Abstract
The invention relates to a method for carrying out post-processing on a first set of samples measuring the magnitude of a WASAB1 signal delivered by a magnetic-resonance medical-imaging apparatus. Such a method comprises a step of detecting the samples of a first set Z, for which samples the respective polarities of the values of the measured signal are known, and of constructing a second set Y of “polarised” samples. Such a method further comprises a step of fitting a determined model to said second set Y, the two parameters of the determined model describing the static magnetic field B0 and excitation magnetic field B1 of the magnetic-resonance medical-imaging apparatus, respectively, and of producing an estimation of the parameters B0 and B1 of the model. Such a method relates to any magnetic-resonance-imaging application in which a correction for inhomogeneities in the fields B0 and B1 is required.
Claims
1. A method for carrying out post-processing on a first set Z of samples Z(Δω) of an experimental signal resulting from a WASAB1 acquisition sequence by a medical magnetic resonance imaging device, linked with an elementary volume of an organ, the respective values of the samples Z(Δω) of said first set Z describing the magnitude of a theoretical experimental signal according to frequency offsets Δω with respect to the resonant frequency of water, said method being implemented by a processing unit of an imaging analysis system, and comprising: detecting the samples Z(Δω) of the first set Z for which the polarities of the values of the theoretical experimental signal are considered to be certain and of constructing a second set Y of samples Y(Δω) such that: a. Y(Δω)=Z(Δω) if the polarity of the theoretical experimental signal is considered to be certain and positive; b. Y(Δω)=−Z(Δω) if the polarity of said theoretical experimental signal is considered to be certain and negative; and adjusting a determined model to the second set Y, the two parameters of said determined model describing respectively the static B0 and excitation B1 magnetic fields of the medical magnetic resonance imaging device, and of producing a first estimation of said parameters B0 and B1 of said model.
2. The method according to claim 1, including: estimating the polarity of the values of the theoretical experimental signal for all or some of the samples Z(Δω) from the thus-adjusted model and of enhancing the second set Y of samples comprising a set of samples Y(Δω) such that Y(Δω)=Z(Δω) if the polarity of the theoretical experimental signal is estimated to be positive and Y(Δω)=−Z(Δω) if the polarity of said theoretical experimental signal is estimated to be negative; and adjusting the determined model to the second set Y of samples and of producing a second estimation of said parameters B0 and B1.
3. The method according to claim 1, wherein: detecting the samples Z(Δω) of the first set Z, for which the polarities of the values of the theoretical experimental signal are considered to be certain, includes: for any sample Z(Δω), from the largest negative frequency offset (Δω) in absolute values to such a frequency offset of zero, extrapolating the value of said sample from the value or values of one or more samples respectively associated with different frequency offsets; for any sample Z(Δω), from the largest frequency offset (Δω) to such a frequency offset of zero, extrapolating the value of said sample from the value or values of one or more samples respectively associated with different frequency offsets; wherein: the polarity of the theoretical experimental signal for any frequency offset Δω is determined by the extrapolated value sign Z(Δω)′ of the sample Z(Δω) for said frequency offset, and the polarity of the theoretical experimental signal for a given frequency offset Δω is considered to be certain and positive as long as an extrapolated value Z(Δω)′ of a sample Z(Δω) remains positive.
4. The method according to claim 3, wherein the extrapolation of the value of a sample Z(Δω) comprises, for the first and second sub-steps, a prior evaluation of the largest interval (Gm) between the respective values of two samples Z(Δω) associated with successive frequency offsets and the subtraction of said largest interval (Gm) from the value of the sample associated with the frequency offset that is greater in absolute values than the one associated with the sample Z(Δω) the value of which is extrapolated.
5. The method according to claim 1, wherein detecting the samples Z(Δω) of the first set Z, for which the polarities of the measured values of the theoretical experimental signal are considered to be certain, includes: calculating the derivative of a first discrete signal resulting from an ordering of the samples of said first set Z according to increasing frequency offsets; detecting any discontinuity of the polarity of said derivative; wherein the polarity of the theoretical experimental signal is considered to be certain for the set of the frequency offsets Δω under consideration, said polarity being inverted when any discontinuity is detected in the polarity of said derivative.
