Method for material density measurement using computed tomography with diffraction artifact correction

Abstract

Embodiments determine the density of materials and objects imaged using computed tomography (CT). An embodiment collectively images a material of unknown density with a calibrator of known density. The digitally reconstructed CT image is segmented into an unknown material phase and a known material phase of the calibrator. And obtaining an image intensity histogram of the unknown material. An intensity-density map is calculated using the known calibrator density to determine an unknown material density based on its measured CT intensity. The methods described herein utilize novel deconvolution of intensity histograms to correct for CT imaging artifacts that affect the material phase intensity. By using the embodiment, the density and characteristics of micronized materials, such as particles, microspheres, porosity and multiphase composites, which are difficult to measure by conventional techniques can be measured. Design and uncertainty estimation of custom sample reservoirs for co-imaging materials with calibrators are also described.

Description

[0001] Related Applications

[0002] This application claims the benefit of U.S. Provisional Application No. 63 / 367,532, filed on July 1, 2022. The entire teachings of the above application are incorporated herein by reference. Background Art

[0003] The density of a material (defined as the mass per unit volume) is a fundamental property of a material. For homogeneous materials such as metals, density is directly related to the underlying crystal structure of the material and is a useful parameter for identifying different metallic materials. Similarly, for homogeneous polymeric materials, density can be used to determine the relative amorphous and crystalline fractions, as well as to identify the presence of specific crystalline polymorphs. The overall mechanical, thermal, and electrical properties of many materials can depend on their underlying crystalline fraction and crystalline phase. Therefore, density is a fundamental metric for the classification, comparison, performance evaluation, and quality assessment of materials. For example, the polymer poly(vinylidene fluoride) (PVDF) has five known crystalline polymorphs, of which the β phase exhibits piezoelectric, pyroelectric, and thermoelectric behavior (Steiner and Zimmerer

[12] ; Lovinger [9]; Kawai [7]) (numbers in parentheses in this document refer to the reference list cited below). The unique chain conformation and crystal structure of the β phase results in a significantly higher density of β phase PVDF compared to the more common α phase crystalline and amorphous PVDF (Steiner and Zimmerer

[12] ; Lovinger [9]). Density can therefore be a key measurement in determining the crystalline phase of PVDF and therefore a performance indicator for potential electroactive products. Density measurements are considered mandatory by the scientific community when characterizing material products and, likewise, by regulatory agencies when products and their constituent raw materials are subject to regulation, such as in the case of pharmaceuticals.

[0004] In the case of heterogeneous products composed of multiple different materials, density is a linear combination of the different phases and can be used to infer the relative fractions of the different component phases. In the development of pharmaceutical products, active pharmaceutical ingredients (APIs) are often blended with a wide range of excipient materials. Excipients can aid in the manufacturability of the API and modulate the release of the API from the pharmaceutical product. In the case of long-acting injectables, parenteral products, and drug-eluting implants or devices, encapsulation of the API within polymeric excipients is central to product functionality, while for oral solid dosage forms, excipients make it possible to tablet the drug product for human consumption (Fredenberg et al. [4]; Zhong et al.

[17] ; Yost et al.

[14] ). Assessing the density of these products not only enhances the understanding of encapsulation efficiency and mixing, but also provides a means to assess the microstructural characteristics of the product (such as porosity), which have been shown to have a significant impact on product performance (Zhang et al.

[15] ). From an upstream processing perspective, measuring the density of API and excipients at different manufacturing time points (e.g., before granulation, after granulation, before extrusion, after extrusion) is a powerful tool for product quality control. Changes in density before and after these steps may imply changes in chemical state between crystalline and amorphous or structural state between dispersed and aggregated. The potential introduction and evolution of porosity may have a significant impact on dissolution properties, release rate, and drug product stability.

[0005] The measurement of the density of a material is usually accomplished using one of several techniques. The most direct approach is to directly measure the mass and volume of the material in question and calculate the density. This approach is simple and practical. However, problems arise with objects of inhomogeneous shape that make it difficult to measure the volume or with objects that are too small to be weighed using conventional means (such as microspheres in early development or very limited quantities of API substances). Other techniques for density measurement include density gradient columns and gas pycnometry, which can be used for materials with inhomogeneous shapes. Gradient columns are advantageous because they allow the density of an object to be measured directly. However, the range of gradient columns is limited by the choice of gradient liquid used in the column (Oster and Yamamoto

[10] ). In addition, the practicality of gradient columns is limited because the amount of material being measured must be large enough to be directly visualized within the gradient column. Gas pycnometry measures the density of a material by determining the volume of gas displaced by the test material in a test cell of known volume (Richards and Bouazza

[11] ). Although pycnometry can be used to determine the density of inhomogeneous solids and the density of porous materials, pycnometry is not a technique designed to measure density directly. In contrast, pycnometry measures the volume of the test material and requires knowledge of the mass of the test material, which prevents density determination of objects that are too small to be effectively weighed. To date, there is no technology that can reliably and accurately measure the density of materials with microscopic features, such as powders, composite particles (e.g., drug-encapsulated polymer microspheres), samples with microporosity, or very small amounts of samples. For these materials, density is usually reported as "bulk density" or "tapped density." Bulk density is the density of a sample of particles or powder loaded into a container of known volume, and tap density is the density of the powder after it has been mechanically tapped to promote powder sedimentation. Both measurements are estimates and do not capture the "true density" of the material. In the case of drug product development, bulk density measurements provide little insight into the solid-state phase changes of these products at different stages. This is because bulk density measurements are more of a measure of particle packing efficiency, which depends on the shape, size, and brittleness of the particles and the compaction method. In addition, bulk density provides little insight into the phase distribution in heterogeneous drug products, especially when the underlying density of the phase is unknown. For parenteral microspheres, granulated products and raw powder materials, it is difficult or impossible to perform true density measurements by conventional methods due to the microscopic characteristics of the samples. Therefore, different measurement techniques need to be developed.

[0006] Computed tomography (CT) imaging is an imaging modality that is sensitive to the true density of the object being imaged because the source signal is transmitted through the entire object. For example, in X-ray imaging, X-ray photons pass through the object and are recorded at a detector that measures the total X-ray count (Huda and Slone [5]). As the X-ray photons pass through the material, they interact with the electron cloud of the underlying atoms in the material. The electrons excited by the X-rays will re-emit X-ray photons, which can then pass through the material and land on the detector. The strength of the X-ray-electron interaction within the material is determined by the energy of the incident X-ray photon, the structure and shape factor of the electrons and atoms, and the atomic number of the underlying atoms. Therefore, the measured X-ray signal intensity depends on the specific elemental composition of the material and how many absorbing atoms are in the path of the photons. If the elemental composition of two samples is the same, then the variation in the X-ray signal intensity comes primarily from the variation in the density of the two samples. Although the interaction between the source signal and the atomic structure of the material object may be different, the intensity captured by other tomography techniques (such as optical tomography, electron tomography, and magnetic tomography) has a similar dependence on the true density of the material that makes up the object.

[0007] The density of an object can be determined by calibrating the measured CT imaging intensity using known standards. This forms the basis for clinical X-ray imaging and medical CT in determining bone damage, the progression of osteoporosis, and degenerative lung disease (Chen Mayer et al. [3]; Boone and Yellen-Nelson [2]; Lang et al. [8]). For objects and powder samples with microscopic features, micro-CT and X-ray microscopy (XRM) are required to capture the interaction between X-ray photons and the material with sufficient resolution. Micro-CT and XRM operate under the same physical principles as medical CT, with the main difference being that the imaging resolution has been improved by several orders of magnitude, from 0.5-50 mm / voxel in clinical CT to 0.5-50 μm / voxel in micro-CT and XRM. These higher resolution X-ray imaging methods provide a potential way to determine the true density of materials with microscopic features. Determining density using micro-CT and XRM can provide a robust understanding of the properties of a material and provide a powerful quality control indicator.

[0008] To date, several challenges unique to micro-CT and XRM have hampered their use as a true density measurement tool. The first challenge is to identify and construct appropriate density standards. Density standards must be composed of elements with atomic masses comparable to those of the material of interest. The density range of the standard material should cover the density of the material of interest to allow interpolation. On the other hand, the density differences of the standard material should be spaced to support the accuracy of the interpolation. Due to the variability of CT instruments, lack of operational consistency, and the relatively small field of view when imaging at very high resolutions, the density standard must be small enough to be co-imaged with the material of interest without obstructing the field of view. The second challenge is to mitigate and correct X-ray imaging artifacts, which can have a significant impact on the overall measured intensity of the sample. Such imaging artifacts become significant when the features of interest are small enough that optical effects such as Fresnel diffraction and X-ray beam hardening affect a large fraction of the imaged voxels. To date, these challenges have hampered the development of X-ray-based methods for determining the true density of materials with microscopic features. Summary of the invention

[0009] Embodiments solve the aforementioned problems and provide functionality for determining the density of a material. One such embodiment relates to a computer-implemented method for determining the density of a material. The method first segments imaging data of a material and a standard material (interchangeably referred to herein as a "calibrant") into multiple phases, e.g., intensity phases. For each of the multiple phases, a corresponding histogram is determined based on the pixel intensity of the imaging data obtained corresponding to the phase. In turn, a given histogram corresponding to the material is deconvolved into (i) a function corresponding to an artifact, e.g., the intensity of the artifact, and (ii) a function corresponding to the material, e.g., the intensity of the material. Continuing, one or more histograms corresponding to the calibrant are used to determine the relationship between density and pixel intensity. This determined relationship is applied to a function corresponding to the material (e.g., a function corresponding to the intensity of the material) to determine the density of the material.

