Method for Measuring Density of Material by Computed Tomography Using Refraction Artifact Correction

Abstract

Determine the density of materials and objects imaged using computed tomography (CT). **SOLUTION**: One embodiment co-images a material of unknown density with a calibration of known density. The digitally reconstructed CT image is segmented into the unknown material phase and the known material phase of the calibration. An image intensity histogram of the unknown material is obtained. Using the known calibration density, an intensity-density mapping is calculated and the density of the unknown material is determined based on the measured CT intensity. The method described herein corrects CT imaging artifacts that affect the material phase intensity using a novel deconvolution of the intensity histogram. Densities of particulate materials that are difficult to measure with prior art, and features such as particles, microspheres, porosity, and multiphase composite materials can be measured using this embodiment. Also described are the design of a custom sample holder for co-imaging the material and calibration, and uncertainty estimation.

Description

Technical Field

[0001] Related Applications 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

[0002] The density of a material is defined as the mass per unit volume and is a fundamental property of the material. In the case of a homogeneous material such as a metal, density is directly related to the underlying crystal structure of the material and is a useful parameter for identifying various metal materials. Similarly, in the case of a homogeneous polymeric material, density can be used to determine the relative amorphous and crystalline fractions and to identify the presence of specific crystal polymorphs. The bulk mechanical, thermal, and electrical properties can depend on the underlying crystal fraction and crystal phase in many materials. Therefore, density is a fundamental metric for the classification, comparison, performance evaluation, and quality assessment of materials. As an example, the polymer poly(vinylidene fluoride) (PVDF) has five known crystal polymorphs with a β-phase that exhibits piezoelectric, pyroelectric, and thermoelectric behavior (Steiner and Zimmerer

[12] , Lovinger [9], Kawai [7]) (the numbers in parentheses in this document refer to the following list of references). Due to the unique chain and crystal structure of the β-phase, the density of β-phase PVDF is significantly higher compared to the more common α-phase crystals and amorphous PVDF (Steiner and Zimmerer

[12] , Lovinger [9]). Therefore, density is an important measurement in determining the PVDF crystal phase and can thus be a performance metric for potential electroactive products. Density measurement is regarded as essential by the scientific community when characterizing material products, and similarly, when the product and its constituent raw materials require regulation, such as in the case of pharmaceuticals, density measurement is regarded as essential by the regulatory authorities.

[0003] In the case of heterogeneous products composed of multiple different materials, density is a linear combination of different phases and can be used to estimate the relative fractions of different component phases. In pharmaceutical development, the active pharmaceutical ingredient (API) is routinely blended with various excipient materials. Excipients can assist in the manufacturability of the API and regulate the release of the API from the pharmaceutical product. In the case of long-acting injectables, parenterals, and drugs that escape from implants and devices, encapsulation of the API within the polymeric excipient is central to the function of the product, and in the case of oral solid dosage forms, the excipient enables the tableting of the pharmaceutical product for human consumption ((Fredenberg et al. [4], Zhong et al.

[17] , Yost et al.

[14] ). Evaluating the density of these products not only provides insights into encapsulation efficiency and mixing but also offers a means to assess the microstructure characteristics (such as porosity) of the product that have been shown to have a significant impact on product performance (Zhang et al.

[15] ). From an upstream process perspective, measuring the density of the API and excipient at various manufacturing points (such as pre-granulation, post-granulation, pre-extrusion, post-extrusion, etc.) is a powerful tool in product quality control. Changes in density before and after these steps can indicate changes in either the chemical state between crystalline and amorphous or the structural state between dispersion and aggregation. The potential for the introduction and evolution of porosity can have a significant impact on dissolution performance, release rate, and pharmaceutical stability.

[0004] The measurement of the density of a material is typically performed using one of several techniques. The simplest method is to measure the mass and volume of the material in question and calculate the density directly. This method is convenient due to its simplicity. However, complex problems arise with objects of non-uniform shape where volume measurement becomes difficult, or with objects that are too small to be weighed by conventional methods, such as microspheres or API substances in the early stages of development where the amount is very limited. Other techniques for density measurement include density gradient columns and gas pycnometry, which can be used with materials having non-uniform shapes. Gradient columns have the advantage that they can directly measure the density of an object. However, the range of gradient columns is limited by the choice of gradient liquid used in the column (Oster and Yamamoto

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

[11] ). Pycnometry can be used to determine the density of non-uniform solids or porous materials, but pycnometry is not a technique designed to directly measure density. Rather, pycnometry measures the volume of the test material and requires that the mass of the test material be known, thus preventing the measurement of the density of objects that are too small to be effectively weighed. To date, there has been no technique that can reliably and accurately measure the density of materials with microscopic features, such as powders, composite particles (such as drug-encapsulating polymer microspheres), microporous samples, or very small amounts of samples. In these materials, the density is often reported as "bulk density" or "tap density". Bulk density is the density of a particulate or powder sample loaded into a container of known volume, and tap density is the density after the powder has been mechanically tapped to promote sedimentation of the powder. Both of these measurements are estimates that do not capture the "true density" of the material. In the case of pharmaceutical development, bulk density measurements provide little insight into the variability of the solid phase of these products at various stages. This is because bulk density measurement is a measure of particle packing efficiency that depends on particle shape, size, brittleness, and compression method.Furthermore, bulk density provides little or no understanding of the non-uniform phase distribution of a pharmaceutical, especially when the underlying density of the phase is unknown. In the case of parenteral microspheres, granular products, and raw powder materials, the microscopic characteristics of the sample make it difficult or impossible to perform true density measurements by conventional methods. Therefore, the development of different measurement techniques is necessary.

[0005] Computed tomography (CT) imaging is an imaging modality that is sensitive to the true density of the imaged object 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 by a detector that measures the total number of X-rays (Huda and Slone [5]). As X-ray photons pass through a material, the X-ray photons interact with the electron clouds of the underlying atoms in the material. The electrons excited by the X-rays re-emit the X-ray photons, and the X-ray photons pass through the material and reach the detector. The intensity of the X-ray–electron interaction within the material is determined by the energy of the incident X-ray photons, factors of the structure and shape of the electrons and atoms, and the atomic number of the underlying atoms. Therefore, the measured X-ray signal intensity varies depending on the specific elemental composition of the material and how many absorbing atoms are in the path of the photons. If the elemental composition is the same between two samples, the variation in the X-ray signal intensity mainly results 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 intensities captured by other tomography techniques such as optical tomography, electron tomography, and magnetic tomography share a similar dependence on the true density of the materials that make up the object.

[0006] By calibrating the CT imaging intensity measured using known standards, the density of an object can be determined. This forms the basis of clinical X-ray imaging and medical CT for determining bone damage, the progression of osteoporosis, and degenerative lung diseases (Chen-Mayer et al. [3], Boone and Yellen-Nelson [2], Lang et al. [8]). For objects or powder samples with microscopic features, MicroCT and X-ray microscopy (XRM) are necessary to capture the interaction between X-ray photons and the material with sufficient resolution. MicroCT and XRM operate on the same physical principles as medical CT, but the main difference is that the imaging resolution improves by several orders of magnitude, from 0.5 - 50 mm / voxel for clinical CT to 0.5 - 50 μm / voxel for microCT and XRM. These high-resolution X-ray imaging methods provide a potential route for determining the true density of materials with microscopic features. Measuring density using MicroCT and XRM can not only provide a firm understanding of the material's properties but also provide a powerful quality control metric.

[0007] Several challenges specific to MicroCT and XRM have, so far, prevented their use as true density measurement tools. The first challenge is the identification and construction of appropriate density standards. The density standards need to be composed of elements with an atomic weight equivalent to that of the material of interest. The density range of the standard material needs to cover the density of the material of interest in order to enable interpolation. On the other hand, the density differences of the standard materials need to be spaced out in order to support the accuracy of interpolation. Due to the variability in CT devices, lack of inter-run consistency, and relatively small field of view when imaging at very high resolutions, the density standards need to be small enough to co-image with the material of interest without obscuring the field of view. The second challenge is the reduction and correction of X-ray imaging artifacts that can significantly affect the overall measurement intensity of the sample. Such imaging artifacts become important when the features of interest are small enough that optical effects such as Fresnel diffraction and X-ray beam hardening affect a significant portion of the imaged voxels. These challenges have, so far, prevented the development of X-ray-based methods for determining the true density of materials with microscopic features.

