Method for calculating density of multiple substances based on x-ray spectral information

Abstract

The application provides a multi-substance density calculation method based on X-ray energy spectrum information, S1, multi-energy spectrum projection data collection: single X-ray exposure is performed on a measured object by using a photon counting detector to obtain projection values of each pixel in each energy interval; S2, multi-substance multi-energy spectrum decomposition model establishment: a nonlinear relationship model is established for multiple substances to be decomposed; S3, substance area density solving: a target function is constructed by the difference between the actual projection values obtained in step S1 and the model calculation values in step S2, and a numerical optimization algorithm is used to solve the target function; S4, quantitative image generation: all pixels are traversed to generate the area density distribution map of each substance. The application obtains multi-energy spectrum information by using a photon counting detector, combines a nonlinear model and an optimization algorithm, realizes synchronous quantitative calculation of the densities of multiple substances, overcomes the defects of limited substance type differentiation and insufficient energy information utilization, and improves the accuracy of substance identification.

Description

Technical Field

[0001] This invention relates to the field of X-ray imaging technology, specifically to a method for calculating the density of multiple materials based on X-ray energy spectrum information. Background Technology

[0002] In existing two-dimensional X-ray imaging, the imaging result is usually a single grayscale image, whose grayscale values ​​reflect the spatial distribution of the measured object's response to X-ray attenuation. However, this attenuation is the result of the combined effects of the object's thickness, density, and atomic number (type of matter). Its core limitation is that for regions composed of overlapping multiple basic substances (such as bone, fat, and muscle in human tissue), single-energy or broadband grayscale images cannot distinguish and quantitatively analyze these different material components.

[0003] To address this issue, dual-energy X-ray absorptiometry (DAX) has been applied, for example, in bone densitometers where high- and low-energy X-rays are used to distinguish bone from soft tissue and calculate density values. However, this technique has the following limitations: First, it has a limited range of distinguishable substances. This method is typically based on a "two-substance model," which can only resolve two preset substances (such as bone and soft tissue). For real-world scenarios involving three or more substances, this model fails, and it requires significant differences in the attenuation responses of the two substances to high- and low-energy X-rays. Second, it underutilizes energy information. By simply dividing the broad spectrum of X-rays into two wide energy bands (high and low) through high- and low-voltage switching, the energy resolution is low, limiting the accuracy of substance identification and its resistance to interference. Third, it is significantly affected by beam hardening. When X-rays penetrate material, low-energy photons attenuate preferentially. This non-uniform attenuation effect can cause measurement errors when relying on ideal dual-energy decomposition algorithms.

[0004] In recent years, photon counting detectors (PCDs) have emerged as a novel type of X-ray imaging detector. They can detect and count every incident X-ray photon and categorize them into multiple preset energy ranges (or "energy boxes") based on their energy levels. Compared to traditional energy integration detectors, photon counting detectors can acquire multi-spectral projection data, providing attenuation information for each imaging pixel covering multiple narrow energy bands, rather than just two broad energy spectra: "high" and "low." Summary of the Invention

[0005] The purpose of this invention is to provide a method for calculating the density of multiple materials based on X-ray energy spectrum information, so as to solve the problems mentioned in the background art.

[0006] To achieve the above objectives, the present invention provides the following technical solution: A method for calculating the density of multiple materials based on X-ray energy spectrum information includes the following steps: S1. Multi-energy spectrum projection data acquisition: The X-ray object under test is exposed to a single X-ray using a photon counting detector. The detected X-ray photons are classified into at least three preset energy ranges according to their energy values, and the projection value of each pixel in each energy range is obtained. S2. Establishment of a multi-substance multi-energy spectrum decomposition model: For the multiple substances to be decomposed, based on the functional relationship between the mass decay coefficient of each substance and energy, and the system response function, a nonlinear relationship model between the projection value and the surface density of each substance along the ray path is established. S3. Calculation of material surface density: For each pixel, construct an objective function based on the difference between the actual projection value obtained in step S1 and the model calculation value in step S2, and solve the objective function using a numerical optimization algorithm to obtain the estimated surface density of each material at that pixel. S4. Quantitative Image Generation: Traverse all pixels to generate surface density distribution maps of each substance.

