METHOD AND DEVICE FOR MAGNETIC RESONANCE IMAGING

专利摘要:
The present invention relates to an MRI device (1), comprising: means (2) for applying a main magnetic field BO along a Z axis to a sample area (8); means (3) for transmitting a magnetic field gradient and means (4) for transmitting a radio frequency pulse, and control means (5) arranged to control the means for transmitting a magnetic field gradient and means for transmitting a radiofrequency pulse. The control means are programmed to perform at least one set of repeated applications, on the sample area, of a sequence comprising: a radiofrequency pulse possibly of amplitude and / or variable phase at each repetition; and after the radiofrequency pulse, a spatial gradient of the component along the Z axis of the magnetic field. The control means are programmed so that, during repeated applications of the radiofrequency pulse and the spatial magnetic field gradient of the sequence of the same set: the radiofrequency pulse follows, between its different repeated applications, a periodic sequence (preferably not constant) for its amplitude and for a sequence a + 1 = vn + 1 - vn; and each repeated application of the magnetic field spatial gradient of the sequence a, in a so-called coding spatial direction, a temporal integral equal to non-zero A and identical for each gradient application of this set. The invention also relates to the method implemented by this device.
公开号:FR3036189A1
申请号:FR1554358
申请日:2015-05-13
公开日:2016-11-18
发明作者:Rochefort Ludovic Marie Xavier De
申请人:Centre National de la Recherche Scientifique CNRS；Universite Paris Sud Paris 11；
IPC主号:

专利说明:

