Object-Space Optimization of Tomographic Reconstructions for Additive Manufacturing.

Volumetric 3D printing motivated by computed axial lithography enables rapid printing of homogeneous parts but requires a high dimensionality gradient-descent optimization to calculate image sets. Here we introduce a new, simpler approach to image-computation that algebraically optimizes a model of the printed object, significantly improving print accuracy of complex parts under imperfect material and optical precision by improving optical dose contrast between the target and surrounding regions. Quality metrics for volumetric printing are defined and shown to be significantly improved by the new algorithm. The approach is extended beyond binary printing to grayscale control of conversion to enable functionally graded materials. The flexibility of the technique is digitally demonstrated with realistic projector point spread functions, printing around occluding structures, printing with restricted angular range, and incorporation of materials chemistry such as inhibition. Finally, simulations show that the method facilitates new printing modalities such as printing into flat, rather than cylindrical packages to extend the applications of volumetric printing.

Highly Tunable Thiol-Ene Photoresins for Volumetric Additive Manufacturing.

Volumetric additive manufacturing (VAM) forms complete 3D objects in a single photocuring operation without layering defects, enabling 3D printed polymer parts with mechanical properties similar to their bulk material counterparts. This study presents the first report of VAM-printed thiol-ene resins. With well-ordered molecular networks, thiol-ene chemistry accesses polymer materials with a wide range of mechanical properties, moving VAM beyond the limitations of commonly used acrylate formulations. Since free-radical thiol-ene polymerization is not inhibited by oxygen, the nonlinear threshold response required in VAM is introduced by incorporating 2,2,6,6-tetramethyl-1-piperidinyloxy (TEMPO) as a radical scavenger. Tuning of the reaction kinetics is accomplished by balancing inhibitor and initiator content. Coupling this with quantitative measurements of the absorbed volumetric optical dose allows control of polymer conversion and gelation during printing. Importantly, this work thereby establishes the first comprehensive framework for spatial-temporal control over volumetric energy distribution, demonstrating structures 3D printed in thiol-ene resin by means of tomographic volumetric VAM. Mechanical characterization of this thiol-ene system, with varied ratios of isocyanurate and triethylene glycol monomers, reveals highly tunable mechanical response far more versatile than identical acrylate-based resins. This broadens the range of materials and properties available for VAM, taking another step toward high-performance printed polymers.

Simulation study of quantitative precision of the PET/X dedicated breast PET scanner.

The goal for positron emission tomography (PET)/X is measuring changes in radiotracer uptake for early assessment of response to breast cancer therapy. Upper bounds for detecting such changes were investigated using simulation and two image reconstruction algorithms customized to the PET/X rectangular geometry. Analytical reconstruction was used to study spatial resolution, comparing results with the distance of the closest approach (DCA) resolution surrogate that is independent of the reconstruction method. An iterative reconstruction algorithm was used to characterize contrast recovery in small targets. Resolution averaged [Formula: see text] full width at half maximum when using depth-of-interaction (DOI) information. Without DOI, resolution ranged from [Formula: see text] to [Formula: see text] for scanner crystal thickness between 5 and 15 mm. The DCA resolution surrogate was highly correlated to image-based FWHM. Receiver-operating characteristic analysis showed specificity and sensitivity over 95% for detecting contrast change from 5:1 to 4:1 (area under curve [Formula: see text]). For PET/X parameters modeled here, the ability to measure contrast changes benefited from higher photon absorption efficiency of thicker crystals while being largely unaffected by degraded resolution obtained with thicker crystals; DOI provided marginal improvements. These results assumed perfect data corrections and other idealizations, and thus represent an upper bound for detecting changes in small lesion radiotracer uptake of clinical interest using the PET/X system.

DOI-based reconstruction algorithms for a compact breast PET scanner.

