Perfusion curve estimation method based on contrast enhancement imaging

Abstract

The invention discloses a perfusion curve estimation method based on contrast enhanced imaging, which comprises the following steps: S1, according to a series of T2 * weighted brain images, calculating the time when a contrast agent passes through blood capillaries and a pixel value corresponding to each time point in a region of interest (ROI) to obtain a signal-time curve with signal decline; s2, the signal-time curve is converted into a contrast agent concentration-time curve, and a gamma function is adopted as an ideal model concentration-time curve for modeling; s3, defining an area enclosed by a concentration-time curve under the region of interest according to a central volume principle and a normalized first moment to describe physiological parameters to be calculated; and S4, under the condition that the model is definite and parameters are unknown, selecting a maximum likelihood estimation method to estimate the established model, and forming a concentration-time curve simulation diagram. The method still shows satisfactory performance fitting ability under the condition of small samples.

Description

Technical Field

[0001] The present invention relates to a method for estimating a perfusion curve based on dynamic contrast-enhanced imaging. Background Art

[0002] Concentration-time curves from dynamic contrast-enhanced magnetic resonance imaging (MRI) are widely used to calculate cerebrovascular parameters. This process involves fitting a gamma-distributed probability density function to the measured concentration curve in the region of interest. Currently, the traditional approach is the log-linear least squares (LL-LS) method, which provides a simplified approach to estimating cerebrovascular parameters and avoids the initial value problem. However, the logarithmic operation complicates the statistics of the recorded data, causing the noise to no longer conform to a Gaussian distribution, resulting in biased estimates when only a small number of data points are available.

[0003] Since quantitative analysis of cerebrovascular parameters is required at a finer voxel scale throughout the brain, the data sampling interval becomes relatively long, and only 5 or 6 valid data points are collected in the first stage of curve fitting. The performance of existing methods is not satisfactory. Summary of the Invention

[0004] The present invention overcomes the disadvantage of large deviation in the prior art and proposes a perfusion curve estimation method based on contrast-enhanced imaging.

[0005] In order to achieve the above-mentioned object of the invention, the present invention provides the following technical solutions:

[0006] A perfusion curve estimation method based on contrast-enhanced imaging specifically comprises the following steps:

[0007] S1, based on a series of T2 * The brain image is weighted, and the time it takes for the contrast agent to pass through the capillaries and the pixel value corresponding to each time point are calculated within the region of interest (ROI), obtaining a signal-time curve with signal decline;

[0008] S2, converting the signal-time curve into a contrast agent concentration-time curve, and using a gamma function as an ideal model concentration-time curve for modeling;

[0009] S3, based on the central volume principle, defines the area enclosed by the concentration-time curve under the region of interest and the normalized first-order moment to describe the physiological parameters to be calculated;

[0010] S4. When the model is determined but the parameters are unknown, the present invention selects the maximum likelihood estimation method to estimate the established model and form a concentration-time curve simulation diagram.

[0011] As a preferred embodiment of the present invention, step S1 specifically includes:

[0012] S11, reading the magnetic resonance signal intensity value, that is, the grayscale value of each pixel in the MRI image, and corresponding it to the time point when the contrast agent passes through the blood vessel;

[0013] S12, connecting the series of signal intensity value points in sequence to form a line graph of contrast-enhanced imaging signal intensity values.

[0014] As a preferred embodiment of the present invention, in step S2, a gamma function is selected to model the concentration expression, which specifically includes the following steps:

[0015] S21, the change in transverse relaxation rate is proportional to the contrast agent concentration in brain tissue, which can be expressed as a function of magnetic resonance signal intensity. Therefore, the local change in signal intensity after contrast agent injection can be converted into a concentration-time curve;

[0016] S22, since perfusion parameters extracted from uncorrected concentration-time curves are often affected by the recirculation effect of contrast agents, the gamma function was used to model the concentration expression to eliminate the influence of the recirculation effect;

[0017] The gamma distribution density function is similar to the concentration trend of the contrast agent bolus when it first passes through the artery, with a relatively steep and large downward slope and then gradually returning to the baseline.

