

Keywords

Magnetic field magnetic resonance imaging radio-frequency coil radiolucent composite plates electromagnetic wave electro-magneto-mechanical coupling

Introduction

Fiber-reinforced polymer (FRP) composites have been a prominent field of research because of their high specific strength, specific modulus, and opportunities to tailor their properties, making them a promising material in most industrial and engineering applications. One such application is the medical industry, where the material needs to perform all the required functions that a conventional material delivers and be inert to its surroundings. There is a strong need for a class of materials compatible with medical imaging techniques like x-ray, Computed Tomography (CT) scans, and Magnetic Resonance Imaging (MRI) in medical imaging applications. X-ray and CT scans deal with high-intensity x-rays photons to capture the image. In contrast, MRI uses radio waves in strong magnetic fields (MF) and MF gradients to generate images of human organs. Researchers have continuously incorporated reinforced composites in medical imaging techniques for a long time and have been testing the radiolucent behavior of the materials. Early research shows that carbon-fiber-reinforced composites were used as patient positioning tables in x-rays because of their low attenuation, which led to investigating a class of materials that have radiolucent properties. Bie De Ost et al.¹ made one of the first reports on using carbon fiber as excellent material for radiotherapy by using carbon fiber plates along conventional table tops for three types of photon beams and confirmed its radiolucent properties. Meara et al.² did a similar study by comparing the effects of photon beams with different energies. Both observed that carbon fibers had a better transmission of photon beams than conventional materials. But the use of carbon fiber had a significant effect on human skin because of burns caused by prolonged exposure of carbon fiber to x-rays. It directed to the improvement in the manufacturing process of carbon fiber as prepregs to reduce its effect on human skin, leading to an increase in the manufacturing cost. Ernestberger et al.^3,4 proved that the carbon fiber susceptibility artifacts were lesser than titanium spacers in the MRI system. They examined carbon fiber samples and discussed heat produced by carbon fiber samples when used under an MRI system. The heat produced caused distortion in the images created, and the images contained shadowing artifacts due to the conductive properties of carbon fiber samples.

Paley et al.⁵ developed a neonatal MR compatible incubator made of carbon fiber to transport babies to the MRI unit to detect problems and diagnose them early. Radiofrequency (RF) shadowing artifacts were visible in the diagnosed images due to the conductive nature of carbon fiber. Langmack et al.⁶ studied the effects of using glass fiber with polypropylene and observed similar transmission efficiency as carbon fiber. Robert et al.^7,8 used composites made out of natural fibers. They suggested that the natural fiber composites exhibit better imaging capabilities than carbon fiber and have minimal impact on the images produced. Jaffar et al.⁹ tested the heat produced in MRI using carbon fiber flatbed inserts. They noticed that the heat produced was well within the limit, but severe RF shielding artifacts rendered images with distortions. Several simulation models are being studied by researchers to understand the physics behind the birdcage coils and the effect of each design parameter on the field homogeneity.^10–16 Most of the articles have focused on studying human tissue’s specific absorption rate (SAR) at different MF strengths, the effects of capacitance on the field homogeneity, and designing birdcage coils with diverse approaches. However, research on the effect of radiolucent composites for patient positioning devices, electromagnetic (EM) waves, and RF birdcage coils on radiolucent composite materials is inadequate in the literature.

Any material in the presence of an electromagnetic wave absorbs the radiation and stores it as heat energy, thus increasing its temperature. Considering the implants or stents present in a patient’s body, many studies on this phenomenon have been reported. As a result of these high-energy electromagnetic waves, the temperature of these implants increases, causing tissue burns.^17–22 Kangarlu et al.²³ studied the effect of coil dimensions and field polarization of RF heating. They found that increasing the length of the birdcage coil increases the temperature change in the samples.

Another aspect of the research field would be to study the behaviour of materials in the main MF of the MRI system. It is interesting to note that in the presence of a static MF and electric field, a conducting material experiences Lorentz force and ponderomotive force due to the coupling of mechanical and electromagnetic fields. The main parameters that affect these forces are the strength of the material’s magnetic and electrical field properties. These forces would be a more distinct mechanical response than the response in the absence of an electromagnetic field. Snyder et al.²⁴ initially studied by conducting experiments to study the effectiveness of laser photography and understand the propagation of cracks in composite materials due to electromagnetic loading. It led to a series of research focusing on the electro-magneto-mechanical coupling to study the effect of multiphysics interactions of materials. One area that utilizes the coupling phenomenon is the piezoelectric/piezomagnetic materials known as magneto-electric-elastic composites. Zhupanska et al.^25–26 and Barakati et al.^27–31 primarily focused on the coupling interactions of electro-magneto-thermo-mechanical fields to understand the effect on the mechanical response of carbon fiber-reinforced composites.

