Controlled excitation and saturation of magnetisation transfer systems

Abstract

The present invention relate to a system and associate method of MRI and MR spectroscopy which provide stable measurements of the relaxation times, T1 and T2, by using tailored multi-band RF pulses that direct control of the saturation conditions in the background pool of macro-molecular protons, and hence provide a flexible means to induce constant Magnetisation Transfer (MT) effects. In doing this, equal saturation of the background pool is obtained for all measurements independent of the parameters that may be changed, for example, the rotation rate used to obtain a desired flip angle, that is, the degree of change in the magnetisation of the free pool of protons.

Claims

1. A method of calculating a multi-band radio frequency (RF) pulse for use in magnetic resonance (MR) imaging or MR spectroscopy, wherein the multi-band RF pulse comprises an on-resonance band and at least one off-resonance band, and wherein the method comprises: defining a target degree of rotation in the magnetisation, M, of a free pool of protons in an object; and calculating the parameters of the on-resonance band and the at least one off-resonance band based on the target degree of rotation, wherein the calculated parameters of the on-resonance band the at least one off-resonance band are such that, when the multi-band RF pulse is used as a parameter of MR imaging or spectroscopy, a predetermined amount of saturation of magnetisation occurs in a bound pool of protons in the object, wherein the free pool of protons is a first spin population such that in use the duration of the multi-band RF pulse is shorter than a first transverse relaxation time (T2) of the first spin population, and wherein the bound pool of protons is a second spin population such that in use the duration of the multi-band RF pulse is longer than a second transverse relaxation time (T2) of the second spin population.

2. An apparatus for calculating a multi-band RF pulse for use in magnetic resonance (MR) imaging or MR spectroscopy, wherein the multi-band RF pulse comprises an on-resonance band and at least one off-resonance band, the apparatus comprising: a processor; a computer readable medium, the computer readable medium storing on or more instruction(s) arranged such that when executed the processor is caused to: (a) define a target degree of rotation in the magnetisation, M, of a free pool of protons in an object; and (b) calculate the parameters of the on-resonance band and the at least one off-resonance band based on the target degree of rotation, wherein the calculated parameters of the on-resonance band the at least one off-resonance band are such that, when the multi-band RF pulse is used as a parameter of MR imaging or spectroscopy, a predetermined amount of saturation of magnetisation occurs in a bound pool of protons in the object, wherein the free pool of protons is a first spin population such that in use the duration of the multi-band RF pulse is shorter than a first transverse relaxation time (T2) of the first spin population, and wherein the bound pool of protons is a second spin population such that in use the duration of the multi-band RF pulse is longer than a second transverse relaxation time (T2) of the second spin population.

3. A method according to claim 1, wherein the calculating the parameters of the on-resonance band and the at least one off-resonance band comprises: calculating the parameters of the on-resonance band based on the target degree of rotation, wherein the calculated parameters of the first band are such that, when the multi-band RF pulse is used as a parameter of MR imaging or spectroscopy, the target degree of rotation is induced in the free pool of protons; and calculating the parameters of the at least one off-resonance band based on the on-resonance band, wherein the calculated parameters of the at least one off-resonance band are such that, when the multi-band RF pulse is used as a parameter of MR imaging or spectroscopy, the predetermined amount of saturation of magnetisation occurs in the bound pool of protons.

4. A method according to claim 1, further comprising: calculating a plurality of multi-band RF pulses corresponding to a plurality of target degrees of rotation, wherein the predetermined amount of saturation of magnetisation is constant for the plurality of multi-band RF pulses such that, when used as a parameter of MR imaging or spectroscopy, the plurality of multi-band RF pulses achieve controlled Magnetisation Transfer conditions.

5. A method according to claim 4, wherein the plurality of multi-band RF pulses achieve constant Magnetisation Transfer conditions.

6. A method according to claim 1, further comprising setting the predetermined amount of saturation of magnetisation based on a reference multi-band RF pulse.

7. A method according to claim 6, wherein the setting the predetermined amount of saturation of magnetisation comprises: (i) defining a reference degree of rotation in the magnetisation, M of a free pool of protons in an object; (ii) calculating a reference multi-band RF pulse corresponding to the reference degree of rotation; (iv) determining the amount of saturation of magnetisation occurring in a bound pool of protons of the object when the reference multi-band RF pulse is used as a parameter of MR imaging or spectroscopy; and (iii) setting the predetermined amount of saturation of magnetisation based on the determined amount of saturation of magnetisation.

8. A method according to claim 1, further comprising setting the predetermined amount of saturation of magnetisation based on a target amount of saturation.

9. A method according to claim 1, wherein defining the target degree of rotation of magnetisation, M, comprises defining a target flip angle, α.

10. A method of magnetic resonance (MR) imaging, comprising: calculating a plurality of multi-band RF pulses according to claim 1; performing an MR scan on an object using the plurality of multi-band RF pulses to thereby obtain a plurality of MR signals, wherein each of the plurality MR signals corresponds to one of the plurality of a multi-band RF pulses; and generating an image of the object based on the plurality of MR signals.

