CN103714521B - Liver R2* figure measuring method based on inquiry table - Google Patents

Abstract

A liver R2* map measurement method based on a lookup table: including: (1) obtaining a magnetic resonance liver image, and drawing a region of interest including the liver; (2) spline the confluent hypergeometric function with a given number of receiving coil channels Interpolation to establish a corresponding lookup table; (3) For each pixel in the liver region of interest, fit its gray level and echo time to the first-order moment model of the single exponential model under the influence of non-central Chi noise, An R2* map including the liver is obtained. The invention can accurately and rapidly measure the R2* diagram of the liver.

Description

Liver R2* Diagram Measurement Method Based on Query Table

technical field

The invention belongs to the technical field of transverse relaxation rate R2* map measurement in magnetic resonance, and specifically relates to a liver R2* map measurement method based on a lookup table that can quickly and accurately measure the liver R2* map to measure liver iron concentration.

Background technique

If there is too much iron deposition in the human body in the liver, heart and other endocrine organs, it is easy to cause serious lesions, especially for patients with sickle cell anemia and thalassemia, long-term blood transfusion treatment will lead to excessive iron deposition. Since 70% to 90% of excess iron in the human body will be deposited in the liver, liver iron concentration is usually used as an important indicator of iron content in the body.

Compared with the direct method of liver biopsy, the method of measuring liver iron concentration based on MRI R2* map can effectively avoid complications such as liver hemorrhage, and the measurement accuracy will not be affected by factors such as sample size, location, and uneven distribution of liver iron. influences.

At present, there are two main methods for measuring liver iron concentration by MRI parameter R2*: one is based on multiple small liver ROIs, this method first averages the gray levels of pixels in the ROI, and then obtains The averaged gray value and the corresponding echo time were fitted according to a suitable curve model to obtain the R2* value representing the liver. Since liver iron is not evenly distributed in the liver, and there are artificial differences in the selection of the size and location of the region of interest, it often leads to inaccurate final measurement results.

Another method is based on the R2* map of magnetic resonance imaging. In this method, for each pixel in the liver, its gray level and echo time are fitted to an appropriate curve model to obtain the R2* map of the entire liver. Since each pixel needs to be fitted, the amount of calculation is huge and the calculation is time-consuming, especially in some curve models.

Some researchers proposed to use noise-corrected first-order moment model to measure R2* value (Feng Y, He T, GatehousePD, Li X, Harith Alam M, Pennell DJ, Chen W, Firmin DN. Improved MRI R2*relaxometry of iron-loaded liver with noise correction. Magn Reson Med 2013;70:1765-1774.), obtained R2* estimates with good accuracy and precision. Since this method only considers multiple small regions of interest in the liver, the signals in the region are averaged and then fitted once. In the artificial selection of the region of interest, sometimes some lesions or artifacts cannot be ruled out for the R2* measurement. In addition, the calculation of the confluent hypergeometric function in the fitting takes up most of the time, and a single fitting is relatively time-consuming but still within an acceptable range. However, if the pixel-by-pixel fitting is performed to calculate the liver R2* Graph, which is estimated to take tens of hours, limits its application in clinical practice.

Therefore, it is necessary to provide a fast and accurate liver R2* map measurement method to overcome the shortcomings of the existing technology.

Contents of the invention

The present invention proposes a liver R2* map measurement method based on a lookup table, which can effectively avoid the R2* measurement error caused by improper sampling of the region of interest and the time-consuming problem of confluent hypergeometric function calculation in the noise-corrected first-order moment model , can get accurate whole liver R2* map within a few minutes.

The above object of the present invention is achieved by the following technical means.

A method for measuring liver R2* diagram based on a lookup table, comprising the following steps in sequence:

(1) Acquire magnetic resonance liver images, and draw the region of interest including the liver on the obtained magnetic resonance liver images;

(2), for the known number of receiving coil channels The confluent hypergeometric function of Carry out spline interpolation, and establish a lookup table composed of interpolation nodes and interpolation function coefficients corresponding to the interpolation subintervals;

(3) Fit the grayscale and echo time of each pixel to the first-order moment model formula (I) of the single exponential model under the influence of non-central Chi noise to obtain the R2* value corresponding to each pixel, through The R2* value of each pixel obtains the R2* map containing the liver;

Wherein, formula (I) is:

... (I);

In formula (I), expressed expectations, represents the observed signal value, represents the standard deviation of the Gaussian noise for each receiver coil channel, represents the double factorial (i.e. , Indicates the number of receiving coil channels; represents the spline interpolation function of the confluent hypergeometric function, represents the echo time, express The noise-free true signal value at , Indicates the transverse relaxation rate; due to the signal in the noise-free background region of the image , so the standard deviation in formula (I) It can be obtained by formula (II):

...(II).

