Effects of sampling strategy on image quality in noncontact panoramic fluorescence diffuse optical tomography for small animal imaging

Sensitivity Laplacian Ratio-Based Optimization of the Projection Selection for Diffuse Optical Tomography

BACKGROUND

In diffuse optical tomography, determining the optimal angle between the source and detector is an effective method to reduce the number of projections while maintaining the quality of the reconstructed images. In this study, a new parameter is introduced to evaluate the source-detector geometries.

METHODS

A two-dimensional mesh with the radius of 20 mm and 7987 nodes were built. In each reconstruction, 0.5 mm heterogeneity with the absorption coefficient of 0.06 mm^-1 and the dispersion coefficient of 0.6 mm^-1 was added in different parts of the sample randomly. The relationship between the mean square error (MSE), sensitivity Laplacian ratio (SLR), and sensitivity standard deviation ratio (SSR) was evaluated based on their correlation coefficients. The quality of the images achieved using the optimized projections were compared with that of the full projections for the same depths.

RESULTS

MSE decreases by increasing the SLR magnitudes which indicate that the parameter could be used to evaluate the scanning geometries. There was a negative correlation coefficient (R = -0.76) with the inverse relationship between the SLR and MSE indices. SSR does not have a significant relationship with the quality of the reconstructed images. For each scanning depth, the comparison of the images obtained using the full and optimized-selective projections did not show any considerable difference despite the decrease of the projection numbers in scanning geometry with the optimized-selective projections.

CONCLUSION

The unnecessary projections could be eliminated by placing the detectors at the specific angles, which were determined using the SLR. Thus, a proper compromise between the quality of the reconstructed images and reconstruction time might establish.

Sensitivity Uniformity Ratio as a New Index to Optimize the Scanning Geometry for Fluorescent Molecular Tomography

Background:

Molecular fluorescence imaging is widely used as a noninvasive method to study the cellular and molecular mechanisms. In the optical imaging system, the sensitivity is the change of the intensity received by the detector for the changed optical characteristics (fluorescence) in each sample point. Sensitivity could be considered as a function of imaging geometry. A favor imaging system has a uniform and high-sensitivity coefficient for each point of the sample. In this study, a new parameter was proposed which the optimal angle between the source and detector could be determined based on this parameter.

Methods:

For evaluation of the new method, a two-dimensional mesh with a radius of 20 mm and 5133 nodes was built. In each reconstruction, 0.5-mm fluorescence heterogeneity with a contrast-to-purpose ratio of fluorescence yield of 10 was randomly added at different points of the sample. The source and the detector were simulated in different geometric conditions. The calculations were performed using the NIRFAST and MATLAB software. The relationship between mean squared error (MSE) and sensitivity uniformity ratio (SUR) was evaluated using the correlation coefficient. Finally, based on the new index, an optimal geometrical strategy was introduced.

Results:

There was a negative correlation coefficient (R = −0.78) with the inverse relationship between the SUR and MSE indices. The reconstructed images showed that the better image quality achieved using the optimal geometry for all scanning depths. For the conventional geometry, there is an artifact in the opposite side of the inhomogeneity at the shallow depths, which has been eliminated in the reconstructed images achieved using the optimal geometry.

Conclusion:

The SUR is a powerful computational tool which could be used to determine the optimal angles between the source and detector for each scanning depth.

Optical property uncertainty estimates for spatial frequency domain imaging

Spatial frequency domain imaging (SFDI) is a wide-field diffuse optical imaging modality that has attracted considerable interest in recent years. Typically, diffuse reflectance measurements of spatially modulated light are used to quantify the optical absorption and reduced scattering coefficients of tissue, and with these, chromophore concentrations are extracted. However, uncertainties in estimated absorption and reduced scattering coefficients are rarely reported, and we know of no method capable of providing these when look-up table (LUT) algorithms are used to recover the optical properties. We present a method to generate optical property uncertainty estimates from knowledge of diffuse reflectance measurement errors. By employing the Cramér-Rao bound, we can quickly and efficiently explore theoretical SFDI performance as a function of spatial frequencies and sample optical properties, allowing us to optimize spatial frequency selection for a given application. In practice, we can also obtain useful uncertainty estimates for optical properties recovered with a two-frequency LUT algorithm, as we demonstrate with tissue-simulating phantom and in vivo experiments. Finally, we illustrate how absorption coefficient uncertainties can be propagated forward to yield uncertainties for chromophore concentrations, which could significantly impact the interpretation of experimental results.