11. A method according to claim 10, wherein the method further comprises measuring the relaxation times T1 and T2 of the plurality of MR signals, wherein the generating an image of the object preferably further comprises generating a T1 map and/or a T2 map.

12. A method according to claim 10, wherein the generating an image further comprises calculating a myelin water fraction from the plurality of MR signals.

13. A method according to claim 10, wherein the generating an image comprises generating a saturation weighted image.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) Embodiments of the invention will now be further described by way of example only and with reference to the accompanying drawings, wherein like reference numerals refer to like parts, and wherein:

(2) FIG. 1 is a process diagram illustrating the method of MR imaging according to embodiments of the invention;

(3) FIG. 2 is a system block diagram which forms the basis for embodiments of the invention;

(4) FIG. 3 is a series of images relating to results of the operation of the described embodiments

(5) FIG. 4 is a set of charts relating to results of the operation of the described embodiments;

(6) FIG. 5 is a set of charts relating to results of the operation of the described embodiments;

(7) FIG. 6 is a set of charts relating to results of the operation of the described embodiments;

(8) FIG. 7 is a set of charts relating to results of the operation of the described embodiments;

(9) FIG. 8 is a set of charts relating to results of the operation of the described embodiments;

(10) FIG. 9(a) is a chart relating to results of the operation of the described embodiments;

(11) FIG. 9(b) is an image showing results of the operation of the described embodiments;

(12) FIG. 10 is a set of charts and images relating to results of the operation of the described embodiments;

(13) FIG. 11 is a set of charts relating to results of the operation of the described embodiments;

(14) FIG. 12 illustrates the present invention in use;

(15) FIG. 13 is a set of charts relating to results of the operation of the described embodiments;

(16) FIG. 14 is a set of charts relating to results of the operation of the described embodiments;

(17) FIG. 15 is a chart relating to results of the operation of the described embodiments;

(18) FIG. 16 illustrates a multi-pool system in which the present invention is used.

DETAILED DESCRIPTION OF EMBODIMENTS OF THE INVENTION

(19) A brief overview of embodiments of the invention will now be given.

(20) In biological samples, where multiple pools of magnetization are always present, applied RF pulses induce not only rotation of the free pool of protons but also a simultaneous partial saturation of the background pool of restricted protons. The background pool of protons is characterized by its short T2 (shorter than the duration of the RF pulse) and as a consequence does not produce an observable signal, however, since the energy of the applied RF pulses is absorbed by the background pool, this ultimately affects the relaxometry measurements of the free pool, specifically, the T1 measurement. This phenomenon is known as Magnetisation Transfer (MT). If the effects of MT are not taken into account, this can lead to errors in the T1 and T2 measurements. To take the saturation of the background pool into consideration, multi-pool modelling is usually required which is considerably time consuming. The present invention addresses this by enabling single pool assumptions to be validly made, that is, by eliminating the need to consider the effects of the background pool of restricted protons.

(21) A schematic representation of a two-pool system is shown by FIG. 16. Both the free pool and the macromolecular pool have their own equilibrium magnetisation (M0) and spin lattice interaction rate (R1). The free pool also has an intrinsic spin-spin interaction rate (R2), whilst the macromolecular spin-spin interaction is parameterised by the absorption line-shape G. Both pools can exchange at a first order exchange rate.

(22) In variable flip angle (VFA) relaxometry, a series of relaxometry measurements are obtained for a tissue sample by acquiring images under different RF pulses, for example, RF pulses of finite time and varying amplitude (or vice versa) to achieve a variety of flip angles, α, in the free pool. In this respect, the RF pulse is used to rotate the magnetisation, M, of the free pool of protons in order to obtain an observable signal, with the achieved flip angle being used to characterises this rotation. However, as different RF conditions are employed, an unavoidable variable saturation of the background pool is induced.

(23) To get the measurements for all the required flip angles under control, the energy of the RF pulse can be balanced to ensure that the saturation of the background pool is kept constant for every target flip angle.

(24) Normally, to account for the complex nature of biological samples, VFA relaxometry can be extended such that multiple-pool (normally 2-pool) magnetization is assumed. To characterize this, typically, a sequence of RF pulses is employed, varying between on-resonance pulses and off-resonance pulses. Both the on-resonance and off-resonance pulses have a saturation effect on the background pool, whilst only the on-resonance pulses have an excitation effect on the free pool. That is, the on-resonance excitation causes rotation in the magnetisation, M, of the free pool.

(25) The present invention implements a single non-selective multi-band (MB) RF pulse of finite time that has both on-resonance and off-resonance contributions, wherein changes in the on-resonance contribution required to achieve a particular flip angle is balanced with a matching off-resonance contribution such that the total RF energy is the same for any target flip angle. However, in some cases, the off-resonance contribution may be set independent of the flip angle. That is, the total RF energy can be altered such that, saturation of the background pool is kept independently of the desired rotation of the free pool and imaging timings.

