Perfluorooctyl bromide (PFOB)

Perflubron or PFOB is a perfluorinated derivative of the hydrocarbon octane, where all 18 hydrogen atoms have been replaced with 17 fluorine (19F) and 1 bromine (Br) atoms leading to 1 terminal CF3 group, 1 terminal CF2Br group, and 6 CF2 groups (Fig. 1). In the 19F MR spectrum, these groups have different chemical shifts of \(_}_\text}=+18.1 \text\) and \(_}_}=-40.1 \text\) relative to the central CF3 resonance (here set to \(_}_}=0 \text\)) [8, 21]. The terminal Br atom breaks the structural symmetry of the molecule and gives rise to small variations in chemical shift of the CF2 resonances ranging from \(-35.7 \text\) for the closest CF2 group, β, to the most distant group η at \(-44.8 \text\). In this work, these resonances cannot be resolved so that we consider only three distinct resonances.

Fig. 1

Chemical structure and chemical shift spectrum of PFOB at 3 T

Hadamard-encoding scheme

In MRI with conventional Cartesian encoding, chemical shift artifacts manifest as ghost images of the different resonances that appear spatially shifted along the readout direction by

$$\Delta x=\delta \cdot \frac_},$$

(1)

where BW is the receiver bandwidth and \(\delta\) is the chemical shift of the resonance. The most common occurrence of chemical shift correction is the fat–water shift in 1H MRI. Many methods were developed to remove the chemical shift artifacts by suppressing the fat signal [22]. However, in 19F-MRI, the tracer concentration is low, and signal from all resonances is desired to improve SNR. Thus, rather than using suppression techniques to avoid chemical shift artifacts, we propose a spectral encoding/decoding scheme that allows for the simultaneous acquisition of signal from all resonances.

HE has been previously applied in MRI, for example, to counteract aliasing artifacts [23], or in simultaneous multislice acquisitions [24]. The general concept is to encode a vector of information by multiplying it with a matrix of orthogonal column vectors, which can later be decoded by multiplication with the transposed matrix. Here, we use a Hadamard matrix \(\mathcal\), to encode the signal from each separate resonance, by acquiring the same k-space data four times with four different RF excitation pulses \(_\).

$$\left.\left(\begin_}\left(t\right)\\ _}\left(t\right)\\ _}\left(t\right)\\ _}\left(t\right)\end\right.\right)=\mathcal}=\left(\begin1& 1& 1\\ 1& -1& -1\\ 1& 1& -1\\ 1& -1& 1\end\right)\cdot \left(\begin_\left(t\right)\cdot \text\left(-i_t\right)\\ _\left(t\right)\\ _\left(t\right)\cdot \text\left(-i_t\right)\end\right),$$

(2)

where \(_\) is the RF-envelope of the CF2Br-Peak, \(_\) of the CF3-Peak, and \(_\) of the CF2-Peaks and \(\delta _=\gamma ___Br}\) and \(\delta _=\gamma ___}\) are the off-resonances of the respective resonances relative to the CF3 group. Note that the Hadamard matrix is reduced to 4 × 3, because we only need to encode three resonances and the fourth encoding combination is not needed. The frequency of the MRI system is set to the resonance frequency of the CF3 resonance. Negative signs in the encoding matrix are effectively 180° phase shifts in the excitation, which means that received signals of the same resonance excited with a negative and a positive sign cancel out after addition of the raw data. While it would be possible to separate the individual CF2 resonances as well using a larger Hadamard matrix, this would require longer pulses causing signal loss due to the longer echo time, while only gaining a minimal amount of signal.

During post-processing, the signal from the three resonances can, therefore, be Hadamard-decoded using the following combinations of signals:

$$\left(\begin_\\ _\\ _\end\right)=}^}=\left(\begin1& 1& 1& 1\\ 1& -1& 1& -1\\ 1& -1& -1& 1\end\right)\left.\left(\begin_\\ _\\ _\\ _\end\right.\right),$$

(3)

where \(_,\dots ,_\) are the signals received after each HE pulse, \(_\). In Eq. (3), the signals from the resonances \(_, _,\) or \(_\) add up constructively, while signals from the other resonances cancel, such that after the four pulses each resonance has been acquired without time loss compared to selective excitation with four averages. After reversing the chemical shift for each of the resonances individually, their signals can be added using a sum of squares combination (Fig. 2). In the ideal case, where all resonances contribute equally, the 3 fluorine atoms from the CF3 resonance, the 2 fluorine atoms from the CF2Br resonance and the 12 fluorine atoms of the CF2 resonances would increase the signal by a factor of \(\frac^+^+^}}=1.04\), over an acquisition with the CF2 resonances alone—thus, only a 4% gain would be measurable. In reality, however, the CF2-signals dephase quickly and blur due to the uncorrected chemical shifts, which reduces their contribution to the total signal, making it more worthwhile to add the contribution from the other resonances.