SUMMARY OF THE INVENTION

[0008] Embodiments solve the aforementioned problems and provide a function for determining the density of a material. One such embodiment is directed to a computer-implemented method for determining the density of a material. The method begins by segmenting the imaging data of the material and a standard material (interchangeably referred to herein as a “calibrant”) into a plurality of phases, such as intensity phases. For each of the plurality of phases, a respective histogram is determined based on the pixel intensities of the acquired imaging data corresponding to the phase. Next, a given histogram corresponding to a phase of the material is deconvolved with (i) a function corresponding to the artifact, such as the intensity of the artifact, and (ii) a function corresponding to the material, such as the intensity of the material. To proceed, the relationship between density and pixel intensity is determined using one or more histograms corresponding to the calibrant. This determined relationship is applied to a function corresponding to the material, such as a function corresponding to the intensity of the material, to determine the density of the material.

[0009] In one embodiment, the material and calibration object within the sample holder are subjected to CT imaging to obtain imaging data of the material and calibration object.

[0010] According to one embodiment, the segmentation of 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) processing the imaging data using at least one of a machine learning algorithm or an artificial intelligence algorithm to identify data corresponding to each phase of a plurality of phases, thereby segmenting the imaging data.

[0011] In an exemplary embodiment, the step of deconvolving a given histogram corresponding to a certain phase of a material includes performing an analysis, such as a regression analysis, to deconvolve, i.e., approximate the data of the given histogram to (i) a function corresponding to an artifact and (ii) a function corresponding to the material. Further, the embodiment is not limited to deconvolving a single histogram into a single function corresponding to an artifact and a single function corresponding to a material. Instead, a plurality of histograms resulting from the imaging data can be deconvolved into a plurality of functions corresponding to a plurality of different artifacts and a plurality of functions corresponding to a plurality of materials. For example, note that this is for a material phase of a sample where density is determined. For example, one embodiment can deconvolve a given histogram 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.

[0012] The calibration object may include a plurality of calibration object materials (i.e., standard materials), each having a known density. In such an embodiment, the step of determining the relationship between density and pixel intensity using one or more histograms corresponding to the calibration object includes determining the average pixel intensity of each of the plurality of calibration object materials using each histogram corresponding to each of the plurality of calibration object materials. Next, the relationship is determined using the average pixel intensity determined for each of the plurality of calibration object materials and the known density of each of the plurality of calibration object materials. According to one embodiment, the step of determining the average pixel intensity of each of the plurality of calibration object materials using each histogram corresponding to each of the plurality of calibration object materials includes deconvolving each histogram corresponding to each of the plurality of calibration object materials with (i) an artifact function and (ii) a calibration object material function. Next, the average pixel intensity of each of the plurality of calibration object materials is determined using the corresponding calibration object material function. According to one embodiment, the determined relationship is a mathematical function, such as a linear function, between the average pixel intensity determined for each of the plurality of calibration object materials and the known density of each of the plurality of calibration object materials.

[0013] Embodiments may also perform various additional functions, either alone or together. For example, one embodiment determines the average density of a material. Embodiments may also be able to determine the uncertainty of the determined density. Further, in response to the material being composed of discrete particles, one embodiment determines the density distribution of the particles, the density of each particle, and the standard deviation of each particle over a range of particle sizes. In response to the material being composed of a continuous material phase, an exemplary embodiment determines the density distribution along any orientation in at least one of a Cartesian coordinate system, a cylindrical coordinate system, and a spherical coordinate system. Further, it should be noted that in one embodiment, the aforementioned functions may be implemented as part of determining the density of a material.

[0014] Embodiments can also be configured to implement systematic iterative improvements where non-physical density measurements caused by folding non-uniformities are experienced. For example, one embodiment can 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., through iterative improvements), or determine that a corrected density cannot be identified.

[0015] According to one embodiment, the step of determining a corrected density includes at least one of: (i) processing imaging data using a feature size threshold to generate corrected imaging data by removing resolution artifacts, and using the corrected imaging data to repeat steps of segmentation, determination of respective histograms, deconvolution, determination of relationships, and application; (ii) obtaining new imaging data of materials and new calibrations, and using the new imaging data to repeat steps of segmentation, determination of respective histograms, deconvolution, determination of relationships, and application; (iii) obtaining high-resolution imaging data that corrects at least one of the geometries, shapes, and morphologies that caused the non-uniformity, and using the high-resolution imaging data to repeat at least one of the steps of segmentation, determination of respective histograms, deconvolution, determination of relationships, and application.

[0016] In one embodiment, iterative improvements include: (i) correcting resolution artifacts with a feature size threshold in units of pixel count and excluding small particle features that complicate the total density measurement by not being fully resolved to provide accurate density measurement; (ii) introducing new calibrants that include atomic elements in the third row or above of the periodic table, where the selection of the new calibrant material is determined based on either a non-physical measurement of the material of interest or a known atomic composition, and then repeating the workflow (i.e., segmenting, determining each histogram, deconvolving, determining relationships, repeating the application); and (iii) correcting the geometry, shape, and morphology that caused diffraction non-uniformity, which often requires a higher-resolution scan. Embodiments may be configured to implement systematic iterative improvements, but embodiments may also be configured to determine that the methods described herein for determining density are not applicable if the diffraction non-uniformity is too strong. Further, one embodiment may include a function for determining that the output value, i.e., the density, is not physically correct, and such an embodiment may also include a function for suggesting a way to obtain a physically accurate result. For example, in a microsphere sample composed of two materials with known densities, 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 high density of the two materials or lower than the low density of the two materials, the measurement is non-physical. Unanticipated materials, diffraction artifacts not currently considered, and the density range of the current calibrant may be the root causes that require the iterative determination described herein.

[0017] Another embodiment is directed to a system including a processor and a memory, on which computer code instructions are stored. In such an embodiment, the processor and the memory are configured, together with the computer code instructions, to cause the system to implement any embodiment or combination of embodiments described herein.

[0018] Yet another embodiment is directed to a computer program product for determining the density of a material. The computer program product includes one or more non-transitory computer-readable storage devices and program instructions stored in at least one of the one or more storage devices. The program instructions, when loaded and executed by a processor, cause an apparatus associated with the processor to perform any embodiment or combination of embodiments described herein.

[0019] An exemplary embodiment is directed to a system for positioning a material. The system, according to one embodiment, includes a material, a calibrator, and a holder. The holder defines (i) a material chamber configured to receive the material, (ii) a calibrator chamber configured to receive the calibrator, and (iii) an air channel separating the material chamber from the calibrator chamber.

[0020] In one embodiment of the material positioning system, the calibrator includes one or more of a plurality of thin film layers, a plurality of sample holder materials, and a plurality of particles. In one such embodiment, the plurality of thin film layers includes a first polymer thin film layer, a second polymer thin film layer, and a third polymer thin film layer, with the first polymer thin film layer and the third polymer thin film layer sandwiching the second polymer thin film layer. According to an exemplary embodiment, the second polymer thin film layer includes a first polymer thin film strip and a second polymer thin film strip separated by an air channel. In an embodiment, the plurality of polymer thin film layers may be disposed on an adhesive layer. Further, in one embodiment, each thin film layer is composed of at least one of poly(propylene) (PP) with a density of 0.91 g / cm 3 ³, poly(ethylene terephthalate) (PET) with a density of 1.38 g / cm 3 ³, and poly(tetrafluoroethylene) (PTFE) with a density of 2.2 g / cm 3 ³.

[0021] According to one embodiment, the holder is configured to consistently position and orient the calibration object. Thus, such an embodiment facilitates the imaging attenuation of the material to uniformly affect the calibration object. Thereby, for example, in one embodiment that improves the determination of bone density among other examples, the density measurement can be improved. Further, in one embodiment of the system, the calibration object is loaded into the holder in a consistent manner, such that when the holder (containing the material and the calibration object) is imaged, the X-ray attenuation of the material is uniformly affected by the calibration object. For example, when a strip-shaped calibration object is positioned perpendicular to the X-ray beam, the calibration object is positioned perpendicular on the sample to be compared, i.e., the calibration object is positioned / oriented in the same way (consistently) among different samples to be compared. Returning to the example where the calibration object is positioned perpendicular for further illustration, the calibration object is not positioned horizontally with respect to the X-ray beam of another sample being compared.

