WO2014124250A2

WO2014124250A2 - Selective spectral displacement projection magnetic resonance elastography

Info

Publication number: WO2014124250A2
Application number: PCT/US2014/015294
Authority: WO
Inventors: Temel Kaya YASAR; Dieter Klatt
Original assignee: The Board Of Trustees Of The University Of Illinois
Priority date: 2013-02-11
Filing date: 2014-02-07
Publication date: 2014-08-14
Also published as: WO2014124250A3

Abstract

The invention disclosed herein provides an example method and system for implementing Selective Spectral Displacement Projection Magnetic Resonance Elastography ("SDP-MRE"), based on simultaneous encoding and acquisition of multiple vibration frequency components using motion encoding gradients (MEG) with different MEG frequencies. A mechanical vibration having multiple vibration frequency components can be induced in an object in a magnetic resonance imaging (MRI) system, while a magnetic resonance (MR) signal is applied to the object. By applying to the object simultaneously in each of three dimensions a MEG having a different MEG frequency component in each of the three dimensions, motion of three different vibration frequency components can be simultaneously encoded into the phase of the MR signal. Three-dimensional, multi-frequency magnetic resonance elastography (MRE) data including the MR signal phase encoded with the three different vibration frequency components can be acquired simultaneously at the multiple frequencies of vibration.

Description

Selective Spectral Displacement Projection Magnetic Resonance Elastography

BACKGROUND

Magnetic resonance imaging (MRI) is commonly used to image the internal tissues of a subject. Magnetic resonance elastography (MRE) is a technique for determining mechanical properties of a subject under study by introducing mechanical vibrations in the subject undergoing MRI, encoding the displacements into the MR signal phase and analyzing the acquired mechanical wave fields.

MRI is typically performed by placing the subject or object to be imaged at or near the isocenter of a strong, uniform magnetic field, Bo, known as the main magnetic field. The main magnetic field causes the atomic nuclei (spins) that possess a magnetic moment in the matter comprising the subject or object to become aligned in the magnetic field. The spins form a magnetization that precesses around the magnetic field direction at a rate proportional to the magnetic field strength. For hydrogen nuclei (which are the common nuclei employed in MRI), the precession frequency is approximately 64 MHz in a magnetic field of 1.5 Tesla. If the magnetization is perturbed by a small radio-frequency magnetic field, known as a Βχ magnetic field, the spins emit radiation at a characteristic radio frequency (RF). The emitted RF radiation can be detected and analyzed to yield information that may be used to produce an image of the subject or object. For purposes of the discussion herein, the term "object" will be used to refer to either a subject (e.g., a person) or an object (e.g., a test object) when describing magnetic resonance imaging of that "object."

In practice, magnetic field gradients are also applied to the subject or object in addition to the main magnetic field. The field gradients are typically applied along one or more orthogonal axes, (x, y, z), the z-axis usually being aligned with the B₀, and introduce spatially-distributed variations in frequency and/or phase of the precessing nuclear spins. By applying the radio-frequency Bi magnetic field and gradient fields in carefully devised pulses and/or sequences of pulses that are switched on and off, the RF radiation emitted can carry spatially encoded information that, when detected and analyzed, can be used to produce detailed, high resolution images of the subject or object. Various techniques utilizing both specific pulse sequences and advanced image reconstruction methods have been developed, providing new advances, as well as introducing new challenges. An MRI system typically includes hardware components, including a plurality of gradient coils positioned about a bore of a magnet, an RF transceiver system, and an RF switch controlled by a pulse module to transmit RF signals to and receive RF signals from an RF coil assembly. The received RF signals are also known as magnetic resonance (MR) signal data. An MRI system also typically includes a computer programmed to cause the system to apply to an object in the system various RF signals, magnetic fields, and field gradients for inducing spin excitations and spatial encoding in an object, to acquire MR signal data from the object, to process the MR signal data, and to construct an MR image of the object from the processed MR signal data. The computer can include one or more general or special purpose processors, one or more forms of memory, and one or more hardware and/or software interfaces for interacting with and/or controling other hardward components of the MRI system.

MR signal data detected from an object are typically described in mathematical terms as "k-space" data (k-space is the 2D Fourier transform of the image). An image in actual space is produced by a Fourier transform of the k-space data. MR signal data are acquired by traversing k-space over the course of applying to the object the various RF pulses and magnetic field gradients. In practice, techniques for acquiring MR signal data from an object are closely related to techniques for applying the various RF pulses and magnetic field gradients to the object.

In MRE, external vibrations are introduced into an object, such as biologic tissue, under examination. Vibrations in the tissue (or object) are encoded in the MR signal phase using standard MRI sequences upgraded with motion encoding gradients (MEGs), and can be measured via phase-contrast based MRI. Mechanical properties of the tissue can be determined by analyzing the measured data. When just one frequency of vibration is applied to the tissue, mechanical behavior of the tissue can be identified only at that one frequency, so that possible frequency-dependence of the mechanical behavior cannot be addressed. By contrast, "multi-frequency MRE," in which multiple frequencies of vibration are applied to the tissue (or object), can be used to determine frequency-independent material parameters according to rheological models.

Applied in one spatial dimension, multi-frequency MRE has been used to study the correlation of pathophysiological changes and mechanical structure of tissue. In this approach, only out-of-plane displacements due to vibrational motion can be examined. Techniques for acquiring a three dimensional (3D) displacement field have been applied for mono-frequency MRE, and used, for example, to separate the shear wave from the compression wave.

Conventional 3D mono-frequency MRE techniques have also been extended to 3D multi-frequency MRE by application of consecutive mono-frequency experiments at different frequencies. However, the requirement of acquiring MRE data at multiple frequencies in multiple, individual monofrequency experiments have proven to be time consuming. Furthermore, breaking up the process into individual experiments can give rise to errors due to such factors as misalignment of image slices, or varying transmission of mechanical energy from different vibrational states of the tissue.

An alternative approach to successive application of 3D mono-frequency MRE could be the use of fractional motion encoding schemes in order to simultaneously measure an excited vibration spectrum for each displacement projection. This could result in only three individual experiments, for example. However, the reduced motion sensitivity of fractional motion encoding schemes cannot be compensated for by increasing the number of MEG cycles applied.

