Fatty liver magnetic resonance diffusion weighted imaging quantitative parameter prediction method

Abstract

The invention relates to the technical field of magnetic resonance diffusion weighted imaging quantitative parameter prediction, in particular to a fatty liver magnetic resonance diffusion weighted imaging quantitative parameter prediction method, which comprises the following steps: giving a fat fraction, and constructing a three-dimensional virtual liver tissue model with uniformly distributed fat droplets; simulating distribution of magnetic field intensity in the model; simulating Brownian motion of protons in the model to generate a proton position sequence; simulating a pulse gradient spin echo sequence; accumulating phases of all protons in the echo, and synthesizing a magnetic resonance diffusion weighted imaging signal; and analyzing the synthesized signal, and calculating to obtain predicted values of ADC and D. According to the method, the predicted values of ADC and D under different fat fractions are obtained, the predicted value under the corresponding fat fraction of the patient is subtracted from the DWI quantitative parameter (such as the ADC value) obtained through measurement of the hepatic fibrosis patient, interference of fat on the DWI quantitative parameter can be reduced, and the DWI-based hepatic fibrosis diagnosis accuracy can be improved.

Description

Technical Field

[0001] The present invention relates to the technical field of predicting quantitative parameters of magnetic resonance diffusion weighted imaging, and specifically to a method for predicting quantitative parameters of magnetic resonance diffusion weighted imaging of fatty liver. Background Art

[0002] Non-alcoholic fatty liver is a liver lipid metabolism disorder caused by obesity, insulin resistance and metabolic syndrome. One in ten patients with non-alcoholic fatty liver may develop into liver fibrosis, cirrhosis or even liver cancer. Liver fibrosis is a progressive pathological process characterized by excessive deposition of extracellular matrix and abnormal remodeling of liver connective tissue. The aggravation of liver fibrosis may cause pathological changes such as portal hypertension, hypersplenism, esophageal and gastric varices, etc., seriously threatening the life and health of patients. Therefore, the accurate assessment of liver fibrosis has important clinical significance for the early diagnosis and efficacy monitoring of diseases.

[0003] At present, liver biopsy is the "gold standard" for evaluating liver steatosis and liver fibrosis, but biopsy is an invasive examination, which is easy to cause serious complications, and there are sampling errors in the diagnosis results. With the development of medical imaging technology, ultrasound and computed tomography can diagnose chronic liver diseases to a certain extent, but these technologies can only identify the morphological changes of mature liver fibrosis. In contrast, magnetic resonance spectroscopy and magnetic resonance diffusion weighted imaging (Diffusion Weighted Imaging, DWI) can provide non-invasive information on liver steatosis and liver fibrosis respectively. For example, the quantitative parameters measured by magnetic resonance diffusion weighted imaging, including apparent diffusion coefficient (Apparent Diffusion Coefficient, ADC) and pure molecular diffusion coefficient (Pure Molecular Diffusion, D), are quantitative indicators reflecting the diffusion of water molecules in tissues and can be used as biomarkers of liver fibrosis. Since steatosis often accompanies the whole process of liver fibrosis, and biopsy has confirmed that DWI quantitative parameters are affected by liver steatosis, fat is a confounding factor in DWI diagnosis of liver fibrosis. However, there are conflicting conclusions about the relationship between fat and quantitative parameters in clinical practice, and clinical experiments are limited by many factors such as repeatability and scanning parameters, which will consume huge amounts of manpower and material resources.

[0004] Therefore, in view of the above problems, it is particularly important to provide a method for predicting quantitative parameters of magnetic resonance diffusion weighted imaging of fatty liver to quantify the influence of fat on DWI quantitative parameters. Summary of the Invention

[0005] To solve the above technical problems, the present invention proposes a prediction method for quantitative parameters of magnetic resonance diffusion weighted imaging of fatty liver. This method obtains the predicted values of ADC and D at different fat fractions (FatFraction, FF). By subtracting the predicted value corresponding to the fat fraction of a patient from the DWI quantitative parameter (such as the ADC value) measured in a liver fibrosis patient, the interference of fat on the DWI quantitative parameter can be reduced, which helps to improve the accuracy of diagnosing liver fibrosis based on DWI.

