System and Method for Phase-Contrast MRI with Hybrid One- and Two-Sided Flow-Encoding and Velocity Spectrum Separation (HOTSPA)

Abstract

A system and method is provided for acquiring flow encoded data from a subject using a magnetic resonance imaging (MRI) system. The method includes acquiring flow encoded (FE) data with alternating encoding polarities and along two of three orthogonal directions through the subject over at least two cycles of the flow within the subject; and separating the FE data into directional FE datasets using a temporal filter that separates the FE data based on temporal modulation of the FE directions caused by the alternating encoding polarities extending over the at least two cycles of the flow within the subject that shift the Fourier spectrum of velocity waveforms corresponding to the FE data. The method also includes using the directional FE datasets to generate an image of the subject showing flow within the subject caused by the at least two cycles of flow within the subject.

Claims

1. A method for acquiring flow encoded data from a subject using a magnetic resonance imaging (MRI) system to reconstruct an image of the subject illustrating flow within the subject, the method includes steps comprising: (i) using the MRI system, acquiring flow encoded (FE) data with alternating encoding polarities and along at least two of three orthogonal directions through the subject over at least two cycles of the flow within the subject; (ii) separating the FE data into directional FE datasets using a temporal filter that separates the FE data based on temporal modulation of FE directions caused by the alternating encoding polarities extending over the at least two cycles of the flow within the subject that shift the Fourier spectrum of velocity waveforms corresponding to the FE data; and (iii) using the directional FE datasets, generating an image of the subject showing flow within the subject caused by the at least two cycles of flow within the subject.

2. The method of claim 1 wherein the flow includes vascular flow and the at least two cycles include cardiac cycles.

3. The method of claim 2 wherein step (i) further includes: acquiring the FE data that is encoded along a first direction (FE.sub.1 data), wherein phase for the acquired FE.sub.1 signal ϕ.sub.1(t) is ϕ.sub.0(t)+ϕ.sub.v,1(t) for odd cardiac phases and ϕ.sub.0(t)−ϕ.sub.v,1(t) for even cardiac phases, and wherein ϕ.sub.0(t) is a waveform for flow compensated (FC) background phase signal and ϕ.sub.v,1(t) is a phase signal along the first direction; and acquiring FE data that is encoded over a second direction (FE.sub.2 data) and a third direction (FE.sub.3 data) during each repetition time (TR), wherein phase of combined FE.sub.2 and FE.sub.3 data, ϕ.sub.32(t), is ϕ.sub.0(t)+ϕ.sub.v,3(t)+ϕ.sub.v,2(t) for odd cardiac phases and is ϕ.sub.0(t)+ϕ.sub.v,3 (t)−ϕ.sub.v,2(t) for even cardiac phases, wherein ϕ.sub.v,2 (t) is a phase signal along the second direction and ϕ.sub.v,3 (t) is a phase signal along the third direction.

4. The method of claim 3 wherein step (ii) includes: filtering the acquired FE.sub.1 data to produce a background phase ϕ.sub.0(t) and the first phase signal ϕ.sub.v,1(t); subtracting the FC background phase signal ϕ.sub.0(t) from the phase signal along the second direction ϕ.sub.v,2 (t) and the phase signal along the third direction ϕ.sub.v,3 (t); separating the second direction ϕ.sub.v,2 (t) and the phase signal along the third direction ϕ.sub.v,3 (t).

5. The method of claim 1 wherein step (ii) includes retrospectively determining temporal filter bandwidth for each direction for a given voxel using composite spectra of the PE data for the given voxel.

6. The method of claim 1 wherein the accelerated imaging technique includes at least one of a parallel imaging, non-Cartesian sampling trajectories, sequence gradient optimization techniques, or a compressed sensing technique.

7. The method of claim 1 wherein the Fermi filter includes a plurality of filters with different pass bandwidths or shapes for different voxels.

8. A magnetic resonance imaging (MRI) system comprising: a magnet system configured to generate a polarizing magnetic field about at least a portion of a subject arranged in the MRI system; a plurality of gradient coils configured to apply a gradient field to the polarizing magnetic field; a radio frequency (RF) system configured to apply an excitation field to the subject and acquire MR image data therefrom; a computer system programmed to: control the plurality of gradient coils and RF system to acquire flow encoded (FE) data with alternating encoding polarities and along two of three orthogonal directions through the subject over at least two cycles of physiological flow within the subject; separate the FE data into directional FE datasets using a temporal filter that separates the FE data based on temporal modulation of the FE directions caused by the alternating encoding polarities extending over the at least two cycles of the flow within the subject that shift the Fourier spectrum of velocity waveforms corresponding to the FE data; and using the directional FE datasets, generate an image of the subject showing flow within the subject caused by the at least two cycles of flow within the subject.

9. A method for acquiring flow encoded data from a subject using a magnetic resonance imaging (MRI) system to reconstruct an image of the subject illustrating flow within the subject, the method includes steps comprising: (i) using the MRI system, acquiring flow encoded (FE) data with alternating encoding polarities and along at least one direction through the subject; (ii) determining a velocity of the flow within the subject in the at least one direction by analyzing a Fourier spectrum of the FE data to determine temporal modulation caused by the alternating encoding polarities that shift the Fourier spectrum; and (iii) using the FE data and the velocity of flow determined in step (ii), generating an image of the subject showing the velocity of flow within the subject.