[0010] One embodiment obtains imaging data of the material and calibrants in a sample reservoir by subjecting the material and calibrants to CT imaging.

[0011] According to one embodiment, segmenting the imaging data includes at least one of: (i) segmenting the imaging data based on intensity, (ii) segmenting the imaging data based on gradient, and (iii) segmenting the imaging data by processing the imaging data with at least one of a machine learning algorithm or an artificial intelligence algorithm to identify data corresponding to each of a plurality of phases.

[0012] In an example embodiment, deconvolving a given histogram corresponding to a material includes performing an analysis (e.g., a regression analysis) to deconvolute (i.e., fit) the data of the given histogram into (i) a function corresponding to an artifact and (ii) a function corresponding to the material. Additionally, it should be noted that embodiments are not limited to deconvolving a single histogram into a single function corresponding to an artifact and a single function corresponding to the material, and that, instead, multiple histograms generated by the imaging data may be deconvolved into multiple functions corresponding to multiple different artifacts and multiple functions corresponding to multiple materials, e.g., material phases of a sample whose density is being determined. For example, an embodiment may deconvolute a given histogram into (i) multiple functions corresponding to multiple different artifacts and (ii) multiple functions corresponding to multiple materials.

[0013] The calibrant may include a plurality of calibrant materials (i.e., standard materials), each of which has a corresponding known density. In one such embodiment, determining the relationship between density and pixel intensity using one or more histograms corresponding to the calibrant includes determining an average pixel intensity for each of the plurality of calibrant materials using a corresponding histogram corresponding to each of the plurality of calibrant materials. In turn, the relationship is determined using an average pixel intensity determined for each of the plurality of calibrant materials and a corresponding known density for each of the plurality of calibrant materials. According to an embodiment, determining an average pixel intensity for each of the plurality of calibrant materials using a corresponding histogram corresponding to each of the plurality of calibrant materials includes deconvolving each histogram corresponding to each of the plurality of calibrant materials into (i) an artifact function and (ii) a calibrant material function. The average pixel intensity for each of the plurality of calibrant materials is then determined using the corresponding calibrant material function. According to an embodiment, the determined relationship is a mathematical function, e.g., a linear function, between the average pixel intensity determined for each of the plurality of calibrant materials and the corresponding known density for each of the plurality of calibrant materials.

[0014] Embodiments may also perform various additional functions (alone or together). For example, one embodiment determines an average density of a material. Embodiments may also determine the uncertainty of the determined density. Still further, in response to the material being composed of discrete particles, one embodiment determines the density distribution of the particles within a certain range of particle sizes, the density of each particle, and the standard deviation of each particle. In response to the material being composed of a continuous material phase, an example embodiment determines the density distribution along an arbitrary orientation in at least one of the following: a Cartesian coordinate system, a cylindrical coordinate system, and a spherical coordinate system. In addition, it is worth noting that in one embodiment, the aforementioned functions can be implemented as part of determining the density of a material.

[0015] Embodiments may also be configured to implement iterative refinement of a system in which non-physical density measurements due to diffraction heterogeneity are experienced. For example, an embodiment may identify that a determined density is non-physical, and in response to identifying that the determined density is non-physical, determine a corrected density (e.g., by iterative refinement) or determine that a corrected density cannot be identified.

[0016] According to one embodiment, determining the corrected density includes at least one of the following: (i) generating corrected imaging data by processing the imaging data using a feature size threshold to remove resolution artifacts, and repeating the segmentation, determining the corresponding histogram, deconvolution, determining the relationship, and applying using the corrected imaging data; (ii) obtaining new imaging data of the material and a new calibrator, and repeating the segmentation, determining the corresponding histogram, deconvolution, determining the relationship, and applying using the new imaging data; and (iii) obtaining higher resolution imaging data that corrects for at least one of geometry-induced heterogeneity, shape-induced heterogeneity, and morphology-induced heterogeneity, and repeating the segmentation, determining the corresponding histogram, deconvolution, determining the relationship, and applying using the higher resolution imaging data.

[0017] In one embodiment, iterative refinement may include: (i) correcting resolution artifacts by feature size thresholding in units of number of pixels to exclude incompletely resolved small particle features to give an accurate density measurement, thereby convolving the total density measurement; (ii) introducing a new calibrant including atomic elements from the third row or higher of the periodic table, where the new calibrant material selection is determined based on non-physical measurements or known atomic composition of the material of interest, and then repeating the workflow (i.e., repeating segmentation, determining corresponding histograms, deconvolution, determining relationships, and applying); and (iii) correcting for diffraction heterogeneity caused by geometry, shape, and morphology, which generally requires a higher resolution scan. While an embodiment may be configured to implement system iterative refinement, an embodiment may also be configured to determine that the method for determining density described herein is not applicable when the diffraction heterogeneity is too strong. In addition, an embodiment may include a function to determine that an output value (i.e., density) is physically incorrect, and such an embodiment may include a function to suggest how to obtain a physically accurate result. For example, in a microsphere sample composed of two materials of known density, the true density of the microsphere sample should be between the known densities of the two materials. If the true density measurement is higher than the higher density of the two materials, or lower than the lower density of the two materials, then the measurement is unphysical. The inclusion of unexpected materials, diffraction artifacts not currently considered, and density ranges of current calibrants may be root causes for the need for the iterative determination described herein.

[0018] Another embodiment relates to a system comprising a processor and a memory having computer code instructions stored thereon. In such embodiments, the processor and the memory having computer code instructions are configured to cause the system to implement any embodiment or combination of embodiments described herein.

[0019] Yet another embodiment relates to a computer program product for determining the density of a material. The computer program product comprises one or more non-transitory computer-readable storage devices and program instructions stored on at least one storage device of the one or more storage devices. When loaded and executed by a processor, the program instructions cause a device associated with the processor to perform any embodiment or combination of embodiments described herein.

[0020] Example embodiments relate to a system for positioning a material. According to one embodiment, the system includes a material, a calibrant, and a reservoir. The reservoir defines (i) a material chamber configured to hold the material, (ii) a calibrant chamber configured to hold the calibrant, and (iii) a passage, such as an air passage, separating the material chamber and the calibrant chamber.

[0021] In one embodiment of the material positioning system, the calibrant comprises one or more of the following: a plurality of film layers, a plurality of sample reservoir materials, and a plurality of particles. In one such embodiment, the plurality of film layers comprises a first polymer film layer, a second polymer film layer, and a third polymer film layer, wherein the first polymer film layer and the third polymer film layer sandwich the second polymer film layer. According to an example embodiment, the second polymer film layer comprises a first polymer film strip and a second polymer film strip separated by a channel (e.g., an air channel). In an embodiment, the plurality of polymer film layers may be disposed on top of an adhesive layer. Additionally, in one embodiment, each film layer is composed of at least one of the following: a polymer having a density of 0.91 g / cm 3 Polypropylene (PP), density 1.38g / cm 3 Poly(ethylene terephthalate) (PET) and a density of 2.2 g / cm 3 of poly(tetrafluoroethylene) (PTFE).

[0022] According to one embodiment, the reservoir is configured to consistently position and orient the calibrant. In this way, such an embodiment facilitates the imaging attenuation of the material to uniformly affect the calibrant. This can improve density measurements, for example, in one embodiment, the determination of bone density can also be improved, among other examples. In addition, in one embodiment of the system, the calibrant is loaded into the reservoir in a consistent manner so that when the reservoir (containing the material and the calibrant) is subjected to imaging, the X-ray attenuation of the material is uniformly affected by the calibrant. For example, if the bar calibrant is vertically positioned relative to the x-ray beam, the calibrant is vertically positioned on the sample to be compared, that is, the calibrant is positioned / oriented in the same manner (consistently) across different compared samples. For further explanation, returning to the example of the vertical positioning of the calibrant, the calibrant is not horizontally positioned relative to the x-ray beam in another sample being compared.

[0023] Another embodiment of the system further includes an imaging instrument. In one embodiment, the parameters of the imaging instrument are calibrated using the calibrant and the calibration material of interest. The density of the calibration material of interest is known, which is different from the density of the calibrant. In this way, in such embodiments, the density measurements obtained using the imaging instrument, materials, calibrants, and reservoirs are independent of the vendor, magnification (e.g., local tomography magnification, geometric magnification, etc.), parameters (e.g., exposure time), and imaging contrast (e.g., adsorption contrast, phase contrast, etc.).

[0024] According to an embodiment, the reservoir can be in any suitable geometry that facilitates co-imaging of the material (i.e., the material of unknown density) and the calibrant. For example, in one embodiment, the reservoir is rectangular and the calibrant is attached to the exterior of the reservoir. In another embodiment, the reservoir is tubular and the material chamber, calibrant chamber, and channel are defined within an interior region of the tubular reservoir.

