Abstract
PURPOSE:
To compare imaging performance of a cadmium telluride (CdTe) based photon counting detector (PCD) with a CMOS based energy integrating detector (EID) for potential phase sensitive imaging of breast cancer.
METHODS:
A high energy inline phase sensitive imaging prototype consisting of a microfocus X-ray source with geometric magnification of 2 was employed. The pixel pitch of the PCD was 55μm, while 50μm for EID. The spatial resolution was quantitatively and qualitatively assessed through modulation transfer function (MTF) and bar pattern images. The edge enhancement visibility was assessed by measuring edge enhancement index (EEI) using the acrylic edge acquired images. A contrast detail (CD) phantom was utilized to compare detectability of simulated tumors, while an American College of Radiology (ACR) accredited phantom for mammography was used to compare detection of simulated calcification clusters. A custom-built phantom was employed to compare detection of fibrous structures. The PCD images were acquired at equal, and 30% less mean glandular dose (MGD) levels as of EID images. Observer studies along with contrast to noise ratio (CNR) and signal to noise ratio (SNR) analyses were performed for comparison of two detection systems.
RESULTS:
MTF curves and bar pattern images revealed an improvement of about 40% in the cutoff resolution with the PCD. The excellent spatial resolution offered by PCD system complemented superior detection of the diffraction fringes at boundaries of the acrylic edge and resulted in an EEI value of 3.64 as compared to 1.44 produced with EID image. At equal MGD levels (standard dose), observer studies along with CNR and SNR analyses revealed a substantial improvement of PCD acquired images in detection of simulated tumors, calcification clusters, and fibrous structures. At 30% less MGD, PCD images preserved image quality to yield equivalent (slightly better) detection as compared to the standard dose EID images.
CONCLUSION:
CdTe-based PCDs are technically feasible to image breast abnormalities (low/high contrast structures) at low radiation dose levels using the high energy inline phase sensitive imaging technique.
Keywords
Introduction
Diagnosing early-stage breast cancer is vital for successful treatment. The need for detecting early-stage cancer at reduced radiation dose levels motivates to improve the current screening technology. Various studies have estimated that the X-ray radiation itself can result in breast cancer as a direct result of digital mammography (DM) and digital breast tomosynthesis (DBT) [1, 2]. Thus, by decreasing the dose in DM and DBT, the number of examination-induced collateral effects can be significantly reduced. Clinical DM and digital breast tomosynthesis (DBT) rely on the absorption coefficient differences within the breast tissues for image formation and utilize low energy X-ray beams as the absorption coefficients differences are highest at those energies [3–5]. However, this approach also increases the absorbed radiation dose to breast tissue as the photoelectric absorption is dominant at low energies [6–8]. Phase contrast imaging (PCI) provides better tissue discrimination by simultaneously recording the attenuation and phase shifts experienced by the traverse X-ray beam [9–12]. For breast tissue, phase shift coefficients are at least 2–3 orders of magnitude larger than their absorption coefficients within the diagnostic energy range of 20 keV to 150 keV [13–15]. This fact allows the opportunity of breast imaging with PCI techniques at high photon energies to reduce the photoelectric absorption, thus decrease the absorbed radiation dose without compromising the image quality. Numerous studies have shown the advantages of the high-energy phase sensitive X-ray breast imaging prototype systems [16–25].
Nearly all DM and DBT systems, along with newly developed phase sensitive imaging systems, utilize the energy integrating detectors (EIDs) for image acquisition. In EIDs, noise originates mainly from quantum noise and electronic noise of the detection system. Quantum noise is associated with the random nature of photon interactions and is directly related to the number of detected photons. Electronic noise is unrelated to the number of detected photons and does not carry any useful information. It is related to the random liberation of electrons due to thermal energy and readout circuits. At low photon flux levels, such as during the acquisition of multiple angular projection views in DBT and breast CTs, EIDs electronic noise becomes more critical because the detected signal may become comparable to the electronic noise levels [26]. Thus, electronic noise limits the ability of a system to reduce the radiation dose levels while keeping adequate image quality needed for the accurate diagnosis of the disease [27].