10. The method of claim 9 wherein step (ii) includes retrospectively determining temporal filter bandwidth for the at least one direction for a given voxel using composite spectra of the PE data for the given voxel.

11. The method of claim 10 wherein the temporal filter includes a Fermi filter.

12. The method of claim 9 wherein step (i) is performed using an accelerated imaging technique that includes at least one of a parallel imaging, non-Cartesian sampling trajectories, sequence gradient optimization techniques or a compressed sensing technique.

13. The method of claim 9 where step (i) wherein acquiring the FE data includes a 4-point acquisition to acquire data across multiple directions.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0020] FIG. 1 is a block diagram of an MRI system for use with the present disclosure.

[0021] FIG. 2 is a schematic representation of a transceiver system for use with the MRI system of FIG. 1.

[0022] FIG. 3A is a flow chart of some examples of steps of a PC MRI imaging process.

[0023] FIG. 3B is an example of one flow contrast pulse sequence that extends over one cardiac phase.

[0024] FIG. 4 is an example of one pulse sequence diagram of an imaging process in accordance with the present disclosure, showing only FC (three gradients) and ±FE gradients (bipolar gradients). For each cardiac phase, a traditional PC MRI pulse sequence requires four samples while, as illustrated in FIG. 4, the present disclosure the requisite data is acquired with two samples.

[0025] FIG. 5 is a schematic diagram of a data acquisition and processing technique in accordance with the present disclosure.

[0026] FIG. 6 is a flow chart setting forth some examples of steps of a process implementing some of the techniques described with respect to FIG. 5.

[0027] FIG. 7A is a graph showing 3D mean flow velocity comparison between reference FC/3FE data and the HOTSPA data.

[0028] FIG. 7B is a graph showing a magnitude mean flow velocity comparison between the reference FC/3FE data and the HOTSPA data.

[0029] FIG. 7C is a graph showing a 3D peak velocity comparison between reference FC/3FE data and the HOTSPA data.

[0030] FIG. 7D is a graph showing a magnitude peak velocity comparison between the reference FC/3FE data and the HOTSPA data.

[0031] FIG. 7E is a graph showing a total volumetric flow comparison between the reference FC/3FE data and the HOTSPA data.

[0032] FIG. 7F is a graph showing a maximum magnitude peak velocity comparison between the reference FC/3FE data and the HOTSPA data.

[0033] FIG. 8A is a graph showing an example of comparisons of z-directional peak velocity waveforms reconstructed by simulated HOTSPA and SVE with different temporal resolution when the temporal resolution is 25 ms.

[0034] FIG. 8B is a graph showing an example of comparisons of z-directional peak velocity waveforms reconstructed by simulated HOTSPA and SVE with different temporal resolution when the temporal resolution is 50 ms.

[0035] FIG. 9A is a graph showing through-plane mean flow velocity waveforms comparing the techniques of the present disclosure to traditional PC MRI techniques.

[0036] FIG. 9B is a graph showing magnitude peak velocity waveforms comparing the techniques of the present disclosure to traditional PC MRI techniques.

[0037] FIG. 9C is a graph showing Bland-Altman plot of total volumetric flow measurements comparing the techniques of the present disclosure to traditional PC MRI techniques.

[0038] FIG. 9D is a graph showing Bland-Altman plot of maximum magnitude peak velocity measurements comparing the techniques of the present disclosure to traditional PC MRI techniques.

[0039] FIG. 10A is a graph showing through-plane mean flow velocity waveforms and magnitude peak velocity waveforms.

[0040] FIG. 10B is a graph showing through-plane mean flow velocity waveforms of one selected slice from the 4 VPS FC/3FE with 98.08 ms temporal resolution, and HOTSPA with 51.36 ms temporal resolution.

[0041] FIG. 10C is a graph showing Bland-Altman plots of total volumetric flow measurements based on data acquired using 4D FC/3FE and 4D HOTSPA.

DETAILED DESCRIPTION

[0042] Referring particularly to FIG. 1, an example of a magnetic resonance imaging (MRI) system 100 is illustrated. The MRI system 100 includes a workstation 102 having a display 104 and a keyboard 106. The workstation 102 includes a processor 108 that is commercially available to run a commercially-available operating system. The workstation 102 provides the operator interface that enables scan prescriptions to be entered into the MRI system 100. The workstation 102 is coupled to four servers: a pulse sequence server 110; a data acquisition server 112; a data processing server 114; and a data store server 116. The workstation 102 and each server 110, 112, 114, and 116 are connected to communicate with each other.

[0043] The pulse sequence server 110 functions in response to instructions downloaded from the workstation 102 to operate a gradient system 118 and a radiofrequency (RF) system 120. Gradient waveforms necessary to perform the prescribed scan are produced and applied to the gradient system 118, which excites gradient coils in an assembly 122 to produce the magnetic field gradients G.sub.x, G.sub.y, and G.sub.z used for position encoding MR signals. The gradient coil assembly 122 forms part of a magnet assembly 124 that includes a polarizing magnet 126 and a whole-body RF coil 128 (or a head (and neck) RF coil for brain imaging).

[0044] RF excitation waveforms are applied to the RF coil 128, or a separate local coil, such as a head coil, by the RF system 120 to perform the prescribed magnetic resonance pulse sequence. Responsive MR signals detected by the RF coil 128, or a separate local coil, are received by the RF system 120, amplified, demodulated, filtered, and digitized under direction of commands produced by the pulse sequence server 110. The RF system 120 includes an RF transmitter for producing a wide variety of RF pulses used in MR pulse sequences. The RF transmitter is responsive to the scan prescription and direction from the pulse sequence server 110 to produce RF pulses of the desired frequency, phase, and pulse amplitude waveform. The generated RF pulses may be applied to the whole body RF coil 128 or to one or more local coils or coil arrays.