6. The method according to claim 1, further comprising repeating the steps that are necessary for the estimation of the parameters B0 and B1 linked with an elementary volume of the organ, in order to produce a plurality of estimations of said parameters B0 and B1 linked respectively with a plurality of elementary volumes of said organ.
7. The method according to claim 6, further comprising producing an image in the form of a parametric map having pixels which encode respectively the values of the parameter B0 or B1 estimated for elementary volumes of interest.
8. The method according to claim 7, including displaying said image by a human-machine output interface of the imaging analysis system.
9. An imaging analysis system including a processing unit, an interface for communicating with the outside world, and storage media, wherein: the communication interface is arranged to receive, from said outside world, experimental data resulting from a WASAB1 acquisition sequence of data produced by spectral sampling of an elementary volume of an organ; and the storage media include program instructions, the interpretation of which by said processing unit implements a method according to claim 1.
10. A non-transitory computer-readable medium storing a program including one or more instructions that can be interpreted by a processing unit of an imaging analysis system wherein the interpretation of said program instructions by said processing unit implements a method according to claim 1.
11. (canceled)
Description
[0054] Other features and advantages will become more clearly apparent on reading the following description and on examining the figures which accompany it, in which:
[0055] FIG. 1, already described, illustrates a simplified description of a system for analysing images obtained by nuclear magnetic resonance;
[0056] FIG. 2, already described, illustrates a simplified description of a variant of a system for analysing images obtained by nuclear magnetic resonance;
[0057] FIG. 3, already described, shows a first example of a Z-spectrum in the form of a set of ordered samples Z(Δω) linked with an elementary volume of interest of an organ;
[0058] FIG. 4, already described, shows the same example of a Z-spectrum in the form of a set of samples Z(Δω) ordered like that in FIG. 3, superimposed on an estimated continuous experimental signal after adjustment of a determined model to the samples of said Z-spectrum according to the state of the art;
[0059] FIG. 5, already described, shows the same example of a Z-spectrum in the form of a set of samples Z(Δω) ordered like that in FIG. 3, superimposed on an estimated continuous experimental signal after adjustment of a determined model to the samples of said Z-spectrum according to the state of the art, after correction and fine-tuning of the medical imaging device;
[0060] FIG. 6A, already described, shows an estimation of a first biomarker from samples of a Z-spectrum according to the state of the art after correction and fine-tuning of the imaging device;
[0061] FIG. 6B, already described, shows an estimation of a second biomarker from samples of a Z-spectrum according to the state of the art after correction and fine-tuning of the imaging device;
[0062] FIG. 7, already described, shows several examples of a Z-spectrum in the form of a set of samples Za(Δω), Zb(Δω) ordered for a plurality of elementary volumes Va, Vb of a human brain, as well as parametric maps associated with the static B0 and excitation B1 fields of a medical imaging device;
[0063] FIG. 8 describes a first embodiment of a step of a method for carrying out post-processing on a WASAB1 spectrum, according to the invention, with the aim of detecting the samples of said spectrum describing magnitudes of a theoretical experimental signal the polarity of which is considered to be positive at the frequency offsets under consideration;
[0064] FIG. 9 describes a second embodiment of a step of a method for carrying out post-processing on a WASAB1 spectrum, according to the invention, with the aim of detecting the samples of said spectrum describing magnitudes of a theoretical experimental signal the polarity of which is considered to be known at the frequency offsets under consideration;
[0065] FIG. 10 illustrates a functional algorithm example of a method for carrying out post-processing on a WASAB1 spectrum, according to the invention.
[0066] In connection with FIG. 10, an example of a method will now be described for carrying out post-processing 100, according to the invention, on a first set Z of samples Z(Δω) of an experimental signal 10, 12, resulting from a WASAB1 acquisition sequence by a medical magnetic resonance imaging device 1, such as the one described previously in connection with FIG. 1 or 2.
[0067] Such a method 100 includes a processing 100a which can be implemented iteratively for a plurality of elementary volumes of an organ of interest.