Accordingly, there is a need to reduce the number of individual, temporally-resolved MRE experiments necessary for 3D multi-frequency MRE.

SUMMARY

The invention disclosed herein provides motion encoding for 3D multi-frequency MRE using techniques for acquiring MRE data simultaneously in three different vibrational frequencies and in three spatial dimensions, thereby yielding high-quality phase imaging in less time than conventional approaches.

Example embodiments are disclosed herein for applying MEGs in an arrangement capable of encoding simultaneously in three spatial dimensions three different frequencies of vibrational motion induced simultaneously in an object under study. The technique, referred to herein as "Selective Spectral Displacement Projection Magnetic Resonance Elastography" (SDP-MRE), employs a different MEG component along each of three spatial dimensions, each of the three MEG components having a frequency matched to a different one of three frequencies of vibrational motion. The frequency matching is specified by a filter condition, and results in vibrational displacements at each of the three vibrational frequencies being encoded along a different spatial dimension of MR signal phase. Simultaneous application of three spatial components of the frequency-matched MEGs enables all three frequencies of displacement components to be acquired simultaneously. Thus 3D multi-frequency MRE acquisition using SDP-MRE is faster than in conventional 3D multi-frequency MRE, and allows all three frequencies of displacements in the different spatial dimensions to be derived from the same temporally-resolved MR phase images.

Example embodiments SDP-MRE disclosed herein provide a method and system for 3D multi-frequency MRE with three individual, temporally-resolved MRE experiments, compared with nine required in conventional 3D multi-frequency MRE. At the same time, SDP-MRE results in no reduction in motion sensitivity compared with conventional 3D multi-frequency MRE.

Furthermore, SDP-MRE can be integrated in most pulse sequences typically used in MRE, such as gradient-echo, spin-echo, and EPI.

Example embodiments herein provide a method for determining tissue mechanical properties with a MRI system, in which MEGs of different frequencies are applied simultaneously along the three spatial components of a tissue sample (or other object).

In accordance with the example embodiments, the method entails exciting a vibration spectrum composed of three frequencies.

In further accordance with the example embodiments, the MEGs are applied while also obeying filter conditions.

Also in accordance with the example embodiments, the MEGs are applied to a phantom consisting of an agarose bead embedded in agarose gel.

Hence, in one aspect, various embodiments of the present invention provide, in a magnetic resonance imaging (MRI) system, a computer-implemented method comprising: while inducing multi-frequency vibrational motion in an object in the MRI system, applying a magnetic resonance (MR) signal to the object, the MR signal having a phase; encoding into the MR signal phase simultaneously along each of three spatial dimensions a different frequency component of the induced multi-frequency vibrational motion of the object by applying to the object simultaneously in each of the three dimensions a motion encoding gradient (MEG) having a different MEG frequency component in each of the three dimensions; and acquiring simultaneously at multiple MEG frequencies multi-frequency magnetic resonance elastography (MRE) data comprising the MR signal phase encoded with the different frequency component of the induced multi-frequency vibrational motion of the object in each of the three dimensions.

In another aspect, various embodiments of the present invention provide magnetic resonance imaging (MRI) system comprising: one or more processors; memory; a main magnet; one or more gradient coils; and machine-readable instructions stored in the memory that, when executed by the one or more processors, cause the MRI system to carry out functions including: activating a mechanical actuator for inducing multi-frequency vibrational motion in an object in the MRI system, while applying a magnetic resonance (MR) signal to the object, wherein the MR signal has a phase; encoding into the MR signal phase simultaneously along each of three spatial dimensions a different frequency component of the induced multi-frequency vibrational motion of the object by applying to the object simultaneously in each of the three dimensions a motion encoding gradient (MEG) having a different MEG frequency component in each of the three dimensions; and acquiring simultaneously at multiple MEG frequencies multi-frequency magnetic resonance elastography (MRE) data comprising the MR signal phase encoded with the different frequency component of the induced multi-frequency vibrational motion of the object in each of the three dimensions.

These as well as other aspects, advantages, and alternatives will become apparent to those of ordinary skill in the art by reading the following detailed description, with reference where appropriate to the accompanying drawings. Further, it should be understood that this summary and other descriptions and figures provided herein are intended to illustrate the invention by way of example only and, as such, that numerous variations are possible.

BRIEF DESCRIPTION OF THE DRAWINGS

Figure 1 illustrates simultaneous application of three spatial components of magnetic encoding gradients for an example of eight sampling intervals, in accordance with an example embodiment.

Figure 2 shows MRE images for both conventional MRE and SDP-MRE, in accordance with an example embodiment

Figure 3 is a flowchart depicting an example embodiment of selective spectral displacement projection magnetic resonance elastography. Figure 4 illustrates an example experimental setup, in accordance with an example embodiment.

DETAILED DESCRIPTION

1. Overview

An analytical formulation of SDP-MRE can be derived by defining an index j = 1, 2, 3 to correspond to the read-, phase-, and slice-directions, respectively, in the MRI scanner system. The index j = 1, 2, 3 can also be taken to correspond to the x-, y-, and z-directions, respectively, of a Cartesian spatial coordinate system. In MRE, vibrational motion induced in an object in a MRI scanner system can be encoded in the MR signal phase φ by applying a motion encoding gradient (MEG) to the object. In accordance with example embodiments of SDP-MRE, no harmonic motion is encoded into φ if the frequency / of the harmonic motion satisfies a "filter condition" related to periodicity of the applied MEG.

More specifically, for a harmonic MEG (e.g., sinusoidal) having an MEG period z/ in the jth direction, and a MEG duration T of N_j individual MEG cycles in the jth direction, the filter condition is given by:

According to the filter condition, harmonic motion with frequencies that satisfy equation (1) will not be encoded into φ by the MEG. This holds for all harmonic frequencies, except for /= 1/TJ (i.e., n = Nj). That is, the MEG can be arranged to have a different frequency 1/z/ in each direction indexed by j, and only the harmonic vibration frequency with / = 1/z/ is encoded into φ by the MEG in the jth direction.