[0006] The technical problems to be solved by the present invention are realized by the following technical solutions:

[0007] A prediction method for quantitative parameters of magnetic resonance diffusion weighted imaging of fatty liver, comprising the following steps:

[0008] Step (1), given a fat fraction, construct a three-dimensional virtual liver tissue model with uniformly distributed fat droplets;

[0009] Step (2), simulate the distribution of magnetic field strength in the model;

[0010] Step (3), simulate the Brownian motion of protons in the model to generate a proton position sequence;

[0011] Step (4), simulate the pulsed gradient spin echo sequence;

[0012] Step (5), accumulate the phases of all protons in the echo to synthesize the DWI signal;

[0013] Step (6), analyze the synthesized signal above to calculate the predicted values of ADC and D.

[0014] As a further improvement of the present invention, in step (1), the three-dimensional virtual liver tissue model is a cube with a specific side length.

[0015] As a further improvement of the present invention, the construction process of the three-dimensional virtual liver tissue model in step (1) is as follows:

[0016] Given a fat fraction and the radius of the fat droplet; simulate the fat droplet as a sphere, fix the radius of each small sphere, calculate the volume ratio of the fat droplet to determine the number of small spheres; place the small spheres inside the model and randomly generate the initial position coordinates of the small spheres; if a collision occurs between the small spheres, place the target small sphere on the surface of the collided small sphere until all small spheres are evenly distributed in the three-dimensional virtual liver tissue model without overlap.

[0017] As a further improvement of the present invention, in step (2), the three-dimensional virtual liver tissue model is meshed, and the magnetic field strength at any point within the model is approximately calculated by cubic spline interpolation based on the magnetic field strength at the grid points. The total magnetic field strength at any grid point is the vector sum of the magnetic field perturbations of each fat droplet. The calculation formula for the magnetic field perturbation generated by a single fat droplet at this point is:

[0018]

[0019] In formula (1), B0 is the main magnetic field, χ L is the set magnetic susceptibility coefficient of fat, R is the radius of the fat droplet, r is the radial distance between the fat droplet and the grid point, and θ is the azimuth angle with the magnetic axis.

[0020] As a further improvement of the present invention, in step (3), a certain number of protons are randomly placed within the three-dimensional virtual liver tissue model, and each proton undergoes isotropic Gaussian diffusion, and its displacement satisfies:

[0021]

[0022] In formula (2), D0 is the proton diffusion rate, and its value is determined according to the initial position of the proton. Δ t is the time step of proton movement.

[0023] As a further improvement of the present invention, in step (4), a pulse gradient spin echo sequence is applied. In the idealized free diffusion state of the rectangular pulse, the calculation formula for the diffusion sensitivity factor b is:

[0024]

[0025] In formula (3), G is the magnetic field gradient strength, δ and Δ are respectively the duration and pulse interval time of the gradient pulse, and γ is the gyromagnetic ratio of the proton.

[0026] As a further improvement of the present invention, step (5) includes the following process:

[0027] Step (51): Under the influence of the inhomogeneous magnetic field and the pulse gradient spin echo sequence, the phase calculation formula for each proton is:

[0028]

[0029] In formula (4), M is the total number of time steps, and are respectively the gradient vector and the proton position coordinates at the k-th time step;

[0030] Step (52): Calculate the signal intensities for different b values by accumulating the phases of all protons in the echo, and synthesize the DWI signal. The signal intensity calculation formula for each b value is as follows:

[0031]

[0032] In Equation (5), S b and S0 are the signals at a specific b value (b≠0 s / mm 2 ) and at b value of 0 s / mm 2 respectively. N is the total number of protons, T2 is the transverse relaxation time of the liver, t is the echo time, and i is the imaginary unit.

[0033] As a further improvement of the present invention, in the step (6), the ADC is calculated for the synthesized signal using a mono-exponential signal model. The formula of the mono-exponential signal model is as follows:

[0034] S b = S0·exp(-b·ADC) (6).

[0035] As a further improvement of the present invention, in the step (6), the D is calculated for the synthesized signal using a bi-exponential signal model. The formula of the bi-exponential signal model is as follows:

[0036] S b = S0·(f·exp(-b·D * +(1 - f)·exp(-b·D)) (7)

[0037] In Equation (7), f is the perfusion fraction, whose value ranges between 0 and 1, and D * is the pseudo-diffusion coefficient related to perfusion.