[0068] Such a processing 100a, implemented for a voxel or elementary volume, includes two steps 110 and 120, possibly supplemented by two steps 130 and 140, as will be seen later in connection with two advantageous embodiments. A first objective of this processing 100a consists of constructing, in a step 110, a second set Y of samples from the set of samples of a first Z-spectrum following from a WASAB1 sequence. Contrary to said Z-spectrum, for which the samples Z(Δω) can describe an amplitude of a theoretical experimental signal 10, 12 the polarity of which is uncertain or variable, the second set Y of samples includes samples Y(Δω) describing amplitudes of said theoretical experimental signal 10, 12 the polarity of which is known. Such a construction of the second set Y will be examined successively in connection with FIGS. 8 and 9, which describe two distinct embodiments.
[0069] According to a first embodiment illustrated jointly by FIGS. 8 and 10, the second set Y of samples can be put together in the form of a sub-set of the Z-spectrum for which the samples Y(Δω) are respectively equal to the samples Z(Δω) when the polarity of the theoretical experimental signal the magnitude of which is measured is certain and positive. For this purpose, step 110 includes sub-steps 111 and 112, such that certain samples of the first set Z are moved apart and therefore not reproduced in the second set Y if the polarity of the theoretical experimental signal the magnitude of which is measured, at the frequency offsets Δω under consideration, is uncertain, or even in all likelihood negative.
[0070] As a variant, in connection with the example in FIG. 9, when step 110 includes sub-steps 113 and 114, the samples Y(Δω) of the second set Y of samples are respectively equal to the samples Z(Δω) of the first set Z when the polarity of the theoretical experimental signal the magnitude of which is measured is certainly positive. Said samples Y(Δω) are respectively equal to the −Z(Δω) when the polarity of said theoretical experimental signal the magnitude of which is measured is certainly negative. The second set Y of samples is therefore “polarized” contrary to the Z-spectrum.
[0071] Whatever the embodiment used, the model for estimating the parameters B0 and B1, when it is adjusted, in a step 120 or even 140, to the second set Y of samples of which the polarity of the theoretical experimental signal is known the magnitude of which is measured at the frequency offsets under consideration, no longer integrates the notion of absolute values, contrary to the model according to the state of the art. Owing to the contribution of the invention, said model is therefore simpler to adjust and more robust. It will also be seen that this model can be “reduced” from four parameters to two parameters, increasing by a factor of one hundred the performance in implementing a post-processing method 100 according to the invention in relation to the state of the art.
[0072] A first embodiment of the first step 110 of a post-processing method 100 according to the invention will be examined in connection with FIGS. 8 and 10. Said step 110 consists of detecting the samples Z(Δω) of the first set Z for which the polarity of the values of the theoretical experimental signal the magnitude of which is measured is certain and positive. Said step 110 moreover consists of constructing a second set Y of samples Y(Δω) such that Y(Δω)=Z(Δω) from the single samples Z(Δω) previously detected as describing measurements of a theoretical experimental signal with a positive polarity at the frequency offsets Δω under consideration. FIG. 8 illustrates, in the left-hand part, a Z-spectrum the samples Z(Δω) of which are represented by points and are ordered according to increasing frequency offsets, in this particular case from a frequency offset equal to −2 ppm to a frequency offset equal to +2 ppm. This first set Z of samples only includes positive values translating measurements of the magnitude of a theoretical experimental WASAB1 signal the polarity of which is not known a priori. A second set Y of samples constructed from the first set Z is shown in the right-hand part of said FIG. 8, according to a same ordering of frequency offsets Δω. The objective of this step 110 is to construct the set Y in such a way that it only includes samples Y(Δω) that are identical to the Z(Δω) of the first set Z if, and only if, said samples Z(Δω) translate respectively measurements of the magnitude of a theoretical experimental signal the polarity of which is certain and positive at the frequency offsets Δω under consideration. The samples Z(Δω) of the first set Z translating measurements of a theoretical experimental signal the polarity of which is uncertain, or even in all likelihood negative, at the frequency offsets under consideration, are moved apart. The second set Y of samples is therefore, as indicated in FIG. 8, a sub-set of the first set Z. The set Y can be considered to be a set of polarized samples since the polarity of the theoretical experimental signal the magnitude of which is measured is known for the frequency offsets under consideration.
