Automated recovery of the center of rotation in optical projection tomography in the presence of scattering

Online geometry calibration for retrofit computed tomography from a mouse rotation system and a small-animal imager

BACKGROUND

Computed tomography (CT) generates a three-dimensional rendering that can be used to interrogate a given region or desired structure from any orientation. However, in preclinical research, its deployment remains limited due to relatively high upfront costs. Existing integrated imaging systems that provide merged planar X-ray also dwarfs CT popularity in small laboratories due to their added versatility.

PURPOSE

In this paper, we sought to generate CT-like data using an existing small-animal X-ray imager with a specialized specimen rotation system, or MiSpinner. This setup conforms to the cone-beam CT (CBCT) geometry, which demands high spatial calibration accuracy. Therefore, a simple but robust geometry calibration algorithm is necessary to ensure that the entire imaging system works properly and accurately.

METHODS

Because the rotation system is not permanently affixed, we propose a structure tensor-based two-step online (ST-TSO) geometry calibration algorithm. Specifically, two datasets are needed, namely, calibration and actual measurements. A calibration measurement detects the background of the system forward X-ray projections. A study on the background image reveals the characteristics of the X-ray photon distribution, and thus, provides a reliable estimate of the imaging geometry origin. Actual measurements consisted of an X-ray of the intended object, including possible geometry errors. A comprehensive image processing technique helps to detect spatial misalignment information. Accordingly, the first processing step employs a modified projection matrix-based calibration algorithm to estimate the relevant geometric parameters. Predicted parameters are then fine-tuned in a second processing step by an iterative strategy based on the symmetry property of the sum of projections. Virtual projections calculated from the parameters after two-step processing compensate for the scanning errors and are used for CT reconstruction. Experiments on phantom and mouse imaging data were performed to validate the calibration algorithm.

RESULTS

Once system correction was conducted, CBCT of a CT bar phantom and a cohort of euthanized mice were analyzed. No obvious structure error or spatial artifacts were observed, validating the accuracy of the proposed geometry calibration method. Digital phantom simulation indicated that compared with the preset spatial values, errors in the final estimated parameters could be reduced to 0.05° difference in dominant angle and 0.5-pixel difference in dominant axis bias. The in-plane resolution view of the CT-bar phantom revealed that the resolution approaches 150 μ $\umu$ m.

CONCLUSIONS

A constrained two-step online geometry calibration algorithm has been developed to calibrate an integrated X-ray imaging system, defined by a first-step analytical estimation and a second-step iterative fine-tuning. Test results have validated its accuracy in system correction, thus demonstrating the potential of the described system to be modified and adapted for preclinical research.

Automatic synchrotron tomographic alignment schemes based on genetic algorithms and human-in-the-loop software

Tomography imaging methods at synchrotron light sources keep evolving, pushing multi-modal characterization capabilities at high spatial and temporal resolutions. To achieve this goal, small probe size and multi-dimensional scanning schemes are utilized more often in the beamlines, leading to rising complexities and challenges in the experimental setup process. To avoid spending a significant amount of human effort and beam time on aligning the X-ray probe, sample and detector for data acquisition, most attention has been drawn to realigning the systems at the data processing stages. However, post-processing cannot correct everything, and is not time efficient. Here we present automatic alignment schemes of the rotational axis and sample pre- and during the data acquisition process using a software approach which combines the advantages of genetic algorithms and human intelligence. Our approach shows excellent sub-pixel alignment efficiency for both tasks in a short time, and therefore holds great potential for application in the data acquisition systems of future scanning tomography experiments.