It may further be seen that the MEG duration T = N_jT_j is the same for all spatial projections (j = 1, 2, 3) of the MEG.

SDP-MRE exploits the filter condition by employing a multi-frequency vibration spectrum of three frequencies, each selected to match a different one of the MEG frequencies l/T_j along the jth direction. Thus, all multiples of f_b are filtered out except for 1/z/. The filter condition ensures that of the three components of vibrational motion, only the one component with a frequency that matches the MEG frequency in a given direction contributes to φ in the given direction. The resulting MR phase φ can thus be represented by a sum of phase components each corresponding to a distinct spatial projection and vibration frequency. A Fourier transform of the 0(5), where s is the start time of the MEG, can be calculated in order to determine the frequency components, which may then be scaled to displacements.

As part of an illustrative demonstration, SDP-MRE was applied in example trial runs to a "phantom" (e.g., test object) made up of an agarose bead (0.7%) embedded in agarose gel (1.1%) in a MRI scanner system. A sample bin (9 mm) was positioned inside a 10 mm birdcage RF coil and was driven by a piezostack actuator attached to an inertial ground mass. A gradient-echo sequence upgraded with motion encoding gradients was used for data acquisition in an axial slice with the following sequence parameters: repetition time for pulse sequences TR = 500 ms; echo time TE = 7.94 ms; flip angle = 30°; FOV = 10x10 mm²; matrix size = 128²; slice thickness = 0.25 mm; MEG amplitude = 80 G/cm.

For the trial runs, the MR excitation signal was a superposition of 5 kHz, 6 kHz, and 7 kHz sinusoidal waveforms and the number of MEG cycles was 15, 18, and 21, respectively. More specifically, l/z/ = 5 kHz, 6 kHz, and 7 kHz in the read-, phase-, and slice-directions (j = l, 2, 3) respectively, while N_j = 15, 18, and 21 in the respective directions. These example values correspond to a MEG duration T = 0.003 seconds = 3 milliseconds (ms) for all three directions. As specified by the filter condition of SDP-MRE, the mechanical vibration was made up of a superposition of a 5 kHz sinusoidal vibration component, a 6 kHz sinusoidal vibration component, and a 7 kHz sinusoidal vibration component.

Figure 1 is a schematic illustration of SDP-MRE during one repetition time TR applied with example parameters of trial runs. At the top of the Figure, a multi-frequency mechanical vibration 102 is applied at an initial trigger of the MR excitation signal. In the trial runs, the trigger was shifted 16 times in order to acquire 0(s) as a function of start time s of the MEG, and a delay was included to wait for the vibration in the phantom to reach a steady state. Below the vibration 102 in Figure 1, the slice-direction MEG 104, the phase- direction MEG 106, and the read-direction MEG 108 are illustrated.

MRE data acquired in the trial runs were analyzed by calculating the Fourier transform of 0(s) to decompose the frequency components. The respective components were then scaled to displacements. A 2-dimensional (2D) local frequency estimation (LFE) algorithm was applied to the derived images and the resulting wavelength was spatially averaged over the bead of the phantom. For purposes of comparison of SDP-MRE and conventional MRE, the same experiment was repeated three times, but this time with only one of the three MEGs shown in Figure 1 applied in each of the repetitive experiments.

Results obtained from the trial runs are shown in Figure 2, and serve to illustrate applicability of SDP-MRE by way of example. Specifically, Figure 2 displays complex wave images 200 acquired with SDP-MRE and with conventional MRE. The agarose bead inside the agarose gel is demarcated with dashed lines. The three images in the top row correspond to conventional MRE experiments conducted in individual, consecutive steps. Images in the bottom row were acquired simultaneously in accordance with SDP-MRE. The motion encoding directions for the 5 kHz, 6 kHz and 7 kHz-vibration were read, phase and slice, respectively, and are displayed in three columns, as indicated.

In the Figure, the wavelength λ varies from column to column, as both the vibration frequency and the displacement projection changes. Similarly, different wave amplitudes in different projections were also observed using the same method. There is a less pronounced difference in wave amplitude visible in the same projection measured with each of the two methods, but no systematic variation is evident.

As is evident from Figure 2, similar wave structures for same projections were observed for both conventional MRE and SDP-MRE. Consequently, the LFE-derived wavelengths are identical within the error margins. For the trials described, the spatial average of λ over the agarose bead results in (0.7±0.1) mm, (0.5±0.1) mm and (0.4±0.1) mm for the 5 kHz-, 6 kHz- and 7 kHz-vibration, respectively, for both conventional MRE and SDP-MRE. However, SDP-MRE achieved the results with three MRE experiments, compared with nine for conventional MRE. In addition, all three vibrational frequency components of the SDP-MRE data were acquired simultaneously, and therefore aligned in both space and time.

2. Example Method

Embodiments disclosed herein by way of example of SDP-MRE provide example techniques applicable in an MRI system that includes capabilities for applying motion encoding gradients (MEGs), and further includes a mechanism for inducing one or more forms of mechanical viabrations in an object under study in the MRI system. As described above, an MRI system typically comprises hardware components including one or more gradient coils positioned about a bore of a magnet, an RF transceiver system, and an RF switch controlled by a pulse module to transmit RF signals to and receive RF signals from an RF coil assembly. The received RF signals are also known as magnetic resonance (MR) signal data. An MRI system also typically includes one or more computers programmed to cause the system to apply to an object in the system various RF signals, magnetic fields, and field gradients for inducing spin excitations and spatial encoding in an object, to acquire MR signal data from the object, to process the MR signal data, and to construct an MR image of the object from the processed MR signal data. The one or more computers can include one or more general or special purpose processors, one or more forms of memory, and one or more hardware and/or software interfaces for interacting with and/or controling other hardware components of the MRI system.

In an example embodiment, acquisition of MRE data simultaneously in vibrational frequency components and in three dimensions (3D) in accordance with SDP-MRE can be accomplished by way of a computer-implemented method configured for execution by the MRI computer. The steps of the method can augment and/or enhance conventional MRE operation in order to achieve the advantages of SDP-MRE. Figure 3 is a flowchart illustrating an example method of SDP-MRE applied to an object in an MRI system.