On the use of the Cramér-Rao lower bound for diffuse optical imaging system design

We evaluated the potential of the Cramér-Rao lower bound (CRLB) to serve as a design metric for diffuse optical imaging systems. The CRLB defines the best achievable precision of any estimator for a given data model; it is often used in the statistical signal processing community for feasibility studies and system design. Computing the CRLB requires inverting the Fisher information matrix (FIM), however, which is usually ill-conditioned (and often underdetermined) in the case of diffuse optical tomography (DOT). We regularized the FIM by assuming that the inhomogeneity to be imaged was a point target and assessed the ability of point-target CRLBs to predict system performance in a typical DOT setting in silico. Our reconstructions, obtained with a common iterative algebraic technique, revealed that these bounds are not good predictors of imaging performance across different system configurations, even in a relative sense. This study demonstrates that agreement between the trends predicted by the CRLBs and imaging performance obtained with reconstruction algorithms that rely on a different regularization approach cannot be assumed a priori. Moreover, it underscores the importance of taking into account the intended regularization method when attempting to optimize source-detector configurations.

Super-resolution method for arbitrary retrospective sampling in fluorescence tomography with raster scanning photodetectors

Dense spatial sampling is required in high-resolution optical imaging and many other biomedical optical imaging methods, such as diffuse optical imaging. Arrayed photodetectors, in particular charge coupled device cameras are commonly used mainly because of their high pixel count. Nonetheless, discrete-element photodetectors, such as photomultiplier tubes, are often desirable in many performance-demanding imaging applications. However, utilization of the discrete-element photodetectors typically requires raster scan to achieve arbitrary retrospective sampling with high density. Care must be taken in using the relatively large sensitive areas of discrete-element photodetectors to densely sample the image plane. In addition, off-line data analysis and image reconstruction often require full-field sampling. Pixel-by-pixel scanning is not only slow but also unnecessary in diffusion-limited imaging. We propose a super-resolution method that can recover the finer features of an image sampled with a coarse-scale sensor. This generalpurpose method was established on the spatial transfer function of the photodetector-lens system, and achieved super-resolution by inversion of this linear transfer function. Regularized optimization algorithms were used to achieve optimized deconvolution. Compared to the uncorrected blurred image, the proposed super-resolution method significantly improved image quality in terms of resolution and quantitation. Using this reconstruction method, the acquisition speed with a scanning photodetector can be dramatically improved without significantly sacrificing sampling density or flexibility.

Investigations on X-ray luminescence CT for small animal imaging

X-ray Luminescence CT (XLCT) is a hybrid imaging modality combining x-ray and optical imaging in which x-ray luminescent nanophosphors (NPs) are used as emissive imaging probes. NPs are easily excited using common CT energy x-ray beams, and the NP luminescence is efficiently collected using sensitive light based detection systems. XLCT can be recognized as a close analog to fluorescence diffuse optical tomography (FDOT). However, XLCT has remarkable advantages over FDOT due to the substantial excitation penetration depths provided by x-rays relative to laser light sources, long term photo-stability of NPs, and the ability to tune NP emission within the NIR spectral window. Since XCLT uses an x-ray pencil beam excitation, the emitted light can be measured and back-projected along the x-ray path during reconstruction, where the size of the X-ray pencil beam determines the resolution for XLCT. In addition, no background signal competes with NP luminescence (i.e., no auto fluorescence) in XLCT. Currently, no small animal XLCT system has been proposed or tested. This paper investigates an XLCT system built and integrated with a dual source micro-CT system. Two novel sampling paradigms that result in more efficient scanning are proposed and tested via simulations. Our preliminary experimental results in phantoms indicate that a basic CT-like reconstruction is able to recover a map of the NP locations and differences in NP concentrations. With the proposed dual source system and faster scanning approaches, XLCT has the potential to revolutionize molecular imaging in preclinical studies.