[0018] As a preferred embodiment of the present invention, perfusion imaging generally provides assistance for clinical decision-making by estimating physiological parameters. Step S3 specifically includes the following steps:

[0019] S31, the relative cerebral blood volume value in a specific image voxel near the bolus is proportional to the amount of contrast agent flowing through the area, that is, it is proportional to the integrated area under the contrast agent concentration-time curve. The expression for relative cerebral blood volume can be obtained by calculating the integrated area under the curve;

[0020] S32, cerebral blood flow is related to cerebral blood volume and mean transit time. Calculating the ratio of first-order moments can provide a relative blood flow measurement method. The expression of the normalized first-order moment under each region of interest is calculated;

[0021] S33. Considering the concentration-time curve characteristics of magnetic resonance imaging, a probability density function in the form of a gamma distribution is used to rewrite the expressions obtained in steps S31 and S32 into a probability distribution function form of a gamma distribution.

[0022] As a preferred solution of the present invention, set t1, t2, ..., t nLet n be discrete random samples from independent distributions, representing different time points in the MRI scan. For each time point t i The corresponding contrast agent concentration values ​​are considered to obey a given gamma distribution probability density function. In this model, time is considered as a random variable, and the concentration value observed at each time node represents the frequency of that time point as a random variable in the entire data set. The concentration value at each time node reflects the probability weight at these time points.

[0023] As a preferred solution of the present invention, the maximum likelihood estimation method is selected for parameter estimation, and step S4 specifically includes the following steps:

[0024] S41, establishing a likelihood function based on the gamma distribution probability density function;

[0025] S42, to determine the two parameters that make the likelihood function reach the maximum value, take the natural logarithm of the constructed likelihood function;

[0026] S43, calculating partial derivatives of the two parameters respectively, and setting the partial derivative equations to zero, thereby solving the parameter estimates that maximize the likelihood function;

[0027] As a preferred solution of the present invention, the Euler-Maclaurin formula is selected to expand the function, and step S43 specifically includes the following steps:

[0028] S431, simplifying the two partial derivative expressions can get the relationship between the two parameters, but the two parameters are implicit in the formula, and it is difficult to get the analytical relationship between the two parameters;

[0029] S432, select the Euler-McLaughlin formula to expand the function, and use numerical methods to obtain the numerical solution of the parameters, and further determine the two parameters of the concentration-time curve.

[0030] As a preferred embodiment of the present invention, according to the above algorithm, a corresponding program is edited in Matlab, the collected signal intensity data points are processed, converted into a concentration-time curve, an estimation model is established, and then the estimation model is calculated according to the above estimation algorithm, thereby forming a perfusion curve estimation method based on contrast-enhanced imaging.

[0031] The method of the present invention estimates the data to obtain a fitting curve. At the same time, the traditional method is used to estimate the collected data. The fitting effects of the two methods are compared and it is found that the estimation method proposed by the present invention is significantly better than the traditional method.

[0032] This paper develops a fitting method that exhibits satisfactory performance even with small sample sizes. It assumes that time t is represented by n independently distributed discrete random samples, with each corresponding contrast agent concentration value following a given gamma distribution probability density function. In other words, time is treated as a random variable, and the concentration value corresponding to each time point is considered the frequency of occurrence of the random variable t in the dataset. This method also provides a closed-form correction for parameter estimation, significantly reducing bias in small sample sizes while maintaining low computational complexity.

[0033] The advantages of the present invention are:

[0034] The present invention uses the probability density function of the gamma distribution to model the magnetic resonance concentration-time curve. The gamma distribution has two parameters: a shape parameter α and a scale parameter β. By adjusting these two parameters, it can adapt to MRI parameter distributions of different shapes and scales, thereby improving the accuracy of parameter estimation. In magnetic resonance imaging, due to the influence of noise or other interference, the acquired data may contain extreme values ​​or outliers. Due to the shape characteristics of its probability density function, the gamma distribution can effectively reduce the impact of outliers on the parameter estimation results, thereby improving the robustness of the estimation. At the same time, the maximum likelihood estimation method used in parameter estimation has the advantages of low computational complexity and no need to guess initial values, making it a fitting method that can demonstrate satisfactory performance in small sample sizes. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 It is a flow chart of the method of the present invention.