PURPOSE: The authors discuss the design and evaluate the performance of combined event estimation and image reconstruction algorithms designed for a proposed high-resolution rectangular breast PET scanner (PETX). The PETX scanner will be capable of measuring the depth of interaction by utilizing detector modules composed of depth-of-interaction microcrystal element (dMiCE) crystal pairs. This design allows a unique combination of event estimation and fast projection methods. METHODS: The authors implemented a Monte Carlo simulator to model the PETX system using only true coincident events. The performance of the dMiCE crystal pairs was determined experimentally over a range of depths of interaction. This distribution was used to simulate the noisy dMiCE detector signals and to estimate the line of response for each decay. Three different statistical methods were implemented to determine photon event positioning. Images were reconstructed from these line of response estimators with the exact planogram frequency distance rebinning algorithm, which is an exact analytical reconstruction algorithm for planar systems. Reconstructed images were analyzed with contrast, noise, and spatial resolution metrics. RESULTS: The authors' simulations demonstrate the ability for the PETX system to produce quantitatively accurate images from true coincident events with a contrast recovery coefficient of greater than 0.8 for 5 mm spheres at the axial center of the scanner and a spatial resolution (FWHM) of 3 mm throughout most of the imaging field of view. CONCLUSIONS: The authors' proposed positioning and reconstruction algorithms for the PETX system show the potential for creating high-quality, high-resolution, and quantitatively accurate images within a clinically feasible reconstruction time.

Advancements to the planogram frequency-distance rebinning algorithm.

In this paper we consider the task of image reconstruction in positron emission tomography (PET) with the planogram frequency-distance rebinning (PFDR) algorithm. The PFDR algorithm is a rebinning algorithm for PET systems with panel detectors. The algorithm is derived in the planogram coordinate system which is a native data format for PET systems with panel detectors. A rebinning algorithm averages over the redundant four-dimensional set of PET data to produce a three-dimensional set of data. Images can be reconstructed from this rebinned three-dimensional set of data. This process enables one to reconstruct PET images more quickly than reconstructing directly from the four-dimensional PET data. The PFDR algorithm is an approximate rebinning algorithm. We show that implementing the PFDR algorithm followed by the (ramp) filtered backprojection (FBP) algorithm in linogram coordinates from multiple views reconstructs a filtered version of our image. We develop an explicit formula for this filter which can be used to achieve exact reconstruction by means of a modified FBP algorithm applied to the stack of rebinned linograms and can also be used to quantify the errors introduced by the PFDR algorithm. This filter is similar to the filter in the planogram filtered backprojection algorithm derived by Brasse et al. The planogram filtered backprojection and exact reconstruction with the PFDR algorithm require complete projections which can be completed with a reprojection algorithm. The PFDR algorithm is similar to the rebinning algorithm developed by Kao et al. By expressing the PFDR algorithm in detector coordinates, we provide a comparative analysis between the two algorithms. Numerical experiments using both simulated data and measured data from a positron emission mammography/tomography (PEM/PET) system are performed. Images are reconstructed by PFDR+FBP (PFDR followed by 2D FBP reconstruction), PFDRX (PFDR followed by the modified FBP algorithm for exact reconstruction) and planogram filtered backprojection image reconstruction algorithms. We show that the PFDRX algorithm produces images that are nearly as accurate as images reconstructed with the planogram filtered backprojection algorithm and more accurate than images reconstructed with the PFDR+FBP algorithm. Both the PFDR+FBP and PFDRX algorithms provide a dramatic improvement in computation time over the planogram filtered backprojection algorithm.

Attenuation-emission alignment in cardiac PET/CT based on consistency conditions.

