Showing papers by "Richard M. Leahy published in 2009"

A three-dimensional multispectral fluorescence optical tomography imaging system for small animals based on a conical mirror design

Abstract: We have developed a three dimensional (3D) multispectral fluorescence optical tomography small animal imaging system with an innovative geometry using a truncated conical mirror, allowing simultaneous viewing of the entire surface of the animal by an EMCCD camera. A conical mirror collects photons approximately three times more efficiently than a flat mirror. An x-y mirror scanning system makes it possible to scan a collimated excitation laser beam to any location on the mouse surface. A pattern of structured light incident on the small animal surface is used to extract the surface geometry for reconstruction. A finite element based algorithm is applied to model photon propagation in the turbid media and a preconditioned conjugate gradient (PCG) method is used to solve the large linear system matrix. The reconstruction algorithm and the system feasibility are evaluated by phantom experiments. These experiments show that multispectral measurements improve the spatial resolution of reconstructed images. Finally, an in vivo imaging study of a xenograft tumor in a mouse shows good correlation of the reconstructed image with the location of the fluorescence probe as determined by subsequent optical imaging of cryosections of the mouse.

Information theoretic regularization in diffuse optical tomography

Abstract: Diffuse optical tomography (DOT) retrieves the spatially distributed optical characteristics of a medium from external measurements. Recovering the parameters of interest involves solving a nonlinear and highly ill-posed inverse problem. This paper examines the possibility of regularizing DOT via the introduction of a priori information from alternative high-resolution anatomical modalities, using the information theory concepts of mutual information (MI) and joint entropy (JE). Such functionals evaluate the similarity between the reconstructed optical image and the prior image while bypassing the multimodality barrier manifested as the incommensurate relation between the gray value representations of corresponding anatomical features in the two modalities. By introducing structural information, we aim to improve the spatial resolution and quantitative accuracy of the solution. We provide a thorough explanation of the theory from an imaging perspective, accompanied by preliminary results using numerical simulations. In addition we compare the performance of MI and JE. Finally, we have adopted a method for fast marginal entropy evaluation and optimization by modifying the objective function and extending it to the JE case. We demonstrate its use on an image reconstruction framework and show significant computational savings.

Excitation spectroscopy in multispectral optical fluorescence tomography: methodology, feasibility and computer simulation studies

Abstract: Molecular probes used for in vivo optical fluorescence tomography (OFT) studies in small animals are typically chosen such that their emission spectra lie in the 680-850 nm wavelength range. This is because tissue attenuation in this spectral band is relatively low, allowing optical photons even from deep sites in tissue to reach the animal surface and consequently be detected by a CCD camera. The wavelength dependence of tissue optical properties within the 680-850 nm band can be exploited for emitted light by measuring fluorescent data via multispectral approaches and incorporating the spectral dependence of these optical properties into the OFT inverse problem-that of reconstructing underlying 3D fluorescent probe distributions from optical data collected on the animal surface. However, in the aforementioned spectral band, due to only small variations in the tissue optical properties, multispectral emission data, though superior for image reconstruction compared to achromatic data, tend to be somewhat redundant. A different spectral approach for OFT is to capitalize on the larger variations in the optical properties of tissue for excitation photons than for the emission photons by using excitation at multiple wavelengths as a means of decoding source depth in tissue. The full potential of spectral approaches in OFT can be realized by a synergistic combination of these two approaches, that is, exciting the underlying fluorescent probe at multiple wavelengths and measuring emission data multispectrally. In this paper, we describe a method that incorporates both excitation and emission spectral information into the OFT inverse problem. We describe a linear algebraic formulation of the multiple wavelength illumination-multispectral detection forward model for OFT and compare it to models that use only excitation at multiple wavelengths or those that use only multispectral detection techniques. This study is carried out in a realistic inhomogeneous mouse atlas using singular value decomposition and analysis of reconstructed spatial resolution versus noise. For simplicity, quantitative results have been shown for one representative fluorescent probe (Alexa 700) and effects due to tissue autofluorescence have not been taken into account. We also demonstrate the performance of our method for 3D reconstruction of tumors in a simulated mouse model of metastatic human hepatocellular carcinoma.

