METHOD OF QUANTIFYING MAGNETIC RESONANCE DIFFUSION PARAMETERS BY USING DIFFUSION WEIGHTED MAGNETIC RESONANCE IMAGES

Disclosed is an unsupervised deep learning method, which simultaneously performs registration between diffusion weighted magnetic resonance images and quantification of diffusion parameters. The unsupervised deep learning method decreases a registration error caused by a contrast difference by comparing a similarity between images of the same contrast, increases the performance of registration, and increases the accuracy of quantifying magnetic resonance diffusion parameters.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application claims the priority benefit of Korean Patent Application No. 10-2022-0149013 filed on Nov. 9, 2022, and Korean Patent Application No. 10-2022-0187041 filed on Dec. 28, 2022, in the Korean Intellectual Property Office, the disclosure of which is incorporated herein by reference for all purposes.

BACKGROUND

One or more embodiments relate to a method of quantifying magnetic resonance diffusion parameters.

2. Description of Related Art

Diffusion magnetic resonance imaging is a technique for non-invasively obtaining information regarding the inside of a human body by imaging the diffusion of water molecules. The diffusion of water molecules inside the human body may be affected by microstructures, such as cell fibers or membranes, different from diffusion in uniform water. The diffusion magnetic resonance imaging may image the structure of cells or the feature of cells by obtaining information on the diffusion of water molecules. To quantify a degree of the diffusion of water molecules inside the human body, diffusion weighted magnetic resonance images (DW-MRIs) may be obtained and registered with one another, and the registered images may be applied to a diffusion model. A person may inevitably move in a magnetic resonance imaging (MRI) system while capturing DW-MRIs, and the obtained DW-MRIs may accordingly be unaligned with one another. When performing quantification by using the unaligned DW-MRIs, the accuracy of quantification may decrease. Therefore, the DW-MRIs obtained for quantification may necessarily be registered with one another. As such, the accuracy of quantification may depend on the accuracy of registration, and thus, accurate registration between images may be highly important. Typical techniques have attempted registration between DW-MRIs by spatially transforming the DW-MRIs in order to increase a similarity to a reference image after obtaining the DW-MRIs. However, the accuracy of registration in a method of increasing a similarity may decrease when image contrast is highly different between images.

SUMMARY

An aspect provides a method of quantifying magnetic resonance diffusion parameters for increasing the accuracy of quantifying the magnetic resonance diffusion parameters.

The technical goal obtainable from the present disclosure is not limited to the above-mentioned technical goal, and other unmentioned technical goals may be clearly understood from the following description by those having ordinary skill in the technical field to which the present disclosure pertains.

According to an aspect, there is provided is a method of quantifying magnetic resonance diffusion parameters by using diffusion weighted magnetic resonance images. The method may include (i) preparing a reference image and diffusion weighted magnetic resonance images; (ii) controlling the reference image to be input to first neural networks and the diffusion weighted magnetic resonance images to be respectively input to the first neural networks, in which the first neural networks respectively include different first weights, the first neural networks are configured to estimate transformation functions representing a spatial transformation to the reference image from the diffusion weighted magnetic resonance images respectively corresponding to the first neural networks, and the first neural networks are configured to respectively provide first output images in response to the input of the reference image and the diffusion weighted magnetic resonance images respectively corresponding to the first neural networks; (iii) controlling the first output images to be input to a second neural network, in which the second neural network includes different second weights and the second neural network is configured to provide at least one second output image in response to the input of the first output images; (iv) providing third output images of which the number is the same as the number of first output images by applying intravoxel incoherent motion-diffusion kurtosis imaging (IVIM-DKI) to the reference image and the at least one second output image; (v) providing fourth output images by applying inverse functions of the transformation functions to the third output images; (vi) updating the first weights and the second weights by using the diffusion weighted magnetic resonance images, the first output images, the third output images, and the fourth output images; and (vii) repeating operations (ii) to (vi) a plurality of times.

The reference image may be a magnetic resonance imaging (MRI) image obtained in the setting of a b value to 0[s/mm2], and the diffusion weighted magnetic resonance images may be MRI images obtained while changing a b value to different values except 0[s/mm2].

