Bryant T. Svedin^{1}, Allison Payne^{1}, and Dennis L. Parker^{1}

A
multi-echo pseudo-golden angle stack of stars sequence for use in free-breathing interventional procedures is evaluated in vivo
with 5 healthy volunteers for use in MR thermometry in the breast. High spatial
and temporal resolution (1.3 mm^{3}, 1.43 s) is achieved through
k-space filtering. PRF temperature, T2*, ρ (signal magnitude at TE = 0),
respiration correction and fat/water separation are simultaneously measured.
Use of a pseudo-golden angle increment allows for the removal of phase (and
therefore PRF temperature) artifacts due to changing k-space sampling between
reconstructed time points. k-Space sampling based phase reference library greatly
improves temperature standard deviation compared to a single baseline reference.

The slope of the phase vs TE at the
center of k-space was used for respiration correction1. Data was then
reconstructed using a sliding KWIC filter with 13 innermost lines, with each
successive ring using the next higher Fibonacci number until 377 lines in the
outermost ring. The sliding window was advanced 13 views between each reconstruction
time point providing a temporal resolution of 1.43 seconds. The k-space sampling
pattern was repeated after 29 reconstructed time points.
Water and fat images were produced using
the three point Dixon method with the first three echoes. T2*/ρ maps were
calculated using linear regression of the log of the magnitude images vs TE, weighted
by the magnitude *M(TE _{j})*, as shown in Equation 1.
$$\chi^2=\sum_{j=1}^nM_j (ln(M_j)-(a+bTE_j))^2,\quad a=ln(\rho),\quad b = \frac{-1}{T_2^*}\quad [1]$$Phase data (ψ) from each echo was combined using
linear regression of the phases vs TE, weighted by the magnitude squared, as
shown in Equation 2.
$$\chi^2=\sum_{j=1}^nM_j^2 (\psi_j - (a+bTE_j))^2, \quad a=\psi_0, \quad b = \beta \quad [2]$$
PRF temperatures were calculated using four
different methods. Method 1: The first image was used as the single reference phase
for each echo independently. Method 2: A multi-baseline library was used where
the reference image had the same k-space sampling pattern as the current time
point for each echo independently. Method 3: The combined echo phase was used
with the first image as the reference. Method 4: The combined echo phase was
used with the k-space sampling pattern multi-baseline library.

1. Svedin BT, Payne A, & Parker DL. Respiration artifact correction in three-dimensional proton resonance frequency MR thermometry using phase navigators. Magn Reson Med. 2015;doi:10.1002/mrm.25860

2. Song HK, & Dougherty L. k-space weighted image contrast (KWIC) for contrast manipulation in projection reconstruction MRI. Magn Reson Med, 2000;44(6), 825-832.

3. Winkelmann S, Schaeffter T, Koehler T, Eggers H, & Doessel O. An optimal radial profile order based on the Golden Ratio for time-resolved MRI. IEEE Trans Med Imaging, 2007;26(1), 68-76.

4. Payne A, Merrill R, Minalga E, Vyas U, de Bever J, Todd N, Hadley R, Dumont E, Neumayer L, Christensen D, Roemer R, Parker D. Design and characterization of a laterally mounted phased-array transducer breast-specific MRgHIFU device with integrated 11-channel receiver array. Medical physics 2012;39(3):1552-1560.

5. Baron P, Ries M, Deckers R, de Greef M, et al. In vivo T2 -based MR thermometry in adipose tissue layers for high-intensity focused ultrasound near-field monitoring. Magn Reson Med, 2014;72(4), 1057-1064.

6. Rieke V, Butts Pauly K. MR thermometry. J Magn Reson Imaging 2008;27(2):376-390.

Figure
1. Separated water (left) and fat (right) images for in vivo breast coronal
(left column) and sagittal (right column) for five volunteers.

Figure
2. Standard deviation through time
maps of PRF temperature in aqueous tissue for the four calculation methods for volunteer 2. Left column: 1st image used as phase reference. Right
column: Library of baseline images based on sampling trajectory. Top Row: PRF
temperature calculated from the last echo. Bottom row: PRF temperature
calculated from the combined phase.

Figure
3. Spatially averaged PRF standard deviation in aqueous tissue in the breast
for volunteer 3. Red) PRF temperature calculated using method 1. Blue) PRF
temperature calculated using method 2. Green) PRF temperature calculated using
method 3. Black) PRF temperature calculated using method 4. The combined phases
only used the echoes up to and including the displayed TE.

Table
1. Spatially averaged PRF standard deviation values in aqueous tissue in the
breast for each volunteer in the coronal and sagittal orientations for each of
the four calculation methods.

Figure 4. Standard
deviation through time maps of the percent difference in initial signal
magnitude ρ
in adipose tissue for two cases.
Left column: 1st
image used as reference for magnitude difference. Right column: Library of
baseline images based on sampling trajectory.