[0025] One embodiment relates to the construction of a density calibrant. According to one such embodiment, the calibrant is constructed of three or more materials of varying densities to ensure an accurate final strength-density calibration curve. Although three calibrant materials are used in one embodiment, including more materials can improve the accuracy and precision of the calibration curve. In one embodiment, the geometry of the calibration material is determined by the sample of interest, and can be in the form of a strip of a composite of materials, or in the form of a separate identifiable object, such as a calibrant sphere that is co-imaged with the material of interest. An example of a calibrant is a calibration strip constructed of three polymers of established density: poly(propylene) (abbreviated herein as PP, density = 0.91 g / cm 3 ), poly(ethylene terephthalate) (abbreviated as PET in this article, density = 1.38 g / cm 3 ) and poly(tetrafluoroethylene) (abbreviated herein as PTFE, density = 2.2 g / cm 3 ). In such embodiments, the elements comprising the polymer are low atomic weight elements in the first two rows of the periodic table, commonly found in organic compounds. This makes such calibrants suitable for measuring the density of common organic materials used in pharmaceuticals and foods.

[0026] One embodiment features a customized CT sample reservoir designed to enclose both the sample of interest and the calibrant. The sample reservoir allows for co-imaging of the sample of interest and the density standard (i.e., calibrant material) so both the sample and the density standard are within the field of view.

[0027] Another feature of an embodiment is a system for determining measured intensity histograms of reconstructed CT images. The system has the ability to segment different observed material phases with appropriate resolution and contrast, the computing power to process these images and segmentation, and the storage capacity to host and provide access to the imaging and segmentation data.

[0028] An additional feature of an embodiment is a deconvolution method for correcting the effects of diffraction artifacts on the measured intensities of segmented imaging data including material of interest, interstitial air voids, and calibration objects.

[0029] An additional feature of an embodiment is to construct an intensity-density calibration function using the CT imaging intensity and the known density of the material of the calibrant. This relationship calculated according to such an embodiment can be used to determine the density of an unknown material of interest in a sample co-imaged with the calibrant. An additional feature of an embodiment is to calculate a 95% confidence interval for the density of the unknown material to provide a measure of the uncertainty of the density calculated using this method.

[0030] In one embodiment, a material phase histogram is obtained by sampling the segmented phase intensities, binning the intensity values, and employing an algorithm to determine the appropriate number of bins given the size of the segmented phase voxels.

[0031] One embodiment determines an intensity-density calibration curve by calculating a linear relationship between the density of the calibrant module and its deconvoluted signal intensity using at least one regression method, such as least squares regression, orthogonal distance regression, and maximum likelihood estimation. One embodiment uses the intensity of the deconvoluted material histogram and the intensity-density calibration function to determine the density of the material of interest.

[0032] To achieve the advantages described herein, one embodiment includes, among other things, the following steps in part:

[0033] (1) A sample is imaged by CT using a material of interest of unknown density, co-imaged with a calibrant, wherein (1.1) material standards of known density in the calibrant are selected and assembled based on the material of interest. (1.2) A sample reservoir is constructed using appropriate methods and materials (e.g., by 3D printing with poly(lactic acid) or acrylonitrile butadiene styrene (ABS). (1.3) The calibrant is loaded into the sample reservoir so that the calibrant can be co-imaged with the material of interest. (1.4) The imaging apparatus can be any CT imaging method used with an appropriate field of view and resolution. (1.5) The calibrant is loaded into the sample reservoir in a consistent manner so that the x-ray attenuation of the material of interest is uniformly affected by the calibrant. (1.6) Calibrate imaging instrument parameters using the calibrant and a calibration material of interest; the density of the calibration material of interest is known and different from the density of the material used in the calibrant, so that the density measurement results are independent of the supplier, magnification (local tomography magnification or geometric magnification), parameters (e.g., exposure time), and imaging contrast (e.g., adsorption contrast or phase contrast).

[0034] (2) A three-dimensional digital representation of the co-imaged material of interest and the calibrant, used to extract CT intensities corresponding to all materials, wherein (2.1) the image is segmented into different phases using supervised machine learning, deep learning, conventional threshold segmentation, or any image segmentation method. (2.2) Intensity histograms are extracted from the segmented phases, including the material of interest phase of unknown density, interstitial air, and the material phase from the calibrant.

[0035] (3) The material phase intensity histogram is artifact corrected, where (3.1) To correct for diffraction artifacts, the material phase histogram is deconvolved into two underlying intensity contributions, one caused by diffraction artifacts and the other caused by the tomographic interaction between the source imaging signal and the actual material. (3.2) To correct for resolution artifacts, the smallest features are deconvolved from larger features based on a feature size threshold in number of pixels.

[0036] (4) Determine the material density, where (4.1) an intensity-density calibration curve is calculated by regression using the intensities of the material in the calibrant and its known material density. (4.2) The diffraction-corrected intensities of the material phase of unknown density are positioned along the intensity-density calibration curve to provide an interpolation of the material phase density. (4.3) A 95% confidence interval for the material phase density is determined from the calibration curve to provide upper and lower intensity limits. (4.4) If the material of interest is composed of discrete particles, the density distribution of the particles within a certain range of particle sizes, the density of each particle, and the standard deviation of each particle should be provided. (4.5) If the material of interest is composed of a continuous material phase, the density distribution along any orientation in a Cartesian coordinate system, a cylindrical coordinate system, or a spherical coordinate system.

[0037] (5) Systematic iterative refinement of non-physical density measurements due to diffraction heterogeneity, including (5.1) introducing new calibrants including atomic elements from row 3 or higher of the periodic table, where the new calibrant material selection can be determined based on non-physical measurements or the known atomic composition of the material of interest, followed by repeating steps from (1.1) to (4.4). (5.2) Diffraction heterogeneity caused by geometry / shape / morphology, which generally requires higher resolution scans. (5.3) When diffraction heterogeneity is so strong that iterative refinement in the correction makes the measurement unrepresentative, the mechanism of determining the method is not applicable. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The foregoing will be apparent from the following more particular description of example embodiments, as illustrated in the accompanying drawings, in which like reference numerals refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the embodiments.

[0039] Figure 1is a schematic block diagram of a workflow of modules and features according to an embodiment, including a calibration module, a deconvolution module and a density determination module, wherein each module has defined steps.

[0040] Figure 2A and Figure 2B A cross-section and side view, respectively, of a schematic representation of a polymer density calibration object of an example configuration according to an embodiment showing three different polymer layers and associated dimensions.

[0041] Figure 3A , Figure 3B , Figure 3C and Figure 3D Top, bottom, side, and three-dimensional projection views, respectively, of an exemplary customized 3D-printed sample reservoir capable of imaging both polymer density calibrants and unknown samples at appropriate sizes according to an embodiment.

[0042] Figure 4A A graphic representation of the effect of a diffraction artifact called Fresnel diffraction on a microsphere, with light and dark fringe artifacts indicated.

[0043] Figure 4B is a graphic representation of Fresnel diffraction artifacts of irregularly shaped particles according to an embodiment.

[0044] Figure 4C is a grayscale X-ray micro-CT image of polymer microspheres showing the Fresnel diffraction fringes of the spherical particles across the entire 3D field of view of the image.

[0045] Figure 4D is a grayscale X-ray micro-CT image of sintered glass beads, showing the Fresnel fringes of the inhomogeneous particles.

[0046] Figure 5 is a schematic block diagram of a computational workflow and functionality for a segmented CT image to correct for diffraction artifacts and construct an intensity-density relationship to determine unknown density, according to an embodiment.

[0047] Figure 6 is a graphical representation of deconvolution of a histogram of a material phase corresponding to a material label by segmentation, wherein the original histogram is plotted in addition to the underlying two Gaussian bands corresponding to the material and diffraction artifacts, according to an embodiment.

[0048] Figure 7is a graphical representation of a density-intensity linear relationship (dashed line) constructed using known polymer and air densities (shown as circles) according to one embodiment, and the density of an unknown material determined based on its CT image intensity (squares) and upper and lower limits of density (error bars).

[0049] Figure 8 is a flow chart of a method for determining the density of a material according to an embodiment.

[0050] Fig.9A Depicted are representative 2D slices of reconstructed x-ray microscopy (XRM) scans of poly(methyl methacrylate) (PMMA) microspheres co-imaged with polymer calibrants in a custom 3D-printed PLA reservoir.

[0051] Fig. 9B yes Fig.9A Magnified view of a polymer calibrant indicating the specific polymer used.

[0052] Fig. 10A Shown are intensity histograms of five calibrant materials segmented from an image according to an embodiment.

[0053] Fig. 10B are plots of the known calibrant densities as a function of mean intensity, and the linear model.

[0054] Fig.11 is the density histogram of deconvoluted PMMA spheres (circles) and fitted to a Gaussian distribution (line).

[0055] Fig.12 is a graph of the intensity of PMMA microspheres as a function of the equivalent sphere diameter before (light shaded symbols) and after deconvolution (dark shaded symbols).

[0056] Fig.13A Depicted are representative 2D slices of reconstructed images acquired from a synchrotron light source.

[0057] Fig. 13B yes Fig.13A Magnified view of a 2D slice.

[0058] Fig.14A is an XRM image with the calibration phase indicated.

[0059] Fig. 14B yes Fig.14A Calibrator histogram of the calibrants.

[0060] Fig.15A is a graph showing the results of converting histogram intensities to density using linear regression.

[0061] Fig. 15B Graphs showing the distribution of microsphere density (circles) and Gaussian fit (dashed line).

[0062] Fig.16A is a graph of the intensity of the original microspheres (light shaded circles) and the deconvoluted spheres (dark shaded circles) as a function of the equivalent sphere diameter.