As operation (vii) is performed, the first output images may get closer to the diffusion weighted magnetic resonance images and be closely registered with the reference image.

The diffusion weighted magnetic resonance images may be respectively generated by using diffusion weighted magnetic resonance images each obtained in a readout direction, in a phase encoding direction, and in a slice selection direction.

The at least one second output image may include at least one of a diffusion coefficient image representing values of diffusion coefficients D on the biometrics represented by the diffusion weighted magnetic resonance images, a perfusion coefficient image representing values of perfusion coefficients Dpon the biometrics represented by the diffusion weighted magnetic resonance images, a kurtosis image representing values of kurtoses K on the biometrics represented by the diffusion weighted magnetic resonance images, and a perfusion fraction image representing values of perfusion fractions f on the biometrics represented by the diffusion weighted magnetic resonance images.

As operation (vii) is performed, the third output images may get closer to the first output images.

As operation (vii) is performed, the fourth output images may get closer to the diffusion weighted magnetic resonance images.

Operation (vi) may include configuring a loss function by using the diffusion weighted magnetic resonance images, the first output images, the third output images, and the fourth output images and calculating the first weights and the second weights to minimize the loss function.

The loss function is defined by the following equations:

in which loss denotes the loss function, loss1denotes a first loss function, loss2denotes a second loss function, Sin(b) denotes the diffusion weighted magnetic resonance images, Ŝout(b) denotes the fourth output images, Sa(b) denotes the first output images, Ŝa(b) denotes the third output images, λ denotes a weight, and NCC(X; Y) denotes a normalized cross correlation between X and Y.

According to embodiments, there is a technical effect of increasing the accuracy of quantifying magnetic resonance diffusion parameters.

DETAILED DESCRIPTION

Terms, such as “first”, “second”, and the like, may be used herein to describe components. Each of these terminologies is not used to define an essence, order or sequence of a corresponding component but used merely to distinguish the corresponding component from other component(s). For example, a “first” component may be referred to as a “second” component, or similarly, and the “second” component may be referred to as the “first” component within the scope of the right according to the concept of the present disclosure.

It should be noted that if it is described that one component is “connected”, “coupled”, or “joined” to another component, a third component may be “connected”, “coupled”, and “joined” between the first and second components, although the first component may be directly connected, coupled, or joined to the second component.

Unless otherwise defined, all terms used herein including technical or scientific terms have the same meaning as commonly understood by one of ordinary skill in the art to which examples belong. Terms, such as those defined in commonly used dictionaries, are to be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art, and are not to be interpreted in an idealized or overly formal sense unless expressly so defined herein.

The present disclosure proposes an unsupervised deep learning method, which simultaneously performs registration between diffusion weighted magnetic resonance images and quantification of diffusion parameters. The unsupervised deep learning method may decrease a registration error caused by a contrast difference by comparing a similarity between images of the same contrast, increase the performance of registration, and increase the accuracy of quantifying magnetic resonance diffusion parameters. The unsupervised deep learning method may not require a large amount of data for learning. An economic effect may be expected because rescanning is not required even if patients move during a magnetic resonance imaging (MRI) scan. In addition, accurate quantification of diffusion parameters may assist diagnosing various diseases, such as cancer or a stroke, which may be diagnosed by using disease diffusion parameters.

Hereinafter, the examples are described in detail with reference to the accompanying drawings. When describing the examples with reference to the accompanying drawings, like reference numerals refer to like elements and a repeated description related thereto is omitted.

FIG.1is a flowchart illustrating a method of quantifying magnetic resonance diffusion parameters by using diffusion weighted magnetic resonance images, according to an embodiment, andFIGS.2to11are diagrams illustrating operations performed by the method described with reference toFIG.1, according to an embodiment.