[0036] Figure 2 It is the original data signal intensity and time relationship curve of the present invention.

[0037] Figure 3 1 is a curve showing the relationship between the contrast agent concentration and time of the present invention.

[0038] Figure 4 This is a perfusion curve estimation diagram obtained by the method of the present invention.

[0039] Figure 5 This is a comparison chart of the estimation effects of the method of the present invention and the traditional estimation method. DETAILED DESCRIPTION

[0040] In clinical applications, the number of valid sample points collected is relatively small. Therefore, a new statistical optimization algorithm is proposed to transform the problem of fitting the MRI concentration-time curve into the parameter estimation problem of the probability density function of the gamma distribution. Specifically, the concentration-time curve is considered to be a random sample of the gamma distribution with time as the random variable, and the contrast agent concentration is considered as the corresponding frequency of occurrence. The optimal model parameters are then solved using the maximum likelihood estimation method (MLE), thereby completing the curve fitting and further calculating the relevant physiological parameters. The present invention is further described in detail below with reference to experimental examples and specific embodiments.

[0041] A perfusion curve estimation method based on contrast-enhanced imaging, the flow chart is as follows Figure 1 As shown, the following steps are included:

[0042] S1, based on a series of T2 * The brain image is weighted, and the time it takes for the contrast agent to pass through the capillaries and the pixel value corresponding to each time point are calculated within the region of interest (ROI), obtaining a signal-time curve with signal decline;

[0043] S2, converting the signal-time curve into a contrast agent concentration-time curve, and using a gamma function as an ideal model concentration-time curve for modeling;

[0044] S3, based on the central volume principle, defines the area enclosed by the concentration-time curve under the region of interest and the normalized first-order moment to describe the physiological parameters to be calculated;

[0045] S4. When the model is determined but the parameters are unknown, the present invention selects the maximum likelihood estimation method to estimate the established model and form a concentration-time curve simulation diagram.

[0046] Wherein, step S1 specifically includes the following steps:

[0047] S11, read the magnetic resonance signal intensity value. In dynamic contrast-enhanced magnetic resonance imaging analysis, according to a series of T2 * Weighted brain images require signal reading, specifically the grayscale value of each pixel in the MRI image. These grayscale values ​​reflect the signal intensity of different tissues at specific points in time and are important indicators of tissue characteristics. To capture the temporal changes of the contrast agent within the region of interest (ROI), the acquired signal intensity values ​​must be precisely correlated with the specific time points at which the contrast agent passes through blood vessels and tissues. This temporal correlation forms the basis for subsequent analysis, helping to reveal the hemodynamic characteristics, perfusion status, and other physiological parameters of the tissue.

[0048] S12, draw a line graph of the contrast-enhanced imaging signal intensity values. Figure 2As shown in Figure 1, by connecting the acquired signal intensity values ​​in chronological order, a line graph reflecting the contrast enhancement process can be formed. This line graph intuitively shows the trend of signal intensity changes over time, which is usually manifested as a signal decline pattern.

[0049] In step S2, the gamma function is selected to model the concentration expression, which specifically includes the following steps:

[0050] The signal-time curve can be converted into a relative concentration-time curve of the contrast agent. The change in transverse relaxation rate is proportional to the contrast agent concentration in the brain tissue, where the contrast agent concentration can be expressed as a function of the magnetic resonance signal intensity. Therefore, the local change in signal intensity after contrast agent injection can be converted into a concentration-time curve as follows:

[0051] Δ(1 / T2 * )=ΔR2 * (1)

[0052]

[0053] where k is a constant (depending on tissue type, pulse sequence, and field strength), TE is the echo time of 23 ms, C(t) is the contrast agent concentration at time t, S(t) is the signal intensity at time t, and S0 is the signal intensity before contrast agent administration. To calculate relative concentration values, k is set to 1.0.

