Magnetic resonance imaging method with hybrid filling of k-space

Abstract

A method for generating an image data set of an image area located in a measurement volume of a magnetic resonance system comprising a gradient system and an RF transmission/reception system, comprises the following method steps: —reading out k-space corresponding to the imaging area, by: (a) activating a frequency encoding gradient in a predetermined spatial direction and with a predetermined strength G.sub.0 by means of said gradient system, (b) after the activated frequency encoding gradient achieves its strength G.sub.0, radiating a non-slice-selective RF excitation pulse by means of said RF transmission/reception system, (c) after a transmit-receive switch time Δt.sub.TR following the radiated excitation pulse, acquiring FID signals with said RF transmission/reception system and storing said FID signals as raw data points in k-space along a radial k-space trajectory that is predetermined by the direction and strength G.sub.0 of the frequency encoding gradient, (d) repeating (a) through (c) with respectively different frequency encoding gradient directions in each repetition until k-space corresponding to the image area is read out in an outer region of k-space along radial k-space trajectories, said radial k-space trajectories each having a radially innermost limit k.sub.gap which depends on said switch time Δt.sub.TR, (e) reading out a remainder of k-space that corresponds to the imaging area, said remainder being an inner region of k-space not being filled by said first region and including at least a center of k-space, in a read out procedure that is different from (a) through (d), and storing all data points read out in (d) and (e); and —reconstructing image data from the read out data points in k-space by implementing a reconstruction algorithm; In order to constrain image fidelity and optimize scan duration under given circumstances, the inner k-space region is subdivided into a core region and at least one radially adjacent shell region.

Claims

1. A method for generating an image data set of an image area located in a measurement volume of a magnetic resonance system, the magnetic resonance system comprising a gradient system and an RF transmission/reception system, the method comprising: reading out k-space corresponding to the imaging area, by: (a) activating a frequency encoding gradient in a predetermined spatial direction and with a predetermined strength G.sub.0 via said gradient system, (b) after the activated frequency encoding gradient achieves its strength G.sub.0, radiating a non-slice-selective RF excitation pulse via said RF transmission/reception system, (c) after a transmit-receive switch time Δt.sub.TR following the radiated excitation pulse, acquiring FID signals with said RF transmission/reception system and storing said FID signals as raw data points in k-space along a radial k-space trajectory that is predetermined by the direction and strength G.sub.0 of the frequency encoding gradient, (d) repeating (a) through (c) with respectively different frequency encoding gradient directions in each repetition until k-space corresponding to the image area is read out in an outer region of k-space along radial k-space trajectories, said radial k-space trajectories each having a radially innermost limit k.sub.gap which depends on said switch time Δt.sub.TR, (e) reading out a remainder of k-space that corresponds to the imaging area, said remainder being an inner region of k-space not being filled by said first region and including at least a center of k-space, in a read out procedure that is different from (a) through (d), and storing all data points read out in (d) and (e); and reconstructing image data from the read out data points in k-space by implementing a reconstruction algorithm; wherein the inner k-space region is subdivided into a core region and at least one radially adjacent shell region with raw data points in the core region being acquired as Cartesian raw data, and raw data points in the shell region (S) being acquired along radial k-space trajectories using a gradient strength G that is smaller than the gradient strength G.sub.0.

2. The method according to claim 1, wherein the boundary k.sub.gap subdividing the inner and outer k-space regions is given by the product of bandwidth BW and dead time Δt.sub.0, wherein the dead time Δt.sub.0 is given by Δt.sub.RF, which is a part of the RF pulse plus the transmit-receive switch time Δt.sub.TR.

3. The method according to claim 1, wherein the core region has an outer limit k.sub.core given by: $k_{core}=\frac{\Delta t_0}{\Delta t}.Math.s_{min}$ wherein the dead time Δt.sub.0 is given by Δt.sub.RF, which is a part of the RF pulse plus the transmit-receive switch time Δt.sub.TR, the allowed acquisition duration Δt is given by −T.sub.2 ln(1−A) wherein A is an amplitude parameter selected between 0 and 1, the minimum shell thickness s.sub.Min is selected to be between 0.1 and 10.

4. The method according to claim 1, wherein the shell region comprises at least two shell regions (S.sub.1, S.sub.2, . . . ), each shell region S.sub.i having a shell thickness s.sub.i given by $s_i=\frac{\Delta t}{\Delta t_0}.Math.k_{in}$ wherein dead time Δt.sub.0 is given by Δt.sub.RF, which is a part of an RF pulse plus the transmit-receive switch time Δt.sub.TR, and allowed acquisition duration Δt is given by −T.sub.2 ln(1−A) wherein A is an amplitude parameter selected between 0 and 1, each shell region having an inner radius k.sub.in defined by the thickness of the next radially inward core or shell region.