Fig. 2

Different steps during the reconstruction process shown with the same windowing. Left: Chemical shift artifacts in a radial sequence, Middle: Reconstructed signals for each peak after Hadamard-decoding. Due to chemical shifts within the CF2 multi resonance, this image appears blurred. Right: Combination of all signals via sum of squares

Chemical shift correction

In radial imaging, the readout direction is different for each k-space line (spoke). Thus, artifacts from chemical shifts do not result in a constant spatial offset as in Cartesian imaging, but rather in a blurring of the reconstructed image [15]. Therefore, a chemical shift correction must be performed prior to regridding of the radial data to a Cartesian grid. The evolution of the MR signal phase during data acquisition of an isochromate with chemical shift \(\delta\) is given by:

$$\varphi \left( t} \right) = \gamma \left( \right)\smallint B_ + G\left( } \right)r}t^ = \left( \right)\gamma B_ t + \smallint \gamma G\left( } \right)r}t^ + \smallint \delta \gamma G\left( } \right)r}t^ .$$

(4)

The first term describes a linearly increasing phase over time, independent of the spatial location, compared to the resonant signal. The second term is the desired on-resonant phase evolution due to spatial encoding in a magnetic field gradient \(G\). The last term is also location dependent, but can be neglected as \(_\gg G\cdot r\). The phase evolution of the chemical shift is, therefore, governed by \(\delta \gamma _t\), i.e. a linear increase of the phase with time. Thus, after signals of the different resonances are separated using HE, the chemical shift can be corrected by multiplication of each acquired line in k-space with a linearly increasing phase factor \(\text\left(+i\delta \gamma _\kappa \tau \right)\), where \(\kappa\) is the index of the pixel within that line and \(\tau\) is the dwell time.

RF pulse shapes

To excite the individual resonances, both Gaussian and sinc shapes were tested as RF-pulses. The Gaussian pulses were defined as

$$_^\left(t\right)=_^\cdot \text\left(-\frac^_^^}\right).$$

(5)

Compared to Gauss pulses, sinc pulses can excite a broader range of the spectrum homogeneously. Here, a Hamming-windowed pulse [25] was applied:

$$_^\left(t\right)=_^\cdot \left(0.54+0.46\cdot \text\left(\frac_}\cdot t}\right)\right)\cdot \frac\left(\pi \cdot \delta _}\cdot t\right)}_}\cdot t},$$

(6)

where \(\delta _}=541 \text\) and \(\delta _}=4000\text\) describe the width of the pulse in the frequency domain. The respective bandwidths were chosen for a field strength of 3 T, which is the clinical field strength which will later be applied (see below). Phantom measurements with a 10% PFOB fat–water emulsion were performed with both pulse shapes for all resonances using a single-channel Tx/Rx 19F solenoid coil. The signal intensities and chemical shift artifacts of the multi-resonance were compared.

UTE sequence with Hadamard-encoding

K-space data were acquired using a center-out radial trajectory with a spiral phyllotaxis pattern [26]. Here, all acquired spokes in k-space intersect a spherical spiral, where the azimuthal angle is rotated by the golden angle for consecutive points (Fig. 3). The spokes are acquired in an interleaved fashion starting with every n-th point, then rotating the starting point by a golden angle. For n being a Fibonacci number, consecutively acquired spokes are close to each other, reducing eddy current effects and improving gradient spoiling [27]. This approach was taken for two reasons: First, from FID measurements, we estimated T2* values for all resonances to be below 10 ms, so that an ultra-short echo time (UTE) sequence was chosen to maximize the signal. Second, to acquire images in the abdomen, the sequence needs to be robust to motion. While this is the case for radial imaging, the phyllotaxis trajectory ensures homogeneous sampling of k-space over small time scales compared to the total imaging time.

Fig. 3

Phyllotaxis pattern of consecutively acquired spokes intersecting the unit sphere. The end-points of consecutive k-space spokes follow a spiral on the surface of a sphere with radius kMax. A spiral where the kz-component decreases with every spoke (red) is followed by a spiral with increasing kz-component (orange)

PFOB nanoemulsion

A nanoemulsion consisting of 35% PFOB was used for the in vivo experiments. The PFOB nanoemulsion (PFOB-NE) was produced similar as described previously [12]: a buffer of sodium dihydrogen phosphate (0.24 g), disodium hydrogen phosphate (2.46 g), sodium chloride (1.15 g) in sterile water for injection (284.5 g) was mixed with 18.4 g Lipoid E 80SN (Lipoid GmbH, Ludwigshafen, Germany), 322 g perfluorooctyl bromide (PFOB) and 8.62 g 1-perfluoro-n-hexy-decane (both abcr GmbH, Karlsruhe, Germany). This mixture was pre-emulsified with a tip sonicator (Branson Ultrasonics Corporation) for 5 min in portions of 50 ml and then transferred to a CF1 homogenizer (Constant Systems Ltd., Daventry, UK) for 10 cycles of 1000 bar. Then, after renewed emulsification with the tip sonicator, the resulting emulsion was autoclaved for 15 min at 121 °C. The nanoparticles of the final emulsion had a typical mean of the number average size distribution of 170–190 nm measured by dynamic light scattering (Malvern Panalytical). The PFOB-NE was injected 3–4 days after production and was stored at 4 °C.

