A method intended in the magnetic resonance imaging (MRI) field for simulation-based reconstruction (SBR)

Abstract

The present invention describes a method intended in the magnetic resonance imaging (MRI) field, said method comprising - determining a number of physical properties encoded in a vector ξx = (T1,x, T2,x, …); - determining a set of sequence parameters encoded in a vector αt = (TEt, TRt, FAt, …); - characterizing an MR signal at a certain time t of a simulation-based reconstruction (SBR) acquisition as S(αt, ξx, t) for deciding a model signal, - determining a dt series of measurements of the MR signal on a scanner; - performing inverse calculation(s) in accordance with arg minξ Σt ||dt - S(αt, ξx, t)||2 (1) for deciding spatial dependent parametric maps that minimize the discrepancy between a signal measured and a predicted model signal.

Description

[0001]A METHOD INTENDED IN THE MAGNETIC RESONANCE IMAGING (MRI) FIELD FOR SIMULATION-BASED RECONSTRUCTION (SBR) Field of the invention The present invention relates to a method intended in the magnetic resonance imaging (MRI) field for simulation-based reconstruction (SBR) purposes. Technical Background Simulation-based reconstruction (SBR) is a quantitative Magnetic Resonance Imaging (qMRI) technique used to obtain accurate physical parametric maps of a scanned object after a fast acquisition. First, a train of radiofrequency (RF) pulses and gradients, commonly denominated as MRI sequence, is applied during the examination, resulting in a magnetization signal generated from the scanned subject. Then, the SBR uses the knowledge of the physical processes happening in the scanner for that same MRI sequence to simulate the obtention of that magnetization signal, hence providing an accurate tool to solve the inverse problem resulting from the search for the unknown physical properties of the subject. The MRI sequence is a key element in the whole SBR framework since the signal generated and its properties are strongly dependent on the parameters that control the sequence. In particular, the well-posedness of the problem, i.e. how difficult is to reconstruct the magnetic properties of interest, is inherently related to the suitability of the sequence for SBR purposes. In contrast to traditional MRI, current knowledge of appropriate MRI sequences for qMRI is still very limited. Some of the experience about what works well in traditional MRI can be used to build MRI sequences for SBR, however, it is still a vast field to be explored. More specifically, these series of radiofrequency pulses and changes in the magnetic gradients describing an MRI sequence are defined by multiple parameters, such as time to echo (TE), time to repetition (TR), flip angle (FA), inversion pulse(s), or the echo train length (ETL), to give some examples. Defining an MRI sequence consists then in effectively programming the value of each one of those parameters during the MRI acquisition. In the case of SBR, the design aims to achieve an MR signal that facilitates the process of distinguishing the physical properties of the scanned object. One aim of the present invention is to provide a novel framework to optimize MRI sequences for SBR purposes, but the same framework could be adapted to any other qMRI or model-based MR technique. Summary of the invention Let us first define the SBR problem more systematically. This process can be expressed mathematically as given a set of unknown physical properties encoded in a vector ξx= (T1,x, T2,x, …) and a set of sequence parameters encoded in a vector αt= (TEt, TRt, FAt, …) we can characterize the signal at a certain time t of an SBR acquisition as S(αt, ξx, t), a value governed by the well-known Bloch equations. Please notice the subscripts x and t in ξxand αt, indicating that ξ and α are spatial and temporal dependent respectively. Therefore, given dta series of measurements of the signal on the scanner and knowing αt, the SBR problem consists of solving the following inverse problem: arg minξ Σt||dt- S(αt, ξx, t)||2(1), i.e. finding the spatial dependent parametric maps that minimize the discrepancy between the signal measured and the signal predicted by the model. Based on the stated purpose and further description above, according to one embodiment the present invention refers to a method intended in the magnetic resonance imaging (MRI) field, said method comprising - determining a number of physical properties encoded in a vector ξx= (T1,x, T2,x, …); - determining a set of sequence parameters encoded in a vector αt= (TEt, TRt, FAt, …); - characterizing an MR signal at a certain time t of a simulation-based reconstruction (SBR) acquisition as S(αt, ξx, t) for deciding a model signal, - determining a dtseries of measurements of the MR signal on a scanner; - performing inverse calculation(s) in accordance with arg minξΣt||dt- S(αt, ξx, t)||2(1) for deciding spatial dependent parametric maps that minimize the discrepancy between a signal measured and a predicted model signal. Further details of the present invention are provided below. Brief description of the drawings In fig.1 there is shown the estimation results obtained using different sequences for SBR purposes, where alternatives c) and d) show results when utilizing the method according to the present invention. Specific embodiments of the invention Below some specific embodiments of the present invention are disclosed and discussed further. If we consider the case in which the ground-truth values of the parametrical maps ξgt are known, for a fixed sequence defined by its set of parameters