Photon counting detectors (PCDs) utilize direct conversion semiconductor sensors, which convert incident X-rays directly into an electrical signal. Compared to EIDs that work in a continuous current mode, PCDs operate in a pulse mode based on single-event interaction within their sensor material. The advanced application-specific integrated circuits (ASICs) for readout allow the PCDs to have sharp pixel response, high dynamic range, spectral energy discrimination, and completely suppressing the electronic noise [28]. Silicon (Si) sensors have been used in PCDs for breast imaging applications because Si wafers can achieve high crystal quality and wide production [29–31]. However, their stopping power is constrained due to the low atomic number (Z = 14), which results in low quantum efficiencies at high energies. Continuing interest and research have pushed the advancements in designing PCDs with smaller pixel areas along with sensor materials composed of higher atomic numbers such as cadmium telluride (CdTe) (Z = 48/52) which increase the conversion efficiencies within the diagnostic energy range [32]. CdTe based PCDs with large pixel areas have been used in CT imaging and other biomedical imaging applications [25, 33–37]. CdTe based PCDs with small pixel areas, when coupled with X-ray phase sensitive imaging, can potentially reduce the radiation dose in breast imaging applications by operating at high energies while providing adequate image quality for accurate diagnosis.
In this work, using an inline phase sensitive breast imaging prototype, we evaluated and compared the imaging performance of CdTe-based PCD with a modern EID at equal and 30% less radiation dose levels. The pixel pitch of both PCD and EID are small enough to make them well suited for breast imaging. Using an advanced translational/rotating stage, we imaged several large area breast tissue-equivalent phantoms to evaluate the image quality of the two detector-based systems. Based on the examination of relevant literature, no prior investigation has been conducted to compare the imaging performances of PCD and EID in imaging large FOV of breast cancer mimicking phantoms using the inline phase sensitive imaging technique.
Materials and methods
Technical details
The imaging performances of the photon counting and energy integrating detectors were investigated with an inline phase sensitive X-ray imaging prototype. The photon counting detector (PCD) consists of five Medipix3RX chips aligned in one row (Model Widepix, Advacam, s.r.o. Czech Republic). Each chip has a hybrid architecture in which the sensor and readout electronics (ASIC) are coupled with the bump-bonding technique allowing for independent readout for each pixel. The sensor is a 1 mm thick cadmium telluride (CdTe) based semiconductor, and the combined ASIC active area is 1280×256 pixels with a pixel pitch of 55μm. Each pixel of the chip has two thresholds and two 12-bit counters.
There are two main modes of operations for the detector: single-pixel mode (SPM) and charge summing mode (CSM). In SPM, each pixel works independently of its neighbor, and the user has ability to utilize either one or two energy thresholds depending on the application. In CSM, two thresholds can be used for the energy discrimination in order to suppress the charge sharing effects efficiently. This study used the CSM mode for imaging by setting the two energy thresholds at TH0 = 8.9 keV and TH1 = 14.9 keV for suppressing charge sharing and electronic noise. The detector was calibrated to optimally bias the analog circuitry by the appropriate setting of the DACs and performing the threshold equalization.
The energy integrating detector (EID) was a complementary metal-oxide-semiconductor (CMOS) flat panel detector (C7942SK-25, Hamamatsu Photonics, Japan), having a gadolinium sulfoxylate (GOS) scintillator, a pixel pitch of 50μm, an active area of 120 mm×120 mm and a 12-bit digital output. The flat panel detector has been used in the previous studies for comparison with the conventional standard of care breast imaging systems [37–42].
The phase sensitive benchtop prototype incorporates a microfocus X-ray source (Model L8121-06, Hamamatsu Photonics, Japan) consisting of a tungsten (W) target and a 500μm thick Beryllium (Be) output window with tube voltage and tube current ranging from 10–130 kV and 10–300μA, respectively. The source focal spot size varies from 16–50μm with respect to the output power of the tube [43]. The intrinsic emission beam angle is 100°, and a specialized collimator was employed to limit the X-ray beam to the size of the detector. A 1.5 mm thick aluminum (Al) was used for beam hardening. The source to object distance (SOD) and object to detector distance (ODD) were 68.58 cm, resulting in a geometric magnification factor of 2. The benchtop prototype incorporated with the PCD is shown in Fig. 1. All the phase contrast images were acquired at 59 kV, 300μA with a focal spot size of about 27μm. A customized multi-axis motorized stage (Optosigma Corp, CA, USA), with the ability of linear translation in XYZ direction and 360° angular rotation, was used to place and position the imaging samples. The high-resolution stage allows the PCD to image large-sized samples by scanning and stitching the series of images to cover the entire region of interest. This approach likes to use a detector with a larger field of view. Once the phase contrast images were acquired with the PCD and EID, flat field correction was performed, and a phase retrieval method based on the phase attenuation duality (PAD) based principle was employed to yield quantitative information as well as to improve the image quality in terms of signal-to-noise ratio [44, 45]. The resultant phase retrieved images are designated as phase sensitive images.

