F16HighFieldMRI

Quantitative Characterization of Radiofrequency Coils Designed for Human Ultrahigh Field Magnetic Resonance Imaging

Vandon T. Duong

University of Minnesota – Twin Cities

School of Physics and Astronomy

Minneapolis, MN 55455

Abstract

The thermal responses to radiofrequency (RF) energy deposition from RF coils in ultrahigh field magnetic resonance imaging (MRI) were investigated. Temperature records were taken by iteratively heating cylindrical gel phantoms using 7 T MR system at the Center for Magnetic Resonance Research (CMRR). The specific absorption rate (SAR) was mapped for a single-loop RF coil by observing the phase evolution at sequential stages of heating. Heating of the gel phantom by the RF coil was inhomogeneous, with elevated SAR near the proximity of the electric current. SAR calculated at a particular voxel supported that thermal conductivity can be ignored for heating a gel phantom, but the value varied by approximately 20% across measurements at three different echo times.

Introduction

Magnetic field and temperature mapping characterization of radiofrequency (RF) coils is essential for the safety testing of magnetic resonance imaging (MRI) systems. During an MRI scan, RF pulses can generate dielectric heating due to the rapidly rotating and vibrating water molecules, potentially damaging biological tissue [1]. The alternating electrical field from the RF pulse is what elevates the thermal energy of dipolar molecules (e.g. water). Inhomogeneous heating can be especially prominent in high or ultrahigh field MRI scan [2]. Compared with standard clinical scanners operating between 1.5 T and 3 T, ultrahigh field scanners provide substantial gains in signal to noise ratio (SNR) [3]. This has encouraged the investigation of how the heating may be distributed and quantitatively assess the risk of tissue damage. The specific absorption rate (SAR) is the rate that tissue absorbs energy when exposed to RF signal, which can be evaluated by monitoring the temperature changes of an object. We will characterize both the magnetic field and temperature mapping of a single-loop RF coil for use in a 7 T MR system on a 1 L gel phantom.

Theory

Protons and electrons are particles which obey the Pauli Exclusion Principle; these particles are known as fermions, which have half-integer spin. The Pauli Exclusion Principle states that at any given moment, identical fermions cannot occupy the same state within a quantum system [4]. The spin quantum number of a fermion is either ±1/2, colloquially known as spin-up or spin-down, which corresponds to the z-component of the spin angular momentum [5]. The spin is an intrinsic angular momentum which is associated with a magnetic moment. Figure 1 depicts the spin angular momentum vector at an angle to the z-direction, with total magnitude of √3/2 ℏ.

The angled magnetic moment gives rise to precession when the particle is in an external magnetic field. The torque τ experienced is the cross product of the magnetic moment μ and the external magnetic field B_0 [6]:

τ=μ×B_0 (1)

The magnet moment μ is determined by the charge e, particle mass m_p, and the spin angular momentum I. Equation 1 can be re-written as:

τ=μB_0 sin⁡θ=(e/(2m_p ) I) B_0 sin⁡θ (2)

The torque can also be expressed as a rate of change of the spin angular momentum.

τ=ΔI/Δt=(I sin⁡θ Δϕ)/Δt (3)

Equating Equation 2 and 3 and rearranging for angular velocity dϕ/dt gives rise to a precession. The frequency ω associated with the precession, also known as the Larmor frequency, is proportional to the external magnetic field B_0 by the gyromagnetic ratio γ [6]:

ω=dϕ/dt=(e/(2m_p )) B_0=γB_0 (4)

Where the gyromagnetic ratio for hydrogen is 42.58 MHz/T [7]. For MRI systems at 7 T, the Larmor frequency is 298.06 MHz. Resonance absorption is the absorption of an electromagnetic photon at a frequency equal to the quantized excitation of nuclear spins [6]. In other words, resonance absorption can be detected using radiofrequency (RF) pulses matching the Larmor frequency. The RF pulse, which is perpendicular to the external magnetic field, will disturb the net magnetization vector and induce the collection of protons to precess in phase [6]. The protons release this energy through interaction with other nuclei; this is the relaxation of the magnetization vector. The RF signal is received by an RF coil, converted by an analog-to-digital converter (ADC), and processed by a 2D Fourier transform to acquire the MR image.

Humans are mostly made of water and are effectively dielectric since water molecules are molecules with dipoles. At frequencies in the RF range, heating within a dielectric material can occur due to dipole rotation [8]. Dipole rotation is caused by the high frequency oscillation of an electric field, increasing the average kinetic energy of the particles (i.e. temperature increases). This is also the principle behind using microwave ovens to cook food.

Theories from [1] and [9] were used to construct the derivation of the heat equation in the context of this experiment. First consider the continuity equation for energy conservation, where u is the energy density, q is the energy flux, and t is the time [9]:

∂u/∂t+∇∙q=0 (5)

The energy density u for heat is related to the material density ρ, specific heat capacity c, and the temperature T. The energy flux q for heating is related to the conductivity k and the temperature gradient ∇T. The relationships are [1]:

u=ρcT (6)

q=-k∇T (7)

However, heat is not necessarily conserved for a system. The right side of Equation 5 is replaced by the power density term SARρ. SAR is the specific absorption rate (SAR) which describes the amount of RF power absorbed by the tissue, which is effectively the dielectric heating [1]. The heat equation is therefore:

ρc dT/dt-∇∙(k∇T)=SARρ (8)

Assuming that thermal conductivity is negligible, the ∇∙(k∇T) term is zero. The validity of no diffusion must be examined by experiment; that is, heating should be linear throughout the experiment given this assumption. Convection can be neglected in the case of a gel phantom. Therefore Equation 8 can be arranged as:

SAR=c dT/dt (9)

The SAR is therefore monitored as the temperature change multiplied by the specific heat capacity of the object. If the temperature can be monitored during MR experiments, then the potential for heating can be described by Equation 9.