αt, we can calculate the suitability of this sequence for SBR as a function of the agreement between the estimated values for ξxdenoted by ξ’and the ground-truth values ξgt, which can be any standard metric such as the root-mean-square-error (RMSE) or a more specific metric that for instance take into account the different tissues composing the scanned object. In the following, we will write L(ξ’, ξgt) to refer to this function of the differences between the estimated and ground-truth parametric maps. Hence, on a high level, we can define the process of optimizing an MR sequence for SBR as the problem of: arg minα L(ξ’, ξgt) s.t ξ’= arg minξ Σt||dt- S(αt, ξx, t)||2(2). Based on the description above, according to one embodiment of the present invention, the MR signal S(αt, ξx, t) is obtained using a Bloch simulator that allows solving the inverse calculation arg minξ Σt||dt- S(αt, ξx, t)||2by using an iterative method. Furthermore, according to yet another embodiment, the method involves providing multiple MRI sequences for simulation-based reconstruction (SBR). Moreover, according to yet another embodiment of the present invention, the method involves calculation of the suitability of an MRI sequence for simulation-based reconstruction (SBR) as a function of an agreement between estimated values for ξxdenoted by ξ’and ground-truth values ξgt., preferably in accordance with arg minα L(ξ’, ξgt) s.t ξ’= arg minξ Σt||dt- S(αt, ξx, t)||2(2) where L(ξ’, ξgt) refers to a function of the differences between the estimated and ground-truth parametric maps. The signal S(αt, ξx, t) is obtained using a very optimized Bloch simulator that allows efficiently solving the inverse problem using iterative methods. In fact, in this previously mentioned formulation we are omitting the dependence of the data measurements dtfrom the ground-truth magnetic properties ξgtand the sequence parameters αt. Therefore, according to one embodiment of the present invention, the method is based on omitting the dependence of the data measurements dtfrom the ground-truth magnetic properties ξgtand the sequence parameters αt. This implies that in a truly real scenario, to optimize the sequence parameters, new data should be acquired in the scanner with each updated sequence, making it not practically possible for more than very few variations. Instead, the data samples are also simulated using the same Bloch simulator, usually in a higher spatial resolution to replicate more realistic conditions. The search space of the sequence parameters is vast and the optimization of all the parameters at once results unfeasible. In what follows, we describe the optimization of a single parameter, namely the flip angle, but the same procedure could be executed for other sequence parameters. The goal of the optimization is then to find the values for the flip angle (FA) of the RF pulse at each time point, i.e. ^ = (^^^^t0, ^^^^t1, …, ^^^^tT), during the SBR acquisition that minimize the distance between the estimation of the tissue parameters ξ’and the actual known values ξgt. Let us describe this procedure in the form of pseudo-code: 1. Consider an object from which its magnetization properties ξgtare known, consider also the rest of the sequence parameters fixed and known 2. Set an initial set of FA values ^k = ^0 3. Generate D = (dt0, dt1, …, dtT), the simulated data samples for this object and MR sequence 4. Solve the inverse problem (1) and find the estimated parameters, which from now on we write as ξ’(^k) to indicate the dependence of the FA values 5. Compute ℓ = L(ξ’(^k), ξgt) 6. If the value of ℓ is not good enough, generate a new set of FA values ^k + 1. Go back to step 3 and repeat until ℓ is below a certain pre- defined value The above procedure should also be seen as one embodiment of the method according to the present invention. Moreover, based on the description above, according to one embodiment of the present invention, the parameter P is one or more of time to echo (TE), time to repetition (TR), flip angle (FA), inversion pulse(s), or the echo train length (ETL). The biggest challenge of this method consists of finding a new set of FA values that improve the accuracy of the estimation of the parameters since derivatives are not available, falling into the field of derivative-free optimization. The method may further comprise determining values for a sequence parameter at each time point ^ = (^^^^t0, ^^^^t1, …, ^^^^tT), during the SBR acquisition, that minimize a difference between an estimated value ξ’ for ξx, and a ground- truth value ξgt, Thus, it may be ensured that the sequence parameters are finely tuned to closely match the actual tissue characteristics, leading to more accurate and reliable imaging results. By minimizing discrepancies between estimated and true values, the method enhances the fidelity of the acquired data, thereby improving the overall quality of the diagnostic images. The method may further comprise determining an evolution of a sequence parameter to maximize an accuracy of the spatial dependent parametric maps. Hence, by continuously optimizing the sequence parameter throughout the SBR acquisition, the method ensures that the spatial dependent parametric maps closely reflect the true spatial distribution of tissue properties. Hereby, enhanced precision and reliability of the imaging process may be provided, e.g., leading to higher quality images. Additionally, the method hence also allows for the use of shorter acquisition times without compromising image quality. As described above, optimization of SBR sequences with respect