Yicun Wang1, Gregor Adriany2, Jiaen Liu1, Xiaotong Zhang1, Pierre-Francois Van de Moortele2, and Bin He1,3
1Department of Biomedical Engineering, University of Minnesota, Minneapolis, MN, United States, 2Center for Magnetic Resonance Research, University of Minnesota, Minneapolis, MN, United States, 3Institute for Engineering in Medicine, University of Minnesota, Minneapolis, MN, United States
Synopsis
Electrical Properties Tomography (EPT) is
a promising technique to provide high specificity in breast cancer diagnosis. Previous
studies have demonstrated that multi-transmit coils array enables
reconstruction of the electrical properties free of transmit phase and local
homogeneity assumptions. In this study, the strengths and drawbacks of a
microstrip array and a loop array for EPT reconstruction in the breast at 3T
were investigated based on numerical simulations. It has been discovered that with
the same driving power, a loop array provides higher signal to noise ratio on
the reconstructed image while a microstrip array performs better at delineating
tissue boundaries.Introduction
Reconstructing the electrical properties
(EP) in vivo using MRI has drawn significant attention due to its great
potential of high specificity for tumor diagnosis. However, the assumptions of
equal transmit and receive phase distribution in a quadrature volume coil and
locally homogenous tissue EP values in the Helmholtz equation may substantially
degrade reconstruction fidelity, especially in the breast with a highly complex
structure. These hurdles could be overcome by employing multiple transmit B
1
maps obtained from a coil array, a potent tool which could significantly push EPT
further towards assumption-free reconstruction
1.
Theory
The central
equation of EPT can be written as a partial differential equation concerning
each specific transmit B1 (B+1) distribution as[∇2B+1(∂B+1∂x−i∂B+1∂y)+12∂Bz∂z∂B+1∂z−12(∂Bz∂x+i∂Bz∂y)]T[γc∂γc∂x+i∂γc∂y∂γc∂z]=−ω2μ0B+1
which relates
conductivity σ
and relative permittivity ϵr
in γc=1ϵrϵ0−iσ/ω
to time-harmonic B+1 and Bz
field at angular frequency ω.2,3 The red terms in the equation are B+1
dependent of which the magnitude and relative
phase can be mapped using a multi-transmit coil array4,5. However,
the Bz-related terms in blue are
not directly tractable from MRI signal. 1) For reconstruction strategies
ignoring EP gradient, the central equation reduces to Helmholtz equations6σ=1ωμ0Im(∇2B+1B+1)ϵr=−1ω2μ0ϵ0Re(∇2B+1B+1)It is desirable
to combine multiple transmit channels for elevated reconstruction performance as
a result of improved
B+1 coverage and SNR. 2) For strategies
considering EP gradient when the full equation (1) is employed, a carefully
designed coil, which has enhanced red terms
dominating over the blue terms, should
be used. Long rectangular microstrips7 and loops8
aligning in z direction are good candidates for serving this purpose due to
their relatively constant
B+1 along z direction and relatively insignificant
Bz variation in the middle of the coil. However,
for the loop element, due to the opposite polarity of currents flowing in the
two long sides, the
Ez-related term
(∂B+1∂x−i∂B+1∂y) destructively interferes
while the
Bz-related term constructively interferes with
each other, causing difficulty to retrieve EP gradient without
Bz information. This interference is not prominent
for microstrips as the field is generated by current flowing in a single-sided
conductor. Therefore, it is expected that EPT reconstruction with EP gradient
consideration prefers microstrips to loops.
Methods
Eight-channel
microstrip and loop array coils for a breast model were constructed in SEMCAD
and loaded with either a homogenous phantom mimicking saline water (conductivity
0.56S/m, relative permittivity 76) or a realistic female chest model (breast part
from Phantom Repository, UMCEM; chest part from Ella, Virtual Population). All
microstrips are 150mm in length and 30mm in width, and distributed azimuthally following
the circumference of a half-cylinder 180mm in diameter. All loops are 140mm in
length and 50mm in width in plane, decoupled by proper overlaps, and arched to
the same half-cylinder circumference (Figure 1). Input power to each coil
element at 128MHz was normalized to 1 Watt. The coil elements were driven
sequentially, and the resultant steady-state time-harmonic
B+1 maps for each element were extracted. Same
level of complex white noise was added separately to
B+1
maps from the two arrays loaded with the
homogeneous phantom. The final reconstructed conductivity of the phantom was a
|B+1|-weighted sum of the reconstructed
conductivity using all eight individual complex B
1 map based on Helmholtz
equation. The conductivity of the breast model was reconstructed by solving the
concatenated linear system of equations associated with all eight channels
regularized by Total Variation
9.
Results
Helmholtz
reconstruction of the conductivity in the phantom is shown in figure 2. Compared
to the microstrips, reconstruction is more accurate and precise with the loop
coil, especially at locations further away from the coils because of deeper
B+1 penetration. At SNR=50, reconstructed mean ±
standard deviation in the box is 0.52±0.11S/m for microstrips and 0.54±0.05S/m
for the loops. The reconstructed conductivity distributions in the breast model
are shown in figure 3. Result from the loop array coil manifests substantially
lower contrast between tissues due to its more dominant
Bz-related term which
results in inaccurate preservation of the EP gradient
information as discussed above. The reconstruction error pervades to
homogeneous tissue as well owing to the nature of spatial partial differential
equation which links together all pixels in the region of interest.
Discussion
and Conclusion
With
theoretical analysis and numerical simulation results, this study has
demonstrated that loop array is preferable for local EPT reconstruction within
homogeneous tissue while microstrip array is superior when considering EP
gradient in the reconstruction process. It is expected that other specially
designed coil hardware could further improve the reconstruction fidelity of the
EP values for various body parts.
Acknowledgements
NIH
R21EB017069, R01EB006433, R21EB009133, R21EB014353, P30NS057091, U01HL117664, P41EB015894
and S10RR026783 of WM KECK Foundation.References
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