The present paper has made an effort to build a simulation model to study the effects of using reinforced radiolucent composite plates as table inserts in a patient positioning device. The study consists of two parts, one focusing on the effect of RF coils on composite samples; the second; focuses on the impact of electro-magneto-mechanical coupling interaction. Five different fiber-reinforced composite materials (Bamboo, Jute, Glass, Kevlar, and Carbon) are considered for the study. The selected material samples are analyzed under the RF birdcage coils to determine the effect of electromagnetic waves and electromagnetic heating on the composite plates. Further, the influence of electro-magneto-mechanical coupling on the dynamic response of the above-mentioned fiber-reinforced composites has been evaluated. The effect of stacking sequence, ply orientation, and boundary conditions are estimated by building the models in COMSOL multiphysics software.

Methodology and governing equations

The geometric model considered is a square plate of 200 mm with a thickness of 2 mm. The material of the plate is epoxy composite reinforced with carbon fiber, kevlar fiber, glass fiber, jute fiber, and bamboo fiber, with a fiber volume fraction of 60%.^14,32–34

Radio frequency coil

The RF birdcage coil models used for the simulation are volumetric coil with 12 legs and two end rings, as shown in Figure 1. The plates studied here are 4-layered composite plates with a stacking sequence of [0/90]_s. The RF coils considered here are microstrip-based coils for both high pass and low pass configurations, i.e., the RF coils are modeled using boundary elements. Copper has been assigned as a material for the RF coil. A sphere of air domain encloses the entire model. The scattering boundary condition is given to the outer surface of the sphere domain to prevent the reflection from the outer boundary surrounding the coil geometry. A total of 24 capacitors have been considered, 12 on each end ring, for a case of high pass birdcage coil and 12 capacitors in case of low pass birdcage coils. The capacitors in a high pass and low pass birdcage configuration are shown in Figure 2. The capacitor positions are highlighted in red for both high pass and low pass configurations. A tetrahedral mesh element is used for meshing to facilitate simulation. The excitation of the coil has been carried out by supplying a continuous voltage using two-port feeding shown in a black color strip in Figure 2, which is 90° apart and has a phase difference of 90°. This type of excitation is called a Quadrature excitation and is essential to create a homogeneous circularly polarized B₁ field inside the coil.

Figure 1.

Radiofrequency coil birdcage model used for simulation.

Figure 2.

Radiofrequency Birdcage coil configurations for an magnetic resonance imaging (a) High pass birdcage coil (b) Low pass birdcage coil.

The RF coil in an MRI machine generates an electromagnetic field B₁, perpendicular to the main magnetic field B_0, while rotating at a resonance frequency called the Larmor frequency. It is dependent on the main MF of the MRI system and is given by

f = v * B_{0}

(1)

where f is the Larmor frequency, gyromagnetic ratio v equals 42.56 MHz/T for hydrogen as most of the human body contains hydrogen atoms. For a 1.5 T MRI, the Larmor frequency is about 64 MHz. When the human body is exposed to an RF coil, it absorbs the EM radiation energy and stores it as heat. After modeling the RF coil, the next step is to define the physics used to solve the RF coil problems. The physics interface added is the EM wave interface under the RF physics domain. The EM wave equation solved is given by

\nabla x {μ_{r}}^{- 1} (\nabla x E) - {k_{0}}^{2} (ϵ_{r} - \frac{j σ}{f ϵ_{r}}) E = 0

(2)

{k_{0}}^{2} = f \sqrt{ϵ_{r} μ_{0}}

(3)

where μ_r is relative permeability, k₀ is the wavenumber of free space, ϵ_r is the relative permittivity, and μ₀ is the permeability of free space. The radiation energy emitted by the RF coil as surface loss is also absorbed by the body and is stored as heat energy, increasing the temperature. An RF coil heating simulation is necessary to quantify the effects of change in temperature due to the absorption of these energies. The equations that govern the coupling between thermal and electromagnetic radiation domain is given by

ρ C_{p} \frac{\partial T}{\partial t} + ρ C_{p} u \cdot \nabla T + \nabla \cdot (- k \nabla T) = Q

(4)

where k is the thermal conductivity of the material, u is the velocity field, Cp is the material’s heat capacity, and Q is the heat source; in this case, surfaces lose from the RF coil. The RF birdcage coil has essential components like a resistor, inductor, and capacitor to control the homogeneity of the produced field B₁. A characteristic impedance of 50 Ω has been assumed across the feeding lines, and the inductance and capacitance required are calculated by using the dimensions of the RF birdcage coil.

f = \frac{1}{2 π \sqrt{L C}}

(5)

where L is the inductance and C is the capacitance. Inductance for a rectangular strip can be calculated by,¹⁶

L = \frac{μ_{0} * l}{2 π} [\ln (\frac{2 l}{w}) + \frac{1}{2}]

(6)

where l and w are the length and width of the rectangular microstrip of the RF coil. μ₀ is the permeability of free space, which is equal to 4πx10⁻⁷ N/A².