[0054] Since perfusion parameters extracted from uncorrected concentration-time curves are often affected by the recirculation effect of contrast agents, the original concentration-time curves cannot be directly used to calculate cerebral vascular parameters. The gamma function is used to model the concentration expression to eliminate the influence of the recirculation effect:

[0055] C Γ (t) = A·(t-KT) α ·e -(t-KT) / β (3)

[0056] Where A is a constant amplitude factor, representing the peak concentration. α is a shape parameter, reflecting the rate of increase in the concentration curve. β is a proportionality parameter, related to the rate of decrease in concentration. KT is the time at which the contrast agent begins to take effect. The gamma distribution density function resembles the concentration trend of the contrast agent after the initial arterial bolus injection, with a relatively steep and large downward slope followed by a gradual return to baseline.

[0057] Wherein, step S3 specifically includes the following steps:

[0058] In perfusion imaging studies, quantitative physiological information such as relative cerebral blood volume (rCBV) and mean transit time (rMTT) is often calculated to aid clinical decision-making. The relative cerebral blood volume value in a specific image voxel near the bolus is proportional to the amount of contrast agent flowing through that region, that is, it is proportional to the integrated area under the contrast agent concentration-time curve. Calculating the integrated area under the curve yields an expression for relative cerebral blood volume. Cerebral blood flow is related to cerebral blood volume and mean transit time. Calculating the ratio of the first-order moments provides a relative blood flow measurement method. The expression for the normalized first-order moment is calculated for each region of interest.

[0059]

[0060]

[0061] in, is the general form of the gamma function.

[0062] In the application scenario of the present invention, taking into account the characteristics of the concentration-time curve of magnetic resonance imaging, a probability density function in the form of a gamma distribution is used:

[0063]

[0064] Γ(α) is the normalization factor of the Gamma function, which ensures that the integral of the probability density function is 1.

[0065]

[0066] Considering the characteristics of the concentration-time curve of magnetic resonance imaging, assuming KT = 0, the concentration-time curve is written as a probability distribution function of the gamma distribution:

[0067]

[0068] Among them, rCBV is the relative cerebral blood volume value, α>0, β>0, t>0.

[0069] Set t1, t2, ..., t n Let n be discrete random samples from independent distributions, representing different time points in the MRI scan. For each time point t iThe corresponding contrast agent concentration value is considered to obey a given gamma distribution probability density function. Specifically, in this model, time is regarded as a random variable, and the concentration value observed at each time node represents the frequency of occurrence of that time point as a random variable in the entire data set. This method can describe the dynamic change characteristics of the concentration-time curve at a statistical level by introducing the probability density function of the gamma distribution. In other words, the fluctuation of the concentration value is no longer simply regarded as a fixed deterministic function, but is composed of a series of random variables with uncertainty. The concentration value at each time node reflects the probability weight at these time points.

[0070] The maximum likelihood estimation method is selected for parameter estimation, and step S4 specifically includes the following steps:

[0071] S41, establishing a likelihood function based on the gamma distribution probability density function;

[0072] When the model is known but the parameters are unknown, the maximum likelihood estimation method (MLE) has the best asymptotic properties. The proposed model is estimated using MLE, and the likelihood function is established based on the gamma distribution probability density function:

[0073]

[0074] Set t1, t2, …, t n is n independently distributed discrete random samples, and each of its corresponding C Γ (t i ) values ​​obey the given gamma distribution probability density function, that is, time is regarded as a random variable, and the concentration value corresponding to each time node is regarded as the frequency of occurrence of the random variable t in the data set.

[0075] S42, to determine the two parameters that make the likelihood function reach the maximum value, take the natural logarithm of the constructed likelihood function;

[0076] According to the basic principles of maximum likelihood estimation, in order to determine the two parameters that maximize the likelihood function, the natural logarithm of the constructed likelihood function is usually taken. Through logarithmic transformation, the original product form can be converted into a more manageable sum form, thereby simplifying the derivation and optimization process.

[0077]

[0078] S43, calculating partial derivatives of the two parameters respectively, and setting the partial derivative equations to zero, thereby solving the parameter estimates that maximize the likelihood function;

[0079]

[0080] in, is the Digamma function.