Referring toFIG.1, the method of quantifying the magnetic resonance diffusion parameters may initiate with operation105of preparing a reference image S0, diffusion weighted magnetic resonance images Sin(b) obtained in a readout direction, diffusion weighted magnetic resonance images Sin(b) obtained in a phase encoding direction, diffusion weighted magnetic resonance images Sin(b) in obtained in a slice selection direction. The reference image S0may be an MRI image obtained in the setting of a b value, that is, a parameter set during an MRI scan, to 0[s/mm2] The diffusion weighted magnetic resonance images Sin(b) obtained in a readout direction, the diffusion weighted magnetic resonance images Sin(b) obtained in a phase encoding direction, and the diffusion weighted magnetic resonance images Sin(b) obtained in a slice selection direction may be MRI images obtained while changing the b value to different values except 0[s/mm2]. The diffusion weighted magnetic resonance images Sin(b) obtained in a readout direction may be MRI images obtained while changing the b value and applying a diffusion gradient in left and right directions. The diffusion weighted magnetic resonance images Sin(b) obtained in a phase encoding direction may be MRI images obtained while changing the b value and applying the diffusion gradient in forward and backward directions. The diffusion weighted magnetic resonance images Sin(b) obtained in a slice selection direction may be MRI images obtained while changing the b value and applying the diffusion gradient in upward and downward directions. In operation110, an index i indicating an iteration number may be initialized to 1.

In operation115, as illustrated inFIG.2, the reference image S0may be controlled to be input to 1-1 neural networks210, and the diffusion weighted magnetic resonance images Sin(b) obtained in a readout direction may be controlled to be respectively input to the 1-1 neural networks210respectively corresponding to the diffusion weighted magnetic resonance images Sin(b) obtained in a readout direction. Each of the 1-1 neural networks210may include an input layer, hidden layers, and an output layer. Each of the hidden layers may include nodes. Nodes in the lowest hidden layer may be implemented to receive input vectors output from the input layer. Values of nodes in a relatively lower hidden layer may be transmitted to nodes in a relatively higher hidden layer after different 1-1 neural network weights are applied to the values. The output layer of the 1-1 neural network210may include nodes, to which the different 1-1 neural network weights are respectively applied, connected to nodes in the highest hidden layer. In an embodiment, the 1-1 neural network210may implement a deep neural network (DNN), a convolutional neural network (CNN), or a fully connected neural network (FCNN). The 1-1 neural networks210may be neural networks suitable for estimating a spatial transformation, such as parallel translation, scaling, shearing, rotation, and the like. In an embodiment, each of the 1-1 neural networks210may estimate a 1-1 transformation function representing a spatial transformation to the reference image S0from the diffusion weighted magnetic resonance image Sin(b), corresponding to the 1-1 neural network210, obtained in a readout direction. Each of the 1-1 neural networks210may provide a 1-1 output image Sa(b) in response to the input of the reference image S0and the diffusion weighted magnetic resonance image (Sin(b)), corresponding to the 1-1 neural network210, obtained in a readout direction.

Referring toFIG.1, in operation120, as illustrated inFIG.3, the reference image S0may be controlled to be input to 1-2 neural networks320, and diffusion weighted magnetic resonance images Sin(b) obtained in a phase encoding direction may be controlled to be respectively input to the 1-2 neural networks320respectively corresponding to the diffusion weighted magnetic resonance images Sin(b) obtained in a phase encoding direction. The 1-2 neural networks320may respectively include different 1-2 neural network weights. The 1-2 neural networks320may be neural networks suitable for estimating a spatial transformation, such as parallel translation, scaling, shearing, rotation, and the like. In an embodiment, the 1-2 neural networks320may have the same structure as the 1-1 neural networks210. In an embodiment, each of the 1-2 neural networks320may estimate a 1-2 transformation function representing a spatial transformation to the reference image S0from the diffusion weighted magnetic resonance image Sin(b), corresponding to the 1-2 neural network320, obtained in a phase encoding direction. Each of the 1-2 neural networks320may provide a 1-2 output image Sa(b) response to the input of the reference image S0and the diffusion weighted magnetic resonance image Sin(b), corresponding to the 1-2 neural network320, obtained in a phase encoding direction.

