Fast MRI of RF Heating Via Phase Difference Mapping

Abstract

A method is presented for the rapid acquisition of temperature maps derived from phase difference maps. The temperature-dependent chemical shift coefficients (TDCSCs) of various concentrations of aqueous cobalt and dysprosium-based compounds were measured. The largest TDCSC calculated was for 100 mM DyEDTA, which had a TDCSC of −0.09 PPM/K; 160 mM CoCl₂ had a TDCSC of −0.04 PPM/K. These temperature-dependent chemical shifts (TDCSs) result in phase changes in the MR signal with changing temperature. Agarose phantoms were constructed with each paramagnetic metal. A fast gradientecho (FGRE) MR image was acquired to serve as the baseline image. A “test” MRI procedure was then performed on the phantom. Immediately afterwards, a second FGRE MR image was acquired, serving as the probing image. Proper image processing as a phase difference map between the probing image and the baseline image resulted in an image which quantitatively described the temperature increase of the phantom in response to a particular “test” imaging experiment. Applications of this technique in assessing the safety of pulse sequences and MR coils are discussed.

The growth of high-field MRI has brought attention to the fact that many MRI procedures that are routinely practiced at clinical field strengths may not be allowable at higher field strengths, due to an excessive specific absorption rate (SAR) for radiofrequency (RF) power (1). These SAR regulations are in place to prevent excessive heating of tissues during the MRI examination, caused by the interaction of the sample with electric fields (2). This has challenged the MR community to develop methods to analyze and measure power deposition in subjects and tissue-mimicking phantoms. Numerous investigations into the effects on the tissue MR signal from heating have been conducted, either measuring T₁ differences (3–5) and water proton chemical shift differences (5–11), or using physical temperature measurement devices (12–14). Computer simulations of Maxwell’s equations, using various computational methods, show that both B₁ inhomogeneity and power absorption by the sample become much more severe at higher field strengths (15–18).

Chen and Hoult (19) showed experimentally, for the first time, the heating patterns that can be generated when sending current through an MRI coil. Recently, we described (20) a modification of Chen and Hoult’s experiment, wherein a 3D temperature map was obtained by phase difference mapping of the MR signal. This temperature map measured the heating of a phantom caused by the absorption of RF energy from a transmit/receive surface coil during an MRI experiment. This was accomplished using an agarose phantom doped with 40 mM Na₄HTm(DOTP). The ²³Na signal in this complex exhibited a −0.5 PPM/K temperature-dependent chemical shift coefficient (TDCSC) (21). This frequency shift generated a phase shift governed by Δωτ, where Δω is the frequency shift and τ is the echo time (TE) in a gradient-echo pulse sequence. Appropriate image processing yielding phase difference maps allowed direct quantitation of the temperature increase. The major drawback of this method was the lengthy acquisition times, on the order of 2 min.

Here the use of similar ¹H-based methods to investigate the heating effects of the birdcage coil is described. The overall goal was to create a procedure that could acquire images very rapidly and would be useful for accessing clinical MRI coils, most of which are ¹H coils. Agarose phantoms doped with paramagnetic cobalt and dysprosium compounds were constructed to measure the heating produced by MRI procedures. These paramagnetic compounds enhance the TDCSC of water, making it more sensitive to temperature changes. This is conceptually different from the method of MR thermometry, in which resonances from the shift reagents themselves are measured (see, for example, Refs. 22–24). Additionally, these compounds also enhance the T₁ relaxation in water, making rapid image acquisition possible. Furthermore, the addition of these compounds provided the necessary electrolytes to yield electrical conductivity.