Exact and approximate Fourier rebinning of PET data from time-of-flight to non time-of-flight

Abstract: The image reconstruction problem for fully 3D TOF PET is challenging because of the large data sizes involved. One approach to this problem is to first rebin the data into one of the following lower dimensional formats: 2D TOF, 3D non TOF or 2D non TOF. Here we present a unified framework based on a generalized projection slice theorem for TOF data that can be used to compute each of these mappings. We use this framework to develop approaches for rebinning into non TOF formats without significant loss of information. We first derive the exact mappings and then describe approximations which address the missing data problem for oblique sinograms. We evaluate the performance of approximate rebinning using Monte Carlo simulations. Our results show that rebinning into non TOF sinograms retains significant SNR advantages over sinograms collected without TOF information.

A Parameterization-Based Numerical Method for Isotropic and Anisotropic Diffusion Smoothing on Non-Flat Surfaces

Abstract: Neuroimaging data, such as 3D maps of cortical thickness or neural activation, can often be analyzed more informatively with respect to the cortical surface rather than the entire volume of the brain. Any cortical surface-based analysis should be carried out using computations in the intrinsic geometry of the surface rather than using the metric of the ambient 3D space. We present parameterization-based numerical methods for performing isotropic and anisotropic filtering on triangulated surface geometries. In contrast to existing FEM-based methods for triangulated geometries, our approach accounts for the metric of the surface. In order to discretize and numerically compute the isotropic and anisotropic geometric operators, we first parameterize the surface using a p-harmonic mapping. We then use this parameterization as our computational domain and account for the surface metric while carrying out isotropic and anisotropic filtering. To validate our method, we compare our numerical results to the analytical expression for isotropic diffusion on a spherical surface. We apply these methods to smoothing of mean curvature maps on the cortical surface, a step commonly required for analysis of gyrification or for registering surface-based maps across subjects.

Spatial Distortion Correction and Crystal Identification for MRI-Compatible Position-Sensitive Avalanche Photodiode-Based PET Scanners

Abstract: Position-sensitive avalanche photodiodes (PSAPDs) are gaining widespread acceptance in modern PET scanner designs, and owing to their relative insensitivity to magnetic fields, especially in those that are MRI-compatible. Flood histograms in PET scanners are used to determine the crystal of annihilation photon interaction and hence, for detector characterization and routine quality control. For PET detectors that use PSAPDs, flood histograms show a characteristic pincushion distortion when Anger logic is used for event positioning. A small rotation in the flood histogram is also observed when the detectors are placed in a magnetic field. We first present a general purpose automatic method for spatial distortion correction for flood histograms of PSAPD-based PET detectors when placed both inside and outside a MRI scanner. Analytical formulas derived for this scheme are based on a hybrid approach that combines desirable properties from two existing event positioning schemes. The rotation of the flood histogram due to the magnetic field is determined iteratively and is accounted for in the scheme. We then provide implementation details of a method for crystal identification we have previously proposed and evaluate it for cases when the PET detectors are both outside and in a magnetic field. In this scheme, Fourier analysis is used to generate a lower-order spatial approximation of the distortion-corrected PSAPD flood histogram, which we call the ldquotemplaterdquo. The template is then registered to the flood histogram using a diffeomorphic iterative intensity-based warping scheme. The calculated deformation field is then applied to the segmentation of the template to obtain a segmentation of the flood histogram. A manual correction tool is also developed for exceptional cases. We present a quantitative assessment of the proposed distortion correction scheme and crystal identification method against conventional methods. Our results indicate that our proposed methods lead to a large reduction in manual labor and indeed can routinely be used for calibration and characterization studies in MRI-compatible PET scanners based on PSAPDs.