[0022] Another embodiment of the system further includes imaging equipment. In one embodiment, the parameters of the imaging equipment are calibrated using the calibration object and the calibration material of the object. The calibration material of the object has a known density different from that of the calibration object. Thus, in such an embodiment, the density measurements obtained using the imaging equipment, the material, the calibration object, and the holder are independent of the vendor, magnification (e.g., local tomography magnification, geometric magnification, etc.), parameters (e.g., exposure time), and imaging contrast (e.g., absorption contrast, phase contrast, etc.).

[0023] According to one embodiment, the holder can be of any suitable geometric shape that facilitates the co-imaging of the material, i.e., the material of unknown density, and the calibration object. For example, in one embodiment, the holder is rectangular and the calibration object is attached outside the holder. In another embodiment, the holder is tubular and the material chamber, calibration object chamber, and channels are defined within the internal region of the tubular holder.

[0024] One embodiment relates to the composition of the density calibrant. According to one such embodiment, the calibrant is composed of three or more materials with different densities to ensure an accurate final strength-density calibration curve. In one embodiment, three calibrant materials are used, but 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 composite material strip or in the form of a separate distinguishable object such as a calibration sphere co-imaged with the material of interest. An example of a calibrant is a calibration strip composed of three polymers with established densities: poly(propylene) (abbreviated as PP herein, density = 0.91 g / cm 3 ), poly(ethylene terephthalate) (abbreviated as PET herein, density = 1.38 g / cm 3 ), and poly(tetrafluoroethylene) (abbreviated as PTFE herein, density = 2.2 g / cm 3 ). In such an embodiment, the elements containing the polymers are low atomic weight elements in the first two rows of the periodic table commonly found in organic compounds. Thus, such calibrants are suitable for measuring the density of common organic materials used in pharmaceuticals and foods.

[0025] A feature of one embodiment is a custom CT sample holder designed to encapsulate both the sample of interest and the calibrant. The sample holder allows for co-imaging of the sample of interest and the density standard, i.e., the calibrant material, such that both the sample and the density standard are within the field of view.

[0026] A further feature of one embodiment is a system for determining the measured intensity histogram of the reconstructed CT image. The system has the ability to segment different observed material phases with appropriate resolution and contrast, the computational ability to process these images and segmentations, and the storage ability to host and provide access to the imaged and segmented data.

[0027] A further feature of one embodiment is a deconvolution approach for correcting the effect of diffraction artifacts on the measured intensity of segmented imaging data that includes a target material, interstitial voids, and a calibrant.

[0028] A further feature of one embodiment is the construction of an intensity-density calibration function using the known density of the CT imaging intensity and the material of the calibrant. This relationship calculated according to such an embodiment can be used to determine the density of an unknown target material in a sample co-imaged with the calibrant. A further feature of one embodiment is the calculation of a 95% confidence interval for the density of the unknown material, providing a measure of the inaccuracy of the density calculated using this method.

[0029] In one embodiment, a material phase histogram is obtained by sampling the segmented phase intensity, binning the intensity values, and employing an algorithm for determining an appropriate amount of bins given the size of the segmented phase voxels.

[0030] One embodiment determines an intensity-density calibration curve by calculating a linear relationship between the calibrant module density and their deconvolution signal intensity using at least one regression method such as least squares regression, orthogonal distance regression, and maximum likelihood estimation. One embodiment determines the density of the target material using the intensity of the deconvolved material histogram and the intensity-density calibration function.

[0031] To achieve the advantages described herein, among other things, one embodiment includes, in part, the following steps.

[0032] (1) Image the sample with the target material of unknown density using CT imaging and co-image it with a calibration object. (1.1) A material standard with a known density within the calibration object is selected and assembled based on the target material(s). (1.2) The sample holder is constructed using appropriate methods and materials (e.g., 3D printing with poly(lactic acid) or acrylonitrile butadiene styrene (ABS)). (1.3) The calibration object is loaded into the sample holder so that it can be co-imaged with the target material. (1.4) The imaging device can be any CT imaging method used with an appropriate field of view and resolution. (1.5) Since the calibration object is loaded into the sample holder in a consistent manner, the X-ray attenuation of the target material is uniformly affected by the calibration object. (1.6) The parameters of the imaging device are calibrated using the calibration object and one calibration material of the target. The calibration material of the target has a known density that is not the same as the density of the material used in the calibration object. Therefore, the density measurement is independent of the vendor, magnification (local tomography magnification or geometric magnification), parameters (such as exposure time), and imaging contrast (such as absorption contrast or phase contrast).

[0033] (2) It is a three-dimensional digital representation of the calibration object for the extraction of the CT intensities corresponding to the co-imaged material of the target and all material phases. (2.1) The image is segmented into different phases using any of teacher-assisted machine learning, deep learning, conventional threshold segmentation, or any image segmentation methodology. (2.2) The intensity histogram is extracted from the segmented phases including the target material phase of unknown density, interstitial air, and material phases from the calibration object.

[0034] (3) The material phase intensity histogram is corrected for artifacts. (3.1) To correct diffraction artifacts, the material phase histogram is deconvolved into two basic intensity contributions: those arising from diffraction artifacts and those arising from tomographic interactions between the source imaging signal and the actual material. (3.2) To correct resolution artifacts, the smallest features are deconvolved from the larger features according to a characteristic size threshold in units of pixel number.

[0035] (4) The material density is determined. (4.1) The intensity-density calibration curve is calculated by regression using the intensities of the materials in the calibrant and their known material densities. (4.2) The diffraction-corrected intensities of the material phases with unknown density are placed along the intensity-density calibration curve to provide interpolated values of the material phase density. (4.3) The 95% confidence interval of the material phase density is determined from the calibration curve to obtain the upper and lower limits of the intensity. (4.4) For the target material composed of discrete particles, the density distribution of the particles over a range of particle sizes, the density of each particle, and the standard deviation of each particle are determined. (4.5) For the target material composed of a continuous material phase, the density distribution along any orientation in the Cartesian coordinate system, cylindrical coordinate system, or spherical coordinate system is determined.

[0036] (5) Systematic iterative improvements in the case of non-physical density measurements due to diffraction non-uniformity include 5.1 to 5.3. (5.1) The introduction of a new calibrant containing atomic elements in the third row or above of the periodic table. The selection of the new calibrant material can be determined based on non-physical measurements or the known atomic composition of the target material, and then the steps from (1.1) to (4.4) are repeated. (5.2) In many cases, a higher-resolution scan is required, which is the geometry / shape / morphology caused by diffraction non-uniformity. (5.3) When the diffraction non-uniformity is too strong, it is a mechanism to determine that the method cannot be applied. The representativeness of the measurement is lost due to the iterative improvement of the correction.

[0037] The foregoing will become apparent from a more detailed description of the following exemplary embodiments, as illustrated in the accompanying drawings. In the accompanying drawings, like reference characters refer to the same parts throughout the different figures. The drawings are not necessarily to scale, instead emphasis has been placed upon illustrating embodiments.

Brief Description of the Drawings

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DETAILED DESCRIPTION OF THE INVENTION

[0039] A description of exemplary embodiments will be given below.

[0040] Overview of an Exemplary Workflow The CT-based determination of density for materials with microscopic features utilizes, according to one embodiment, three modules 110, 111, and 112 as illustrated in the workflow diagram of FIG. 1. Module 110 is a calibration module that implements four main steps 101, 102, 103, and 104. Module 110 starts with an initial calibration object design, followed by the preparation of the calibration object and its attachment to the sample holders (101 and 102). After loading the sample into the sample holder (103), CT imaging of the material of interest encapsulated in the holder with the calibration object can be obtained (104) by operating with the required resolution and contrast using an appropriate CT imaging device.