At step 302, the MRI system applies a MR signal to the object in the MRI system while multi-frequency vibrational motion is induced in the object. The MR signal may be characterized by one or more properties, including a phase, referred to herein as the "MR signal phase." More particularly, inducing the multi-frequency vibrational motion in the object in the MRI system could entail inducing a mechanical vibration having at least three different, concurrent frequency components. Multi-frequency mechanical vibrations induced in the object may manifest as vibrations of the material of the object, and can be described analytically as time-dependent (e.g., multiple periods) physical displacements of the material in one or more spatial dimensions. An example mechanism for introducing mechanical vibrations in the object while it is subject to the MR signal is described below.

At step 304, the MR signal phase is encoded simultaneously along each of three spatial dimensions with a different frequency component of the induced multi-frequency vibrational motion of the object. In particular, the encoding is achieved by applying to the object simultaneously in each of the three dimensions a motion encoding gradient (MEG) having a different MEG frequency component in each of the three dimensions. Encoding the MR signal phase with vibrational motion yields a signal that carries time-dependent displacement information, which can be recovered and analyzed to determine mechanical properties of the material of the object. The motion-encoded MR signal phase is referred to herein as a "magnetic resonance elastography" (MRE) signal, and forms a basic element of what is referred to herein as MRE data. In accordance with example embodiments, the MRE signal is generated simultaneously in three spatial dimensions and for multiple frequency components of vibration.

Finally, at step 306, multi-frequency MRE data are acquired simultaneously at multiple MEG frequencies. In accordance with example embodiments, the multi-frequency MRE data correspond to the MR signal phase encoded with the different frequency component of the induced multi-frequency vibrational motion of the object in each of the three dimensions.

In accordance with example embodiments, the three spatial dimensions can be taken as corresponding to spatial dimensions x, y, and z of a Cartesian coordinate system. In addition, the three spatial dimensions can also be taken as corresponding to read-, phase-, and slice-directions of the MRI system.

Also in accordance with example embodiments, the induced multi-frequency vibrational motion could be a superposition of three vibration components. Namely, a first vibration component having a frequency f_\, a second vibration component having a frequencyi, and a third vibration component having a frequency _?. Then, in further accordance with example embodiments, the MEG frequency component in each of the three dimensions could have a frequency selected to equal a different one of f_\, fi, or f₃, based on an analytic filter condition that specifies phase encoding of a different one of the three vibration components in each of the three dimensions.

With the three frequency components of vibration described by f_\, fi, and fi, the simultaneous encoding of step 304 could entail simultaneously applying a first MEG of MEG frequency equal to f_\ along a first of the three dimensions, a second MEG of MEG frequency equal tof₂ along a second of the three dimensions, and a third MEG of MEG frequency equal tofi along a third of the three dimensions.

In accordance with example embodiments, inducing the multi-frequency vibrational motion in the object in the MRI system could entail inducing mechanical vibrations of different frequencies. In particular, inducing the multi-frequency vibrational motion could entail inducing a superposition of all three of a first harmonic waveform of frequency fi\, a second harmonic waveform of frequency^, and a third harmonic waveform of frequency fi. In further accordance with example embodiments, /!, ^, and f could all be different, but all three sharing a common divisor with no remainder.

In further accordance with example embodiments, and with f, f, and f being different harmonic frequencies, the simultaneous encoding of step 304 could entail applying a first harmonic MEG of MEG frequency equal to f along a first of the MRI system, applying a second harmonic MEG of MEG frequency equal to f along a second of the MRI system, and applying a third harmonic MEG of MEG frequency equal to f along a third of the MRI system. In particular, the first direction of the MRI system could be a read-direction, the second direction of the MRI system could be a phase-direction, and the third direction of the MRI system could be a slice-direction.

Also in accordance with example embodiments, MEG frequencies and vibrational frequencies could be selected to be equal or matched based on a filter condition. More specifically, an analytic filter condition that specifies phase encoding of a different one of the first, second, and third harmonic waveforms in each of the three dimensions could be used to select: (i) the MEG frequency of the first harmonic MEG and f to be equal, (ii) the MEG frequency of the second harmonic MEG and f to be equal, and (iii) the MEG frequency of the third harmonic MEG and _? to be equal.

In further accordance with example embodiments, the first harmonic MEG could have cycle duration z_\, the second harmonic MEG could have a cycle duration ¾ and the third harmonic MEG could have a cycle duration z¾, where MEG cycle duration is the inverse of MEG frequency. More specifically, τ_\ = l/f, ¾ = I 2, and z¾ = l/ . Further, each of the first, second, and third harmonic MEGs could have a common duration T, such that the number of MEG cycles for each dimension times the MEG cycle duration in that dimension is equal to T. With the number of cycles in each dimension specified as N_j, j = 1, 2, 3, this can be expressed as Ni = 77 τ_\, N2 = 77 ¾ and N3 = 77 z¾.

In accordance with example embodiments, the method could also include generating from the acquired multi-frequency MRE data MRE images corresponding to vibrational displacements for each of three different frequencies. More specifically, generating the MRE images could entail generating spatially and temporally aligned MRE images corresponding to three different frequencies of vibrational displacements occurring in the object during at least one common vibrational state of the object. In further accordance with example embodiments, generating the spatially and temporally aligned MRE images could entail calculating a Fourier transform of the encoded MR signal phase, and then determining the three different frequencies of vibrational displacements from a frequency decomposition based on the calculated Fourier transform. By acquiring 3D MRE data at three frequencies simultaneously, any frequency dependence of mechanical behavior of the object can be accounted for, thereby allowing determination of a frequency- independent material property of the object.

In addition, the example method can also include analysis of three dimensions of the acquired multi-frequency MRE data in order to separate shear from a compression wave in the object.

It will be appreciated that the example method steps of the example embodiment of SDP-MRE can be embodied as executable instructions stored on a non-transitory computer- readable medium, such as magnetic disk, CD-ROM, or the like. It will also be appreciated that the method steps described above can be modified or rearranged, and that additional steps can be added, without changing the scope or spirit of the example embodiment or other SDP-MRE embodiments.

3. Example Analytical Description

Without being limited to any theory of the underlying basis for the invention one of ordinary skill will appreciate the following features of the MRE methods set forth herein.