(26) Under fixed conditions, the saturation of the background pool has a benign effect such single pool assumptions can be made. That is, a single pool model can be used to accurately fit the variable flip angle data producing reliable relaxation parameter values that do not depend the particular choices of flip angle deployed. This allows for an accurate measurement of M0, T1 and T2 under a reported RF power, and subsequently improved tissue characterisation using T1 and T2 maps.

(27) In further detail, an embodiment of the present invention allows rapid generation of high resolution T1 and T2 maps of biological samples. For example, it enables rapid generation of high resolution T1 and T2 maps of the brain within approximately 15 minutes. As such, embodiments of the prior art are able to generate T1 and T2 maps in around the same time as previous methods (15, 18), but with a higher signal to noise ratio.

(28) A method of imaging a biological sample according to the present invention is shown in FIG. 1. In the first step, the user selects which RF-power is desired. At s.1.2, a target flip angle, α.sub.n, and imaging times are defined. At s.1.4, the multi-band CSMT pulse required for each target flip angle α.sub.n is determined given the RF-power and imaging timings requested. The resulting CSMT pulse is then applied to obtain and collect image data for that flip angle, at s.1.6. The sampled image will then reconstructed and stored, at s.1.8. Steps 1.2-1.8 can then be repeated for every prescribed flip angle. As described above, the on-resonance contribution for each defined flip angle is balanced with a matching off-resonance contribution in order to maintain the saturation conditions set in the first iteration. Once all of the sample images have been collated, the relaxation values T1.sup.app and T2 of the free pool are measured, at s.1.10. Once signal measurements for each defined target angle have been obtained, T1 and T2 maps of the biological sample, for example, a brain is generated at s.1.10.

(29) An example of a T1 map of a brain generated using the above method is illustrated by items (a) and (b) in FIG. 3. Items (c) and (d) of FIG. 3 show a T1 map of the same brain which have been generated using a conventional pulse. There is a clear improvement in the relaxation time resolution achieved using the CSMT pulse.

(30) FIGS. 4 to 7 further demonstrate the improved relaxation measurements obtained using embodiments of the present invention. FIG. 4 illustrates histograms of T1 relaxation times for the brain of a normal volunteer (i.e. having no tissue abnormalities) when measured using a conventional pulse and a CSMT pulse. Graph (a) shows the T1 relaxation times for white matter, whilst graph (b) shows the T1 relaxation times for grey matter. Both graphs show how the use of a CSMT pulse leads to a narrower distribution values, which indicates a reduced level of modelling errors.

(31) Similarly, FIG. 5 illustrates histograms of T2 relaxation times for the brain a normal volunteer (i.e. having no tissue abnormalities) when measured using a conventional pulse and a CSMT pulse. Graph (a) shows the T2 relaxation times for white matter, whilst graph (b) shows the T2 relaxation times for grey matter. Both graphs show that use of the CSMT pulse restores the estimate T2 to the correct value, wherein the correct value is normally assessed by a much slower method (“gold standard”) that does not provide high resolution over the whole brain, and is thus not suitable for clinical use.

(32) FIGS. 6 and 7 illustrates the estimated median relaxation times in White Matter of a normal volunteer vary as the details of the acquisition protocol are changed, that is, as different sets of flip angles α.sub.n are employed. Graph (a) of both FIGS. 6 and 7 shows the median T1 relaxation time, whilst graph (b) of FIGS. 6 and 7 shows the median T2 relaxation time. All of these graphs show that the use of CSMT pulses greatly reduces the variations caused by protocol changes. For example, in graph (a) of FIGS. 6 and 7, the median T1 values for conventional pulses (top line) vary greatly, whilst the median T1 values for CSMT pulses (bottom line) stay substantially constant. Similarly, in graph (b) of FIGS. 6 and 7, the median T2 values for conventional pulses (bottom line) is variable, whilst the median T2 values for CSMT pulses (top line) stays substantially constant. Furthermore, the T2 values for the CSMT pulses are again shown to be restored to their true value, as determined by the slower “gold standard” method.

(33) FIG. 2 illustrates, by way of example, the system components that may form the platform for embodiments of the present invention. The computer system 100 comprises a central processing unit (CPU) 110, a working memory 120, input interface 130 arranged to receive control inputs from the user via an input device 131 such as a computer with a keyboard, mouse or other controller, and output hardware 140 arranged to provide output information to the user via a visual display unit 141 such as a computer, television or other visual display.

(34) The computer system 100 may also be provided with a computer readable storage medium 150 such as a hard disk drive (HDD), flash drive, solid state drive, or any other form of general purpose data storage, upon which stored data 156 and various control programs are arranged to enable the system to operate according to embodiments of the present invention. For example, a control program 155 is provided and arranged to provide overall control of the system to perform the embodiments of the present invention. This control program 155 may, for example, receive user inputs and launch other programs to perform specific tasks. The other programs under the control of the control program 155 include a CSMT calculation program 151, an RF pulse generation program 152, a relaxometry map program 153 and an image generation program 154. These programs 151-154 will be discussed in more detail below.