Referring toFIG.1, in operation125, as illustrated inFIG.4, the reference image S0may be controlled to be input to 1-3 neural networks430, and diffusion weighted magnetic resonance images Sin(b) obtained in a slice selection direction may be controlled to be respectively input to the 1-3 neural networks430respectively corresponding to the diffusion weighted magnetic resonance images Sin(b) obtained in a slice selection direction. The 1-3 neural networks430may respectively include different 1-3 neural network weights. The 1-3 neural networks430may be neural networks suitable for estimating a spatial transformation, such as parallel translation, scaling, shearing, rotation, and the like. In an embodiment, the 1-3 neural networks430may have the same structure as the 1-1 neural networks210and/or the 1-2 neural networks320. In an embodiment, each of the 1-3 neural networks430may estimate a 1-3 transformation function representing a spatial transformation to the reference image S0from the diffusion weighted magnetic resonance image , corresponding to the 1-3 neural network430, obtained in a slice selection direction. Each of the 1-3 neural networks430may provide a 1-3 output image Sa(b) in response to the input of the reference image S0and the diffusion weighted magnetic resonance image , corresponding to the 1-3 neural network430, obtained in a slice selection direction.

Although operations115to125are described above as separate operations, those skilled in the art will recognize that the operations may be performed practically at the same time. In addition, those skilled in the art will recognize that operations115to125may be performed in different orders. For example, those skilled in the art will recognize that operation120may be performed before operations115and125. Accordingly, it should be understood and recognized that all such modified embodiments are within the scope of the present disclosure.

Referring toFIG.1, in operation130, as illustrated inFIG.5, the 1-1 output images Sa(b) may be controlled to be input to a 2-1 neural network540. The 2-1 neural network540may be a neural network for quantifying diffusion parameters depending on at least one direction and may include different 2-1 neural network weights. The 2-1 neural network540may provide at least one 2-1 output image in response to the input of the 1-1 output images. The at least one 2-1 output image may include at least one of a diffusion coefficient image representing values of diffusion coefficients D on biometrics represented by the diffusion weighted magnetic resonance images Sin(b) obtained in a readout direction, a perfusion coefficient image representing values of perfusion coefficients Dpon the biometrics represented by the diffusion weighted magnetic resonance images Sin(b) in obtained in a readout direction, and a kurtosis image representing values of kurtoses K on the biometrics represented by the diffusion weighted magnetic resonance images Sin(b) in a readout direction.

Referring toFIG.1, in operation135, as illustrated inFIG.6, the 1-2 output images Sa(b) may be controlled to be input to a 2-2 neural network650. The 2-2 neural network650may be a neural network for quantifying diffusion parameters depending on at least one direction and may include different 2-2 neural network weights. In an embodiment, the 2-2 neural networks650may have the same structure as the 2-1 neural networks540. The 2-2 neural network650may provide at least one 2-2 output image in response to the input of the 1-2 output images. The at least one 2-2 output image may include at least one of a diffusion coefficient image representing values of diffusion coefficients D on biometrics represented by the diffusion weighted magnetic resonance Sin(b) obtained in a phase encoding direction, a perfusion coefficient image representing values of perfusion coefficients Dpon the biometrics represented by the diffusion weighted magnetic resonance images Sin(b) obtained in a phase encoding direction, and a kurtosis image representing values of kurtoses K on the biometrics represented by the diffusion weighted magnetic resonance images Sin(b) in a phase encoding direction.

Referring toFIG.1, in operation140, as illustrated inFIG.7, the 1-3 output images Sa(b) may be controlled to be input to a 2-3 neural network760. The 2-3 neural network760may be a neural network for quantifying diffusion parameters depending on at least one direction and may include different 2-3 neural network weights. In an embodiment, the 2-3 neural networks760may have the same structure as the 2-1 neural networks540and/or the 2-2 neural networks650. The 2-3 neural network760may provide at least one 2-3 output image in response to the input of the 1-3 output images. The at least one 2-3 output image may include at least one of a diffusion coefficient image representing values of diffusion coefficients D on biometrics represented by the diffusion weighted magnetic resonance images Sin(b) obtained in a slice selection direction, a perfusion coefficient image representing values of perfusion coefficients Dpon the biometrics represented by the diffusion weighted magnetic resonance images Sin(b) obtained in a slice selection direction, and a kurtosis image representing values of kurtoses K on the biometrics represented by the diffusion weighted magnetic resonance images Sin(b) a slice selection direction.

