B1 Mapping
Martijn A. Cloos1
1University of Queensland, St Lucia, Australia

Synopsis

Keywords: Physics & Engineering: Physics, Physics & Engineering: High-Field MRI, Image acquisition: MR Fingerprinting

This talk reviews key principles used to map the transmit field ($$$ B_1^+$$$), in Magnetic Resonance Imaging (MRI). After a brief review of the physics that shapes the $$$ B_1^+$$$, we will spend most of our time developing a sense for the challenges associated with $$$ B_1^+$$$ mapping and briefly highlight how some of the more popular solutions in use today deal with these challenges.

One of the great strengths of MRI, its ability to produce a plethora different of contrasts, also is its Achilles heel. MRI is not only sensitive to various tissue properties, such as the longitudinal ($$$T_1$$$) and transverse ($$$T_2$$$) relaxation time, but also a great many of experimental factors, such as magnetic field variations ($$$ \Delta B_0$$$) and $$$ B_1^+$$$. The problem thus becomes, how to separate tissue contrast form experimental imperfections. Clinically, one would like to have sequences that maximize sensitivity to tissue properties and minimize sensitivity to experimental factors. In a $$$ B_1^+$$$ mapping sequence we want the exact opposite.

At equilibrium, the net magnetization ($$$M_0$$$) is aligned with $$$B_0$$$. To obtain a MR signal, the net-magnetization vector must be tipped out of equilibrium first. This is achieved using a magnetic field that oscillates at the Larmor frequency, called ($$$ B_1^+$$$). For a rectangular pulse, the rotation angle of the net magnetization relative to the longitudinal axis, i.e. the flip-angle ($$$\theta$$$), is determined by: $$$ \theta = \gamma B_1^+ \tau$$$ where $$$\gamma$$$ is the gyromagnetic ratio and $$$\tau $$$ is the pulse duration. So, if $$$B_1^+$$$ is not uniform throughout space, it can produce signal changes that do not reflect the anatomy we are trying to image [1,2,3].

The $$$B_1^+$$$ is shaped by a the transmit coil. Unfortunately, transmit coils tend to create standing radiofrequency waves, either by design [4, 5, 6] or through complex tissue interactions [7,8,9]. The RF wavelength ($$$\lambda$$$) is $$$\frac{2 \pi c}{\sqrt{\epsilon_r} \gamma B_0},$$$ where $$$c$$$ is the speed of light and $$$\epsilon_r$$$ is the relative permittivity of medium the wave travels through. In air $$$\epsilon_r$$$ is approximately $$$1$$$, but in tissue it generally closer to $$$50$$$ [10]. So, let’s take 1.5T MRI system as an example [11]. At this field strength the Larmor frequency is 64MHz. So, in air $\lambda$ is about 4-5 meters. But, in tissue it is only ~0.6m. At higher field strengths the wavelength becomes even shorter. Take a 7 Tesla MRI system, for example. Now the Larmor frequency is about 300 MHz and the wavelength in tissue reduces to 0.14m [5,9].

Short RF wavelengths would not be a problem if the waves travelled through the tissue freely with minimal reflections and attenuation [7,8]. Unfortunately, this is not the case. At 3 Tesla the RF wavelength at is comparable width of an adult human torso, and at 7 Tesla it is comparable to the width of the adult human brain. The nodes in the antinodes in the standing wave correspond to the valleys and peaks in the $$$B_1^+$$$. That is why we commonly see dark areas in the temporal lobes and bright spot in the center of the brain at 7 Tesla [9].

Let’s suppose for a moment that $$$B_1^+$$$ was uniform. Now you know the flip-angle will be uniform thought your images, but do you know what the flip-angle is? The amplitude of $$$B_1^+$$$ still depends on the power send to the coil. How much power is needed depends on the efficiency of the coil, but also on sample inside the coil. So, we need a way to calibrate the transmit system at the start of each experiment.