(35) The computer system 100 is connected to an MR scanner 170 comprising a magnet 171 for generating the static magnetic field, B.sub.0, a set of gradient coils 172, a patient table 174, and an RF coil 173. The RF coil 173 may comprise a single coil arranged to both transmit the RF pulse and receive the MR signal. Alternatively, a separate RF transmitter and RF receiver may be used to transmit the RF pulse and receive MR signal, respectively. The RF coil 173 may be connected to an RF system 160 which receives inputs from the RF pulse generation program 152 to transmit an RF pulse to the RF coil 173, and conversely receive an MR signal back from the RF coil 173 for processing.

(36) It should be appreciated that various other components and systems would of course be known to the person skilled in the art to permit the MR system to operate. For example, the gradient coils 172 may be connected to a gradient system that receives instructions from a program stored on the computer readable storage medium 150 to produce magnetic field gradients.

(37) To scan an object on the patient table 174 according to the present invention, the user may first input the RF-power level desired as well as a set of target flip angles, α=1 . . . n, via the input device 130 and input interface 130, as in s.1.2 of FIG. 1. The CSMT calculation program 151 is then launched to calculate the CSMT pulse required for each defined flip angle and imaging timings, that is, to perform s.1.4 as described above. The parameters of the CSMT pulse for a defined flip angle are then input to the RF pulse generation program 152, which instructs the RF system 160 to transmit the CSMT pulse to the RF coil 173, as in s.1.6. The MR scanner 170 then scans the object on the patient table 174 using the generated CSMT pulse, and a signal from the RF coil 173 is transmitted back through the RF system 160 to the computer system 100. Once a signal has been transmitted back to the computer system 100, the control program 156 launches the image generation program 154 to reconstruct and store the image data collected by the RF system 160, as in s.1.8. This process will be repeated for each of the n target flip angles. Once signal measurements have been made for every target flip angle, the relaxometry program 153 will be launched to generate T1 and T2 maps of the scanned object to be displayed on the visual display device 141, as in s.1.10.

(38) As such, the present invention may be implemented on all modern MRI systems and therefore paves the way to quantitative MR imaging for routine diagnosis and to support clinical trials.

Experimental Methods and Results

(39) For the case of constant saturation, controlled saturation MT (CSMT) conditions are achieved by creating a pulse that balances changes in on-resonance (Δ=0) RF to achieve a required flip angle (α.sub.free) with a matched off resonance contribution to keep P.sub.RF at a desired value. For example, starting with a sinc-gauss RF pulse scaled to produce a reference flip angle, α.sub.ref=2πγ ∫.sub.0.sup.T.sup.RF ω.sub.1.sup.ref(t)dt, the CSMT excitation was created with symmetric bands at offset frequencies ±Δ by adding a scaled cosine modulated replica of the on-resonant pulse, as illustrated in FIG. 8. By enforcing a relative scaling of the two components as defined in equation [2], not only is the saturation state of the background pool kept under control, it is kept constant regardless of the defined flip angle:

(40) $\begin{array}{cc}{\omega }_1^{\mathrm{CSMT}}\left(t\right)=2\mathrm{\pi \gamma }\left[\frac{{\alpha }_{\mathrm{free}}}{{\alpha }_{\mathrm{ref}}}{\omega }_1^{\mathrm{ref}}\left(t\right)+{\mathrm{\kappa \omega }}_1^{\mathrm{ref}}\left(t\right)\cos \left(\Delta t\right)\right],s.t.{\int }_0^{T_{\mathrm{RF}}}{\left({\omega }_1^{\mathrm{CSMT}}\left(t\right)\right)}^2\mathrm{dt}={\int }_0^{T_{\mathrm{RF}}}{\left({\omega }_1^{\mathrm{ref}}\left(t\right)\right)}^2\mathrm{dt}& \left[2\right]\end{array}$
where κ is varied to satisfy the equal power constraint. Ideally, the background pool saturation should be independent of the balance between on- and off-resonance bands. Since G(Δ) is not completely flat, Δ should be minimised, but without introducing direct on-resonant saturation of free water.

(41) FIG. 8 illustrates a time representation of the proposed CSMT pulse designed to keep P.sub.RF constant while achieving different flip angles (a), and frequency representation of the rotation induced due to the CSMT pulse for each flip angle (b). Note that the off-resonance rotation has no meaning due to the inherently short T2 of the restricted-pool of magnetization (˜14 μs).