[0007] Preferably, in step S1, among the preset N energy boxes, N=3, and the three energy boxes correspond to energy ranges of 40-60keV, 60-80keV, and 80-100keV respectively; the projection value output by each pixel is P(x, y) = [P1(x,y), P2(x, y), P3(x, y)], where Pᵢ(x, y) represents the linear attenuation value measured by the i-th energy box at pixel coordinates (x, y), and the linear attenuation value is the negative logarithm of the transmittance. By setting three narrow energy bands, the attenuation differences of different substances in specific energy ranges can be captured more precisely, thereby improving the accuracy and stability of substance decomposition.

[0008] Preferably, in step S2, for the i-th energy box, the model expression is:

[0009] in , , The known mass decay coefficients are for bone minerals, fat, and lean meat, respectively. Bone minerals are represented by an equivalent of hydroxyapatite, and lean meat by an equivalent of water, acrylic, polyethylene, or a mixture of fatty acids. These mass decay coefficients were obtained from the NIST Standard Physics Database. , , The areal densities of the three substances to be determined were calculated using internationally recognized standard databases and equivalent materials, ensuring the accuracy and repeatability of the model parameters and providing a reliable basis for quantitative calculations.

[0010] Preferably, in step S2, The system response function of the i-th energy box is obtained by pre-scanning a standard phantom with known thickness and composition. The standard phantom is an aluminum phantom or an acrylic phantom. The system response is obtained through actual calibration, which can effectively correct the errors introduced by the X-ray source energy spectrum and detector response characteristics, and further improve the accuracy and robustness of the model.

[0011] Preferably, in step S3, an objective function is constructed for each pixel (x, y): the difference between the actual measured projection value and the calculated value in the model is minimized, a least squares objective function is constructed, and the Levenberg-Marquardt algorithm is used as the optimizer to solve the least squares objective function to obtain the surface density estimate of each material at the pixel. The mature and stable nonlinear optimization algorithm can efficiently converge to the global optimum, ensuring the accuracy and computational efficiency of the surface density solution.

[0012] Preferably, in step S4, all pixels are traversed to obtain three independent sets of bone mineral areal density distribution maps, fat areal density distribution maps, and lean meat areal density distribution maps, realizing the spatial distribution visualization of multiple substances, enabling clinicians or researchers to intuitively assess the density distribution of different tissues.

[0013] Preferably, in step S4, after generating the surface density distribution map of each substance, the local surface density value of the region of interest and the proportion of each substance in the region can be calculated according to the requirements, a substance proportion map can be generated and relevant quantitative analysis can be completed, providing a flexible quantitative analysis tool that can conduct in-depth evaluation of specific regions and meet the personalized needs in scientific research and clinical diagnosis.

[0014] Compared with the prior art, the beneficial effects of the present invention are: This invention employs a photon counting detector, which can classify X-ray photons into multiple preset energy ranges according to their energy values, thereby obtaining true multi-energy spectral projection data. Compared with the traditional dual-energy X-ray technology, which only obtains two wide energy spectral bands by switching between high and low voltage, this invention significantly improves energy resolution and provides a richer data foundation for material identification and quantitative analysis based on energy spectral information.

[0015] This invention, by setting at least three energy ranges, can establish decomposition models for three or more substances, enabling simultaneous quantitative calculation of multiple substances such as bone minerals, fats, and lean meat. It overcomes the limitations of existing dual-energy X-ray absorption methods, which are based on a "two-substance model" and can only distinguish two preset substances, and is suitable for more complex biological tissue component analysis scenarios.

[0016] This invention establishes a nonlinear model based on the mass attenuation coefficient and the system response function, and uses a numerical optimization algorithm to solve for the surface density. This effectively corrects measurement errors introduced by factors such as X-ray source energy spectrum, detector response characteristics, and beam hardening, thereby improving the accuracy and anti-interference capability of quantitative calculation of material density.

[0017] This invention can generate independent areal density distribution maps for each substance, and can further calculate the local areal density value and substance proportion of the region of interest, providing intuitive visualization results and flexible quantitative analysis tools for clinical diagnosis and scientific research, and has high practical value. Attached Figure Description

[0018] Figure 1 This is a flowchart of the method of the present invention. Detailed Implementation

[0019] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0020] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installed," "equipped with," "sleeved with," "connected," etc., should be interpreted broadly. For example, "connection" can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium; it can be a connection within two components. For those skilled in the art, the specific meaning of the above terms in this invention can be understood according to the specific circumstances.