Electromagnetic coupling

The model used for the multiphysics coupling simulation is presented in Figure 3 and consists of a square plate and a cylinder enclosed inside a sphere of the air domain. An MFs interface and solid mechanics interface have been selected to couple the electromagnetic and mechanical fields with the Lorentz force coupling interface. The cylinder depicts a large solenoid to create the required primary MF using a coil domain in the MF physics interface. The required external current density is provided by using a suitable domain interface. For the case of mechanical domain interface, only the plate is considered for the study, as the study involves obtaining the plate’s dynamic response. The simply supported boundary conditions are provided to the plate’s lower edges using hinged support and roller support at the lower edges. A tetrahedral mesh setting was used for the plate, and fine mesh settings for the cylinder. The composite plate is subjected to a transversely applied impact pressure load P(x,t) given by

P (x, t) = {\begin{array}{c} p \sqrt{1 - {(\frac{x}{b})}^{2}} * \sin \frac{π t}{τ}, | x | \leq b, 0 < t < τ \\ 0, b < | x | \leq \frac{a}{2}, t > τ \end{array}

(7)

where p is the maximum pressure (p = 1 MPa), τ characteristic time parameter (τ = 0.01s), b is the half-size impact zone (b = 1 mm). Further, equation (7) is selected based on the Hertz contact theory, and the values are chosen based on the results obtained by Barakati A et al.³⁰ to maximize the EM effect on the dynamic response of the plate. The plate is assumed to be initially at rest, and the load is assumed to cause only elastic deformation. The EM loading is applied by an electric current density J(t) in the presence of a static MF B. The electrical loading is applied by passing the current density along the fiber direction of the composite plate. The loading configurations for the electromagnetic-mechanical coupling are shown in Figure 4. The electric current density is provided in the form of a DC, AC, and pulsed current, respectively, as expressed in equation (8). The AC and DC excitation is a continuous one, whereas the pulsed current has a decay sine function to depict the pulsed interaction of current density. Thus, it helps to understand the effects of electrical loading on composite plates.

J (t) = J_{0}, J (t) = J_{0} \sin \frac{π t}{τ}, J (t) = J_{0} e^{(- t / τ)} \sin \frac{π t}{τ}

(8)

B = {0, B_{y}, 0} = B_{0}

(9)

Figure 3.

Model used for the electromagnetic mechanical coupling.

Figure 4.

Loading configuration depicting electromagnetic and mechanical loads.

The mathematical coupling between EM fields and mechanical fields is primarily due to Lorentz force and ponderomotive force exerted by EM fields. The equation of motion in the presence of an EM field is given by³⁰

\nabla \cdot T + ρ (F + F^{L}) = ρ \frac{\partial^{2} u}{\partial t^{2}}

(10)

where T is the mechanical stress tensor, F is the body force vector per unit mass, FL is the Lorentz force vector per unit mass, ρ is the material density, u is the displacement vector, and ∇ is the gradient operator. The Lorentz force for an electrically anisotropic and magnetically isotropic material is given by,³⁰

F^{L} = ρ_{e} (E + \frac{\partial u}{\partial t} \times B) + (σ \cdot (E + \frac{\partial u}{\partial t} \times B)) \times B + {(((ε - ε_{0} \cdot I) \cdot E) \times B)}_{α} \nabla {(\frac{\partial u}{\partial t})}_{α} + (J \times B)

(11)

where E is the electrical field, B is the magnetic flux, ρ_e is the charge density, J is the external current density, ε₀ is the vacuum permittivity, ε and σ are the electrical permittivity and conductivity of the material, respectively.

Results and discussions

Radio frequency coil

Capacitance tuning

Capacitance tuning is a process where the required capacitance is calculated using Larmor frequency and the coil dimensions. Further studies include the capacitance at which homogenous MF B₁ is obtained. The value of capacitance required for the birdcage configurations is calculated using equation (5) and (6) and is recorded in Table 1. Figure 5 shows the MF homogeneity for an air phantom for the obtained capacitance value at 64 MHz and 127.68 MHz for 1.5 T and 3.0 T, respectively. Air phantom is generally chosen as a material for tuning the capacitance to obtain field homogeneity. The field produced here is the secondary MF B₁ which helps in the excitation and reception of MR signals during diagnosis. Moreover, in the case of high pass birdcage coils, the MF produced is minimum at the centre and increases uniformly in the radial direction. As a result, the images created using high pass birdcage coils in MRI are more accurate and undistorted when compared with MRI’s that use low pass birdcage coils.

Table 1.

Capacitance of the radiofrequency birdcage models.