[0001] FIELD OF THE INVENTION The present invention relates to a method of magnetic resonance imaging (MRI). It also relates to a device implementing this method. Such a method or device may, for example, preferably enable a user to generate and exploit co-located images of the same spatial resolution, with the same echo (TE) and repetition time (TR) for the nuclear magnetization, the longitudinal (Ti) and transverse (T2) relaxation times, the diffusion coefficient (D), the amplitude of the radiofrequency field (B1) and the inhomogeneities of the main magnetic field BO. STATE OF THE PRIOR ART MRI is a clinical and preclinical imaging modality routinely used in radiological medical diagnosis or for evaluation of animal models. Its non-invasive appearance and the multiple contrasts available make it indispensable in the evaluation of many diseases. A typical MRI scan contains a protocol for acquiring multiple imaging sequences each with a different purpose. The so-called 'proton density' sequences will provide information on the amount of free water in the tissue. The so-called 'T-weighted' sequences are generally used for anatomical evaluation because they generate a good contrast between biological tissues. The 'T1-weighted' sequences also serve to visualize contrast agents that can be injected into angiography or for tumor characterization. The so-called `T2-weighted 'sequences generally have the property of making it possible to clearly distinguish the fluid contents and inform for example on the presence of edemas. Again, T2 contrast agents can be used to modulate T2 weighting for some applications. Diffusion, which also influences the contrast of the images generated with specific so-called 'diffusion weighted' sequences, is also used to push tissue characterization, for example to distinguish viable areas from necrotic areas in tumors, a distinction not always possible with other types of weighting, or to make brain tract tractography based on the preferred direction of water diffusion. Depending on the disease studied and the anatomical area, several sequences are applied during an examination. These are applied sequentially, which already requires a parameterization time electroradiology manipulators to adapt each sequence to the area studied. For constraints of acquisition time, weighting type and location, the various information are generally not acquired with the same spatial resolutions, do not cover the same fields of view and may even suffer from different spatial deformations depending in particular echo times and 3036189 2 different acquisition bandwidths. For example, the need in some cases for rectification of posterior images or image registration techniques to partially compensate for these effects. These aspects combine to make the MRI limited to an interpretation based solely on visual comparisons, or to introduce bias or inaccuracy resulting from the correction algorithms. To improve the diagnosis, there is a need to co-locate exactly the same information on the same imaging voxels. Moreover, the choice of the sequences applied and the parameterization of the sequences belong to each center of radiology, and the implementations of the sequences can vary between the constructors. There is no sequence standard and associated parameters applicable in all cases. These elements make the multi-centric comparison of the imaging results difficult and slow down, if not prevent, consensus on the sequences and their parameterization. To make reliable the diagnosis, the direct quantification of physical parameters such as nuclear magnetization, Ti and T2, and diffusion coefficient is a possibility to standardize the imaging results. Again, to quantify the different parameters Ti, T2 and the diffusion coefficient, multiple sequences exist, each adapted to the parameter to be quantized. For example, the inversion-recovery sequence with several inversion times for quantizing T 1, the spin echo sequence with several spin echo times for quantizing T2, the weighted spin echo sequence diffusion to quantify the diffusion coefficient. These different sensitizing patterns can then be combined with different sequences allowing location with all the aforementioned disadvantages of spatial deformation between acquisitions, of different field of view or area covered, reducing the possibility of coupling voxel to voxel extracted parameters. A fast standard acquisition sequence is based on fast gradient echo. This imaging sequence consists in repeating all the TRs a pattern including a fixed amplitude excitation, possibly combined with a so-called 'selection' gradient to perform a spatial selection, followed by 25 imaging gradients (reading and coding phase). Multiple variants of this sequence have been proposed. To synthesize the differences between the variants, note the following elements: the total compensation of the gradient areas between the repetitions (so-called balanced sequence), or on the contrary the non-compensation of this gradient area (so-called unbalanced sequence). This latter non-balanced variant creates different coherency orders that may possibly be exploited. An order of consistency is noted k. It is an integer that corresponds to the order of the discrete Fourier series that can be used to describe the configuration states of the magnetization, as proposed and used in the art.
[0002] 3036189 3 The particular cycling of phase 0, from the radiofrequency pulse to the repetition n without changing its amplitude with 0n + 1 = On + (n + 1) 4. The variants work either with a fixed phase according to the repetitions (4 = 0), or with a quadratic cycle of the phase (0), equivalent to a constant increment A and not zero from one repetition to another. A is of course defined modulo 27r 5 The measurement between the pulses of 1 or more echoes, in particular corresponding to the orders of coherence of phase (k = 0, in general the only acquired, and / or k = -1 and / or k = 1 which can be also) The addition or not of additional gradients between the pulses to sensitize differently to the diffusion The acquisition of the signal during the transient phase or during the stationary phase For the transient phase, the magnetization The starting material may be the thermal equilibrium state or a prepared state using preparation motifs and the information used for the analysis is the signal variation as a function of the repetitions. The stationary acquisition is, on the contrary, based on the acquisition of a dynamic equilibrium reached after several repetitions.
[0003] Recall here that the magnetization is decomposable into a component aligned with the main magnetic field BO, called the longitudinal component, and a transverse component, the latter being detectable by induction in a radio frequency detector and can be modulated spatially with the gradients . Recall that the effect of a radiofrequency pulse applied to resonance and amplitude B1 (t), phase phi (relative to an internal reference of the RF synthesizers) and applied for a duration T is to switch the magnetization of An angle α with BO, the angle being proportional to the integral of the RF field during the duration T, the axis of rotation is it phase shifted from 0 = phi + zr / 2 radians with respect to the reference rotating at resonance. Recall that the longitudinal and transverse components relax with a characteristic time T1 and T2, respectively, time depending on the local environment and possibly influenced by the transfer of magnetization.
[0004] Finally, let us recall that the atoms or molecules carrying the nuclear magnetization diffuse over time, which is macroscopically described by the Bloch-Torrey equations. An important complexity in the fast sequences (with in general TR <T2), is that the transverse component which is out of phase with the gradients and with the inhomogeneities of field is "recycled" by the following excitation transferring a part in longitudinal and vice versa. This phase shift remaining between two pulses, combined with the non-suppression of the magnetization by purely dispersive relaxation and diffusion phenomena, is at the origin of different states k as mentioned previously. It is then difficult to describe the magnetization by including the effects of relaxation, diffusion, angle, and the person skilled in the art also often evokes the impossibility of describing the effects or limitation under certain restrictive conditions. of validity or even confusion over the creation of coherence states when the phase is modulated or finally the negation of diffusion effects. The object of the present invention is to solve at least one of the following problems of the state of the art: to propose a new type of sequence or new equilibrium state forms, and / or to facilitate a determination, by Ernst angle, the effect of the radiofrequency pulse producing the flip-flop angle, and / or almost simultaneously determining several parameters among a nuclear magnetization, a flip-flop angle of the magnetization, a coefficient diffusion, a rate or longitudinal relaxation time R1 or T1, and a rate or relaxation time R2 or T2 of the same point of space, and / or improve the consideration of diffusion. SUMMARY OF THE INVENTION This object is achieved with a magnetic resonance imaging method, comprising - (preferably continuous) application of a main magnetic field BO along a Z axis on a sample, and - at least one set of repeated applications, on the sample and according to a period TR, of a sequence, said sequence comprising: o a radio frequency pulse possibly of amplitude and / or variable phase at each repetition, and o after the pulse radiofrequency of the sequence, a spatial gradient of the component along the Z axis of the magnetic field, characterized in that, during repeated applications of the radio frequency pulse and the spatial magnetic field gradient of the sequence of the same together: - the radiofrequency pulse follows, between its different repeated applications, a periodic sequence: o for its amplitude and o for a + 1 = yn + 1 -, where n is an integer greater than or equal to where 1 represents the number of the repetition of the sequence for this set, and where an IF is a sequence of relative integers which makes it possible to define the sequence yn at an arbitrary constant near y1 such that rp = vx A and (p. , = 9, -On_i with A which is a constant real number for all the repeated applications of the sequence of this set and cp, which is the increment between the on-phase phase of the radiofrequency pulse at its nth repetition in this set and the On 1 phase of the radiofrequency pulse at its (n-1) 1st repetition in this set, with 00 an arbitrary value, and - each repeated application of the spatial magnetic field gradient of the sequence a, according to a 5 said gradient direction of said coding direction for each gradient application of this set, a temporal integral equal to A non-zero and identical for each gradient application of this set. The method according to the invention preferably further comprises an acquisition, during at least one of the repetitions of the sequence, of at least one nuclear magnetic resonance signal.
[0005] During repeated applications of the radiofrequency pulse and the spatial magnetic field gradient of the sequence of the same set, the sequence un + 1 = vn + 1-vn may be a non-constant periodic sequence. During repeated applications of the radiofrequency pulse and the spatial magnetic field gradient of the sequence of the same set, the amplitude of the radio frequency pulse can follow a non-constant periodic sequence. The nuclear magnetic resonance signal is preferably acquired at least one dynamic equilibrium state of the magnetization of the sample. During repeated applications of the radiofrequency pulse and the spatial magnetic field gradient of the sequence of the same set: the sequence a + 1 = vn + 1-vn may be a non-constant periodic sequence, and / or the amplitude of the radiofrequency pulse can follow a non-constant periodic sequence, so as to obtain different equilibrium states of the magnetization of the sample interleaved within this set respectively for different periodic values of the sequence a + 1 = vn + 1 -v and / or the amplitude of the radio frequency pulse, and the nuclear magnetic resonance signal is preferably acquired at these different interleaved equilibrium states. Several sets may be sequentially issued, with: - A whose value differs between the different sets, and / or - the amplitude of the radio frequency pulse which follows a periodic sequence which differs between the different sets, so as to obtain different sequential sample magnetization equilibrium states for different values of A and / or the amplitude of which at least one equilibrium state per set, and the nuclear magnetic resonance signal is preferably acquired at these different sequential equilibrium states. The method according to the invention may comprise: an acquisition of a signal for two equilibrium states corresponding to two identical amplitudes of the radio frequency pulse but two different ones, a comparison of the signal for these two equilibrium states; and - a deduction, from this comparison, of whether the amplitude of the radio frequency pulse produces an effective flip-flop angle greater than or smaller than or equal to the Ernst angle for the sample; In this case, one of the two different 4s is preferably zero. The method according to the invention may comprise: an acquisition of a signal for equilibrium states corresponding to different amplitudes of the radio frequency pulse and / or of the different 4 and / or different values of the sequence a + 1 = vn + 1 - periodic constant or not, and 15 - for at least one point in the sample, a determination of at least one datum (preferably at least three, preferably all) among a nuclear magnetization, a rocking angle magnetization, a scattering coefficient, a longitudinal relaxation rate or time R1 or Ti, and a transverse relaxation rate or time R2 or T2, from the acquired signal for these equilibrium states; in this case: the determination being preferably carried out, either by comparison with a pre-calculated dictionary or by iterative estimation, according to a minimization of a norm of the difference between the acquired signal expressed in complex form with a real part and an imaginary part and a model of the signal expressed in complex form with a real part and an imaginary part. Minimization may include a least squares minimization algorithm, preferably using the Gauss-Newton algorithm applied to non-linear problems; and / or the method according to the invention may comprise an acquisition of a signal for equilibrium states corresponding to different 4, including: o several points for an absolute value of 4 between 4 = 0 ° inclusive and 4 = 32 ° includes 30 modulo 360 °, and / or o several points for an absolute value of 4 between 4 = 164 ° inclusive and 4 = 196 ° inclusive modulo 360 °, and / or o several points for an absolute value of 4 between 4 = 112 ° inclusive and 4 = 128 ° inclusive modulo 360 °, and / or 3036189 7 o several points, for an absolute value of A among 45 °, 60 °, 72 °, 90 °, and 144 ° modulo 360 °; and / or the amplitude of the radiofrequency pulse preferably always corresponds to a flip-flop angle of the magnetization: greater than the Ernst angle for a longitudinal relaxation time T1 equal to 2000 milliseconds, and / or o less than or equal to 90 °; and / or the determination may comprise a condition of spatial continuity of each given datum among the nuclear magnetization, the rocking angle of the magnetization, the diffusion coefficient, the rate or longitudinal relaxation time R1 or T1, and the rate or transverse relaxation time R2 or T2 between different points of the sample. Several sets can be sequentially issued, with: the coding direction which differs between different sets, and / or the value of A which differs between different sets, and / or the shape of the magnetic field gradient in the direction of coding that differs between different sets; in this case, the method according to the invention preferably further comprises: - a quantification of a diffusion coefficient in the sample or - a determination of a preferred direction of diffusion in the sample or - a weighting of the diffusion in the sample, by exploiting the difference of A and / or direction of coding and / or of the shape of the gradient between the different sets. According to yet another aspect of the invention, there is provided a magnetic resonance imaging device, comprising: - means for applying, preferably in a continuous manner, a main magnetic field BO along a Z axis over an area of sample, and means for transmitting a magnetic field gradient and means for transmitting a radio frequency pulse, and control means arranged to control the means for transmitting a magnetic field gradient and means for transmitting a radio frequency pulse, the control means being arranged for or programmed to perform at least one set of repeated applications, on the sample area and according to a period TR, of a sequence, said sequence comprising: a radiofrequency pulse optionally of amplitude and / or phase at each repetition, and o after the radiofrequency pulse of the sequence, a spatial gradient of the in the Z-axis of the magnetic field, characterized in that the control means are arranged for or programmed so that, during repeated applications of the radio frequency pulse and the magnetic field spatial gradient of the sequence of a same set: the radiofrequency pulse follows, between its different repeated applications, a periodic sequence: 10 o for its amplitude and o for un_, 1 = v '_, 1-v', where n is an integer greater than or equal to 1 representing the number of the repetition of the sequence for this set, and where an IF is a sequence of relative integers which makes it possible to define the sequence v 'at an arbitrary constant near v1 such that yin = x A and pn = 9, - 9, with A which is a real number constant for all the repeated applications of the sequence of this set and cp, which is the increment between the phase 0, of the radiofrequency pulse at its nth repetition in this set and phase 0, 1 of the radio pulse frequency at its (n-1) 1st repeat in this set, with an arbitrary value, and each repeated application of the spatial magnetic field gradient of the sequence a, in a gradient spatial direction called the same coding direction for each application gradient of this set, a temporal integral equal to A non-zero and identical for each gradient application of this set. The device according to the invention preferably further comprises means for acquiring, during at least one of the repetitions of the sequence, at least one nuclear magnetic resonance signal. The control means may be arranged for or programmed so that, during repeated applications of the radio frequency pulse and the spatial magnetic field gradient of the sequence of the same set, the sequence un_, 1 = v '_, 1 -v 'be a non-constant periodic sequence. The control means may be arranged for or programmed so that, during repeated applications of the radio frequency pulse and the spatial magnetic field gradient of the sequence of the same set, the amplitude of the radio frequency pulse follows a periodical sequence not constant.
[0006] The control means are furthermore preferably arranged for or programmed to control the acquisition means so as to acquire the nuclear magnetic resonance signal in at least one state of dynamic equilibrium of the magnetization in the zone of sample. The control means may be arranged for or programmed so that, during the repeated applications of the radio frequency pulse and the spatial magnetic field gradient of the sequence of the same set: the sequence a + 1 = vn + 1 or a non-constant periodic sequence, and / or the amplitude of the radiofrequency pulse follows a non-constant periodic sequence, so as to obtain different interlace equilibrium states of the magnetization in the sample area at 10 within this set respectively for different periodic values of the sequence a + 1 = vn + 1-vn and / or the amplitude of the radio frequency pulse, the control means being furthermore preferably arranged for or programmed to control the acquisition means so as to acquire the nuclear magnetic resonance signal at these different interlace states of equilibrium. The control means may be arranged for or programmed to sequentially transmit several sets, with: - A whose value differs between the different sets, and / or - the amplitude of the radio frequency pulse which follows a sequence periodic state which differs between the different sets, so as to obtain different states of sequential equilibriums of the magnetization in the sample zone 20 for different values of A and / or the amplitude of which at least one equilibrium state together, the control means being preferably further arranged for or programmed to control the acquisition means so as to acquire the nuclear magnetic resonance signal at these different sequential equilibrium states. The control means can be arranged for or programmed to control the acquisition means so as to acquire a signal for two equilibrium states corresponding to two identical amplitudes of the radio frequency pulse but two different A's, the device further comprising calculating means arranged for or programmed to: - compare the signal for these two equilibrium states, and - deduce, from this comparison, whether the amplitude of the radio frequency pulse 30 produces an effective flip-flop angle more greater than or less than or equal to the Ernst angle in the sample area; in this case, one of the two different A's is preferably zero.
