Matthew J. Middione1, Michael Loecher1, Kévin Moulin1,2, and Daniel B. Ennis1,2,3
1Department of Radiology, Stanford University, Palo Alto, CA, United States, 2Cardiovascular Institute, Stanford University, Palo Alto, CA, United States, 3Veterans Administration Health Care System, Division of Radiology, Palo Alto, CA, United States
Synopsis
In DWI, applied diffusion
gradients are assumed to be linear in space, but in practice are accompanied by
additional undesired concomitant gradient (CG) fields that arise as a
consequence of Maxwell’s equations. These CG fields contribute a residual gradient
moment for asymmetric diffusion encoding strategies, which may impact the
quantitative accuracy of the measured ADC. In this work, a CG correction method
that does not increase the minimum achievable TE was implemented for clinically
relevant asymmetric diffusion encoding DWI protocols and the mean ADC error reduction
was characterized.
Introduction
Diffusion-weighted MRI (DWI) uses
strong magnetic field gradients to encode the diffusion of water. Conventional
methods of diffusion encoding, such as Stejskal‐Tanner1, use
symmetric monopolar gradient waveforms on either side of a refocusing RF pulse.
The applied diffusion gradients are assumed to be linear in space, but Maxwell’s
equations dictate that whenever a linear magnetic field gradient is applied,
accompanying spatially dependent concomitant
gradient (CG) fields are present2.
These CG fields contribute a residual non-zero gradient moment that leads to
intravoxel phase dispersion and may impact the quantitative accuracy of the
apparent diffusion coefficient (ADC). Conventional symmetric diffusion encoding
strategies ensure that the effects of CG fields from each lobe are self-cancelling.
More recently, DWI methods have incorporated asymmetric
diffusion encoding strategies that encode the same b-value in a shorter TE3-8.
While these methods improve SNR due to the reduced TE, the asymmetry does not
ensure cancellation of CG fields. Optimization methods have been proposed to
incorporate a CG field constraint to ensure cancellation of the effect7-9,
but these methods can have long compute times and/or significantly increase the
minimum achievable TE.
One CG field correction strategy
calculates the CG fields at a specific location in space and then compensates
the applied waveform(s)10,11 using “gradient lifting”, which lifts
the gradient amplitude such that the ensuing CG fields will be nullified. Gradient
lifting corrects the CG field error at a single pixel location, but data
acquired distant from this location may still be affected by residual CG fields
or made worse by the gradient lifting. To the best of our knowledge, no formal
analysis has been conducted to define which pixel location to select for prospective
CG field correction for asymmetric diffusion encoding strategies.
In this work, a CG correction
method that does not increase the minimum achievable TE was implemented for clinically
relevant asymmetric diffusion encoding DWI protocols and the mean ADC error reduction
was characterized.Methods
CG fields ($$$G_{c}$$$)
can be approximated at a given $$$(x,y,z)$$$ position using a second-order Taylor
series expansion2:
$$G_{c}(x,y,z,t)\approx \frac{1}{4B_{0}}\left[{\begin{matrix}G_{z}^2(t)&0&-2G_{x}(t)G_{z}(t)\\0&G_{z}^2(t)&-2G_{y}(t)G_{z}(t)\\-2G_{x}(t)G_{z}(t)&-2G_{y}(t)G_{z}(t)&4G_{x}^2(t)+4G_{y}^2(t)\\\end{matrix}}\right]\left[{\begin{matrix}x\\y\\z\\\end{matrix}}\right]\quad \quad \quad Eq. [1]$$
As per Eq. [1], CG
fields can only be corrected at a single pixel location. To identify the location
that maximizes the reduction of the CG field effects throughout the entire
imaging FOV, numerical simulations were performed for typical cardiac, neuro,
and liver DWI protocols (Table 1). Time-optimal asymmetric diffusion gradient
waveforms were generated using an open source Gradient Optimization Toolbox
(GrOpt, https://github.com/cmr-group/gropt).
A brute force approach was used to analyze the
impact of the choice of pixel location on the ability to correct for CG fields.
For each of the tested protocols, every pixel location, $$$(x',y',z')$$$,
within the imaging FOV was used as input to Eq.
[1]. The resulting $$$G_{c}(x,y,z,t,x',y',z')$$$
was used to generate a phase error map, $$$\phi(x,y,z,x',y',z')$$$,
calculated by
taking the product of the residual zeroth gradient moment along each axis and
the pixel location. The pixel location that, on average, minimized the mean
phase error across all slices was then identified as the optimal pixel
location for CG field correction. ADC maps were
generated for each protocol using the optimal pixel input and Eqs. [2-3] with 81
simulated spins per voxel (j=81):
$$S_{D}(x,y,z)=\sum_{j=1}^{81}S_{0}(x,y,z)e^{-bD}e^{-i\phi_{j}(x,y,z)} \quad \quad \quad Eq. [2] \quad \quad \quad D(x,y,z)=\frac{ln(|S_{D}(x,y,z)|/|S_{0}(x,y,z)|)}{-b} \quad \quad \quad Eq. [3]$$
DICOM datasets acquired for each of the three
protocols were masked and multiplied by the ADC maps. The mean ADC error across
all slices was computed for each protocol as mean(D$$$(x,y,z)$$$).Results
The brute force
method identified a pixel location of $$$(0,0,z)$$$ as the ideal location to use for
CG field correction for all axial protocols. Simulated ADC maps for the cardiac
(Fig. 1), neuro (Fig. 2), and liver (Fig. 3) protocols are shown before and
after CG field correction.Discussion
The gradient lifting CG field correction technique
resulted in the mean ADC error across all slices being reduced by ~2.5x (16%
vs. 6.4%) for the cardiac protocol (Fig. 1), ~1.75x (16.7% vs. 8.9%) for the
neuro protocol (Fig. 2), and ~2.25x (22.4% vs. 9.8%) for the liver protocol
without incurring a TE penalty.
Although the gradient
lifting CG field
correction reduces the average ADC error, some pixel locations may have an
increased error while others are eliminated. Perfect cancellation of CG fields
with asymmetric diffusion encoding strategies can be achieved with a phase
symmetry constraint7-9, but these methods increase the TE, which decreases
the SNR and can decrease ADC accuracy.
A
number of parameters used in these simulations were fixed, such as B0,
GMax, scan orientation, and imaging volume size. Errors arising due
to CG fields depend on the values chosen for these parameters, but the
protocols chosen herein are representative of a subset of clinically relevant
imaging volumes.Conclusion
This work shows that the
gradient lifting CG field correction technique using a single pixel location
can mitigate the impact of CG fields for asymmetric diffusion encoding
strategies such that the ADC error is ≤10%. This work enables the use of
time-optimal asymmetric diffusion encoding strategies, without the need to constrain
for CG fields and unnecessarily increasing the minimum achievable TE.Acknowledgements
This project was supported, in part, by NIH
R01 HL131823 to DBE.References
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