[0045] The RF system 120 also includes one or more RF receiver channels. Each RF receiver channel includes an RF preamplifier that amplifies the MR signal received by the coil 128 to which it is connected, and a detector that detects and digitizes the quadrature components of the received MR signal. The magnitude of the received MR signal may thus be determined at any sampled point by the square root of the sum of the squares of the I and Q components:

M=√{square root over (I.sup.2+Q.sup.2)}  (1);

[0046] and the phase of the received MR signal may also be determined:

[00001]$\begin{array}{cc}\varphi ={\tan }^{-1}\left(\frac{Q}{I}\right).& \left(2\right)\end{array}$

[0047] The pulse sequence server 110 also optionally receives patient data from a physiological acquisition controller 130. The controller 130 receives signals from a number of different sensors connected to the patient, such as electrocardiograph (ECG) signals from electrodes, or respiratory signals from a bellows or other respiratory monitoring device. Such signals are typically used by the pulse sequence server 110 to synchronize, or “gate,” the performance of the scan with the subject's heart beat or respiration.

[0048] The pulse sequence server 110 also connects to a scan room interface circuit 132 that receives signals from various sensors associated with the condition of the patient and the magnet system. It is also through the scan room interface circuit 132 that a patient positioning system 134 receives commands to move the patient to desired positions during the scan.

[0049] The digitized MR signal samples produced by the RF system 120 are received by the data acquisition server 112. The data acquisition server 112 operates in response to instructions downloaded from the workstation 102 to receive the real-time MR data and provide buffer storage, such that no data is lost by data overrun. In some scans, the data acquisition server 112 does little more than pass the acquired MR data to the data processor server 114. However, in scans that require information derived from acquired MR data to control the further performance of the scan, the data acquisition server 112 is programmed to produce such information and convey it to the pulse sequence server 110. For example, during prescans, MR data is acquired and used to calibrate the pulse sequence performed by the pulse sequence server 110. Also, navigator signals may be acquired during a scan and used to adjust the operating parameters of the RF system 120 or the gradient system 118, or to control the view order in which k-space is sampled. In all these examples, the data acquisition server 112 acquires MR data and processes it in real-time to produce information that is used to control the scan.

[0050] The data processing server 114 receives MR data from the data acquisition server 112 and processes it in accordance with instructions downloaded from the workstation 102. Such processing may include, for example: Fourier transformation of raw k-space MR data to produce two or three-dimensional images; the application of filters to a reconstructed image; the performance of a backprojection image reconstruction of acquired MR data; the generation of functional MR images; and the calculation of motion or flow images.

[0051] Images reconstructed by the data processing server 114 are conveyed back to the workstation 102 where they are stored. Real-time images are stored in a data base memory cache (not shown), from which they may be output to operator display 112 or a display 136 that is located near the magnet assembly 124 for use by attending physicians. Batch mode images or selected real time images are stored in a host database on disc storage 138. When such images have been reconstructed and transferred to storage, the data processing server 114 notifies the data store server 116 on the workstation 102. The workstation 102 may be used by an operator to archive the images, produce films, or send the images via a network or communication system 140 to other facilities that may include other networked workstations 142.

[0052] The communications system 140 and networked workstation 142 may represent any of the variety of local and remote computer systems that may be included within a given clinical or research facility including the system 100 or other, remote location that can communicate with the system 100. In this regard, the networked workstation 142 may be functionally and capably similar or equivalent to the operator workstation 102, despite being located remotely and communicating over the communication system 140. As such, the networked workstation 142 may have a display 144 and a keyboard 146. The networked workstation 142 includes a processor 148 that is commercially available to run a commercially-available operating system. The networked workstation 142 may be able to provide the operator interface that enables scan prescriptions to be entered into the MRI system 100.

[0053] As shown in FIG. 1, the RF system 26 may be connected to the whole body RF coil 34, or as shown in FIG. 2, a transmitter section of the RF system 26 may connect to one RF coil 151A and its receiver section may connect to a separate RF receive coil 151B. Often, the transmitter section is connected to the whole body RF coil 34 and each receiver section is connected to a separate local coil 151B.

[0054] Referring particularly to FIG. 2, the RF system 26 includes a transmitter that produces a prescribed RF excitation field. The base, or carrier, frequency of this RF excitation field is produced under control of a frequency synthesizer 200 that receives a set of digital signals from the pulse sequence server 18. These digital signals indicate the frequency and phase of the RF carrier signal produced at an output 201. The RF carrier is applied to a modulator and up converter 202 where its amplitude is modulated in response to a signal R(t) also received from the pulse sequence server 18. The signal R(t) defines the envelope of the RF excitation pulse to be produced and is produced by sequentially reading out a series of stored digital values. These stored digital values may, be changed to enable any desired RF pulse envelope to be produced.

[0055] The magnitude of the RF excitation pulse produced at output 205 is attenuated by an exciter attenuator circuit 206 that receives a digital command from the pulse sequence server 18. The attenuated RF excitation pulses are applied to the power amplifier 151 that drives the RF coil 151A.