[0007] The control means may be arranged for or programmed to control the acquisition means so as to acquire a signal for equilibrium states corresponding to different amplitudes of the radio frequency pulse and / or of the different 4 and / or different values of the sequence a + 1 = vn + 1 - vn periodic constant or not, 5 the device preferably further comprising calculating means arranged for or programmed for, for at least one point in the sample area, determine at least one datum (preferably at least three, preferably all) among a nuclear magnetization, a magnetization flip angle, a diffusion coefficient, a longitudinal relaxation rate or time R1 or Ti, and a rate or time transverse relaxation R2 or T2, from the acquired signal for these equilibrium states; In this case: the calculation means are preferably arranged for or programmed to perform this determination, either by comparison with a pre-calculated dictionary or by iterative estimation, according to a minimization of a norm of the difference between the acquired signal; expressed in complex form with a real part and an imaginary part and a model of the signal expressed in complex form with a real part and an imaginary part. Minimization may include a least squares minimization algorithm, preferably using the Gauss-Newton algorithm applied to non-linear problems; and / or the control means can be arranged for or programmed to control the acquisition means so as to acquire a signal for equilibrium states corresponding to different ones, of which: o several points for an absolute value of 4 between 4 = 0 ° inclusive and 4 = 32 ° inclusive modulo 360 °, and / or o several points for an absolute value of 4 between 4 = 164 ° inclusive and 4 = 196 ° inclusive 25 modulo 360 °, and / or o several points for an absolute value of 4 between 4 = 112 ° inclusive and 4 = 128 ° inclusive modulo 360 °, and / or o several points, for an absolute value of 4 among 45 °, 60 °, 72 °, 90 °, and 144 ° modulo 360 °; and / or the control means are preferably arranged for or programmed so that the amplitude of the radio frequency pulse always corresponds to a flip-flop angle of the magnetization: o greater than the Ernst angle for a time of T1 longitudinal relaxation equal to 2000 milliseconds, and / or less than or equal to 90 °, and / or - the calculation means can be arranged for or programmed so that the determination comprises a condition of spatial continuity of each given data among the nuclear magnetization, the magnetization flip-flop angle, the scattering coefficient, the longitudinal relaxation rate or time R1 or Ti, and the transverse relaxation rate or time R2 or T2 between different points in the region of the magnetization zone; 'sample. The control means can be arranged for or programmed to sequentially transmit several sets, so that: the coding direction differs between different sets, and / or the value of A differs between different sets, and / or the form the magnetic field gradient in the coding direction differs between different sets; in this case, the device according to the invention may further comprise calculation means arranged for or programmed to: - quantify a diffusion coefficient in the sample area or - determine a preferred direction of diffusion in the area of sample or - weight diffusion in the sample area, by exploiting the difference of A and / or direction of coding and / or shape of the gradient between the different sets.
[0008] DESCRIPTION OF THE FIGURES AND EMBODIMENTS Other advantages and particularities of the invention will appear on reading the detailed description of implementations and non-limiting embodiments, and the following appended drawings: FIG. schematically, for a first embodiment of the method according to the invention, the sequence of repeated RF pulses all the TR (n is the number of the repetition) modulated in amplitude (an) and phase (0 u). The longitudinal (Pu) and transverse (Qn) components of the magnetization after the number n-1 pulse evolve to P u + and Q u + just before the number n pulse. The shape of the gradient (G) is represented here in the direction of the reading which leaves a nonzero gradient area between each repetition. FIG. 2 illustrates a summary of different operators and their respective action represented graphically: a) For a polynomial denoted U (a) which describes one of the longitudinal or transverse components of the magnetization in the form of configuration states of which the detail is described 3036189 12 farther, the index j is represented along horizontal lines along Y-1, different index k being illustrated by different vertically superimposed lines along Z-1. b) The convolution with the weighting polynomials W, or W2 is equivalent to a term-to-term multiplication of the coefficients according to 71 5 c) The multiplication by Z-1 shifts the coefficients by one notch in this direction, d) the operation The conjugation corresponds to a central symmetry e) The convolution with S_, leans the different lines along Y-1 and Z-1 by a coefficient which varies linearly with k. Its action is represented on a limited range and, depending on the discretization according to Y-1, the folding from one side to the other must be implemented. The iterative calculation is then performed by combining these basic operations. FIG. 3 is a representation of the transverse component of the magnetization Q 'in terms of coefficients according to configuration states, for a = 30 °, TR / T1 = TR / T2 = 0.05 and Ed = 0.995 (a, corresponds to at n = 1 with only a nonzero coefficient at the center), n = 4 (b); n = 8 (c), n = 16 (d), stationary state (e). Gradually, the plane of size N, 180 (index j, according to Y-1), Nz = 128 (index k, according to Z-1) is filled with non-zero coefficients which tend towards the steady state. the steady state without diffusion (f) has many more non-zero coefficients illustrating the significant attenuating effects of diffusion (in comparison with e). FIG. 4 illustrates a simulation result of the influence of T2 and of the diffusion on the transversal magnetization at the stationary state for the order k = 0 and for A ranging between -180 ° and 180 ° with a following a = 1 constant as well as a constant amplitude. The transverse magnetization is represented after a Fourier transform according to Y-1: the real part (line referenced 41), the imaginary part (line referenced 42) and the absolute value (line referenced 43) for a = 30 °, TRITi = 0.05 and Ny = 720. The Ernst equilibrium is drawn using the dashed line. Several cases are presented: the magnetization obtained without diffusion and with TRIT2 = 0.05 (a), without diffusion and with TRIT2 = 0.25 (b), with a weak diffusion (Ed = 0.995, which corresponds to b = 2.39 s mm-2 if D = 2.1 10-9 m2.s-1) and TRIT2 = 0.05 (c), with significant scattering (Ed = 0.95, which corresponds to b = 24.4 s.mm-2 if D = 2.1 10-9 m2s -i) and TRIT2 = 0.05 (d). Transverse relaxation T2 and diffusion both tend to smooth the magnetization profile as a function of A, which limits the formation of stimulated echoes. The steady state takes values smaller and larger than Ernst's equilibrium which is never exactly reached. FIG. 5 illustrates a simulation result of the effects of tilt angle on stationary magnetization for k = 0 with quadratic phase cycling (following a = 1 constant, constant amplitude). The transverse magnetization Q0 (a, c, e) is represented after having carried out a Fourier transform according to Y-1: the real part (line referenced 51), the imaginary part (line referenced 52) and the absolute value (referenced line 53) for TRITi = TRIT2 = 0.05, Ed = 0.995 and 3036189 13 Ny = 720. The Ernst equilibrium is represented using the dashed line. From top to bottom are presented the results for different tilt angles: for a = 9 ° (a), for Ernst angle a = 18 ° (c), and for a = 75 ° (e). The right column represents the 3D longitudinal and transverse components (b, d, f) for the angles corresponding to (a, c, e), respectively. The magnetization is contained in a plane which passes through the equilibrium of Ernst and which is oriented with an effective angle aeff with respect to Bo and such that tan (aeff) = (Ei-c) / s. When A varies, the magnetization rotates in this plane around Ernst's equilibrium. FIG. 6 illustrates a stationary state simulation for k = 0. The transverse magnetization Q0 (a, d, e) is presented after having carried out a Fourier transform according to Y-1: real part (line 10 referenced 61), imaginary part (line referenced 62) and absolute value (line referenced 63) for TR / T1 = TR / T2 = 0.05, Ed = 0.995 and Ny = 720. The standard case with a constant series (a = 75 ° and constant apparent frequency offset un = 1) (a) is given for reference. The application of a constant angle of amplitude (a = 75 °) with an alternation of the apparent frequency offset with a (+1, -1) (b) which creates complex conjugate stationary states (a single state presented here) with relatively smooth dependence on A. For alternate amplitudes (75 °, 37.5 °) and an apparent offset of constant frequency a = 1, interleaved equilibria (c after 75 °, after 37.5 °) with dependence complex in function of A. - Figure 7 illustrates experimental results obtained after fitting the average signals on the tubes. The signals have been normalized by the adjusted magnetization value M, and are represented in the complex plane. 'Real' and 'Imag' represent real and imaginary parts, respectively. The point with the largest real part corresponds to A = 0 °. The points are presented every 2 ° increments according to the gray dotted line. The measures (circles and triangles) are comparable to the results of the calculation (lines and crosses). For an angle of 45 ° with sequence 1 for the Gd tube at 1.25 mM (a, best fit with T1 / T2 = 180/157 ms, Ed = 0.99669 or D = 2.29 10-9 mes-1, a = 44.01 °), and for the ION tube at 160 μM (b, best fit with T1 / T2 = 444/75 ms, Ed = 0.99671 or D = 2.26 10-9 mes-1, a = 44.23 °). The stationary states interleaved for 45 ° (dotted line) / 22.5 ° (solid line) obtained with sequence 2 for the Gd tube at 1.25 mM (c, best fit with T1 / T2 = 177/156 ms, Ed = 0.9996 or D = 2.19 10-9 mes-1, a = 44.64 °), and for the ION tube at 160 μM (better fit with T1 / T2 = 518/73 ms, Ed = 0.9997 or D = 1.67). 9 mg-1, a = 44.09 °). The measured steady states are very well modeled by the simulations and the adjusted parameters correspond to the expected values. FIG. 8 illustrates different multiparametric images: maps of M (a), tilt angle (b in °), R1 (c in si), R2 (d in s-1) and diffusion coefficient ( e in 10-9m2s-1) obtained for 45 ° with the sequence 1 treated with the proposed inverse problem. Figure 9 illustrates the estimated mean longitudinal and transversal relaxivities on the tubes for Gd (a) and ION (b) are shown with their associated standard deviation. The molar relaxivities are estimated by adjusting the relaxivities by a straight line as a function of the concentration (equation given on the graph, C corresponds to the concentration in mM). The relaxivities are linear in function of the concentration demonstrating a reliable measure of R1 and R2 over a wide range of values. - Figure 10 is a schematic perspective view of a first embodiment of the device according to the invention. FIG. 11 illustrates the sequence containing the repeated RF pulse every TR with a magnetic field gradient area A remaining between repetitions in a coding direction and inserted into a gradient echo sequence. The logical axes of imaging gradients Gx for reading, Gy for a first direction of phase coding and Gz for the selection of section and any additional phase coding are shown. All these imaging gradients have zero area between each repetition. The coding direction may be applied in any Gx, Gy or Gz direction as well as in an oblique direction, which naturally leads to optimization of the resulting combination of gradients. Different variants are represented to illustrate the type of acquisition possible: the variant a consists of the acquisition of the order only 0; variant b consists of the acquisition of the order k alone; variant c consists of the acquisition of 3 orders during the same repetition.
[0009] These embodiments being in no way limiting, it will be possible to consider variants of the invention comprising only a selection of characteristics described or illustrated subsequently isolated from the other characteristics described or illustrated (even if this selection is isolated within a sentence including these other features), if this selection of features is sufficient to confer a technical advantage or to differentiate the invention from the state of the prior art.
[0010] This selection comprises at least one preferably functional feature without structural details, and / or with only a portion of the structural details if that portion alone is sufficient to confer a technical advantage or to differentiate the invention from the state of the invention. prior art. Subsequently, the reference numbers in parentheses will be bibliographic reference numbers listed at the end of the present description, and the reference numbers without parentheses will be numerical reference numbers of the figures.
[0011] In spite of the relatively simple dependence on T1 and the flip angle of the applicable Ernst equilibrium when the transverse magnetization is completely eliminated between two identical radio frequency (RF) pulses (1), the development of D Early imaging in the early days of MRI soon showed that it was essential to take into account the recycling of the transverse component of magnetization after repeated excitations. Steady-state free precession (SSFP) sequences have been proposed as an effective way of combining good signal-to-noise ratio (SNR) and mixed contrast in proton density. , T1 and T2 (2). Rapid RF phase scrambling (RF spoiling), which uses quadratic cycling of the excitation phase on the other combined with a nonzero gradient area between the 10 pulses, has been proposed to effectively limit the coherence formation of the transverse magnetization (3-5). Theoretical and practical descriptions were then introduced to analyze the action of repeated pulses on the magnetization. These tools are based on the formalism of the configuration states applied to the longitudinal and transverse components of the magnetization which are then decomposed in discrete Fourier series, as is the case in the extended phase graph (6-9), or Again through the polynomial decomposition which has made it possible to relate RF pulse design to digital filtering (10,11). Due to the mixture of the longitudinal and transverse components, whether on the transient (11-14) or steady state (SSFP), the magnetization is complexly dependent on the physical parameters (such as relaxation times and diffusion coefficient) and sequence parameters (flip-flop angle, amplitudes and phases of the RF pulses, repetition time and repetition index, shape and total area of the gradients). A wide range of sensitization can be obtained and parameters extracted from this type of repeated pulse sequences. In particular, the steady state has been largely exploited. On the one hand, considering a perfect interference (obtained approximately with quadratic phase cycling with increments of 117 °, or other values (4, 15, 16)), sequential acquisitions with different angles (variable flip angles) is used to map T1 and / or the flip angle (15-21). On the other hand, without phase scrambling, multi-state acquisitions of k (22) configurations can be used to characterize transverse relaxation (23-26). Concerning diffusion sensitivity, which is, like transverse relaxation, an irreversible mechanism that limits the formation of stimulated echoes, its influence on stationary equilibrium SSFP without phase cycling has been treated with the help of the formalism configuration states in spectroscopy (27), before being applied to imaging (28-31) until the use of multiple configuration states k to map the diffusion coefficient (24,32). Between the extreme cases of the absence of interference without phase cycling and perfect interference eliminating all the transverse magnetization, the partial interference 3036189 16 using a quadratic phase increment of low value around 0 ° a has been proposed to quantify transverse relaxation (33-35). It is proposed, in the context of the present description of certain embodiments and variants according to the invention, to unify these different approaches by extending the formalism of the configuration states to RF phase cycling. Using this extended formalism, an algorithm is proposed to compute the magnetization after repeated pulses of any amplitude and phase including relaxation and diffusion effects. Within this framework of description, the components associated with each configuration state are real numbers and the action of the RF pulses (amplitude and phase modulated) is reduced to digital linear filtering, linear combinations and offset operations. indices, operations that have a simple graphical representation. It is deduced that any periodic series of amplitude and apparent frequency offset makes it possible to obtain interleaved stationary equilibriums, which opens the possibility of extending the sensitization capabilities of the signal to the physical and sequence parameters. For the particular case of constant angle amplitude with quadratic RF phase cycling (equivalent to a constant apparent frequency offset), the SSFP signal can be calculated taking relaxation and scattering into account very efficiently. Finally, based on the acquisition of multiple series of amplitude and phase cycling scheme, an inverse problem is proposed to reconstruct the maps of the underlying parameters. The theory, practical implementation and experimental proof of concept on a clinical apparatus is given introducing new methods for multiparameter mapping based on acquisitions with fast sequences including repeated RF pulses. We will then describe the magnetization after the repeated application of amplitude and phase modulated radiofrequency (RF) pulses interleaved with a constant gradient area, and then derive a generic inverse problem for multiparametric imaging allowing Quantitation of nuclear magnetization, flip angle, longitudinal and transverse relaxation rates, and diffusion coefficient. As will be seen later, the formalism of the configuration states, which takes into account the phase shift due to the gradient (through orders k), is extended in the context of the present description of certain embodiments and variants of the invention. invention to include phase modulation of RF pulses (orders j). The action of repeated pulses is reduced to filtering operations and has a simple graphical representation. The manipulation of the contrast in steady-state free precession (SSFP) sequences is extended to the case of interlaced stationary equilibria. A non-linear least squares minimization algorithm is proposed for mapping multiple parameters based on the acquisition of order states k = 0. Solutions of contrast agents are imaged with 3D sequences applying the multiple modulations of the RF pulses validating the proposed direct and inverse problems. A quick calculation of the magnetization states after repeated pulses is obtained, both in the standard case of quadratic cycling of the constant amplitude phase of the pulses, and in more complex cases. The calculation is in perfect agreement with the experiments and the resolution of the inverse problem gives access to the nuclear magnetization, the angle, the relaxation rates and the diffusion coefficient. Thus, by a simplification of the description of the magnetization following repeated pulses modulated in phase and in amplitude, the possibilities of manipulation of the contrast in this type of sequences are extended and demonstrates that the multiple parameters of interest in MRI 10 can be extracted through this. First embodiment of a method and a device according to the invention With reference to FIG. 10, the first embodiment of device 1 according to the invention comprises: means 2 for applying, in a continuous manner, a main magnetic field BO along a Z axis on a sample zone (comprising, for example, a permanent magnet or a superconducting coil or a solenoid as found in an MRI machine) means 3 for emitting a magnetic field gradient (comprising by for example, three conductive coils as found in an MRI machine), means 4 for transmitting a radio frequency pulse (comprising for example a Radio Frequency antenna called "Body" or "Body" as found in an MRI machine), control means 5 arranged to control the means for transmitting a magnetic field gradient and the means for transmitting a radio frequency pulse, means 6 for acquiring at least one nuclear magnetic resonance signal (comprising for example several receiving antennas mounted in phased array as found in an MRI machine), calculation means 7. The various means 2, 3, 4, 6 are typically in the walls of an enclosure 13 (typically cylindrical in shape, typically of internal dimensions: diameter = 60 cm; length = 2 30 meters) for the clinical systems within which the sample area 8 is located, and are not illustrated in detail in FIG. 10. Each of the steps of the method according to the invention is not carried out in a purely abstract or purely intellectual way but involves the use of a technical means.
[0012] Each of the control means 5, the acquisition means 6 and the calculation means 7 comprises a computer, and / or a central or calculation unit, and / or an analog electronic circuit (preferably dedicated), and / or a digital electronic circuit (preferably dedicated), and / or a microprocessor (preferably dedicated), and / or software means.