The above step (1) is specifically to obtain a magnetic resonance liver image by using a multi-echo gradient echo sequence.

The above step (2) specifically uses the cubic spline interpolation method under non-node boundary conditions to approximate the confluent hypergeometric function, and establishes a corresponding lookup table.

The selection of interpolation nodes in the above step (2) specifically selects non-equally spaced interpolation nodes.

Preferred Interpolation Node , ;when The time interval is chosen as 0.1, when The time interval is selected as 50, and the boundary conditions are non-node boundary conditions.

The above step (3) specifically adopts the curve fitting of the noise-modified first-order moment model based on the look-up table to approximate the confluent hypergeometric function.

The liver R2* map measurement method based on the lookup table of the present invention can effectively avoid the R2* measurement error caused by improper sampling of the region of interest in the prior art and the time-consuming defect of confluent hypergeometric function calculation in the noise-corrected first-order moment model , can get an accurate R2* map of the whole liver within minutes.

Description of drawings

The present invention will be further described by using the accompanying drawings, but the content in the accompanying drawings does not constitute any limitation to the present invention.

Fig. 1 is a schematic flow sheet of the method of the present invention;

Fig. 2 is a schematic diagram of the lookup table structure corresponding to the cubic spline interpolation function of the confluent hypergeometric function;

Fig. 3 is the R2* map and its comparison results obtained by using the method of the present invention and using the noise-corrected first-order moment model M ¹ NCM method for simulation data of different signal-to-noise ratios, and the simulation image includes R2* values ranging from 100 to 1000 s ^-1 ;

Fig. 4 uses the method of the present invention and the ^M1NCM method to calculate the comparison result form of the time used in the R2* figure respectively for the simulation data of different signal-to-noise ratios and the number of receiving coil channels;

Fig. 5 is two groups of real liver data using the method of the present invention and the M ¹ NCM method to obtain the R2* graph and its comparison results;

Fig. 6 is a comparison result table of the time used to calculate the R2* map by using the method of the present invention and the M ¹ NCM method respectively for two groups of real liver data.

detailed description

The present invention is further described in conjunction with the following examples.

Example 1.

A method for measuring liver R2* diagram based on a lookup table, as shown in Figure 1, comprises the following steps in turn:

(1) Acquire a magnetic resonance liver image, and draw a region of interest including the liver on the obtained magnetic resonance liver image.

(2), for the known number of receiving coil channels The confluent hypergeometric function of Carry out spline interpolation, and establish a lookup table consisting of interpolation nodes and interpolation function coefficients corresponding to the interpolation subintervals one by one, as shown in Figure 2.

(3) Fit the grayscale and echo time of each pixel to the first-order moment model formula (I) of the single exponential model under the influence of non-central Chi noise to obtain the R2* value corresponding to each pixel, through The R2* value of each pixel was obtained for an R2* map containing the liver.

Wherein, formula (I) is:

... (I);

In formula (I), expressed expectations, represents the observed signal value, represents the standard deviation of the Gaussian noise for each receiver coil channel, represents the double factorial (i.e. , Indicates the number of receiving coil channels; represents the spline interpolation function of the confluent hypergeometric function, represents the echo time, express The noise-free true signal value at , represents the transverse relaxation rate.

Since the signal in the noise-free background region of the image , so the standard deviation in formula (I) It can be obtained by formula (II):

...(II).

Wherein, step (1) may adopt a multi-echo gradient echo sequence to obtain a magnetic resonance liver image.

Wherein, step (3) specifically adopts the curve fitting of the noise-modified first-order moment model based on the look-up table to approximate the confluent hypergeometric function.

The liver R2* map measurement method based on the lookup table of the present invention can effectively avoid the R2* measurement error caused by improper sampling of the region of interest in the prior art and the time-consuming defect of confluent hypergeometric function calculation in the noise-corrected first-order moment model , can get an accurate R2* map of the whole liver within minutes.