Directed mammalian gene regulatory networks using expression and comparative genomic hybridization microarray data from radiation hybrids

Abstract: Meiotic mapping of quantitative trait loci regulating expression (eQTLs) has allowed the construction of gene networks. However, the limited mapping resolution of these studies has meant that genotype data are largely ignored, leading to undirected networks that fail to capture regulatory hierarchies. Here we use high resolution mapping of copy number eQTLs (ceQTLs) in a mouse-hamster radiation hybrid (RH) panel to construct directed genetic networks in the mammalian cell. The RH network covering 20,145 mouse genes had significant overlap with, and similar topological structures to, existing biological networks. Upregulated edges in the RH network had significantly more overlap than downregulated. This suggests repressive relationships between genes are missed by existing approaches, perhaps because the corresponding proteins are not present in the cell at the same time and therefore unlikely to interact. Gene essentiality was positively correlated with connectivity and betweenness centrality in the RH network, strengthening the centrality-lethality principle in mammals. Consistent with their regulatory role, transcription factors had significantly more outgoing edges (regulating) than incoming (regulated) in the RH network, a feature hidden by conventional undirected networks. Directed RH genetic networks thus showed concordance with pre-existing networks while also yielding information inaccessible to current undirected approaches.

A Framework for Brain Registration via Simultaneous Surface and Volume Flow

Abstract: Volumetric registration of brain MR images presents a challenging problem due to the wide variety of sulcal folding patterns. We present a novel volumetric registration method based on an intermediate parameter space in which the shape differences are normalized. First, we generate a 3D harmonic map of each brain volume to unit ball which is used as an intermediate space. Cortical surface features and volumetric intensity are then used to find a simultaneous surface and volume registration. We present a finite element method for the registration by using a tetrahedral volumetric mesh for registering the interior volumetric information and the corresponding triangulated mesh at the surface points. This framework aligns the convoluted sulcal folding patterns as well as the subcortical structures by allowing simultaneous flow of surface and volumes for registration. We describe the methodology and FEM implementation and then evaluate the method in terms of the overlap between segmented structures in coregistered brains.

Lesion Detection in Dynamic FDG-PET Using Matched Subspace Detection

Abstract: We describe a matched subspace detection algorithm to assist in the detection of small tumors in dynamic positron emission tomography (PET) images. The algorithm is designed to differentiate tumors from background using the time activity curves (TACs) that characterize the uptake of PET tracers. TACs are modeled using linear subspaces with additive Gaussian noise. Using TACs from a primary tumor region of interest (ROI) and one or more background ROIs, each identified by a human observer, two linear subspaces are identified. Applying a matched subspace detector to these identified subspaces on a voxel-by-voxel basis throughout the dynamic image produces a test statistic at each voxel which on thresholding indicates potential locations of secondary or metastatic tumors. The detector is derived for three cases: using a single TAC with white noise of unknown variance, using a single TAC with known noise covariance, and detection using multiple TACs within a small ROI with known noise covariance. The noise covariance is estimated for the reconstructed image from the observed sinogram data. To evaluate the proposed method, a simulation-based receiver operating characteristic (ROC) study for dynamic PET tumor detection is designed. The detector uses a dynamic sequence of frame-by-frame 2-D reconstructions as input. We compare the performance of the subspace detectors with that of a Hotelling observer applied to a single frame image and of the Patlak method applied to the dynamic data. We also show examples of the application of each detection approach to clinical PET data from a breast cancer patient with metastatic disease.

Posture matching and elastic registration of a mouse atlas to surface topography range data

Abstract: Estimation of internal mouse anatomy is required for quantitative bioluminescence or fluorescence tomography. However, only surface range data can be recovered from all-optical systems. These data are at times sparse or incomplete. We present a method for fitting an elastically deformable mouse atlas to surface topographic range data acquired by an optical system. In this method, we first match the postures of a deformable atlas and the range data of the mouse being imaged. This is achieved by aligning manually identified landmarks. We then minimize the asymmetric L2 pseudo-distance between the surface of the deformable atlas and the surface topography range data. Once this registration is accomplished, the internal anatomy of the atlas is transformed to the coordinate system of the range data using elastic energy minimization. We evaluated our method by using it to register a digital mouse atlas to a surface model produced from a manually labeled CT mouse data set. Dice coefficents indicated excellent agreement in the brain and heart, with fair agreement in the kidneys and bladder. We also present example results produced using our method to align the digital mouse atlas to surface range data.