Referring toFIG.1, in operation145, as illustrated inFIG.8, the 1-1 output images Sa(b), the 1-2 output images Sa(b), and the 1-3 output images Sa(b) may be controlled to be input to a 2-4 neural network870. The 2-4 neural network870may be a neural network for quantifying diffusion parameters not depending on a direction and may include different 2-4 neural network weights. The 2-4 neural network870may provide a 2-4 output image in response to the input of the 1-1 output images, 1-2 output images, and 1-3 output images. The 2-4 output image may be a perfusion fraction image representing values of perfusion fractions f on the biometrics represented by the diffusion weighted magnetic resonance images Sin(b). Although the 1-1 output images Sa(b), 1-2 output images Sa(b) and 1-3 output images Sa(b) are controlled to be respectively input to the 2-1 neural network540, the 2-2 neural network650, and the 2-3 neural network760in operations130to140, the 1-1 output images Sa(b), the 1-2 output images Sa(b), and the 1-3 output images Sa(b) may be controlled to be input to the 2-4 neural network870in operation145because the 2-1 neural network540, the 2-2 neural network650, and the 2-3 neural network760are neural networks for quantifying diffusion parameters depending on a direction, such as the diffusion coefficients D, the perfusion coefficients Dp, and the kurtoses k, but the 2-4 neural network870is a neural network for quantifying a diffusion parameter not depending on a direction, such as the perfusion fractions f.

Although operations130to145are described above as separate operations, those skilled in the art will recognize that the operations may be performed practically at the same time. In addition, those skilled in the art will recognize that operations130to145may be performed in different orders. For example, those skilled in the art will recognize that operation145may be performed before operations130to140. Accordingly, it should be understood and recognized that all such modified embodiments are within the scope of the present disclosure.

Referring toFIG.1, in operation150, as illustrated inFIG.9, an intravoxel incoherent motion-diffusion kurtosis imaging (IVIM-DKI) model930may be applied to the reference image S0and at least one of at least one 2-1 output image, at least one 2-2 output image, at least one 2-3 output image, and the 2-4 output image, and 3-1 output images Ŝa(b) of which the number is the same as the number of 1-1 output images, 3-2 output images Ŝa(b) of which the number is the same as the number of 1-2 output images, and 3-3 output images Ŝa(b) of which the number is the same as the number of 1-3 output images may be provided. The IVIM-DKI model930may be expressed by Equation 1.

denotes the 3-1 output images, the 3-2 output images, and the 3-3 output images, S0denotes a reference image, D denotes a diffusion coefficient image, Dpdenotes a perfusion coefficient image, K denotes a kurtosis image, f denotes a perfusion fraction image, b denotes b values used to obtain the diffusion weighted magnetic resonance images Sin(b) obtained in a readout direction, the diffusion weighted magnetic resonance images Sin(b) obtained in a phase encoding direction, or the diffusion weighted magnetic resonance images Sin(b) obtained in a slice selection direction.

When the number of diffusion weighted magnetic resonance images Sin(b) obtained in a readout direction, the number of diffusion weighted magnetic resonance images Sin(b) obtained in a phase encoding direction, and the number of diffusion weighted magnetic resonance images Sin(b) obtained in a slice selection direction each are N, the number of 3-1 output images Ŝa(b), the number of 3-2 output images Ŝa(b), and the number of 3-3 output images Ŝa(b) a may each be N. (b) In this case, for example, to provide N 3-1 output images Sin(b), N b values used to obtain the diffusion weighted magnetic resonance images Sin(b) obtained in N readout directions, the diffusion coefficient image D, the perfusion coefficient image Dp, the kurtosis image K, and the perfusion fraction image f, that is, at least one 2-1 output image, and the reference image S0may be used. In another example, to provide N 3-2 output images Ŝa(b), N b values used to obtain the diffusion weighted magnetic resonance images in Sin(b) obtained in N phase encoding directions, the diffusion coefficient image D, the perfusion coefficient image Dp, the kurtosis image , and the perfusion fraction image f, that is, at least one 2-2 output image, and the reference image S0may be used. Yet another example, to provide N 3-3 output images Ŝa(b), N b values used to obtain the diffusion weighted magnetic resonance images Sin(b) obtained in N slice selection directions, the diffusion coefficient image D, the perfusion coefficient image Dp, the kurtosis image K, and the perfusion fraction image f, that is, at least one 2-3 output image, and the reference image S0may be used.