Drift Artifacts Correction for Laboratory Cone-Beam Nanoscale X-ray Computed Tomography by Fitting the Partial Trajectory of Projection Centroid

A self-correction method for the drift artifacts of laboratory cone-beam nanoscale X-ray computed tomography (nano-CT) based on the trajectory of projection centroid (TPC) is proposed. This method does not require additional correction phantoms, simplifying the correction process. The whole TPC is estimated by the partial TPC in the optimal projection set. The projection drift is calculated by the measured TPC and the estimated TPC. The interval search method is used so that the proposed method can adapt to the case of a truncated projection due to drift. The fixed-angle scanning experiment of the Siemens star and the partial derivative analysis of the projection position show the necessity of correcting drift artifacts. Further, the Shepp–Logan phantoms with different drift levels are simulated. The results show that the proposed method can effectively estimate the horizontal and vertical drifts within the projection drift range of ±2 mm (27 pixels) with high accuracy. Experiments were conducted on tomato seed and bamboo stick to validate the feasibility of the proposed method for samples with different textures. The correction effect on different reconstructed slices indicates that the proposed method provides performance superior to the reference scanning method (RSM) and global fitting. In addition, the proposed method requires no extra scanning, which improves the acquisition efficiency, as well as radiation utilization.

Fast and noise-tolerant determination of the center of rotation in tomography

High-quality tomographic reconstruction is not possible without the accurate localization of the center of rotation. Poor localization leads to artifacts in the data and can even cause reconstructions to fail. There are many approaches to solving this problem, some of which involve the collection of full sinograms, or even provisional tomographic reconstructions, in order to determine the center of rotation. Here, a simple method based on the expected symmetry of the Fourier transform of summed projections approximately 180° apart is presented; unlike cross-correlation methods, it requires only a single Fourier transform to compute, and uses mainly low spatial frequency information which is less susceptible to noise. This approach is shown to be fast, and robust against poor signal-to-noise as well as to projection images acquired at angles that are not exactly 180° apart. This rapid method can be useful as a first step in the processing of tomographic data.

Estimating the Center of Rotation of Tomographic Imaging Systems with a Limited Number of Projections

For a tomographic imaging system, image reconstruction quality is dependent on the accurate determination of coordinates for the true center of rotation (COR). A significant COR offset error may introduce ringing, streaking, or other artifacts, while smaller error in determining COR may blur the reconstructed image. Well known COR correction techniques including image registration, center of mass calculation, or reconstruction evaluation work well under certain conditions. However, many of these methods do not consider various real-world cases such as a tilted sensor or non-parallel projections. Furthermore, a limited number of projections introduces stripe artifacts into the image reconstruction that interfere with many of these classic COR correction techniques. In this paper, we propose a revised variance-based algorithm to find the correct COR position automatically prior to tomographic reconstruction. The algorithm was tested on both simulated phantoms and acquired datasets, and our results show improved reconstruction accuracy.

High resolution optical projection tomography platform for multispectral imaging of the mouse gut

Optical projection tomography (OPT) is a powerful tool for three-dimensional imaging of mesoscopic biological samples with great use for biomedical phenotyping studies. We present a fluorescent OPT platform that enables direct visualization of biological specimens and processes at a centimeter scale with high spatial resolution, as well as fast data throughput and reconstruction. We demonstrate nearly isotropic sub-28 µm resolution over more than 60 mm3 after reconstruction of a single acquisition. Our setup is optimized for imaging the mouse gut at multiple wavelengths. Thanks to a new sample preparation protocol specifically developed for gut specimens, we can observe the spatial arrangement of the intestinal villi and the vasculature network of a 3-cm long healthy mouse gut. Besides the blood vessel network surrounding the gastrointestinal tract, we observe traces of vasculature at the villi ends close to the lumen. The combination of rapid acquisition and a large field of view with high spatial resolution in 3D mesoscopic imaging holds an invaluable potential for gastrointestinal pathology research.