The inline-based phase sensitive imaging prototype employing a microfocus X-ray source, a photon counting detector, and a motorized stage. A collimator is employed to limit the size of the beam, while aluminum (Al) filtration is used for beam hardening.
The spatial resolution for the PCD and EID based phase sensitive imaging prototypes were quantitatively measured by computing the modulation transfer function (MTF) using a slanted edge technique [46, 47]. A tungsten (W) sheet with 50μm thickness was slightly angulated (∼4°) for the generation of oversampled ESF with a data interval smaller than the size of the pixel pitch. Then, the line spread function, LSF, was computed by differentiating the ESF function. A 3rd order Gaussian function was used to fit the LSF, which made the overall MTF curve better behaved by forcing a smoothing transition of the LSFs to zeros. The MTF curves were obtained from the fast Fourier transform (FFT) of the LSF and normalization to unity at zero spatial frequency (f). An ultra-high contrast resolution bar chip phantom (Model 016B, CIRS, Virginia, USA) was utilized to qualitatively compare the spatial resolution of the two-phase sensitive imaging systems. The phantom has a 17.5μm thick gold–nickel alloy bar pattern with 18 segments ranging from 5 lp/mm to 28 lp/mm.
A 2.2 mm thick acrylic plate, which is the top cover of an ACR phantom (Model 156D, Sun Nuclear, FL, USA), was imaged to quantify the edge enhancement effects in the phase contrast images. Edge profiles were determined across the vertical edge of the acrylic plate using the phase contrast images acquired by the PCD and EID. An edge-enhancement index (EEI) was defined, which compares the degree of edge enhancement effect relative to the absolute change in the intensity from absorption differences across the edge [48, 49]. The EEI was defined as
We used a modular phantom (CIRS Inc., Norfolk, VA, USA) for simulated tumor imaging comparisons consisting of multiple slabs mimicking a 50/50 adipose-glandular breast tissue. Three slabs were sandwiched together to create a 5 cm thick phantom, with the middle slab having a thickness of 1 cm. The middle slab was machined to include a contrast detail (CD) test pattern to simulate different tumor sizes. This pattern consisted of a 6×6 matrix of circular discs having diameters of 0.25, 0.5, 1, 2, 3 and 4.25 mm with drilled depths of 0.1, 0.2, 0.4, 0.6, 0.8 and 1 mm. The images were randomly presented to 4 independent observers for the analyses, which involved each observer identifying the minimum perceptible disk for each diameter in the image. Contrast detail (CD) curves were generated for each image according to the averaged observers’ scores to compare the relative performances of the systems. The CD curve relates the threshold contrast necessary to perceive an object as a function of the object’s diameter [50, 51]. A student t confidence interval was constructed around each data point to determine the standard deviation among the observers. This study utilized a 95% confidence interval with n – 1 degree of freedom, where n represents the number of observers. For quantitative comparison, contrast-to-noise ratios (CNRs) were calculated for several discs in the CD phantom as
To simulate the imaging of microcalcifications, we used an ACR accredited mammographic phantom (Model 156D, Sun Nuclear, FL, USA). The phantom simulates a 4.2cm thick compressed breast of 50/50 adipose-glandular density. The phantom has a 7 mm thick wax insert containing four sets of speck groups composed of aluminum oxide (Al2O3) grits. The grit diameters were 0.54 mm, 0.32 mm, 0.24 mm, and 0.2 mm, respectively. Due to the relatively small size of the Al2O3 grits, the signal-to-noise-ratio (SNR) metric was used to compare the detectability of the two systems. The SNR was calculated as
To simulate the imaging of the fibrous structures within a breast, we used a 2 mm thick 3D printed insert that had five fibers printed on top in thicknesses of 0.62, 0.4, 0.3, 0.18, and 0.12 mm. The printing material of the insert was epoxy resin (C21H25ClO5). The 2 mm thick insert was sandwiched between two 50/50 adipose-glandular slabs to make the overall thickness of the phantom as 4.2 cm. We measured the CNR values for two fibers with thicknesses of 0.62 and 0.4 mm. Finally, a beetle was imaged with the two different detector systems to highlight the image quality comparisons with heterogeneous samples. The 7 mm thick beetle was placed instead of the wax insert inside the ACR phantom.
