CN110680322B - Method for describing non-exponential attenuation of magnetic resonance imaging signal and application thereof - Google Patents
Method for describing non-exponential attenuation of magnetic resonance imaging signal and application thereof Download PDFInfo
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Abstract
The invention discloses a method for describing non-exponential decay of a magnetic resonance imaging signal and application thereofA model, which is used for establishing a mathematical model of magnetic resonance signal attenuation; selecting a diffusion process in a specific complex medium as a research object, determining experimental conditions such as time sequence distribution of adopted radio frequency pulses and the like, and obtaining experimental data s (b) of a magnetic resonance imaging experiment; obtaining a parameter D in a magnetic resonance signal attenuation mathematical model through fitting data0，D1A value of (d); will be parameter D0And D1Substituting the value of (A) into a mathematical model of the magnetic resonance signal attenuation to draw a curve of the model, and simulating the magnetic resonance signal by using the mathematical model so as to accurately describe the non-exponentially attenuated magnetic resonance imaging signal in the complex medium. Compared with the existing method, the method reflects the influence of a complex medium structure on the diffusion process, has more accurate description and wide application prospect, and can be used for material detection and the like.
Description
Technical Field
The invention relates to a magnetic resonance imaging technology, in particular to a method for describing non-exponential decay of a magnetic resonance imaging signal and application thereof.
Background
The magnetic resonance imaging technology is a common detection technology, can realize nondestructive detection without damaging the internal structure of a detected sample, and is widely applied to the aspects of medical research, chemistry, petrochemical industry, archaeology and the like due to the advantages of no radiation, high resolution and the like. The research result of the magnetic resonance imaging signal model can be directly applied to diagnosis of diseases, detection of structures and the like, and the accurate description of the non-exponential decay magnetic resonance signal of the complex medium is the basis for analyzing the change of the tissue structure and has important significance.
The traditional diffusion magnetic resonance imaging attenuation signal is often quantified by a single exponential model, the premise is that water molecules in a medium are assumed to be free diffusion, the displacement conforms to Gaussian distribution, the characteristic function of the displacement is represented as a single exponential function of time, and the corresponding magnetic resonance signal attenuation model is S (b)/S0Exp (-b · ADC), ADC is the apparent diffusion coefficient. However, a large number of experiments have proved that complex media such as biological tissues and the like do not satisfy the condition of free diffusion, wherein the diffusion process is abnormal diffusion, the mean square displacement of water molecules is a nonlinear function of time, and the corresponding magnetic resonance signal attenuation curve also deviates from a single exponential form. Especially when the b value is larger, the influence of the inhomogeneity of the tissue on the diffusion motion is more obvious, the deviation of the magnetic resonance signal is more obvious, and the accurate description can not be realized by using a single exponential model.
Therefore, it is necessary to provide a method that can accurately describe the non-exponential decay of the magnetic resonance imaging signal, so as to describe the abnormal diffusion phenomenon in the complex medium.
Disclosure of Invention
The purpose of the invention is as follows: in order to solve the problems, the invention provides a novel method capable of accurately describing the non-exponential decay of a magnetic resonance imaging signal and application thereof, so as to accurately and quickly realize the depiction of the magnetic resonance signal in a complex medium.
The technical scheme is as follows: in order to achieve the purpose, the invention adopts the following technical scheme:
a method of describing a non-exponential decay of a magnetic resonance imaging signal, comprising the steps of:
(1) according to a classical constant diffusion coefficient magnetic resonance signal attenuation model, a variable diffusion curvature model is adopted to establish a mathematical model of magnetic resonance signal attenuation;
(2) selecting a diffusion process in a specific complex medium as a research object, determining a time sequence distribution experiment condition of an adopted radio frequency pulse, and obtaining experiment data s (b) of a magnetic resonance imaging experiment;
(3) combining the experimental data s (b) of the magnetic resonance imaging experiment in the step (2), and obtaining the parameter D in the magnetic resonance signal attenuation mathematical model through fitting the data0，D1A value of (d);
(4) will be parameter D0And D1Substituting the value of (2) into the mathematical model of the attenuation of the magnetic resonance signal in the step (1), drawing a curve of the model, and simulating the magnetic resonance signal by using the mathematical model, thereby accurately describing the non-exponentially attenuated magnetic resonance imaging signal in the complex medium.