(42) Experiments were performed on three Healthy Volunteers (HV) (ages 22-58 years) who gave informed consent. The CSMT pulse was simulated and tested with increasing E.sub.RF values of 0.86 μT.sup.2 ms, 3.45 μT.sup.2 ms, 13.81 μT.sup.2 ms and 55.24 μT.sup.2 ms on an Agarose phantom with 2%, 4% and 8% volume/volume concentrations to find combinations of T.sub.RF and that minimised direct on resonance saturation when =0, while providing efficient sequences, leading to 3 ms and 6 KHz respectively. Data was acquired with: 6°, 8°, 10°, 12°, 14°, 16° for SPGR (Spoiled Gradient recalled acquisition in the steady state) and 15°, 25°, 35°, 45°, 55°, 65° for SSFP (Steady-state free precession) with RF phase increment 180° per excitation, plus 25° and 55° for SSFP with RF phase increment 0°. To keep exchange effects between magnetization pools constant, readout (TE) and repetition (TR) times were kept constant at 3.5 ms and 7 ms respectively. In-vivo measurement used a sagittal geometry with 250×250×250 mm.sup.3 FOV, SENSE-2 for both AP and RL and acquired voxel size 0.83 mm.sup.3, total time 2 m13 s per FA. An AFI.sup.6 map with resolution of 43 mm3 was acquired to correct for spatial transmit field inhomoegeneities. For comparison, the same data was acquired using a simple scaled block pulse (T.sub.RF=0.6 ms). To assess stability of the estimation with and without CSMT, multiple flip angle subsets of the acquired measurements (Table 1) were used to estimate T.sub.1 using DESPOT1 and T.sub.1,T.sub.2 using a Joint System Relaxometry (JSR) approach.sup.7 which simultaneously fits SPGR and SSFP signal models.

(43) Table 1 provides a summary of flip angle subsets explored in order to inspect stability of the relaxometry estimation. The highlighted flip angles correspond to each measurement used at its corresponding subset.

(44) TABLE-US-00001 TABLE 1 SPGR (°) SSFP-180(°) SSFP-0 (°) Subset 1 6 8 10 12 14 16 15 25 35 45 55 65 25 55 Subset 2 6 8 10 12 14 16 15 25 35 45 55 65 25 55 Subset 3 6 8 10 12 14 16 15 25 35 45 55 65 25 55 Subset 4 6 8 10 12 14 16 15 25 35 45 55 65 25 55 Subset 5 6 8 10 12 14 16 15 25 35 45 55 65 25 55 Subset 6 6 8 10 12 14 16 15 25 35 45 55 65 25 55

(45) Results

(46) FIGS. 9(a)-(b) summarise how apparent T.sub.1 (from DESPOT1) alters for Agarose as the E.sub.RF of the CSMT pulse is increased. FIG. 9(a) shows how the apparent mean DESPOT T1 measurement alters as a function of CSMT pulse energy. FIG. 9(b) provides an example of a DESPOT T1 map of the 3-layer phantom at increasing concentration of Agarose from top to bottom.

(47) FIG. 10 shows T.sub.1 (top) and T.sub.2 (bottom) maps in an example axial slice using all measured data for both a typical block pulse (a) and a CSMT pulse (b). This shows the comparison between JSR T1 and T2 maps when using a block pulse or a CSMT pulse to generate excitation. For each case, all available flip angles were used to estimate the relaxometry parameters. Deep grey matter shows improved estimation when using the CSMT compared to the standard block pulse. Furthermore, T2 relaxation times are more consistent with reported spin-echo measurements (15).

(48) FIG. 11 show histograms of T.sub.1 and T.sub.2 values from white matter for subsets 1-6 of Table 1 for the block and CSMT pulse. The CMST pulse stabilises the T.sub.1 values and results in higher T.sub.2 values, more consistent with spin echo measurements at 3T. Use of constant saturation aligns the T1 histograms (removes systematic bias in measurement), however, there is still a range of different standard deviations which is to be expected since the different flip angle sets will yield estimates with different precision.

Discussion & Conclusion

(49) Relaxation times from VFA methods are influenced by RF saturation, as shown by FIG. 8. Use of a controlled saturation pulse can be used to hold the background pool in a constant state of saturation for all measurements and this results in data that is internally consistent, providing very similar relaxation time estimates when using different excitation flip angles. This is not the case when using standard block pulse excitation, as shown by FIG. 11. Interestingly, not only does the CSMT approach stabilise T.sub.1, it also leads to T.sub.2 values (previously reported as underestimated using gradient echo methods (13, 18, 20)) that are more consistent with spin echo methods (19). The proposed CSMT pulses may also be useful for deliberately adding MT weighting to SSFP sequences (12, 16) and potentially measuring z-spectra.

(50) Controlling Magnetisation Transfer and exchange effects in mcDESPOT relaxometry Magnetisation transfer (MT) has been found to contribute to parameter estimation bias in sequences used in the multi-pool relaxometry technique, mcDESPOT (multicomponent driven equilibrium single pulse observation of T1 and T2). Recent work shows that using controlled saturation magnetisation transfer (CSMT) RF-pulses, a two-pool system (free- and bound-pools) can behave as a single pool with modified equilibrium magnetisation and longitudinal relaxation rate. It is also possible to use CSMT to model MT-effects in a three-pool system (exchange+MT) and show that under these conditions, the signal behaves as a two-pool system and matches a mcDESPOT model but characterised by different parameters than those originally assumed.

Introduction

(51) Multicomponent DESPOT (mcDESPOT) models tissue response using a system of two or more exchanging ‘free’ (i.e. MR-visible) magnetisation components. In its two-pool form, mcDESPOT has been used for characterisation of white matter, with the two components usually identified as intra/extracellular water (slow-relaxing) and myelin-water (fast-relaxing). The myelin water fraction (MWF), defined as the fractional size of the fast-relaxing pool relative to the total magnetization, is normally interpreted as a myelin biomarker and has been shown to consistently overestimate the value derived from multiecho CPMG methods (21, 22). White matter is known to yield a strong MT-effect that is not ordinarily modelled in mcDESPOT, and other work has suggested this to be a source for MWF overestimation (23).