[0013] As will be seen below, each of the control means 5, the acquisition means 6 and the calculation means 7 can be arranged for (for example by including a dedicated electronic card) and / or more precisely programmed for (for example by including software means) performing certain functions or operations or command or calculation etc. With reference to FIGS. 1, 10 and 11, the first embodiment of a magnetic resonance imaging method implemented by the first device embodiment according to the invention comprises: an application (by the means 2 ) continues from the main magnetic field BO (homogeneous throughout the sample area 8) along the Z axis to a sample located in the sample area (hereinafter referred to as sample or sample area, these two expressions being interchangeable since for example a field emitted in the sample and emitted in the sample area and vice versa), and - at least one set of repeated applications (by the control means 5 which are arranged for or programmed to perform this at least one set of repeated applications), on the sample and according to a period TR, of a sequence (of the "unbalanced" type), said sequence comprising: an RF radiofrequency pulse of variable amplitude B1 and / or of variable phase at each repetition, and o after the radio frequency pulse of the sequence, a spatial gradient of the component along the Z axis of the magnetic field; typically, the spatial gradient of the Bz (x, y, z) component along Z of the magnetic field at the coordinate point (x, y, z) varies along three orthogonal directions (e.g., X, Y, Z), this gradient can thus typically decompose in the form (dB (x, y, z) dB (x, y, z) dB (x, y, z) zzzz)) and this gradient corresponds to dx dy dz typically to the sum - i) a coding gradient Gcoding in a coding direction as introduced thereafter; this gradient Gcodage has a time integral (over time TR) nonzero between each repetition of the sequence. Ii) a reading gradient Glecture (equal for example to Gx along the X axis in FIG. 11); this reading gradient has a temporal integral (over time TR) zero between each repetition of the sequence. Iii) a phase coding gradient Gphase 1 (equal for example to Gy along the Y axis in FIG. 11); this phase coding gradient has a temporal integral (over time TR) of zero between each repetition of the sequence. iv) a gradient selection gradient Gcouple optionally combined with a second phase coding gradient Gphase2 (whose combination is equal for example to Gz along the Z axis in Figure 11); these phase selection and phase coding gradients have a temporal integral (over time TR) of zero between each repetition of the sequence. The gradients set forth in (ii) (iii) and (iv) of reading and phase coding and section selection being defined along three orthogonal distinct axes; the use of the gradients set out in (ii) (iii) and (iv) of reading, phase coding and section selection are known in the state of the art and therefore will not be further detailed. By "continuous application" of BO is meant in the present description an application of constant value over time of BO throughout the duration of the at least one set of repeated applications of the sequence. As seen in Figure 10, the magnetic field 9 is parallel to the Z axis throughout the sample area 8. The spatial gradient dBz (x '' z) of the Z component of the magnetic field along the X-axis is illustrated by the line 10. The spatial gradient dBz (x, y, z) of the Z-component of the magnetic field along the Y axis is illustrated by line 11. The line 12 does not show a slope or gradient, but we can see along this line 12 different values of the component according to Z of the magnetic field which clearly illustrate the spatial gradient dBz (x, y, z) of the component according to Z of the field dz along the Z axis. During repeated applications of the radiofrequency pulse and the magnetic field spatial gradient of the sequence of the same set (the control means 5 being arranged for or programmed for this): The radiofrequency pulse follows, between its different repeated applications, a sequence periodic: o for its amplitude and o for u '_, 1 = v-va, where n is an integer greater than or equal to 1 representing the number of the repetition of the sequence for this set, and where a, 1 is a continuation of relative integers 5 which makes it possible to define the sequence y 'at an arbitrary constant near y1 such that yin = x A and pn = 9, -9, with A which is a constant real number for all the repeated applications of the sequence of this set and rp which is the increment between phase 0, of the radiofrequency pulse at its nth repetition in this set and the phase 6'_1 of the radiofrequency pulse at its (n-1) 1 st repetition in this together, with an arbitrary value, and - each repeated application of the spatial magnetic field gradient of the sequence a, in a gradient spatial direction called the same coding direction for each gradient application of this set, a time integral equal to A non-zero (on time TR) and id entique for each gradient application of this set; the gradient in the coding direction is, at each given instant, preferably the same for all the points of the sample; the gradient in the coding direction also preferably has an identical shape for each gradient application of this set; the direction of coding may be in the direction of the axis X, Y or Z or any direction oblique to these axes: the case of Figure 1 corresponds to the particular case where the direction of coding is parallel to the axis X of the reading gradient 20 Glecture = Gx, and the reference G of Figure 1 is equal to the sum - Gstore + Gcodage = Gx + Gcodage. The first embodiment of the method according to the invention implemented by the first embodiment of the device according to the invention further comprises an acquisition (by the acquisition means 6 which are arranged for or programmed for that), during at least one of the repetitions of the sequence of at least one nuclear magnetic resonance signal (at an echo time TE (less than TR) between an application of the RF pulse and the acquisition), preferably corresponding at least one order of coherence obtained when the application, for this at least one sequence repetition, of the magnetic field spatial gradient in the coding direction reaches a multiple (by a relative integer) integral integral of A (such as the order 0 (corresponding to 0 * A), the order -1 (corresponding to -1 * A), the order 1 (corresponding to 1 * A), or higher order multiples), preferably to the order of consistency equal to zero. Various variants are shown in FIG. 11: the variant a consists of the acquisition 3036189 21 of the order 0 alone; variant b consists of the acquisition of the order k alone; variant c consists of the acquisition of 3 orders during the same repetition. According to the variant considered of the invention, during repeated applications of the radio frequency pulse and the spatial magnetic field gradient of the sequence of the same set (the control means 5 being arranged for or programmed for this): the sequence un41 = vn41-vn is a non-constant periodic sequence, and / or the amplitude of the radio frequency pulse follows a non-constant periodic sequence. If the sequence un41 = vn41-vn is not constant, it has a period Nu which is a natural integer: - greater than 1, 10 The case Nu = 1 is the case of the constant sequence. An example of a continuation un41 = vn41-vn with Nu = 3 is for example: - for n = 1, u1 is equal to a first value, - for n = 2, u2 is equal to a second value, - for n = 3 , u3 is equal to a third value, 15 - for n = 4, u4 is equal to the first value - for n = 5, u5 is equal to the second value u2, - for n = 6, u6 is equal to the third value value u3, - etc. If the sequence of amplitude of the radiofrequency pulse is non-constant, it has a period Na which is a natural integer: greater than 1, the case Na = 1 is the case of the constant sequence. An example of amplitude sequence of the radiofrequency pulse with Na = 3 is for example: for n = 1, the amplitude of the radiofrequency pulse is equal to a first value, for n = 2, the amplitude of the radiofrequency pulse is equal to a second value, - for n = 3, the amplitude of the radiofrequency pulse is equal to a third value, - for n = 4, the amplitude of the radio frequency pulse is equal to at the first value, - for n = 5, the amplitude of the radio frequency pulse is equal to the second value, - for n = 6, the amplitude of the radiofrequency pulse is equal to the third value, 30 - etc. In the first embodiment of the method according to the invention implemented by the first device embodiment according to the invention, the nuclear magnetic resonance signal is acquired at least one dynamic equilibrium state of the invention. magnetization of the sample, the control means 5 being arranged for or programmed to control the acquisition means 6 to perform such an acquisition. According to the variant considered of the invention: 1) during repeated applications of the radio frequency pulse and the magnetic field spatial gradient of the sequence of the same set (the control means 5 being arranged for or programmed for this) : o following a + 1 = vn + 1 - vn is a non-constant periodic sequence, and / or where the amplitude of the radiofrequency pulse follows a non-constant periodic sequence, so as to obtain different equilibrium states of the magnetization of the sample intertwined within this set respectively for different periodic values of the sequence a + 1V n and / or the amplitude of the radiofrequency pulse, and the nuclear magnetic resonance signal is acquired at these different Interleaved equilibrium states, the control means 5 being further arranged for or programmed to control the acquisition means 6 for effecting such acquisition, and / or 2) sequentially transmitting more their sets (one or more of which may be of the general type of paragraph (1) of this paragraph), with (control means 5 being arranged for or programmed for that purpose): value differs between the different sets, and / or o the amplitude of the radiofrequency pulse which follows a periodic sequence (constant or not) which differs between the different sets, so as to obtain different equilibrium states of the magnetization of the sequential sample for different values of A and / or the amplitude of which at least one equilibrium state per set, and the nuclear magnetic resonance signal is acquired at these different sequential equilibrium states, the control means 5 being further arranged for or programmed to control the acquisition means 6 to effect such an acquisition. Within each set of repeated sequence applications, the number of iterations of the sequence necessary to achieve a magnetization very close to the dynamic equilibrium state is of the order of 5 T1. Since Ti is not a priori known, it will be possible to consider typically a value of Tl target TR (for example of the order of 1 second), and it will then be necessary to apply the repetitions during at least one set-up time. balance on the order of 5 * T and ensure that the dynamic equilibrium is reached for all samples with a smaller T1. The acquisition and storage of data will preferably start after this time of establishment. However, the acquisition can be triggered before this set-up time, ie during the transitional phase: 5 - by acquiring high spatial frequencies during the equilibrium phase while ensuring that the central spatial frequencies (in particular the center of the Fourier plane) are acquired at least at or after this time of establishment of the equilibrium, - Or, in particular to refine the quantification in the variant known as "multiparametric imaging" , including transient state modeling during the equilibrium phase. Particular case of the decomposition of the magnetization in two-dimensional configuration states The action of repeated RF pulses spaced a time TR is considered here (Figure 1). As in most SSFP sequences a gradient is applied which produces a spatial phase shift between the pulses characterized by a spatial frequency: TR (1) 44 = = 27r G (t) dt 0 Where y is the gyromagnetic ratio, a is a characteristic distance corresponding to the inverse of a spatial frequency Ak, and G (t) is the shape of the gradient. Without losing in generality, the net phase shift is represented in an arbitrary direction which will be noted z. The variable Z = exp (-127rAkz) represents the resulting spatial modulation between two excitations, characterized by the total area of the gradients between the RF pulses. To describe the magnetization in such repetitive sequences, the 1D configuration state formalism can be used in which the longitudinal and transverse components are decomposed into Z4 polynomials. These polynomials will be denoted P and Q respectively for the longitudinal and transverse components. This formalism has been proposed in multiple studies either without RF phase modulation (9,10,24,27,29-31), or directly by including it in a 1D approach of the extended phase graph or using solutions analytical (8,33). The RF phase increment between the excitation n and the excitation n-1 will be noted (p, = 6 -) This increment between two TRs makes it possible to define an instantaneous apparent frequency (pn I 27rTR. The phase increment is a multiple of a phase A, such that (pn = vx A, where vn is an arbitrary series of integers.) This allows the variable Y = exp (- / A) to be introduced. expressions, we can consider that the transverse component is demodulated by using the phase of the preceding RF pulse (the reference rotating at the transmission frequency (4)), similarly to the formalism of the configuration states (8,9, 27), the magnetization can be thus decomposed into a 2D series in y-1 and zl: k =. J = .0 Pn = 1119., knY jZ k 5 k = -cj = -c (2) k = bones The effects of relaxation, diffusion and rocking angle In a recent review (9), it was recalled that relaxation and diffusion can be taken into account by convolution operations in the spatial domain with appropriate filters. This convolution 10 is equivalent to the term-to-term multiplication of the coefficients of the polynomial series in the Z-1 direction. To keep the derivation as general as possible, the evolution of the longitudinal and transversal components between two pulses will be synthesized using a weighting polynomial in Z-1: k = m = E wikZk (3) k = m W2 = E w2kz kk For simplicity, the relaxation and the free diffusion will be considered here for which the coefficients of the weighting polynomials of the longitudinal magnetization Wi and transverse W2 are real, producing attenuation of the coefficients of, respectively, P and Q. L extension to other types of weighting polynomials is discussed below. The following variables are introduced to account for relaxation and free diffusion: E = exp (- TRIT), E2 = exp (-TR / T2), Ed = exp (-D x TRx (27r / a) 2) = exp (-bx D). The variables E1 and E2 correspond to the resulting attenuation of the longitudinal and transverse relaxation respectively between the two pulses. The variable Ed is a resultant attenuation of free diffusion, where D is the free diffusion coefficient, and where b is defined as b = TRx (27c / a) 2. In Appendix 1, the two polynomials W1 and W2 are expressed as a function of E1, E2 and Ed. As reported in (27) and in Appendix 1, W1 is a symmetric Gaussian filter 3036189 W1, -k) , while W2 depends on the exact shape of the gradient which makes it possible to selectively attenuate different configuration states according to the evolution of the longitudinal component P n just after the RF pulse number n-1 to Pn + just before the impulse number n is given by: Pn + = 1- + Wi * Pn, (4) expression in which the longitudinal recovery and the diffusion weighting are taken into account. The notation * represents the convolution operation, calculated as the multiplication of pj, k, n with the weights wu for all j and k. The transverse component of the magnetization evolves in: Qin + = 1 "Z-1 (W2 * Qn) (5) 10 Indeed, the coefficients of the transverse component are attenuated (convolution with W2), and an additional phase shift is taken in account: spatial phase shift resulting from the nonzero gradient area (multiplication by Z ') and placing the magnetization along an axis ready to be tilted using the RF pulse to follow (17' ') The real and imaginary parts of Qn + are: ## EQU1 ## where the bar represents the conjugated complex. has been performed with respect to the phase of the RF pulse, only the real part of the transverse component is assigned to the next RF pulse.After the RF pulse number n, the magnetization is tilted to an angle by This is reflected in the polynomials as - Pn + i = c '(1- E, + W, * P) - s'R' (7) Qn +, = sn (1- E, + W, * Pn) + cnRn + In- where c, = cos (a ') and s, = sin (a'). In this 2D description of the configuration states, starting from the thermal equilibrium for which Po = 1 and a = 0, it can be easily shown by recurrence that the coefficients P j, k, n and q jk, are real numbers. , which simplifies the iterative calculation of the coefficients of the polynomials. Nevertheless, equation Eq.7 makes the recurrence relation difficult to analyze.
[0014] Simplifying Recurrence Using the Apparent Frequency Offset To account for RF phase cycling and simplify the recursion relationship, an operator can be introduced based on the following polynomial: ## EQU1 ## Sv = Y kv Z k (8) k = -. As shown in Appendix 2, this polynomial has properties of combinations Si * Sv = Su 'and of symmetry S, = Sv. Applied to U, representing an arbitrary polynomial at Y-1 and Z1-, the effect of phase cycling can be simplified to Y'Z-1 (Su * U) = * (Z-1U). By exploiting these properties, the magnetization 5 can be described as deconvolved polynomials: P s = es = S _ ,, * Q '. This is equivalent to demodulating the magnetization with respect to the apparent instantaneous frequency. After the introduction of these expressions in the recurrence relation, we obtain simplified expressions with respect to RF phase cycling: * /), cn (1-4 + * /), $) - snRns = su 1- + Wi * Pns) ± cnRns + ns R s = 2 [Z1 (W2 * Qns) + Z1 (W2 * Qns) 1 (9) ns = [Z-1 (if, * Qns) - Z-1 (w2 * Qns) In which u n + 1 = vn-F1. Since vn x 4 / 27rTR represents an apparent instantaneous frequency, x4 / 27rT1 2 represents an apparent frequency offset between two TRs. In the general case of a modulation as well in amplitude as in phase, by combining the equation Eq.9, one obtains: Su, a * (cn + is -snPn + is) = Rns + cn / ns (10 This allows to express the longitudinal polynomial Pns as a function of the transverse polynomial: S '' '* = S' '- -, (11) and the relation of recurrence as a function of the transverse polynomial over three consecutive iterations: sn_isn ( 1- Ej + (12) s n-1Su, + u * Qn + ls * (s ncn-1W1 * Qns nRns ns) s nWl * (Rnls c n-1-1 n-ls) This expression indicates that, instead to use Pn and Qn to obtain P n + i and Qn + i, it is possible simply to study the two transverse polynomials corresponding to the previous iterations Qn and Qn_ 20 i to obtain Qn + i, from which P n + i can be deduced using equation Eq.11 Depending on the choice of the amplitude range an, and the apparent frequency offset series summarized by the series one, the recurrence relation can be exploited at will.
[0015] Stationary states The coefficients of the equation Eq.12 do not depend on n if and only if the operator Sn is constant and the amplitude of the angle (ie c '= c and sn = s). In this case a + 1 = 1 ,,, 1-1 ,, = 1 is a solution that implies vn = n yo is a linear evolution of the phase increment (pn = (n + y0) 4, leading to 5 Standard quadratic cycling for On This is a discrete version, with its associated folding, of an experiment of progressive shifting of the frequency with a constant rate.It will be noted in passing the presence of vo which equates to a central frequency different from the The RF pulse thus indicates that this parameter is not decisive for reaching a steady state as long as the RF pulses are considered instantaneous.It is known, from simulations and thanks to the attenuation effects, that a stationary state Qoos is reached for which: S2 * Q0: = s (1- E,) ± S, * (cW, * Q0: ± cRoos + 101-W, * (Ro: + dol (13) Another advantage resulting of the discretization is the possibility to play on the relation of recurrence to reach multiple stationary states intertwined with series For example, if one alternates the amplitude of the angle such that cc2 = a and a2. + 1 = a 'as well as the apparent frequency offset with u2 = u and u2 1 = u', two stationary states Qcos and Qcos 'will be reached such that s' Sn '* Qe: = s' (1- Ei) + Su * (sc 'Wi * Qe: + cRe: + sWi * (Re: + c' ( 14) sSn * = ss (1- Ei) + S., * (S 'cW, * Qess' c' Re: + s'W, * (Re: + This periodization of the angle series allows to sensitize differently the stationary states as a function of the physical parameters and sequences in an interlaced manner, potentially allowing the introduction of quantization methods based on these interleaved equilibria. Graphical representation and implementation To synthesize the action of the various operators involved, a graphical representation of the index offsets can be used from the 2D decomposition into defined configuration states using the basic functions 17-1 and Z '. From equation Eq.9, we can see that the relation of recurrence can be decomposed into elementary operations represented in Figure 2. If we consider a polynomial U (Figure 2a), the action of the convolution with a polynomial The weighting is equivalent to a term-to-term multiplication of all the coefficients having the same index k according to Z '(Figure 2b). The longitudinal relaxation towards the state of thermal equilibrium is also taken into account by adding the cosine 3036189 and the sinus of (1-E1) in the center (j = 0, k = 0), respectively for P and Q. multiplication by Z 'corresponds to an index shift (k-> k + 1, Figure 2c), the conjugate complex is a central symmetry k - * - k (Figure 2d, the coefficients are real). Convolution with S '' tilts '' the coefficients as j-j-k.v (Figure 2e).
[0016] To compute the transient and stationary signals for Ny x Nz configuration states and arbitrary amplitude and phase series, a recursion computation can be realized from equation Eq.9 on 2D grids for Pns and Qns with I [-Ny12 + 1, Ny / 21 and ke [-I / / 2 +1, N / 2] initialized to thermal equilibrium (Pos = 1, Q0s = 0). To obtain the order k of the actually measured magnetization, a Fourier transform of Qns can be made in the Y-1 direction, which directly supplies the values for all the increments A. Note that the discretization according to Fl (the fact to take only Ny step) can be processed by implementing the folding in the offset operator S '. On the other hand, limiting the number of steps in the Zi direction requires estimating when the coefficients of the different polynomials become negligible. To estimate this value Nz of necessary step, one can consider the transversal relaxation and the diffusion because their action tends to attenuate the transverse component. During the state transfer with the term Z-1 (W 2 * as), considering k> 0 with a transfer to the state k + 1, the attenuation of the coefficients is of the order of E2E /, if although the cumulative attenuation from zero order to k is of the order of E2kEdk3 / 3. We can then define a limit on the cumulative attenuation E, ..., 2 of the coefficients, which makes it possible to estimate the order k which would produce this attenuation via the relaxation: k2 = f (E 2), orm via the diffusion : k- .131n (E, ',,, yin (Ed) (rounded to the nearest integer) The minimum 20 N = 2x min (k2, kdiff) then provides an estimate of the order number to be considered If ka'ff> k2, this also implies a limited effect of the diffusion with respect to the transverse relaxation.While applicable to arbitrary pulse series, the case of periodic series allows a state to be reached. stationary The calculation of this state requires a sufficient number of iterations neq If we consider Ti> T2, the longitudinal relaxation appears as the limiting factor for reaching equilibrium Similarly, define a limit for attenuation cumulative to Eh no provides an order of magnitude of the number of repetitions needed to reach re stationary state ri n n (- eq hm1 (E1) Numerically, a criterion such as relative variation can be used to stop the iterative calculation. It will be noted that the particular case of the SSFP signal achieved with quadratic phase cycling and constant angle (an = a, u, 1) can be calculated more efficiently. This aspect has been proposed elsewhere with relaxation (33). To take into account any W1 and W2 weighting polynomials, including diffusion, a similar derivation based on the formulation of a tridiagonal linear system is given in Appendix 3 to efficiently calculate the steady state with quadratic cycling. phase and constant angle.