5. The method according to claim 1, wherein the reconstruction algorithm comprises a Fourier transformation of the data points.

6. The method according to claim 2, wherein Δt.sub.RF is half of the RF pulse for symmetric RF pulses.

7. The method according to claim 3, wherein Δt.sub.RF is half of the RF pulse for symmetric RF pulses.

8. The method according to claim 3, wherein the minimum shell thickness s.sub.Min is between 0.5 and 2.

9. The method according to claim 3, wherein the minimum shell thickness s.sub.Min is about 1.

10. The method according to claim 2, wherein the shell region comprises at least two shell regions (S.sub.1, S.sub.2, . . . ), each shell region S, having a shell thickness s.sub.i given by $s_i=\frac{\Delta t}{\Delta t_0}.Math.k_{in}$ wherein allowed acquisition duration Δt is given by −T.sub.2 ln(1−A), wherein A is an amplitude parameter selected between 0 and 1, each shell region having an inner radius k.sub.in defined by the thickness of the next radially inward core or shell region.

11. The method according to claim 3, wherein the shell region comprises at least two shell regions (S.sub.1, S.sub.2, . . . ), each shell region S, having a shell thickness s.sub.i given by $s_i=\frac{\Delta t}{\Delta t_0}.Math.k_{in}$ each shell region having an inner radius k.sub.in defined by the thickness of the next radially inward core or shell region.

12. The method according to claim 2, wherein the reconstruction algorithm comprises a Fourier transformation of the data points.

13. The method according to claim 3, wherein the reconstruction algorithm comprises a Fourier transformation of the data points.

14. The method according to claim 4, wherein the reconstruction algorithm comprises a Fourier transformation of the data points.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The above mentioned and other features and objects of this invention and the manner of achieving them will become more apparent and this invention itself will be better understood by reference to the following description of embodiments of this invention taken in conjunction with the accompanying drawings, wherein:

(2) FIG. 1 shows data acquisition in zero echo time-based techniques: a) the gradient (G) is ramped up (upper trace) before spin excitation (middle trace); The beginning of the resulting FID cannot be probed due to the dead-time gap (Δt.sub.0) (white dots in lower trace); b) between excitations, the gradient direction is changed slowly to acquire different projections in order to fill the k-space volume of interest; c-e) PETRA, WASPI, and HYFI differ in the way they provide the missing data; Left: 1D depiction of k-space T2 weighting; Right: 2D depiction of inner k-space acquisition geometry; c) in PETRA, the inner k-space is acquired single-pointwise in a Cartesian fashion leading to constant T2 weighting; d) in WASPI, a second set of radial acquisitions is performed at lower gradient strength, giving rise to increased and potentially strong T2 weighting; e) HYFI, the method of this invention, is a hybrid between PETRA and WASPI: a combination of Cartesian SPI and multiple sets of radial acquisitions is used to keep the T2 decay in a given range R, wherein R is chosen such as to allow higher scan efficiency with minimum loss of image quality;

(3) FIG. 2 shows relevant timing intervals in relation to the applied RF pulse; Δt.sub.0 includes a part of the pulse Δt.sub.RF, half of the pulse duration for symmetric pulses, and the transmit-receive switch time Δt.sub.TR; and Δt is the time window corresponding to the acquisition of each shell;

(4) FIG. 3 shows some fundamental relations holding for a given temporal decay of transversal magnetization M.sub.xy(t);

(5) FIG. 4 shows an example of HYFI acquisition wherein the inner region of-k space, of radius equal to the gap, is subdivided into a core region surrounded by two radially adjacent shell regions S1 and S2 of thickness equal to respectively s1 and s2;

(6) FIG. 5 shows the number of excitations required by each technique to fill the inner k-space, assuming a T2 decay of 64 Nyquist dwells; circles at the top illustrate the acquisition geometries; in 3D, the number of excitations evolves with k.sub.gap.sup.3 for PETRA and k.sub.gap.sup.2 for WASPI; in the proposed method, inner k-space is filled by a combination of SPI and radial acquisitions, and thus the green area enclosed by the curves for PETRA and WASPI becomes accessible; green lines represent selected HYFI acquisitions with amplitude coefficients A=0.1 and 0.3;

(7) FIG. 6 shows a simulation of point spread functions: 1D HYFI acquisitions were simulated with the following fixed parameters: image matrix size=128, T2=64 Nyquist dwells. PSFs are displayed for different combinations of gap sizes (a-c) and amplitude coefficients A (0=PETRA, 1=WASPI); and

(8) FIG. 7 shows a comparison of magnetic resonance imaging acquired with PETRA (left column), WASPI (middle column) and HYFI (right column).

