3293
Conical readouts in free-running 3D bSSFP imaging1Lausanne University Hospital (CHUV) and University of Lausanne (UNIL), Lausanne, Switzerland, 2IHU Liryc Bordeaux, Bordeaux, France
Synopsis
Keywords: New Trajectories & Spatial Encoding Methods, New Trajectories & Spatial Encoding Methods
Motivation: The 3D radial golden angle phyllotaxis pattern integrated into the Free Running framework, supports 5D imaging of the heart during free breathing and without the need for an ECG or navigators. However, it inherently oversample low k-space frequencies with sparser coverage at the periphery of k-space.
Goal(s): Our proposed approach relies on the same phyllotaxis pattern but substitutes the radial readout with spiral sections, enhancing high-frequency sampling, and reduces the overall number of radial readouts needed.
Approach: We formulated the cone equations to account for un-aliasing and hardware limitations and validated our method by simulating bSSFP acquisition.
Results: We obtained improved image quality.
Impact: 3D spirals span a broader extent of k-space compared to radial readouts and allow for a higher sampling density at the periphery of k-space. This may help support higher spatial resolution, reduced noise, and improved image quality.
Introduction
Acquiring images with minimal echo time (TE) demands the use of center-out non-Cartesian k-space trajectories,which are well-matched with radial acquisition strategies.The 3D radial approach,especially when paired with compressed sensing,has proven highly effective in cardiac MRI for its self-navigating capabilities and minimal eddy current impact,as demonstrated by the Free Running technique1,2,3,4.Yet,this radial approach inherently results in a non-uniform distribution of k-space sampling—overemphasizing the center while neglecting higher frequency regions—thereby heavily relying on the count and configuration of radial spokes.In contrast,3D spiral trajectories surpass radial readouts in k-space coverage,yield a higher signal-to-noise ratio (SNR),and reduce the dependency on the point spread function5,necessitating fewer readouts which leads to more efficient scanning and image reconstruction. Radial trajectories, however, have the advantage of over-sampling the center of k-space,which confers greater robustness against motion artifacts and insensitivity to off-resonance effects. Our proposed method synergizes the strengths of both trajectory variants by shaping cones, similar to the method described in5,but organized in a phyllotaxis pattern as detailed in1.Methods
Both conical radial trajectories were implemented in Matlab and used to produced in silico images using a previously described numerical simulation framework 6,4.A balanced Steady State Free Precession (bSSFP) sequence was simulated with 70◦degrees RF excitation angle,TE/TR=1.6/3.52[ms],FOV=(224[mm])3,matrix_size=(112)3.Reconstruction was performed using standard NUFFT gridding8.On the reconstructed images,RMSE9 was used as a metric for comparison derived from an ROI as shown in Fig.1.The trajectory was parameterized as follows:
kx(t)=a(t−t0)cos(bt)H(t−t0)
ky(t)=a(t−t0)sin(bt)H(t−t0)
kz(t)=c1tH(t0−t)+(c2(t−t0)+c1t0)H(t−t0)
Where H(t) is the Heaviside function and t0 defines the end of the radial part of the trajectory at $$$\vec{k}_0$$$ . Below the un-aliasing and hardware constraints:
•Spacing between consecutive twists: $$$\left[\Delta_pr^2+\Delta_p k_z^2\right]^{\frac{1}{2}}\leq(FOV)^{-1}$$$ where $$$P=\frac{2 \pi}{b}$$$ (period of revolution), $$$r(t)=a(t-t_0)$$$ and $$$\Delta_p j = j(t+P)-j(t)$$$.
•Separation between neighboring spokes at $$$\vec{k}_0$$$ is $$$(FOV)^{-1}$$$ (see 5): $$$||\vec{k}_0||=(2FOV \sin(\frac{\alpha}{2}))^{-1}$$$ where $$$\alpha\approx\frac{\pi}{\sqrt{\mathcal{N}}}$$$ in the current pattern for $$$\mathcal{N}$$$ spokes.
•Distance between samples on the radial part: $$$||\vec{k}(t+\Delta t)||-||\vec{k}(t)||=(FOV)^{-1}$$$.
•Spacing between neighboring cones at the surface of the sphere of radius $$$k_{max}=||\vec{k}(t_{max})||$$$ : $$$\mathcal{N}\approx\frac{4k_{max}^2}{(a(t-t_0)+\frac{1}{2}(FOV)^{-1} )^2}$$$, where $$$\mathcal{N}$$$ is the number of cones.
•Hardware constraints: $$$||\vec{k}(t)|| \leq k_{max},||\dot{\vec{k}}(t)||\leq\frac{\gamma}{2\pi} G_{max}$$$ and $$$||\ddot{\vec{k}}(t)||\leq\frac{\gamma}{2\pi} S_{max}$$$ where $$$\dot{\vec{k}}=\frac{d\vec{k}}{dt}$$$, $$$\gamma$$$ is the gyromagnetic factor, $$$G_{max}$$$ is the maximum gradient amplitude and $$$S_{max}$$$ the maximum gradient slew rate.
•Maximum arc length separation : $$$\max(s(t))=s(t_{max})=\Delta t\left[ \sum_{j=x,y,z}\dot{k}_j(t_{max})^2 \right]^{\frac{1}{2}}=(FOV)^{-1}$$$,where $$$\Delta t$$$ is the dwell time.
These constraints provide a solution for a,b,c1,c2 and t0. An optimal number of cones Nopt can be derived by constraining the maximal radius. First,a cone is paired with its negative transversal counterpart to form an alternative to the radial readout,this last is rotated following the phyllotaxis pattern1 with M interleaves and P readouts per interleave (Fig.1). Nopt was used to get the analytical solution of the readout,then the effective number of cones Neff =M×P was used for the spiral phyllotaxis pattern where P was fixed at P=22 and M=[55,89] is a Fibonacci number1,which results in a 1.5% and 2.5% Nyquist limit respectively. The difference |Neff −Nopt| was [19,17] for M=[55,89] respectively,while the number of samples in the radial section ⃗k0 was n0=[8,10].
Results
For M = 55 and 89 respectively,RMSE amounted to 0.15 and 0.14 on radial reconstructions and to 0.15 and 0.12 on those from cones. Overall, the proposed cones trajectory covers the peripheral k-space more densely and promotes a clearer depiction of the simulated cardiac anatomy with reduced artifacts, especially at a very low level of Nyquist sampling. Also note that visually, signal-to-noise and tissue interface sharpness consistently improves on images generated with the cones trajectory when compared to those obtained from a purely radial acquisition.These qualitative results are corroborated by quantitative evaluation of RMSE.Discussion
The conical trajectory improves image quality, with less noise and better interface definition.As expected, denser sampling of higher frequencies results in a reduction of artifacts. However,conical readouts show some residual artifacts, hence may necessitate a custom-designed phyllotaxis pattern to fully maximize the geometric characteristics of the trajectory.These promising initial results motivate further exploration of self-navigation and multidimensional image reconstruction using the proposed trajectory.This should be achieved by further in silico optimization followed by translation to the scanner environment for validation in physical phantoms and healthy volunteers.Conclusion
We have implemented a framework to flexibly design 3D cones trajectories to be integrated as part of a free-running sequence. Initial in silico results suggest that images are more conspicuous while the SNR has improved. Therefore the framework should be applied to design cones k-space trajectories on the MRI scanner and to rigorously explore their parameter space and ascertain their performance in vitro and in vivo relative to results obtained from the baseline free-running 3D radial bSSFP sequence.Acknowledgements
No acknowledgement found.References
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