[0081] Simplifying the above partial derivatives, we can get the relationship between the two parameters:

[0082]

[0083]

[0084] in, It can be regarded as the average value of the given data, denoted as Will Substituting into formula (12), we can get:

[0085]

[0086] According to formula (14), it is difficult to calculate the analytical relationship between α and β. In order to obtain the numerical solution of the two parameters, the Euler-Maclaurin formula is selected to expand the Digamma function.

[0087]

[0088] Define a specific difference A to calculate the parameter α,

[0089] Combined with the above formula, the numerical solution of parameter α is calculated. Because equation (14) has no simple analytical solution, this solution is obtained by numerical method, and the symbolic analytical expressions of the two parameters cannot be given specifically. The value of shape parameter α is obtained by solving ψ(α)=A, and then according to The value of the proportional parameter β is solved to determine the two parameters of the concentration-time curve and further calculate the corresponding physiological parameters.

[0090] According to the above algorithm, the corresponding program was edited in Matlab to implement the above perfusion curve estimation method based on contrast-enhanced imaging. Specifically, it can be divided into the following main steps:

[0091] First, read the signal intensity data. In this step, the signal intensity data of each pixel in the acquired magnetic resonance image needs to be imported into Matlab.

[0092] The next step is to convert the signal intensity into a concentration-time curve. This step involves processing the signal intensity values ​​and converting them into contrast agent concentration using the MRI signal equation. This process converts the signal intensity data into a curve that reflects the changes in contrast agent concentration in the tissue, allowing for a more accurate assessment of the dynamic behavior of the tissue.

[0093] Then, an estimation model was established. Based on the concentration-time curve, a gamma distribution probability density function modeling method was used to construct a perfusion model. By fitting the concentration-time curve, estimated values ​​of important perfusion parameters could be obtained.

[0094] Finally, the perfusion model is calculated using the estimation algorithm described above, and the final perfusion curve is generated. By inputting the concentration-time data into the estimation model, the perfusion curve is calculated. This curve provides detailed information about the tissue perfusion status.

[0095] After processing the data, this method first fits the collected concentration-time data through the established estimation model to generate a fitting curve reflecting the tissue perfusion characteristics. In order to further verify the effectiveness and accuracy of this method, the logarithmic linear least squares method is also used to estimate the same data. By logarithmizing the data, LL-LS can simplify the solution process of nonlinear problems, thereby obtaining a fitting curve for the data. In the comparative analysis, the fitting curves generated by this method and the LL-LS method are compared to observe the performance of the two methods in capturing the trend of changes in contrast agent concentration, curve smoothness, fitting accuracy, etc. Figure 5 As can be clearly seen in the figure, the proposed estimation method outperforms traditional methods in many aspects. It can more accurately reflect the rapid changes and slow disappearance of the contrast agent. The fitting curve also significantly improves its ability to handle noise and smooth out abnormal data points, reducing errors caused by data fluctuations.

[0096] The contents described in the embodiments of this specification are merely an enumeration of the implementation forms of the inventive concept. The scope of protection of the present invention should not be regarded as limited to the specific forms described in the embodiments. The scope of protection of the present invention also extends to equivalent technical means that can be conceived by those skilled in the art based on the inventive concept.

Claims

1. A method for estimating a perfusion curve based on contrast-enhanced imaging, comprising the following steps: S1, based on a series of T2 * The brain image is weighted, and the time for the contrast agent to pass through the capillaries and the pixel value corresponding to each time point are calculated in the region of interest (ROI) to obtain a signal-time curve with signal decline; S2, converting the signal-time curve into a contrast agent concentration-time curve, and using a gamma function as an ideal model concentration-time curve for modeling; S3, based on the central volume principle, the area enclosed by the concentration-time curve under the region of interest and the normalized first-order moment are defined to describe the physiological parameters to be calculated; S4, when the model is determined and the parameters are unknown, the maximum likelihood estimation method is selected to estimate the established model to form a concentration-time curve simulation diagram.