Proton resonant frequency (PRF) is an MR-compatible technique to monitor temperature; the formulation for PRF follows from [7]. A study of the model of water from [10] is used to aid in the understanding of the PRF technique. Water molecules tend to form short-lived networks or clusters (see Figure 3) due to intermolecular hydrogen bonds, which are weaker than the intramolecular hydrogen bonds of water. The number of intermolecular hydrogen bonds is determined by the equilibrium between water clusters and individual particles, which shifts for different environment temperatures. Heating the local environment will disrupt the intermolecular hydrogen bonds and release electrons from the interactions forming the clusters. The diamagnetic response alters as electrons are transferred or shifted due to bonds forming, breaking, bending, or stretching. In an external magnetic field, electrons will orient in a way to produce an opposing magnetic field (i.e. nuclear shielding) [11]. This nuclear shielding by electrons (also known as electron screening) will cause the protons to experience a lower magnetic field. The local magnetic field B_l can be described as the external magnetic field B_0 reduced by a term σ describing the nuclear shielding:

B_l=(1-σ) B_0 (10)

The reduction of the magnetic field will lower the Larmor frequency by equation 4. This is called chemical shift, where the change in the resonance frequency is caused by the electron orbital coupling to the external magnetic field [11]. Temperature increases are linearly proportional with stronger electron screening by a temperature coefficient a (-0.01 ppm/°C):

Δσ=aT (11)

Increased nuclear shielding follows from elevated temperature, resulting in a lower magnetic field and therefore reduced resonant frequency. A phase shift can be observed when monitored at two separate time points. Hence, the temperature change can be calculated from the corresponding phase shift Δϕ and echo time T_E using a gradient-recalled echo (GRE):

ΔT=Δϕ/(aγB_0 T_E ) (12)

Methods

Experiments will be conducted using the 7 T human MR system at the Center for Magnetic Resonance Research (CMRR). The MR system is located in a room with an iron and copper barrier for blocking external magnetic fields and RF noise. Figure 5 depicts the setup used for the heating experiments. The RF coil is a single loop with an inner diameter of 10.7 cm and outer diameter of 13.1 cm. The gel phantom is contained by a glass beaker. The cylindrical beaker has an inner diameter of 10.3 cm and height of 12 cm; it is filled with 1 L of gel formula (1000 mL of water, 14 g of hydroxyethyl cellulose, and 2.97 g of sodium chloride). Two controls filled with vegetable oil are used, shaped as a sphere and a conical. The thermal conductivity and heat capacity were measured with a KD2 Pro thermal properties meter equipped with an SH1 sensor (see Figure 6) [14]. Prior to the experiment, the thermal conductivity was measured as 0.6 W/mK and the specific heat capacity was measured as 4.4 MJ/m^3 K.

Results

Figure 7 depicts the 2D thermal slices acquired for the study; the second slice was taken as the reference temperature. This demonstrates the inhomogeneous, incremental heating of the phantom. By initial observation, the heating seems to localize around the single loop RF coil. There is no observable heating for the oil controls, as the color map remained constant and similar to that of the reference slice. This was expected since nonpolar molecules do not have molecular dipoles and therefore do not experience dielectric heating.

Figure 8 depicts the volume of interest (VOI) selections for quantitative evaluation. Two phantom VOIs (indicated as brown) and two control VOIs (indicated as orange) were selected. The two phantom VOIs were chosen to be closer to (VOI 1) and farther from (VOI 2) the source of heating (RF coil) based on Figure 7.

Figure 9 depicts the phase evolutions, or the phase change over time, for phantom VOIs at three different echo times (TE). Effectively, this is simultaneously acquiring three measurements for the same data point. All phase evolutions for each VOI and TE exhibited linear, decreasing slopes. This was expected since each step had an equivalent heating (RF pulse) and increasing temperature decreased the resonant frequency (lower phase). Figure 10 depicts the temperature changes, calculated by equation 10, corresponding the phase evolutions in Figure 9. For all echo times, VOI 1 had a greater slope for temperature change compared with VOI 2. This resulted from the selection of the VOIs such that VOI 1 was closer to the RF coil compared with VOI 2. Note, all time courses exhibit a kink after the first heating measurement. Figure 10 has the time axis scaled to the operation time rather than the actual heating time. During the operation, the experiment was paused after the reference slices were acquired to set up the heat cycling measurements. Each heating step was 500 s, so the time scale correction would be to consider only the time for heating. The corrected temperature changes for VOI 1 are plotted in Figure 11.

Conclusions

Overall, this experiment has been very successful in developing a procedure to characterize the heating deposition on a gel phantom by a custom RF coil during an MRI experiment. Heating at a particular voxel was linear so thermal conductivity can be neglected. This reduces the complexity of the calculations for future experiments. Additionally, it was observed that heating of the phantom was inhomogeneous and correlated at locations where the highest electric field strength was. This procedure seems to be a reliable method to monitor temperature in MR experiments and exams, but should be validated by comparison with other thermometry experiments performed in parallel with PRF.

References

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Acknowledgements

Thank you to the advisors which have made this project possible!

Physics Advisor: Dr. Dan Dahlberg

MRI Advisor: Dr. Pierre-Francois Van de Moortele

MRI Advisor: Dr. Andrea Grant