[0056] Referring still to FIG. 2, the signal produced by the subject is received by the receiver coil 152B and applied through a preamplifier 153 to the input of a receiver attenuator 207. The receiver attenuator 207 further amplifies the signal by an amount determined by a digital attenuation signal received from the pulse sequence server 18. The received signal is at or around the Larmor frequency, and this high frequency signal is down converted in a two-step process by a down converter 208 that first mixes the NMR signal with the carrier signal on line 201 and then mixes the resulting difference signal with a reference signal on line 204. The down converted NMR signal is applied to the input of an analog-to-digital (ND) converter 209 that samples and digitizes the analog signal and applies it to a digital detector and signal processor 210 to produce the I values and Q values corresponding to the received signal. As described above, the resulting stream of digitized I and Q values of the received signal are output to the data acquisition server 20 of FIG. 1. The reference signal, as well as the sampling signal applied to the ND converter 209, is produced by a reference frequency generator 203.

[0057] Referring to FIG. 3A, a PC method 300 is generally performed using a first data acquisition is performed at process block 302. As illustrated in the associated pulse sequence diagram of FIG. 3B, 4D flow PCT MRI a pulse sequence is performed that, samples four waveforms within the cardiac cycle (i.e. the FC signal phase, and 3 FE signal phase waveforms in three orthogonal directions with adequate sampling frequency such that accurate 3D cardiac-phase-resolved velocity vectors for each voxel can be reconstructed by subtracting the FC waveform from each of the three FE waveforms). That is, a first acquisition is performed at process block 302, a second acquisition is performed at process block 304. These pulse sequences are repeated, until, at decision block 338, all data has been acquired. Thereafter, the data set formed from repetition of the first data acquisition at process block 302 and the data set formed from repetition of the second data acquisition at process block 304 is subtracted at process block 308. From this subtraction, at process block 310, the final images may be provided.

[0058] Referring to FIG. 4, and as will be further described, using a hybrid one- and two-sided FE strategy 400, a hybrid spectra (after Fourier transform in time) for each pair of the four waveforms can be efficiently encoded by modulating the temporal frequencies of these spectra.

[0059] Before turning specifically to a detailed description of particular implementations of techniques in accordance with the present disclosure, some simplified explanations will be provided, starting with a description relative to an implementation of PC MRI that relies on an FC-free, two-sided FE acquisition. Consider, for example, a conventional 2D PC-MRI acquisition, such as described above with respect to FIG. 3, that includes a single view-per-segment (VPS), where the FC and FE in the z-direction (FE.sub.z) data are acquired in an interleaved fashion. In this acquisition, the data for each cardiac phase is acquired within two repetition times (TRs).

[0060] Then consider a two-sided FE strategy where only FE.sub.z data is sampled, but the polarity of the FE.sub.z M1 is alternated between successive cardiac phases. Such a 2D PC-MRI acquisition strategy is the same as the SVE technique described above. The phase for the acquired FE.sub.z signal, ϕ.sub.z(t), is therefore ϕ.sub.0(t)+ϕ.sub.v,z(t) for odd cardiac phases and ϕ.sub.0(t)−ϕ.sub.v,z(t) for even cardiac phases, where ϕ.sub.0(t) is the waveform for the FC background phase and ϕ.sub.v,z(t) is the signal phase associated with the z component of the blood velocity. If one performs a Fourier transform of ϕ.sub.z(t) in the time direction, there will be two separate spectra: the spectrum for ϕ.sub.0(t) will occupy the lower frequency region, whereas the spectrum of ϕ.sub.v,z(t) will be shifted by half of the spectral support due to the alternating 0°-180° phase modulations of the ϕ.sub.v,z(t) waveform. The FC background phase generally does not change quickly in time; therefore, the spectrum for ϕ.sub.0(t) will have narrower bandwidth compared to ϕ.sub.v,z(t).

[0061] Referring to FIG. 5 this is illustrated in a first acquisition 500. In this acquisition the FC phase 502 is constant and the FC-Free Two-Sided FE (FE.sub.z) alternates 504 during the cardiac cycle, which corresponds to a delta function banded by positive and negative velocity waveform 504a and 504b.

[0062] Applying a Fourier transform (506) yields a DC component corresponding to the constant FC 508 and separated FT signals 510 at Nyquist area. Due to the shifted spectrum, a filter 512 can be applied to separate the two spectra 514, 516 and recover ϕ.sub.0(t) and ϕ.sub.v,z(t) after inverse Fourier transforms 518. That is, the FT 506 of data acquired from the paired FC-free two-sided FE velocity waveform separates the velocity spectrum FT(V.sub.z) at Nyquist area and FC at low frequency region. Application of a Fermi filter (512) is applied to separate the two components.

[0063] In this scenario, due to the asymmetrical spectral support needed for the FC and FE.sub.z signals, this process approximately doubles the sampling rate for FE.sub.z and allocates the majority of the spectral bandwidth for the ϕ.sub.v,z(t) signal and narrower bandwidth for the ϕ.sub.0(t) signal. This stands in contrast to conventional 2D PC-MRI, where one is forced to assign the same spectral support for both the FC and the FE.sub.z signal. It is noted that, in this case, the temporal resolution is doubled and the temporal footprint is halved for each cardiac phase compared to conventional 2D PC-MRI (1 TR vs. 2 TR's for n VPS sampling) since no FC data is acquired.