MATERIALS AND METHODS

Measurement of TDCSC and Construction of Imaging Phantoms

The absolute shifts and TDCSC of water containing various concentrations of four aqueous shift reagents were measured at various pH. These shift reagents included cobalt chloride (CoCl₂), dysprosium chloride (DyCl₃), dysprosium tripolyphosphate ($\mathrm{Dy}{\left(\mathrm{TPP}\right)}_2^{7-}$) and dysprosium ethylenediaminetetraacetic acid (DyEDTA^1–), all as solutions in doubly deionized (DDI) water. Two concentrations were used for the CoCl₂ investigations: 150 and 160 mM. These were both at pH 5.9. A single concentration, 100 mM, was used for the DyCl₃ investigation. Solvation of DyCl₃ in DDI water occurred only at pH < ~1.5. For the $\mathrm{Dy}{\left(\mathrm{TPP}\right)}_2^{7-}$ examinations, three concentrations were used: 20, 50, and 100 mM. $\mathrm{Dy}{\left(\mathrm{TPP}\right)}_2^{7-}$ was formed by the simple addition of DyCl₃ to a modest excess of two molar equivalents of sodium tripolyphosphate (Na₅TPP), followed by rigorous shaking. This was described in greater detail by Gupta and Gupta (25). The modest excess accounted for the high percentage of impurities present in the Na₅TPP (~90% pure). The pH values of these samples were brought to 8.0 using concentrated sodium hydroxide, as this is where the largest downfield shift of the water resonance occurs (26). Additionally, the effect of three and four molar equivalents of Na₅TPP on the TDCSC was examined. A 100-mM concentration was used in the DyEDTA^1– investigations. The experimental methods of Waiter and Foster (27) were generally followed. However, following a structure for Eu(1,2 propanediaminetetraacetate)^– published by Kabuto and Sasaki (28), showing a 1:1 stoichiometry between the chelate and the metal, an equimolar amount of the DyCl₃ was added directly to the aqueous EDTA. Waiter and Foster had used two molar equivalents of EDTA with respect to lanthanide solution. One molar equivalent was sufficient to solvate all of the Dy without having to acidify further. In fact, the pH of the 50 mM DyEDTA^1– was 1.3 upon mixing of the two components. Significant precipitation occurred within 10 min when left at this pH. To evaluate the pH dependence on the TDCSC, the absolute shift of each concentration was measured at four different pH’s: 2.0, 6.0, 8.0, and 10.0.

NMR spectroscopy was performed on two spectrometers. All TDCSC experiments were carried out on a 500 MHz Bruker spectrometer. Heating was performed in the magnet with a Bruker variable temperature ensemble. A waiting period of 10 min was used to equilibrate the sample at each temperature point. The temperature was increased from 300 to 320 K in steps of 2 K. The pH dependence on the TDCSC of DyEDTA^1– was measured on a 200-MHz Bruker spectrometer at room temperature. In all instances, a capillary tube containing a saturated solution of 3-(trimethylsilyl)proprionic-2,2,3,3-d₄ acid (TSP) in D₂O was placed inside the NMR tube containing the aqueous shift reagent, providing both a deuterium lock signal and a 0.0 PPM reference. Conductivity was measured with an Oakton conductivity/temperature meter (Fisher Scientific Company, Pittsburgh, PA).

Cylindrical 4% agarose and 10% gelatin gel phantoms of various sizes were constructed, approximating the sizes of a human head and appendages. The volumes of the phantoms ranged from 400 (5.4-cm diameter) to 1800 ml (16.5-cm diameter). The walls of the containers were glass. Gels were formed by the addition of the proper amount of either agarose or gelatin to a stirring solution of the shift reagent in a large beaker. The gel/solution mixture was then heated to a boil, at which point the stirring mixture became translucent. The hot liquid was then poured into the phantom container and sealed. A small sample was set aside to spectroscopically verify the expected TDCSC as just described. The phantoms were kept in the magnet room where the MRI experiment was performed to maintain thermal equilibrium with the environment.