[0063] Fig. 16B is by changing the intensity from Fig.16A The graph is converted to microsphere density by determining the density versus sphere diameter.

[0064] Fig.17 A computer network or similar digital processing environment is shown in which embodiments of the present invention may be implemented.

[0065] Fig.18 yes Fig.17 A diagram of an example internal structure of a computer (e.g., a client processor / device or a server computer) in a computer system of FIG. DETAILED DESCRIPTION

[0066] The following is a description of example embodiments.

[0067] Example workflow overview

[0068] According to one embodiment, the determination of CT-based material density with microscopic features utilizes three modules 110, 111, and 112, such as Figure 1 Module 110 is the calibration module, which implements four main steps 101, 102, 103, and 104. Module 110 begins with initial calibrant design, followed by preparation and attachment of the calibrants to the sample reservoirs (101 and 102). After loading (103) the sample into the sample reservoir, CT imaging of the material of interest enclosed in the reservoir loaded with the calibrants can be acquired using an appropriate CT imaging instrument operating at the necessary resolution and contrast (104).

[0069] The functionality of the calibration module 110 is followed by that of the deconvolution module 111. The deconvolution module 111 has three main steps 105, 106, and 107. The CT image is initially segmented into individual material phases using an appropriate segmentation algorithm (105). This segmentation (105) can be achieved and refined using iterative artificial intelligence (AI) methods such as deep learning to improve the phase segmentation (106). The now segmented image is then subjected to a diffraction deconvolution algorithm to correct for the effects of imaging artifacts caused by diffraction artifacts (107). After the deconvolution module 111, the data is subjected to a density module 112, which determines an intensity-density calibration curve using a calibrant (108), and then determines the density of the material of interest and upper and lower density limits (109).

[0070] Calibration module: calibrant design, reservoir design and sample loading

[0071] The design and preparation of the calibrant and sample reservoir (101 and 102) according to one embodiment depends on the material being studied as well as the geometric structure and imaging settings. An example of the design and preparation of a calibration for studying organic spherical particles is disclosed as one embodiment of this article. However, it should be noted that the embodiments are not limited to determining the density of the material described herein and the type of material. A polymer film can be selected for use as a calibrant. The polymer film can be selected so that changes in the intensity of the X-ray signal are caused only by the density of the material, rather than by changes in the atomic X-ray absorption spectrum. According to one embodiment of the present invention, the preparation of a polymer density standard (alternatively referred to as a calibrant) can be achieved using poly(propylene) (PP), poly(ethylene terephthalate) (PET) and poly(tetrafluoroethylene) (PTFE). In an exemplary embodiment, the density of each polymer is 0.91 g / cm 3 , 1.38g / cm 3 and 2.20g / cm 3 These density values ​​are well-established for commercial grades of PP, PET, and PTFE, with PP being isotactic and semi-crystalline, PET being completely amorphous, and PTFE also being semi-crystalline. The polymers are commercially available as uniform, non-porous films with an acrylic adhesive backing, allowing the film to be applied to a surface.

[0072] like Figure 2A and Figure 2B As shown in cross-sectional view 220a and side cross-sectional view 220b, respectively, in one embodiment, the composite density standard is assembled from an adhesive 224, a PP layer 221 at the bottom, followed by a PTFE layer 222, and then a PET layer 223, as shown in FIG. Figure 2AAs shown. A gap 225 is formed in the PTFE layer to ensure that there is an isolated air pocket within the calibrant, allowing the use of air as a fourth density calibrant to improve robustness (if one calibrant fails) and increase regression accuracy. Prior to loading into the sample reservoir, the assembled 3-layer calibrant can be cut to a size appropriate for the sample's field of view. In one embodiment, due to its density in the range of 0.5–2.5 g / cm 3 The calibrant polymer was selected as the density calibrant because of its distribution within a range of and its composition of low atomic number elements. This density range was optimized to be large enough so that the CT signal intensity has comparable brightness relative to the unknown organic sample, thereby improving the accuracy of the density of materials within the range by interpolation (rather than extrapolation). The range is also not too large to support reasonable sensitivity of this method.

[0073] Depending on the calibrant and sample geometry, according to one embodiment, by 3Extended3D printer uses poly(lactic acid) (PLA, density = 1.24g / cm 3 ) A customized sample reservoir is prepared by 3D printing. The design and size of the sample reservoir 330 are as follows: FIG. 3A to FIG. 3D As shown in the top view 331a, bottom view 331b, side view 331c and 3D projection view 331d.

[0074] According to one embodiment, a reservoir (e.g., 330) for holding a sample of interest has a primary compartment separated from a secondary compartment designed to hold a polymer calibrant strip. A small gap is left on the sample reservoir in the calibrant chamber to provide another undisturbed air space for further density calibration. The reservoir is printed with flat sides adjacent to the calibrant strip to provide orientation for imaging and subsequent alignment. The calibrant is inserted into the appropriate compartment in the sample reservoir and the excess is trimmed. Alternative sample reservoirs constructed of different materials and different dimensions can be used for samples with different compositions and sizes. The sample is loaded into the sample chamber of the reservoir (e.g., in Figure 1 For powder and granular samples, a funnel is used to ensure that the sample does not contaminate the calibrant strip or air gaps in the sample reservoir. In the case of a single sample such as an implant or tablet, the sample can be loaded directly.

[0075] According to an embodiment, the reservoir 330 is configured to consistently position and orient the calibrants. In this manner, such embodiments facilitate imaging attenuation of the material to uniformly affect the calibrants. This can improve density measurements, for example, in an embodiment, determination of bone density, among other examples. Furthermore, in an embodiment of the system, the calibrants are loaded into the reservoir in a consistent manner, such that when the reservoir (holding the material and calibrants) is subjected to imaging, the X-ray attenuation of the material is uniformly affected by the calibrants.

[0076] Imaging of samples

[0077] CT imaging of a sample according to an embodiment (e.g., at step 104) can be performed with an appropriate CT imaging instrument. Using X-ray CT as an example, suitable CT imaging instruments include laboratory-scale X-ray microscopes, micro-CT instruments, nano-CT instruments, or synchrotron X-ray sources. For imaging experiments performed according to an embodiment, a Zeiss Xradia520Versa X-ray microscope was used. At the beginning of the scan, an initial X-ray photo was taken using an exposure of 0.5 seconds and an X-ray source energy of 80keV. After this initial exposure, the sample was rotated 0.09 degrees before acquiring another radiograph with the same exposure time and X-ray source energy. This procedure was iterated to obtain 4000 radiographs. Using a filtered back-projection algorithm, the scan was reconstructed into a 3D image with 1000×1000×1000 voxels, with a box average of 2, resulting in an effective voxel size of 0.5μm. The field of view was set to include both the sample of interest and the polymer density standard.

[0078] According to one embodiment, the 3D reconstructed image is digitally represented as a grayscale image, where different areas are illuminated with different brightness based on the relative intensity of the X-ray signal. The relative intensity of the X-ray signal is determined by the number of photons arriving at a given detector pixel, which is affected by the material composition of the sample through which the X-rays pass. X-rays emitted from the primary source pass through the sample and interact with the atoms of the sample between the source and the detector. X-rays that interact with the atoms will become attenuated and lose energy (Swinehart

[13] ). This process is described by the Beer-Lambert Law, where the transmittance T of the X-ray beam is given by the following equation:

[0079]

[0080] where Φ t is the transmitted X-ray flux, Φ i is the incident X-ray flux, and A is the absorbance of the atomic species, given by the following expression:

[0081] A=εlc

[0082] Where ε is the attenuation coefficient of the atomic species, l is the optical path length that the photon travels, and c is the atomic species concentration. The attenuation coefficient is uniquely determined by the atomic structure and form factor of a given element and the X-ray energy, while the optical path length is determined by the sample and instrument geometry. In view of this, for a sample with uniformly sized particles, subjected to X-ray imaging at a constant X-ray source energy, the only factor that will affect the brightness of a pixel in the reconstructed image is the concentration / density of the material that the photon passed through. In one embodiment, the relationship between absorbance and density is linear, meaning that a higher density material will be brighter than a lower density material in a linear manner.

[0083] Deconvolution module: Phase segmentation intensity extraction

[0084] According to one embodiment, the intensities of the different material phases are extracted in order to determine the intensity corresponding to each phase. To do this, one embodiment segments the 3D reconstructed image into the corresponding material phases (e.g., Figure 1 At step 105). Conventional segmentation methods such as intensity thresholding, drainage, gradient-based methods, or other methods can be utilized. In order to process the large number of 2D slices that constitute the 3D imaging data, one embodiment utilizes a segmentation method that can accurately and automatically identify material phases. To achieve this high degree of accuracy and automation, one embodiment uses an image segmentation method based on artificial intelligence (AI). According to one embodiment, for example, an AI image segmentation model is trained by a human operator to identify which pixels correspond to which material phase using multiple criteria including intensity, position, shape, and relationship to its neighboring pixels. Once the AI ​​model is trained, the model is automatically applied to an image set containing a 3D image of the current sample, or images from different samples calibrated to the same intensity range. The segmentation results can be further refined (e.g., at step 106) using iterative AI methods (such as deep learning methods). A complete description of AI-based methods that can be used with an embodiment can be found here (Zhang

[16] ).