[0038] The beneficial effects of the present invention are as follows:

[0039] The present invention provides a prediction method for quantitative parameters of magnetic resonance diffusion-weighted imaging of fatty liver, and obtains the predicted values of ADC and D at different fat fractions. By subtracting the DWI quantitative parameter (such as ADC value) measured from a liver fibrosis patient from the predicted value corresponding to the fat fraction of this patient, the interference of fat on the DWI quantitative parameter can be reduced, which helps to improve the accuracy of diagnosing liver fibrosis based on DWI. In addition, the simulation can flexibly adjust parameters such as the fat magnetic susceptibility coefficient and the proton diffusion rate, and can systematically study the influence of different physiological conditions on the DWI quantitative parameters. Therefore, the present invention can objectively, accurately and comprehensively reflect the relationship between liver fat and the quantitative parameters of magnetic resonance diffusion-weighted imaging. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The present invention will be further described below in conjunction with the drawings and embodiments:

[0041] Figure 1 Flow chart of the present invention

[0042] Figure 2 In one embodiment of the present invention, three-dimensional virtual liver tissue models with fat fractions of 5%, 10%, and 15% and schematic diagrams of their two-dimensional slices (the purple dots in the models represent fat droplets);

[0043] Figure 3 Flow chart for generating a proton position sequence in one embodiment of the present invention

[0044] Figure 4 In one embodiment of the present invention, schematic diagram of the relationship between the simulated diffusion parameters and the fat fraction at a magnetic field strength of 3.0T Detailed implementation manners

[0045] In order to make the technical means, creative features, achieved purposes, and effects of the present invention easy to understand, the present invention will be further described below with reference to the accompanying drawings and embodiments

[0046] As Figure 1 shown, a method for predicting quantitative parameters of magnetic resonance diffusion weighted imaging of fatty liver includes the following steps

[0047] Step (1), given a fat fraction, construct a three-dimensional virtual liver tissue model with uniformly distributed fat droplets

[0048] In step (1), the three-dimensional virtual liver tissue model is a cube with a specific side length; the fat droplets are simulated as spheres, the radius of each small sphere is fixed, and the number of small spheres is calculated according to the fat fraction; the small spheres are placed inside the model, and the initial position coordinates of the small spheres are randomly generated; any collision between the small spheres is solved by placing the target small sphere on the surface of the collided small sphere until all the small spheres are uniformly distributed in the three-dimensional virtual liver tissue model without overlap

[0049] Further, in this embodiment, a total of 25 three-dimensional virtual liver tissue models with fat fractions ranging from 1% to 25% are specifically constructed. Each virtual liver tissue model is a cube with a size of 480×480×480 μm3. All fat droplets are simulated as spheres with a unified radius of 9.27 μm. In the model, the small spheres are evenly distributed and do not overlap. As Figure 2 shown, three-dimensional virtual liver tissue models with fat fractions of 5%, 10%, and 15% and their corresponding two-dimensional slices are given. The purple dots in the models represent fat droplets

[0050] Step (2), simulate the distribution of the magnetic field strength in the model

[0051] Further, in this embodiment, the fat magnetic susceptibility is set to 0.2 ppm, a uniform magnetic field of 3.0 T is applied, and the three-dimensional virtual liver tissue model is divided into 480×480×480 grid points with a grid spacing of 1 μm.

[0052] It should be noted that to balance the calculation efficiency and accuracy, the magnetic field intensity at any point within the three-dimensional virtual liver tissue model is approximately calculated by cubic spline interpolation based on the magnetic field intensity at the grid points. The total magnetic field intensity at any grid point is the vector sum of the perturbations of each fat droplet, and the calculation formula for the magnetic field perturbation generated by a single fat droplet at this point is:

[0053]

[0054] In formula (1), B0 is the main magnetic field, χ L is the set fat magnetic susceptibility, R is the radius of the fat droplet, r is the radial distance between the fat droplet and the grid point, and θ is the azimuth angle with the magnetic axis.

[0055] Step (3): Simulate the Brownian motion of protons within the model to generate a proton position sequence.

[0056] Further, in this embodiment, 1×10 4 protons are randomly placed within the three-dimensional virtual liver adipose tissue model. It should be noted that considering the sufficient convergence of the Monte Carlo simulation, the product of the number of protons and the number of time steps should be greater than 10 8 ~10 9 .