Results
Figure 2 (a) compares the MTF curves calculated for phase sensitive images of PCD and EID. The MTF50 % were 5 lp/mm and 3.5 lp/mm with PCD and EID, indicating well percieved sharpness obtained with the PCD. The MTF10 % for the PCD and EID were 12.2 lp/mm and 8.7 lp/mm, indicative of the high cutoff resolution offered by the PCD. Figures 2(b) and 2(c) provide the qualitative measurement of the spatial resolution, which validates the MTF curve results. One can see that the 11 lp/mm bar lines are distinguishable with the PCD, while 8 lp/mm bar lines are barely distinguishable with the EID.

(a) Comparison of MTF curves calculated with the phase sensitive images acquired with the PCD and EID based prototype systems. (b) PCD acquired phase sensitive image of the bar pattern displaying the differentiation of 11 lp/mm bar lines. (c) EID acquired phase sensitive image of the bar pattern, barely differentiating the 8 lp/mm bar lines.
The phase contrast images of the acrylic edge and their respective edge profiles are given in Fig. 3. From a visual inspection, it is clear that edge enhancement effects are much prominent with the PCD acquired phase contrast image 3(a), compared to the EID acquired image 3(b). The conspicuous overshooting at the boundaries by the PCD acquired phase contrast image can be further highlighted from the edge profiles in Fig. 3(c). The calculated EEI values for PCD and EID acquired phase contrast images were 3.64 and 1.44.

Phase contrast images of a 2.2 mm thick acrylic edge acquired with (a) PCD at 59 kV, 1.5 mAs. (b) EID at 59 kV, 1.5 mAs. (c) The intensity profiles were drawn across the step edge showing the dark-bright fringes.
Figure 4 provides the phase sensitive images of the CD phantom simulating the 50/50 adipose-glandular breast density acquired with the two detectors. Figure 4(a) is the standard dose PCD image, 4(b) is the lower dose PCD image, and 4(c) is the standard dose EID acquired image. From a visual inspection, one can see that the difficult disks to perceive are in the upper right (smaller with lower contrast), and the easiest disks to perceive are in the lower left (larger with higher contrast) on these phantom images.

Phase sensitive images of the 5cm thick CD phantom acquired with (a) PCD at 59 kV, 10 mAs, 1.14 mGy. (b) PCD at 59 kV, 7 mAs, 0.8 mGy (c) EID at 59 kV, 10 mAs, 1.14 mGy.
Figure 5 compares the threshold contrast detection of the PCD and EID based phase sensitive imaging systems. At the same (standard) dose level, the PCD based image is superior to the EID acquired. This is evident from the C-D curves generated from the average scores of 4 independent observers, where the observers perceived more discs for all the diameters. As the radiation dose was reduced to 30% with the PCD, the contrast and spatial resolutions were comparable or slightly better than the standard dose EID acquired image. The superiority of the PCD based phase sensitive imaging system as seen in the observer study is further backed by the CNR values. The results provided in Table 1 demonstrate that the CNR values of the PCD image are 20–45% higher than the standard dose EID image at standard dose. Furthermore, with the reduced radiation dose, the CNR values of the PCD image are 3–20% higher than the standard dose EID image.

Contrast detail curve comparison of the phase sensitive images acquired with the PCD and EID detectors. The bar lines specify the 95% confidence interval for which the average detected threshold contrast would fall within that interval for each disc diameter.