[0017] Non-resonance and flux effects The proposed calculation method is preferably implemented with a resonance frequency which is exactly that of the excitation RF pulse. In practice, the static field Bo is not perfectly homogeneous which produces effects on the measured signal. The off-resonance effects as well as the motion-induced phase shifts produce an additional phase modulation q = yAB, TR + 7r leen, where AB0 represents the field inhomogeneities or possibly the chemical shift, and where Veo represents the coding velocity related to the moment of order 1 of the shape of the gradient. By introducing the complex exponential z, = exp (-400), the action of this additional phase shift according to Z-1 in the 2D representation in configuration state (9) is expressed in a similar way by considering a phase-shifted polynomial in Y and (ZoZ) -1 for which all the coefficients remain real as in the case previously considered. Between the end of the RF pulse and the echo time, the signal is attenuated by the effects of apparent transverse relaxation E; = exp (-TE / T2) and shifted by a factor ZTE = exp ((pTE) with (pTE = (pi + yABoTE + (pv which includes a possible phase shift (pi between transmission and reception, the effects of the inhomogeneity of the Bo field and possible speed coding (pv.
[0018] Variant of the first embodiment of a method and a device according to the invention: multiparameter imaging; Implementation of an inverse problem based on the acquisition of the state k = 0 In a variant (called "multiparametric imaging") of the first embodiment of the method according to the invention implemented by the first embodiment device according to the invention (and described only with respect to its differences or peculiarities with respect to this first embodiment), the method according to the invention comprises: - an acquisition of a signal (preferably for the order coherence equal to zero) for equilibrium states corresponding to different amplitudes of the radiofrequency pulse and / or different A and / or different values of the sequence un_, 1 = - constant periodic or not, the means 5 being arranged for or programmed to control the acquisition means 6 to effect such an acquisition, and for at least one point in the sample, a determination (by the calculation means 7, which i are arranged for or programmed for this) several data (preferably at least 3, preferably all 3036189) among a nuclear magnetization, a rocking angle of the magnetization, a diffusion coefficient, a rate or relaxation time longitudinal R1 or T1, and a rate or transverse relaxation time R2 or T2, from the acquired signal for these equilibrium states. As will be discussed in more detail below, the determination is preferably carried out, (by the computing means 7, which are arranged for or programmed for it) either by comparison with a pre-calculated dictionary or by iterative estimation, according to a minimization of a norm of the difference between the acquired signal expressed in complex form with a real part and an imaginary part and a model of the signal expressed in complex form with a real part and an imaginary part. In the example, the minimization comprises a least squares minimization algorithm, preferably using the Gauss-Newton algorithm applied to non-linear problems. For this variant of multiparametric imaging, one can place oneself in the case in which sequential equilibrium states such as previously described with several sets of sequence applications are exploited. In this case, this multiparameter imaging variant comprises an acquisition of a signal (preferably for the order of coherence equal to zero) for equilibrium states (preferably with a sequence a + 1 = vn + 1 -vn constant for each set) corresponding to different (the control means 5 being arranged for or programmed to control the acquisition means 6 to perform such an acquisition), including: - several points for an absolute value of 4 close to 0 °, between 4 = 0 ° inclusive and 4 = 32 ° 20 inclusive modulo 360 °, and / or - several points for an absolute value of 4 close to 180 °, between 4 = 164 ° inclusive and 4 = 196 ° included modulo 360 °, and / or - several points for an absolute value of 4 close to 120 °, between 4 = 112 ° inclusive and 4 = 128 ° inclusive modulo 360 °, and / or 25 - several points, for an absolute value of 4 at 45 °, 60 °, 72 °, 90 °, and 144 ° modulo 360 ° for a total of preferably at least five points. We see in Figures 6 and 7 the interest of these points, especially close to 0 °, 120 ° and 180 °. In this variant of multiparameter imaging, the amplitude of the radiofrequency pulse 30 always corresponds to a flip-flop angle of the magnetization: - greater than the Ernst angle for a longitudinal relaxation time T1 equal to 2000 milliseconds (this which leaves freedom on the TR and on the type of target fabric), and - less than or equal to 90 ° the control means 5 being arranged for or programmed for that.
[0019] In this variant of multiparameter imaging, the determination may comprise a condition of spatial continuity of each of the determined data among the nuclear magnetization, the magnetization flip angle, the diffusion coefficient, the rate or time. longitudinal relaxation R1 or T1, and the rate or transverse relaxation time R2 or T2 between different points of the sample (the control means 5 being arranged for or programmed for it), preferably the flip angle. We will now explain in more detail this variant of multiparameter imaging with a first detailed example. Multiple parametric imaging methods have been proposed based on the acquisition of several k (28-31) states, but much less based on different phase cycling (33-35). To illustrate the direct calculation according to the "multiparametric imaging" variant according to the invention and to validate it in the presence of relaxation and diffusion, an inverse problem is proposed based on the acquisition of the state k = 0. The description given here considers the case of the stationary state signal for a constant angle in amplitude a and with quadratic increments of different phases, but the expression is general and can be extended to the other cases of stationary equilibrium, or even in the case of 15 transient phases (out of dynamic equilibrium). For each voxel in the image space, the measured signals are placed in a vector denoted Q0, ','. The inverse problem is expressed as minimization in the least squares sense: H2 min 11Q0, '-M x Q0 (El, E2, Ed, a .a Ma = In this expression, a number of parameters are unknown: M which represents The amplitude of the echo signal, relaxation and diffusion attenuations, as well as the magnitude of the angle actually achieved, multiple methods can be used to solve this non-linear least squares problem. implementation based on the combination of an initialization by comparison with a dictionary, followed by the application of the Gauss-Newton algorithm is proposed here.First, it can be noted that the problem is linear in M, so that if the model vector Q0 (E1, E2, E d, a) is known, then the best solution for M in the least squares sense is: M = Q01 I QI ° (16) The superscript notation H represents the transpose Hermitian of the vector Q0 To initialize the parameters to (Mrru, Eure, E2, ioit, amit), we can calculate Ed, init by considering the coefficient of free diffusion of water and choose am, as being the prescribed angle. This reduces the calculation of Qo to two dimensions (according to E1 and E2) and different values for E1 and E2 can be selected in the range of 0 to 1. The linear estimation of M for each pair of values (E1, E2) using the equation Eq.16 allows to choose values (M; rut, Eure, E2, '111) which minimizes the residual norm given by the equation Eq.15. Subsequently, in the iterative nonlinear calculation, the signal is normalized by the estimation of M and, to ensure that physical attenuation values are obtained, a change of variables is performed with 4 = exp (- 11x12), E2 / 4 = exp (-11x2n2), Ed = exp (-11xd2). The Jacobian matrix is then given by: J = real (a) real (Q ° real initial imag (real (real fflo (17) and can be calculated day is then obtained imag (Q,) imag (ffl ° imag Q ' `) numerically set imagery by: aie a , a2 / 1 '/ , of / fflo' 1) ( 1 a Q '" 1) , a2 / 1) d) A vector vector [1, xunit, [dr, a5c1, cbc211, c1xcl, daf = (- 11141 JH real (Q0) - real (Q, m '/ M) imag (Q0) imag (Q0, m' / M) (18) The functions real and imag respectively represent real and imaginary parts.
[0020] The addition of this up-to-date vector to the previous estimate refines the solution. M can then be estimated as M x (1+ dr) and used to normalize the measured signal for the next iteration. The procedure is repeated until the relative variation of the residual norm given by Equation Eq.15 is sufficiently small. The JHJ matrix is assumed to be invertible. If one considers the Gaussian nature of the MRI noise, characterized by its identical variance 62 on the real and imaginary parts, the Fisher information matrix (36) is equal to F = (JHJ, if it is invertible, its inverse F-1 = (01 M1) 2 -1 represents the noise covariance matrix from which the lower Cramer-Rao bounds can be extracted to estimate the accuracy on the adjusted parameters if an unbiased estimator is obtained at Using the proposed algorithm If the Fisher matrix is not invertible or poorly conditioned, the pseudo-inverse is computed to provide numerical stability, and constraints can be added on the parameters to avoid to obtain outliers and reduce numerical instabilities: M is positive, the flip-flop angle remains in a given range (from 2 ° to 90 ° for example), the attenuation terms are bounded between exp (-1) and exp (-101. The generic adjustment procedure can be adapted to both the adjustment of the transient signal and the inclusion of acquisitions obtained in an interlaced or sequential manner by varying the series of RF pulses.
[0021] 3036189 33 If the example of this multiparameter imaging variant that has just been detailed is placed in the context of sequential equilibria with several sets each having only one dynamic equilibrium, this variant of multiparametric imaging can also be implemented according to the invention with several sets by exploiting interleaved equilibrium states (preferably at least two interleaved states of equilibrium), thus: in a second example, we will rather use a sequence a + 1 = vn + 1 - vn constant, 4 obviously constant for each set, and the amplitude of the radiofrequency pulse which follows a non-constant periodic sequence (with thus a period at least equal to two repetitions with two different amplitudes sufficiently different between 0 ° and 90 °, so as to obtain the at least two states of different interleaved equilibria), as shown in FIGS. 6c and 6d. For each point of interest in the sample, the data (nuclear magnetization, magnetization flip angle, diffusion coefficient, R1 or T1 longitudinal relaxation rate or time, and R2 or T2 transverse relaxation rate or time) are then determined with the proposed fit, as shown in Figures 7c and 7d. It should be noted that the use of different amplitudes does not add any unknown to the inverse problem because, if there may be an uncertainty on the tilt angle achieved with a given amplitude, the angles are proportional to the series. amplitude. For example, the adjustment will be adapted by considering the largest angle of the amplitude series as an unknown to be determined, the other angles being directly proportional to this angle of a known factor derived from the amplitude sequence. imposed. In a third example, we will use rather an amplitude of the constant angle and a series a + 1 = v. + 1 periodic non constant with 4 constant for each set, but primarily close to 0 ° and / or close to 180 °, as shown in Figure 6b. For each point of interest in the sample, the data (nuclear magnetization, magnetization flip angle, scattering coefficient, R1 or Ti longitudinal relaxation rate or time, and R2 or T2 transverse relaxation rate or time ) are then determined with the proposed adjustment. Of course, this variant of "multiparametric imaging" can be imagined by mixing the sequential acquisition of interleaved equilibrium states generated by the periodicity of the amplitude and of the sequence a + 1 = vn + 1 -vn, by example by mixing the second example and the third example. The extreme case of the acquisition of a single set of interleaved equilibria with non-constant periodic sequences of amplitude and / or un-constant, is also possible. For this purpose, preference will be given to: 3036189 34 - In the case where the amplitude is constant, a + 1 Vn + 1 non-constant lin will have a periodicity of preferably at least five points and A will be constant by a value of preferably 180 °. The sequence u '_, 1 = v' can be chosen arbitrarily. In the case where the sequence of amplitude will be periodic, non-constant, preferably of a period of at least five repetitions, the sequence u '_, 1 = v', 1-v 'may be chosen either constant or not. -constant with the same period. One will choose A, which is then unique and constant for this single set, preferably of a value of 0 ° or 180 ° or close to these values. The amplitude sequence can be chosen arbitrarily between -90 ° and 90 ° with sufficiently different values between them, for example distributed uniformly between 0 ° and 90 °. The sequence a + 1 = v ,,, 1-- T, may be chosen arbitrarily, preferably with a zero average over the period. For each point of interest in the sample, the data (nuclear magnetization, magnetization flip angle, scattering coefficient, R1 or T1 longitudinal relaxation rate or time, and R2 or T2 transverse relaxation rate or time ) are then determined with the proposed adjustment. Similarly, the adjustment will be adapted in the case of a non-constant periodic amplitude, for example by considering the largest angle of the amplitude series as an unknown to be determined, the other angles being directly proportional to this amplitude. angle of a known factor deduced from the imposed amplitude sequence.
[0022] Ghost Experiments To illustrate the 2D extension of configuration state formalism, experiments were performed with different solutions of contrast agents diluted in water. Imaging was done at 1.5T (Achieva, Philips Healthcare, Best, The Netherlands) using a quadrature head antenna for reception. Gadolinium chelates (10, 5, 2.5, 1.25, 0 mM, Dotarem, Guerbet, Villepinte, France) and iron oxide nanoparticles (0.32, 0.16, 0.08, 0.04, 0 mM, CL-30Q02-2 , Molday ION, Biopal, Worcester, MA, USA) were prepared and placed in cylindrical 15 mL containers aligned with the Bo magnetic field. A spatially unselective 3D gradient echo sequence was modified to allow multiple Fi values sequentially starting with ri = 1 (no RF interference, 4 = 0 °) until the entire unit circle is covered. Rectangular RF pulses were used (time 150 days for 45 degrees of prescribed angle). A parameter has also been added to allow the interlace of the amplitude of the angles such that cc2 = a and 6c2. + 1 = a / 2 (by dividing by two in real time the amplitude of the emission field B1). The scrambling gradient has been placed on the direction of reading such that its area corresponds to a = 1 / Akz equal to the size of the imaging pixel. The acquisition parameters were either TRITE = 9.214 ms, acquisition matrix 168x84x9 and voxel size 0.5x1x8 mm, bandwidth per pixel 217 Hz / pix, acquisition time Tacq = 7 s per volume (which will be noted thereafter 'sequence I', with a diffusion sensitivity of b = 1.45 s mm-2) or TR / TE = 4.8 / 2.4 ms, 84x84x9 acquisition matrix and voxel size 1x1x8 mm, bandwidth per pixel 434 Hz / pix, acquisition time Tacq = 3.5 s by volume (which will be noted here after 'sequence 2', with diffusion sensitivity of b = 0.19 s mm 2) The size of the reconstruction voxels was 0.47x0.47x8 mm Several prescribed angles were tested sequentially (between 7.5 ° to 75 °), as well as intertwined. Multiple Ny steps have been made (in steps of 2 ° for A). Given these acquisition parameters, for each step A, the center of the Fourier space was sampled after a few seconds. There was no delay between the acquisitions of the different steps A, and 2 to 4 volumes of preparation were made before storing the first volume of data so that one can consider that the stationary state was reached. The reconstruction of each volume was performed by the manufacturer software by removing the phase corrections present by default and by using an absolute storage scale of the NMR signal in the DICOM files. The amplitude and phase images were saved. Data Analysis The DICOM images were analyzed offline using Matlab (2011b version; The Mathworks, Natick, MA) on a recent laptop (Intel Core i7, 16 GB RAM, 2.7 GHz) running under Microsoft Windows 8. Only the central section of the 3D volume has been analyzed. A region of interest was drawn on each tube to perform the analysis of the average signal per tube. A pixel-to-pixel reconstruction was also performed. The images were normalized by the standard deviation of noise that was estimated over a region without a signal. To guarantee that the signal has Hermitian symmetry with respect to Y-1 (the phase of the first step A = 0 ° was used to estimate Z1F which was then Qo, mes (y -1) = Q0, mes (Y). It was noted that a slight time shift was noted during the acquisition of the different steps, and corrected.This shift was attributed to a thermal drift of the gradients and it was considered that this drift varied linearly in the To estimate this drift, the acquisition corresponding to A = 0 ° was repeated at the beginning and at the end of all the other steps, or the acquisition obtained for A = 2 ° (at the beginning) and for A = 358 ° (at the end) have been compared, these different steps are supposed to be complex conjugates so that their products must be real.The phase of this product is therefore characteristic of the drift of time phase. , the signal measured for each step has been rephased for r provide the signal Q0 on which the proposed inverse problem has been applied. In the iterative estimation of the parameters in the inverse problem, the proposed stationary state calculation algorithm 3036189 in Annex 3 was used for cases where a constant angle of amplitude and apparent frequency offset been applied. The order number Nz was chosen by setting Ehm, 2 = 0.01. In all other cases, the iterative calculation was done by setting the maximum number of repetitions to max (neq, no) where no was the number of repetitions applied to reach the center of the Fourier plane in imaging, 5 and nec, obtained for Eh ',, / = 0.01. Initialization was performed on 32 values for E1 and E2 / Ei. Iterations were stopped when the normalized standard norm by the signal standard varied by less than 10-6. Results Simulations The calculation of the magnetization using the 2D extension of the configuration state formalism is illustrated in Figure 3. The transverse magnetization coefficients q ,, k, n, which were initialized to the thermal equilibrium, are displayed for n = 1 (with only a central coefficient at j = k = 0, Figure 3-a). Gradually, non-zero coefficients appear, until reaching a steady state after a large number of pulses. The steady-state coefficients are very strongly influenced by diffusion (Figure 3-e and f). Each iteration lasted -1 ms with Ny = 360, and the number of iterations necessary to reach the stationary state was of the order of 5 Ti / TR, whatever the series of angle applied. With regard to the calculation of the stationary state following the quadratic phase cycling, the two approaches (iterative based on the successive impulse and direct application derived from the tridiagonal algorithm) gave the same stationary states L '. Fast algorithm took -10 ms to provide stationary state on the same number of points Ny = 360. The proposed algorithm provided the same results as previously published when the effects of diffusion were neglected (Figure 4-a). The steady state is very strongly dependent on A with the creation of multiple stimulated echoes. Specific peaks are visible when A is a rational number of 360 ° (0 °, 180 °, 120 °, 90 °, ...). Transverse relaxation and diffusion both reduce the formation of stimulated echoes which brings the signal closer to a pure Ernst equilibrium (Figure 4-b-d). The transverse magnetization varies between larger and smaller values, and never reaches the Ernst equilibrium which is purely real, even if there exist values of A for which the modulus of magnetization is equal to it. . The stationary state dependence obtained as a result of a constant series in amplitude and apparent frequency offset is complex and mixed contrasts in T1, T2 and diffusion are obtained. Nevertheless, general features can be extracted. Indeed, the stationary states are contained in a plane which itself contains the Ernst equilibrium and which is tilted by an effective angle oce = arctan ((E1 -c) / s) (Figure 5) with respect to the axis of the main field, regardless of T2 or the diffusion coefficient. This implies a particular dependence on the Ernst angle. For angles of amplitude smaller than the Ernst angle (Figure 5-ab), the effective angle is negative and the magnetization varies between 'peaks' which are smaller than the Ernst equilibrium and 'scrambled' values that are larger. For angles larger than the Ernst angle (Figure 5-e-f), the opposite is observed. Between the two, if the angle is exactly equal to the Ernst angle (Figure 5-cd), the effective angle is zero: only the imaginary part of the transverse component of the magnetization varies with A and the part real is always equal to Ernst's balance. The proposed algorithm is not only able to simulate the case of standard phase quadratic cycling (constant amplitude and apparent frequency offset), but also to compute interlaced stationary states that can be obtained with periodic amplitude and lag series apparent frequency. This is shown in Fig. 6 where a constant angle of 75 ° with constant apparent frequency offset is compared to a series having a constant angle of 75 ° with oscillation of the apparent frequency offset (+ A, -A), as well as a series that oscillates in amplitude (75 ° / 37.5 °) and is constant in apparent frequency offset. The steady states obtained are very different. The case of the alternating amplitude gives rise to a very complex dependence on A. The case of a constant amplitude angle but with an alternation of the apparent frequency offset (u2 1, 15 /12.+1--1) gives rise to two conjugate complex stationary states. For the latter case, a slow transition is obtained between A = 0 and A = n (these two states are respectively the same as those obtained for an apparent offset of constant frequency with A = 0 and A = n). This alternation of apparent frequency offset is obtained for example with an effective phase of RF pulses O which alternates between + A / 2 and -412.