Further, the variable diffusion curvature model in the step (1) is as follows:
wherein b is a magnetic resonance imaging experiment parameter, S represents signal intensity, S0Is the signal intensity when b is 0, D is the diffusion coefficient of the complex medium, and u is the integral variable.
Wherein, the diffusion coefficient of the complex medium is expressed by the following function with b as a variable:
wherein D is0As an apparent diffusion coefficient, D1Is a measure of the complexity of the structure.
Further, the mathematical model of the magnetic resonance signal attenuation established in the step (1) is as follows:
wherein b is a magnetic resonance imaging experiment parameter, S0Signal strength when b is 0, D0As an apparent diffusion coefficient, D1Is a measure of the complexity of the structure under investigation.
Further, the step (3) adopts a least square method to fit the data to determine the value D of the parameter in the non-exponential decay magnetic resonance signal0，D1。
Further, the value D of the parameter is determined in the step (4)0And D1Substituting the magnetic resonance signal into a mathematical model of magnetic resonance signal attenuation to simulate the magnetic resonance signal, and drawing an image of S (b) by Matlab software to visually describe the attenuation of the magnetic resonance signal.
Wherein the complex media is a porous media.
Wherein the variable diffusion curvature model is an S-T pulse sequence or a double echo diffusion sequence.
The invention also provides application of the method for describing the non-exponential decay of the magnetic resonance imaging signal, which is used for analyzing the magnetic resonance signal in the complex medium and obtaining the related information of the microstructure of the complex medium through signal analysis.
Has the advantages that: compared with the prior art, the method adopts a variable diffusion curvature model to deduce a method model for describing the non-exponential attenuation of the magnetic resonance imaging signal, then combines the diffusion magnetic resonance experiment conditions and the experiment data of the complex medium to determine the parameter values in the model, and finally visually describes the attenuation of the magnetic resonance signal through the curve image of the model. The present invention describes the non-exponential decay characteristic of a magnetic resonance signal requiring only two parameters, the apparent diffusion coefficient and the structural complexity. The changes in these parameters reflect changes in the diffusion coefficient due to changes in the structure and composition of the complex medium, and thus may reflect complex properties of the tissue such as porosity, tortuosity, permeability, etc. during attenuation of the magnetic resonance signal. Compared with the existing method, the method reflects the influence of a complex medium structure on the diffusion process, has more accurate description and wide application prospect, and can be used for material detection and the like.
Drawings
FIG. 1 is a flow chart of the method of the present invention;
figure 2 is signal attenuation data for a magnetic resonance experiment;
figure 3 is a graph comparing simulated curves of decay signals in a magnetic resonance experiment.
Detailed Description
The following detailed description of the present invention will be provided in conjunction with the accompanying drawings and specific embodiments to facilitate a more thorough understanding of the present invention by those skilled in the art. It is to be understood that the present disclosure is only one representative embodiment. It will be apparent that the invention is not limited to any specific structure, function, device and method described herein, but may have other embodiments and the scope of the invention is not limited to the described embodiments.
The invention relates to a method for describing non-exponential decay of a magnetic resonance imaging signal. The method is suitable for analyzing magnetic resonance signals of porous media and other various diffusion environments. This example selects Sephadex as the subject of study, and details the specific method of analysis. It should be noted that the analytical procedure of the present invention is not limited to sephadex, nor to porous media of this type, and that other diffusion environments can be used in a similar manner.