2. A method for estimating a perfusion curve based on contrast-enhanced imaging according to claim 1, characterized in that: Step S1 specifically includes: S11, reading the magnetic resonance signal intensity value, that is, the gray value of each pixel in the MRI image, and corresponding it to the time point when the contrast agent passes through the blood vessel; S12, connecting the series of signal intensity value points in sequence to form a line graph of contrast-enhanced imaging signal intensity values.

3. The method for estimating a perfusion curve based on contrast-enhanced imaging according to claim 1, characterized in that: In step S2, the gamma function is selected to model the concentration expression, which specifically includes the following steps: S21, the change in transverse relaxation rate is proportional to the contrast agent concentration in the brain tissue, which can be expressed as a function of the magnetic resonance signal intensity. Therefore, the local change in signal intensity after contrast agent injection can be converted into a concentration-time curve; S22, since the perfusion parameters extracted from the uncorrected concentration-time curves are often affected by the recirculation effect of the contrast agent, the concentration expression was modeled using the gamma function to eliminate the influence of the recirculation effect; The gamma distribution density function is similar to the concentration trend of the contrast agent bolus when it first passes through the artery, with a steeper and larger downward slope and then gradually returning to the baseline.

4. The method for estimating a perfusion curve based on contrast-enhanced imaging according to claim 1, characterized in that: The perfusion imaging in step S3 usually provides assistance for clinical decision making by estimating physiological parameters, and specifically includes the following steps: S31, the relative cerebral blood volume value in a specific image voxel near the bolus is proportional to the amount of contrast agent flowing through the area, that is, it is proportional to the integrated area under the contrast agent concentration-time curve. The expression of relative cerebral blood volume can be obtained by calculating the integrated area under the curve; S32, cerebral blood flow is related to cerebral blood volume and mean transit time, and the ratio of first-order moments can provide a relative blood flow measurement method. The expression of the normalized first-order moment under each region of interest is calculated; S33, taking into account the concentration-time curve characteristics of magnetic resonance imaging, a probability density function in the form of a gamma distribution is used to rewrite the expressions obtained in steps S31 and S32 into a probability distribution function form of a gamma distribution.

5. The method for estimating a perfusion curve based on contrast-enhanced imaging according to claim 4, characterized in that: Set t1, t2, ..., t n are n independently distributed discrete random samples representing different time points in the MRI scan. For each time point t i The corresponding contrast agent concentration value is considered to obey a given gamma distribution probability density function. In this model, time is regarded as a random variable, and the concentration value observed at each time node indicates the frequency of occurrence of the time point as a random variable in the entire data set, and the concentration value at each time node reflects the probability weight at these time points.

6. The method for estimating a perfusion curve based on contrast-enhanced imaging according to claim 1, characterized in that: In step S4, the maximum likelihood estimation method is selected to perform parameter estimation, which specifically includes the following steps: S41, establishing a likelihood function according to the gamma distribution probability density function; S42, to determine two parameters that make the likelihood function reach the maximum value, take the natural logarithm of the constructed likelihood function; S43, calculating partial derivatives of the two parameters respectively, and setting the partial derivative equations to zero, thereby solving the parameter estimation value that makes the likelihood function reach the maximum value.

7. The method for estimating a perfusion curve based on contrast-enhanced imaging according to claim 1, characterized in that: In step S43, the Euler-Maclaurin formula is selected to expand the function, which specifically includes the following steps: S431, simplifying the two partial derivative expressions, we can get the relationship between the two parameters, but the two parameters are implicit in the formula, and it is difficult to get the analytical relationship between the two parameters; S432, the Euler-McLaughlin formula is selected to expand the function, and the numerical solution of the parameters can be obtained by numerical method, and the two parameters of the concentration-time curve can be further determined.

8. The method for estimating a perfusion curve based on contrast-enhanced imaging according to claim 1, characterized in that: The method also includes step S5, wherein according to the algorithm of steps S1-S4, a corresponding program is edited in Matlab to process the collected signal intensity data points, convert them into concentration-time curves, establish an estimation model, and then calculate the estimation model according to the above estimation algorithm, thereby forming a perfusion curve estimation method based on contrast-enhanced imaging.

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