[0041] The functionality of the calibration module 110 is followed by the functionality of the deconvolution module 111. The deconvolution module 111 has three main steps 105, 106, and 107. The CT image is first segmented into separate material phases using an appropriate segmentation algorithm (105). This segmentation (105) can be achieved and improved using iterative artificial intelligence (AI) approaches such as deep learning to improve the phase segmentation (106). Next, the now segmented image is subjected to a diffraction deconvolution algorithm to correct for the effects of imaging artifacts resulting from diffraction artifacts (107). Following the deconvolution module 111, the data is subjected to the density module 112, which determines the intensity-density calibration curve using the calibration object (108), and subsequently determines the density of the material of interest and the upper and lower limits of the density (109).

[0042] Calibration Module: Calibration Object Design, Holder Design, Sample Loading The design and fabrication of the calibration object and sample holder (101 and 102) according to one embodiment depends on the material under investigation as well as the shape and imaging setup. An example of a calibration design and fabrication for investigating organic spherical particles is disclosed as one embodiment herein. However, it should be noted that the embodiments are not limited to determining the density and type of materials described herein. Polymer thin films can be selected for use as calibration objects. The polymer thin film can be selected such that the variation in X-ray signal intensity arises only from the material density and not from the variation in the atomic X-ray absorption spectrum. The fabrication of a polymer density standard (or called calibration object) according to one embodiment of the present invention can be achieved using poly(propylene) (PP), poly(ethylene terephthalate) (PET), and poly(tetrafluoroethylene) (PTFE). The density of each polymer in the exemplary embodiment is 0.91 g / cm 3 , 1.38 g / cm 3 , and 2.20 g / cm 3 respectively. These density values are well established for commercial grades of PP, PET, and PTFE where PP is isotropic and semi-crystalline, PET is completely amorphous, and PTFE is semi-crystalline. The polymers are commercially available as uniform non-porous films with a backing of acrylic adhesive, and the films can be coated on the surface.

[0043] As shown respectively in cross-sectional view 220a and side view 220b of FIGS. 2A and 2B, in one embodiment, the composite density standard is assembled with a PP layer 221, on top of an adhesive 224, at the bottom of a PTFE layer 222, and then a PET layer 223, as shown in FIG. 2A. A gap 225 is made in the PTFE layer to ensure isolated air pockets within the calibration object, increasing robustness (in case one calibration object fails), and enabling the use of air as a fourth density calibration object to add regression accuracy. The assembled three-layer calibration object can be cut to a size suitable for the field of view of the sample before loading into the sample holder. In one embodiment, the calibration object polymer is 0.5 - 2.5 g / cm 3They are selected for the density calibrant due to the spread of those densities and the composition of those low atomic number elements over the range. This density range is optimized to be large enough to have a CT signal intensity of equivalent brightness compared to the unknown organic sample, so that the accuracy of the material density within the range is improved by interpolation (rather than extrapolation). Also, the range should not be too large to support the proper sensitivity of this method.

[0044] According to the calibrant and sample geometry, the custom sample holder is created by 3D printing via an Ultimaker (copyright) 3 Extended 3D printer, according to one embodiment, using poly(lactic acid) (PLA, density = 1.24 g / cm 3 ). The design and dimensions of the sample holder 330 are shown in the top view 331a, bottom view 331b, side view 331c, and 3D projection view 331d of FIGS. 3A - 3D, respectively.

[0045] According to one embodiment, the main compartment of the holder for accommodating the sample of interest, e.g., holder 330, is separated from the secondary compartment designed to accommodate the polymer calibrant strip. A small gap is left in the sample holder of the calibrant chamber to provide another unobstructed air space for further density calibration. The holder is printed with a flat surface adjacent to the calibrant strip to provide an orientation for imaging and later registration. The calibrant is inserted into the appropriate compartment of the sample holder and the excess is trimmed. Alternative sample holders composed of different materials and different dimensions are available for samples of different compositions and sizes. The sample is loaded into the sample compartment of the holder (e.g., at step 103 depicted in FIG. 1). In the case of powder and particulate samples, a funnel is used to prevent the sample from contaminating the calibrant strip or the air gap of the sample holder. In the case of specific samples such as implants and tablets, the sample can be loaded directly.

[0046] According to one embodiment, the holder 330 is configured to consistently position and orient the calibration object. In this way, such an embodiment facilitates the imaging attenuation of the material for uniformly affecting the calibration object. Thereby, for example, in one embodiment for improving the determination of bone density among other examples, the density measurement can be improved. Further, in one embodiment of the system, the calibration object is loaded into the holder in a consistent manner, such that when the holder (containing the material and the calibration object) is imaged, the X-ray attenuation of the material is uniformly affected by the calibration object.

[0047] Imaging of the Sample CT imaging of a sample according to one embodiment (e.g., step 104) can be accomplished using suitable CT imaging equipment. Taking X-ray CT as an example, suitable CT imaging equipment includes laboratory-scale X-ray microscopes, micro-CT equipment, nano-CT equipment, or synchrotron X-ray sources. For imaging experiments conducted according to one embodiment, a Zeiss Xradia 520 Versa X-ray microscope is used. The first radiograph is taken using an exposure of 0.5 seconds and an X-ray source energy of 80 keV at the start of the scan. After this first exposure, the sample is rotated by 0.09 degrees and then another radiograph is acquired with the same exposure time and X-ray source energy. This procedure is repeated to acquire 4000 radiographs. The scan is reconstructed into a 3D image with 1000x1000x1000 voxels using a filtered back-projection algorithm with a bin average value of 2, resulting in an effective voxel size of 0.5 μm. The field of view is set to include both the sample of interest and the polymer density standard.

[0048] According to one embodiment, the 3D reconstructed image is digitally represented as a grayscale image, where different regions are illuminated with different brightnesses 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 reaching a given detector pixel, which is affected by the material composition of the sample through which the X-ray passes. The X-rays emitted from the primary source pass through the sample and interact with the atoms of the sample between the sample and the detector. The X-rays that interact with the atoms are attenuated and lose energy (Swinehart

[13] ). This process is explained by Lambert-Beer's law, and the transmittance T of the X-ray beam is given as follows:

Number

Number

Number

[0049] Deconvolution Module: Phase Segmentation Intensity Extraction According to one embodiment, the strength of each material phase is extracted and the strength corresponding to each phase is determined. To do this, one embodiment segments the 3D reconstructed image into each material phase (e.g., at step 105 in FIG. 1). Conventional segmentation methods such as intensity thresholding, watershed, gradient-based approaches can be utilized. To process the numerous 2D slices that make up the 3D imaging data, one embodiment utilizes a segmentation method that can accurately and automatically identify the material phases. To achieve this high accuracy and automation, one embodiment uses an artificial intelligence (AI)-based image segmentation method. According to one embodiment, the AI image segmentation model is trained, for example, by a human operator, to identify which pixels correspond to which material phases using a number of criteria including intensity, position, shape, and its relationship with adjacent pixels. Once the training of the AI model is complete, the model is automatically applied to the 3D image of the current sample or a series of images including images of different samples calibrated to the same intensity range. The segmentation results can be further improved using an iterative AI approach such as a deep learning method (e.g., step 106). A complete description of the AI-based approach that can be utilized in embodiments is available here (Zhang

[16] ).

[0050] Deconvolution module: Intensity histogram deconvolution According to one embodiment, the intensity histogram undergoes a preprocessing step (107) before determining the intensity-density relationship. In conventional optical microscopy, XRM, and CT, the image is subject to diffraction effects, which can 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 reaches the detector F is given by the following equation,

Equation

[0051] According to one embodiment, a correction function is employed to correct other intensity modulation artifacts that are essentially diffraction-based, such as Fresnel diffraction and beam hardening (e.g., step 107). A schematic workflow diagram of such a correction function, according to one embodiment (which can be performed at step 107 by the deconvolution module 111), is shown in FIG. 5. The correction function takes the 3D reconstruction image (510) and AI segmentation (511) as initial inputs and extracts the material phase labels (514). The intensity histogram of the target material is calculated (515) using the material phase IDs (514) extracted from these initial images (510) and AI segmentation inputs (511). In one embodiment, this calculation is performed by counting the total number of voxels of the material label and determining their intensity values from the 3D reconstruction image. The voxel intensities are then classified into intensity bins, where the total number of bins is, in one embodiment, at least 1000 bins. If a large number of voxels (about 109 voxels) in the imaging set are less than 1000 bins, an intensity histogram that does not represent the given material label may be generated. The number of bins can be set manually to an empirically determined minimum number (default is 1000) or set to an automatic binning algorithm procedure.