T 1 measurements

To optimize the flip angle for each resonance individually, T1 was determined in a 10% PFOB fat–water emulsion. To estimate T1, the flip angle of an FID MRS sequence (TE > 1.5 ms, dwell time = 50 µs) was varied (α = 0°–45°) in steps of 1° at a fixed TR = 30 ms, again using the single-channel Tx/Rx 19F solenoid coil. For RF excitation, a sinc pulse (duration: 3 ms, spectral width: 100 ppm) was used to ensure homogeneous excitation over the entire PFOB spectrum. Spectral boundaries for five resonances (CF2Br, CF3 and the three most prominent peaks \((\beta ,\delta +\epsilon ,\eta )\) from the CF2 multi-peak spectrum) were chosen, over which the signal strength was integrated for each flip angle. T1 was then estimated for each of these resonances using the FLASH signal equation [25].

Phantom experiments

To test the validity of the method, phantom experiments were performed using the coil setup for the in vivo experiments, which consists of an eight-channel Tx loop coil array and an eight-channel Rx coil array containing two coils posterior and a six-channel anterior flexible array of coils [28]. The measurement was performed using the HE UTE sequence with TE = 1.7 ms, TR = 10 ms, readout bandwidth = 390 Hz/px, with 377 spirals and 26 spokes per spiral. The FWHM of the point-spread function was 15.7 mm in every direction, considering both regridding artifacts and T2*-decay, as well as the CF2 off-resonances. Regridding was performed using a voxel size of (5 mm)3. 8 Phantoms containing a 5% PFOB fat–water emulsion were measured ten times consecutively, resulting in a total acquisition time of 65:20 min:s. Due to the uneven distribution of noise in radial images, this allowed for a better noise estimation by creation of a standard deviation map [29]. SNR values of the reconstructed images for each peak and of the combined image were compared.

Comparison with iterative deconvolution

We compared the HE UTE reconstruction with an iterative deconvolution as it is the most commonly used method for chemical shift artifact correction of PFOB, and can be applied to the same data set, allowing for a direct comparison. For this, we acquired an image of the same phantoms as before using the HE UTE sequence (TE = 1.7 ms, TR = 10 ms, readout bandwidth = 390 Hz/px, with 1597 spirals and 26 spokes per spiral) and measured an FID with the same bandwidth and TR with 500 averages. Then we applied an iterative sparse deconvolution algorithm to the signal for which each peak was excited with a positive sign, minimizing the function

$$x=\underset}} -y\Vert }_^+\lambda \Vert }_,$$

(7)

where C is the convolution matrix calculated from the FID signal, y the acquired data and \(\lambda\) an arbitrary factor for LASSO (least absolute shrinkage and selection operator) regularization [18, 30]. \(\lambda\) was chosen by trial and error, such that the final image yielded the maximum SNR without showing major artifacts. Reconstruction was done with Matlab (R2023a, The MathWorks Inc., Natick, USA) and took 2–4 h for each value of \(\lambda\) using a GPU (NVIDIA GeForce RTX 2080 Super). SNR was measured for both methods, adjusted by a factor of 2 for the deconvolution method, as only ¼ of the data was used, and compared.

In vivo experiments

One healthy juvenile pig (German landrace, 63 kg) was injected with a PFOB nanoemulsion (5 ml per kilogram body weight), and 19F-MRI scans were performed with the proposed HE UTE sequence 2, 4 and 7 days after the injection. To estimate the evolution of the 19F signal over time, the mean values of the acquired signals were compared in regions of the spleen that were equidistant from the coils in all measurements. Anesthesia was introduced and maintained as described previously [31]. The MRI protocol consisted of a T1 VIBE-Dixon sequence for 1H images, with TE = 1.29 ms, TR = 3.97 ms, readout bandwidth 1042 Hz/px and a matrix size of 260 × 320 per slice, 52 slices, voxel size 1.19 mm × 1.19 mm × 5 mm acquired in one breath hold through a brief interruption of mechanical ventilation. The HE UTE sequence to measure the 19F signal had the following acquisition parameters: TE = 1.7 ms, TR = 10 ms, readout bandwidth = 390 Hz/Px, with 1597 spirals and 26 spokes per spiral, resulting in a total acquisition time of 27:41 min:s. All measurements were performed on a clinical 3 T system (Prisma, Siemens Healthineers, Erlangen, Germany) and the 19F images were reconstructed using Kaiser–Bessel regridding in Matlab (R2023a, The MathWorks Inc., Natick, USA).