As shown in fig. 1, a method for non-exponential decay of a magnetic resonance imaging signal is described, which comprises the following specific operation steps:
(1) according to a classical constant diffusion coefficient magnetic resonance signal attenuation model, a variable diffusion curvature model is adopted to establish a mathematical model of magnetic resonance signal attenuation;
the variable diffusion curvature model is as follows:
wherein b is a magnetic resonance experiment parameter, S0Is the signal intensity when b is 0, D is the diffusion coefficient of the complex medium, and u is the integral variable.
The diffusion coefficient expression for complex media is:
wherein D is0As an apparent diffusion coefficient, D1Is a measure of the complexity of the structure under investigation.
According to the variable diffusion curvature model, the mathematical model for obtaining the magnetic resonance signal attenuation is as follows:
(2) selecting a diffusion process in a specific complex medium as a research object, determining experimental conditions such as time sequence distribution of adopted radio frequency pulses and the like, and obtaining experimental data s (b) of a magnetic resonance imaging experiment.
(3) Determining the value D of the parameter in the non-exponential decay magnetic resonance signal by fitting the data in combination with the experimental data s (b) of the magnetic resonance imaging experiment in the step (2)0，D1。
(4) Will be parameter D0And D1Substituting the value into the mathematical model of the magnetic resonance signal attenuation in the step (1) to draw a curve of the model, namely simulating the magnetic resonance signal by using the mathematical model so as to accurately describe the non-exponentially attenuated magnetic resonance imaging signal in the complex medium.
The method can be used for analyzing the magnetic resonance signal in the diffusion medium, and the related information of the microstructure of the diffusion medium can be obtained through signal analysis. If the diffusion media is porous media, information such as pore size and position distribution of the porous media can be obtained.
Here, several points need to be explained: the non-exponential decay signal model provided by the invention is based on a variable diffusion curvature model, is not limited to a specific pulse sequence, and can be used for an S-T pulse sequence, a double-echo diffusion sequence and the like; the present invention is applicable to various media, not limited to the above two complex media.
Example (b):
1. this example selects Sephadex as the subject of investigation. Sephadex has a swollen polymer cross-linked network structure that is commonly used for protein isolation when Sephadex beads are formed. Before the experiment, the dry powder beads are soaked in distilled water, and after several days, the hydrated gel is put into a magnetic resonance imaging centrifugal tube for experiment. The diffusion time in the experiment ranged from 27 to 200ms, the pulse length was 5ms, and the variation of the b value ranged from 100 to 4000s/mm2The diffusion gradient strength G varied from 0.01 to 0.4T/m. the experimental data for the dextran gel model G25-50 at diffusion times of 200ms was selected in this example].Magnetic Resonance Imaging,2018,56:110-118”。
The experimental parameters can be arbitrarily selected when the invention is used, and are not limited to the specific examples adopted in the invention.
As shown in fig. 2, s (b) is signal attenuation data of the magnetic resonance experiment.
2. Substituting the measured experimental signal s (b) into the variable diffusion curvature model in step (1)
Determination of model parameters D by fitting experimental data0，D1I.e. the apparent diffusion coefficient of the medium and the complexity of the medium.
3. Substituting the fitted parameter values into the signal attenuation model, drawing a signal attenuation curve, and simulating the magnetic resonance signal by numerical value, thereby accurately describing the magnetic resonance imaging signal of the sephadex. The numerical simulation results are shown in fig. 3 as a solid line.
In order to verify the effectiveness of the invention in describing the non-exponential decay of the magnetic resonance imaging signal, a classical single exponential model S (b)/S is adopted0The sephadex diffusion imaging signals in the examples are described by exp (-b · ADC). And substituting the signal s (b) obtained by the experiment into a single exponential model, and determining the value of a parameter ADC (analog to digital converter) through data fitting, namely the apparent diffusion coefficient of the medium. And substituting the fitted parameter values into the single exponential model, and drawing a numerical simulation curve of the model, wherein the result is shown by a dotted line in figure 3.