Frame localisation optical projection tomography

We present a tomographic reconstruction algorithm (flOPT), which is applied to Optical Projection Tomography (OPT) images, that is robust to mechanical jitter and systematic angular and spatial drift. OPT relies on precise mechanical rotation and is less mechanically stable than large-scale computer tomography (CT) scanning systems, leading to reconstruction artefacts. The algorithm uses multiple (5+) tracked fiducial beads to recover the sample pose and the image rays are then back-projected at each orientation. The quality of the image reconstruction using the proposed algorithm shows an improvement when compared to the Radon transform. Moreover, when adding a systematic spatial and angular mechanical drift, the reconstruction shows a significant improvement over the Radon transform.

zOPT: an open source optical projection tomography system and methods for rapid 3D zebrafish imaging

Optical projection tomography (OPT) is a 3D imaging alternative to conventional microscopy which allows imaging of millimeter-sized object with isotropic micrometer resolution. The zebrafish is an established model organism and an important tool used in genetic and chemical screening. The size and optical transparency of the embryo and larva makes them well suited for imaging using OPT. Here, we present an open-source implementation of an OPT platform, built around a customized sample stage, 3D-printed parts and open source algorithms optimized for the system. We developed a versatile automated workflow including a two-step image processing approach for correcting the center of rotation and generating accurate 3D reconstructions. Our results demonstrate high-quality 3D reconstruction using synthetic data as well as real data of live and fixed zebrafish. The presented 3D-printable OPT platform represents a fully open design, low-cost and rapid loading and unloading of samples. Our system offers the opportunity for researchers with different backgrounds to setup and run OPT for large scale experiments, particularly in studies using zebrafish larvae as their key model organism.

Gaussian Light Model in Brightfield Optical Projection Tomography

This study focuses on improving the reconstruction process of the brightfield optical projection tomography (OPT). OPT is often described as the optical equivalent of X-ray computed tomography, but based on visible light. The detection optics used to collect light in OPT focus on a certain distance and induce blurring in those features out of focus. However, the conventionally used inverse Radon transform assumes an absolute focus throughout the propagation axis. In this study, we model the focusing properties of the detection by coupling Gaussian beam model (GBM) with the Radon transform. The GBM enables the construction of a projection operator that includes modeling of the blurring caused by the light beam. We also introduce the concept of a stretched GBM (SGBM) in which the Gaussian beam is scaled in order to avoid the modeling errors related to the determination of the focal plane. Furthermore, a thresholding approach is used to compress memory usage. We tested the GBM and SGBM approaches using simulated and experimental data in mono- and multifocal modes. When compared with the traditionally used filtered backprojection algorithm, the iteratively computed reconstructions, including the Gaussian models GBM and SGBM, provided smoother images with higher contrast.

Supervised learning to quantify amyloidosis in whole brains of an Alzheimer's disease mouse model acquired with optical projection tomography

Alzheimer's disease (AD) is characterized by amyloidosis of brain tissues. This phenomenon is studied with genetically-modified mouse models. We propose a method to quantify amyloidosis in whole 5xFAD mouse brains, a model of AD. We use optical projection tomography (OPT) and a random forest voxel classifier to segment and measure amyloid plaques. We validate our method in a preliminary cross-sectional study, where we measure 6136 ± 1637, 8477 ± 3438, and 17267 ± 4241 plaques (AVG ± SD) at 11, 17, and 31 weeks. Overall, this method can be used in the evaluation of new treatments against AD.

A mathematical model and iterative inversion for fluorescent optical projection tomography

Solving the fluorophore distribution in a tomographic setting has been difficult because of the lack of physically meaningful and computationally applicable propagation models. This study concentrates on the direct modelling of fluorescence signals in optical projection tomography (OPT), and on the corresponding inverse problem. The reconstruction problem is solved using emission projections corresponding to a series of rotational imaging positions of the sample. Similarly to the bright field OPT bearing resemblance with the transmission x-ray computed tomography, the fluorescent mode OPT is analogous to x-ray fluorescence tomography (XFCT). As an improved direct model for the fluorescent OPT, we derive a weighted Radon transform based on the XFCT literature. Moreover, we propose a simple and fast iteration scheme for the slice-wise reconstruction of the sample. The developed methods are applied in both numerical experiments and inversion of fluorescent OPT data from a zebrafish embryo. The results demonstrate the importance of propagation modelling and our analysis provides a flexible modelling framework for fluorescent OPT that can easily be modified to adapt to different imaging setups.