[0085] Deconvolution module: Intensity histogram deconvolution

[0086] According to an embodiment, the intensity histogram is subjected to a preprocessing step (107) before the intensity-density relationship is determined. In conventional optical microscopy as well as XRM and CT, the image is subject to diffraction effects, which may change the intensity of light near the edges of the imaged object. The Fresnel number N of the electromagnetic wave that passes through the aperture and falls at the detector is F Given by:

[0087]

[0088] where a is the radius of the aperture through which the light passes, λ is the wavelength of the incident light at the detector, and L eff is the effective distance from the light to the detector and is given by:

[0089]

[0090] where d SD is the distance from the sample to the detector, and d SS is the distance from the source to the sample (Kalasová et al. [6]). F When N is much larger than one, the beam is in the near-field regime. For most conventional X-ray imaging setups, the small wavelength of the X-ray photons ensures that most of the image is in the near-field approximation. F As θ approaches unity, this approximation begins to break down and eventually there may be significant effects in the detected image due to diffraction. These diffraction effects appear as intensity variations near the edges of the material / object at the detector and are known as Fresnel diffraction artifacts. Examples of Fresnel diffraction for a spherical imaged particle 440a and an irregularly shaped particle 440b are shown in Figures 4 and 5, respectively. Figure 4A and Figure 4B Displayed graphically in . Figure 4C and Figure 4D Actual XRM images of organic microspheres and sintered glass particles are shown, respectively. Brighter / higher intensity bands 441a-b are observed inside the particle near the edge, while darker / lower intensity bands 442a-b are observed adjacent to the brighter bands in the surrounding medium. In the case of clinical CT scans, the features of interest are often on the mm to cm scale to ensure that the effects of Fresnel diffraction are minimal. In the case of objects with microscopic features observed by XRM, the features of interest can be on the micrometer scale, which can produce significant artifacts due to Fresnel diffraction (Kalasová et al. [6]). For quantitative analysis using intensities from segmented images, this effect needs to be corrected.

[0091] According to an embodiment, a correction function is employed that corrects for Fresnel diffraction and other intrinsically diffraction-based intensity modulation artifacts, such as beam hardening (eg, at step 107 ). Figure 5A schematic diagram of the workflow of such a correction function according to one embodiment is shown in FIG (which may be performed by the deconvolution module 111 at step 107). The correction function takes as initial input the 3D reconstructed images (510) and the AI ​​segmentation (511) to extract material phase labels (514). An intensity histogram of the material of interest is calculated (515) using these initial images (510) and the material phase IDs (514) extracted from the AI ​​segmentation input (511). In one embodiment, this calculation is done by counting the total number of voxels of the material label and determining their intensity values ​​from the 3D reconstructed image. The voxel intensities are then sorted into intensity bins, where in one embodiment, the total number of bins is at least 1000 bins. Given the large number of voxels in the imaging set (approximately 109 voxels), fewer than 1000 bins may produce an intensity histogram that is not representative of a given material label. The number of bins may be manually set to an empirically determined minimum number, which defaults to 1000, or may be set to an algorithmic program for automatic binning.

[0092] The histogram of the material of interest is then subjected to a Gaussian fit (517) and deconvolution (518) algorithm. The Gaussian fit (517) computes an initial best Gaussian function to fit to the histogram, from which the mean, height, and standard deviation are extracted. The deconvolution algorithm (518) operates by taking the initial best Gaussian fit (517) as an initial condition, and iteratively deconvolving the Gaussian fit into a sum of two (or more) underlying Gaussian functions, such that the combined two (or more) Gaussian functions improve the fit to the histogram:

[0093] I tot =I M +I A

[0094] Among them I tot is the Gaussian fit of the best combination of intensity histograms of the segmented material phases, I M is a Gaussian fit of the strength contribution from the underlying real material, and I A is a Gaussian fit of the intensity contribution corresponding to the imaging artifact. Assuming the underlying material and artifact intensities are Gaussian distributed, it has the following form:

[0095]

[0096] Among them, M i is the amplitude of the ith Gaussian distribution, μ i is the mean of the ith Gaussian distribution, and σ iis the standard deviation of the i-th Gaussian distribution. The total histogram is fit to the sum of Gaussian distributions using an appropriate curve fitting algorithm (517), such as least squares fitting, orthogonal distance regression or maximum likelihood estimation methods, among others. According to one embodiment, the fitting parameters are the amplitude, mean and standard deviation of the underlying Gaussian distribution. In the previous example (where the histogram of the material was deconvolved into 2 Gaussian distributions, one for the actual material and one for Fresnel artifacts), a total of six fitting parameters were determined. Assuming a minimum number of bins of 1000 bins, this system has a minimum number of degrees of freedom of 993, ensuring that the fit is not over-constrained. When assuming a Gaussian distribution for fitting, the embodiment is explained similarly, because the number of voxels corresponding to each phase is large enough that the central limit theorem is applicable. Figure 6 An example of this deconvolution and fitting procedure for an organic microsphere sample is shown in Graph 660 of Graph 660. Graph 660 is a graph of counts 664 versus histograms of intensity 665, where series 661 corresponds to the full intensity spectrum, series 662 corresponds to the material, and series 663 corresponds to the diffraction.

[0097] After fitting (517) and deconvolution (518), a composition Gaussian curve corresponding to the material is determined (519). Figure 4A and Figure 4C In the case of the organic microsphere phase identified in , the Gaussian distribution with a lower average intensity corresponds to the material phase, while the Gaussian distribution with a higher average intensity corresponds to the diffraction band. Figure 4A and Figure 4C The lower intensity band near the microspheres corresponds to the diffraction band, while the higher intensity peak corresponds to the underlying air phase.

[0098] Additionally, iterative refinement may be implemented to manage diffraction heterogeneity caused by scale heterogeneity and resolution limitations (523). Diffraction heterogeneity correction (523) may implement an iteration of determining a calibrant design (selecting an alternative at step 101), performing alternative imaging (at step 104), performing alternative 3D reconstruction (510), performing alternative AI segmentation (511), and performing alternative diffraction deconvolution (518).

[0099] Density Module: Linear intensity-density determination and density measurement

[0100] According to one embodiment, as a first step (108) of the density module 112, an intensity-density calibration curve is constructed using the intensity of the polymer calibrant. As previously discussed, in the case of materials with the same elemental composition, the X-ray image intensity depends on the optical path length of the X-rays and the number of atoms with which the X-ray beam will interact. In the case of computed tomography methods such as XRM and micro-CT, the sample is maintained at a constant distance between the source and the detector, ensuring that only optical path length variations occur within the sample. In addition, during CT scanning, the sample is rotated to collect radiographs in multiple orientations, ensuring that optical path length variations within the sample are averaged. Therefore, the X-ray absorbance will depend on the concentration of atomic species within the sample, as described by Beer-Lambert's law. Given the form of Beer-Lambert's law, the overall X-ray absorbance and therefore the intensity of the final image will be linearly related to the density.

[0101] Based on this linear intensity-density relationship, and according to one embodiment, the intensity of the density calibrant is used to construct an explicit linear relationship between density and X-ray intensity, such as Figure 5 The construction of the linear relationship can be found in the above Figure 1 The described step 108 is implemented. The inputs for determining the linear relationship are the 3D reconstructed image and the AI ​​segmentation of the different phases (510 and 511). These inputs (510 and 511) are used to identify the calibrant phase (512) and determine the average intensity of the calibrant in the image (516). The average intensity of the calibrant in the image (516) is used in conjunction with the a priori known calibrant density (513) to obtain a calibration curve through an appropriate linear regression model (520) (such as least squares or orthogonal distance regression). In the case of organic microspheres with composite polymer calibrants, the polymer standard segmentation is considered to be the brightness of a given phase. The order of the polymer density standards (i.e., calibrants) in the 3-layer composite material is known, and thus, the known polymer densities are plotted as a function of their X-ray intensities. In addition, the intensity of the undisturbed air within the 3-layer calibrant or prepared sample reservoir channel is also plotted, and its known density at STP is 0.0012 g / cm 3 Through these four points (intensities of the 3 calibrant layers and air versus the known densities of the calibrant layers and air), a linear relationship is obtained using least squares regression. This linear relationship serves as a calibration curve and allows direct comparisons between CT scans from different instruments or at different times, which may have differences in measured intensities due to experimental / instrumental variations or due to reconstruction variations.

[0102] Figure 7An example of the density of a calibrant 775 plotted as a function of its intensity 776 is shown in graph 770 of FIG. In graph 770 , the calibrants are circles 771a-d and the derived linear relationship is dashed line 772.

[0103] According to one embodiment, the density of the unknown material can be determined using this density-strength relationship (109), for example, from Figure 7 772. In one embodiment, the diffraction-corrected intensity (523) of the material phase is used with the calibration curve (determined at 520) to calculate the density (522) of the phase (ie, the material of interest). Figure 7 An example is shown in , where the unknown material density is shown as a square 773, where the square 773 is placed on the line 772 based on the strength 776 of the unknown material. The uncertainty in the density 773 measurement is determined by evaluating the 95% confidence interval (521) of the linear regression, which gives the upper and lower limits of the potential material density. In the graph 770, the error bars 774a-b show the 95% confidence of the density 773. The 95% confidence interval is obtained by initially assuming a two-parameter linear model (e.g., slope and intercept) for the regression. The specific significance level is specified by the user; in the case of the 95% confidence interval, this corresponds to a significance level of 0.05. From this significance level, the student's t-test is used to determine the appropriate test statistic. Next, the covariance matrix of the regression is determined based on the given fit parameters, and the maximum residual between the fit and the data is determined. A 95% confidence interval for the regression is then obtained by multiplying the test statistic by the square root of the sum of the largest squared residual and the determined value of the covariance matrix. This estimate provides a region around the values ​​of the regression that are statistically acceptable for the given inputs. In the case of intensity-density regression, this allows the determination of upper and lower bounds on the density of the material given the measured CT intensity. A more detailed description of the determination of confidence intervals is given elsewhere (Bevington and Robinson [1]).