[0052] Next, the histogram of the target material is subjected to Gaussian approximation (517) and deconvolution (518) algorithms. The Gaussian approximation (517) calculates an initial optimal Gaussian function that approximates the histogram, from which the mean value, height, and standard deviation are extracted. The deconvolution algorithm (518) takes the initial optimal Gaussian approximation (517) as an initial condition and operates to improve the approximation to the histogram by repeatedly deconvolving the Gaussian approximation into the sum of two (or more) underlying Gaussian functions, such that the approximation to the histogram by the combination of two (or more) Gaussian functions is improved.

[0053]

Number

Equation

[0054] Following approximation (517) and deconvolution (518), a constituent Gaussian curve corresponding to the material phase is determined (519). In the case of the organic microsphere phase identified in FIGS. 4A and 4C, the Gaussian distribution with a low average intensity corresponds to the material phase, and the Gaussian distribution with a high average intensity corresponds to the diffraction band. Conversely, for the segmented air phase adjacent to the microspheres in FIGS. 4A and 4C, the low-intensity band near the microspheres corresponds to the diffraction band, while the high-intensity peak corresponds to the underlying air phase.

[0055] Furthermore, iterative improvements can be implemented to manage diffraction non-uniformities resulting from scale non-uniformities and resolution limitations (523). Diffraction non-uniformity correction (523) may implement iterations of calibration object design decision (selection of alternatives in step 101), alternative imaging execution (step 104), alternative 3D reconstruction execution (510), alternative AI segmentation execution (511), and alternative diffraction deconvolution execution (518).

[0056] Density module: Linear intensity-density determination and density measurement According to one embodiment, the intensity of the polymer calibration object is used to construct an intensity-density calibration curve as the first step (108) of the density module 112. As described above, for materials with the same elemental composition, the X-ray image intensity depends on the optical path length of the X-ray and the number of atoms with which the X-ray beam interacts. In the case of computed tomography methods such as XRM and micro-CT, since the sample is held at a fixed distance between the light source and the detector, only fluctuations in the optical path length occur within the sample. Furthermore, in a CT scan, by rotating the sample and collecting radiographs in multiple directions, the fluctuations in the optical path length within the sample are averaged. Therefore, X-ray absorbance depends on the concentration of atomic species within the sample, as explained by Lambert-Beer's law. Considering the form of Lambert-Beer's law, the overall X-ray absorbance, and thus the intensity of the final image, depends linearly on density.

[0057] In light of this linear intensity-density relationship and in accordance with one embodiment, the intensity of the density calibration is used to construct an explicit linear relationship between density and X-ray intensity, as shown in FIG. 5. The construction of the linear relationship may be implemented in step 108 described above herein in connection with FIG. 1. The inputs used to determine the linear relationship are the 3D reconstruction image and the AI segmentations of different phases (510 and 511). These inputs (510 and 511) are used to identify the phase of the calibrator (512) and to determine the average intensity of the calibrator in the image (516). The average intensity of the calibrator in the image (516) is used in combination with the a priori known calibrator density (513) to obtain a calibration curve through an appropriate linear regression model such as the least squares method or orthogonal distance regression (520). In the case of organic microspheres with a composite polymer calibrator, the polymer standard segmentation is considered the brightness of its given phase. The order of the polymer density standards (i.e., calibrators) in the three-layer composite material is known, and from this, the known polymer densities are plotted as a function of their X-ray intensities. Further, the intensity of the non-turbulent air within the three-layer calibrator or within the created sample holder channels is also plotted at a known density of 0.0012 g / cm at STP. 3 At these four points (the intensities of the three calibrator layers and air versus the known densities of the calibrator layers and air), a linear relationship is obtained using least squares regression. This linear relationship functions as a calibration curve, enabling direct comparison between CT scans of different devices or at different times, where measurement intensities may vary due to experimental / device variations or reconstruction variations.

[0058] An example of the density of the calibrator 775 plotted as a function of their intensity 776 is shown in plot 770 of FIG. 7. In plot 770, the calibrators are circles 771a-d and the derived linear relationship is the dotted line 772.

[0059] According to one embodiment, the density of an unknown material can be determined, for example, by line 772 from FIG. 7 using this density-strength relationship (109). In one embodiment, the diffraction corrected intensity of the material phase (523) is used together with the calibration curve (determined at 520) to calculate the density of the phase, i.e., the material (522) of interest. This example is shown in FIG. 7, where the density of the unknown material is shown as square 773, based on the intensity 776 of the unknown material, where square 773 is placed on line 772. The uncertainty of this density 773 measurement is determined by evaluating the 95% confidence interval of the linear regression (521) that gives the range of the upper and lower limits of the potential material density. In plot 770, the 95% confidence of the density 773 is shown by error bars 774a - b. The 95% confidence interval is obtained by first performing a regression assuming a two-parameter linear model (such as slope and intercept). A specific significance level is specified by the user, and in the case of the 95% confidence interval, this corresponds to a significance level of 0.05. From this significance level, an appropriate test statistic is determined using Student's t-test. Next, the covariance matrix of the regression is determined based on the specified approximate parameters, and the maximum residual between the approximation and the data is determined. Next, the 95% confidence interval of the regression is obtained by multiplying the test statistic by the square root of the sum of the maximum residual squared and the determined value of the covariance matrix. This evaluation provides a region of values near the regression that are statistically acceptable values of the regression for a particular input. In the case of the intensity-density regression, this allows the upper and lower limits of the density of the material to be determined based on the measured CT intensity. A more detailed explanation of the determination of the confidence interval is given elsewhere (Bevington and Robinson [1]).

[0060] Furthermore, if the results (522) are inaccurate, iterative improvements for validation and verification (524) are made. Validation and verification 524 may implement iterations of decisions for calibration object design (selection of alternative calibration object design (at 101), implementation of alternative imaging (iteration 104), execution of alternative 3D reconstruction (iteration 510), execution of alternative AI segmentation (iteration 511), execution of alternative diffraction deconvolution (iteration 518), and implementation of alternative diffraction non-uniformity correction (iteration 523), i.e., iterations may be implemented.

[0061] Figure 8 is a flowchart of a computer-implemented method 880 for determining the density of a material according to one embodiment. The method 880 begins, in step 881, by segmenting the imaging data of the material and the calibration object into a plurality of phases, for example, intensity phases, using an image segmentation method such as AI segmentation (511). For each of the plurality of phases, in step 882, a respective histogram is determined based on the pixel intensities of the acquired imaging data corresponding to the phase, i.e., using the imaging data segmented in step 881. To continue, in step 883, a given histogram corresponding to a phase of the material is deconvolved with (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, in step 884, the relationship between density and pixel intensity is determined using one or more histograms corresponding to the calibration object. This determined relationship is applied, in step 885, to a function corresponding to the material, e.g., the function corresponding to the intensity of the material from step 883, to determine the density of the material.

[0062] One embodiment of the method 880 acquires imaging data of the material and the calibration object by subjecting the material and the calibration object in the sample holder to CT imaging.

[0063] According to one embodiment, the segmentation of the imaging data in 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 using at least one of a machine learning algorithm or an artificial intelligence algorithm to identify data corresponding to each phase of the plurality of phases.

[0064] In an exemplary embodiment, deconvolving a given histogram corresponding to the phase of the material at step 883 includes performing an analysis, such as a regression analysis, to deconvolve, i.e., approximate the data of the given histogram to (i) a function corresponding to artifacts and (ii) a function corresponding to the material. Further, embodiments of method 880 are not limited to deconvolving a single histogram into a single function corresponding to artifacts and a single function corresponding to the material at step 883; rather, a plurality of histograms resulting from the imaging data can be deconvolved at step 883 into a plurality of functions corresponding to a plurality of different artifacts and a plurality of functions corresponding to a plurality of materials, for example, note that the material phase of the sample whose density is determined. For example, one embodiment can deconvolve a given histogram at step 883 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.