Comparison of the CNRs calculated with various discs within the CD phantom images acquired with the PCD and EID
Figure 6 provides the simulated microcalcifications within the ACR phantom along with the grayscale profiles, with 6(a) is the PCD image acquired at 1.24 mGy, 6(b) is the PCD image acquired at 0.87mGy, and 6(c) is the EID acquired image at 1.24 mGy. It is worth mentioning that a DM/DBT system must detect the 0.24 mm speck group within an ACR phantom to meet the MQSA minimum standards [53]. For this phantom, the 0.240 mm speck corresponds to the 3rd group. One can see that with a standard dose PCD image, all 4 speck groups are detected and perceived, with the 4th group (0.20 mm) highlighted in red dotted circles. At 30% less radiation dose, the 3rd speck group was fully detected, and half of the 4th group specks were detected with the PCD image. With the EID image acquired at standard dose, the 3rd group was detected with relatively weak contrast while the 4th speck group was half detected as highlighted by the red dotted circles. The grayscale profiles represent the measured intensities along the yellow lines drawn through the central speck of the 4th group and show the signal of the Al2O3 spec relative to the background. The computed SNR for each set of images is also given. At the same radiation dose, the SNR for the PCD image is at least 2 times higher than the SNR of the EID image.

Phase sensitive images of a 4.2 cm thick ACR phantom showing the speck groups. The dotted circles highlight the individual specks in the 4th group. Line profiles were drawn across the yellow dotted line for the computation of SNR. The images were acquired with the (a) PCD at 59 kV, 10 mAs, 1.24 mGy. (b) PCD at 59 kV, 7 mAs, 0.87 mGy. (c) EID at 59 kV, 10 mAs, 1.24 mGy.
The fiber images simulating the fibroglandular tissue are given in Fig. 7. One can see that the fibers on the PCD acquired images are more conspicuous with well-preserved boundaries than the EID image. Four fibers are easily detected with the standard dose PCD image, with the fifth fiber partially detected. With the low-dose PCD image, four fibers are well detected. On the other hand, the third and fourth fibers are partially detected with the EID acquired image at standard dose.

Phase sensitive images of the 4.2 cm thick phantom showing the simulated fibers. The images were acquired with the (a) PCD at 59 kV, 10 mAs, 1.24 mGy. (b) PCD at 59 kV, 7 mAs, 0.87 mGy. (c) EID at 59 kV, 10 mAs, 1.24 mGy.
The CNR analyses endorse the superiority of the PCD phase sensitive imaging system, as provided in Table 2. For example, with the 0.60 mm thick fiber, the CNR with the PCD image was 4.68 compared to the 2.97 of EID image at standard dose. The PCD image acquired at 30% less dose still outperforms the standard dose EID image in terms of the CNR values. For example, with the 0.40mm thick fiber, the CNR with the PCD image was 2.53 compared to 2.05 with the EID-based image.
Comparison of the CNRs and FOM ratios calculated with the various fibers within the phase sensitive images acquired by the PCD and EID
Figure 8 shows the images of a beetle embedded phantom acquired with the PCD and EID based phase sensitive systems. The dotted arrows highlight some significant morphology. With the PCD image, Fig. 8(a), the mouthparts, femur, and claws are sharper, brighter, and their boundaries are better defined than the EID image shown in Fig. 8(b). The thorax region, such as prothorax and metathorax, is also sharper and better depicted in the PCD image than the EID image.

Phase sensitive images show an embedded beetle within a 4.2cm acrylic. The images were acquired with the (a) PCD at 59 kV and 10 mAs. (b) EID at 59 kV and 10 mAs.
In this study, we demonstrated the image quality improvements and dose reduction capabilities offered by the photon counting detector (PCD) for the potential diagnosis and detection of breast cancer using a high-energy inline phase sensitive X-ray imaging system. For a PCD, not all the incoming X-ray photons are counted since they are not fully absorbed in the sensor layer as per Beer-Lambert’s law (i.e., absorption A = ln(I/ I0) = - μt with t thickness and μ material/energy dependent parameter). The sensor material was chosen to be CdTe with a 1 mm thickness to ensure sufficient detection at high energies. One should remember that the thicker the sensor layer, the higher the probability of charge sharing effects. That is why we operated the PCD in charge summing mode to mitigate the effects of charge sharing. For the image quality comparisons, we used a CMOS flat-panel detector with a pixel pitch slightly smaller than that of the PCD.