DETAILED DESCRIPTION OF THE INVENTION

(9) Theory

(10) k-Space Acquisition:

(11) The norm of the acquired k-space point {tilde over (k)} is related to the acquisition time t:
{tilde over (k)}(t,G)=γ.Math.G.Math.t[m.sup.−1]  (1)
with γ the gyromagnetic ratio [Hz/T], G the gradient [T/m], t the acquisition time [s]. Moreover, it is useful to express the k-space norm in number of Nyquist dwells (1 dwell has a length of

(12) $\frac{1}{FOV}\left[m^{-1}\right]$
with FOV the field of view of the experiment) instead of [m.sup.−1]. To do so, {tilde over (k)} should be multiplied by the field of view FOV:
k(t,G)={tilde over (k)}.Math.FOV=γ.Math.G.Math.t.Math.FOV  (2)

(13) In PETRA, WASPI and HYFI, acquisition of the outer k-space is performed with a gradient strength G.sub.0 and the first data point is sampled at k.sub.gap, after the dead time Δt.sub.0:
k.sub.gap=k(Δt.sub.0,G.sub.0)=γ.Math.G.sub.0.Math.Δt.sub.0.Math.FOV  (3)

(14) All k-space points smaller than k.sub.gap are missed during the acquisition of the outer k-space. However, PETRA, WASPI and HYFI recover the missing data with additional acquisitions performed with lower gradient strengths G (G<G.sub.0) such that k-space samples smaller than the gap can be reached after the dead time.
k(Δt.sub.0,G)<k(Δt.sub.0,G.sub.0)=k.sub.gap  (4)
k-Space T2 Weighting:

(15) Lowering the gradient strength decreases the k-space acquisition velocity v.sub.k which express the number of Nyquist dwells acquired per unit time:

(16) $\begin{array}{cc}{v}_k=\frac{\mathrm{dk}}{\mathrm{dt}}=\gamma .Math.G.Math.\mathrm{FOV}\left[s^{-1}\right]& \left(5\right)\end{array}$

(17) Hence, the k-space regions acquired with a lower gradient strength have a stronger T2 weighting because the amplitude decays faster for a given k-space range.

(18) PETRA vs WASPI:

(19) In PETRA, only one point is acquired per excitation after the dead time Δt.sub.0 and gradient strengths and amplitudes are changed between each excitation in order to acquire the k-space center on a Cartesian grid. Since all points are measured after the same time, the inner k-space has a constant T2 weighting (FIG. 1c). The number of required excitations to fulfil the Nyquist criterion at the gap evolves with the third power of k.sub.gap.
n.sub.PETRA≈4/3.Math.π.Math.k.sub.gap.sup.3  (6)

(20) In WASPI, several points are measured radially after each excitation. Due to the use of low gradient strengths, the k-space is acquired slowly and a strong T2 weighting appears in the inner k-space. This lead to large amplitude jumps at the gap (FIG. 1d) which in turns gives rise to unwanted point spread function (PSF) side lobes (FIG. 6), see [1]. However timewise, WASPI acquisitions are more efficient than PETRA and especially at large gaps because the number of required excitation evolves with the second power of k.sub.gap.
n.sub.WASPI≈4.Math.π.Math.k.sub.gap.sup.2  (7)

(21) To summarize, the PSF of PETRA is preferred to the PSF of WASPI in view of better image fidelity due to smaller side lobes, but PETRA acquisitions are significantly longer at large gaps.

(22) Detailed HYFI Description:

(23) The goal of HYFI is to optimize scan duration while constraining depiction fidelity.

(24) To this end, a radial acquisition geometry is used whenever possible to optimize scan efficiency but the T2 decay is restricted to a range R (FIG. 1e) to avoid large amplitude jumps and limit PSF side lobes.

(25) The range R is defined proportionally to the amplitude of the transverse magnetization at the dead time M.sub.xy(Δt.sub.0) (FIG. 3).

(26) $\begin{array}{cc}R=\left[1-\exp \left(-\frac{\Delta t}{T_2}\right)\right].Math.M_{xy}\left(0\right).Math.\exp \left(­\frac{\Delta t_0}{T_2^{*}}\right)=A.Math.M_{xy}\left(\Delta t_0\right)& \left(8\right)\end{array}$

(27) The amplitude factor A corresponds to the proportion of signal amplitude lost during the acquisition duration Δt due to an exponential decay of time constant T.sub.2.