Image Acquisition and Processing

The investigations reported herein involved the use of two birdcage coils. Each was operated in both linear and quadrature modes. One was an eight-strut birdcage, with an inner diameter of 17.9 cm, hereafter referred to as the “small birdcage.” The other was a clinical size, 28.1-cm inner diameter, 16-strut head coil, hereafter referred to as the “head coil.” Phantoms were placed either in the center of the coils or along the inner wall of the coils, as described in the figure legends All imaging was performed on a 4.0 Tesla GE Signa Scanner at the Hospital of the University of Pennsylvania. The resonant frequency for protons at this field strength is 170 MHz, considerably higher than the standard operational frequency at 1.5 Tesla, 64 MHz. Offline data processing was performed using custom-written Interactive Data Language (Boulder, CO) programs. The imaging protocol involved three steps. The first was the acquisition of a baseline image using a 2D fast gradientecho (FGRE) sequence with the following image parameters: 2 NEX; 256 × 128 matrix; 16 × 16-cm FOV; 2-mm slice thickness; 30° flip angle; 8.7-, 7.9-, or 7.0-ms TE; and 46-ms repetition time (TR). This acquisition was 12 s in duration. The second step was performing the “test” MRI procedure. Our test MRI procedure was a 10-min-long, high-power 2D spin-echo sequence, using a time-averaged power of 18.0 W. We used a high-power imaging sequence to exaggerate the effects of RF-induced heating. It is here that any “test” MRI experiment would be substituted to analyze the resultant heating effects from performing that experiment. Lastly, a probing image was acquired, with the identical sequence and imaging parameters as the baseline image.

The phase difference images were processed in the following manner. The raw data files from the baseline image and the probe image were Fourier transformed after bilinear interpolation to 256 × 256. In the complex image space, the signal in each pixel is described by M·e^i(ωτ+ϕ). Pixel-by-pixel division of the baseline image by the corresponding probe image yielded:

$$\frac{M_1\cdot e^{i(\omega \tau +\varphi )}}{M_2\cdot e^{i(\omega \tau +\varphi +\Delta \varphi )}}=\frac{M_1}{M_2}\cdot e^{-i\left(\Delta \varphi \right)}.$$ [1]

Performing the operation,

$$\arctan \frac{M_1}{M_2}\cdot e^{-i\left(\Delta \varphi \right)}=\Delta \varphi$$ [2]

returns the phase difference. Since this procedure was executed on the entire image, a phase difference map was generated. Quantitating the temperature increase from the phase difference map (Δϕ) was readily accomplished using the equation,

$$\Delta T=\frac{\Delta \varphi }{K\cdot \mathit{TE}\cdot \left(\gamma B_0\right)}$$ [3]

where ΔT is the temperature difference, TE is the gradient echo time, and K is the TDCSC (7). The background magnetic field drift was previously measured to be −0.04 PPM/hr. The temperature maps shown later account for this background drift by subtracting the phase difference due to the drift from the measured phase difference.

RESULTS AND DISCUSSION

Figure 1 plots the temperature dependence of the chemical shifts for the various compounds. Also included is the temperature-dependent chemical shift (TDCS) measurement of water, an impurity in the D₂O inside the capillary. This is reported to validate the measurement system and to provide a baseline TDCSC for calculating comparison factors for the different reagents. The given slopes are the TDCSCs. Of particular note is the linearity these trends exhibit over this temperature range, as evidenced by the R² values. The magnitude of the two electron-nucleus interactions that cause the increased TDCS phenomenon are temperature-dependent as kT⁻¹ (29), the generalized expression for the isotropic shift being:

$${\left(\frac{\Delta H}{H}\right)}^{\mathit{iso}}=-\frac{g\beta S(S+1)}{3\hslash {\gamma }_{n}kT}A$$ [4]

where (ΔH/H)^iso is the isotropic shift, g is = 2.002322 for a free electron, β is the Bohr magneton, S is the spin quantum number for the electron, γ_n is the gyromagnetic ratio, k is the Boltzmann constant, T is absolute temperature, and A is the hyperfine coupling constant. Therefore, as the temperature changes, the chemical shift of the ligands change as well. Even though Eq. [4] shows that the isotropic shift is inversely proportional to T, it is convenient to analyze the shift linearly with respect to T over a small temperature range. The high R² values for the fits confirm this assumption. For clarity, the TDCSCs are summarized in Table 1, in addition to the initial chemical shift of water at 300 K and the conductivity of the solutions at the pH used in the imaging phantoms. The largest TDCSC measured were for the dysprosium compounds, the maximum being for 100 mM DyEDTA^1–, which had a TDCSC of −0.09 PPM/K. The presence of the reagent shifted the water peak to nearly 24 PPM. The 160 mM CoCl₂ sample had a TDCSC of −0.04 PPM/K, shifting the water to 12.7 PPM. The TDCSC of water was measured to be −0.01 PPM/K, in agreement with the known TDCSC of water. Interestingly, no detectable shift was observed in the aqueous DyCl₃ sample, even at pH < 1.5. Varying the proportion of Na₅TPP to Dy in $\mathrm{Dy}{\left(\mathrm{TPP}\right)}_2^{7-}$ caused no additional effect on the shift of the water resonance, or on the TDCSC. Similarly, varying the pH of the DyEDTA^1– samples had no additional effect on the shift of the water peak or the TDCSC.