Magnetic field (T)	Calculated capacitance (pF)
Magnetic field (T)	High pass	Low pass
1.5	43.5	12.5
3.0	10	3

Figure 5.

Magnetic Field of an air phantom for calculated capacitance.

RF energy absorption by composite plate

When the composite plates are placed inside the RF birdcage coil, it absorbs the radiation as energy due to the presence of EM waves. A simulation model is built to quantify the energy absorbed by the plate. The SAR value obtained would be the rate of energy absorbed by the composite plates due to radiation. For the validation of the simulation model a gel phantom has been introduced. The respective properties of three different human tissue types are given to this phantom, and the corresponding SAR values are calculated and compared with the available literature.^12,14 The obtained results are shown below in Table 2. Then the simulation is attained for a frequency domain problem by setting the frequency to Larmor frequency (64 MHz for 1.5 T and 127 MHz for 3.0 T). The results obtained for the low pass and high pass birdcage coils are presented in Table 3.

Table 2.

Comparison of specific absorption rate values of different tissues.

Tissue type	SAR (W/kg) from Thiyagarajan et al.¹⁴	SAR (W/kg) from Kawamura et al.¹²	SAR (W/kg) from Present COMSOL simulation
Brain	2.9	2.87	2.72
Bone	0.91	1.25	0.89
Skin	3.74	3.62	3.56

SAR: specific absorption rate.

Table 3.

Average specific absorption rate values of fiber-reinforced composite plates for 1.5 T and 3.0 T.

Sample	Average SAR for 1.5 T (W/kg)		Average SAR for 3.0 T (W/kg)
Sample	High pass	Low pass	High pass	Low pass
Bamboo FRP	3.54 × 10⁻⁷	5.569 × 10⁻⁶	1.3427 × 10⁻⁶	1.9389 × 10⁻⁵
Jute FRP	3.316 × 10⁻⁷	5.2171 × 10⁻⁶	1.2578 × 10⁻⁶	1.8164 × 10⁻⁵
Glass FRP	2.2757 × 10⁻⁷	3.6979 × 10⁻⁶	8.6667 × 10⁻⁷	1.2874 × 10⁻⁵
Kevlar FRP	0.12229	2.4565	0.5297	8.7357
Carbon FRP	2.2928	1.5652	2.8906	1.5381

SAR: specific absorption rate; FRP: fiber-reinforced polymer.

The rate of energy absorbed is directly proportional to the conductivity of the material, and the electric field produced due to the excitation of the RF coil. The materials with lower conductivity, like glass fiber, jute fiber, and bamboo fiber-reinforced composites, absorb lesser energy than carbon and kevlar reinforced composites. Interestingly, the kevlar reinforced composites have higher average energy absorption than the carbon fiber reinforced plates. It may be due to carbon fiber composites more resistant to absorbing radiation energy than kevlar composites. The composite plates in the low pass configuration have a higher energy absorption rate than those in high pass configurations for both 1.5 T and 3.0 T MF. It is due to the higher number of capacitors in the high pass configuration than in the low pass coil. Also, they are placed on the end ring, which helps to absorb the EM energy and attain field homogeneity.

RF heating of composite plates

As composite plates absorb EM radiation energy, the atoms within the composite plates get charged. The radiation energy gets converted into kinetic energy of the atoms, which is then released as heat energy. As a result, the composite plate becomes the source of heat generation, which leads to an increase in the temperature of these plates. The temperature change can be calculated using a multiphysics coupling interaction between an EM wave and heat transfer. Surface to ambient radiation is considered, where a part of radiation heat transfer occurs between the outer surface of the composite plates and the surrounding. The temperature change is noticed for a period of 30 mins with a step size of 3 mins. The maximum difference in the temperature obtained for high pass and low pass birdcage coils is tabulated in Table 4 and Table 5.

Table 4.

Temperature change in composite plates due to RF-heating for 1.5 T.

Sample	Ambient temp. (K)	Maximum temp. (K)		Temperature change (K)
Sample	Ambient temp. (K)	High pass	Low pass	High pass	Low pass
Bamboo FRP	293.15	293.1500012	293.15011	1.2 × 10−6	1.1 × 10−5
Jute FRP	293.15	293.1500013	293.1500113	1.3 × 10−6	1.13 × 10−4
Glass FRP	293.15	293.1500011	293.1500352	1.1 × 10−6	3.52 × 10−4
Kevlar FRP	293.15	293.6900	298.4854	0.54	5.3354
Carbon FRP	293.15	298.0300	295.5635	4.88	2.4135

Table 5.

Temperature change in composite plates due to radiofrequency-heating for 3.0 T.