[0023] Ghost Experiments The average signals on the tubes could be efficiently modeled using the proposed approaches over the range of tilt angles tested, both using a constant series of amplitude and apparent frequency offset with series more complex periodicals. After the initialization step, the average number of iterations of the nonlinear minimization least squares algorithm was -35. For all series of angles tested, the relaxivity values R1 and R2 extracted from the analysis on the mean signal of the tubes were linear with the concentration for the solutions of Gd and ION, the adjusted angles as well as the value of the attenuation Ed were consistent with respectively the prescribed angle and the coefficient of free diffusion of water. For the case of a constant amplitude at 45 ° obtained with the sequence 1, the molar relaxivities were ri / r2 = 3.9 / 4.6 mM-is-1 for the agent based on Gd and 86.4 / 12.7 mM-1 s. 1 for the ION-based agent, the adjusted angle was 44.3 ± 0.3 °, the MB magnetization was 471 ± 54 (mean ± standard deviation on the tubes) and the diffusion attenuation coefficient was Ed = 0.9967 ± 0.0003, corresponding to D = 2.29 ± 0.17 10 'mes', which is in agreement with the theory. Representative measured signals as well as the corresponding adjusted parameters are shown in Figure 7 for tubes of 1.25 mM Gd and 160 μM ION in the 45 ° and 45 / 22.5 ° interleaved cases. As expected, the case of the amplitude of the interlaced angle produces a complex equilibrium. To demonstrate the possibility of performing multiparametric imaging from the proposed approach, the signals obtained with sequence 1 with 45 ° were adjusted pixel by pixel. The parametric magnetization, tilt angle, R1, R2 and diffusion coefficient maps are shown in Figure 8. The average values and the standard deviations calculated on these reconstructed images are given in Table 1. below, and associated with the theoretical value calculated from the diagonal element of the noise covariance matrix. All the parameters to be adjusted are in very good agreement with the expected values. R1 and R2 are linear with the concentration (FIG. 9) and make it possible to estimate molar relaxivities in agreement with those measured on the mean signals of the tubes. The amplitude of the rocking angle is very close to the prescribed value, and the diffusion coefficient indicates a free diffusion in all the tubes. As can be seen, the estimation of the parameters is influenced by the propagation of the noise, and the precision depends on a complex way of the parameters. The diagonal elements of the noise covariance matrix, while they include only a part of the noise propagation, already provide a good estimate of accuracy over R1, R2 and D, but are less efficient at predicting the propagation of the noise on M and on the amplitude of the angle, in particular because the estimates of these two parameters are more strongly correlated.
[0024] Water Gd Gd Gd GON ION ION ION 1.25 mM 2.5 mM 5 mM 10 mM 40 mt 80 mtb 160 mt 320 mt m / 6 797 588 570 548 511 620 623 635 604 ± 217 ± 114 ± 113 ± 112 ± 117 ± 107 ± 89 ± 89 ± 84 (± 115) (± 6) (± 4) (± 3) (± 4) (± 36) (± 33) (± 29) (± 22) a (°) 45.53 44.06 44.01 44.13 44.17 43.90 44.21 44.23 ± 3.54 ± 0.26 ± 0.21 ± 0.23 ± 0.51 ± 1.87 ± 0.85 ± 0.52 ± 0.41 (± 0.01) (± 0.05) (± 0.10) (± 0.13) (± 0.29) (± 0.11 ) (± 0.05) (± 0.11) (0.24) R1 (s-1) 0.28 5.54 10.05 20.14 39.57 0.78 1.26 2.19 4.24 ± 0.07 ± 0.13 ± 0.20 ± 0.42 ± 1.98 ± 0.12 ± 0.15 ± 0.18 ± 0.29 (± 0.04) ( ± 0.06) (± 0.10) (± 0.19) (± 0.57) (± 0.05) (± 0.07) (± 0.11) (± 0.18) R2 (s-1) 0.73 6.47 11.69 23.82 46.78 3.10 6.43 13.47 27.90 ± 0.27 ± 0.20 ± 0.28 ± 0.55 ± 1.79 ± 0.39 ± 0.49 ± 0.56 ± 0.88 (± 0.17) (± 0.10) (± 0.14) (± 0.25) (± 0.67) (± 0.16) (± 0.22) (± 0.33) (± 0.55) D 1.96 2.23 2.27 2.36 2.72 2.27 2.21 2.19 2.15 10 ± 0.28 ± 0.14 ± 0.18 ± 0.52 ± 2.53 ± 0.27 ± 0.27 ± 0.40 ± 0.78 91112S-1 (± 0.14) ( 0.08) (± 0.12) (± 0.32) (± 1.66) (± 0.17) (± 0.20) (± 0.29) (± 0.63) Table 1 above presents the results obtained after analyzing multiparameter images reconstructed from the data. obtained with sequence 1 with a prescribed angle of 45 ° and Ny = 91 (A between 0 ° to 180 ° in steps of 2 °). Mean value ± standard deviation measured on the tubes for the various adjusted parameters. The number in parenthesis corresponds to the Cramer-Rao bound from the diagonal elements of the inverse of the Fisher matrix estimated at adjusted average values. Although not all sources of noise are present in the diagonal elements, this theoretical number already provides a good estimate of the standard deviation, with values close to the standard deviation measured on the tubes, for Ri, R2 and D.
[0025] Discussion The repeated application of RF pulses interleaved with a constant gradient area was analyzed using extended configuration state formalism to account for the phase modulation of RF pulses. Effective algorithms for calculating magnetization including relaxation and diffusion have been deduced. Multiparametric imaging based on signal fit acquires the order Ic = 0 with several apparent frequency offsets as well as alternate amplitude angles has been demonstrated for a wide range of R1, R2 and ratio R2 / R1. Nuclear magnetization, tilt angle, free diffusion coefficient and relaxation parameters could be measured, validating the direct and inverse approaches. The formalism of the configuration states is equivalent to the extended phase graph approach (6-9), in which the magnetization is decomposed into time-varying Fourier coefficients, which can therefore be extended with a similar graphical representation. (8) the action of a given amplitude and phase tilt angle, and attenuation by relaxation and diffusion. The approach is also similar to the polynomial decomposition performed in the extended RF pulse design (10,11) in 2D, suggesting the possibility of using digital filtering techniques for the design of potentially RF pulses sensitive to relaxation and diffusion. It will be appreciated that the proposed derivation can be adapted to varying TRs and gradient areas (9) by adapting the weighting polynomials and shifts according to F 1 and Z 1 to efficiently calculate the response to such sequences. In the case of a constant TR and a constant gradient area as treated here, quadratic phase cycling leads to the highly studied steady state (3-5). The order k = 0 at steady state in this case is contained in a plane that passes through the Ernst equilibrium and is tilted at a determined effective angle leading to a particular dependence that could be used to quickly estimate if the prescribed angle is larger or smaller than the Ernst angle. This could be done by comparing the signals of some values of A (such as 0 ° and another phase increment). A decay of the real part indicates an angle greater than the angle of Ernst, and vice versa. The derivation of a fast algorithm based on the expression of a tri-diagonal linear system for calculating the stationary state in this case, previously proposed with a different derivation (33), also includes here the effects of diffusion and can be generalized to more complex weighting polynomials. In addition, the description according to the configuration states makes it possible to demonstrate that periodic series, modulated in amplitude and in phase, produce interlace stationary states, thus extending the possibilities of manipulation of the contrast in this type of sequences. Since the physical parameters (relaxation rate, diffusion coefficient) and sequences (TR, amplitude of the angle) are taken into account in the calculation of the direct problem, the inverse problem is based on the acquisition of different series of angles. This type of inverse problem has already been proposed by using different states k (28-31) or by using partial interference around 0 ° with quadratic cycling of the phase to quantize T2 (33-35). It was chosen here to use only the state k = 0 and multiple apparent offsets of 3036189 frequency. This allowed to validate experimentally, on a standard clinical system, the direct problem, as well as to demonstrate the possibility of performing multiparametric imaging. The inverse problem can be extended to include different states k and multiple sets of angles. The determination of the k-states and optimal series to be measured is a complex problem that would require further study of the noise covariance matrix. For the question of the selection of a minimum number of measurements to optimally estimate a parameter of interest (relaxation, diffusion, etc.) while maintaining a total acquisition time that can be achieved in practice, elements can be specified. . At first, the magnetization to Hermitian symmetry so that there is no need to acquire increment values of -A (modulo 360 °) if the value A is acquired. On the other hand, if we restrict ourselves to the acquisition of the state k = 0 with an apparent frequency offset, as proposed with partial scrambling around 0 ° (33-35), the regions around fraction of 360 ° seem to be the most informative (0 °, 180 °, 120 °, ...) so that the partial interference, defined as a sampling around these values, could be sufficient. In addition, as can be seen in FIG. 7a-b, the first two ellipses correspond to the partial interference around 0 ° and 180 °, and the speed of variation increases around 180 ° with respect to 0 ° (visible by comparing the position of the signals obtained for 0-2 -4 ° and 180-182-184 °, for example), suggesting that 1) a geometric evolution of the type 0-2-4-8-16 ° around 0 ° for example, and 2) a reduction of steps such as 180-181-182-184-188 ° around 180 ° may be sufficient to modulate the stationary state sufficiently to estimate the parameters.
[0026] The measured signal was pre-processed to remove the phase at echo time as well as drift over time. These parameters were estimated and corrected before applying the inverse problem but could also be included as parameters to be adjusted. The phase of the signal, always available in an MRI sequence, remains sensitive to the inhomogeneities of the Bo field, making it possible to map them, or to quantify phase shifts due to the flux. To reduce the effects of flux phases (9) which do not remain constant during acquisition and therefore do not necessarily reach a stationary state, flux compensated gradient forms may be used. With respect to the drift attributed to thermal effects of gradients, reducing the number of steps sampled would limit these effects. Calibration is always possible by acquiring increments of 0 ° several times, or by comparing images obtained with increments A and -A acquired at different times.
[0027] The proposed implementation for solving the inverse problem has the limitation of the large computation time when it is applied on the basis of a pixel-to-pixel adjustment. Nevertheless, this algorithm is highly parallelisable, and graphics card processors can be used to accelerate the reconstruction. The tilt angle was considered as an adjustable parameter providing a less accurate estimate of the other parameters by noise propagation. To improve the accuracy of the other parameters, one can set the tilt angle to the value of the prescribed angle or add spatial regularity on it. The angle values used here (between 7.5 and 75 °) seem to provide sufficient variation of the measured signal to adjust the different parameters. For small angles (Fig 5a-b), the magnetization varies less than for larger angles (Fig.5c-f). For even larger angles (not shown here), the magnetization suffers from saturation phenomena which indicates that an angle maximizing signal variations as a function of A lies in the amplitude range of 0 ° to 90 ° . This optimal angle depends on relaxation and diffusion. The ability to map tilt angle, relaxation, and scattering in the <90 ° small angle range used in gradient echo sequences, significantly lower angles than those used in spin echo sequences, suggests that the proposed approach could be used independently of the spatial homogeneity of the B1 emission field typically obtained at higher Bo magnetic field or with surface antennas, and with lower specific absorption rates. The use of interleaved or sequential angle amplitude series (techniques of the variable or current angle type (15-21)) would improve the conditioning of the inverse problem and hence the adjustment of the parameters. The fact that the purely real Ernst equilibrium is difficult to achieve, even for the quadratic phase evolution used for scrambling with increments of 117 ° or other suitable values (4,15,16) indicates that both transversal relaxation and diffusion must be taken into account to describe the signal, and there is a potential improvement if both the real and imaginary parts are used. In fact, the analyzes in most of the previous works only exploit the transverse magnetization module and thus lose information in the passage (15-20). Interestingly, the action of scattering is very important even with the low values of b used here. Indeed, the value reported here only considers the first-order diffusion weighting between two TRs. On the one hand the weighting of the higher orders increases to the power Ic 2, and these orders are maintained by coherence on the longitudinal and transverse components. The effective diffusion time is therefore greater than TR. The effective diffusion weighting is then more complex to define. An effective diffusion time T, which depends on T1, T2 and the tilt angle, can be defined; this one is bounded by T2 <Ti. The sequence is then equivalent to the application of a constant gradient during this time, and the diffusion weighting then increases in Y. A very rapid increase is then expected: with a TR of -10 ms and considering T-100 ms, the value of effective b is then (TITR) 3 = 103 times greater than that defined between each TR. The counterpart is that the diffusion weight is dependent on the relaxation parameters. This aspect of inhomogeneous scattering weighting can be seen as a limit, or as an additional way of filtering the signals of certain tissue types by applying different values of b by playing on the sequence parameter. a or equivalently on the shape of the gradient and its total area. This may allow more specific access to compartments on a scale smaller than the size of the imaging voxel. Playing on the direction of the gradient could also allow access to the 5 preferred diffusion directions (37,38), with the advantage of a gradient echo sequence (good spatial resolution, short echo time, high bandwidth and limited spatial deformations). In vivo, diffusion may also be restricted, magnetization transfer phenomena or partial volume effects may exist. These phenomena could be taken into account by using more complex weighting polynomials (37,38), by modeling the exchange (39) or the multi-compartmentalization, and could be characterized using steady-state fast sequences. described by the formalism of the configuration states. To reduce the total acquisition time, the proposed modulations of RF pulses could be combined with parallel imaging (40), compressed sensing (41) or fingerprinting (42), approaches for which the formalism of Extended configuration states could provide a method for selecting pseudo-random sampling patterns. Variant of the first embodiment of a method and a device according to the invention: rapid estimation of the prescribed angle; In response to what has been said in the previous paragraphs in the discussion section concerning the possibility of rapidly estimating whether the prescribed angle is larger or smaller than the Ernst angle, a variant (called "Ernst angle") of the first embodiment of the method according to the invention implemented by the first device embodiment according to the invention (and described only with respect to its differences or particularities with respect to this first embodiment of the invention. realization) lies within the framework of sequential equilibrium states and comprises: an acquisition of a signal (necessarily for the order of coherence equal to zero) for two equilibrium states corresponding to two amplitudes of the same radio frequency pulse but two different A, the control means 5 being arranged for or programmed to control the acquisition means 6 to perform such an acquisition, - a comparison (by the computing means 7, which are arranged for or programmed for that) of the signal for these two equilibrium states, and - a deduction (by the calculation means 7, which are arranged for or programmed for this), from this comparison, if the amplitude of the radio frequency pulse produces an effective flip-flop angle greater than or smaller than or equal to the angle of Ernst (equal to acos (exp (-TR / T1))) for the 'sample.
[0028] One of the two different A's, which will be denoted by A 1, is preferably zero but other values may be taken as 180 °, or 120 °, or 90 °, or any other value producing a visible 'peak' in FIG. 5. The second value, denoted A2, will be chosen preferentially for a 'hollow' for example that around zero (approximately between 25 ° and 40 °), or around 180 ° (approximately between 192 ° and 202 °) °), or around 120 ° (approximately between 106 ° and 112 ° or between 128 ° and 134 °). As can be understood from the view of FIG. 5, in which the real part (line numbered 51) oscillates around the value of the Ernst equilibrium (dashed line having the value s * (1-E1) / (1 -c * E1): - if the real part of the signal Sig 1 obtained for A1 is greater than the real part of the signal Sig2 obtained for A2 ,, then the effective flip angle is greater than the angle of Ernst, If the real part of the signal Sig1 obtained for A1 is equal to the real part of the signal Sig2 obtained for A2 ,, then the effective flip angle is equal to the angle of Ernst, if the real part of the signal Sigl obtained for A1 is smaller than the real part of the signal Sig2 obtained for A2 ,, then the effective flip-flop angle is smaller than the angle of Ernst, preferably A1 is equal to zero and A2 corresponds to one of given in the preceding paragraph, if A1 is chosen equal to 0 ° or 180 °, it will be possible, for example, to perform the complex signals Sig2 / Sigl and base directly on the real part of this ratio: if it is greater than 1 then the angle is less than the Ernst angle, if it is equal to 1 then the angle is equal to the Ernst angle, if it is less than 1 then the angle is greater than the Ernst angle.
[0029] Variant of the first embodiment of a method and a device according to the invention: modulation of the effects of diffusion; As a follow-up to what has been said in the previous section in the discussion section about the importance of diffusion, a variant (so-called "diffusion") of the first embodiment of the method according to the invention implemented by the first embodiment of device 25 according to the invention (and described only with respect to its differences or particularities with respect to this first embodiment) lies in the context of states of sequential equilibria (possibly combinable with states interleaved equilibria): sequentially several sets are emitted, and (the control means 5 being arranged for or programmed for this): the coding direction differs between different sets, and / or the value of A differs between different sets, and / or - the shape of the magnetic field gradient according to the coding direction differs between different sets. This "diffusion" variant also comprises a quantization (by the calculation means 7, which are arranged for or programmed for this) of a diffusion coefficient in the sample or a determination of a preferred direction of diffusion in the sample. the sample or a weighting of the diffusion in the sample by exploiting the difference of A and / or direction of coding and / or shape of the gradient between the different sets. This quantization or determination or weighting is typically carried out by applying several sets with values of b (cf. Appendix 1, in particular Equation 19 applied to the coding gradient to calculate b) and / or directions of application of the different coding gradient. We will manage to define a value b. preferably between 0.1 and 5000 mm 2 s-1, from which the corresponding area A (denoted Amax) and the shape of the coding gradient will be determined by calculation (preferably for a trapezium with the maximum amplitude of the gradients applicable on this or these axis (s) and with feasible ramps for the gradient system). From the determination of A. and the shape, as well as by combining with the constraints imposed by the imaging gradients, a minimum TRmin value applicable TRmin will be determined We will therefore choose a minimum TR equal to TRmin for the different sets. We will also define a value of bmin preferably between 0.1 and 5000 mm 2 s -1 and less than b max. This value of bmin is then achievable with the same TR, and will preferably be achieved by changing the amplitude of the coding gradient rather than its shape. The generation of diffusion weighted images can be made with two sets made for an identical sequence = 1 constant for the sets, an identical value of A between the sets, and an identical constant tilting angle amplitude for the sets, preferably larger than the Ernst angle and preferably less than 90 °.