[0057] Each proton performs isotropic Gaussian diffusion within the model, and its displacement satisfies:

[0058]

[0059] In formula (2), D0 is the proton diffusion rate. In this embodiment, if the initial position of the proton is inside the fat droplet, its D0 is set to 0 μm 2 / ms, and if the initial position of the proton is outside the fat droplet, its D0 is set to 0.76 μm 2 / ms. Δ t is the time step of proton motion, which is set to 7.5 μs in this embodiment.

[0060] Protons are restricted to move within the model. If a proton collides with the model boundary, only the direction of proton motion is changed while the distance of proton motion remains unchanged. In addition, protons outside the fat droplet cannot pass through the fat droplet, and any proton that touches or enters the interior of the fat droplet will be placed back on the surface of the fat droplet.

[0061] Step (4): Simulate the pulsed gradient spin echo sequence.

[0062] Furthermore, in this embodiment, a pulsed gradient spin echo sequence with a magnetic field gradient strength of 1.18 T / μm, and gradient pulse durations and intervals of 35 ms and 40 ms respectively is applied. The calculation formula for the diffusion sensitivity factor b is as follows:

[0063]

[0064] In Equation (3), G is the magnetic field gradient strength, δ and Δ are the durations and intervals of the gradient pulses respectively, and γ is the gyromagnetic ratio of the proton. In this embodiment, it is set to 267.5 rad·μs -1 ·T -1 .

[0065] Step (5): Accumulate the phases of all protons within the echo and synthesize the DWI signal.

[0066] Furthermore, in this embodiment, it specifically includes the following steps:

[0067] Step (51): Under the influence of the inhomogeneous magnetic field and the pulsed gradient spin echo sequence, the phase calculation formula for each proton is:

[0068]

[0069] In Equation (4), M is the total number of time steps. In this embodiment, it is set to 1×10 4 time steps; and are the gradient vector and the proton position coordinates at the k-th time step respectively.

[0070] Step (52): Calculate the signal intensities for different b values by accumulating the phases of all protons within the echo and synthesize the DWI signal. The calculation formula for the signal intensity of each b value is as follows:

[0071]

[0072] In Equation (5), S b and S0 are the signals at a specific b value (b≠0 s / mm 2 ) and at a b value of 0 s / mm 2 respectively. N is the total number of protons. As known from step (3), there are 1×10 4 protons in total. T2 is the transverse relaxation time of the liver, t is the echo time. In this embodiment, they are set to 50 ms and 75 ms respectively, and i is the imaginary unit.

[0073] It should be noted that the echo time needs to fully cover the action time of the gradient pulse, that is, t = δ + Δ, so as to ensure the full evolution of the spin phase under the action of the gradient field.

[0074] It should be noted that the specific combination of b values will be elaborated in more detail in step (6).

[0075] Step (6): Analyze the synthesized signal above and calculate the predicted values of ADC and D.

[0076] Furthermore, in this embodiment, DWI signals with b values of 0, 100, 200, 500, and 700 s / mm 2 are synthesized and analyzed, and the single-exponential signal model is used to calculate ADC. The calculation formula is as follows:

[0077] S b = S0·exp(-b·ADC) (6).

[0078] Furthermore, in this embodiment, DWI signals with b values of 0, 100, 300, 500, and 800 / 1000 s / mm 2 are synthesized and analyzed, and the biexponential signal model is used to calculate D. The calculation formula is as follows:

[0079] S b = S0·(f·exp(-bD*)+(1 - f)·exp(-b·D)) (7)

[0080] In formula (7), f is the perfusion fraction, whose value ranges between 0 and 1, and D * is the pseudo-diffusion coefficient related to perfusion.

[0081] As Figure 4 shown, the relationship between the parameters predicted by simulation and the fat fraction at a field strength of 3.0T is given. Through Bland-Altman analysis, it is found that the predicted values of ADC and D are both highly consistent with the clinical calibration values.

[0082] The above shows and describes the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited by the above embodiments. What is described in the above embodiments and the specification is only the principle of the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of protection claimed by the present invention is defined by the appended claims and their equivalents.

Claims

1. A prediction method for quantitative parameters of magnetic resonance diffusion weighted imaging of fatty liver, characterized in that: It includes the following steps: Step (1): Given the fat fraction, construct a three-dimensional virtual liver tissue model with uniformly distributed fat droplets; Step (2): Simulate the distribution of magnetic field strength within the model; Step (3): Simulate the Brownian motion of protons within the model to generate a sequence of proton positions; Step (4): Simulate the pulsed gradient spin echo sequence; Step (5): Accumulate the phases of all protons within the echo to synthesize the DWI signal; Step (6): Analyze the synthesized signal above to calculate the predicted values of ADC and D.