[0064] Now a hybrid, one- and two-sided FE acquisition can be described where the HOTSPA technique is used to simultaneously acquire FE data in two orthogonal directions rather than a FC/FE pair as described above. Referring again to FIG. 5, without loss of generality, the flow velocity in the X and Y directions can be encoded using n VPS 520. In conventional PC-MRI, one would acquire the FE.sub.x and FE.sub.y signal in two successive TRs and each cardiac phase would be formed from data spanning 2 TRs. Again, the FC phase 522 is constant. However, in accordance with the present disclosure and the HOTSPA technique, both FE.sub.x and FE.sub.y are simultaneously acquired in each TR 524. More particularly, the hybrid one- and two-sided FE acquisition is shown by dash line 525, the outlines of FC+V.sub.x±V.sub.y are shown in dash lines 526a and 526b, and the true flow waveforms of V.sub.x and V.sub.y are shown by lines 527a and 527b. Since velocity V.sub.x/y/z is proportional to the phase difference ϕ.sub.v,x/y/z, these can be treated in the above-described scheme of the HOTSPA technique as being the same. However, showing V.sub.x/y/z provides a more clear physics meanings than showing ϕ.sub.v,x/y/z.

[0065] The FT of data acquired using the hybrid one- and two-sided FE technique yields the spectrum of two-sided velocity encoding (i.e. V.sub.y) that is separated from the DC component FE.sub.x(=FC+V.sub.x). As shown, the flow encoding polarity is alternated between two successive cardiac phases for one direction (in this example the Y direction only), such that the signal phase ϕ.sub.xy(t) is ϕ.sub.0(t)+ϕ.sub.v,x(t)+ϕ.sub.v,y(t) for odd cardiac phases and is ϕ.sub.0(t)+ϕ.sub.v,x(t)−ϕ.sub.v,y(t) for even cardiac phases. To achieve this, it is recognized that such an encoding may be conceptualized as 45 degree rotation of the FE axes; however, the sampling rate is doubled since each TR is now considered a separate cardiac phase. Similar to the above-described FC-free, two-sided FE case, a Fourier transform 528 of the ϕ.sub.xy(t) waveform produces three distinct spectra, one for ϕ.sub.0(t) 529, one for ϕ.sub.v,x(t) 530, and one for ϕ.sub.v,y(t) 532. The spectra of ϕ.sub.0(t) 529 and ϕ.sub.v,x(t) 530 overlap as both are at the low temporal frequency region, whereas the spectrum of ϕ.sub.v,y(t) 532 is shifted by half the spectral support due to the alternating phase of the sampling function for the ϕ.sub.v,y(t) signal. Again, using the shifted spectrum, a filter 534 can be applied to separate the two spectra 536, 538 and recover ϕ.sub.0(t) and ϕ.sub.v,z(t) after inverse Fourier transforms 540. For example, a Fermi filter can be applied to separate the spectra of two in-plane velocities. Thus, as illustrated in FIG. 5, from top to bottom, four separated velocity waveforms 514, 516, 536, 538 are provided after filtering and inverse Fourier transform (FT.sup.−1). Thus, with these four waveforms, any PC weighted images can be provided.

[0066] This acquisition strategy can be extended to provide a HOTSPA 4D flow technique 542, which utilizes both the above-described FC-free, two-sided FE strategy 500 and the hybrid one- and two-sided FE strategy 520, as further illustrated in FIG. 4. Specifically, for a VPS=1 case, each cardiac phase contains data from two TRs, one for FE.sub.z using the FC-free, two-sided FE strategy 500, and one for FE in the X and Y directions, using the hybrid one- and two-sided FE strategy 520. The flow encoding polarity is alternated for the Z and Y directions during two successive cardiac phases. It is noted that the XYZ directions can be rotated to any arbitrary set of orthogonal basis in the 3D M1 space. As described, from the data acquired using the FC-free, two-sided FE strategy 500, the background phase ϕ.sub.0(t) and the Z velocity ϕ.sub.v,z(t) can be separated using a filter. The ϕ.sub.0(t) spectrum can subsequently be subtracted 544 from the spectrum from the hybrid one- and two-sided FE strategy 520 and a filter can be finally applied in the resulting spectrum to separate the ϕ.sub.v,x(t) and the ϕ.sub.v,y(t) data. The subtraction between FC and FE.sub.x gives the velocity waveform in x-direction.

[0067] Thus, the above-described approaches can be applied to four-point balanced PC-MRI sampling (i.e., tetrahedral M.sub.1 space sampling). Typical four-point balanced PC-MRI sequentially acquires: ϕ.sub.0+ϕ.sub.x+ϕ.sub.y+ϕ.sub.z, ϕ.sub.0−ϕ.sub.x−ϕ.sub.y+ϕ.sub.z, ϕ.sub.0−ϕ.sub.x+ϕ.sub.y−ϕ.sub.z, and ϕ.sub.0+ϕ.sub.x+ϕ.sub.y−ϕ.sub.z. However, the above-described systems and methods can be used to apply HOTSPA, for example, in two stages. First, four functions are defined as: f(t)=ϕ.sub.0+ϕ.sub.y, f′(t)=ϕ.sub.0−ϕ.sub.y, g(t)=ϕ.sub.z+ϕ.sub.x, and g′(t)=ϕ.sub.z−ϕ.sub.x. Hence, the four-point balanced PC-MRI samples the following flow waveforms: f(t)+g(t), f(t)−g(t) f′(t)+g′(t), and f′(t)−g′(t).