The basic equation of MRE is represented by an integral over time (Muthupillai et al, Magnetic resonance elastography by direct visualization of propagating acoustic strain waves. Science 1995, 269(5232): 1854-1857), which describes the encoding of the displacement u(t) of an isochromat into the phase 0(s) of the MR signal by applying a time- harmonic magnetic field gradient G

(p(s = _Y f*^+T G(t - u(t dt. (2)

In Equation (2), γ and s represent the gyromagnetic ratio and the start time of the MEG, respectively, while T corresponds to the duration of the applied MEG.

The MEG can be composed of MEG projections in each of three spatial dimensions of a Cartesian coordinate system indexed by j = 1, 2, 3. With this labeling, the phase φ of the MR signal can be expressed as the sum of three integrals over time of the projections of G and u onto the axes of a Cartesian system:

ΦΟ) =∑]₌i = Y∑]₌i C^T G_j (t)^■ Uj (t)dt. (3) In this formulation the MEG-projections can all be considered as having the same start time s and duration T.

The indexes j = 1, 2, 3 could correspond to three spatial dimensions x, y, and z, or any permutation thereof, of a Cartesian coordinate system. Alternatively, the indexes could correspond or any three linearly independent axes of a spatial coordinate system. In the context of a MRI system the three spatial Cartesian coordinates could also correspond to read-, phase-, and slice-directions.

In accordance with example embodiments, the MEG projections can be taken to be sinusoidal time-harmonic functions with frequencies 1/z/, where z/ is the duration (period) of a single MEG cycle of the MEG projection in the jth direction. Also in accordance with example embodiments, the mechanical vibration induced in the object under study (e.g., tissue sample, phantom, live subject, etc.) can be represented by a superposition of Q sinusoidal waveforms with frequencies f_q, q = 1, 2, ..., Q. It then follows that the solution of the integral Equation (3) can be expressed as:

ΦΟ) = Σ]=ι Φ ω =∑j³ ₌₁∑^Q _q=i i^uM sin(2⁷- + Qj,_q), (4) with:

ygjTj s (nN_jT_jf_q) 1

In Equations (4) and (5a,b), u°_q represents the amplitude of the harmonic displacement projection, represents the encoding efficiency, and Q_{j q} is a phase shift. All three are specified for each frequency component q and projection j.

Equation (4) also identifies parameters of the MEG projections on the Cartesian axes. Specifically, gj is the amplitude, N_j is the number of MEG cycles, and, as noted η is the duration of one harmonic cycle of the respective MEG projection in the jth direction. In accordance with example embodiment, SDP-MRE specifies that the MEG duration T is equal to T = N_jT_j for all j, and where N_j is a positive integer. In addition, SDP-MRE includes a filter condition that specifies a relation between the vibrational frequencies f_q, q = 1, 2, ..., Q and the MEG projection frequencies 1/x_j. More particularly, the vibration spectrum can be represented by a superposition of three sinusoidal waveforms with frequencies f_q, q = l, 2, 3, that are equal to the frequencies l/x_j,y = 1, 2, 3 of the MEG projections. In accordance with example embodiments of SDP-MRE, taking N_j to be a positive integer, the filter condition can be derived from Equation (5 b) by observing that no harmonic motion is encoded into (s) if the argument of the sine function is equal to an integer multiple of π. It follows that the filter condition can be expressed as:

=^ ⁼ i'^{n e N\}W ^→ ¾« ⁼ °- ⁽⁶⁾

Equation (6) can be interpreted as specifying that the base frequency fi,, defined as the reciprocal of the MEG duration T, does not contribute to the phase accumulation unless fib is equal to one of the frequencies 1/xj. Further, all multiples of fi, are filtered out with the exception of the vibration frequency that is equal to the frequency 1/x_j of the respective MEG projection. Therefore, the total MR phase is represented by a sum of phase portions (pj s), each corresponding to a distinct spatial projection and vibration frequency. In accordance with example embodiments, the individual components can be decomposed by applying a Fourier transform to along the MEG-start time s.

4. Example Operation and Results

The following discussion describes an example embodiment of SDP-MRE implemented in a MRI system, as well as an example SDP-MRE procedure carried out using a test object. Results of the example procedures are discussed in a subsequent section.

a. Demonstration system and example procedure

A demonstration SDP-MRE procedure was carried out using a mechanical excitation signal composed of a superposition of 5 kHz, 6 kHz and 7 kHz harmonic vibrations. Encoding of all three components simultaneously was achieved according to the SDP-MRE technique described above. Conventional, multiple application mono-frequency MRE was also applied for comparison purposes. Details of the demonstration system and procedure are discussed below, as is a comparison of results obtained using SDP-MRE with those from the conventional approach.

Experimental Setup

Experiments were performed in an 1 1.7 Tesla vertical bore Bruker MRI system having an inner diameter (ID) of 56 mm. A clear bore 10 mm internal diameter saddle RF coil was used inside a 19 mm internal diameter gradient coil with a maximum magnetic field gradient of 300 Gauss/cm. This system can be considered a specific example of a generic MRI system, such as one described above in the Background section herein. The test tube attached to a piezoelectric stack (6.5 mm x 6.5 mm x 18 mm, Thor Labs Inc.), which was fixed to a counter mass, was centered in the RF saddle coil. As a test object, an inhomogeneous sample composed of an agarose bead embedded in agarose gel formed from a different concentration was used.

For mechanical excitation, the piezoelectric stack was excited with a signal of 5 ms duration that was a superposition of sinusoidal wave forms of 5 kHz, 6 kHz and 7 kHz with equal amplitudes. A direct current bias was added to the harmonic signal in order to prevent negative voltages which are harmful to the integrity of the piezoelectric stack. The axisymmetric experimental setup causes a geometric focusing of mechanical shear waves within the sample, and this configuration compensates for the strong damping of soft tissue in the kHz-range. Due to the inhomogeneous composition of the sample, displacements could be generated in all three spatial dimensions within an image slice caused by reflection and refraction of the mechanical shear wave at the spherical surface of the bead.