(28) Hence, restricting the decay range R amounts to limiting A which is done by limiting the acquisition duration Δt.

(29) Typically, the factor A can be optimized with preliminary acquisitions or simulations as illustrated in FIGS. 5 and 6. In this case, limiting A to 10-30% strongly decreases the number of excitations to be performed and largely preserves the PSF lineshape.

(30) After optimization, the allowed acquisition duration can be calculated as (FIG. 3)
Δt=−T.sub.2.Math.ln(1−A)  (9)

(31) However, the allowed acquisition duration may not be long enough to acquire the full inner k-space. Therefore, the inner k-space is split in an onion-like fashion with a core surrounded by one or several shells.

(32) The gradient strength required to reach the core (or 0.sup.th shell) corresponds to such a low k-space speed that the signal amplitude of the second point would be outside of the allowed range R at the time of its acquisition. Hence, the core is acquired single-pointwise on a Cartesian grid.

(33) On the other hand, in the shells surrounding the core, several points can be measured after each excitation. Thus, in this case, k-space is acquired radially (FIG. 4).

(34) Calculation of Shell Thickness:

(35) The shell thickness, is given by the allowed acquisition duration Δt and the k-space acquisition velocity v.sub.k.
s=Δt.Math.v.sub.k=Δt.Math.γ.Math.G.Math.FOV=Δt.Math.BW  (10)
with BW the imaging bandwidth.

(36) The k-space acquisition velocity, v.sub.k, is proportional to the gradient G (Eq. 5) which is determined by the inner radius of the shell, k.sub.in. The inner radius k.sub.in is by definition always acquired after the dead time Δt.sub.0 and given by:

(37) $\begin{array}{cc}\gamma .Math.G.Math.\Delta t_0.Math.\mathrm{FOV}=k_{in}& \left(11\right)\\ .fwdarw.G=\frac{k_{in}}{\gamma \Delta t_{0}FOV}\left[T/m\right]& \left(12\right)\end{array}$

(38) From Equ. 11 and Equ. 12, we can rewrite the shell thickness, s, as follow

(39) $\begin{array}{cc}s=\frac{\Delta t}{\Delta t_0}.Math.k_{in}& \left(13\right)\end{array}$

(40) Note: shell thickness increases linearly with inner radius k.sub.in.

(41) HYFI Step by Step:

(42) 1) Define targeted transverse relaxation time T2 2) Define maximum allowed decay range R within the shell (optimize amplitude parameter A). 3) Calculate maximum acquisition duration
Δt=−T.sub.2.Math.ln(1−A) 4) Define s.sub.Min, the minimum shell thickness required to do radial acquisitions. Generally, s.sub.Min is selected to be between 0.1 and 10, preferably between 0.5 and 2, and is typically chosen to be 1. 5) Calculate core radius, k.sub.core, delimiting the boundary between SPI and radial acquisitions.

(43) $\mathrm{Acquisition}\mathrm{geometry}=\{\begin{array}{cc}\mathrm{Cartesian}\mathrm{SPI},& k\le k_{\mathrm{core}}\\ \mathrm{radial},& k>k_{\mathrm{core}}\end{array}{k}_{\mathrm{core}}=\frac{\Delta t_0}{\Delta t}.Math.s_{\mathrm{Mi}n}$ 6) Calculate inner radius k.sub.in.sub.j and outer radius k.sub.out.sub.j for each shell j.

(44) $k_{i{n}_1}=k_{\mathrm{core}}{s}_j=\frac{\Delta t}{\Delta t_0}.Math.k_{i{n}_j}$$k_{ou{t}_j}=k_{i{n}_j}+s_j$$k_{i{n}_{j+1}}=k_{ou{t}_j}+\delta k\mathrm{with}0\le \mathrm{\delta k}\le 1\mathrm{and}\left\{\forall j|k_{in}j<k_{gap}\right\}.$

(45) Note: if δk=0, Nyquist criterion is fulfilled everywhere. If δk=1, Nyquist criterion is not strictly fulfilled at shell boundaries. As an option, it would also be possible to linearly merge shells over an overlap region in order to decrease irregularities in the k-space weighting. 7) Calculate k-space directions a. SPI i. All k-space point on Cartesian grid fulfilling
|k|≤k.sub.core b. Radial i. Calculate number of shots (or radial spokes) to fulfill Nyquist criterion on the outer surface of each shell j
n=4.Math.π.Math.k.sub.out.sub.j.sup.2 ii. Calculate the directions of each shot by spreading these points on the surface of each shell following a suitable trajectory with approximately equal density. 8) Measure data on calculated trajectory 9) Reconstruct image
Concluding Remarks