Detection of event-related modulations of oscillatory brain activity with multivariate statistical analysis of MEG data.

Abstract: We describe a method to detect brain activation in cortically constrained maps of current density computed from MEG data using multivariate statistical inference. We apply time-frequency (wavelet) analysis to individual epochs to produce dynamic images of brain signal power on the cerebral cortex in multiple time-frequency bands. We form vector observations by concatenating the power in each frequency band, and fit them into separate multivariate linear models for each time band and cortical location with experimental conditions as predictor variables. The resulting Roy's maximum statistic maps are thresholded for significance using permutation tests and the maximum statistic approach. A source is considered significant if it exceeds a statistical threshold, which is chosen to control the familywise error rate, or the probability of at least one false positive, across the cortical surface. We compare and evaluate the multivariate approach with existing univariate approaches to time-frequency MEG signal analysis, both on simulated data and experimental data from an MEG visuomotor task study. Our results indicate that the multivariate method is more powerful than the univariate approach in detecting experimental effects when correlations exist between power across frequency bands. We further describe protected F-tests and linear discriminant analysis to identify individual frequencies that contribute significantly to experimental effects.

Exact and approximate rebinning of time-of-flight pet positron emission tomography data

Abstract: A technique for processing of data from time-of-flight (TOF) PET scanners. The size of TOF PET data may be reduced without significant loss of information through a process called rebinning. The rebinning may use the Fourier transform properties of the measured PET data, taken with respect to the time-of-flight variable, to perform data reduction. Through this rebinning process, TOF PET data may be converted to any of the following reduced representations: 2D TOF PET data, 3D non-TOF PET data, and 2D non-TOF PET data. Mappings may be exact or approximate. Approximate mappings may not require a Fourier transform in the axial direction which may have advantages when used with PET scanners of limited axial extent. Once TOF PET data is reduced in size using this rebinning, PET images may be reconstructed with hardware and/or software that is substantially less complex and that may run substantially faster in comparison to reconstruction from the original non-rebinned data.

Direct estimation of patlak parameters from list mode PET data

Abstract: We describe a method to directly estimate Patlak parameters from list mode data. Based on the Patlak model, the uptake rate function of each voxel can be written as a linear combination of the blood input function and its integral, with the slope and intercept of the Patlak model as the corresponding weight. The positron emission rate in each voxel is then modeled as an inhomogeneous Poisson process with this rate function. The Patlak parameters are estimated directly from list mode data by maximizing the objective function, formed by the sum of the likelihood of arrival times and a spatial smoothness penalty, using a convergent four dimensional incremental gradient algorithm. Fully four dimensional simulations in a liver phantom demonstrate application of this method to realistic time activity curves.

Optimal illumination patterns for fluorescence tomography

Abstract: Fluorescence tomography has become increasingly popular for detecting molecular targets for imaging gene expression and other cellular processes in vivo in small animal studies. In this imaging modality, multiple sets of data are acquired by illuminating the animal surface with different excitation patterns, each of which produces a distinct spatial pattern of fluorescence. This work addresses one of the most intriguing, yet unsolved, problems of fluorescence tomography, which is to determine how to optimally illuminate the animal surface so as to maximize the information content in the acquired data. The key idea of this work is to parameterize the illumination pattern and to maximize the information content in the data by improving the conditioning of the Fisher information matrix. We formulate our problem as a constrained optimization problem. We compare the performance of different geometric illumination schemes with those generated by this optimization approach using the Digimouse atlas.