(52) The MT-effect may be modelled by the addition of a ‘bound’ (i.e. macromolecular) pool of magnetisation (24). RF-pulses rotate ‘free’ magnetisation, but saturate ‘bound’ magnetisation according to applied RF-power W, where B.sub.1,rms is the RMS pulse amplitude over the whole sequence and G is the bound-pool absorption factor, the RF-power being described as follows:
W=πGγ.sup.2B.sub.1,rms.sup.2  [3]

(53) The above proposed controlled saturation magnetisation transfer (CSMT) approach has been shown to allow a simple two-pool MT-system (i.e. one free-pool, one bound-pool) to behave as a single free-pool during DESPOT-style relaxometry by keeping W constant over all acquisitions, irrespective of the applied flip angle (FA) (25).

(54) This approach can be extended to consider a system with two free components, of the type typically modelled in mcDESPOT, and how a ‘ground-truth’ scenario with three pools (i.e. two free-pools and one bound-pool) will produce parameter estimation bias when fitted using a two-pool model that does not include any bound component (hereafter referred to as the ‘mcDESPOT’ model).

(55) Methods

(56) FIG. 12 illustrates the three-pool configuration, including a bound-pool to account for MT-effects (24). Here, Bloch-McConnell equations are used to model the evolution of magnetisation for such a system and calculate steady-state solutions independently for SPGR and bSSFP. A mcDESPOT model is then fit to three-pool (ground-truth) signals, simulated using either controlled (i.e. the same W regardless of FA) or uncontrolled saturation methods.

(57) In more detail, FIG. 12 shows a three- and a two-pool model, where alternative water-pool exchange pathways are highlighted and chemical equilibrium is assumed for the three-pool model. Here, F represents a fast-relaxing myelin water pool, S is a slow-relaxing free intra/extracellular water pool and B is a bound or macromolecular pool. The aim is to see whether a three-pool system (labelled ground-truth) can behave as a simpler two-pool model (labelled apparent).

(58) Comparison of the differential equations governing mcDESPOT and three-pool models suggests that the three-pool model can be fitted using a two-pool mcDESPOT model, with ‘apparent’ parameters shown in the below series of equations. Note that the assumption made in this derivation is that the bound-pool is in a steady-state.

(59) $\begin{array}{cc}{k}_{\mathrm{FS}}^{\mathrm{app}}=k_{\mathrm{FS}}+\frac{k_{\mathrm{BS}}{k}_{\mathrm{FB}}}{R_{1B}+k_{\mathrm{BF}}+k_{\mathrm{BS}}+W}=k_{\mathrm{FS}}+\Delta k_{\mathrm{FS}}& \left[4\right]\\ k_{\mathrm{SF}}^{\mathrm{app}}=k_{\mathrm{SF}}+\frac{k_{\mathrm{BF}}{k}_{\mathrm{SB}}}{R_{1B}+k_{\mathrm{BF}}+k_{\mathrm{BS}}+W}=k_{\mathrm{SF}}+\Delta k_{\mathrm{SF}}& \left[5\right]\\ T_{1F}^{\mathrm{app}}\frac{1}{R_{1F}+k_{\mathrm{FB}}-\left(\frac{k_{\mathrm{BS}}{k}_{\mathrm{FB}}-k_{\mathrm{BF}}{k}_{\mathrm{FB}}}{R_{1B}+k_{\mathrm{BF}}+k_{\mathrm{BS}}+W}\right)};T_{1S}^{\mathrm{app}}=\frac{1}{R_{1S}+k_{\mathrm{SB}}-\left(\frac{k_{\mathrm{BF}}{k}_{\mathrm{SB}}-k_{\mathrm{BS}}{k}_{\mathrm{SB}}}{R_{1B}+k_{\mathrm{BF}}+k_{\mathrm{BS}}+W}\right)}& \left[6\right]\\ M_{0F}^{\mathrm{app}}=\frac{M_{0F}{R}_{1F}+\frac{k_{\mathrm{BF}}{M}_{0B}{R}_{1B}}{R_{1B}+k_{\mathrm{BF}}+k_{\mathrm{BS}}+W}}{R_{1F}+k_{\mathrm{FB}}-\left(\frac{k_{\mathrm{BS}}{k}_{\mathrm{FB}}-k_{\mathrm{BF}}{k}_{\mathrm{FB}}}{R_{1B}+k_{\mathrm{BF}}+k_{\mathrm{BS}}+W}\right)};M_{0S}^{\mathrm{app}}=\frac{M_{0S}{R}_{1S}+\frac{k_{\mathrm{BS}}{M}_{0B}{R}_{1B}}{R_{1B}+k_{\mathrm{BF}}+k_{\mathrm{BS}}+W}}{R_{1S}+k_{\mathrm{SB}}-\left(\frac{k_{\mathrm{BF}}{k}_{\mathrm{SB}}-k_{\mathrm{BS}}{k}_{\mathrm{SB}}}{R_{1B}+k_{\mathrm{BF}}+k_{\mathrm{BS}}+W}\right)};& \left[7\right]\\ {\mathrm{MWF}}^{\mathrm{app}}=\frac{M_{\mathrm{OF}}^{\mathrm{app}}}{M_{0F}^{\mathrm{app}}+M_{0S}^{\mathrm{app}}}& \left[8\right]\end{array}$