[0073] In order to detect the samples Z(Δω) describing measurements of a theoretical experimental signal with a certainly positive polarity at the frequency offsets Δω under consideration, step 110 includes a first sub-step 111 consisting, for any sample Z(Δω), from the largest negative frequency offset Δω, in absolute values, to such a frequency offset of zero, of extrapolating the value of said sample Z(Δω) from the value or values of one or more samples respectively associated with negative frequency offsets which are greater in absolute values. By way of preferred but non-limitative example, according to FIG. 8, the extrapolated value Z(Δω)′, represented by an ‘x’ in FIG. 8, of a sample Z(Δω), can consist of a prior evaluation of the largest interval, given the reference Gm in FIG. 8, between the respective values of two samples Z(Δω) associated with successive frequency offsets. Said step 111 then consists of calculating the extrapolated value Z(Δω)′ by subtracting said largest interval Gm from the value of the sample associated with the frequency offset that is greater in absolute values than the one associated with the sample Z(Δω) the value of which is extrapolated. The vertical bars, connected to the extrapolated values represented by ‘x’ in FIG. 8, thus illustrate this extrapolation operation, performed from left to right, of the samples Z(Δω) from the frequency offset Δω close to −2 ppm to the frequency offset close to 0 ppm. The polarity of the theoretical experimental signal the measured magnitude of which corresponds to the sample Z(Δω) is considered as being certain and positive as long as the extrapolated values Z(Δω)′ remain positive or as long as the frequency offset Δω under consideration is not zero. As soon as an extrapolated value Z(Δω)′ is negative, this means that the discrete experimental signal described by the samples of the first set Z has a cusp. Step 111 stops, the subsequent samples, i.e. those associated with the greater frequency offsets Δω, are considered as describing measurements of a theoretical experimental signal the polarity of which is uncertain or negative. Only the preceding samples are detected as describing measurements of the magnitude of a theoretical experimental signal with a positive polarity at the frequency offsets under consideration. These detected samples are thus reproduced in the second set Y such that Y(Δω)=Z(Δω). Thus, in the example of FIG. 8, at the end of the implementation of sub-step 111, only the first sixteen samples are considered favourably for putting together the set Y. The first sample Z(Δω), i.e. the one that is associated with the largest frequency offset in absolute values, is, hypothetically, detected favourably for initializing step 111.
[0074] Step 110 moreover includes a sub-step 112 describing a behaviour mirroring that of sub-step 111. It consists of running through the samples Z(Δω), from right to left in FIG. 8, i.e. from the largest frequency offset Δω to a frequency offset of zero, in order to detect the samples Z(Δω) of the first set Z translating measurements of the magnitude of a theoretical experimental signal the polarity of which is certain and positive at the frequency offsets under consideration. It moreover consists of enhancing the second set Y of samples starting from these single detected samples, such that Y(Δω)=Z(Δω) and of moving apart the samples Z(Δω) describing measurements of the magnitude of a theoretical experimental signal with an uncertain or in all likelihood negative polarity for the frequency offsets under consideration.
[0075] For this purpose, the sub-step 112 consists, for any sample Z(Δω), from the largest positive frequency offset Δω to such a frequency offset of zero, of extrapolating the value of said sample Z(Δω) from the value or values of one or more samples Z(Δω) respectively associated with greater positive frequency offsets Δω. By way of preferred but non-limitative example, according to FIG. 8, the extrapolated value Z(Δω)′, represented by an ‘x’ in FIG. 8, of a sample Z(Δω) can consist of the calculation of the extrapolated value Z(Δω)′ of a sample Z(Δω) by subtracting the largest interval Gm between the respective values of two samples associated with two consecutive frequency offsets, interval Gm already mentioned within the framework of sub-step 111, from the value of the sample associated with the frequency offset smaller than the one associated with the sample Z(Δω) the value of which is extrapolated. The vertical bars, connected to the extrapolated values represented by ‘x’ in FIG. 8, thus illustrate this extrapolation operation, performed from right to left, of the samples Z(Δω) from the frequency offset Δω close to +2 ppm to the frequency offset Δω close to 0 ppm. The polarity of the theoretical experimental signal the magnitude Z(Δω) of which is measured for the frequency offsets Δω is considered as being certain and positive as long as the extrapolated values Z(Δω)′ remain positive and as long as the frequency offset Δω under consideration is not zero. As soon as an extrapolated value Z(Δω)′ is negative, this means that the discrete signal, described by the samples of the first set Z, has a cusp. Sub-step 112 stops, the subsequent samples, i.e. those associated with the smaller frequency offsets Δω, are considered as describing measurements of a theoretical experimental signal the polarity of which is uncertain or negative. Only the preceding samples are detected as describing measurements of a theoretical experimental signal the polarity of which is positive at the frequency offsets under consideration. These samples are thus reproduced in the second set Y such that Y(Δω)=Z(Δω). Thus, in the example of FIG. 8, at the end of the implementation of sub-step 112, only the first fifteen samples are considered favourably for enhancing the set Y, the sample Z(Δω) associated with the largest frequency offset being, hypothetically, detected favourably for initializing sub-step 112.