[0030] The study of the variation of the signal as a function of b indicates that the value of A to be produced is close to 0 °, between A = 0 ° inclusive and A = 32 ° inclusive modulo 360 °, or close to 180 °. between A = 164 ° inclusive and A = 196 ° inclusive modulo 360 °, or, for an absolute value of A close to 120 °, between A = 112 ° inclusive and A = 128 ° inclusive modulo 360 °, or, for a value absolute of A among 45 °, 60 °, 72 °, 90 °, and 144 ° modulo 360 °. The two sets are then made sequentially with the coding gradient having a value bmax (set 1) and bmin (set 2). The diffusion-weighted image can then be visualized by the difference of the signals obtained between the set obtained with bmin minus the set obtained with bmax. Since the signals are complex, an important module (referred to as a high signal) then corresponds to a region having a large diffusion, information displayed in a qualitative way. It should be noted here that the larger the diffusion coefficient, the more the equilibrium dynamic signal is attenuated and approaches the Ernst equilibrium for the set corresponding to bmax with respect to the set corresponding to bmin. the way of weighting the diffusion images from two sets with different values of b, it is possible to extend the method to the determination of a preferred diffusion direction using the known diffusion tensor concept of art (Mori S, Zhang J. Principles of diffusion and its applications to basic neuroscience research Neuron 2006; 51 (5): 527-539). In these techniques, multiple images are made with different diffusion weighting gradient application directions. The signals are adjusted to a 3x3 symmetric matrix which makes it possible to extract three eigenvalues and three associated eigenvectors. Similarly here, for example, the signals of several sets acquired sequentially with identical values of bmax and different directions, possibly supplemented by a reference acquisition with a low value of bmin, will be used. With this signal which depends on the direction of application of the coding gradient and which is then closer to the Ernst equilibrium when the diffusion is strong, it is then possible by adjusting the components of a tensor on the measured signals to determine the preferred direction of diffusion, corresponding for example to the eigenvector having the largest eigenvalue, or even to extract other parameters such as the anisotropy fraction as reported in the state of the art. From a process point of view, how to optimize the overall number and determine the orientations to be applied are therefore aspects available in the art. As in diffusion tensor imaging techniques, for this variant, the value of bmax to be retained depends on the relaxation parameters and is to be optimized for each target tissue to ensure that it sufficiently attenuates the signal as a function of orientation, but not too much not to be too close to Ernst's equilibrium. These optimization principles are known to those skilled in the art. It will be noted here the interest of the method according to the proposed invention which has a greater sensitivity to diffusion than current techniques according to the state of the art, as mentioned in the 'discussion' part. Having emphasized the possibility of sensitizing the signal to diffusion using a coding gradient having different values of b, it should be noted that this aspect can be combined with the so-called "multiparameter imaging" variant. Sets with different values of b can also be acquired sequentially to increase the scatter sensitivity of certain sets and make the determination of this parameter using the more precise inverse problem. The choice of the different sets are derivable from the preceding paragraph as well as from the description of the measurement points given in the description of the variant called "multiparameter imaging". In the present description of some embodiments and variants of the invention, the configuration state formalism has been extended to take into account the phase modulation of the RF pulses in repetitive sequences including interlaced radio frequency pulses. nonzero gradient area. This extension provides a framework for efficiently calculating and understanding the formation of stimulated echoes through a graphical representation. Relaxation and diffusion have been taken into account, and the concepts are generalizable to other types of mitigation mechanisms. In addition, periodic steady states can be maintained which extends the possibilities of manipulation of the contrast. A generic inverse problem has been proposed to adjust the magnetization, the amplitude of the tilt angle, the relaxation rates and the scattering coefficient based on the acquisition of multiple amplitude-modulated and / or phase-modulated series. quantative imaging tools based on configuration states (or QuICS for "Quantitative Imaging using 10 Configuration States"). Of course, the invention is not limited to the examples that have just been described and many adjustments can be made to these examples without departing from the scope of the invention. Of course, the various features, shapes, variants and embodiments of the invention may be associated with each other in various combinations to the extent that they are not incompatible or exclusive of each other. In particular all the variants and embodiments described above are combinable with each other. Appendix 1: Effects of diffusion on weighting polynomials The value of b (b-value) is used to characterize the diffusion gradients and is defined for an axis of application: TR z 2 b = -y2. I = -f yG (t) dt dr. . (19) 0 ") The diffusion effect differs for a given order k (the phase shift in the plane is 7k), because just after the RF pulse, this order already has a phase equal to 27r kl a: TRI 27c (20) bk = -y2 .Ik = -J 1. 0 k- + jyG (t) dt a 0 If the gradient is constant as in (31), the integration gives: (27r 2 ( 1 bk = -y2 k = - - TR k2 + k + - (21) 3i a k2 + k + 1 This makes it possible to define the coefficients of the weighting polynomial W2 1122k = E2E d 3. If the extreme case in which the gradient can be approximated by a Dirac applied before the next RF pulse 3036189 48 k2 is considered, then W2 k E2E d: the weighting polynomial then corresponds to a symmetric Gaussian filter A more accurate take into account of the shape of the gradients is feasible, and there is the possibility of modulating the diffusion filtering through the gradient form to reduce the effects on predefined k-orders, for example, if the gradient is applied according to the directio n of the reading, as what is presented experimentally in the present description, if one considers that TE is at the center of the acquisition window (which lasts Tobs), the effects of the prephase gradient (considered to be applied during a time TE-T obsI2) followed by the reading and the interference gradients (considered to be applied during a time TR-TE-T obsI2), the calculation of the weighting polynomial gives 1.2 + 1 (4 5TE3 Tob; k + ( In any case, these expressions can be put under TR 2 TR, 12 12 TR 24 TR, = E 2E d xx,) 2 + cst 10 form W 2 2, which shows that, for free diffusion, a Gaussian filtering is applied centered on k = k, and with an attenuation E2Edcst applied on all the coefficients (where cst is a constant). Similarly, the coefficients of the weighting polynomial W1 attenuating the longitudinal magnetization x2 correspond to a Gaussian zero centered filter, Wl k ErEd, since an order k is maintained between two TRs without any additional phase shift. Appendix 2: The shift operator The action of changing the phase increment from one pulse to another is equivalent to an apparent frequency change. Therefore, in the polynomial description used here, each coefficient must be rephased appropriately. We can decompose the magnetization into: + so U = uk (y1) zk (22) k = -co where Uk (y-1) are Y-1 polynomials. The convolution with S, has for action to realize this apparent change of frequency: + so sv * = EU k (171) y-vk zk (23) k = -m With the extension in 2D of the formalism the states of configuration, the action is to translate each Uk (Y- ') polynomial in the Y direction of an index which depends on the order k as shown in Fig.2. Advantageous relationships are exploitable: ## EQU1 ## 49 It can be noted that s, is equal to its conjugate complex, and that operators can be combined: Sv = E yvk zk = Ey-vk zk = s1v (25) k = -co k = -co * Su Sv = Su +,. (26) 5 Appendix 3: Fast calculation of the stationary state from the tridiagonal matrices algorithm To calculate the steady state in the case of quadratic phase cycling it is possible to use the recurrence relation between three successive iterations For this, the polynomial representing the transverse magnetization is written as a polynomial sum in 174: + SO = qk (y-1) zk (27) k-so 10 If this expression is substituted in the relation steady-state recurrence: -cW1) * Q, os = s (1-El) + - c +21 (s, A wi) * (z 1w2 * c; 1 (s, ± wi) * (zw 2 * Qs) (28) sA * (es -Q005) = * Qoos _z-iw-2 * Qcos (29) The following expressions are obtained: qkak = s (1- El), 3k, o + LnkZkqk-1 KkY kq-k-11 (30) qk Zkqk-1 = qk Kkq-k-1 (31) 1 ff With ak = 1- cYk 13k c Yk Yk iY2k Pk) '11k iY2k Pk)' Zk w2, k-lYk Kk w2, -k-lYk 8k. = 1 if m = k, and 0 everywhere else (the Dirac distribution). The conjugation operation is eliminated by combining the previous expression and shifting the indices: ak (1-4) Yk Yk ro 5k, 0 = -Kkq-k-1 (32) + s (1-4), qk -1 qk 'uk-1.0 = qk (33) K k-11 k-1 Kk-1 Yk-1 KO ro so that the following expression provides a recurrence between three consecutive states k: (34) -akqk_1 + bkqk-ckqk_4 = r18k + 1.0 ± ro6k, where X krik Ykk Pk + 1 1- El (1-4) k = b = 1 + K rik + 1 KkY k, ro = S, r 1 = This can be rewritten as a tridiagonal linear system: ## EQU1 ## This can be rewritten as a tridiagonal linear system: ## EQU1 ## c -c_1 b0 -a -a1 -c0 -c1 g, = -a-2 b_2 -c-2 1 0 1 q_2 q_1 go q1 -a_1 b 1 b1 -1 -a -an bo 1_ go 1_ 0 Who is classical way solved by an algorithm of the tridiagonal matrices: With Ck + 1 1 -g, q-2 n 1- oo ak (36) calculated 1 go o hk 1 -g 2 ql PO = 1 q3 0, -ho 1 g - h1 1 1 -ho 1 Which is calculated iteratively considering gk + 1 = ak-pigk bk -Ckhk + 1 bk + lr 5 considering k = 0, po = r ° and) 9_1 = -1. The final value for k = 0, .70 is then b0 -ch 0 0 1 b_1 -a_1g_2 obtained by inverting the central 2x2 matrix: go = po + hop (37) 1-hog As well as the term q_1 P_I g_IPo q_1 (38) Using this approach, each order k of the steady state can be calculated using the upside-down relationship. The value of po is determined by p = c 1- E1sw2, -1 q-1 q-1. The computation can be done for a series of complex exponentials Fi and follow a Fourier transform to get the coefficients of the polynomial in. This algorithm is similar to the otherwise proposed continuous fraction expansion (33), with a different derivation and expression that includes the effects of scattering, and by extension of any weighting. 0 0 r 1 - ro 0 0 (35) 3036189 51 References 1. Ernst RR, Bodenhausen G, Wokaun A. Principles of nuclear magnetic resonance in one and two dimensions. In: Clarendon O, editor; 1987. p 125. 5 2. Darrass L, Mao L, St. Jalmes H. Steady-State management in Fast Low-Angle Imaging. 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权利要求:
Claims (17)
[0001]
REVENDICATIONS1. Magnetic resonance imaging method, comprising: - a continuous application of a main magnetic field BO along a Z axis on a sample, and - at least one set of repeated applications, on the sample and according to a period TR, a sequence, said sequence comprising: o a radiofrequency pulse possibly of amplitude and / or variable phase at each repetition, and o after the radiofrequency pulse of the sequence, a spatial gradient of the component along the Z axis of the magnetic field, characterized in that, during repeated applications of the radiofrequency pulse and the spatial magnetic field gradient of the sequence of the same set: the radio frequency pulse follows, between its different repeated applications, a periodic sequence : o for its amplitude and o for a + 1 = y ', 1 -va, where n is an integer greater than or equal to 1 representing the number of the repetition of the sequence for this set e, and where an IF is a sequence of relative integers that allows us to define the sequence y 'to an arbitrary constant near y1 such that yin = v' x A and pn = 9, -9, i with A which is a number constant real for all the repeated applications of the sequence of this set and cp, which is the increment between phase 0, of the radiofrequency pulse at its nth repetition in this set and the phase 0, 1 of the pulse radiofrequency at its (n-1) 1 st C repetition in this set, with 00 an arbitrary value, and - each repeated application of the magnetic field spatial gradient of the sequence a, according to a spatial direction of gradient said coding direction identical for each application gradient of this set, a temporal integral equal to A non-zero and identical for each gradient application of this set, the method further comprising an acquisition, during at least one of the repetitions of the sequence, of at least one signal of reso nuclear magnetic resonance.
[0002]
2. Method according to claim 1, characterized in that, during repeated applications of the radiofrequency pulse and the magnetic field spatial gradient of the sequence of the same set, the sequence un + 1 = y ', 1 - v 'is a non-constant periodic sequence. 3036189 57
[0003]
3. Method according to claim 1 or 2, characterized in that, during repeated applications of the radiofrequency pulse and the magnetic field spatial gradient of the sequence of a same set, the amplitude of the radio frequency pulse follows a non-constant periodic sequence.
[0004]
4. Method according to any one of the preceding claims, characterized in that the nuclear magnetic resonance signal is acquired at least one state of dynamic equilibrium of the magnetization of the sample. 10
[0005]
5. Method according to claim 4 considered as dependent on claim 2 or 3, characterized in that during repeated applications of the radio frequency pulse and the spatial magnetic field gradient of the sequence of the same set: - the following a + 1 = vn + 1 -vn is a non-constant periodic sequence, and / or the amplitude of the radiofrequency pulse follows a non-constant periodic sequence, so as to obtain different equilibrium states of the magnetization of the sample interleaved within this set respectively for different periodic values of the sequence 1'1) 1 + 1 vn + 1 lin and / or the amplitude of the radiofrequency pulse, and in that one acquires the nuclear magnetic resonance signal at these different interlace states of equilibrium. 20
[0006]
6. Method according to claim 4 or 5, characterized in that one emits sequentially several sets, with: - A whose value differs between the different sets, and / or - the amplitude of the radiofrequency pulse which follows a periodical sequence which differs between the different sets, so as to obtain different equilibrium states of the sample magnetization sequential for different values of A and / or the amplitude of which at least one equilibrium state per set , and in that the nuclear magnetic resonance signal is acquired at these different sequential equilibrium states. 30
[0007]
7. Method according to claim 6, characterized in that it comprises: an acquisition of a signal for two equilibrium states corresponding to two identical amplitudes of the radio frequency pulse but two different A's, a comparison of the signal for these two equilibrium states, and - a deduction, from this comparison, of whether the amplitude of the radio frequency pulse produces an effective flip angle larger than or smaller than or equal to the angle of Ernst for the sample. 5
[0008]
8. Method according to claim 7, characterized in that one of the two different 4 is equal to zero.
[0009]
9. Method according to any one of claims 4 to 6, characterized in that it comprises: an acquisition of a signal for equilibrium states corresponding to different amplitudes of the radio frequency pulse and / or 4 different and / or different values of the sequence un_, 1 = vn + 1 - periodic, and - for at least one point in the sample, a determination of a nuclear magnetization, a flip-flop angle of the magnetization , a diffusion coefficient, a longitudinal relaxation rate or time R 1 or T 1, and a transverse relaxation rate or time R2 or T2, from the acquired signal for these equilibrium states.
[0010]
10. Method according to claim 9, characterized in that the determination is made, either by comparison with a pre-calculated dictionary or by iterative estimation, according to a minimization of a norm of the difference between the acquired signal expressed in complex form. with a real part and an imaginary part and a model of the signal expressed in complex form with a real part and an imaginary part.
[0011]
11. The method according to claim 10, characterized in that the minimization comprises a least squares minimization algorithm, preferably using the Gauss-Newton algorithm applied to non-linear problems.
[0012]
12. Method according to any one of claims 9 to 11, characterized in that it comprises an acquisition of a signal for equilibrium states corresponding to 4 different, including: - several points for an absolute value of 4 between 4 = 0 ° inclusive and 4 = 32 ° inclusive modulo 30 360 °, and / or - several points for an absolute value of 4 between 4 = 164 ° inclusive and 4 = 196 ° inclusive modulo 360 °, and / or - several points for an absolute value of 4 between 4 = 112 ° inclusive and 4 = 128 ° inclusive modulo 360 °, and / or 3036189 59 - several points, for an absolute value of A among 45 °, 60 °, 72 °, 90 ° , and 144 ° modulo 360 °.
[0013]
13. Method according to any one of claims 9 to 12, characterized in that the amplitude of the radiofrequency pulse always corresponds to a flip-flop angle of the magnetization: - greater than the Ernst angle for a time longitudinal relaxation T1 equal to 2000 milliseconds, and less than or equal to 90 °. 10
[0014]
14. Method according to any one of claims 9 to 13, characterized in that the determination comprises a condition of spatial continuity of the nuclear magnetization, the rocking angle of the magnetization, the diffusion coefficient, the rate or longitudinal relaxation time R1 or Ti, and the rate or transverse relaxation time R2 or T2 between different points of the sample. 15
[0015]
15. Method according to any one of claims 1 to 14, characterized in that one emits sequentially several sets, and in that: - the coding direction differs between different sets, and / or - the value of A differs between different sets, and / or the shape of the magnetic field gradient in the coding direction differs between different sets.
[0016]
16. The method according to claim 15, characterized in that it further comprises a quantification of a diffusion coefficient in the sample or a determination of a preferred direction of diffusion in the sample or a weighting of the diffusion. in the sample by exploiting the difference of A and / or direction of coding and / or shape of the gradient between the different sets.
[0017]
A magnetic resonance imaging device (1), comprising means (2) for continuously applying a main magnetic field BO along a Z axis to a sample area (8), and - means (3) for transmitting a magnetic field gradient and means (4) for transmitting a radio frequency pulse, and control means (5) arranged to control the means for transmitting a magnetic field gradient and means for transmitting a radio frequency pulse, the control means being arranged for or programmed to perform at least one set of repeated applications, on the sample area and according to a period TR, of a sequence, said sequence comprising: a radio frequency pulse optionally of amplitude and / or of variable phase at each repetition, and o after the radiofrequency pulse of the sequence, a spatial gradient of the component along the Z axis of the magnetic field, characterized in that the control means are arranged for or programmed so that, during repeated applications of the radio frequency pulse and the spatial magnetic field gradient of the sequence of the same set: the radiofrequency pulse follows, between its different repeated applications, a periodic sequence: o for its amplitude and o for a + 1 = y ', 1 -y', where n is an integer greater than or equal to 1 representing the number of the repetition of the sequence for this together, and where a, 1 is a sequence of relative integers that allows us to define the sequence y 'to an arbitrary constant near y1 such that yin = v' x A and pn = 9, -9, i with A which is a constant real number for all the repeated applications of the sequence of this set and cp, which is the increment between the phase 0, of the radiofrequency pulse at its nth repetition in this set and the phase 0'_1 of the radiofrequency pulse at its (n-1) 1 st repetition in c and together, with an arbitrary value, and - each repeated application of the spatial magnetic gradient of the sequence a, in a gradient spatial direction called the same coding direction for each gradient application of this set, a temporal integral equal to A non-zero and identical for each gradient application of this set, the device further comprising means (6) for acquiring, during at least one of the repetitions of the sequence, at least one nuclear magnetic resonance signal. 30