[0021] Example: Please see Figure 1 The present invention provides a technical solution: The method for calculating the density of multiple materials based on X-ray energy spectrum information includes the following steps: S1. Multi-energy spectral projection data acquisition: A single X-ray exposure is performed on the object under test using a photon counting detector. The detected X-ray photons are categorized into at least three preset energy ranges according to their energy values, obtaining the projection value of each pixel in each energy range. Leveraging the energy resolution capability of the photon counting detector, projection data from multiple narrow energy bands are acquired simultaneously in a single exposure. Unlike traditional energy integral detectors that only output a single grayscale value, the photon counting detector can record the energy information of each incident photon and categorize it into multiple preset energy bins. This fully utilizes X-ray energy spectrum information, providing a data foundation for subsequent differentiation of various substances. The single-exposure acquisition method avoids motion artifacts and increased radiation dose problems associated with multiple exposures, while the preset at least three energy ranges ensure sufficient energy spectrum information to support the decomposition calculations of various substances. The multi-energy spectral projection value array output by each pixel includes the differences in the attenuation characteristics of substances at different energy bands.

[0022] S2. Establishment of a Multi-Material Multi-Energy Spectrum Decomposition Model: For the multiple substances to be decomposed, based on the functional relationship between the mass attenuation coefficient of each substance and energy, and the system response function, a nonlinear relationship model is established between the projected values ​​and the surface density of each substance along the X-ray path. A mathematical model that accurately describes the physical imaging process is constructed, linking the multi-energy spectrum projection values ​​obtained in step S1 with the surface density of the substances to be solved. The system response function includes system factors such as the X-ray source energy spectrum distribution and detector response characteristics. Calibration of this function can correct measurement biases introduced by the system. The nonlinear relationship model established by combining these two aspects can accurately reflect the attenuation process of X-rays after penetrating multiple substances, providing an accurate mathematical expression for subsequent quantitative solutions. This model is established for at least three substances, overcoming the limitation of traditional dual-energy methods that can only handle two substances, and laying the theoretical foundation for the simultaneous quantitative calculation of multiple substances.

[0023] S3. Calculation of Material Surface Density: For each pixel, an objective function is constructed based on the difference between the actual projected value obtained in step S1 and the model-calculated value in step S2. A numerical optimization algorithm is used to solve this objective function, yielding an estimated surface density value for each substance at that pixel. The physical model is transformed into a computable mathematical problem, and the surface density of each substance at each pixel is solved using an optimization algorithm. Since the actual measured values ​​include system noise and measurement errors, and the model-calculated values ​​are predictions based on ideal physical processes, minimizing the difference between the two essentially involves finding the material composition scheme that best matches the actual measurement results. Ensuring the convergence and stability of the calculation, and achieving a quantitative conversion from projected data to material surface density, is the core computational step of the entire method, ultimately yielding a quantitative estimate of each substance at each pixel.

[0024] S4. Quantitative Image Generation: This process iterates through all pixels to generate areal density distribution maps for each substance. The areal density values ​​obtained from each pixel are organized into a visual image, intuitively presenting the spatial distribution of each substance. Each image corresponds to the spatial distribution of areal density for one substance, with grayscale values ​​representing the areal density of that substance at the corresponding location. This separation imaging method overcomes the limitation of traditional grayscale images in distinguishing different substances, enabling clinicians and researchers to intuitively assess the density distribution of different tissues.

[0025] In step S1, N=3 of the preset N energy boxes, with the three energy boxes corresponding to energy ranges of 40-60 keV, 60-80 keV, and 80-100 keV, respectively. The specific workflow is as follows: the object to be tested is placed between the X-ray source and the photon counting detector. The data processing and control unit starts the X-ray source for a single exposure and triggers the detector to acquire data. Each pixel unit of the detector records the incident photon energy in real time and automatically categorizes it into the corresponding energy box for counting based on the energy value. After the exposure, each pixel records the cumulative count value of the three energy boxes. The data processing and control unit reads this value and calculates the transmittance of each energy box based on the empty scan reference value, then takes the negative logarithm of the transmittance to obtain the linear attenuation value. Finally, each pixel outputs a projection value array P(x, y) = [P1(x, y), P2(x, y), P3(x, y)], corresponding to the projection values ​​of the three energy boxes, respectively. By setting three narrow energy bands, the attenuation differences of different substances in specific energy ranges can be captured more precisely, thereby improving the accuracy and stability of substance decomposition.