to the quality of the reconstructed quantitative maps may pertain to the choice of key parameters of the sequence, such as the flip angle, excitation phase, repetition time, echo time, read out duration etc. As will be discussed below, SNR of optimized sequences may further be increased. Besides the aforementioned parameters, there is also spatio-temporal encoding which makes actually MRI work. Traditionally, Fourier encoding is used while more recent efforts have focused on other types, e.g., radial, spiral or arbitrary encodings. These encodings refer a way of sampling a k-space, e.g., always respecting the Nyquist limit (for fully sampled sequences). The way the k-space is sampled may affect an overall SNR of the measured signal, for example, especially in sequences where the magnetization does not reach a steady state, as in the case of SBR. On top of the above-mentioned optimization it may be decided on how to sample repetitions of the k-space (because in SBR sequences one may sample the k-space multiple times) in a way that maximizes the SNR of the measured signal. More specifically, by choosing to sample a vicinity of the center of the k-space (which corresponds to reduced de-phasing and hence stronger signal) when the ensemble magnetization of the most representative tissues is stronger. In order to find where in the sequence this happens, the same type of simulation as of the method herein may be used, e.g., with a representative computational phantom. Once the points of maximum magnetization have been identified, k-space encodings may be assigned to these points that belong around the vicinity of the center / origin of the k-space while distributing the rest of the encodings (till Nyquist sampling theorem is satisfied) without a strong preference, hence simplifying the overall process. According to one embodiment the present invention there is provided a method for sampling repetitions of a k-space in simulation-based reconstruction, SBR, sequences to maximize a signal-to-noise ratio, SNR, of a measured signal, the method comprising: determining, by the method of previous embodiment, spatial dependent parametric maps that minimize a discrepancy between the measured signal and a predicted model signal, using a representative computational phantom, sampling a vicinity of a center of the k-space when an ensemble magnetization of representative tissues is stronger based on the determined spatial dependent parametric maps, identifying points of maximum magnetization within the sequence, and assigning k-space encodings to the points of maximum magnetization, such that the k-space encodings are located in the vicinity of the center of the k- space. The method may further comprise assigning k-space encodings to other points in the sequence until the Nyquist sampling theorem is satisfied. The method for sampling repetitions of k-space in SBR sequences enables maximization of the SNR of the measured signal. By utilizing spatially dependent parametric maps determined through the previous method, this method identifies points of maximum magnetization within the sequence. This enables improved assignment of k-space encodings to the vicinity of the center of k-space when the ensemble magnetization of the most representative tissues is strongest. Hence, optimal data acquisition, e.g., enhancing the accuracy of the estimated maps, is enabled. Additionally, the method ensures that the entire k-space is adequately sampled by distributing the remaining k-space encodings, thereby satisfying the Nyquist sampling theorem. The method hence improves image quality, diagnostic reliability, and simplifies the overall process. It is appreciated that the methods described herein integrates computational techniques with physical data acquisition processes to optimize imaging sequences, thereby enhancing quality and reliability of the results. The methods described herein may hence be computer-implemented methods. Detailed description of the drawings In fig.1 there is shown the estimation results obtained using different sequences for SBR purposes, where alternatives c) and d) show results when utilizing the method according to the present invention. Fig.1 shows the estimation results obtained using different sequences for SBR purposes for the same case of study. Each row displays the flip angle (FA) train of each sequence and the mapping results obtained when that sequence is used. This is a case in where we are estimating three parameters, proton density (PD), T1 and T2 relaxation. The first row (a) shows what we can consider a standard SBR sequence, in which the flip angle (FA) train was handcrafted based on knowledge on traditional MRI sequences. This sequence obtains very accurate estimation results for PD, T1and T2mapping for a 5.8 seconds 2D acquisition with 1 mm in-plane resolution. If we want to use the same strategy for designing the FA and reduce the acquisition time, we obtain the results shown in the second row (b), which obtains poorer results, especially in the PD and T2 maps. The last two rows (c) and (d) display the results of two sequences that have been optimized using the proposed framework. In these cases, only the FA train of the sequence was used as variable for optimization. Once the encoding pattern is fixed, and hence the acquisition time, the proposed method can find a suitable FA evolution to maximize the accuracy of the estimated maps. The results showed in 3.5 s and 2.6 s present a comparable accuracy to the ones obtained from the handcrafted SBR sequence with a 1.66 and 2.2 acceleration in acquisition time.