Referring toFIG.1, in operations155to165, as illustrated inFIG.10, the 3-1 output images Ŝa(b), the 3-2 output images Ŝa(b), and the 3-3 output images Ŝa(b) may respectively be inversely transformed and 4-1 output images Ŝout(b), 4-2 output images Ŝout(b), and 4-3 output images Ŝout(b) may be provided. Specifically, in operation155, as illustrated inFIG.10, inverse functions of the 1-1 transformation functions provided in operation115may be respectively applied to the 3-1 output images Ŝa(b), and the 4-1 output images Ŝout(b) may be provided. In operation160, as illustrated inFIG.10, inverse functions of the 1-2 transformation functions provided in operation120may be respectively applied to the 3-2 output images Ŝa(b), and the 4-2 output images Ŝout(b) may be provided. In operation165, as illustrated inFIG.10, inverse functions of the 1-3 transformation functions provided in operation125may be respectively applied to the 3-3 output images Ŝa(b), and the 4-3 output images out Ŝout(b) may be provided. Those skilled in the art will understand that operations155,160, and165may be performed at the same time or in different orders.

Referring toFIG.1, in operation170, as illustrated inFIG.11, the 1-1 neural network weights, the 1-2 neural network weights, the 1-3 neural network weights, the 2-1 neural network weights, the 2-2 neural network weights, the 2-3 neural network weights, and the 2-4 neural network weights may be updated by using the diffusion weighted magnetic resonance images Sin(b) obtained in a readout direction, the diffusion weighted magnetic resonance images Sin(b) obtained in a phase encoding direction, the diffusion weighted magnetic resonance images Sa(b)obtained in a slice selection direction, the 1-1 output images Sa(b), the 1-2 output images Ŝa(b), the 1-3 output images Sa(b), the 3-1 output images Ŝa(b), the 3-2 output images Ŝa(b), the 3-3 output images Ŝa(b), the 4-1 output images Ŝout(b), the 4-2 output images Ŝout(b) and the 4-3 output images Ŝout(b). In operation170, a loss function may be configured by using the diffusion weighted magnetic resonance images Sin(b) obtained in a readout direction, the diffusion weighted magnetic resonance images Sin(b) obtained in a phase encoding direction, the diffusion weighted magnetic resonance images Sin(b) obtained in a slice selection direction, the 1-1 output images Sa(b), the 1-2 output images Sa(b), the 1-3 output images Sa(b), the 3-1 output images Ŝa(b), the 3-2 output images Ŝa(b) the 3-3 output images Ŝa(b), the 4-1 output images Ŝout(b). the 4-2 output images Śout(b), and the 4-3 output images Śout(b). In operation170, the 1-1 neural network weights, the 1-2 neural network weights, the 1-3 neural network weights, the 2-1 neural network weights, the 2-2 neural network weights, the 2-3 neural network weights, and the 2-4 neural network weights may be updated by calculating the 1-1 neural network weights, the 1-2 neural network weights, the 1-3 neural network weights, the 2-1 neural network weights, the 2-2 neural network weights, the 2-3 neural network weights, and the 2-4 neural network weights for minimizing the loss function. In an embodiment, the loss function defined by Equations 2 and 3 may be used to update neural network weights.

In the above equations, loss denotes the loss function, loss1denotes a first loss function, loss2denotes a second loss function, Sin(b) denotes the diffusion weighted magnetic resonance images obtained in a readout direction, the diffusion weighted magnetic resonance images obtained in a phase encoding direction, and the diffusion weighted magnetic resonance images obtained in a slice selection direction, Śout(b) denotes the 4-1 output images, the 4-2 output images, and the 4-3 output images, Sa(b) denotes the 1-1 output images, the 1-2 output images, and the 1-3 output images, Śa(b) a denotes the 3-1 output images, the 3-2 output images, and the 3-3 output images, λ denotes a neural network weight, and NCC (X; Y) denotes a normalized cross correlation between X and Y.