This is where the ‘transmitter reference voltage’ comes in to play, it is the voltage needed to create a specific flip angle using a given pulse [12,13]. For Siemens systems, the transmitter reference voltage refers to the voltage needed to create a $$$90^\circ$$$$ flip-angle using a 0.5ms rectangular RF pulse. The less uniform the $$$B_1^+$$$, the more difficult it becomes to define the appropriate transmitter reference voltage. Depending on the calibration technique used, it may have different meanings. For example, it could mean that the transmitter reference voltage produces an average flip-angle of $$$90^\circ$$$$ across the imaging volume, or $$$90^\circ$$$$ at a specific location. One way to lift this ambiguity is to quantify the $$$B_1^+$$$ in absolute units (Tesla per Volt) as a function of space. i.e. create $$$B_1^+$$$ maps.

If you are an engineer, you might want to collect $$$B_1^+$$$ maps evaluate the performance of your coils. In this case, it may be okey to dedicate an entire scan session to the measurement of $$$B_1^+$$$ maps. In that case logical point could be the spoiled gradient recalled echo (SPGRE) sequence. The SPGRE signal equation is [12,13]:$$S_{SPGRE} \propto sin(\theta)\frac{1-e^{-TR/T_1}}{1-cos(\theta) e^{-TR/T_1}}e^{-TE/{T_2^*}},$$where TR is the repetition time and TE is the echo time.

So, if we use a very long TR, such that the magnetization has ample time to returned to equilibrium (say 10x the longest $$$T_1$$$ in the sample) and fix TE the signal equation reduces to $$$S_{SPGRE}(\theta) \propto sin(\theta)$$$. If we use a non-selective 3D SPGRE sequence (non-selective to avoid slice profile effects), and simply collect a several images using different transmit voltages (V), we can fit for $$$ B_1^+$$$ using:$$S_{SPGRE}(V) = C sin(B_1^+ V \tau),$$ where $$$C$$$ is a scalar that absorbs the proton density, receive sensitivity, and $$$T_2^*$$$ effects. The advantage of this method is that it has excellent dynamic range and can be very precise.

The problem is that even a 32x32x32 volume will take $$$32^2\times T_1\times 10$$$ s to image. That is, several hours! That is not practical in phantoms, let alone in-vivo. Of course, we could cut corners. Maybe reduce TR a bit? The problem is, the more you reduce TR, the more $$$T_1$$$ effects get mixed in. At this point there are two options. Estimate $$$T_1$$$ and $$$B_1+$$$ simultaneously or use a more clever strategy.

Over the years many $$$B_1^+$$$ mapping strategies have been proposed [14-20]. Generally speaking, faster $$$B_1^+$$$ mapping strategies tend to trade accuracy and/or dynamic range for speed. Commonly increased speed leads to a mixing of $$$B_1^+$$$ and $$$T_1$$$ effects [14] or high specific absorption rates (SAR)s [17]. For example, turbo-flash based $$$B_1^+$$$ mapping strategies [15] typically assume that $$$T_1$$$ effects can be neglected during the readout phase of the sequence, which is not true for short $$$T_1$$$ tissues like fat. Other techniques leverage high power off resonant pulses to encode $$$B_1^+$$$ into phase of the signal, which can impose restriction due to high specific absorption rates. Nevertheless, several methods allow $$$B_1^+$$$ mapping across extended volumes in 2-4min with reasonable accuracy, even for use with multi-transmit systems [21-23].

Acknowledgements

No acknowledgement found.

References

[1] Bernstein, Matt A., John Huston III, and Heidi A. Ward. "Imaging artifacts at 3.0 T." Journal of Magnetic Resonance Imaging: An Official Journal of the International Society for Magnetic Resonance in Medicine 24.4 (2006): 735-746.

[2] Van de Moortele, Pierre-François, et al. "T1 weighted brain images at 7 Tesla unbiased for Proton Density, T2⁎ contrast and RF coil receive B1 sensitivity with simultaneous vessel visualization." Neuroimage 46.2 (2009): 432-446.