Claims

Claims 1. A method intended in the magnetic resonance imaging (MRI) field, said method comprising - determining a number of physical properties encoded in a vector ξx= (T1,x, - determining a set of sequence parameters encoded in a vector αt= (TEt, TRt, FAt, …); - characterizing an MR signal at a certain time t of a simulation-based reconstruction (SBR) acquisition as S(αt, ξx, t) for deciding a model signal, - determining a dtseries of measurements of the MR signal on a scanner; - performing inverse calculation(s) in accordance with arg minξ Σt||dt- S(αt, ξx, t)||2(1) for deciding spatial dependent parametric maps that minimize the discrepancy between a signal measured and a predicted model signal.

2. The method according to claim 1, wherein the MR signal S(αt, ξx, t) is obtained using a Bloch simulator that allows solving the inverse calculation arg minξ Σt||dt- S(αt, ξx, t)||2by using an iterative method.

3. The method according to claim 1 or 2, wherein the method involves providing multiple MRI sequences for simulation-based reconstruction (SBR).

4. The method according to any of claims 1-3, wherein the method involves calculation of the suitability of an MRI sequence for simulation-based reconstruction (SBR) as a function of an agreement between estimated values for ξxdenoted by ξ’and ground-truth values ξgt., preferably in accordance with arg minα L(ξ’, ξgt) s.t ξ’= arg minξ Σt||dt- S(αt, ξx, t)||2(2) where L(ξ’, ξgt) refers to a function of the differences between the estimated and ground-truth parametric maps.

5. The method according to claim 4, wherein the method is based on omitting the dependence of the data measurements dtfrom the ground-truth magnetic properties ξgtand the sequence parameters αt.

6. The method according to any of claims 1-5, wherein the method involves the following steps for optimization of one single parameter P: - Consideration of an object from which its magnetization properties ξgtare known, consider also the rest of the sequence parameters fixed and known; - Setting an initial set of P values ^k = ^0; - Generating D = (dt0, dt1, …, dtT), the simulated data samples for this object and MR sequence; - Solving the inverse problem (1) and findingthe estimated parameters, which from now on are written as ξ’(^k) for indication of the dependence of the P values; - Computing ℓ = L(ξ’(^k), ξgt); - If the value of ℓ is not good enough, generating a new set of P values ^k + 1, and the going back to step 3 and repeat until ℓ is below a certain pre-defined value.

7. The method according to claim 6, wherein the parameter P is one or more of time to echo (TE), time to repetition (TR), flip angle (FA), inversion pulse(s), or the echo train length (ETL).

8. The method according to any of claims 1-7, wherein the method further comprises determining values for a sequence parameter at each time point ^ = (^^^^t0, ^^^^t1, …, ^^^^tT), during the SBR acquisition, that minimize a difference between an estimated value ξ’ for ξx, and a ground-truth value ξgt, 9. The method according to any of claims 1-8, wherein the method further comprises determining an evolution of a sequence parameter to maximize an accuracy of the spatial dependent parametric maps.

10. A method for sampling repetitions of a k-space in simulation-based reconstruction, SBR, sequences to maximize a signal-to-noise ratio, SNR, of a measured signal, the method comprising: determining, by the method of claim 1, spatial dependent parametric maps that minimize a discrepancy between the measured signal and a predicted model signal, using a representative computational phantom, sampling a vicinity of a center of the k-space when an ensemble magnetization of representative tissues is stronger based on the determined spatial dependent parametric maps, identifying points of maximum magnetization within the sequence, and assigning k-space encodings to the points of maximum magnetization, such that the k-space encodings are located in the vicinity of the center of the k-space.

11. The method according to claim 10 further comprising: assigning k-space encodings to other points in the sequence until the Nyquist sampling theorem is satisfied.

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