Referring toFIG.1, in operation175, the index i indicating an iteration number may be verified as to whether the index is M (here, M is a natural number greater than or equal to 2). When i is determined to be M as a result of the verification in operation175, a process may be terminated. When i is determined not to be M as the result of the verification in operation175, the process may continue to operation180, in which i may increase by 1, and may return to operation115. In the illustrated embodiments, the 1-1 neural networks210, the 1-2 neural networks320, the 1-3 neural networks430, the 2-1 neural network540, the 2-2 neural network650, the 2-3 neural network760, and the 2-4 neural network870may be repeatedly trained for a certain number M of times. Because the loss function is closer to a minimum value as M increases, the 1-1 neural networks210, the 1-2 neural networks320, the 1-3 neural networks430, the 2-1 neural network540, the 2-2 neural network650, the 2-3 neural network760, and the 2-4 neural network870may be better trained as M increases. However, an excessive number of repetitions may overload a processor. To decrease a load on the processor, the number of repetitions may be limited to a selected number of times or a timeout may be set in a processing time.

When the training is performed as above, the 1-1 output images Sa(b) may respectively get closer to the diffusion weighted magnetic resonance images Sin(b) obtained in a readout direction and be closely registered with the reference image S0. When the training is performed as above, the 1-2 output images a Sin(b) may respectively get closer to the diffusion weighted magnetic resonance images Sin(b) obtained in a phase encoding direction and be closely registered with the reference image S0. When the training is performed as above, the 1-3 output images Sa(b) may respectively get closer to the diffusion weighted magnetic resonance images Sin(b) obtained in a slice selection direction and be closely registered with the reference image S0. When the training is performed as above, the 3-1 output images Ŝa(b) may respectively get closer to the 1-1 output images Sa(b). When the training is performed as above, the 3-2 output images Ŝa(b) may respectively get closer to the 1-2 output images Sa(b). When the training is performed as above, the 3-3 output images Ŝa(b) may respectively get closer to the 1-3 output images Sa(b). When the training is performed as above, the 4-1 output images Ŝout(b) may respectively get closer to the diffusion weighted magnetic resonance images Sin(b) obtained in a readout direction. When the training is performed as above, the 4-2 output images Ŝout(b) may respectively get closer to the diffusion weighted magnetic resonance images Sin(b) obtained in a phase encoding direction. When the training is performed as above, the 4-3 output images Ŝout(b) may respectively get closer to the diffusion weighted magnetic resonance images Sin(b) obtained in a slice selection direction. When the training is performed as above, at least one 2-1 output image, at least one 2-2 output image, at least one 2-3 output image, and at least one 2-4 output image may better represent values of diffusion parameters on the biometrics represented by the diffusion weighted magnetic resonance images Sin(b).

Although a method of inputting the diffusion weighted magnetic resonance images Sin(b) obtained in a readout direction, the diffusion weighted magnetic resonance images Sin(b) obtained in a phase encoding direction, the diffusion weighted magnetic resonance images Sin(b) obtained in a slice selection direction all to the neural networks and simultaneously performing the registration of the images and the quantification of diffusion parameters is described above, it should be recognized that the present disclosure is not limited to the foregoing examples. In some embodiments, the diffusion weighted magnetic resonance images Sin(b) obtained in a readout direction, the diffusion weighted magnetic resonance images Sin(b) obtained in a phase encoding direction, and the diffusion weighted magnetic resonance images Sin(b) obtained in a slice selection direction may be combined to generate combined images. The combined images may be input to the neural networks, and the registration of the combined images and the quantification of diffusion parameters may be performed. In some embodiments, the combined images may respectively be an averaged diffusion weighted magnetic resonance image Sin(b) obtained in a readout direction, an averaged diffusion weighted magnetic resonance image Sin(b) obtained in a phase encoding direction, and an averaged diffusion weighted magnetic resonance image Sin(b) obtained n a slice selection direction.

The above-described devices may act as one or more software modules in order to perform the operations of the above-described examples, or vice versa.