PURPOSE: In cardiac PET and PET/CT imaging, misaligned transmission and emission images are a common problem due to respiratory and cardiac motion. This misalignment leads to erroneous attenuation correction and can cause errors in perfusion mapping and quantification. This study develops and tests a method for automated alignment of attenuation and emission data. METHODS: The CT-based attenuation map is iteratively transformed until the attenuation corrected emission data minimize an objective function based on the Radon consistency conditions. The alignment process is derived from previous work by Welch et al. ["Attenuation correction in PET using consistency information," IEEE Trans. Nucl. Sci. 45, 3134-3141 (1998)] for stand-alone PET imaging. The process was evaluated with the simulated data and measured patient data from multiple cardiac ammonia PET/CT exams. The alignment procedure was applied to simulations of five different noise levels with three different initial attenuation maps. For the measured patient data, the alignment procedure was applied to eight attenuation-emission combinations with initially acceptable alignment and eight combinations with unacceptable alignment. The initially acceptable alignment studies were forced out of alignment a known amount and quantitatively evaluated for alignment and perfusion accuracy. The initially unacceptable studies were compared to the proposed aligned images in a blinded side-by-side review. RESULTS: The proposed automatic alignment procedure reduced errors in the simulated data and iteratively approaches global minimum solutions with the patient data. In simulations, the alignment procedure reduced the root mean square error to less than 5 mm and reduces the axial translation error to less than 1 mm. In patient studies, the procedure reduced the translation error by > 50% and resolved perfusion artifacts after a known misalignment for the eight initially acceptable patient combinations. The side-by-side review of the proposed aligned attenuation-emission maps and initially misaligned attenuation-emission maps revealed that reviewers preferred the proposed aligned maps in all cases, except one inconclusive case. CONCLUSIONS: The proposed alignment procedure offers an automatic method to reduce attenuation correction artifacts in cardiac PET/CT and provides a viable supplement to subjective manual realignment tools.

Statistical LOR estimation for a high-resolution dMiCE PET detector.

We develop a statistical line of response (LOR) estimator of the three-dimensional interaction positions of a pair of annihilation photons in a PET detector module with depth of interaction capability. The three-dimensional points of interaction of a coincidence pair of photons within the detector module are estimated by calculation of an expectation of the points of interaction conditioned on the signals measured by the photosensors. This conditional expectation is computed from estimates of the probability density function of the light collection process and a model of the kinetics of photon interactions in the detector module. Our algorithm is capable of handling coincidences where each annihilation photon interacts any number of times within the detector module before being completely absorbed or escaping. In the case of multiple interactions, our algorithm estimates the position of the first interaction for each of the coincidence photons. This LOR estimation algorithm is developed for a high-resolution PET detector capable of providing depth-of-interaction information. Depth of interaction is measured by tailoring the light shared between two adjacent detector elements. These light-sharing crystal pairs are referred to as dMiCE and are being developed in our lab. Each detector element in the prototype system has a 2 x 2 mm(2) cross section and is directly coupled to a micro-pixel avalanche photodiode (MAPD). In this set-up, the distribution of the ratio of light shared between two adjacent detector elements can be expressed as a function of the depth of interaction. Monte Carlo experiments are performed using our LOR estimation algorithm and compared with Anger logic. We show that our LOR estimation algorithm provides a significant improvement over Anger logic under a variety of parameters.

Statistical Three-Dimensional Positioning Algorithm for High-Resolution dMiCE PET Detector.

Our laboratory is developing a high-resolution PET detector capable of providing depth-of-interaction information (dMiCE) by tailoring the light sharing between two adjacent detector elements. Each detector element in the prototype system has a 2×2 mm(2) cross section and is directly coupled to a micro-pixel avalanche photodiode (MAPD). In this setup the distribution of the ratio of light shared between two adjacent detector elements can be expressed as a function of the depth of interaction. The three-dimensional points of interaction of a coincidence pair of photons within the detector module is estimated by numerical calculation of an expectation of the points of interaction conditioned on the signals measured by the MAPDs (Bayesian estimate). This conditional expectation is computed from estimates of the probability density function of the light collection process and a model of the kinetics of photon interactions in the detector module. Our algorithm is capable of handling coincidences where each photon interacts any number of times within the detector module before being completely absorbed or escaping. In the case of multiple interactions our algorithm estimates the position of the first interaction for each of the coincidence photons.