Optimization of landmark selection for cortical surface registration

Abstract: Manually labeled landmark sets are often required as inputs for landmark-based image registration. Identifying an optimal subset of landmarks from a training dataset may be useful in reducing the labor intensive task of manual labeling. In this paper, we present a new problem and a method to solve it: given a set of N landmarks, find the k(<; N) best landmarks such that aligning these k landmarks that produce the best overall alignment of all N landmarks. The resulting procedure allows us to select a reduced number of landmarks to be labeled as a part of the registration procedure. We apply this methodology to the problem of registering cerebral cortical surfaces extracted from MRI data. We use manually traced sulcal curves as landmarks in performing inter-subject registration of these surfaces. To minimize the error metric, we analyze the correlation structure of the sulcal errors in the landmark points by modeling them as a multivariate Gaussian process. Selection of the optimal subset of sulcal curves is performed by computing the error variance for the subset of unconstrained landmarks conditioned on the constrained set. We show that the registration error predicted by our method closely matches the actual registration error. The method determines optimal curve subsets of any given size with minimal registration error.

Generalized sidelobe canceller for magnetoencephalography arrays

Abstract: In the last decade, large arrays of sensors for magnetoencephalography (MEG) (and electroencephalography (EEG)) have become more commonplace, allowing new opportunities for the application of beamforming techniques to the joint problems of signal estimation and noise reduction. We introduce a new approach to noise cancellation, the generalized sidelobe canceller (GSC), itself an alternative to the linearly constrained minimum variance (LCMV) algorithm. The GSC framework naturally fits within the other noise reduction techniques that employ real or virtual reference arrays. Using expository human subject data with strong environmental and biological artifacts, we demonstrate a straightforward sequence of steps for practical noise filtering, applicable to any large array sensor design.

Controlling Familywise Error Rate for Matched Subspace Detection in Dynamic FDG PET

Abstract: Detection of small lesions in fluorodeoxyglucose (FDG) positron emission tomography (PET) is limited by image resolution and low signal to noise ratio. We have previously described a matched subspace detection method that uses the time activity curve to distinguish tumors from background in dynamic FDG PET. Applying this algorithm on a voxel by voxel basis throughout the dynamic image produces a test statistic image or ldquomaprdquo which on thresholding indicates the potential locations of secondary or metastatic tumors. In this paper, we describe a thresholding method that controls familywise error rate (FWER) for the matched subspace detection statistical map. The method involves three steps. First, the PET image is segmented into several homogeneous regions. Then, the statistical map is normalized to a zero mean unit variance Gaussian random field. Finally, the images are thresholded at a fixed FWER by estimating their spatial smoothness and applying a random field theory maximum statistic approach. We evaluate this thresholding method using digital phantoms generated from clinical dynamic images. We also present an application of the proposed approach to clinical PET data from a breast cancer patient with metastatic disease.

Optimized weighting for Fourier rebinning of three-dimensional time-of-Flight PET data to non-time-of-flight

Abstract: Time-of-flight (TOF) PET scanners provide the potential for significantly improved signal-to-noise ratio (SNR) and lesion detectability in clinical PET. Therefore, it is likely that TOF will become the standard for clinical whole body PET in the near future. However, fully 3D TOF PET image reconstruction is a challenging task due to the huge data size. One solution to this problem is to rebin TOF data into a lower dimensional format. We have recently developed Fourier rebinning methods for mapping TOF data into non-TOF formats and achieved substantial SNR advantages over sinograms acquired without TOF information. However, such mappings for rebinning into non-TOF formats are not unique and optimization of rebinning methods has not been widely investigated. In this paper we address the question of optimal rebinning in order to make full use of TOF information and consequently to maximize image quality. We focus on FORET-3D, which rebins 3D TOF data into 3D non-TOF sinogram formats without requiring a Fourier transform in the axial direction. We optimize the weighting for FORET-3D using a uniformly minimum variance unbiased (UMVU) estimator under reasonable approximations. We show that the rebinned data with optimal weights are a sufficient statistic for the unknown image, implying that any information loss due to rebinning is as a result only of the approximations used in developing the optimal weighting. We demonstrate using simulated and real phantom TOF data that the optimal rebinning method achieves significant variance reduction and better contrast recovery compared to other rebinning weightings.