The experimental setup is shown in Figure 4. A test tube 402 is attached by a plastic rod 404 to the piezoelectric actuator 406, which in turn is connected to the counter mass 408. The test object in the demonstration study includes an agarose bead 410 immersed in an agarose gel 412 within the test tube 402. As shown in the Figure, the test tube 402 had a diameter of 1 cm and a height of 4 cm. Mechanical vibrations were induced along the height of the test tube 402 and perpendicular to the imaging plane 414, as indicated by the double- ended arrows in Figure 4.

Image Acquisition

A gradient-echo based MR pulse sequence was used for data acquisition in one axial slice with the following sequence parameters: repetition time TR=500 ms; echo time TE=2.94 ms; flip angle 30°; Field of View (FOV)=10 mm x 10 mm; slice thickness = 0.25 mm; matrix size = 128 x 128. The MR sequence was upgraded with MEGs with a strength of 80 Gauss/cm in each spatial direction for motion sensitization. Referring again to Figure 1, the filter condition (Equation (6)) was applied by choosing an MEG gradient cycle number of 15, 18 and 21, and an MEG frequency of 5, kHz, 6 kHz and 7 kHz for the MEG component in read-, phase- and slice-direction, respectively. This resulted in an MEG duration of T= 3 ms. Depending on the respective time step, the start of the MEG was delayed between 1 ms and 2 ms relative to the start of the multi-frequency mechanical excitation signal. A forerun of 1 ms was applied to ensure penetration of the shear wave into the sample center before application of the MEG.

In the example demonstration procedure, the motion encoding upgrade of the standard gradient-echo based MR pulse sequence involved an increase of TE from 2.94 ms to 7.94 ms. With the chosen MEG parameters, the base frequency β,, as defined above, is equal to 0. 3 kHz, and all vibration frequencies used were multiples of β,. Consequently, with regard to one motion component, only the vibration corresponding to the frequency of the respective MEG-component contributed to the accumulated MR phase φ, while the other two frequencies were filtered out for this projection. Thus, out of the applied three frequencies, the 5 kHz vibration in read-, the 6 kHz vibration in phase- and the 7 kHz vibration in slice- direction were encoded simultaneously into φ. Finally, the temporal resolution of was achieved by shifting the trigger 16 times over 1 ms period. At each time step, two acquisitions were performed with inverse polarity MEG for calculating phase difference images, which were cleared of biases due to constant field inhomogeneities.

Image Plane

The position of the image slice was determined in MRE-pretests of reduced spatial and temporal resolution in 10 axial slices covering the beads. The image slice was chosen by the decision criterion that displacement in phase-, read-, and slice-directions were maximal. An axial slice in between the equator and the south pole of the bead fulfilled this criterion (e.g., image plane 414 in Figure 4).

Data Processing

The accumulated, temporally-resolved MR phase represents a multi-frequency function of the starting time s of the MEG relative to the start of the vibration. The discrete Fourier transformation of was calculated for obtaining complex phase images Φ(β at the frequency / and Φ(β was scaled to complex wave images using the scaling factor given in Equation (5a). This decomposition procedure is similar to that applied to MR phase data that originated from multi-frequency vibrations along one dimension and that were acquired by exploiting the broad-band motion sensitization nature of the MEG (Klatt et al., Noninvasive assessment of the rheological behavior of human organs using multifrequency MR elastography: a study of brain and liver viscoelasticity, Physics in medicine and biology 2007, 52(24):7281-7294). Comparative Experiment

For purposes of comparison with conventional MRE techniques, a comparative experiment utilizing a conventional motion encoding scheme was also conducted. Specifically, the same sequence parameters as that used in SDP-MRE were used, but the wave images were acquired in three consecutive steps. In each individual step, only one of the three gradients, which are illustrated in Figure 1, was active. As a consequence of the consecutive acquisition of the individual motion components, the total measurement time of the comparative experiment was three times longer than of SDP-MRE. For comparison, a 2D local frequency estimation algorithm (LFE) was applied to the wave images and the resulting images of the wavelength were spatially averaged over the agarose bead.

b. Illustrative Results

Reference is again made to Figure 2, which displays complex wave images acquired with SDP-MRE (bottom row of Figure 2) and with conventional MRE(top row of Figure 2). The wave length varies from column to column, as both the vibration frequency and the displacement projection are different. Different wave amplitudes in different projections determined with the same method can also be observed. The amplitude difference between both methods for same frequencies can be seen to be small. In particualr, similar wave structures for same projections are evident in Figure 2. Consequently, the LFE-derived wave lengths can be considered identical within the error margins. The spatial average of the wave length over the agarose bead results in (0.7±0.1) mm, (0.5±0.1) mm and (0.4±0.1) mm for the 5 kHz, 6 kHz, and 7 kHz vibration, respectively, independent of the used MRE approach.

The motion encoding technique introduced in SDP-MRE for the displacement vector in multi-frequency MRE enables the simultaneous acquisition of three mutually orthogonal displacement components of different frequencies by applying the MRE filter condition represented in Equation (6). As shown by way of example in the demonstration trial, SDP- MRE can be successfully applied to a multi-frequency vibration and selected the 5 kHz, 6 kHz, and 7 kHz frequency for the read-, phase- and slice-projection of the displacement, respectively. For the acquisition of all displacement components of the three frequency vibration spectrum, the relations can be permuted, resulting in a total of three SDP-MRE experiments.

A feature of the arrangement of the MEGs in SDP-MRE is that it is not bound to a specific sequence type, but can be integrated into most pulse sequences typically used in MRE, such as the gradient-echo, spin-echo and EPI sequences. Further, SDP-MRE is not bound to a specific dynamic range. It is applicable all the way from the low frequency range of human MRE to the high frequency range of micro-MRE, as long as the three used frequencies used exhibit a common divisor and the filter condition represented by Equation (6) is satisfied.

In accordance with example embodiments, SDP-MRE is faster than conventional MRE, where all three displacement projections are acquired individually for each frequency component in consecutive steps. By way of example, the hardware setup used in the demonstration trial limited the applied frequency range, which was accommodated by acquiring 16 time steps for frequency decomposition. This number of time steps can be reduced by choosing a spectrum composed of the first three harmonics. For example, in the range of human MRE, 25 Hz, 50 Hz and 75 Hz would be suitable. For the decomposition of such a signal, only eight time steps would be necessary. In conventional, mono-frequency MRE, typically four to eight time steps are acquired. Taking these values for comparison, it can be deduced that SDP-MRE would be 1.5 - 3 times faster than conventional MRE.