Sample	Ambient temp. (K)	Maximum temp. (K)		Temperature change (K)
Sample	Ambient temp. (K)	High pass	Low pass	High pass	Low pass
Bamboo FRP	293.15	293.1500065	293.1500398	6.5 × 10−6	3.98 × 10−5
Jute FRP	293.15	293.1500067	293.1500402	6.7 × 10−6	4.02 × 10−5
Glass FRP	293.15	293.1500054	293.1500355	5.4 × 10−6	3.55 × 10−5
Kevlar FRP	293.15	295.39	312.0069	2.24	18.8569
Carbon FRP	293.15	299.37	296.5067	6.22	3.3567

Figures 6 and 7 show the temperature variations for the radiolucent composite plates for high pass and low pass configurations in a 1.5 T and 3.0 T MRI system. The change in temperature for glass, jute, and bamboo fiber-reinforced composite plates is 10⁻⁶ K. It may be because all the composite plates have minimal electrical conductivity; hence, the energy absorption rate is minimal. However, the energy absorption rate is more significant with carbon and kevlar reinforced composites. Thus, it exhibits a more considerable temperature change. It can also be noticed that the temperature change for kevlar composites is more than that of the carbon composites in low pass birdcage coils, as kevlar fiber composites have a higher average energy absorption rate. In addition, Kevlar composites are identified for their fire-resistant capabilities. Thus, the energy lost to the surroundings through radiation heat transfer is negligible compared to carbon fiber composites. These results can generalize that the temperature change is comparatively more significant for a low-pass birdcage coil than a high pass. It is one of the main reasons behind selecting high pass birdcage coils over other configurations in volume-based radiofrequency birdcage coils in MRI machines.

Figure 6.

Temperature variations of fiber-reinforced composites for 1.5 T (a) High pass birdcage coil, (b) Low pass birdcage coil.

Figure 7.

Temperature variations of fiber-reinforced composites for 3.0 T (a) High pass birdcage coil, (b) Low pass birdcage coil.

Electromagnetic mechanical coupling

Mechanical response of fiber-reinforced composite plates

Figures 8–12 show the mechanical response of fiber-reinforced composite laminates for an external MF of 1.5 T. The mechanical load is the same for the cases with external current density at J = 10⁵ A/m². All the plates are single-layer composite plates subjected to simply supported boundary conditions for all the sides. It is evident from these figures (Figures 8–12) that the effect of Lorentz force is negligible in the case of composites with very low electrical conductivity, as in the case of jute, bamboo, and glass fiber-reinforced composites. Simultaneously, a slight change in the response is also observed for kevlar fiber composites due to higher electrical conductivity than glass, jute, and bamboo fiber composites. It can also be observed that the response from carbon fiber reinforced composites exhibit decay in the vibrational response as the external MF increases. It may be because the Lorentz force influences the reduction of the response, thereby allowing the system to stabilize earlier. Hence carbon fiber composites have been selected for studying the effect of external current density, stacking sequence, and ply orientation in the present study.

Figure 8.

Mechanical response of Glass fiber composites.

Figure 9.

Mechanical response of Kevlar fiber composites.

Figure 10.

Mechanical response of Jute fiber composites.

Figure 11.

Mechanical response of Bamboo fiber composites.

Figure 12.

Mechanical response of Carbon fiber composites.

Effect of an electric current waveform and magnitude of current density

Figure 13 shows the effect of external current density waveform on the mechanical response of a single-layer of carbon fiber composites subjected to an in-plane MF of 1.5 T under simply supported boundary conditions. The response (Figure 13) demonstrates that when the external current density is supplied in pulsed format, the composites tend to decay their response quicker and attain stability. There will be traces of EM load constantly acting on the composite plate for the DC current density. As for the case in AC current density, the responses decay slowly compared to the case of pulsed current density. Hence pulsed current density has been selected for further studies.

Figure 13.

Single Layer composite: Effect of external current density waveform.

Figure 14 depicts the response of single-layer carbon fiber composites under the influence of the magnitude of current density. The composites are subjected to mechanical load and in-plane MF of 1.5 T under simply supported boundary conditions. It can be noticed from the response plot that as the external current density is increased, there is a slight increase in the decay of vibration responses. It is due to the rise of Lorentz force as the current density increases.

Figure 14.

Single Layer composite: effect of the magnitude of external current density.

Effect of stacking sequence, ply orientation, and boundary conditions

Figure 15 shows the response of single-layer carbon fiber composites subjected to a mechanical load P(x, t), external pulsed current density J(t), and in-plane MF (B = 1.5 T) for different boundary conditions. At MF of 1.5 T, the response of plates subjected to cantilever conditions decays slower to attain stability. On the other hand, the plates' response to fixed support deteriorates comparatively faster than those of the simply supported composite plates. Thus, it illustrates the induced stiffness for the composite plates due to boundary conditions. Figure 16 shows the effect of stacking sequence on the response of the carbon fiber composites subjected to similar loading conditions and simply supported boundary conditions. It can be noticed that a 4-layered composite with [0/90]_s configurations have higher stiffness because of the stacking of plies. Figures 17–19 show the effect of ply orientations for simply supported boundary conditions for 2-layered composite plates with a low MF (B = 1.5 T) and a high MF (B = 3.0 T). All the considered composite plates are subjected to identical mechanical and electrical loading. It is evident from these figures (Figures 17–19) that in the presence of a higher MF (B = 3.0 T), the mechanical response decays faster than a relatively lower MF for all the cases. It can also be observed that composites in [0/90] ply orientation has higher stiffness than other ply orientations.