Example 2.

A method for measuring liver R2* diagram based on a lookup table, as shown in FIG. 1 , takes the human liver as the measurement object, and specifically includes the following steps.

Step 1: Acquire a 12-echo liver magnetic resonance image, and draw the whole liver region of interest along the edge of the liver image. The imaging parameters are set as follows: the echo time is respectively selected as 0.93, 2.27, 3.61, 4.95, 6.29, 7.63, 8.97, 10.30, 11.64, 12.98, 14.32 and 15.66 ms, the repetition time is 200 ms, the matrix size is 64×128, flipping The angle is 20 ^o , the layer thickness is 10 mm, and the number of receiving coil channels is 8.

It should be noted that the method of drawing the region of interest in the whole liver can be drawn manually, or drawn in other ways, such as automatic drawing controlled by a program or drawn by other equipment.

Step 2, the number of known receiving coil channels The confluent hypergeometric function of Cubic spline interpolation is performed, and a lookup table composed of interpolation nodes and interpolation function coefficients corresponding to the interpolation subintervals is established.

The parameter settings adopted by the cubic spline interpolation are: interpolation node , ;when The time interval is chosen as 0.1, when The time interval is selected as 50, and the boundary conditions are non-node boundary conditions. The calculation of the cubic spline interpolation function here is common knowledge in the field, and will not be repeated here.

Step 3, use the lookup table obtained in step 2 to replace the calculation of the confluent hypergeometric function in the noise-corrected first-order moment fitting model, and for each pixel in the liver region of interest obtained in step (1), compare its gray level with The echo time is fitted to the first-order moment model of the single exponential model under the influence of non-central Chi noise to obtain the R2* value of each pixel, and then the R2* value including the liver is obtained according to the R2* value of each pixel picture.

... (I);

In formula (I), expressed expectations, represents the observed signal value, represents the standard deviation of the Gaussian noise for each receiver coil channel, represents the double factorial (i.e. , Indicates the number of receiving coil channels, represents the spline interpolation function of the confluent hypergeometric function, represents the echo time, express The noise-free true signal value at , is the effective transverse relaxation rate.

Since the signal in the noise-free background region of the image , the standard deviation in formula (I) is obtained by formula (II):

...(II).

Studies have shown that the calculation of the confluent hypergeometric function is large and time-consuming. The present invention replaces the confluent hypergeometric function with its spline interpolation function, and adopts the first-order moment model (formula (I )) for pixel-by-pixel fitting, experiments show that the proposed model can obtain almost the same R2* map of the liver as the noise-corrected first-order moment method (M ¹ NCM for short) that directly calculates the confluent hypergeometric function, and the calculation time is accelerated by nearly two orders of magnitude.

The method of the present invention first draws the region of interest on the liver image, and then performs cubic spline interpolation on the confluent hypergeometric function in advance for a given number of receiving coil channels, and establishes a corresponding lookup table for fast approximate calculation of the function, Combined with the noise-corrected first-order moment fitting model, that is, the first-order moment model (formula (I)) of the single exponential model under the influence of non-central Chi noise, it speeds up the curve fitting and shortens the time for calculating the liver R2* map .

In order to further verify the effect of the method of the present invention (hereinafter referred to as the M ¹ NCM-LUT method), the M ¹ NCM-LUT method and the method of directly calculating the noise-corrected first-order moment of the confluent hypergeometric function (abbreviated as M ¹ NCM) were tested Compared, the results are as follows:

Fig. 2 shows the structure diagram of the lookup table corresponding to the confluent hypergeometric function established in the second step of the present invention.

Fig. 3 is that the receiving coil channel number is 8, the signal-to-noise ratio is respectively 15, 30 and 60 under the simulation data using the method of the present invention and the ^M1NCM method to obtain the R2* figure and comparison result thereof, it can be seen that for different For the signal-to-noise ratio, the two methods obtained almost the same R2* diagram, with an error in the order of 10 ^-5 s ^-1 .

Fig. 4 shows the comparison result table of the time used to calculate the R2* diagram by using the method of the present invention and the M ¹ NCM method respectively for the simulation data under different signal-to-noise ratios and the number of receiving coil channels. The table shows the simulation under different combinations of signal-to-noise ratio (signal-to-noise ratio is 15, 30, 60) and different receiving coil channel numbers (coil channel number is 1, 2, 4, 8, 16, 32, 64, 128) Data using the accuracy comparison graph of the method of the present invention and the M ¹ NCM method, it can be seen that the method of the present invention has been accelerated by 95 to 418 times, and the R2* map can be obtained in a few minutes.