FIG. 1.

TDCS fits for various compounds. The slopes of the lines are the TDCSC. Even though Eq. [4] shows that the isotropic shift is inversely proportional to T, it is convenient to analyze the shift linearly with respect to T over a small temperature range. The high R² values for the fits confirm this assumption.

Table 1.

NMR Properties and Conductivity for Various Paramagnetic Solutions

Compound	Water chemical shift (PPM)	TDCSC (PPM/K)	Conductivity mS/cm
160 mM CoCl2	12.71	−0.041	29.7
150 mM CoCl2	12.35	−0.036
100 mM DyEDTA1–	23.99	−0.090	57.2
50 mM DyEDTA1–	14.71	−0.046
100 mM $\mathrm{Dy}{\left(\mathrm{TPP}\right)}_2^{7-}$	19.64	−0.061	45.5
50 mM $\mathrm{Dy}{\left(\mathrm{TPP}\right)}_2^{7-}$	12.60	−0.038	30.1
20 mM $\mathrm{Dy}{\left(\mathrm{TPP}\right)}_2^{7-}$	7.83	−0.022	14.7
Water	4.7	−0.011	0.0

These numbers can be used to generate comparative factors to evaluate different chemical shift reagents. This information is summed in Table 2. One such factor is K_shift, a description of the ability of a reagent to shift the water resonance. Using $\mathrm{Dy}{\left(\mathrm{TPP}\right)}_2^{7-}$ as an example, Fig. 2 shows a linear relation of the concentration of shift reagent to the chemical shift. Defining the chemical shift (δ) at a certain temperature as:

$$\text{Shifted}\delta \left(\mathrm{T}\right)=\text{Water}\delta \left(\mathrm{T}\right)+\left[\text{Shifted reagent}\right]\ast {\mathrm{K}}_{\text{shift}}$$ [5]

where 4.7 is chosen as the intercept because it is the chemical shift of pure water at 300 K, yields the K_shift. The K_shift of $\mathrm{Dy}{\left(\mathrm{TPP}\right)}_2^{7-}$ is 149.4 ppm · K⁻¹ · M⁻¹. CoCl₂ gives a K_shift of 50.5 ppm · K⁻¹ · M⁻¹ while DyEDTA^1– gives a K_shift of 192.0 ppm · K⁻¹ · M⁻¹. Another comparative factor can be defined as K_temp, the ability of a reagent to produce a TDCS. The TDCSC can be calculated using the K_temp as:

$$\mathrm{TDCSC}=-0.011+\left[\text{Shift reagent}\right]\ast {\mathrm{K}}_{\mathrm{temp}}.$$ [6]

The intercept here is the TDCSC of pure water determined earlier. K_temp for Dy(TPP)₂^7– is −0.499 ppm · M⁻¹. CoCl₂ gives a K_temp of −0.178 ppm · M⁻¹ while DyEDTA^1– gives a K_temp of −0.790 ppm · M⁻¹. This data is shown graphically in Fig. 3 for Dy(TPP)₂^7–. Reagents that are best have a large K_shift and large K_temp. For instance, based on these two K values, DyEDTA^1– is a better reagent for producing TDCS than Dy(TPP)₂^7–. Additional factors can be brought in such as T₂ and conductivity to modify these values for designing the best phantoms where the properties are more like human tissue. Knowing both the K_shift and the K_temp for a reagent allows one to retrieve the TDCSC by simply measuring the chemical shift at a known temperature. This is accomplished by calculating the K_shift and multiplying by the temperature in K, yielding the K_temp. Multiplication of K_temp by the concentration of the shift reagent and addition of the intercept yields the TDCSC.