[0104] Additionally, when the result (522) is inaccurate, an iterative refinement is performed for validation and verification (524). Validation and verification 524 may implement iterations of determining a calibrator design (selecting an alternative calibrator design at 101), performing alternative imaging (iteration 104), performing alternative 3D reconstruction (iteration 510), performing alternative AI segmentation (iteration 511), performing alternative diffraction deconvolution (iteration 518), and performing alternative diffraction heterogeneity correction (iteration 523).

[0105] Figure 88 is a flow chart of a computer-implemented method 880 for determining the density of a material according to an embodiment. The method 880 begins at step 881 by segmenting the imaging data of the material and the calibration object into a plurality of phases, e.g., intensity phases, using an image segmentation method such as AI segmentation (511). For each of the plurality of phases, a corresponding histogram is determined at step 882 based on the pixel intensity of the obtained imaging data corresponding to the phase (i.e., using the imaging data segmented at step 881). To continue, at step 883, a given histogram corresponding to the phase of the material is deconvolved into (i) a function corresponding to an artifact, e.g., the intensity of the artifact, and (ii) a function corresponding to the material, e.g., the intensity of the material. Next, at step 884, a relationship between density and pixel intensity is determined using one or more histograms corresponding to the calibration object. This determined relationship is applied to a function corresponding to the material (e.g., a function corresponding to the intensity of the material from step 883) at step 885 to determine the density of the material.

[0106] An embodiment of method 880 obtains imaging data of the material and the calibrant in a sample reservoir by subjecting the material and the calibrant to CT imaging.

[0107] According to one embodiment, segmenting the imaging data at step 881 includes at least one of: (i) segmenting the imaging data based on intensity, (ii) segmenting the imaging data based on gradient, and (iii) segmenting the imaging data by processing the imaging data with at least one of a machine learning algorithm or an artificial intelligence algorithm to identify data corresponding to each of the multiple phases.

[0108] In an example embodiment, deconvolving a given histogram corresponding to a material at step 883 includes performing an analysis (e.g., a regression analysis) to deconvolute (i.e., fit) the data of the given histogram into (i) a function corresponding to an artifact and (ii) a function corresponding to the material. Additionally, it should be noted that embodiments of method 880 are not limited to deconvolving a single histogram into a single function corresponding to an artifact and a single function corresponding to the material at step 883, and instead, multiple histograms generated by the imaging data may be deconvolved at step 883 into multiple functions corresponding to multiple different artifacts and multiple functions corresponding to multiple materials, e.g., material phases of a sample whose density is being determined. For example, an embodiment may deconvolute a given histogram at step 883 into (i) multiple functions corresponding to multiple different artifacts and (ii) multiple functions corresponding to multiple materials.

[0109] In an embodiment of method 880, the calibrant may include a plurality of calibrant materials (i.e., standard materials), each of which has a corresponding known density. In one such embodiment of method 880, determining the relationship between density and pixel intensity using one or more histograms corresponding to the calibrant (at step 884) includes determining an average pixel intensity for each of the plurality of calibrant materials using a corresponding histogram corresponding to each of the plurality of calibrant materials. In turn, the relationship is determined at step 884 using the average pixel intensity determined for each of the plurality of calibrant materials and the corresponding known density for each of the plurality of calibrant materials. According to an embodiment, determining the average pixel intensity for each of the plurality of calibrant materials using a corresponding histogram corresponding to each of the plurality of calibrant materials includes deconvolving each histogram corresponding to each of the plurality of calibrant materials into (i) an artifact function and (ii) a calibrant material function. The average pixel intensity for each of the plurality of calibrant materials is then determined using the corresponding calibrant material function. According to one embodiment, the determined relationship (determined at step 884) is a mathematical function, e.g., a linear function, between the average pixel intensity determined for each of the plurality of calibrant materials and the corresponding known density for each of the plurality of calibrant materials.

[0110] Embodiments of method 880 may also perform various additional functions (alone or together). For example, one embodiment determines the average density of a material. Embodiments may also determine the uncertainty of the determined density. Still further, in response to the material being composed of discrete particles, one embodiment of method 880 determines the density distribution of particles within a certain range of particle sizes, the density of each particle, and the standard deviation of each particle. In response to the material being composed of a continuous material phase, an embodiment may determine the density distribution along an arbitrary orientation in at least one of the following: a Cartesian coordinate system, a cylindrical coordinate system, and a spherical coordinate system. In addition, it is worth noting that in one embodiment of method 880, the aforementioned functions may be implemented at step 885 as part of determining the density of the material.

[0111] Embodiments of method 880 may also be configured to implement iterative refinement of a system in which a non-physical density measurement caused by diffraction heterogeneity is experienced. For example, an embodiment of method 880 may identify that the density determined at step 885 is non-physical, and in response to identifying that the determined density is non-physical, determine a corrected density (e.g., through iterative refinement) or determine that a corrected density cannot be identified (e.g., method 880 cannot accurately determine the density). Additionally, an embodiment of method 880 may include functionality to determine that an output value (i.e., density) is physically incorrect, and such embodiments may include functionality to suggest how to obtain physically accurate results.

[0112] According to an example embodiment of method 880, determining a corrected density (e.g., in response to determining that the density determined at step 885 is non-physical) includes at least one of: (i) generating corrected imaging data by processing the imaging data using a feature size threshold to remove resolution artifacts, and repeating segmentation (step 881), determining corresponding histograms (step 882), deconvolution (step 883), determining relationships (step 884), and applying (step 885) using the corrected imaging data; (ii) obtaining new imaging data of the material and a new calibrant, and repeating segmentation (step 881), determining a corresponding histogram (step 882), deconvolution (step 883), determining a relationship (step 884), and applying using the new imaging data (step 885); and (iii) obtaining higher resolution imaging data that corrects at least one of the heterogeneity caused by geometry, the heterogeneity caused by shape, and the heterogeneity caused by morphology, and repeating segmentation (step 881), determining a corresponding histogram (step 882), deconvolution (step 883), determining a relationship (step 884), and applying using the higher resolution imaging data (step 885).

[0113] In one embodiment of method 880, the iterative refinement may include: (i) correcting resolution artifacts by a feature size threshold in units of pixel counts to exclude incompletely resolved small particle features to give an accurate density measurement, thereby convolving the total density measurement; (ii) introducing new calibrants including atomic elements from the third row or higher of the periodic table, wherein the new calibrant material selection is determined based on non-physical measurements or the known atomic composition of the material of interest, and then repeating the workflow (i.e., repeating segmentation, determining corresponding histograms, deconvolution, determining relationships, and applying); and (iii) correcting for diffraction heterogeneity caused by geometry, shape, and morphology, which typically requires higher resolution scans.

[0114] While embodiments of method 880 may be configured to implement iterative refinement of the system, embodiments may also be configured to determine that method 880 is not applicable. In other examples, such embodiments may determine that method 880 cannot determine density when diffraction heterogeneity is too strong.

[0115] The following discussion presents the validation results of the embodiments, for example, Figure 1 Workflow Figure 5 Workflow and Figure 8 Method 880, and other examples.

[0116] Validation Case Study 1: Poly(methyl methacrylate) (PMMA) imaged with a lab-based X-ray microscope Microspheres

[0117] Experimental Summary

[0118] PMMA microspheres (Cospheric LLC, Santa Barbara, CA) with a size distribution of 25-75 μm were imaged using a laboratory-based X-ray microscope (Bruker, Billerica, MA) at a resolution of 1.25 μm / voxel to measure the density of the microspheres using the embodiments (e.g., method 880). The density of PMMA is known in the literature to be 1.19 g / cm 3 , and spheres prepared by solution polymerization are expected to have negligible porosity, resulting in microspheres with expected uniform density. The microspheres were loaded into a 3D printed poly(lactic acid) PLA sample reservoir, where a multilayer film of a known polymer density calibrant was simultaneously loaded into the sample reservoir. The calibrant selected was polypropylene (PP, 0.90 g / cm 3 ), Poly(ethylene terephthalate) (PET, 1.38 g / cm 3 ) and polytetrafluoroethylene (PTFE, 2.22g / cm 3 ). FIG. 9A to FIG. 9B 9 are views 990a-b of a slice 991 from a reconstructed image volume showing different features of the imaged container. Specifically, Fig.9A A representative 2D slice 991 of a reconstructed X-ray microscopy (XRM) scan of poly(methyl methacrylate) (PMMA) microspheres 992 co-imaged with polymer calibrants 993 in a custom 3D printed PLA reservoir 994 is shown. Fig. 9B yes Fig.9A A magnified view 990b of a polymer calibrant 993 is shown indicating the specific polymers used, namely air 995, PP 996, PTFE 997, and PET 998.