(60) Here, T.sub.1.sup.X are longitudinal relaxation times, k.sub.XY are diffusion-driven magnetisation exchange rates and M.sub.0X represents equilibrium magnetisation corresponding to pool X.

(61) Results and Discussion

(62) FIG. 13 illustrates how the mcDESPOT model fits to noiseless uncontrolled (US) saturation and controlled saturation (CS) data. The two-pool apparent signal in the CS data corresponds to a fit provided by values calculated using the apparent expressions defined in equations [4] to [8]. A poor fit is seen for uncontrolled saturation but is significantly improved using controlled saturation. Three-pool parameters were set to: T.sub.1B=1.0 s, T.sub.1F=0.4 s, T.sub.1S=1.15 s, T.sub.2F=0.02 s, T.sub.2S=0.08 s, M.sub.0B=0.2, M.sub.0F=0.25, M.sub.0S=0.2, k.sub.FS=9 s.sup.−1, k.sub.FB=k.sub.SB=5 s.sup.−1, G=1.4×10.sup.−5 s and B.sub.1,rms=2.86 μT.

(63) When saturation is uncontrolled, a mcDESPOT model fits poorly (NRMSE=6.4%) to simulated three-pool data, particularly for SPGR, as shown in FIG. 13(a). This results in inaccurate parameter estimation due to the dependence of each apparent parameter on RF-power. In contrast, the same model fits very well (NRMSE=0.03%) for simulated controlled saturation data, as shown in FIG. 13(b). The signal predicted using the mcDESPOT model with the apparent parameter values in equations [4] to [8] also fits very well (NRMSE=0.25%), although not perfectly because the bound-pool steady-state assumption is an approximation. Using CSMT, a three-pool system behaves as a two-pool model, characterised by the parameters in equations [4] to [8]; model dimensionality is reduced without explicitly modelling a bound-pool, as performed previously (24).

(64) Equations [4] to [8] indicate that given no direct exchange between MR-visible pools, an apparent exchange (Δk.sub.FS) remains that is solely mediated by the bound-pool; these additional exchange pathways are highlighted in FIG. 12. This implies that the exchange rates observed using mcDESPOT could reflect exchange mediated purely by MT. Δk.sub.FS increases almost linearly with k.sub.B but decreases for larger B.sub.1,rms, as magnetisation entering the bound-pool is lost through saturation.

(65) FIGS. 14 and 15 use the derived parameter expressions to investigate how mcDESPOT fitting would be influenced by the presence of a bound-pool, assuming k.sub.FS=0 and k.sub.B=k.sub.BF=k.sub.BS. FIG. 14 shows the dependence of apparent MWF on ground-truth MWF (modelled as a fraction of (a) total magnetisation or (b) MR-visible magnetisation) for different M.sub.0B and pulse amplitudes. For (a) and (b), B.sub.1,rms=2.86 μT is constant and for (c), M.sub.0B=0.2 is constant. FIG. 15 shows the dependence of each pool longitudinal relaxation time on pulse amplitude. For both FIGS. 14 and 15, all other parameters are as for FIG. 13.

(66) FIG. 14 suggests that the apparent MWF, as described by equations [4] to [8], is not the same as the true MWF, defined as

(67) $\frac{M_{0F}}{M_{0F}+M_{0S}},$
but that the relationship is monotonic and relatively insensitive to changes in bound-pool fraction. It also consistently overestimates MWF, as has been observed previously. However, FIG. 14(c) shows that MWF.sup.app is strongly influenced by RF-power level, with lower W leading to a closer relationship to the ground-truth.

(68) FIG. 15 demonstrates that higher B.sub.1,rms leads to reduced apparent longitudinal relaxation times, as has been reported before (25). This has clear implications for the use of T.sub.1 as a quantitative tissue parameter which must therefore be reported with the corresponding B.sub.1,rms with which it was obtained.

CONCLUSIONS

(69) In conclusion, a three-pool system can be modelled using two-pools and derived apparent parameter expressions in [4] to [8]. MT-effects can lead to bias in estimated parameter values and CSMT is needed to obtain a good fit. As such, the ability to achieve CSMT conditions can also improve the reliability of the MWF estimation.