High-resolution reconstruction of fluorescent inclusions in mouse thorax using anatomically guided sampling and parallel Monte Carlo computing

We present a method for high-resolution reconstruction of fluorescent images of the mouse thorax. It features an anatomically guided sampling method to retrospectively eliminate problematic data and a parallel Monte Carlo software package to compute the Jacobian matrix for the inverse problem. The proposed method was capable of resolving microliter-sized femtomole amount of quantum dot inclusions closely located in the middle of the mouse thorax. The reconstruction was verified against co-registered micro-CT data. Using the proposed method, the new system achieved significantly higher resolution and sensitivity compared to our previous system consisting of the same hardware. This method can be applied to any system utilizing similar imaging principles to improve imaging performance.

Highly efficient detection in fluorescence tomography of quantum dots using time-gated acquisition and ultrafast pulsed laser

Quantum dots (QDs) are widely used in fluorescence tomography due to its unique advantages. Despite the very high quantum efficiency of the QDs, low fluorescent signal and autofluorescence are the most fundamental limitations in optical data acquisition. These limitations are particularly detrimental to image reconstruction for animal imaging, e.g., free-space in vivo fluorescence tomography. In animals studies, fluorescent emission from exogenous fluorescent probes (e.g. QDs) cannot be effectively differentiated from endogenous broad-spectral substances (mostly proteins) using optical filters. In addition, a barrow-band fluorescent filter blocks the majority of the fluorescent light and thus makes signal acquisition very inefficient. We made use of the long fluorescent lifetime of the QDs to reject the optical signal due to the excitation light pulse, and therefore eliminated the need for a fluorescent filter during acquisition. Fluorescent emission from the QDs was excited with an ultrafast pulsed laser, and was detected using a time-gated image intensifier. A tissue-simulating imaging phantom was used to validate the proposed method. Compared to the standard acquisition method that uses a narrow-band fluorescent filter, the proposed method is significantly more efficient in data acquisition (by a factor of >10 in terms of fluorescent signal intensity) and demonstrated reduction in autofluorescence. No additional imaging artifact was observed in the tomographic reconstruction.

Free-space fluorescence tomography with adaptive sampling based on anatomical information from microCT

Image reconstruction is one of the main challenges for fluorescence tomography. For in vivo experiments on small animals, in particular, the inhomogeneous optical properties and irregular surface of the animal make free-space image reconstruction challenging because of the difficulties in accurately modeling the forward problem and the finite dynamic range of the photodetector. These two factors are fundamentally limited by the currently available forward models and photonic technologies. Nonetheless, both limitations can be significantly eased using a signal processing approach. We have recently constructed a free-space panoramic fluorescence diffuse optical tomography system to take advantage of co-registered microCT data acquired from the same animal. In this article, we present a data processing strategy that adaptively selects the optical sampling points in the raw 2-D fluorescent CCD images. Specifically, the general sampling area and sampling density are initially specified to create a set of potential sampling points sufficient to cover the region of interest. Based on 3-D anatomical information from the microCT and the fluorescent CCD images, data points are excluded from the set when they are located in an area where either the forward model is known to be problematic (e.g., large wrinkles on the skin) or where the signal is unreliable (e.g., saturated or low signal-to-noise ratio). Parallel Monte Carlo software was implemented to compute the sensitivity function for image reconstruction. Animal experiments were conducted on a mouse cadaver with an artificial fluorescent inclusion. Compared to our previous results using a finite element method, the newly developed parallel Monte Carlo software and the adaptive sampling strategy produced favorable reconstruction results.

Three-dimensional reconstruction in free-space whole-body fluorescence tomography of mice using optically reconstructed surface and atlas anatomy

We present a 3-D image reconstruction method for free-space fluorescence tomography of mice using hybrid anatomical prior information. Specifically, we use an optically reconstructed surface of the experimental animal and a digital mouse atlas to approximate the anatomy of the animal as structural priors to assist image reconstruction. Experiments are carried out on a cadaver of a nude mouse with a fluorescent inclusion (2.4-mm-diam cylinder) implanted in the chest cavity. Tomographic fluorescence images are reconstructed using an iterative algorithm based on a finite element method. Coregistration of the fluorescence reconstruction and micro-CT (computed tomography) data acquired afterward show good localization accuracy (localization error 1.2+/-0.6 mm). Using the optically reconstructed surface, but without the atlas anatomy, image reconstruction fails to show the fluorescent inclusion correctly. The method demonstrates the utility of anatomical priors in support of free-space fluorescence tomography.