[0119] To continue with this illustrative example, after imaging and reconstruction, supervised machine learning was used to segment the different material phases observed in the image. Intensity histograms for the polymer calibrants (PP 996, PTFE 997, and PET 998) were extracted from the segmented image labels, as well as the intensity histograms for the trapped air (995) of the sample reservoir 994 material used as an additional density calibrant and PLA (at STP p 空气 =0.0012g / cm 3 , and ρ PLA =1.25g / cm 3 ). The intensity histogram of the calibrant is Fig. 10A 1000. The histograms are normalized for ease of comparison. Graph 1000 shows a histogram of normalized frequency 1001 relative to intensity 1002 for air 1003, PP 1004, PLA 1005, PET 1006, and PTFE 1007. All five histograms (1003-1007) have similar widths, indicating that an appropriate number of pixels are obtained to generate a representative sample of the material for subsequent calculations. The mean and standard deviation of the calibrant histograms 1003-1007 are used together with the known calibrant density to determine the linear relationship 1013 between intensity 1014 and density 1015, as implied by Beer's Law. Fig. 10B The linear model (R 2 =0.96) 1013. Graph 1016 shows the density 1015 of air 1017, PP 1018, PLA 1019, PET 1020, and PTFE 1021 versus the strength 1014. The error bars in graph 1016 are the standard deviations of the histograms 1003-1007.

[0120] The microsphere phase is subjected to a Gaussian deconvolution preprocessing step to mitigate the effects of Fresnel diffraction by obtaining a conversion from intensity to density (i.e., linear model 1013). Fresnel diffraction appears as brighter fringes at the interface of air and microspheres (as discussed above with respect to FIG. 4A to FIG. 4D 1102 ). A Gaussian deconvolution is performed on the histogram of each sphere to separate the contribution from diffraction from the true material intensity. After deconvolution, the density of each sphere is calculated and binned to produce a density histogram of the microsphere sample. The density histogram is shown in a graph 1100 of frequency 1101 versus density 1102, where circles (e.g., 1103) represent the data for the microspheres and line 1104 is the fit to the Gaussian distribution. The average density 1102 is shown to be 1.21 ± 0.11 g / cm 3 , which is consistent with the literature value of 1.19 g / cm 3 The difference is 1.7%.

[0121] Discover

[0122] The verification cases described above are used to solve four aspects of the embodiment:

[0123] A. Proof of concept of the validity of the density measurement technique on isotropic particles of known density.

[0124] B. Feasibility of co-imaging microscopic specimens with calibrants of appropriate density while ensuring representation of both.

[0125] C. Importance of deconvolution for correcting diffraction-based artifacts.

[0126] D. Critically evaluate the effects of particle size and imaging resolution on the accuracy of density measurements.

[0127] The experiments described above were successful in aspects A (proof of concept) and B (feasibility of co-imaging), and thus demonstrated successful operation from both an imaging perspective (e.g., successful acquisition of imaging data representative of both calibrant material and sample) and method validation (e.g., accurate density measurement of PMMA spheres).

[0128] For aspect C, deconvolution is shown to be important in mitigating the effects of diffraction. Fig.12 Graph 1200 shows the intensity 1201 of the original microsphere phase (lighter shaded series 1203) and the deconvoluted spheres (darker shaded series 1204) versus the equivalent sphere diameter 1202. Deconvolution helps reduce the overall intensity 1201 of the spheres without disturbing the underlying distribution of spheres and produces an accurate measurement of the microsphere density. Without deconvolution, the microsphere density would be unphysically high due to diffraction.

[0129] Aspect D is also addressed in the aforementioned example implementation. The resolution of the images is 1.25 μm / voxel, while the microspheres exhibit an average diameter of 60 μm. This imaging resolution and particle size has been shown to be sufficient for accurate density determination, indicating that for microscopic samples, spherical particles 50 times the imaging resolution can be accurately studied. In addition, at this resolution, each layer of calibrant material can be identified and segmented. The minimum calibrant layer thickness for PP and PET is 50 μm, while the thickness for PTFE is 125 μm. At these thicknesses, the resolution is sufficient to capture a sufficiently large sampling of calibrant pixels for calibration. Therefore, the resolution criterion for the calibrant is that the resolution of the image should be at most 1 / 20 of the thinnest calibrant layer used. The resolution aspect of the embodiment is further demonstrated in the next example case study, in which a synchrotron x-ray source is used at a higher resolution.

[0130] Validation Case Study 2: Poly(methyl methacrylate) (PMMA) microspheres imaged with a synchrotron X-ray source

[0131] Experimental Summary

[0132] In the case study below, the same PMMA microspheres with the same calibrants in the same reservoir as discussed in the previous validation case study were imaged at a synchrotron X-ray source (Canadian Light Source, Saskatoon, Canada) at a resolution of 0.34 μm / pixel. Fig.13A is a view 1330 depicting a representative 2D slice 1331 of a reconstructed image obtained from a synchrotron light source. View 1330 of slice 1331 shows sphere 1332 as well as calibration object 1333 and reservoir 1334. Fig. 13B yes Fig.13A An enlarged view 1335 of the 2D slice 1331 of FIG.

[0133] In this experiment, the workflow remained consistent with the previous case study, whereby the different material phases were determined by segmenting the image and then correlating the intensity to the true material density using the methods disclosed herein (e.g., method 880).

[0134] Fig.14A is an XRM image 1440 with the calibration phases air 1441 , PP 1442 , PLA 1443 , PET 1444 , and PTFE 1445 indicated. Fig. 14B Shows Fig.14A 1450. Specifically, graph 1450 shows a histogram of normalized frequency 1451 versus intensity 1452 for air 1453, PP 1454, PLA 1455, PET 1456, and PTFE 1457.

[0135] With laboratory sources (such as Fig. 10A The same rank ordering of the calibrant intensities is observed in the synchrotron image in graph 1450 as compared to the graph 1000 of FIG. 1450 , indicating similar behavior in the images. Additionally, the calibrant histogram widths are comparable, indicating that a sufficient number of pixels were sampled to obtain these histograms.

[0136] Fig.15A The conversion from intensity to density is shown for the different calibrants used. Specifically, Fig.15A Graph 1550 shows the density 1551 of air 1553, PP 1554, PLA 1555, PET 1556, and PTFE 1557 relative to strength 1552. Graph 1550 is a graph using Fig. 14BThe mean and standard deviation of the calibrant histograms 1453-1457 shown in FIG. 1450 and the known calibrant densities are generated. In addition, a linear relationship 1558 between intensity 1552 and density 1551 is determined in graph 1550, as suggested by Beer's law.

[0137] Similar to laboratory-based measurements, the conversion from intensity 1552 to density 1551 shows a strong linear fit 1558 (R 2 =0.88). To proceed, the individual microspheres were then subjected to Gaussian deconvolution to obtain a density distribution histogram for each microsphere. Each population of microspheres with density measurements was then subjected to standard histogram analysis, which was performed at Fig. 15B , is a density histogram for each sphere. The density histogram is shown in a graph 1560 of frequency 1561 versus density 1562, where circles 1563 represent the data for the microspheres and line 1564 is the fit to a Gaussian distribution. The microspheres exhibited a density of 1.20 ± 0.09 g / cm 3 The average density value of represents a 0.8% difference with the literature value, thus verifying the accurate measurement of PMMA microsphere density using a synchrotron source.

[0138] Discover

[0139] The synchrotron-based experiments were performed both as replicates of the laboratory-based techniques and also addressed several additional aspects of the density measurement embodiments described herein, namely:

[0140] A. Determine the effect of different X-ray sources and resolutions on the accuracy of density measurements.

[0141] B. Evaluation of the impact of enhanced diffraction artifacts produced by different reconstruction techniques.

[0142] C. Understand the impact of 8-bit images compared to 16-bit images in analysis.

[0143] Synchrotron X-ray sources differ from laboratory instruments in three main areas: X-ray beam geometry (parallel beam at synchrotron compared to cone beam in the laboratory), X-ray beam intensity (photon flux at synchrotron is significantly greater), and monochromatic X-ray energy (synchrotron) versus polychromatic (X-ray energy). Given an X-ray photon energy, different atomic species will attenuate the X-ray differently, which can thereby affect the photon intensity at the detector. In the first case study discussed above, the laboratory X-ray source produced polychromatic X-rays by brake radiation, which could potentially bias the density measurement. This was shown to have little effect on the final measurement, potentially due to the similarity of the elements (primarily carbon, oxygen, hydrogen, and fluorine) that make up the calibrants and microspheres. The X-rays at the synchrotron source were 17±2 keV energy, thus ensuring that potential effects from lower or higher energy photons would not produce differential attenuation. From the calibrant histograms at both facilities and the final density measurements of the PMMA spheres, the X-ray energy distribution had little effect on the density measurement.