[0065] In an embodiment of method 880, the calibration object may include a plurality of calibration object materials (i.e., standard materials), each having a known density. In such an embodiment of method 880, the step of determining the relationship between density and pixel intensity (at step 884) using one or more histograms corresponding to the calibration object includes determining the average pixel intensity of each of the plurality of calibration object materials using a respective histogram corresponding to each of the plurality of calibration object materials. Next, at step 884, the relationship is determined using the average pixel intensity determined for each of the plurality of calibration object materials and the known density of each of the plurality of calibration object materials. According to one embodiment, the step of determining the average pixel intensity of each of the plurality of calibration object materials using a respective histogram corresponding to each of the plurality of calibration object materials includes deconvolving each histogram corresponding to each of the plurality of calibration object materials with (i) an artifact function and (ii) a calibration object material function. Next, the average pixel intensity of each of the plurality of calibration object materials is determined using the corresponding calibration object 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 calibration object materials and the known density of each of the plurality of calibration object materials.

[0066] Embodiments of method 880 may also perform various additional functions, either alone or in combination. For example, one embodiment determines the average density of a material. An embodiment can also determine the uncertainty of the determined density. Further, one embodiment of method 880 determines the density distribution of particles, the density of each particle, and the standard deviation of each particle over a range of particle sizes in response to the material being composed of discrete particles. An embodiment can determine the density distribution along any orientation in at least one of a Cartesian coordinate system, a cylindrical coordinate system, and a spherical coordinate system in response to the material being composed of a continuous material phase. Further, note 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.

[0067] Embodiments of method 880 can also be configured to implement systematic iterative improvements where non-physical density measurements caused by diffraction non-uniformities are experienced. For example, one embodiment of method 880 identifies that the density determined at step 885 is non-physical and, in response to identifying that the determined density is non-physical, can determine a corrected density (e.g., through iterative improvements) or determine that a corrected density cannot be identified (e.g., method 880 cannot accurately determine the density). Further, one embodiment of method 880 may include the function of determining that the output value, i.e., the density, is not physically correct, and such an embodiment may include the function of proposing a method to obtain physically accurate results.

[0068] According to an exemplary 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 the steps 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), determination of each histogram (step 882), deconvolution (step 883), determination of relationships (step 884), and application (step 885) using the corrected imaging data; (ii) obtaining new imaging data of the material and a new calibration and repeating segmentation (step 881), determination of each histogram (step 882), deconvolution (step 883), determination of relationships (step 884), and application (step 885) using the new imaging data; (iii) obtaining high-resolution imaging data that corrects at least one of the geometries, shapes, and morphologies that caused the non-uniformity and repeating at least one of the steps of segmentation (step 881), determination of each histogram (step 882), deconvolution (step 883), determination of relationships (step 884), and application (step 885) using the high-resolution imaging data.

[0069] In one embodiment of method 880, the iterative improvement corrects resolution artifacts by a feature size threshold in number of pixels, excluding small particle features that complicate the total density measurement by not being fully resolved to provide an accurate density measurement, introducing a new calibrant that includes atomic elements in the third row or above of the periodic table, where the selection of the new calibrant material is determined based on either a non-physical measurement of the material of interest or a known atomic composition, and then repeating the workflow (i.e., segmenting, determining each histogram, deconvolving, determining relationships, repeating the application), and correcting the geometry, shape, and morphology that caused diffraction non-uniformity, which often requires a higher-resolution scan.

[0070] Embodiments of method 880 may be configured to implement a systematic iterative improvement, but embodiments may also be configured to determine that method 880 is not applicable. Among other examples, such an embodiment may determine that method 880 cannot determine density when the diffraction non-uniformity is too strong.

[0071] The following discussion presents verification results of embodiments, such as the workflows of FIGS. 1, 5, and method 880 of FIG. 8, among other examples.

[0072] Verification Case Study 1: Poly(methyl methacrylate) (PMMA) Microspheres Imaged with a Lab-Based X-Ray Microscope Experimental Overview PMMA microspheres (Cospheric LLC, Santa Barbara, Calif.) with a size distribution of 25-75 μm were imaged with a lab-based X-ray microscope (Bruker, Billerica, Mass.) at a resolution of 1.25 μm per voxel, and the density of the microspheres was measured using an embodiment, such as method 880. The density of PMMA is 1.19 g / cm in the literature 3It is known that the spheres prepared by solution polymerization are expected to have negligible porosity and microspheres with a uniform density are obtained. The microspheres were loaded into a 3D printed poly(lactic acid) PLA sample holder, and at the same time, multilayer films of known polymer density calibrants were loaded into the holder. The selected calibrants were polypropylene (PP, 0.90 g / cm 3 ), poly(ethylene terephthalate) (PET, 1.38 g / cm 3 ), and polytetrafluoroethylene (PTFE, 2.22 g / cm 3 ). Figures 9A - 9B are FIGS. 990a - b of slice 991 from a reconstructed image volume showing different features of the imaging container. Specifically, FIG. 9A shows 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 holder 994. FIG. 9B is an enlarged view 990b of the polymer calibrants 993 of FIG. 9A showing the specific polymers used, namely air 995, PP996, PTFE997, and PET998.

[0073] To continue with this example, following imaging and reconstruction, the various material phases observed in the images were segmented using supervised machine learning. From the segmented image labels, the intensity histograms of the polymer calibrants (PP996, PTFE997, and PET998), and the intensity histogram of the PLA of the sample holder 994 material for the confined air (995) and an additional density calibrant (ρ 空気 = 0.0012 g / cm 3 , ρ PLA = 1.25 g / cm 3) was extracted. The intensity histogram of the calibration objects is shown in plot 1000 of FIG. 10A. The histogram is normalized to facilitate comparison. Plot 1000 shows the normalized frequency 1001 vs. intensity 1002 histograms of air 1003, PP 1004, PLA 1005, PET 1006, and PTFE 1007. All five histograms (1003 - 1007) have a similar width, indicating that an appropriate number of pixels were obtained to generate representative samples of the materials for subsequent calculations. The mean values and standard deviations of the calibration object histograms 1003 - 1007 were used together with the known calibration object densities to determine the linear relationship 1013 between intensity 1014 and density 1015, as implied by Beer's law. The linear model (R 2 = 0.96) 1013 is shown in plot 1016 of FIG. 10B. Plot 1016 shows density 1015 vs. intensity 1014 for air 1017, PP 1018, PLA 1019, PET 1020, and PTFE 1021. The error bars in plot 1016 are the standard deviations of histograms 1003 - 1007.

[0074] Using the obtained conversion from intensity to density (i.e., linear model 1013), the microsphere phase was subjected to a Gaussian deconvolution pre - processing step to mitigate the effects of Fresnel diffraction. Fresnel diffraction appears as brighter fringes at the interface between air and the microspheres (as described hereinabove in connection with FIGS. 4A - 4D). Gaussian deconvolution was performed on the histogram of each sphere to separate the contribution from diffraction from the true material intensity. Following deconvolution, the density of each sphere was calculated and binned to create a density histogram of the microsphere sample. The density histogram is shown in plot 1100 of frequency 1101 vs. density 1102, where the circles, e.g., 1103, represent the microsphere data and the line 1104 is an approximation to a Gaussian distribution. The average density 1102 was shown to be 1.21 ± 0.11 g / cm 3 which is a 1.7% difference from the literature value of 1.19 g / cm 3 .

[0075] Findings The above verification cases served to address four aspects of the embodiments.

[0076] A. Proof of concept of the effectiveness of density measurement techniques for isotropic particles with known density.

[0077] B. Feasibility of performing co - imaging of a microscope sample and an appropriate density calibrant and ensuring the representativeness of both.

[0078] C. Importance of deconvolution for correcting diffraction - based artifacts.

[0079] D. Critically evaluating the influence of particle size and imaging resolution on the accuracy of density measurement.