2. The prediction method of a quantitative parameter for magnetic resonance diffusion weighted imaging of fatty liver according to claim 1, wherein: In step (1), the three-dimensional virtual liver tissue model is a cube with a specific side length.

3. A prediction method for quantitative parameters of magnetic resonance diffusion weighted imaging of fatty liver according to claim 1, characterized in that: In step (1), the construction process of the three-dimensional virtual liver tissue model is as follows: Given the fat fraction and the radius of the fat droplets; simulate the fat droplets as spheres, fix the radius of each small sphere, calculate the volume ratio of the fat droplets to determine the number of small spheres; place the small spheres inside the model and randomly generate the initial position coordinates of the small spheres; if a collision occurs between the small spheres, place the target small sphere on the surface of the collided small sphere until all small spheres are evenly distributed in the three-dimensional virtual liver tissue model without overlap.

4. A prediction method for quantitative parameters of magnetic resonance diffusion weighted imaging of fatty liver according to claim 1, characterized in that: In step (2), perform mesh division on the three-dimensional virtual liver tissue model. The magnetic field strength at any point within the model is approximately calculated by cubic spline interpolation based on the magnetic field strength at the mesh points. The total magnetic field strength at any mesh point is the vector sum of the perturbations of each fat droplet. The calculation formula for the magnetic field perturbation generated by a single fat droplet at this point is: In Equation (1), B0 is the main magnetic field, χ L is the set fat magnetic susceptibility, R is the radius of the fat droplet, r is the radial distance between the fat droplet and the grid point, and θ is the azimuth angle with respect to the magnetic axis.

5. A prediction method for quantitative parameters of magnetic resonance diffusion weighted imaging of fatty liver according to claim 1, characterized in that: In step (3), place a certain number of protons randomly within the three-dimensional virtual liver tissue model. Each proton undergoes isotropic Gaussian diffusion, and its displacement satisfies: In Equation (2), D0 is the proton diffusion rate, and its value is determined according to the initial position of the proton, Δ t is the time step of proton movement.

6. The prediction method of quantitative parameters of magnetic resonance diffusion weighted imaging for fatty liver according to claim 1, wherein: In step (4), apply the pulsed gradient spin echo sequence. In the ideal free diffusion state of the rectangular pulse, the calculation formula for the diffusion sensitivity factor b is: In formula (3), G is the magnetic field gradient strength, δ and Δ are the duration and interval time of the gradient pulse respectively, and γ is the gyromagnetic ratio of the proton.

7. A prediction method for quantitative parameters of magnetic resonance diffusion-weighted imaging of fatty liver according to claim 1, characterized in that: Step (5) includes the following processes: Step (51): Under the influence of the inhomogeneous magnetic field and the pulsed gradient spin echo sequence, the phase calculation formula for each proton is: In Equation (4), M is the total number of time steps, and are the gradient vector and the proton position coordinate at the k-th time step, respectively; Step (52): Accumulate the phases of all protons within the echo to calculate the signal intensity for different b values and synthesize the DWI signal. The calculation formula for the signal intensity for each b value is as follows: In formula (5), S b and S0 are the signals at specific b values (b ≠ 0 s / mm 2 ) and at a b value of 0 s / mm 2 respectively, N is the total number of protons, T2 is the transverse relaxation time of the liver, t is the echo time, and i is the imaginary unit.

8. A prediction method for quantitative parameters of magnetic resonance diffusion weighted imaging of fatty liver according to claim 1, characterized in that: In step (6), use the monoexponential signal model to calculate ADC for the synthesized signal. The formula for the monoexponential signal model is as follows: S b = S0·exp(-b·ADC) (6).

9. A prediction method for quantitative parameters of magnetic resonance diffusion weighted imaging of fatty liver according to claim 1, characterized in that: In step (6), use the biexponential signal model to calculate D for the synthesized signal. The formula for the biexponential signal model is as follows: S b = S0·(f·exp(-b·D * ))+(1 - f)·exp(-b·D)) (7) In Equation (7), f is the perfusion fraction, whose value ranges between 0 and 1, and D * is the pseudo-diffusion coefficient related to perfusion.

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