[0144] The synchrotron reconstructed images were obtained using a phase recovery algorithm that enhances diffraction at the interfaces of the phases in the image, thereby increasing diffraction artifacts at the edges of the microspheres compared to laboratory sources (reconstructed using filtered backprojection). This provided an opportunity to evaluate how different reconstruction algorithms affect the final measurements. FIG. 16A to FIG. 16B Microspheres before and after deconvolution are shown. Fig.16A Graph 1660 shows the intensity 1661 of the original microsphere phase (lighter shaded series 1663) and the deconvoluted spheres (darker shaded series 1664) versus the equivalent sphere diameter 1662. Fig. 16B Graph 1670 shows the density 1671 of the original microsphere phase (lighter shaded series 1673) and the deconvoluted spheres (darker shaded series 1674) versus the equivalent sphere diameter 1672. In graph 1660, the difference in intensity 1661 is visible. Converting these intensities 1661 to density 1671 ( Fig. 16B ) shows that without deconvolution, the microsphere density 1671 is almost twice the final value, again indicating the necessity of this preprocessing step for accurate measurements. In addition, the conversion also demonstrates the robustness of the measurement to changes in the reconstruction algorithm that may have an impact on the image intensity. Similarly, FIG. 16A to FIG. 16B The issue of 8-bit images versus 16-bit images was also addressed, as synchrotron images are 8-bit, resulting in a smaller range of intensity values ​​compared to laboratory sources. This did not produce any significant difference in the accuracy of the final measurements, indicating that the method described in this paper is robust across different image types.

[0145] Computer Support

[0146] Fig.17 1 shows a computer network or similar digital processing environment in which embodiments of the present invention may be implemented. The client computer / device 50 and the server computer 60 provide processing, storage, and input / output devices for executing application programs, etc. The client computer / device 50 may also be linked to other computing devices, including other client devices / processes 50 and server computers 60, via a communication network 70. The communication network 70 may be a remote access network, a global network (e.g., the Internet), a global collection of computers, a local area network or a wide area network, and a currently used corresponding protocol (TCP / IP, Other electronic device / computer network architectures are also suitable.

[0147] Fig.18 yes Fig.17 1 is a diagram of an example internal structure of a computer (e.g., client processor / device 50 or server computer 60) in a computer system of FIG. Each computer 50, 60 contains a system bus 79, where a bus is a set of hardware lines used to transfer data between components of a computer or processing system. The system bus 79 is essentially a shared pipe that connects the different elements of the computer system (e.g., processor, disk storage devices, memory, input / output ports, network ports, etc.) and enables information transfer between the elements. Attached to the system bus 79 is an I / O device interface 82, which is used to connect various input and output devices (e.g., keyboard, mouse, display, printer, speakers, etc.) to the computer 50, 60. The network interface 86 allows the computer to connect to a network attached to the network (e.g., Fig.17 The memory 90 is a computer software instruction 92 and data 94 (e.g., Figure 1 , Figure 5 and Figure 8 The CPU 84 is also attached to the system bus 79 and provides execution of computer instructions.

[0148] In one embodiment, the processor routine 92 and data 94 are a computer program product (generally referenced to 92) comprising a non-transitory computer readable medium (e.g., a removable storage medium such as one or more internal hard drives, external hard drives, DVD-ROMs, CD-ROMs, disks, tapes, etc.) that provides at least a portion of the software instructions for the system of the present invention. The computer program product 92 can be installed by any suitable software installation program well known in the art. In another embodiment, at least a portion of the software instructions can also be downloaded via cable communications and / or wireless connections. In other embodiments, the program of the present invention is a signal product of a computer program propagated on a propagated signal embodied in a propagation medium (e.g., radio waves, infrared waves, laser waves, sound waves, or electric waves propagated through a global network (such as the Internet or other network)). Such carrier media or signals can be used to provide at least a portion of the software instructions of the routine / program 92 of the present invention.

[0149] In alternative embodiments, the propagated signal is an analog carrier wave or a digital signal carried on a propagation medium. For example, the propagated signal may be a digitized signal propagated through a global network (e.g., the Internet), a telecommunications network, or other network. In one embodiment, the propagated signal is a signal transmitted through a propagation medium over a period of time, such as instructions for a software application sent in packets over a network over a period of milliseconds, seconds, minutes, or longer.

[0150] In other embodiments, program product 92 may be implemented as so-called software as a service (SaaS), or to support other installations or communications with end users.

[0151] The teachings of all patents, published applications, and references cited herein are incorporated by reference in their entirety.

[0152] While example embodiments have been particularly shown and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the embodiments as covered by the appended claims.

[0153] References

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Claims

1. A method for determining the density of a material, the method comprising: segmenting imaging data of materials and calibration objects into phases; For each phase of the plurality of phases, determining a corresponding histogram based on pixel intensities of the obtained imaging data corresponding to the phase; deconvolving a given histogram corresponding to the material into (i) a function corresponding to the artifact and (ii) a function corresponding to the material; determining a relationship between density and pixel intensity using one or more histograms corresponding to the calibrant; as well as The determined relationship is applied to a function corresponding to the material to determine the density of the material.

2. The method according to claim 1, further comprising: The imaging data of the material and the calibrant are obtained by subjecting the material and the calibrant in a sample reservoir to computed tomography imaging.

3. The method of claim 1 , wherein segmenting the imaging data comprises at least one of: segmenting the imaging data based on intensity; segmenting the imaging data based on gradients; and The imaging data is segmented by processing the imaging data with at least one of a machine learning algorithm and an artificial intelligence algorithm to identify data corresponding to each of the plurality of phases.

4. The method of claim 1 , wherein deconvolving the given histogram corresponding to the material comprises: An analysis is performed to deconvolute the data of the given histogram into (i) the function corresponding to the artifact and (ii) the function corresponding to the material.

5. The method of claim 1, wherein the calibrant comprises a plurality of calibrant materials, each of the plurality of calibrant materials having a corresponding known density.

6. The method of claim 5, wherein determining the relationship between density and pixel intensity using one or more histograms corresponding to the calibrant comprises: determining a mean pixel intensity for each calibrant material in the plurality of calibrant materials using a respective histogram corresponding to each calibrant material in the plurality of calibrant materials; and The relationship is determined using the average pixel intensity determined for each calibrant material in the plurality of calibrant materials and a corresponding known density for each calibrant material in the plurality of calibrant materials.

7. The method of claim 6, wherein determining the average pixel intensity for each of the plurality of calibrant materials using a respective histogram corresponding to each of the plurality of calibrant materials comprises: deconvolving each histogram corresponding to each calibrant material of the plurality of calibrant materials into (i) an artifact function and (ii) a calibrant material function; and The average pixel intensity for each calibrant material in the plurality of calibrant materials is determined using a corresponding calibrant material function.

8. The method of claim 6, wherein the determined relationship is a mathematical function between the average pixel intensity determined for each of the plurality of calibrant materials and the corresponding known density of each of the plurality of calibrant materials.

9. The method of claim 1, further comprising at least one of the following: determining an average density of the material; Determine the uncertainty in the determined density; In response to the material being comprised of discrete particles, determining a density distribution of the particles within a range of particle sizes, a density of each particle, and a standard deviation of each particle; and Responsive to the material being comprised of a continuous material phase, a density distribution along an arbitrary orientation is determined in at least one of: a Cartesian coordinate system, a cylindrical coordinate system, and a spherical coordinate system.

10. The method of claim 1, further comprising: The given histogram is deconvolved into (i) a plurality of functions corresponding to a plurality of different artifacts and (ii) a plurality of functions corresponding to a plurality of materials.

11. The method according to claim 1, further comprising: Recognizing that the determined density is unphysical; and In response to identifying that the determined density is non-physical, a corrected density is determined or the corrected density cannot be identified.

12. The method of claim 11, wherein determining the corrected density comprises at least one of: generating corrected imaging data by processing the imaging data using a feature size threshold to remove resolution artifacts, and repeating the segmenting, determining corresponding histograms, deconvolving, determining relationships, and applying using the corrected imaging data; obtaining new imaging data of the material and a new calibration object, and repeating the segmenting, determining corresponding histograms, deconvolving, determining relationships, and applying using the new imaging data; as well as Higher resolution imaging data corrected for at least one of geometry-induced heterogeneity, shape-induced heterogeneity, and morphology-induced heterogeneity is obtained, and the segmenting, determining corresponding histograms, deconvolving, determining relationships, and applying using the higher resolution imaging data are repeated.

13. A system for positioning a material, the system comprising: Material; Calibrators; as well as A reservoir defines (i) a material chamber configured to hold the material, (ii) a calibrant chamber configured to hold the calibrant, and (iii) an air passage separating the material chamber and the calibrant chamber.

14. The system of claim 10, wherein the calibrant comprises one or more of: Multiple film layers; A variety of sample storage materials; and Multiple particles.

15. The system of claim 11, wherein the plurality of thin film layers comprises: A first polymer film layer, a second polymer film layer and a third polymer film layer, wherein the first polymer film layer and the third polymer film layer sandwich the second polymer film layer.

16. The system of claim 12, wherein the second polymer film layer comprises a first polymer film strip and a second polymer film strip separated by an air channel.

17. The system of claim 11, wherein each film layer is composed of at least one of: a density of 0.91 g / cm 3 Polypropylene (PP), density 1.38g / cm 3 Poly(ethylene terephthalate) (PET) and a density of 2.2 g / cm 3 of poly(tetrafluoroethylene) (PTFE).

18. The system of claim 11, wherein the reservoir is configured to consistently position and orient the calibration object such that imaged attenuation of the material is uniformly affected by the calibration object.

19. The system of claim 10, further comprising: An imaging instrument wherein parameters of the imaging instrument are calibrated using the calibration object and a calibration material of interest, the calibration material of interest having a known density different from the density of the calibration object.

20. The system of claim 19, wherein density measurements obtained using the imaging instrument, materials, calibrants, and reservoirs are independent of vendor, magnification, parameters, and imaging contrast.

Images