(46) FIG. 5 illustrates the scan efficiency of the different methods. At large gaps, the number of excitations required to fill the inner k-space is significantly larger in PETRA (4/3*π*k.sub.gap.sup.3) than in WASPI (4*pi*k.sub.gap.sup.2). In HYFI, relatively low amplitude coefficients (0.1 to 0.3) allow significant reduction of the number of excitations compared to PETRA while preserving satisfactory PSF lineshapes (FIG. 6). For example, at a gap of 30 Nyquist dwells and a T2 of 64 Nyquist dwells, the use of HYFI with A=0.3 reduces the number of shots required to fill the inner k-space by almost 80% (from 1.15 10.sup.5 to 2.45 10.sup.4). Assuming repetition times between 1 and 10 ms, this leads to a net gain of 1.5 to 15 minutes per scan.

(47) The HYFI method is evaluated with 1D simulations of point spread functions (PSF), see FIG. 6.

(48) One-dimensional point spread functions (PSF) were simulated by application of the following formula:
P=F.Math.T.Math.E.Math.δ.sub.0
wherein F is the pseudo inverse of the encoding matrix E, T is the T2 weighting matrix (T2=64 Nyquist dwells) and δ.sub.0 is the Kronecker delta function located in the center of the field of view.

EXAMPLE

(49) A comparison of magnetic resonance imaging acquired with PETRA (state of the art), WASPI (state of the art) and HYFI (present invention) is shown in FIG. 7. Magnetic resonance imaging was performed with PETRA (equivalent to HYFI with A=0), WASPI (equivalent to HYFI with A=1) and HYFI (A=0.2).

(50) First Row: 1D representations of the signal T2-weighting in k-space. The signal amplitude in the outer k-space region is exponentially decaying and equivalent in all techniques. However, the acquisition of the inner k-space region is specific to each technique. In PETRA, the signal is acquired point by point at a constant time following the spin excitation leading to a constant T2-weighting in the inner k-space region. In WASPI, the inner k-space region is read out radially with a reduced gradient strength causing stronger signal decay and amplitude jumps at the border separating inner and outer k-space regions. In HYFI, the inner k-space region is split into several sub-regions: a core surrounded by shells. The core is read out single-pointwise similarly to PETRA. The shells are read out radially leading exponential decay of the signal amplitude.

(51) Second Row:

(52) a) Number of spin excitations required for the acquisition of the inner k-space region. b) Repetition time (time separating two spin excitations) in milliseconds. c) Total scan duration (min:sec). Note: because of the slow acquisition of the inner k-space region, the repetition time of WASPI was increased to 3 milliseconds causing a strong increase in scan time despite the lower number of required excitations. d) Images. The sample consists of a stack of erasers (T2≈300 μs) standing on a hockey puck (T2≈100 us). In WASPI, the large amplitude jumps in k-space T2-weighting lead to strong artifacts in the image. HYFI offers similar image quality than PETRA with reduced scan time.

(53) Additional Scanning Parameters: Δt.sub.0=100 μs, k.sub.gap=25 Nyquist dwells, imaging bandwidth=250 kHz, duration of excitation pulse=2 μs

REFERENCES

(54) [1] Froidevaux, R. et al. (2017), Filling the dead-time gap in zero echo time MRI: Principles compared. Magn Reson Med. 2017 Aug. 30. doi: 10.1002/mrm.26875. [2] Wu Y, Dai G, Ackerman J L, Hrovat M I, Glimcher M J, Snyder B D, Nazarian A, Chesler D a. Water- and fat-suppressed proton projection MRI (WASPI) of rat femur bone. Magn Reson Med 2007; 57:554-67. [3] Grodzki D M, Jakob P M, Heismann B. Ultrashort echo time imaging using pointwise encoding time reduction with radial acquisition (PETRA). Magn Reson Med 2012; 67:510-8. [4] Weiger M, Pruessmann K P. MRI with Zero Echo Time. eMagRes 2012; 1:311-22. [5] Froidevaux R, Weiger M, Rösler M B, Wilm B, Hennel F, Luechinger R, Dietrich B E, Reber J, Pruessmann K P. Ultra-high-bandwidth, high-resolution MRI of fast relaxing spins Shot-T2 MRI: requirements High resolution. Proc 26th Annu Meet ISMRM, Honolulu 2017:4037.