Fig. 5 is the R2* diagram and comparison of two groups of real liver data obtained by using the method of the present invention and the M ¹ NCM method respectively, one group is severe liver iron overload, and the other group is mild liver iron overload. It can be seen that the two methods obtain almost the same R2* diagram, and the error is in the order of 10 ^-4 s ^-1 .

Fig. 6 shows the time comparison of 6 groups of real liver data using the method of the present invention and the M ¹ NCM method, corresponding to different degrees of liver iron overload. It can be seen that the method of the present invention can also speed up by 120-162 times.

It can be seen from the above results that the liver R2* map measurement method based on the lookup table of the present invention can obtain the same liver R2* map as M ¹ NCM, but the speed is increased by nearly two orders of magnitude, and a complete picture can be obtained within a few minutes. The R2* plot.

It should be noted that the method for measuring the liver R2* map based on the lookup table of the present invention is not only applicable to the measurement of the human liver R2* map, but also applicable to the measurement of the liver R2* map of other animals.

Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than limit the protection scope of the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that Modifications or equivalent replacements are made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention.

Claims (1)

1. a liver R2* graph measurement method based on a look-up table, characterized in that: comprises the following steps successively: (1), collecting a magnetic resonance liver image, and drawing a region of interest including the liver on the obtained magnetic resonance liver image; (2) Carry out spline interpolation to the confluent hypergeometric function ₁ F ₁ (-1/2; N _RC ; -z) of the known receiving coil channel number N _RC , and establish an interpolation node and an interpolation subinterval one by one A look-up table composed of corresponding interpolation function coefficients; (3) For each pixel in the region of interest of the liver obtained in step (1), fit the gray level and echo time of each pixel to the first-order moment of the single exponential model under the influence of non-central Chi noise Obtain the R2* value corresponding to each pixel in the model formula (1), obtain the R2* figure that comprises liver by the R2* value of each pixel; Wherein, formula (I) is: $\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; g</span>}}\sqrt{\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}}\frac{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span><span\; class="notranslate">\; !</span>}{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}{\stackrel{<span\; class="notranslate">\; ~</span>}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; ;</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; ;</span><span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\mathrm{<span\; class="notranslate">\; exp</span>}<span\; class="notranslate">\; (</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; T</span>}\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; \&Center\; Dot;</span>\mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; *</span><span\; class="notranslate">\; )</span>}{\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; g</span>}}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$ In formula (I), E() represents expectation, S _M represents observed signal value, σ _g represents the standard deviation of Gaussian noise of each receiving coil channel, ! ! Indicates double factorial, N _RC indicates the number of receiving coil channels, Represents the spline interpolation function of the confluent hypergeometric function, TE represents the echo time, S ₀ represents the noise-free real signal value when TE=0, R2* represents the transverse relaxation rate, because the signal S in the noise-free image background area ₀ = 0, so the standard deviation σ _g in formula (I) can be obtained by formula (II): ${\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; g</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; E.</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; S</span>}}_{\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>\sqrt{\frac{\mathrm{<span\; class="notranslate">\; \&pi;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}}}\frac{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span><span\; class="notranslate">\; !</span>}{{\mathrm{<span\; class="notranslate">\; 2</span>}}^{{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; N</span>}}_{\mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; C</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; !</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; ...</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; I</span>}\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; ;</span>$ The step (1) is specifically to obtain a magnetic resonance liver image by using a multi-echo gradient echo sequence; Described step (2) specifically adopts the cubic spline interpolation method under the non-node boundary condition to approximate the confluent hypergeometric function, and establishes a corresponding look-up table; The selection of the interpolation node in the step (2) specifically selects non-equally spaced interpolation nodes; Interpolation node 0≤z _m ≤z _max =50000, m=1,2,...,M; when 0≤z _m ≤1000, select the interval as 0.1, when 1000<z _m ≤50000, select the interval as 50, Boundary conditions select non-node boundary conditions; The step (3) specifically adopts the curve fitting of the noise-modified first-order moment model based on the look-up table to approximate the confluent hypergeometric function.