Figure 15.

Single layer composites: Effect of boundary conditions (B = 1.5 T).

Figure 16.

Effect of number of layers and stacking sequence in B = 1.5 T.

Figure 17.

Mechanical response of 2-layer composite ([0/30]).

Figure 18.

Mechanical response of 2-layer composite ([0/60]).

Figure 19.

Mechanical response of 2-layer composite ([0/90]).

Figures 20–22 reveal the influence of ply orientations for a 4-layered composite plate for a low MF (B = 1.5 T) and a relatively high MF (B = 3.0 T). For the identical loading conditions, as the number of layers increases, the materials become stiffer. As a result, the response of the composite plates decays faster even in the absence of EM loading. The effect of EM loading can be seen in the case of [0/30]_s and [0/60]_s composite plates. As the number of 90° layers increases, the material becomes stiffer because of better distribution of properties than any other ply orientations. Therefore, 90° ply plates are preferred over the other ply layers.

Figure 20.

Mechanical response of 4-layer composite ([0/30]s).

Figure 21.

Mechanical response of 4-layer composite ([0/60]s).

Figure 22.

Mechanical response of 4-layer composite ([0/90]s).

Effect of MF on natural frequency and Q-factor

It is evident from the previous section (Section 3.2.2 & 3.2.3) that the mechanical response of composite plates gets decayed in the presence of MF, and the decay rate is proportional to the strength of the external MF. Thus, it is apparent that the presence of EM loading acts like a damper on a mechanical system. Consequently, it becomes interesting to calculate the change in the natural frequency of composite plates under the MF. An eigenfrequency study state simulation is adapted to find the natural frequency of composite plates. As EM loading induces damping into the system, the results obtained from the simulation are complex. The imaginary part of which gives the decay rate caused due to the damping. The damped natural frequency is calculated for the first five vibrational modes for different MFs, and the results are shown in Table 6. It can be seen from Table 6 that as the magnitude of EM loading increases from 0.5 t to 3.0 T, the natural frequency decrease. Further, it is evident that the influence of EM loading is more effective in dampening the systems with single-layer plies than the 2-layer and 4-layer composite plates; the same is also witnessed in Figures 23–25.

Table 6.

Damped Natural frequency of composite plates in a different magnetic field.

Samples	Frequency mode	Natural frequency (Hz)	Damped frequency (Hz)
Samples	Frequency mode	Natural frequency (Hz)	0.5 T	1.0 T	1.5 T	2.0 T	2.5 T	3.0 T
1-layer	1	223.551	223.549	223.54	223.506	223.414	223.218	222.862
	2	348.678	348.675	348.670	348.648	348.589	348.465	348.239
	3	576.371	576.369	576.366	576.353	576.317	576.242	576.106
	4	764.35	764.352	764.349	764.339	764.312	764.255	764.151
	5	865.375	865.372	865.369	865.361	865.337	865.287	865.195
2-layer [0/90]	1	354.918	354.914	354.913	354.907	354.893	354.862	354.806
	2	719.105	719.104	719.1031	719.100	719.093	719.078	719.050
	3	1068.52	1068.506	1068.505	1068.503	1068.499	1068.489	1068.470
	4	1380.04	1380.037	1380.036	1380.035	1380.032	1380.024	1380.010
	5	1407.417	1407.416	1407.415	1407.413	1407.410	1407.402	1407.388
4-layer [0/90/90/0]	1	379.77	379.766	379.765	379.760	379.746	379.717	379.665
	2	895.33	895.333	895.332	895.331	895.325	895.313	895.291
	3	1064.773	1064.769	1064.768	1064.767	1064.762	1064.752	1064.734
	4	1478.408	1478.405	1478.404	1478.403	1478.399	1478.392	1478.379
	5	1790.24	1790.237	1790.236	1790.235	1790.232	1790.226	1790.215

Figure 23.

Single-layer composites: Effect of magnetic field on Q-factor.

Figure 24.

2-layer [0/90] composites: Effect of magnetic field on Q-factor.

Figure 25.

4-layer [0/90/90/0] composites: Effect of magnetic field on Q-factor.