The MTF50 % analysis revealed that the PCD acquired images are much sharper than the EID acquired images. The MTF10 % analysis revealed a 40% improvement in the cutoff resolution of the PCD. The resolution bar pattern qualitatively validated the MTF results by resolving the 11 lp/mm, and 8 lp/mm bar lines on the PCD and EID acquired images. All the image analyses were performed with the phase retrieved processed images, which reduces the noises at the expense of spatial resolution if PAD-based conditions are not fully satisfied [19, 54]. The excellent spatial resolution of the PCD system also complements the superior detection of the interference fringes, which are manifestations of the phase contrast effects. The EEI values demonstrated that the object to detector distance (OOD) of 68.58 cm was sufficient to resolve the interference fringes using the PCD. With EID, one may have to further increase the ODD for effectively resolving the interference fringes. This approach also reduces the number of X-ray photons available for detection according to the inverse square law and constraints dose efficiency.
The phantom analyses demonstrated the feasibility of the PCD with the inline phase sensitive imaging setup. With the CD phantom that simulated various tumor sizes, the observer study and CNR analyses indicated superior standard dose PCD image performance. As the dose was 30% lowered with the PCD, the observers could still perceive slightly more discs than the EID acquired standard dose image. For example, with a 0.25 mm diameter disc, the reported threshold contrasts for the low dose PCD and standard-dose EID images were 0.73 and 0.9, respectively. All 4 speck groups were visible and distinguishable on the standard dose PCD image within the ACR phantom. At 30% reduced radiation dose, PCD image detected 3.5 speck groups, same as the standard dose EID image but with much higher contrast. The SNR analysis performed within a speck group revealed at least two-fold improvement with the PCD image at standard dose. These results are of clinical significance, particularly when diagnosing ductal carcinoma in situ (DCIS), which is considered an early form of breast cancer with the appearance of microcalcification clusters. Number of cluster features are evaluated for correct diagnosis, including their number, size, appearance, and spatial distribution. Clinically it is also essential to track the variations of fibrous structures during the development of breast ductal carcinoma tissues. The simulated fiber structures in varying thicknesses were more conspicuous and had clearly defined edges with the PCD based phase sensitive imaging system. The CNR analysis further endorsed the superiority of the PCD phase sensitive imaging system in terms of image quality. For example, with the 0.40 mm thick fiber at standard dose, the CNR values were 3.4 and 2.06 with the PCD and EID images. The CNR value for the same fiber with a 30% reduced dose was 2.53 with the PCD image, highlighting the dose reduction improvements offered by the PCD phase sensitive imaging system. The beetle embedded phantom, composed of multi heterogeneous structures (Z < 10), also highlighted the superb image quality improvements offered by the PCD based system.
The PCD employed in this study had a limited field of view that can limit its efficacy when using cone-beam imaging geometries. We used a high-resolution motorized stage to image large samples by scanning and stitching a series of images to cover the entire region of interest. We also used a specialized collimator which limited the X-ray beam to the size of the PCD. This scan and stitch approach is equivalent to a detector with a large field of view. Although stitching of multiple images can cause intensity differences, resulting in horizontal and vertical stripes at the stitching points in the final image, such artifacts can be removed with intensity corrections and careful gain calibration of the PCD. Large-area PCDs are currently being developed to eliminate the need for this type of scanning.
Furthermore, superior results of the PCD also indicate that one can further increase the pixel size to an extent where one can get appreciable phase shift generated contrast and higher counts per pixel. This may also reduce the complexities in the fabrication of large-area PCDs. It is expected that the design and architecture of the upcoming Medipix4 chip [55–57] may allow the fabrication of large-area detectors with a field of view equivalent to mammography detectors. Future studies will be conducted with a PCD based phase sensitive tomosynthesis prototype to investigate further how spatial resolution, noise power spectra, spectral resolution, and multiple energy thresholds impact the image quality and material decomposition abilities in the reconstructed planes. We are also currently developing and optimizing phase retrieval algorithms specific to PCDs, which may play a critical role in designing a low-dose phase sensitive breast imaging system.
Conclusion
This study provided an encouraging step in evaluating the feasibility of using PCDs for the potential phase sensitive imaging of breast cancer with state-of-the-art phantom imaging. Our method demonstrated accurate detection of the simulated tumors, microcalcification clusters, and fibrous structures using a PCD. Future work should investigate classification performance in more clinically realistic conditions using a broad range of breast tissues samples containing tumors and microcalcification clusters.
Footnotes
Acknowledgments
This research was supported in part by the National Institutes of Health under grant F32CA250300. We would like to acknowledge the support of the Charles and Jean Smith Chair endowment fund by the University of Oklahoma foundation.