(70) Pulse Rate Dependent Controlled Saturation MT

(71) In relaxometry, the above described ability to control the saturation induced makes it possible to achieve measurements where the amount of saturation remains constant for all images necessary to measure the relaxation times M0, T1 and T2. For fast sequences, where consecutive pulses are applied with times intervals shorter then T1, the saturation can be parameterized by the root mean square amplitude of an arbitrary RF pulse, B.sub.1.sup.rms, the energy of which is spread over a repetition period TR, as follows:

(72) $\begin{array}{cc}.Math.\stackrel{\_}{W}.Math.={\pi \left(\gamma B_1^{\mathrm{rms}}\right)}^{2}G\left(\Delta \right)=.Math.W.Math.\frac{T_{\mathrm{RF}}}{\mathrm{TR}}& \left[9\right]\end{array}$

(73) Typically, different flip angles used to measure MR images induce different instant saturations <W>. The multi-band pulses described above allow <W> to be chosen independent of the desired flip angle, with the parameters of the pulse being calculated based on a target flip angle.

(74) An alternative approach to control the saturation is to allow the total RF energy, <W>, to vary for different flip angles and adjust both T.sub.RF and/or TR in order to obtain the desired value of <W>. As an example, <W> can be doubled in one sequence compared to another, and TR can also be doubled in order to maintain a constant average saturation <W>.

(75) This approach allows CSMT to be achieved using an MR scanner without any software modification. As such, it will be appreciated that any suitable MR scanning system may be used, including but not limited to the system described with reference to FIG. 2. For example, the CSMT calculation program 151 may be configured to calculate the timing parameters of the RF pulse, that is, the repetition period or pulse duration, for each defined flip angle such that a constant average saturation is maintained, and instruct the RF system 160 to transmit the RF pulses to the RF coil 173 according to those parameters. Alternatively, the computer system 100 may comprise a pulse timing program (not shown) configured to define the timing parameters of each RF pulse, and instruct the RF system 160 to transmit the RF pulses to the RF coil 173 according to those parameters. The MR scanner 170 will then scan the object as described above to generate T1 and T2 maps of the scanned object to be displayed on the visual display device 141.

(76) CSMT to Achieve MT Weighting

(77) Conventional MT-weighting typically adds dedicated off-resonance pulses to saturate the background pool prior to imaging. An image of an object, such as a brain, is then obtained with this saturation pulse, S.sub.MT. This is known commonly as MT-weighting. A corresponding image of the same objection is also obtained without the saturation pulse, S.sub.0, in order to generate what is known as an MT-ratio image, (S.sub.0−S.sub.MT)/S.sub.0. The consequent ratio image is known to be extremely sensitive to myelination and has typically been use to access multiple-sclerosis populations.

(78) The RF-pulses described herein can be used to generate these type of contrasts using steady-state sequences such as (and not exclusively) Spoiled Gradient Recalled Echo (SPGR) or balanced Steady State Free Precession (bSSFP), which were previously inaccessible.

(79) Inhomogeneous MT (ihMT) is a further extension of MT-weighting where MT-weighted images are obtained using dedicated off-resonance pulses at positive frequency-offsets, negative frequency-offsets and simultaneous positive and negative frequency-offsets. These MT-weighted images are then used to generate an MT-ratio image relative to an image with no dedicated off-resonance excitation. The obtained ratio images have been shown to be sensitive to MT effects due dipolar interactions which are known to be is specific to lamellar structures such as the ones found in myelin. ihMT has the promise to be a myelin specific biomarker which can be to identify demyelination diseases such as multiple-sclerosis.

(80) The RF-pulses described herein can be used to generate this type of contrasts using fast steady-state sequences such as (and not exclusively) SPGR and bSSFP, which were previously not possible.

(81) CSMT to Obtain Relaxometry in the Limit of B.sub.1.sup.rms=0:

(82) A consequence of the above method is that the measured M0 and T1 values are now direct function of the power, B.sub.1.sup.rms, employed. However, it is not always possible to achieve a set B.sub.1.sup.rms across all equipment. Furthermore, the interference of the measured objects with the RF field is expected to induce spatial variations within the measured object, in other words, the same tissue will have different M0/T1 values depending on whether that tissue is located in the centre or the periphery of the imaged object. For example, M0/T1 measurements for a particular type of brain tissue at the centre of the brain may be different from those measured for the same type of brain tissue at the edges of the brain.

(83) To overcome this, a theoretical limit of using the above CSMT when the RF power is zero, B.sub.1.sup.rms=0, was explored, which will allow M0/T1 maps to be obtained that have no dependency on the particular B.sub.1.sup.rms chosen. To do this, measurements were made with a finite B.sub.1.sup.rms, and then extrapolated to B.sub.1.sup.rms=0. In this limit, both the apparent recovery rate and the equilibrium magnetization can be linearly approximated in the form:
T.sub.1.sup.CSMT≈T.sub.1.sup.0+T.sub.1.sup.slope(γB.sub.1.sup.rms).sup.2  [10]
and
M.sub.0.sup.CSMT≈M.sub.0.sup.0+M.sub.0.sup.slope(γB.sub.1.sup.rms).sup.2  [11]

(84) In doing so, it is possible to obtain relaxation maps which are independent of B.sub.1.sup.rms. This removes the issue of spatial variation, and enables the method described herein to be applied to any MR scanner.

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