Figures 23–25 show the Q-factor variation in different vibrational modes for single-layer, 2-layer, and 4-layer composite plates subjected to external current density and MF under simply-supported boundary conditions. The Q-factor is a dimensionless parameter that describes the damping nature of an oscillating system. A higher Q-factor would mean that the system losses energy at a lower rate during oscillations and decays more slowly. In addition, a Q-factor value greater than ½ is an underdamped system, and less than ½ is overdamped. A low Q-factor means that the energy loss during oscillations is more, and the response decays rapidly in a damped oscillation. For a case of single layer composites, as the magnetic field is increases, the Q factor value reduces to a lower value as compared to 2-layer and 4-layer composites, indicating a higher decay rate for single layer composites. This is also seen in Figure 16. At higher modes, the energy lost by the system is larger, which can be clearly seen in the cases of single-layer, 2-layer, and 4-layer composites in Figure 23–25.

Conclusion

This paper analyzes the mechanical responses of five different fiber-reinforced radiolucent composite materials to predict their suitability under a Radio-Frequency coil and a primary MF of 1.5 T and 3.0 T. The birdcage model is built based on the microstrip-based approach of the birdcage coil. The energy absorption rate and EM simulation show that an EM wave inside the RF coil does not significantly affect materials like glass fiber, jute fiber, and bamboo fiber-reinforced composites. To comprehend the impact of stacking order, ply orientation, and boundary condition on the response of composite plates in an electro-magneto-mechanical environment, a multiphysics coupling simulation is being employed. Hence finds its applications where flatbed inserts can be made up of these materials for patient positioning in MRI machines without causing any distortions in the imaging process. Further, it also helps in reducing the RF shadow artifacts found in the case of carbon fiber reinforced flatbed insert with a higher energy absorption rate. Even though all the reinforced materials are radiolucent and can handle temperature changes in high-pass and low-pass birdcage coil, the kevlar and carbon-reinforced composites do not serve as excellent materials for patient positioning flatbed inserts.

A composite plate modeled as a patient table insert experiences EM loading when placed inside an MRI machine. A multiphysics coupling simulation containing EM and mechanical interfaces is carried out to study the influence of EM loading on composite plates. The results show that the mechanical response of the composite plates decays in the presence of an in-plane MF. This decay in response is directly proportional to the strength of the MF and the external current density. The deterioration in the response of the composite plates starts diminishing with the increase in stacking sequence. The effect of EM loading starts disappearing as the number of 90° layers increases. The damped frequency of the composite plates starts reducing as the external MF increases. This reduction is more in the case of single-layer composites than the 2-layer and 4-layer composites. The presence of 90° ply layers makes the multi-layered composite plates stronger, stiffer, and more resistant to damping under EM loading. Hence the influence of EM loading is more prominent in the case of single-layer and uni-directional composites.

Footnotes

Acknowledgements

The authors would like to register their gratitude to Science and Engineering Research Board (SERB) ASEAN-India S&T Collaborative (AISTDF) Project No. , Govt. of India for providing necessary grants to carry out the research.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the Science and Engineering Research Board (SERB) ASEAN-India S&T Collaborative (AISTDF) (IMRC/AISTDF/CRD/ 2019/000128).

Data availability statement

All obtained and analyzed data during this study are included in the article.

ORCID iDs

Hesam Kamyab

Subhaschandra Kattimani

References

De Ost

Vanregemorter

Schaeken

, et al. The effect of carbon fiber inserts on the build-up and attenuation of high energy photon beams. Radiother Oncology 1997; 45: 275–277.

Meara

Langmack

. An investigation into the use of carbon fiber for megavoltage radiotherapy applications. Phy Med Bio 1998; 43: 1359–1366.

Ernstberger

Heidrich

Bruening

, et al. The interobserver-relevance of intervertebral spacer materials in MRI artifacting. Euro Spine J 2007; 16: 179–185.

Ernstberger

Buchhorn

Baums

, et al. In-vitro MRI detectability of interbody test spacers made of carbon fiber-reinforced polymers, titanium and titanium-coated carbon fiber-reinforced polymers. Acta Orthopaedica Belgica 2007; 73: 244–249.

Paley

MNJ

Hart

Lait

, et al. An MR-compatible neonatal incubator. Br J Radiol 2012; 85: 952–958.

Langmack

. The use of an advanced composite material as an alternative to carbon fiber in radiotheraphy. Radiography 2012; 18: 74–77.

Morris

Trabi

Spicer

, et al. A natural fibre reinforced composite material for multi-modal medical imaging and radiotherapy treatment. Mater Lett 2019; 252: 289–292.

Morris

Geraldi

Stafford

, et al. Woven natural fibre reinforced composite materials for medical imaging. Materials 2020; 13: 1684–1693.

Jafar

Reeves

Ruthven

, et al. Assessment of a carbon fiber MRI flatbed insert for radiotherapy treatment planning. Br J Radiol 2016; 89: 20160108.