Table 2.

Chemical Shift and Temperature Dependent Chemical Shift Inducing Constants for Three Paramagnetic Solutions

Compound	Kshift (PPM K−1 M−1)	Ktemp (ppm · M−1)
CoCl2	50.5	−0.178
$\mathrm{Dy}{\left(\mathrm{TPP}\right)}_2^{7-}$	149.4	−0.499
DyEDTA1–	192.0	−0.790

FIG. 2.

Isotropic chemical shift of Dy(PPP)₂^7– plotted vs. the concentration at 300 K. The reference point for zero concentration is the chemical shift of water.

FIG. 3.

TDCSC of Dy(PPP)₂^7– plotted vs. the concentration. The reference point for zero concentration is the TDCSC of water.

All images shown in this work were acquired using the 4% agarose gels doped with 160 mM CoCl₂. As a solution sample, 160 mM CoCl₂ had a linewidth on the order of 100 Hz, while as an agarose gel, the linewidth increased to 180 Hz. The samples that were set aside from the preparation of the gels exhibited the same TDCSC as the solution samples, within 2%. Unexpectedly, however, the linewidths of the dysprosium-based compounds increased from ~35 Hz as solutions, to nearly 1000 Hz for several agarose and gelatin gels. This rendered the dysprosium-based agarose and gelatin phantoms virtually unusable. Alternate gel matrices are currently being investigated to ameliorate this problem.

Figure 4a shows the magnitude image obtained from imaging the 400-ml phantom with the small birdcage. For this experiment, the birdcage coil was operated in quadrature mode and the phantom was placed along the inner wall of the coil. This was done to exaggerate the observed heating effects. Strong signal intensity is observed where the coil is closest to the coil elements and accurately corresponds to the placement of the coil legs. While this is a uniform phantom, higher signal intensity is observed in the center of the phantom. This is attributed to phase interference effects, present in MR images of conductive materials at high frequency. These effects are explained by the theory of generalized reciprocity when the size of the object approaches the wavelength (30). The corresponding heating map is displayed in Fig. 4b. The scale is temperature rise in K. Electromagnetic theory states that when a conductive material is within a current carrying loop, the electric field density inside the object increases as the square of the radius outwards from the center (31). This means that the highest electric field density in the phantom will be on the outer edges, and will decrease quadratically towards the center. This in turn will cause greater heating at the edges of the phantom. The heating map clearly displays the increased temperature rise in the outer portions of the phantom, in agreement with theory. The maximal temperature rise was 0.68 K and was present where the phantom was closest to the coil elements. There was no observable heating in the center of the phantom, corresponding to the area where the phase interference effects were seen. Figure 4c is a qualitative representation of the electric fields present in the phantom and the birdcage coil during the MRI experiment. The phantom is shaded to depict the gradient of dB/dT-induced electric field within it, where dark shading indicates higher electric field density. The greatest temperature rise occurred where the coil/phantom distance was minimal, consistent with the fact that the dB/dT-induced electric field is highest at the conductors.

FIG. 4.

Small birdcage operated in quadrature mode. a: Magnitude image. b: Heating map; barscale is temperature increase in K. c: Schematic of the experiment. The phantom is against the inner wall of the MRI coil.

In contrast, Fig. 5a shows the magnitude image from the 400-ml phantom in the center of the small birdcage, operating in linear mode. Signal intensity variations are again seen in this example, with high signal intensity in the phantom at the two opposite ends. Again, increased signal intensity is apparent within the center of the phantom due to phase interference effects. Figure 5b is the heating map from this experiment. Heating was most severe where the actual signal was most intense in Fig. 3a, with the highest temperature rise being 1.50 K. This heating pattern can be best explained by the electric field density patterns simply depicted in Fig. 5c. As opposed to a coil operating in quadrature mode, which creates circularly polarized magnetic and electric fields, the linear coil creates linearly polarized magnetic and electric fields which emanate from two “poles” of the coil. This linearly shaped electric field is qualitatively described by the lines of constant electric field magnitude inside the coil. The greatest heating should be where the largest magnetic field is produced, corresponding to the areas nearest the two “poles” in Fig. 5c. As seen in Fig. 5b, this area is the precise area of increased temperature as a result of the imaging procedure.