[0076] Sub-steps 111 and 112 have been described through a preferred implementation example according to which working out the extrapolated value Z(Δω)′, represented by an ‘x’ in FIG. 8, of a sample Z(Δω) can consist of a prior evaluation of the largest interval, given the reference Gm in FIG. 8, between the respective values of two samples Z(Δω) associated with successive frequency offsets then of the subtraction of said largest interval Gm from the value of the sample associated with the frequency offset that is greater in absolute values than the one associated with the sample Z(Δω) the value of which is extrapolated. Other extrapolation techniques could, as a variant or in addition, be implemented. It can more generally be considered that the extrapolated value Z(Δωi)′ of a sample Z(Δωi), i.e. the i.sup.th sample associated with the frequency offset Δω1 of the n samples available, can be written according to the relationship: Z(Δωi)′=ƒ (Z(Δω1), Z(Δω2), . . . , Z(Δωn), P) where n is a positive integer, ƒ is any function whatever and P is any parameter whatever, possibly plural. Thus, according to the preceding example, the function ƒ has the aim of calculating the interval Gm and of performing the subtraction operation and P=1 determines the rank of the sample preceding the one the value Z(Δωi) of which is extrapolated. As a variant, according to a second non-limitative implementation example, the function ƒ could consist of the calculation of the average value of values of P samples subsequent to the sample the value of which it is sought to extrapolate. Other combinations of the pair (ƒ, P) could, as a variant, be used without departing from the scope of the present invention.
[0077] FIG. 9 illustrates a second embodiment of step 110 of a post-processing method 100 according to the invention. Said step 110 consists of detecting the samples Z(Δω) of the first set Z for which the polarity of the values of the theoretical experimental signal the magnitude of which is measured is certain. Said step 110 moreover consists of constructing a second set Y of samples Y(Δω) such that Y(Δω)=Z(Δω) when the samples Z(Δω) describe measurements of a theoretical experimental signal with a certain and positive polarity and such that Y(Δω)=−Z(Δω) from the single samples Z(Δω) describing measurements of a theoretical experimental signal with a certain and negative polarity. FIG. 9, like the previously described FIG. 8, illustrates, in the left-hand part, a Z-spectrum the samples Z(Δω) of which are represented by points and are ordered according to increasing frequency offsets, in this particular case from −2 ppm to +2 ppm. This first set Z of samples includes positive values translating measurements of the magnitude of a theoretical experimental WASAB1 signal the polarity of which is not known a priori. A second set Y of samples constructed from the first set Z is shown in the right-hand part of said figure, according to a same ordering of the frequency offsets Δω. The objective of this step 110 is to construct the set Y in such a way that it only includes samples Y(Δω) identical to those Z(Δω) of the first set Z if, and only if, said samples Z(Δω) translate respectively measurements of the magnitude of a theoretical experimental signal the polarity of which is certain and positive at the frequency offsets Δω under consideration. The samples Z(Δω) of the first set Z translating measurements of the magnitude of a theoretical experimental signal the polarity of which is certainly negative at the frequency offsets under consideration are such that Y(Δω)=−Z(Δω). The second set Y of samples is therefore, as indicated in FIG. 9, a set of samples which can be considered to be “polarized” since the polarity of the theoretical experimental signal is known at the frequency offsets under consideration.