Regularized reconstruction based on joint L1 and total variation for sparse-view cone-beam X-ray luminescence computed tomography

As an emerging hybrid imaging modality, cone-beam X-ray luminescence computed tomography (CB-XLCT) has been proposed based on the development of X-ray excitable nanoparticles. Owing to the high degree of absorption and scattering of light through tissues, the CB-XLCT inverse problem is inherently ill-conditioned. Appropriate priors or regularizations are needed to facilitate reconstruction and to restrict the search space to a specific solution set. Typically, the goal of CB-XLCT reconstruction is to get the distributions of nanophosphors in the imaging object. Considering that the distributions of nanophosphors inside bodies preferentially accumulate in specific areas of interest, the reconstruction of XLCT images is usually sparse with some locally smoothed high-intensity regions. Therefore, a combination of the L₁ and total variation regularization is designed to improve the imaging quality of CB-XLCT in this study. The L₁ regularization is used for enforcing the sparsity of the reconstructed images and the total variation regularization is used for maintaining the local smoothness of the reconstructed image. The implementation of this method can be divided into two parts. First, the reconstruction image was reconstructed based on the fast iterative shrinkage-thresholding (FISTA) algorithm, then the reconstruction image was minimized by the gradient descent method. Numerical simulations and phantom experiments indicate that compared with the traditional ART, ADAPTIK and FISTA methods, the proposed method demonstrates its advantage in improving spatial resolution and reducing imaging time.

Cone-beam x-ray luminescence computed tomography based on x-ray absorption dosage

With the advances of x-ray excitable nanophosphors, x-ray luminescence computed tomography (XLCT) has become a promising hybrid imaging modality. In particular, a cone-beam XLCT (CB-XLCT) system has demonstrated its potential in in vivo imaging with the advantage of fast imaging speed over other XLCT systems. Currently, the imaging models of most XLCT systems assume that nanophosphors emit light based on the intensity distribution of x-ray within the object, not completely reflecting the nature of the x-ray excitation process. To improve the imaging quality of CB-XLCT, an imaging model that adopts an excitation model of nanophosphors based on x-ray absorption dosage is proposed in this study. To solve the ill-posed inverse problem, a reconstruction algorithm that combines the adaptive Tikhonov regularization method with the imaging model is implemented for CB-XLCT reconstruction. Numerical simulations and phantom experiments indicate that compared with the traditional forward model based on x-ray intensity, the proposed dose-based model could improve the image quality of CB-XLCT significantly in terms of target shape, localization accuracy, and image contrast. In addition, the proposed model behaves better in distinguishing closer targets, demonstrating its advantage in improving spatial resolution.

Optical projection tomography for rapid whole mouse brain imaging

In recent years, three-dimensional mesoscopic imaging has gained significant importance in life sciences for fundamental studies at the whole-organ level. In this manuscript, we present an optical projection tomography (OPT) method designed for imaging of the intact mouse brain. The system features an isotropic resolution of ~50 µm and an acquisition time of four to eight minutes, using a 3-day optimized clearing protocol. Imaging of the brain autofluorescence in 3D reveals details of the neuroanatomy, while the use of fluorescent labels displays the vascular network and amyloid deposition in 5xFAD mice, an important model of Alzheimer's disease (AD). Finally, the OPT images are compared with histological slices.

Optical projection tomography via phase retrieval algorithms

We describe a computational method for accurate, quantitative tomographic reconstructions in Optical Projection Tomography, based on phase retrieval algorithms. Our method overcomes limitations imposed by light scattering in opaque tissue samples under the memory effect regime, as well as reduces artifacts due to mechanical movements, misalignments or vibrations. We make use of Gerchberg-Saxton algorithms, calculating first the autocorrelation of the object and then retrieving the associated phase under four numerically simulated measurement conditions. By approaching the task in such a way, we avoid the projection alignment procedure, exploiting the fact that the autocorrelation sinogram is always aligned and centered. We thus propose two new, projection-based, tomographic imaging flowcharts that allow registration-free imaging of opaque biological specimens and unlock three-dimensional tomographic imaging of hidden objects. Two main reconstruction approaches are discussed in the text, focusing on their efficiency in the tomographic retrieval and discussing their applicability under four different numerical experiments.