[0080] The above experiments were successful in aspects A (proof of concept) and B (feasibility of co - imaging), showing successful operations not only from the imaging perspective (e.g., successful acquisition of imaging data including both the calibrant material and the sample), but also from method verification (e.g., accurate density measurement of PMMA spheres).

[0081] Regarding aspect C, it was demonstrated that deconvolution is important for reducing the influence of diffraction. Plot 1200 in Figure 12 shows the intensity 1201 versus the sphere equivalent diameter 1202 for the raw micro - sphere phase (bright - shadowed series 1203) and the deconvolved spheres (dark - shadowed series 1204). Deconvolution helps to reduce the overall intensity 1201 of the spheres without disturbing the underlying distribution of the spheres, resulting in an accurate measurement of the density of the micro - spheres. Without deconvolution, the density of the micro - spheres would be non - physically high due to diffraction.

[0082] Aspect D was treated in the same manner as in the previous implementation example. The image resolution was 1.25 μm / voxel, while the microspheres showed an average diameter of 60 μm. This imaging resolution and particle size were demonstrated to be sufficient for accurate density measurement, suggesting that spherical particles 50 times larger than the imaging resolution could be accurately investigated in the case of microsphere samples. Furthermore, at this resolution, each layer of the calibration material could be identified and segmented. The minimum calibration layer thicknesses of PP and PET were 50 μm, and that of PTFE was 125 μm. At these thicknesses, the resolution was sufficient to capture sampling of calibration voxels large enough to perform calibration. Therefore, the resolution criterion for the calibration object is that the image resolution needs to be at least 20 times smaller than the thinnest calibration layer used. The resolution aspect of the embodiment is further demonstrated in the following exemplary case study where a synchrotron X-ray source was used at a higher resolution.

[0083] Verification Case Study 2: Poly(methyl methacrylate) (PMMA) Microspheres Imaged with a Synchrotron X-ray Source Experiment Summary In the following case study, the same PMMA microspheres with the same calibration object in the same holder were imaged at a resolution of 0.34 μm / pixel with a synchrotron X-ray source (Canadian Light Source, Saskatoon, Canada) as described in the previous verification case study. FIG. 13A is FIG. 1330 depicting a representative 2D slice 1331 of the reconstructed image obtained from the synchrotron light source. FIG. 1330 of slice 1331 shows sphere 1332 along with calibration object 1333 and holder 1334. FIG. 13B is an enlarged view 1335 of the 2D slice 1331 of FIG. 13A.

[0084] In this experiment, the workflow was kept the same as in the previous case study, thereby segmenting the image to determine different material phases and subsequently correlating the intensity with the true material density using the methods disclosed herein, such as method 880.

[0085] Figure 14A is an XRM image 1440 having the indicated calibration phases air 1441, PP 1442, PLA 1443, PET 1444, and PTFE 1445. Figure 14B shows a calibration phase histogram of plot 1450 for the calibration phases of Figure 14A. Specifically, plot 1450 shows a normalized frequency 1451 versus intensity 1452 histogram of air 1453, PP 1454, PLA 1455, PET 1456, and PTFE 1457.

[0086] In the plot 1450 of the synchrotron image, the same rank order of calibration phase intensities is observed compared to the lab source (shown in plot 1000 of Figure 10A) showing similar behavior in the image. Further, the widths of the calibration phase histograms are equivalent, indicating that a sufficient number of pixels were sampled to acquire these histograms.

[0087] Figure 15A shows the conversion from intensity to density for the various calibration phases used. Specifically, plot 1550 of Figure 15A shows density 1551 versus intensity 1552 for air 1553, PP 1554, PLA 1555, PET 1556, and PTFE 1557. Plot 1550 was generated using the mean values and standard deviations of the calibration phase histograms 1453 - 1457 shown in Figure 14B and the known calibration phase densities. Further, from plot 1550, a linear relationship 1558 between intensity 1552 and density 1551, as implied by Beer's law, was determined.

[0088] Similar to the lab-based measurements, the conversion from intensity 1552 to density 1551 is a strong linear approximation 1558 (R 2(= 0.88) is shown. To proceed, individual microspheres were subjected to Gaussian deconvolution, and a density distribution histogram was obtained for each sphere. The population of spheres, each having a density measurement, was then subjected to a standard histogram analysis shown in FIG. 15B as a density histogram for each sphere. The density histogram is shown in a plot 1560 of frequency 1561 versus density 1562, the circle 1563 represents the data of the microspheres, and the line 1564 is an approximation to the Gaussian distribution. The microspheres showed an average density value of 1.20 ± 0.09 g / cm, which represents a difference of 0.8% from the literature value, verifying the accurate measurement of the density of PMMA microspheres using a synchrotron light source. 3

[0089] Findings Synchrotron-based experiments were conducted as repeated measurements of laboratory-based techniques and also to address some additional aspects of the density measurement embodiments described herein, namely,

[0090] A. Determine the influence of different X-ray sources and resolutions on the accuracy of density measurement.

[0091] B. Evaluate the influence of enhanced diffraction artifacts by different reconstruction techniques.

[0092] C. Understand the influence of 8-bit and 16-bit images in the analysis.

[0093] The synchrotron X-ray source differs from laboratory equipment in three main areas: the geometry of the X-ray beam (parallel beam in the synchrotron compared to the cone beam in the laboratory), the X-ray beam intensity (significantly larger photon flux in the synchrotron), and the monochromatic X-ray energy (synchrotron) versus the polychromatic X-ray energy (X-ray energy). Considering the photon energy of X-rays, the attenuation method of X-rays varies depending on the atomic species, which affects the photon intensity of the detector. In the first case study described above, the laboratory X-ray source generated polychromatic X-rays through bremsstrahlung, which could distort density measurements. This was shown to have little effect on the final measurement, probably due to the similarity of the elements (mainly carbon, oxygen, hydrogen, fluorine) that make up the calibrator and the microspheres. Since the X-rays from the synchrotron source have an energy of 17 ± 2 keV, potential effects from low-energy or high-energy photons are prevented from causing different attenuations. From both the calibrator histogram and the final density measurements of the PMMA spheres at both facilities, it was shown that the X-ray energy distribution has little effect on the density measurements.

[0094] Synchrotron reconstruction images are obtained using a phase retrieval algorithm that enhances diffraction at the phase interfaces within the image, and show increased diffraction artifacts at the edges of the microspheres compared to lab sources (reconstructed using filtered back projection). This provides an opportunity to evaluate how different reconstruction algorithms affect the final measurement. FIGS. 16A - 16B show the microspheres before and after deconvolution. Plot 1660 in FIG. 16A shows the intensity 1661 vs. sphere equivalent diameter 1662 for the raw microsphere phase (bright shaded series 1663) and the deconvolved spheres (dark shaded series 1664). Plot 1670 in FIG. 16B shows the density 1671 vs. sphere equivalent diameter 1672 for the raw microsphere phase (bright shaded series 1673) and the deconvolved spheres (dark shaded series 1674). In plot 1660, a difference in intensity 1661 can be seen. When these intensities 1661 are converted to density 1671 (FIG. 16B), it shows that without deconvolution, the microsphere density 1671 is approximately twice the final value, again demonstrating the need for this pre - processing step for accurate measurement. Further, this conversion also demonstrates the robustness of the measurement against variations in the reconstruction algorithm that may affect the intensity of the image. Similarly, FIGS. 16A - 16B also address the issue of 8 - bit vs. 16 - bit images in that synchrotron images are 8 - bit and as a result have a smaller range of intensity values compared to lab sources. This does not introduce a significant difference in the accuracy of the final measurement, indicating that the approach described herein is robust under different image types.

[0095] Computer support FIG. 17 shows a computer network or similar digital processing environment in which embodiments of the present invention may be implemented. Client computer(s) / device(s) 50 and server computer(s) 60 provide a processing device, a storage device, and an input / output device for executing application programs and the like. The client computer(s) / device(s) 50 can also be linked through the communication network 70 to other computing devices, including, for example, other client devices / processes 50 and server computer(s) 60. The communication network 70 can be a remote access network, a global network (e.g., the Internet), a worldwide collection of computers, a local area network or wide area network, and can be part of a gateway that communicates with each other using current respective protocols (TCP / IP, Bluetooth®, etc.). Other electronic device / computer network architectures are suitable.