[0078] In order to detect the samples Z(Δω) describing measurements of the magnitude of a theoretical experimental signal with a certainly positive or negative polarity for the frequency offsets Δω under consideration, step 110 includes a first sub-step 113 consisting, for any sample Z(Δω) from the largest negative frequency offset Δω, of the calculation of the derivative of the discrete Z signal resulting from an ordering of the samples Z(Δω) according to increasing frequency offsets Δω. This derivative appears in the form of a discontinuous curve in FIG. 9. Taking into account the presence of cusps C1 and C2 of said discrete Z signal, the derivative has two clear discontinuities dd1 and dd2 of its sign or polarity. The case would be quite different if such cusps were not present, i.e. if the polarity of the theoretical experimental signal sampled were constant. Step 110 includes a second sub-step 114 of detecting such discontinuities of the polarity of said derivative, the polarity of the measurement of the theoretical experimental signal for one or more successive frequency offsets Δω being inverted during a discontinuity of the polarity of said derivative. Thus, according to the example illustrated by FIG. 9, step 110 makes it possible to consider respectively, upstream and downstream of said cusps C1 and C2, i.e. respectively upstream and downstream of said discontinuities dd1 and dd2, that the polarity of the theoretical experimental signal is certain and positive. Reciprocally, said polarity of the theoretical experimental signal is considered to be certain and negative for the range, appearing greyed out, of the frequency offsets comprised between said cusps C1 and C2. As the shape of the measured signal is substantially a ‘V’, two discontinuities of the sign of the derivative are expected, at the most. This is how the samples Z(Δω) detected as describing measurements of the magnitude of a theoretical experimental signal with a positive polarity at the frequency offsets under consideration are reproduced in the second set Y such that Y(Δω)=Z(Δω) and how the samples Z(Δω) detected as describing measurements of the magnitude of a theoretical experimental signal with a negative polarity at the frequency offsets under consideration are reproduced in the second set Y such that Y(Δω)=−Z(Δω). Thus, in the example of FIG. 9, at the end of the implementation of sub-step 114, the set of the samples of the first set Z is considered favourably for putting together the second set Y of polarized samples, the polarity of the measurement of the theoretical experimental signal being considered to be certain for the set of the frequency offsets Δω under consideration.
[0079] Through the implementation of step 110, the polarity of the theoretical experimental signal from which the second set Y of samples Y(Δω) follows is known at each frequency offset under consideration. Contrary to the state of the art, for which the model of the intensities of a WASAB1 Z-spectrum, on the basis of the Bloch equations, is expressed, in a simplified form, such that a sample of said Z(Δω)-spectrum is a function, in absolute values, of four free parameters c, d, B1 and B0, the use of the second set Y of “polarized” samples, instead of the Z-spectrum, makes it possible to get past the problem of complexity associated with the absolute value since the polarity of the theoretical experimental signal is known for each sample Y(Δω). Thus, the model of the intensities of the Y-spectrum can be written in a simplified form such that Y(Δω)=c−d.Math.ƒ(B0, B1, Δω).
[0080] The parameters of this model can advantageously be obtained by minimizing the sum of the squared error:
[00002] [0081] for which:
[00003] [0082] is the sum of the squared errors.
[0083] Assuming that the parameters B0 and B1 are constant, the model becomes linear in the parameters c and d. These latter can be replaced with their estimation at least of the least squares which is expressed analytically as a function of B0 and B1. By replacing these parameters c and d with their estimations as a function of B0 and B1, the model only has two explicit parameters: B0 and B1. The two linear parameters have been made implicit. According to the invention, the model is no longer a model with four parameters, but one with two parameters, which makes the estimation of B0 and B1 more rapid by two orders of magnitude, more robust and less susceptible to the local minima.
[0084] In fact, the model can be written, for T elementary volumes, in a matrix form, such that Y=M(B0, B1)β, where Y=[Y(Δω1), . . . , Y(Δωn)]{circumflex over ( )}T describes a vector containing the n samples Y(Δω), per elementary volume, for the frequency offsets Δω1 to Δωn, M is a matrix with a size of 2n containing the regressors or variables of the model, namely:
[00004]
[0085] Moreover, β=[c, d]{circumflex over ( )}T is a vector with a size of two, for each elementary volume, containing the linear parameters c and d. The matrix M depends explicitly on the non-linear parameters of the model, in this particular case B0 and B1. Thus, the sum of the squared errors, expressed previously, can now be written in the form:
SSE(B0,B1,β)=(Y−Mβ).sup.T(Y−Mβ)
[0086] For constant B0 and B1, the optimum estimation of β which minimizes the sum of the squared errors can be calculated analytically such that:
{circumflex over (β)}=(M.sup.TM).sup.−1M.sup.TY
[0087] If this estimation of β is replaced in the preceding expression, the following is obtained:
SSE.sub.min(B0,B1)=Y.sup.T(1−M(M.sup.TM).sup.−1M.sup.T)Y
[0088] The parameters c and d can be estimated with:
{circumflex over (β)}=({circumflex over (M)}.sup.T{circumflex over (M)}).sup.−1{circumflex over (M)}.sup.TY
where:
{circumflex over (M)}=M(![custom-character]()
)
[0089] In this way, a post-processing method 100 according to the invention includes a step 120 of adjusting a determined model to the second set Y of polarized samples, the set previously produced in step 110, the two parameters of said determined model describing respectively the static B0 and excitation B1 magnetic fields of the medical magnetic resonance imaging device 1 as described by way of example by FIG. 1. Said step 120 thus produces a first estimation of said parameters B0 and B1 of said model.