Other factors beyond measurement time can also impact the duration of a multi- frequency experiment. For example, the measurement interruption due to the manual adjustment of the waveform generator, which has to be performed in between consecutive conventional MRE experiments, does not contribute to duration in SDP-MRE. Thus, SDP- MRE techniques can save additional time by eliminating interruptions between experiments.

In addition to speeding up the acquisition of a three frequency vibration spectrum along three encoding directions, SDP-MRE can also yield increased measurement accuracy. More particularly, in conventional MRE, nine individual experiments have to be conducted, each during a different physical vibration state. This represents a possible source of error, as misalignment of the image slices can occur between the individual acquisitions, especially when performing in vivo MRE. Data acquisition in accordance with example embodiments of SDP-MRE can be achieved with generation of only three physical vibration states. This again is an improvement compared to the conventional approach.

The time saved by applying SDP-MRE, as described above by way of example might appear to be achievable by applying multi-frequency MRE based on fractional motion encoding (Klatt et al.,a study of brain and liver viscoelasticity, Physics in medicine and biology 2001 , 52(24):7281-7294). Using this approach, the three mechanical frequencies are recorded simultaneously for each of the three directions reducing by a factor of three the number temporally resolved experiments needed for the acquisition of the three frequency spectrum along three encoding directions. However, it is inherent to fractional motion encoding concepts that the encoding efficiency cannot be increased by increasing the number of MEG cycles. By contrast, by applying SPD-MRE, the encoding efficiency can be increased by increasing the number of MEG cycles.

It can therefore be expected that SDP-MRE can be used not only in large scale, low field MRE setups, but also for multi-frequency MRE studies in the high dynamic range, where typically multiple MEG cycles are used to compensate for a strong mechanical damping necessitating increased motion sensitivity. This can allow the number of temporally- resolved MRE experiments to be reduced without any downside. Applying SDP-MRE to the dynamic range of human MRE, for example, configurations of the three frequencies such as 25 Hz, 50 Hz and 75 Hz with a 40 ms MEG duration, or 40 Hz, 60 Hz and 80 Hz with a 50 ms MEG duration can be used. Considerations such as these indicate that SDP-MRE can potentially be adapted for the multi-frequency examination of in vivo human brain.

An example embodiment of the present invention has been described above. Those skilled in the art will understand, however, that changes and modifications can be made to this embodiment without departing from the true scope and spirit of the invention, which is defined by the claims.

Claims

CLAIMS What is claimed:

1. In a magnetic resonance imaging (MRI) system, a computer- implemented method comprising:

while inducing multi-frequency vibrational motion in an object in the MRI system, applying a magnetic resonance (MR) signal to the object, the MR signal having a phase; encoding into the MR signal phase simultaneously along each of three spatial dimensions a different frequency component of the induced multi-frequency vibrational motion of the object by applying to the object simultaneously in each of the three dimensions a motion encoding gradient (MEG) having a different MEG frequency component in each of the three dimensions; and

acquiring simultaneously at multiple MEG frequencies multi-frequency magnetic resonance elastography (MRE) data comprising the MR signal phase encoded with the different frequency component of the induced multi-frequency vibrational motion of the object in each of the three dimensions.

2. The method of claim 1, wherein the three spatial dimensions correspond to spatial dimensions x, y, and z of a Cartesian coordinate system, and to read-, phase-, and slice-directions of the MRI system.

3. The method of claim 1, wherein inducing the multi-frequency vibrational motion in the object in the MRI system comprises inducing a mechanical vibration having three different, concurrent frequency components.

4. The method of claim 1, wherein the induced multi-frequency vibrational motion comprises a superposition of three vibration components, the first vibration component having a frequency f_\, the second vibration component having a frequency ^, and the third vibration component having a frequency fc,

and wherein the different MEG frequency component in each of the three dimensions has a frequency selected to equal a different one of f_\, fi, or f₃, based on an analytic filter condition that specifies phase encoding of a different one of the three vibration components in each of the three dimensions.

5. The method of claim 1, wherein the induced multi-frequency vibrational motion comprises a superposition of three vibration components, the first vibration component having a frequency f_\, the second vibration component having a frequency and the third vibration component having a frequency fi,

and wherein encoding into the MR signal phase simultaneously along each of three spatial dimensions the different frequency component of the induced multi-frequency vibrational motion of the object by applying to the object simultaneously in each of the three dimensions the MEG having a different MEG frequency component in each of the three dimensions comprises:

simultaneously applying a first MEG of MEG frequency equal to f_\ along a first of the three dimensions, a second MEG of MEG frequency equal to f∑ along a second of the three dimensions, and a third MEG of MEG frequency equal to along a third of the three dimensions.

6. The method of claim 1, wherein inducing the multi-frequency vibrational motion in the object in the MRI system comprises inducing a mechanical vibration comprising a superposition of all three of a first harmonic waveform of frequency f_\, a second harmonic waveform of frequency^, and a third harmonic waveform of frequency ?,

and

and are all different.

7. The method of claim 6, wherein encoding into the MR signal phase simultaneously along each of three spatial dimensions the different frequency component of the induced multi-frequency vibrational motion of the object by applying to the object simultaneously in each of the three dimensions the MEG having a different MEG frequency component in each of the three dimensions comprises:

applying a first harmonic MEG of MEG frequency equal to f_\ along a first direction of the MRI system;

applying a second harmonic MEG of MEG frequency equal to fi along a second direction of the MRI system; and applying a third harmonic MEG of MEG frequency equal to _? along a third direction of the MRI system.

8. The method of claim 7, wherein the first direction of the MRI system is a read- direction, the second direction of the MRI system is a phase-direction, and the third direction of the MRI system is a slice-direction.