[0068] From the f(t)+g(t) and f(t)−g(t) data, the spectra for f(t) and g(t) can be separated using HOTSPA temporal filtering. From the f′(t)+g′(t), and f′(t)−g′(t) data, the spectra for f′(t) and g′(t) can be separated using HOTSPA temporal filtering. After solving for all four velocity waveforms, two additional HOTSPA temporal filterings can be applied. First, an alternating pattern of f(t)=ϕ.sub.0+ϕ.sub.y and f′(t)=ϕ.sub.0−ϕ.sub.y can be applied to separate the ϕ.sub.0 and ϕ.sub.y spectra. Second, a filter for the alternating pattern of g(t)=ϕ.sub.z+ϕ.sub.x and g′(t)=ϕ.sub.z−ϕ.sub.x can be applied to separate the ϕ.sub.z and ϕ.sub.x spectra. In the four-point balanced PC-MRI case, all of the aforementioned benefits of HOTSPA apply.

[0069] In one non-limiting example, the filter may be a Fermi filter that is centered at peak of each spectrum as described by:

[00002]$\begin{array}{cc}F\left(f\right)=\frac{1}{1+\exp \left(\frac{f-f_0}{C}\right)}.& \left(3\right)\end{array}$

[0070] In Eqn. (3), the constant C controls the shape of the Fermi filter and C can be empirically chosen, for example, as C=0.22. Also in Eqn. (3), f represents temporal frequency, and f.sub.0 is the frequency corresponding to the full-with-half-maximum (FWHM) of the Fermi filter. In this non-limiting example, f.sub.0 was the frequency component with 10% of the maximum amplitude for the spectrum to be filtered or 25% of the spectral support, whichever results in a larger FWHM.

[0071] Referring to FIG. 6, one non-limiting example of a process implementing the above-described FC-free, two-sided FE strategy 500 and the hybrid one- and two-sided FE strategy 520 to form the HOTSPA 4D flow technique 542 is provided. Specifically, the above-described FC-free, two-sided FE strategy 500 is performed at process block 602, as is the hybrid one- and two-sided FE strategy 520 performed at process block 604 until all data is determined at decision block 606 to have been acquired.

[0072] At process block 608, the data sets are separately processed, as described with respect to FIG. 5. For example, as the HOTSPA PC-MRI reconstruction can be performed separately for each voxel, it is possible to apply Fermi filters with different pass bandwidth and/or shapes for different voxels. For example, for voxels with velocities predominately along the X direction and have negligible Y velocity, then no filter will be needed for the ϕ.sub.xy(t) spectrum. This is because the ϕ.sub.vy(t) would be negligible and the entire spectral support, which is twice as wide as conventional 4D flow, and can be retrospectively allocated for ϕ.sub.vx(t), doubling the temporal resolution for these voxels. The same benefit is achievable for voxels with predominately Y velocity with negligible X velocity. For voxels with comparable X and Y velocity components, both in magnitude and temporal spectral bandwidth, a filter with a pass bandwidth equal to half of the spectral support can be applied to separate the ϕ.sub.vx(t) and ϕ.sub.vy(t) spectra, and in this scenario, the hybrid one- and two-sided FE data does not provide a benefit compared to conventional PC-MRI. Regardless of the flow direction, the FC-free two-sided FE data is can be acquired with a 25% gain in the overall 4D flow MRI acquisition speed compared to traditional PC MRI acquisitions.

[0073] Thereafter, at process block 610, the data sets are subtracted and, at process block 612, the desired velocity/flow encoded images, such as angiographic images, are provided or displayed.

Example

[0074] An example study was performed on a 3T scanner with a 4-channel neck (in vivo studies) coil. As used in this study, “mean flow velocity” means the average velocity within the entire blood vessel lumen. Also, “peak velocity” means the maximum velocity within the entire blood vessel. Further, “magnitude velocity” means the square root of sum of squares of 3D velocities (=√{square root over (V.sub.x.sup.2+V.sub.y.sup.2+v.sub.z.sup.2)}). The magnitude mean flow velocity can be used to indicate the average magnitude velocity within the entire blood vessel lumen, and magnitude peak velocity can be used to indicate the maximum magnitude velocity within the entire blood vessel lumen. Finally, “maximum velocity” means the maximum velocity within the entire cardiac cycle. This often happens in the peak systolic cardiac phases.

Retrospective In Vivo Study (2D)

[0075] The commons carotid arteries (CCAs) of six volunteers were scanned using a 2D PC-MRI sequence with 3 FE directions (FC/3FE). The sequence parameters included: VENC=100-110 cm/s, flip angle=20°, readout bandwidth=500 Hz/Pixel, TE=3.92 ms, TR=6.28 ms, Views-per-segment=1, acquired matrix=256×176, FOV=200×176 mm.sup.2, and slice thickness=7 mm. The imaging plane of each data set was at approximate 50° (instead of 90°) angle to the longitudinal axis of the CCAs so that the flow velocity has significant components in more than one direction. All scans were acquired during free breathing with prospective ECG gating and the 3D flow velocity waveforms were calculated for each pixel using conventional phase-contrast MRI reconstruction. Based on these ground truth velocity waveforms, we simulated a HOTSPA dataset and calculated what ϕ.sub.z(t) and ϕ.sub.xy (t) would have been for each cardiac phase if the HOTSPA acquisition strategy was employed. The quantitative flow and velocities calculated based on the simulated HOTSPA dataset were subsequently compared with the reference 2D FC/3FE PC-MRI results.