[0090] By way of preferred example, although this advantageous embodiment is optional, the invention provides that a method 100 includes two steps 130 and 140 with the aim jointly of producing a second estimation of said parameters B0 and B1, after possible enhancement of the second set Y of polarized samples.
[0091] In fact, since step 120 has delivered a first estimation of the parameters of the model, it is possible to accurately determine the samples of the Z-spectrum corresponding to measurements of the magnitude of the theoretical experimental signal even though the polarity of it is negative for the frequency offsets under consideration. It can be particularly advantageous to enhance the second set Y of samples, in particular if the latter results from an implementation of the first embodiment example of step 110, i.e. when said step 110 includes the sub-steps 111 and 112. In this case, said second set Y of samples is a sub-set of the first set Z the samples Y(Δω) of which are equal respectively to the samples Z(Δω) when the polarity of the theoretical experimental signal is positive, the other samples of Z being moved apart in order to produce the set Y.
[0092] In this case, the invention provides that the method 100 can include an optional step 130 of determining the polarity of the values of the theoretical experimental signal for all or some of the samples Z(Δω) from the model adjusted in this way in step 120 and of constructing the second set Y of samples again such that Y(Δω)=Z(Δω) if the polarity of the theoretical experimental signal is estimated to be positive and Y(Δω)=−Z(Δω) if the polarity (Δω) of the theoretical experimental signal is estimated to be negative. Owing to the successive implementation of steps 111, 112, 120 and 130, the second set Y of samples is more extensive than the one obtained after the single implementation of step 110, like the one obtained when said step 110 includes the previously described sub-steps 113 and 114.
[0093] A method 100 can then include a new iteration of step 120, represented by a step 140 in FIG. 10, subsequent to step 130, of adjusting the model to the thus enhanced set Y of polarized samples. Step 140 thus produces a new estimation of the parameters of the model using more samples without significantly penalizing the implementation of the method 100 taking into account the benefit resulting from the use of a simplified model in relation to that according to the state of the art.
[0094] As the parameters B0 and B1 are in particular estimated accurately and rapidly at the end of one instance of the processing 100a for an elementary volume of interest, the invention provides that a method 100 according to the invention includes as many iterations of said processing 100a for producing estimations in particular of the parameters B0 and B1 for a plurality of volumes of interest.
[0095] A method 100 can then include a step 150 of producing an image in the form of a parametric map, such as the map MB0 or MrB1 described previously in connection with FIG. 7, the pixels of which encode respectively the values of the parameter B0 or B1 estimated for elementary volumes of interest. This or these parametric map or maps can moreover be displayed by a suitable human-machine output interface, such as the interface 5 described in connection with FIGS. 1 and 2, in order that a user 6 of an imaging system S can note the estimations of said parameters B0 or B1, or even any other biomarker that can be produced from said parameters. The implementation of a method for carrying out post-processing on a first set Z of samples Z(Δω) describing the magnitude of a theoretical experimental signal resulting from a WASAB1 acquisition sequence by a medical magnetic resonance imaging device 1 becomes perfectly usable in the clinical field, thus opening the door to said clinical field for the CEST technique in particular, in order to quantify one or more biomarkers linked with a chemical species of interest of a human or animal organ in order, in fine, to characterize different lesions with altered metabolic properties. The invention cannot be reduced to this single use. It thus has a key place in any magnetic resonance imaging application for which a correction of inhomogeneities of static B0 and excitation B1 fields is required.