[0096] FIG. 18 is a diagram of an example of the internal structure of a computer (e.g., client processor / device 50 or server computer 60) in the computer system of FIG. 17. Each computer 50, 60 includes a system bus 79, where the bus is a set of hardware lines used for data transfer between components of a computer or processing system. The system bus 79 is basically a shared conduit that connects different elements of the computer system (e.g., processor, disk storage, memory, input / output ports, network ports, etc.) and enables the transfer of information between the elements. An I / O device interface 82 for connecting various input and output devices (e.g., keyboard, mouse, display, printer, speaker, etc.) to the computers 50, 60 is attached to the system bus 79. The network interface 86 enables the computer to connect to various other devices connected to a network (e.g., network 70 of FIG. 17). The memory 90 provides volatile storage for computer software instructions 92 and data 94 used to implement embodiments of the present invention (e.g., the functions of FIGS. 1, 5, and 8 among other examples detailed herein). The disk storage 95 provides non-volatile storage for computer software instructions 92 and data 94 used to implement an embodiment of the present invention. The central processing unit 84 is also attached to the system bus 79 and provides the execution of computer instructions.

[0097] In one embodiment, the processor routine 92 and data 94 are a computer program product (generally referred to as 92) including a non-transitory computer-readable medium (e.g., one or more built-in hard drives, external hard drives, DVD-ROMs, CD-ROMs, floppy disks, tape, etc., removable storage media) 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 procedure, as is well known in the art. In another embodiment, at least a portion of the software instructions can also be downloaded via cable communication and / or wireless connection. In other embodiments, the program of the present invention is a computer program propagation signal product embodied on a propagation signal on a propagation medium (e.g., radio waves, infrared rays, laser waves, sound waves, or radio waves propagated via the Internet or other global networks such as other networks). Such a carrier medium or signal can be used to provide at least a portion of the software instructions of the routine / program 92 of the present invention.

[0098] In an alternative embodiment, the propagation signal is an analog carrier wave or digital signal carried on a propagation medium. For example, the propagation signal may be a digitized signal propagated via a global network (e.g., the Internet), a telecommunications network, or other networks. In one embodiment, the propagation signal is a signal transmitted via a propagation medium over a period of time, e.g., instructions of a software application transmitted in packets via a network over a period of milliseconds, seconds, minutes, or more.

[0099] In other embodiments, the program product 92 can be implemented as so-called SaaS (Software as a Service), or other installation or communication that supports end users.

[0100] The teachings of all patents, published applications, and references cited herein are incorporated by reference in their entirety.

[0101] Although illustrative embodiments have been specifically shown and described, it will be understood by those skilled in the art that various changes in form and detail may be made therein without departing from the scope of the embodiments encompassed by the appended claims.

Prior Art Documents

Non-Patent Documents

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Non - Patent Document 13

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Claims

1. Segmenting the imaging data of the material and the calibration object into a plurality of phases; For each of the plurality of phases, determining a respective histogram based on the pixel intensities of the acquired imaging data corresponding to the phase; Deconvolving a given histogram corresponding to a certain phase of the material with (i) a function corresponding to an artifact and (ii) a function corresponding to the material; Determining the relationship between density and pixel intensity using one or more histograms corresponding to the calibration object; Applying the determined relationship to the function corresponding to the material to determine the density of the material. A method for determining the density of a material, comprising the above steps.

2. The method according to claim 1, further comprising the step of acquiring the imaging data of the material and the calibration object by subjecting the material and the calibration object in the sample holder to computed tomography imaging.

3. The step of segmenting the imaging data includes at least one of the following steps: Segmenting the imaging data based on intensity; Segmenting the imaging data based on gradient; and Segmenting the imaging data by processing the imaging data using at least one of a machine learning algorithm and an artificial intelligence algorithm to identify data corresponding to each phase of the plurality of phases. The method according to claim 1.

4. The step of deconvolving the given histogram corresponding to a certain phase of the material includes: Performing an analysis to deconvolve the data of the given histogram with (i) the function corresponding to the artifact and (ii) the function corresponding to the material. The method according to claim 1.

5. The method according to claim 1, wherein the calibration object includes a plurality of calibration object materials each having a known density.

6. The step of determining the relationship between density and pixel intensity using one or more histograms corresponding to the calibration object includes: Determining the average pixel intensity of each of the plurality of calibration object materials using a respective histogram corresponding to each of the plurality of calibration object materials; Determining the relationship using the average pixel intensity determined for each of the plurality of calibration material and the known density of each of the plurality of calibration material, the method according to claim 5, comprising.

7. Using each histogram corresponding to each of the plurality of calibration material, the step of determining the average pixel intensity of each of the plurality of calibration material, Each histogram corresponding to each of the plurality of calibration material, (i) the artifact function and (ii) the step of deconvolving the calibration material function, Using the corresponding calibration material function, the method according to claim 6, comprising the step of determining the average pixel intensity of each of the plurality of calibration material.

8. The determined relationship is a mathematical function between the average pixel intensity determined for each of the plurality of calibration material and the known density of each of the plurality of calibration material, the method according to claim 6.

9. Determining the average density of the material, Determining the uncertainty of the determined density, In response to the material being composed of discrete particles, determining the density distribution of the particles, the density of each particle, and the standard deviation of each particle over a range of particle sizes, and In response to the material being composed of a continuous material phase, at least one of the steps of determining the density distribution along an arbitrary orientation in at least one of a Cartesian coordinate system, a cylindrical coordinate system, and a spherical coordinate system, the method according to claim 1, further comprising.

10. The method according to claim 1, further comprising deconvolving the given histogram 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. Identifying that the determined density is non-physical, In response to identifying that the determined density is non-physical, determining a corrected density or determining that a corrected density cannot be identified, the method according to claim 1, further comprising.

12. The step of determining the corrected density is, Processing the imaging data using a feature size threshold to generate corrected imaging data by removing resolution artifacts, and using the corrected imaging data to repeat the determination, deconvolution, determination of relationships, and application of each of the segmentations, Obtaining new imaging data of the material and the new calibration object, and using the new imaging data to repeat the segmentation, determination of each histogram, deconvolution, determination of relationships, and application, and Obtaining high-resolution imaging data that corrects at least one of the geometric shapes, shapes, and morphologies that caused non-uniformity, and using the high-resolution imaging data to perform at least one of the steps of repeating the segmentation, determination of each histogram, deconvolution, determination of relationships, and application, the method according to claim 11.

13. A material, A calibration object, (i) a material chamber configured to accommodate the material, (ii) a calibration object chamber configured to accommodate the calibration object, and (iii) a holder defining an air channel separating the material chamber and the calibration object chamber, a system for positioning the material.

14. The calibration object is One or more of a plurality of thin film layers, A plurality of sample holder materials, and One or more of a plurality of particles, the system according to claim 10.

15. The plurality of thin film layers are Including a first polymer thin film layer, a second polymer thin film layer, and a third polymer thin film layer, and the first polymer thin film layer and the third polymer thin film layer sandwich the second polymer thin film layer, the system according to claim 11.

16. The second polymer thin film layer includes a first polymer thin film strip and a second polymer thin film strip separated by an air channel, the system according to claim 12.

17. Each thin film layer is made of at least one of poly(propylene) (PP) with a density of 0.91 g / cm ３ , poly(ethylene terephthalate) (PET) with a density of 1.38 g / cm ３ , and poly(tetrafluoroethylene) (PTFE) with a density of 2.2 g / cm ３ The system according to claim 11, which is composed of at least one of them.

18. The holder is configured to consistently position and orient the calibration object, whereby the imaging attenuation of the material is uniformly affected by the calibration object, the system according to claim 11.

19. The system according to claim 10, further comprising an imaging device, wherein parameters of the imaging device are calibrated using the calibration object and a calibration material for a target, and the calibration material for the target has a known density different from the density of the calibration object.

20. The system according to claim 19, wherein density measurement values obtained using the imaging device, the material, the calibration object, and the holder are independent of (unrelated to) a vendor, magnification, parameters, and imaging contrast.

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