10.

Collins

Smith

. SAR and B1 field distribution in a heterogenous human head model with a birdcage coil. Magn Reson Med 1998; 40(6): 847–856.

11.

Giovannetti

Landini

Maria

, et al. A fast and accurate simulator for the design of birdcage coils in MRI. MAGMA 2002; 15: 36–44.

12.

Kawamura

Saito

Kikuchi

, et al. Specific absorption rate measurement of birdcage coil for 3.0-T magnetic resonance imaging system employing thermographic method. IEEE Trans Microw Theory Tech 2009; 57: 2508–2514.

13.

Gurler

Ider

. FEM based design and simulation tool for MRI birdcage coils including eigenfrequency analysis, 2012.

14.

Thiyagarajan

Kesavamurthy

Bharath Kumar

. Design and analysis of microstrip-based RF birdcage coil for 1.5T magnetic resonance imaging. Appl Magn Reson Imaging 2014; 45: 255–268.

15.

Manko

Styla

. Design and numerical simulation of a RF coil using the COMSOL Multiphysics software. Przegląd Elektrotechniczny 2019; 95: 168–171.

16.

Kim

Yun

, et al. A simple analytical solution for the designing of the birdcage RF Coil used in NMR imaging applications. Appl Sci 2020; 10: 2242.

17.

Mattei

Triventi

Calcagnini

, et al. Complexity of MRI induced heating on metallic leads: Experimental measurements of 374 configurations. BioMed Eng Online 2008; 7: 11.

18.

Settecase

Hetts

Steven W

Martin

, et al. RF Heating of MRI-Assisted Catheter Steering coils for Interventional MRI. Acad Radiol 2011; 18: 277–285.

19.

Golestanirad

Kirsch

Bonmassar

, et al. RF-induced heating in tissue near bilateral DBS implants during MRI at 1.5 T and 3 T: the role of surgical lead management. Neuroimage 2018; 184: 566–576.

20.

van den Brink

. Thermal effects associated with RF exposures in diagnostic MRI: overview of existing and emerging concepts of protection, concepts in magnetic resonance imaging Part B, 2019.

21.

Winter

Seifert

Zilberti

, et al. MRI-related heating of implants and devices: a review. J Magn Reson Imaging 2020; 53: 1646–1665.

22.

Seo

Wang

. Measurement and evaluation of Specific absorption rate and temperature elevation caused by an artificial hip joint during MRI scanning. Sci Rep 2021; 11: 20211134.

23.

Kangarlu

Ibrahim

Shellock

. Effects of coil dimensions and field polarization on RF heating inside human phantom. Mag Reson Imaging 2005; 23: 53–60.

24.

Snyder

Sierakowski

et al. Preliminary assessment of electro-thermo-magnetically loaded composite panel impact resistance/crack propagation with high speed digital laser photography. 24th international congress on high-speed photography and photonics, Proceedings. Sendai, Japan: of SPIE, September 2000, 2001, 4183, pp. 24488–29513.

25.

Zhupanska

Sierakowski

. Effects of an electromagnetic field on the mechanical response of composites. J Com Mater 2007; 41: 633–652.

26.

Zhupanska

Sierakowski

. Electro-thermo-mechanical coupling in carbon fiber polymer matrix composites. Acta Mechanica 2011; 218: 319–332.

27.

Barakati

Zhupanska

. Effects of coupled fields on the mechanical response of electrically conductive composites. Procedia Eng 2011; 10: 31–36.

28.

Barakati

Zhupanska

. Influence of the electric current waveform on the dynamic response of the electrified composites. Int J Mech Mater Des 2013; 9: 11–20.

29.

Barakati

Zhupanska

. Thermal and mechanical response of a carbon fiber reinforced composite to a transverse impact and in-plane pulsed electromagnetic loads. J Eng Mater Technol 2012; 134(3): 031004.

30.

Barakati

Zhupanska

. Analysis of the effects of a pulsed electromagnetic field on the dynamic response of electrically conductive composites. Appl Mat Model 2012; 36: 6072–6089.

31.

Barakati

Zhupanska

. Mechanical response of electrically conductive laminated composite plates in the presence of an electromagnetic field. Compos Struct 2014; 113: 298–307.

32.

Biswas

Ahsan

Cenna

, et al. Physical and mechanical properties of Jute, bamboo and Coir Natural fiber. Fibers Polym 2013; 14: 1762–1767.

33.

Chand

Sharma

Bapat

, et al. Effect of positional density on DC conductivity of Bamboo fiber. Bioresources 2010; 5(3): 1789–1798.

34.

Jayamani

Hamdan

Rahman

, et al. Comparative study of dielectric properties of hybrid natural fiber composites. Procedia Eng 2014; 97: 536–544.