Phase-Retrieved Tomography enables Mesoscopic imaging of Opaque Tumor Spheroids

We present a new Phase-Retrieved Tomography (PRT) method to radically improve mesoscopic imaging at regimes beyond one transport mean-free-path and achieve high resolution, uniformly throughout the volume of opaque samples. The method exploits multi-view acquisition in a hybrid Selective Plane Illumination Microscope (SPIM) and Optical Projection Tomography (OPT) setup and a three-dimensional Gerchberg-Saxton phase-retrieval algorithm applied in 3D through the autocorrelation sinogram. We have successfully applied this innovative protocol to image optically dense 3D cell cultures in the form of tumor spheroids, highly versatile models to study cancer behavior and response to chemotherapy. We have thus achieved a significant improvement of resolution in depths not yet accessible with the currently used methods in SPIM/OPT, while overcoming all registration and alignment problems inherent to these techniques.

Cone Beam X-ray Luminescence Computed Tomography Based on Bayesian Method

X-ray luminescence computed tomography (XLCT), which aims to achieve molecular and functional imaging by X-rays, has recently been proposed as a new imaging modality. Combining the principles of X-ray excitation of luminescence-based probes and optical signal detection, XLCT naturally fuses functional and anatomical images and provides complementary information for a wide range of applications in biomedical research. In order to improve the data acquisition efficiency of previously developed narrow-beam XLCT, a cone beam XLCT (CB-XLCT) mode is adopted here to take advantage of the useful geometric features of cone beam excitation. Practically, a major hurdle in using cone beam X-ray for XLCT is that the inverse problem here is seriously ill-conditioned, hindering us to achieve good image quality. In this paper, we propose a novel Bayesian method to tackle the bottleneck in CB-XLCT reconstruction. The method utilizes a local regularization strategy based on Gaussian Markov random field to mitigate the ill-conditioness of CB-XLCT. An alternating optimization scheme is then used to automatically calculate all the unknown hyperparameters while an iterative coordinate descent algorithm is adopted to reconstruct the image with a voxel-based closed-form solution. Results of numerical simulations and mouse experiments show that the self-adaptive Bayesian method significantly improves the CB-XLCT image quality as compared with conventional methods.

Fast multislice fluorescence molecular tomography using sparsity-inducing regularization

Fluorescence molecular tomography (FMT) is a rapidly growing imaging method that facilitates the recovery of small fluorescent targets within biological tissue. The major challenge facing the FMT reconstruction method is the ill-posed nature of the inverse problem. In order to overcome this problem, the acquisition of large FMT datasets and the utilization of a fast FMT reconstruction algorithm with sparsity regularization have been suggested recently. Therefore, the use of a joint L1/total-variation (TV) regularization as a means of solving the ill-posed FMT inverse problem is proposed. A comparative quantified analysis of regularization methods based on L1-norm and TV are performed using simulated datasets, and the results show that the fast composite splitting algorithm regularization method can ensure the accuracy and robustness of the FMT reconstruction. The feasibility of the proposed method is evaluated in an in vivo scenario for the subcutaneous implantation of a fluorescent-dye-filled capillary tube in a mouse, and also using hybrid FMT and x-ray computed tomography data. The results show that the proposed regularization overcomes the difficulties created by the ill-posed inverse problem.