[0026] In step S2, physical models are established for the three basic substances: bone minerals, fat, and lean meat. The specific workflow is as follows: First, the mass decay coefficients of the three substances are obtained from standard physics databases such as NIST. , , In this model, bone minerals are represented by hydroxyapatite, and lean meat is represented by water, acrylic, polyethylene, or a mixture of fatty acids. Then, the system response function of each energy cell is calibrated by pre-scanning aluminum or acrylic standard phantoms of known thickness and composition. This function comprehensively reflects the X-ray source energy spectrum distribution and detector response characteristics.

[0027] Substitute the above parameters into the model expression:

[0028] This expression describes the surface density of a given substance. , , The theoretical projection value of the i-th energy box is calculated under the following conditions. This model characterizes the inherent attenuation characteristics of different materials through the mass attenuation coefficient and corrects for measurement bias introduced by the system through the system response function, thus truly reflecting the attenuation process of X-rays after penetrating various materials.

[0029] Preferably, in step S3, since the model is about , , The problem is nonlinear, and this invention employs a numerical optimization method to solve it. The specific workflow is as follows: For each pixel (x, y), a least-squares objective function is first constructed to minimize the difference between the projected values ​​of the three energy boxes actually measured in step S1 and the calculated values ​​from the model in step S2. Then, the Levenberg-Marquardt algorithm is used as the optimizer for iterative solving. This algorithm can efficiently handle nonlinear least-squares problems. In each iteration, the algorithm calculates the model projection value based on the current areal density estimate and compares it with the measured value to obtain the error. The update direction is calculated using the Jacobian matrix, and the step size is adaptively adjusted to gradually approach the optimal solution. When the iteration converges or reaches the preset maximum number of iterations, the areal density estimates of bone minerals, fat, and lean meat at that pixel are output. , , This optimization process transforms the physical model into a computable mathematical problem. By minimizing the difference between the measured values ​​and the model values, it finds the material composition scheme that best matches the actual measurement results, thus realizing the quantitative conversion from multi-energy spectral projection data to the surface density of each material.

[0030] The bone mineral areal density at each pixel obtained in step S3 Fat surface density Lean meat density The areal density data is filled into three corresponding areal density matrices according to the pixel coordinates. After all pixels have been traversed, three complete quantitative images are formed: bone mineral areal density distribution map, fat areal density distribution map, and lean meat areal density distribution map. The gray value of each pixel in each image directly corresponds to the areal density of that substance at that location (unit: g / cm³). 2 Subsequently, based on clinical or research needs, regions of interest can be delineated on the generated distribution map. The system automatically calculates the statistical values ​​of the areal density of each substance within this region, including the average, maximum, minimum, and sum, to obtain the local areal density value. Simultaneously, based on the ratios of the areal densities of each substance, the system can calculate the relative proportions of different substances within the region of interest, generating a substance proportion map that visually presents the compositional ratios of bone, fat, and lean meat within that region.

[0031] This invention provides a method for calculating the density of multiple substances based on X-ray energy spectrum information, which can be implemented using the following system. This system mainly consists of an X-ray source, a photon counting detector, and a data processing and control unit. These components work together to complete the acquisition of multi-energy spectrum data and the quantitative calculation of substance density.

[0032] The X-ray source is used to generate broadband X-rays. The X-ray source provides incident X-rays covering a certain energy range to meet the measurement requirements of attenuation characteristics of different substances in multiple energy bands, based on the region where the attenuation response of typical biological tissues changes significantly with X-ray energy.

[0033] The photon counting detector, positioned opposite the X-ray source, receives X-ray photons passing through the object under test and counts them according to their energy into at least three energy ranges. Utilizing its energy resolution capability, the photon counting detector records the energy information of each incident X-ray photon and categorizes them into different energy bins based on preset energy thresholds. Unlike traditional energy integrating detectors, which only output accumulated energy signals, the photon counting detector can distinguish the energy of individual photons, thus acquiring projection data from multiple narrow energy bands simultaneously in a single exposure. The distance between the X-ray source and the detector can be adjusted according to the object under test to achieve ideal spatial resolution and imaging quality.