9. The method of claim 7, wherein (i) the MEG frequency of the first harmonic MEG and f_\ are selected to be equal, (ii) the MEG frequency of the second harmonic MEG are selected to be equal, and (iii) the MEG frequency of the third harmonic MEG and _? are selected to be equal, based on an analytic filter condition that specifies phase encoding of a different one of the first, second, and third harmonic waveforms in each of the three dimensions.

10. The method of claim 7, wherein the first harmonic MEG has a cycle duration z_\, the second harmonic MEG has a cycle duration ¾ and the third harmonic MEG has a cycle duration z¾,

wherein

¾ = I 2, and z¾ = I/ 3,

wherein each of the first, second, and third harmonic MEGs have a common duration T,

and wherein the first, second, and third harmonic MEGs have respective positive integer numbers of cycles Ni, N₂, and N3 determined as Ni = ΤΙτ_\, N2 = 77 ¾ and N3 = 77 z¾.

11. The method of claim 1, further comprising generating from the acquired multi- frequency MRE data MRE images corresponding to vibrational displacements in each of three different frequencies.

12. The method of claim 1 1, wherein generating from the acquired multi-frequency MRE data the MRE images comprises generating spatially and temporally aligned MRE images corresponding to three different frequencies of vibrational displacements occurring in the object during at least one common vibrational state of the object.

13. The method of claim 12, wherein generating the spatially and temporally aligned MRE images corresponding to the three different frequencies of vibrational displacements occurring in the object comprises:

calculating a Fourier transform of the MR signal phase encoded with the different frequency component of the induced multi-frequency vibrational motion of the object in each of the three dimensions; and

determining the three different frequencies of vibrational displacements from a frequency decomposition based on the calculated Fourier transform.

14. The method of claim 1 1, further comprising determining a frequency- independent material property of the object from the acquired multi-frequency MRE data.

15. A magnetic resonance imaging (MRI) system comprising:

one or more processors;

memory;

a main magnet;

one or more gradient coils; and

machine-readable instructions stored in the memory that, when executed by the one or more processors, cause the MRI system to carry out functions including:

activating a mechanical actuator for inducing multi-frequency vibrational motion in an object in the MRI system, while applying a magnetic resonance (MR) signal to the object, wherein the MR signal has a phase;

encoding into the MR signal phase simultaneously along each of three spatial dimensions a different frequency component of the induced multi-frequency vibrational motion of the object by applying to the object simultaneously in each of the three dimensions a motion encoding gradient (MEG) having a different MEG frequency component in each of the three dimensions; and

16. The MRI system of claim 15, wherein the three spatial dimensions correspond to spatial dimensions x, y, and z of a Cartesian coordinate system, and to read-, phase-, and slice-directions of the MRI system.

17. The MRI system of claim 15, wherein inducing the multi-frequency vibrational motion in the object in the MRI system comprises inducing a mechanical vibration having three different, concurrent frequency components.

18. The MRI system of claim 15, wherein the induced multi-frequency vibrational motion comprises a superposition of three vibration components, the first vibration component having a frequency f, the second vibration component having a frequency /_¾ and the third vibration component having a frequency _?,

and wherein the different MEG frequency component in each of the three dimensions has a frequency selected to equal a different one of f, f, or f, based on an analytic filter condition that specifies phase encoding of a different one of the three vibration components in each of the three dimensions.

19. The MRI system of claim 15, wherein the induced multi-frequency vibrational motion comprises a superposition of three vibration components, the first vibration component having a frequency f, the second vibration component having a frequency /_¾ and the third vibration component having a frequency _?,

simultaneously applying a first MEG of MEG frequency equal to f along a first of the three dimensions, a second MEG of MEG frequency equal to f along a second of the three dimensions, and a third MEG of MEG frequency equal to f along a third of the three dimensions.

20. The MRI system of claim 15, wherein inducing the multi-frequency vibrational motion in the object in the MRI system comprises inducing a mechanical vibration comprising a superposition of all three of a first harmonic waveform of frequency f_\, a second harmonic waveform of frequency^, and a third harmonic waveform of frequency ?,

and

and are all different.

21. The MRI system of claim 20, wherein encoding into the MR signal phase simultaneously along each of three spatial dimensions the different frequency component of the induced multi-frequency vibrational motion of the object by applying to the object simultaneously in each of the three dimensions the MEG having a different MEG frequency component in each of the three dimensions comprises:

applying a second harmonic MEG of MEG frequency equal to f∑ along a second direction of the MRI system; and

applying a third harmonic MEG of MEG frequency equal to/_? along a third direction of the MRI system.

22. The MRI system of claim 21, wherein the first direction of the MRI system is a read-direction, the second direction of the MRI system is a phase-direction, and the third direction of the MRI system is a slice-direction.

23. The MRI system of claim 21, wherein (i) the MEG frequency of the first harmonic MEG and f_\ are selected to be equal, (ii) the MEG frequency of the second harmonic MEG and fi are selected to be equal, and (iii) the MEG frequency of the third harmonic MEG and are selected to be equal, based on an analytic filter condition that specifies phase encoding of a different one of the first, second, and third harmonic waveforms in each of the three dimensions.

24. The MRI system of claim 21, wherein the first harmonic MEG has a cycle duration z_\, the second harmonic MEG has a cycle duration ¾ and the third harmonic MEG has a cycle duration z¾, wherein τ_\ = \lf_\, ¾ = I/ 2, and z¾ = I/ 3,

and wherein the first, second, and third harmonic MEGs have respective positive integer numbers of cycles Ni, N₂, and N₃ determined as Ni = Tlz_\, N₂ = T/T₂, and N₃ = 77 z¾.

25. The MRI system of claim 15, wherein the functions further include generating from the acquired multi-frequency MRE data MRE images corresponding to vibrational displacements in each of three different frequencies.

26. The MRI system of claim 25, wherein generating from the acquired multi- frequency MRE data the MRE images comprises generating spatially and temporally aligned MRE images corresponding to three different frequencies of vibrational displacements occurring in the object during at least one common vibrational state of the object.

27. The MRI system of claim 26, wherein generating the spatially and temporally aligned MRE images corresponding to the three different frequencies of vibrational displacements occurring in the object comprises:

28. The MRI system of claim 25, wherein the functions further include determining a frequency-independent material property of the object from the acquired multi- frequency MRE data.