[3] Marques, José P., et al. "MP2RAGE, a self bias-field corrected sequence for improved segmentation and T1-mapping at high field." Neuroimage 49.2 (2010): 1271-1281.

[4] Tropp, James. "The theory of the bird-cage resonator." Journal of Magnetic Resonance (1969) 82.1 (1989): 51-62.

[5] Hoult, David I. "Sensitivity and power deposition in a high‐field imaging experiment." Journal of Magnetic Resonance Imaging12.1 (2000): 46-67.

[6] Vaughan, J. Thomas, and John R. Griffiths, eds. RF coils for MRI. John Wiley & Sons, 2012.

[7] Brunner, David O., et al. "Travelling-wave nuclear magnetic resonance." Nature 457.7232 (2009): 994-998.

[8] Zhang, Bei, et al. "Whole body traveling wave magnetic resonance imaging at high field strength: homogeneity, efficiency, and energy deposition as compared with traditional excitation mechanisms." Magnetic resonance in medicine 67.4 (2012): 1183-1193.

[9] Collins, Christopher M., et al. "Central brightening due to constructive interference with, without, and despite dielectric resonance." Journal of Magnetic Resonance Imaging: An Official Journal of the International Society for Magnetic Resonance in Medicine 21.2 (2005): 192-196.

[10] Gabriel, Camelia, Sami Gabriel, and Y. E. Corthout. "The dielectric properties of biological tissues: I. Literature survey." Physics in medicine & biology 41.11 (1996): 2231.

[11] Soher, Brian J., Brian M. Dale, and Elmar M. Merkle. "A review of MR physics: 3T versus 1.5 T." Magnetic resonance imaging clinics of North America 15.3 (2007): 277-290.

[12] Bernstein, Matt A., Kevin F. King, and Xiaohong Joe Zhou. Handbook of MRI pulse sequences. Elsevier, 2004.

[13] Brown, Robert W., et al. Magnetic resonance imaging: physical principles and sequence design. John Wiley & Sons, 2014.

[14] Pohmann, Rolf, and Klaus Scheffler. "A theoretical and experimental comparison of different techniques for B1 mapping at very high fields." NMR in Biomedicine 26.3 (2013): 265-275.

[15] Chung, Sohae, et al. "Rapid B1+ mapping using a preconditioning RF pulse with TurboFLASH readout." Magnetic resonance in medicine 64.2 (2010): 439-446.

[16] Nehrke, Kay, and Peter Börnert. "DREAM—a novel approach for robust, ultrafast, multislice B1 mapping." Magnetic resonance in medicine 68.5 (2012): 1517-1526.

[17] Sacolick, Laura I., et al. "B1 mapping by Bloch‐Siegert shift." Magnetic resonance in medicine 63.5 (2010): 1315-1322.

[18] Yarnykh, Vasily L. "Actual flip‐angle imaging in the pulsed steady state: a method for rapid three‐dimensional mapping of the transmitted radiofrequency field." Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine 57.1 (2007): 192-200.

[19] Cunningham, Charles H., John M. Pauly, and Krishna S. Nayak. "Saturated double‐angle method for rapid B1+ mapping." Magnetic Resonance in Medicine: An Official Journal of the International Society for Magnetic Resonance in Medicine 55.6 (2006): 1326-1333.

[20] Cloos, Martijn A., et al. "Multiparametric imaging with heterogeneous radiofrequency fields." Nature communications7.1 (2016): 1-10.

[21] Van de Moortele, Pierre-Francois, and Kamil Ugurbil. "Very fast multi channel B1 calibration at high field in the small flip angle regime." Proc Intl Soc Mag Reson Med. Vol. 17. (2009).

[22] Wu et al., “Velocity selective arterial spin labelling using parallel transmission” In the Proc of the 30thannual meeting of the ISMRM (2022) # 2936.

[23] Lu, et al “Functional MRI of large-scale brain networks involved in motor control using parallel transmission at 7 Tesla” In the Proc of the 30th annual meeting of the ISMRM (2022) # 2093

Proc. Intl. Soc. Mag. Reson. Med. 31 (2023)