Kinetic parameters estimation for heterogeneous tumor model

Abstract: We investigate a heterogeneous kinetic model of tracer uptake in Positron Emission Tomography (PET) for the purposes of improved characterization of small tumors or metastases. Using a mixture model we allow each voxel to contain a mixture of kinetic processes representing different tumor and normal tissue time activity curves and the plasma concentration. We then use a novel nonlinear least squares procedure to estimate the kinetic parameters of these processes from a region of interest consisting of multiple mixture voxels with unknown fractions of these processes. By investigating the Cramer Rao lower bound (CRLB) we determine conditions under which kinetic parameters and mixture fractions can be accurately identified. We also perform Monte Carlo simulations to show that the variance of the rate parameters estimated using nonlinear least squares is close to the bound predicted by our CRLB analysis.

Diffusion optical tomography using entropic priors

Abstract: Diffuse optical tomography (DOT) is a functional imaging modality which aims to retrieve the optical characteristics of the probed tissue, namely light absorption and diffusion. The accurate retrieval of the spatial distribution for each optical characteristic involves the solution of a highly-ill posed, non-linear inverse problem, thus employing a regularization is essential. In this work, we propose an entropic regularization scheme for DOT reconstruction that uses a priori structural information through mutual information (MI) and joint entropy (JE).We compare MI and JE through simulations that illustrate their behavior when the reference and DOT images are not identical in structure. We propose an efficient implementation of these regularizers based on fast Fourier transforms. The method is tested through numerical simulations.

Ultrafast Preconditioned Conjugate Gradient MAP reconstruction for fully 3-D microPET

Abstract: Iterative 3D PET reconstruction represents a very computational challenge due to the large number of lines of response (LOR) collected for each data set. This iterative 3D reconstruction also needs a lot of iterations to achieve an acceptable PET reconstructed image. A Preconditioned Conjugate Gradient (PCG) method was previously shown to have faster convergence rate than expectation maximization (EM) type algorithms. For the microPET, imagea suffer from crystal penetration blurring due to small scanner radius. An exact 2D blur model is needed to achieve high resolution image. A Preconditioned Conjugate Gradient (PCG) method is described for reconstruction of high-resolution 3D images from the microPET Inveon small-animal scanner from Siemens [1, 2, 3]. The projector pair is used as part of a factored system matrix that takes into account detector-pair response by using shift-variant sinogram blur kernels, attenuation correction, and detector efficiency corrections. The system matrix for geometric projection is based on depth dependent solid angle calculation in combination with a spatially variant detector response model. The mircoPET PCG is combined with OSEM to accelerate convergence. This reconstruction model achieves a high resolution animal image; however, it took an hour to reconstruct a frame. Therefore, we describe an ultrafast forward and back projector pair based on Symmetry and SIMD projector (SSP) [4]. The proposed method produces similar quality images when compared to those obtained with the software package from Siemens and requires order of magnitude less computation.

A high sensitivity multi-spectral three-dimensional fluorescence optical tomography system for small animal imaging

Abstract: We have designed a three dimensional (3D) fluorescence optical tomography system for small animal imaging based on an innovative system geometry that uses a truncated conical mirror which permits the entire surface of the animal to be viewed simultaneously by a single CCD camera. Compared with traditional approaches that employ a flat mirror, the conical mirror system has approximately 3 times better measurement sensitivity. By utilizing a fast switching filter wheel (switching time < 100 milliseconds), emission data at multiple wavelengths can be efficiently collected. An array of appropriately shaped neutral density filters, mounted on a linear stage, can be used to increase the system measurement dynamic range by 3 orders of magnitude. An x-y galvo mirror scanning system makes it possible to scan a collimated laser beam to any location on the mouse surface. A pattern of structured light incident on the animal surface is used to extract the surface geometry. A finite element based algorithm is applied to model photon propagation in the turbid media and a preconditioned conjugate gradient (PCG) method is used to solve the large linear system matrix. The reconstruction algorithm and the system performance are evaluated by phantom experiments.