FIG. 5.

Small birdcage operated in linear mode. a: Magnitude image. b: Heating map; barscale is temperature increase in K. c: Schematic of the experiment. The phantom is slightly off center in the MRI coil.

Figure 6a is the magnitude image from an experiment where the head coil was operated in quadrature mode to image the 2100-ml, head-size phantom. The phantom was positioned slightly off center. Again, while the phantom is uniform in construction, the magnitude image shows disparity in the signal intensity. The regions where the coil-to-phantom distance is minimal return higher signal intensity in addition to high signal intensity in the center of the phantom. As in the two previous examples, this center signal intensity heightening is due to phase interference effects. Figure 6b shows the resulting heating map generated from the MRI experiment. The maximal temperature rise is 0.72 K, and occurs where the signal is most intense in the magnitude image. Unlike the small phantom in the small birdcage, the ring of stronger heating on the edges of the phantom is not clearly present. There may be several causes of this effect. One reason may be that the coil is not truly operating in quadrature mode, with the heating distribution reflecting a more linear pattern. Figure 6c depicts the phantom slightly off center within the coil, which may explain the asymmetry in the heating pattern. More accurate modeling of the electromagnetic fields within the coils and phantoms would help answer this question by separating the contributions from the induced and the conservative electric fields.

FIG. 6.

Head coil operated in quadrature mode. a: Magnitude image. b: Heating map; barscale is temperature increase in K. c: Schematic of the experiment. The phantom is slightly off center in the MRI coil.

We are currently exploring techniques to improve the effectiveness of this method in simulating the interactions of these two electric fields with actual tissue. The first is the application of this imaging technique in a 3D manner. The duration of a 3D gradient-echo image acquisition is the product of four parameters: the number of phase encodes, the number of slices, the TR, and the number of acquisitions. To minimize heat dissipation during the acquisition, the probing image data set needs to be acquired in as rapid a manner as possible. We are exploring the use of an ultrashort TR imaging sequence to alleviate this problem. Additionally, the slice thickness can be being adjusted to accelerate the image acquisition.

Another feature that would allow a closer simulation of human tissue interactions would be the reduction of the conductivity of the sample. The conductivities of most tissues at RFs are between 5 and 10 mS/cm. Fat and bone have much lower conductivities, near 1 mS/cm (32). As shown in Table 1, the conductivities of the shift reagents used are all higher. More sophisticated synthetic pathways to produce these shift reagents, avoiding the presence of excess ions (Cl⁻ and Na⁺ in particular), will help reduce the conductivities. Furthermore, novel shift reagents causing larger water TDCSC will improve the experiment by lowering the concentration necessary to produce a desired effect.

In conclusion, a method has been detailed for quantitating the heating effects of an MRI experiment on a tissue-mimicking phantom. This was accomplished through the use of phase difference mapping of images acquired before and after a particular “test” MRI procedure. The tissue-mimicking phantom contained 160 mM CoCl₂, which provided the phantom with a TDCSC of −0.04 PPM/K. The three experiments shown indicated the contributions of the electric field interactions to the heating of the phantoms. Furthermore, the TDCS properties of several shift reagents were characterized. The eventual goal of this project is to create a robust procedure for the evaluation of new coil designs and pulse sequences. Computer simulations of Maxwell’s equations can only provide information based upon ideal situations—for example, assuming constant wire thickness, neglecting solder, and presuming equal spacing of coil elements. In other words, modeling the interactions of an MRI coil running a particular pulse sequence on a particular part of the body obviously will not provide the proper information if a capacitor is bad or if there was error in its construction. This information can only be provided by running an experiment. We are currently testing this procedure on MRI coils purposely constructed with common errors to test the efficacy of this method.