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同族专利:

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EP3295201B1|2021-12-01|

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US10585157B2|2020-03-10|

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EP3295201A1|2018-03-21|

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US20180136300A1|2018-05-17|

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WO2016180947A1|2016-11-17|

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FR3036189B1|2018-07-27|

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US6088488A|1998-04-17|2000-07-11|General Electric Company|Vascular imaging with adaptive averaging|

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US7602183B2|2007-02-13|2009-10-13|The Board Of Trustees Of The Leland Stanford Junior University|K-T sparse: high frame-rate dynamic magnetic resonance imaging exploiting spatio-temporal sparsity|US10241173B2|2016-03-14|2019-03-26|The General Hospital Corporation|Systems and methods for designing magnetic resonance fingerprinting imaging parameters|

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US10782375B2|2017-04-07|2020-09-22|The Regents Of The University Of California|Multi-contrast images from a magnetic resonance imaging scan|

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US20210373107A1|2020-05-29|2021-12-02|Hyperfine, Inc.|Systems and methods for low-field fast spin echo imaging|

法律状态:
2016-05-26| PLFP| Fee payment|Year of fee payment: 2 |

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2016-11-18| PLSC| Publication of the preliminary search report|Effective date: 20161118 |

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2017-05-31| PLFP| Fee payment|Year of fee payment: 3 |

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2018-05-28| PLFP| Fee payment|Year of fee payment: 4 |

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2019-05-28| PLFP| Fee payment|Year of fee payment: 5 |

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2020-05-28| PLFP| Fee payment|Year of fee payment: 6 |

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2021-05-28| PLFP| Fee payment|Year of fee payment: 7 |

优先权:

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申请号 | 申请日 | 专利标题

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FR1554358A|FR3036189B1|2015-05-13|2015-05-13|METHOD AND DEVICE FOR MAGNETIC RESONANCE IMAGING|

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FR1554358|2015-05-13|FR1554358A| FR3036189B1|2015-05-13|2015-05-13|METHOD AND DEVICE FOR MAGNETIC RESONANCE IMAGING|

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PCT/EP2016/060777| WO2016180947A1|2015-05-13|2016-05-12|Method and device for imaging by magnetic resonance|

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US15/573,340| US10585157B2|2015-05-13|2016-05-12|Method and device for imaging by magnetic resonance|

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EP16725787.2A| EP3295201B1|2015-05-13|2016-05-12|Method and device for imaging by magnetic resonance|