[0076] To demonstrate the benefits of HOTSPA over the previously-described SVE technique, one volunteer's two-sided z-directional FE data was used to independently perform the HOTSPA and the SVE velocity calculation, and the maximum peak velocity measurement accuracy of HOTSPA and SVE was compared at two different temporal resolutions (25.12 ms by using all cardiac phase of the simulated two-sided FEz data and 50.24 ms using only odd cardiac phases of the two-sided FE.sub.z data).

Prospective In Vivo Study

[0077] The HOTSPA acquisition strategy was implemented for a 3T MRI system. Six volunteers were scanned at the CCAs using the 2D FC/3FE PC-MRI sequence and our prospective 2D HOTSPA sequence. Both sequences were implemented with: VENC=100-110 cm/s, flip angle=20°, readout bandwidth=500 Hz/Pixel, TE=3.92 ms, TR=6.28 ms, VPS=1 and 2 for FC/3FE, and 2 only for HOTSPA, acquired matrix=256×176, FOV=200×176 mm.sup.2, and slice thickness=7 mm. Imaging plane of each data set was at approximate 50° angle to the longitudinal axis of the CCAs.

[0078] After the 2D study, six additional adult volunteers were scanned at the CCAs using the conventional 4D flow sequence and our 4D HOTSPA sequence with the following parameters: VENC=100-110 cm/s, flip angle=20°, readout bandwidth=815 Hz/Pixel, TE=3.61-3.90 ms, TR=6.13-6.42 ms, Views-per-segment=4 for conventional 4D flow and HOTSPA, acquired matrix=256×176×8, FOV=200×176×20 mm.sup.2. All 2D/4D in vivo scans in this study were acquired during free breathing with prospective ECG gating. For each data set, three slices (slice 2, 4, 6 along z-direction) were selected to compare total volumetric flow measurements and maximum magnitude peak velocity measurements.

Results

Retrospective In Vivo Study

[0079] Referring to FIG. 3A, a comparison of 3D mean flow velocities is provided against reference FC/3FE and the simulated HOTSPA data. In FIG. 3B the magnitude mean flow velocity is shown for this study. The directional and magnitude mean flow velocities within region of interest (ROI) though cardiac cycle show excellent agreement between the reference FC/3FE and the simulated HOTSPA. The average root mean squared error (RMSE) of mean flow velocities of all six volunteer's CCAs were: 1.06 (range: 0.75-1.31) cm/s for z-direction, 0.91 (range: 0.73-1.52) cm/s for y-direction, 0.80 (range: 0.41-1.17) cm/s for x-direction, and 1.16 (range: 0.73-1.72) cm/s for magnitude.

[0080] Also, FIG. 3C shows a comparison of 3D peak velocities between the reference FC/3FE and the simulated HOTSPA and FIG. 3D shows a comparison of magnitude peak velocity between the two techniques. The peak velocity waveforms also showed good agreement between the reference 2D FC/3FE and the simulated HOTSPA data. The average RMSE of peak velocities of all six volunteer's CCAs were: 1.69 (range: 1.33-2.12) cm/s for z-direction, 1.60 (range: 1.28-2.30) cm/s for y-direction, 1.70 (range: 1.25-2.12) cm/s for x-direction, and 2.13 (range: 1.52-3.00) cm/s for magnitude.

[0081] Bland-Altman plots of total volumetric flow and maximum magnitude peak velocity measurements among the 6 volunteers between the two techniques are shown in FIGS. 3E and 3F. The bias of total volumetric flow was −0.02 mL (−0.4% relative bias error) with 95% confidential interval (CI) [−0.07, 0.03] mL. The bias of maximum magnitude peak velocity was −0.59 cm/s (−0.6% relative bias error) with 95% CI [−4.9, 3.7] cm/s. The Bland-Altman plots show that the total volumetric flow and maximum magnitude peak velocity measurements of HOTSPA and FC/3FE had good agreement.

[0082] Thus, FIGS. 7A-7F demonstrate that the above-described HOTSPA 4D flow technique, as well as the components of the HOTSPA 4D flow technique (i.e., FC-free, two-sided FE strategy and the hybrid one- and two-sided FE strategy) provide substantial advantages over traditional PC MRI techniques. Namely, the study demonstrates the ability to deliver reduced temporal resolution and temporal footprint compared to traditional PC MRI techniques, with particular gains in the context of 4D flow acquisitions.

[0083] For example, FIGS. 8A and 8B provide a comparison between HOTSPA and SVE peak velocity waveforms based on the same data from the simulated HOTSPA acquisition. At 25.12 ms temporal resolution described above with respect to FIG. 7A, both HOTSPA and SVE could provide accurate maximum peak velocity measurements compared to the reference. When the FE.sub.z data was decimated to 50.24 ms temporal resolution as described above with respect to FIG. 7B, the HOTSPA was able to provide accurate maximum peak velocity measurement with <1% relative error compared to the reference (82.5 cm/s for HOTSPA vs. 83 cm/s for the reference), while the SVE results under-estimated the maximum peak velocity by 21% (65.7 cm/s vs. 83 cm/s).