4. From the result in the step 3, it can be known that in the magnetic resonance imaging experiment, when the b value is large, the signal attenuation in the complex medium has a trailing phenomenon, a common single exponential model curve obviously deviates from the experimental result, and the phenomenon cannot be numerically simulated.
From the foregoing results, it can be seen that the non-exponential decay of the magnetic resonance imaging signal can be accurately described using the present invention. The method adopts a variable diffusion curvature model, gives the relation between the actual diffusion coefficient and the apparent diffusion coefficient of the complex medium and the structural complexity, deduces the law of magnetic resonance signal attenuation, then combines the experimental conditions and the experimental data of the magnetic resonance experiment in the complex medium, determines the value of parameters in the model through fitting data, and finally accurately describes the magnetic resonance attenuation signal through drawing an attenuation curve. The invention describes that the non-exponential decay of the magnetic resonance imaging signal only needs two parameters, namely the apparent diffusion coefficient and the structural complexity. Compared with the existing model, the method reflects the influence of the structure of the complex medium on the diffusion process, and the description is more accurate, and according to the wide application range of magnetic resonance, the method has a reason that the method has a wide application prospect and can be applied to the detection of various materials and the description of the diffusion phenomenon in the complex medium.
Claims (7)
1. A method of describing a non-exponential decay of a magnetic resonance imaging signal, comprising the steps of:
(1) according to a classical constant diffusion coefficient magnetic resonance signal attenuation model, a variable diffusion curvature model is adopted to establish a mathematical model of magnetic resonance signal attenuation;
the variable diffusion curvature model is:
wherein b is a magnetic resonance imaging experiment parameter, S represents signal intensity, S0The signal intensity when b is 0, D is the diffusion coefficient of the complex medium, and u is the integral variable;
the diffusion coefficient of a complex medium is expressed as a function of b as follows:
wherein D is0As an apparent diffusion coefficient, D1Is a measure of the complexity of the structure;
(2) selecting a diffusion process in a complex medium as a research object, determining a time sequence distribution experiment condition of an adopted radio frequency pulse, and obtaining experiment data s (b) of a magnetic resonance imaging experiment;
(3) combining the experimental data s (b) of the magnetic resonance imaging experiment in the step (2), and obtaining the parameter D in the magnetic resonance signal attenuation mathematical model through fitting the data0，D1A value of (d);
(4) will be parameter D0And D1Substituting the value of (2) into the mathematical model of the attenuation of the magnetic resonance signal in the step (1), drawing a curve of the model, and simulating the magnetic resonance signal by using the mathematical model, thereby accurately describing the non-exponentially attenuated magnetic resonance imaging signal in the complex medium.
2. A method for describing a non-exponential decay of a magnetic resonance imaging signal according to claim 1, wherein the mathematical model of the decay of the magnetic resonance signal established in step (1) is:
3. a method of describing a non-exponential decay of a magnetic resonance imaging signal according to claim 1, characterized by: the step (3) adopts a least square method to fit data to determine the value D of the parameter in the non-exponential decay magnetic resonance signal0，D1。
4. A method of describing a non-exponential decay of a magnetic resonance imaging signal according to claim 1, characterized by: the value D of the parameter in the step (4)0And D1Substituting the magnetic resonance signal into a mathematical model of magnetic resonance signal attenuation to simulate the magnetic resonance signal, and drawing an image of S (b) by Matlab software to visually describe the attenuation of the magnetic resonance signal.
5. A method of describing a non-exponential decay of a magnetic resonance imaging signal according to claim 1, characterized by: the complex media is a porous media.
6. A method of describing a non-exponential decay of a magnetic resonance imaging signal according to claim 1, characterized by: the variable diffusion curvature model is an S-T pulse sequence or a double-echo diffusion sequence.
7. Use of a method for describing a non-exponential decay of a magnetic resonance imaging signal as claimed in any of claims 1-3, characterized in that the method is used for analyzing magnetic resonance signals in a complex medium, and information about the microstructure of the complex medium is obtained by signal analysis.
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