Polarization-sensitive optical projection tomography for muscle fiber imaging

Optical projection tomography (OPT) is a tool used for three-dimensional imaging of millimeter-scale biological samples, with the advantage of exhibiting isotropic resolution typically in the micron range. OPT can be divided into two types: transmission OPT (tOPT) and emission OPT (eOPT). Compared with eOPT, tOPT discriminates different tissues based on their absorption coefficient, either intrinsic or after specific staining. However, it fails to distinguish muscle fibers whose absorption coefficients are similar to surrounding tissues. To circumvent this problem, in this article we demonstrate a polarization sensitive OPT system which improves the detection and 3D imaging of muscle fibers by using polarized light. We also developed image acquisition and processing protocols that, together with the system, enable the clear visualization of muscles. Experimental results show that the muscle fibers of diaphragm and stomach, difficult to be distinguished in regular tOPT, were clearly displayed in our system, proving its potential use. Moreover, polarization sensitive OPT was fused with tOPT to investigate the stomach tissue comprehensively. Future applications of polarization sensitive OPT could be imaging other fiber-like structures such as myocardium or other tissues presenting high optical anisotropy.

A projection selection method to improve image quality in optical projection tomography

Optical projection tomography (OPT) is a very important imaging tool for a mesoscopic-scale. It can provide three dimensional (3D) transmission and emission imaging. However, high-resolution OPT is limited in depth of field (DOF) due to a high numerical aperture, which causes a poor performance of OPT in imaging large samples. Moreover, it is difficult to tune the focus plane (FP) to a fixed position where OPT always has the best image quality in different directions. To address these problems, we developed a projection selection method to improve DOF in OPT. In each direction, our method automatically selects the best projection from several projections with different FP. Then, we use a series of selected projections for 3D reconstruction. The experimental results demonstrate that our method can improve the image quality comparing to a fixed FP. Moreover, our method is flexible to be used in other OPT setups by adding a linear stage.

In-vivo optical tomography of small scattering specimens: time-lapse 3D imaging of the head eversion process in Drosophila melanogaster

Even though in vivo imaging approaches have witnessed several new and important developments, specimens that exhibit high light scattering properties such as Drosophila melanogaster pupae are still not easily accessible with current optical imaging techniques, obtaining images only from subsurface features. This means that in order to obtain 3D volumetric information these specimens need to be studied either after fixation and a chemical clearing process, through an imaging window - thus perturbing physiological development -, or during early stages of development when the scattering contribution is negligible. In this paper we showcase how Optical Projection Tomography may be used to obtain volumetric images of the head eversion process in vivo in Drosophila melanogaster pupae, both in control and headless mutant specimens. Additionally, we demonstrate the use of Helical Optical Projection Tomography (hOPT) as a tool for high throughput 4D-imaging of several specimens simultaneously.

Optical projection tomography as a tool for 3D imaging of hydrogels

An Optical Projection Tomography (OPT) system was developed and optimized to image 3D tissue engineered products based in hydrogels. We develop pre-reconstruction algorithms to get the best result from the reconstruction procedure, which include correction of the illumination and determination of sample center of rotation (CoR). Existing methods for CoR determination based on the detection of the maximum variance of reconstructed slices failed, so we develop a new CoR search method based in the detection of the variance sharpest local maximum. We show the capabilities of the system to give quantitative information of different types of hydrogels that may be useful in its characterization.

Analysis of the rotational center location method in Optical Projection Tomography

In Optical Projection Tomography (OPT), if the rotational center deviates from the central line of the image and this offset is not corrected during the reconstruction, serious blurring will happen in the final 3-dimensional (3D) result. Therefore, the high-precision rotational center location method is very important for OPT. However, existing methods are inconvenient because they need active participation during the location process. Thus, the automated and fast rotational center location method is in great demand. In preliminary work, we proposed an automated rotational center location method which consisted of a high Specimen Signal Intensity (SSI) sinogram selection and a coarse-fine search. Our method had an accuracy of about 1/4 pixel. However, further robustness analysis of our method is lacking. In this paper, we have investigated its location errors on sinograms with various SSIs and analyzed whether it was effective to use high SSI sinograms for rotational center location. Moreover, we have also discussed the relationship between location errors and the starting rotational angles. The experimental results showed that our coarse-fine method was robust under different starting angles. Meanwhile, the high SSI sinogram selection scheme improved the location precision.