Prospective In Vivo Study

[0084] As shown in FIGS. 9A through 9D, an example of through-plane mean flow velocity waveform and magnitude peak velocity waveform within the ROI is provided comparing three different measurements: 1) the standard 2D FC/3FE with 1 VPS and 25.12 ms temporal resolution; 2) the prospective HOTSPA with 2 VPS and 25.12 ms temporal resolution; 3) the standard 2D FC/3FE with 2 VPS and 50.24 ms temporal resolution. The mean through-plane flow velocity is illustrated in FIG. 9A and the magnitude peak velocity waveforms based on the HOTSPA acquisition with 2 VPS were similar to the 2D FC/3FE with 1 VPS is shown in FIG. 9B, although the HOTSPA total acquisition time was 50% of the 1 VPS 2D FC/3FE. However, the 2 VPS 2D FC/3FE underestimated the maximum peak velocity, presumably due to its long temporal footprint and low temporal resolution. The Bland-Altman plot of total volumetric flow within the cardiac cycle measured in the six volunteers using HOTSPA and 1-VPS FC/3FE PC-MRI is shown in FIG. 9C. Using the 1 VPS FC/3FE as the reference, the bias for HOTSPA was −0.005 mL (−0.1% relative bias error) and the 95% CI was [−0.33, 0.32] mL. The Bland-Altman plot of maximum magnitude peak velocity of FIG. 9D shows that the bias was 1.207 cm/s (1.14% relative bias error) and the 95% CI was [−5.10, 7.51] cm/s. The maximum magnitude peak velocities of all 12 CCAs measurements from HOTSPA (average=105.7 cm/s, range: 90.6-130.2 cm/s) and 1 VPS 2D FC/3FE (average=104.5 cm/s, range: 86.1-123.8 cm/s) were significantly higher than the 2 VPS 2D FC/3FE measurements (average=90.6 cm/s, range: 76.7-112.4 cm/s) (P<0.05, one-side paired t-test).

[0085] Finally, FIGS. 10A and 10B show an example of through-plane mean flow velocity and magnitude peak velocity within the ROI in one slice of 4D flow data comparing two different measurements: 1) the standard 4D FC/3FE with 4 VPS and 98.08 ms temporal resolution; 2) the HOTSPA technique with 4 VPS and 51.36 ms temporal resolution. The HOTSPA showed higher maximum magnitude peak velocity compared with FC/3FE due to the shorter temporal footprint and higher temporal resolution. As shown in FIG. 10C, the bias of Bland-Altman of total volumetric flow measurements was −0.02 mL (−0.40% relative bias error compared to 4D FC/3FE) and the 95% CI was [−0.32, 0.28] mL. The maximum magnitude peak velocities from 4 VPS HOTSPA (average=98.0 cm/s, range: 73.7-125.6 cm/s) was significantly higher than the 4 VPS FC/3FE (average=83.2 cm/s, range: 60.2-109.6 cm/s) (P<0.05, one-sided paired t-test). On average, the 4 VPS FC/3FE underestimated the maximum magnitude peak velocity by 18% when compared with the 4 VPS HOTSPA.

DISCUSSION

[0086] Thus, a flexible flow encoding strategy is provided for 4D flow MRI with improved temporal resolution and temporal footprint using temporal modulation of the flow encoding waveforms. In the HOTSPA technique, the four acquisitions (FC and 3 FE directions) of conventional FC/3FE have been reduced to two acquisitions with alternating encoding polarities for two of the three orthogonal FE directions (e.g. Z & Y directions) between two successive cardiac phases. This is clinically feasible because the temporal modulation of the FE directions shifts the Fourier spectrum of the velocity waveform for the direction with alternating polarity, which enables separation of the spectra for all three FE directions using a temporal filter. The conventional PC-MRI flow calculation is typically performed separately for each cardiac phase and recent k-t acceleration methods focus on performing a temporal modulation of sampling pattern in an under-sampled k-space. The HOTSPA technique provided herein provides a temporal modulation strategy for an under-sampled M1 space. Compared to conventional PC-MRI, HOTSPA enables a 50% shorter temporal footprint for each cardiac phase, which translates to more accurate peak flow velocity measurements while maintaining the measurement accuracy of total volumetric flow. Also, HOTSPA allows more flexible temporal filter spectral bandwidth on a voxel-by-voxel basis, whereas conventional PC-MRI effectively forces each FE direction to use the same spectral bandwidth, regardless whether or not there is significant flow in that FE direction for a given voxel. Furthermore, the temporal filter bandwidth for each FE direction can be retrospectively determined using HOTSPA for a given voxel, based on the actual acquired composite spectra for that voxel. It should be noted that HOTSPA can be combined with other k-space acceleration methods, such as parallel imaging and compressed sensing, to further accelerate data acquisition. Other techniques may include non-Cartesian sampling trajectories or sequence gradient optimization techniques that may be used with the above-described systems and methods.

[0087] HOTSPA technique provides more flexible choices of temporal resolution selections. The temporal resolution and footprint of HOTSPA can be controlled, for example, to be equal to 2*TR*views-per-segment, while the conventional FC/3FE equals to 4*TR*views-per-segment. For example, 2D PC-MRI experiments show that the HOTSPA technique can provide 12.5, 25, 37.5, 50 ms temporal resolution and temporal footprint selection; however, conventional FC/3FE can only provide 25, 50 ms. With this in mind, an application that needs 40 ms temporal resolution requires one to choose 1 VPS with 25 ms temporal resolution to maintain the measurement accuracy when using conventional FC/3FE. On the other hand, the HOTSPA technique enables the use of 3 VPS with 37.5 ms temporal resolution.

[0088] The present invention has been described in terms of one or more preferred embodiments, and it should be appreciated that many equivalents, alternatives, variations, and modifications, aside from those expressly stated, are possible and within the scope of the invention.