[0034] The data processing and control unit is connected to the X-ray source and the photon counting detector, respectively, and is used to control data acquisition and execute the calculations in steps S2 to S4. The data processing and control unit coordinates the collaborative work of the X-ray source and the detector, and processes and analyzes the acquired multi-energy spectral projection data. The data processing and control unit controls the X-ray source to perform a single exposure, synchronously triggering the photon counting detector to start acquisition; it receives the projection values ​​of each pixel output by the detector in each energy range; then it executes a pre-stored algorithm program, including steps such as establishing a multi-matter multi-energy spectral decomposition model, constructing an objective function, using a numerical optimization algorithm to solve for the surface density of the matter, and traversing all pixels to generate a surface density distribution map. The hardware of this unit may include a high-performance computer, an embedded processor, or a dedicated image processing unit, while the software includes the algorithm code and user interface for implementing the method of this invention.

[0035] All other parts of this invention not described herein are the same as existing technologies, or are known technologies, or can be implemented using existing technologies, and will not be described in detail here.

[0036] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and variations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A method for calculating the density of multiple materials based on X-ray energy spectrum information, characterized in that, Includes the following steps: S1. Multi-energy spectrum projection data acquisition: The X-ray object under test is exposed to a single X-ray using a photon counting detector. The detected X-ray photons are classified into at least three preset energy ranges according to their energy values, and the projection value of each pixel in each energy range is obtained. S2. Establishment of a multi-substance multi-energy spectrum decomposition model: For the multiple substances to be decomposed, based on the functional relationship between the mass decay coefficient of each substance and energy, and the system response function, a nonlinear relationship model between the projection value and the surface density of each substance along the ray path is established. S3. Calculation of material surface density: For each pixel, construct an objective function based on the difference between the actual projection value obtained in step S1 and the model calculation value in step S2, and solve the objective function using a numerical optimization algorithm to obtain the estimated surface density of each material at that pixel. S4. Quantitative Image Generation: Traverse all pixels to generate surface density distribution maps of each substance.

2. The method for calculating the density of multiple materials based on X-ray energy spectrum information according to claim 1, characterized in that, In step S1, among the preset N energy boxes, N=3, and the three energy boxes correspond to energy ranges of 40-60 keV, 60-80 keV, and 80-100 keV, respectively; the projection value output by each pixel is P(x, y) = [P1(x, y), P2(x, y), P3(x, y)], where Pᵢ(x, y) represents the linear attenuation value measured by the i-th energy box at pixel coordinates (x, y), and the linear attenuation value is the negative logarithm of the transmittance.

3. The method for calculating the density of multiple materials based on X-ray energy spectrum information according to claim 1, characterized in that, In step S2, for the i-th energy box, the model expression is:

4. Among them , , The known mass decay coefficients are for bone minerals, fat, and lean meat, respectively. Bone minerals are represented by an equivalent of hydroxyapatite, and lean meat by an equivalent of water, acrylic, polyethylene, or a mixture of fatty acids. These mass decay coefficients were obtained from the NIST Standard Physics Database. , , These are the surface densities of the three substances to be determined.

5. The method for calculating the density of multiple materials based on X-ray energy spectrum information according to claim 3, characterized in that, In step S2 The system response function of the i-th energy box is obtained by pre-scanning a standard phantom with known thickness and composition, wherein the standard phantom is an aluminum phantom or an acrylic phantom.

6. The method for calculating the density of multiple materials based on X-ray energy spectrum information according to claim 1, characterized in that, In step S3, an objective function is constructed for each pixel (x, y): the difference between the actual measured projection value and the calculated value in the model is minimized, a least squares objective function is constructed, and the Levenberg-Marquardt algorithm is used as the optimizer to solve the least squares objective function to obtain the estimated surface density of each material at the pixel.

7. The method for calculating the density of multiple materials based on X-ray energy spectrum information according to claim 1, characterized in that, In step S4, all pixels are traversed to obtain three independent sets of bone mineral areal density distribution maps, fat areal density distribution maps, and lean meat areal density distribution maps.

8. The method for calculating the density of multiple materials based on X-ray energy spectrum information according to claim 6, characterized in that, In step S4, after generating the surface density distribution map of each substance, the local surface density value of the region of interest and the proportion of each substance in the region can be calculated as needed to generate a substance proportion map and complete the relevant quantitative analysis.

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