Margaret J. Eppstein

Fluorescence-enhanced optical imaging in large tissue volumes using a gain-modulated ICCD camera

A novel image-intensified charge-coupled device (ICCD) imaging system has been developed to perform 3D fluorescence tomographic imaging in the frequency-domain using near-infrared contrast agents. The imager is unique since it (i) employs a large tissue-mimicking phantom, which is shaped and sized to resemble a female breast and part of the extended chest-wall region, and (ii) enables rapid data acquisition in the frequency-domain by using a gain-modulated ICCD camera. Diffusion model predictions are compared to experimental measurements using two different referencing schemes under two different experimental conditions of perfect and imperfect uptake of fluorescent agent into a target. From these experimental measurements, three-dimensional images of fluorescent absorption were reconstructed using a computationally efficient variant of the approximate extended Kalman filter algorithm. The current work represents the first time that 3D fluorescence-enhanced optical tomographic reconstructions have been achieved from experimental measurements of the time-dependent light propagation on a clinically relevant breast-shaped tissue phantom using a gain-modulated ICCD camera.

Three-dimensional, Bayesian image reconstruction from sparse and noisy data sets: Near-infrared fluorescence tomography

A method for inverting measurements made on the surfaces of tissues for recovery of interior optical property maps is demonstrated for sparse near-infrared (NIR) fluorescence measurement sets on large tissue-simulating volumes with highly variable signal-to-noise ratio. A Bayesian minimum-variance reconstruction algorithm compensates for the spatial variability in signal-to-noise ratio that must be expected to occur in actual NIR contrast-enhanced diagnostic medical imaging. Image reconstruction is demonstrated by using frequency-domain photon migration measurements on 256-cm3 tissue-mimicking phantoms containing none, one, or two 1-cm3 heterogeneities with 50- to 100-fold greater concentration of Indocyanine Green dye over background levels. The spatial parameter estimate of absorption owing to the dye was reconstructed from only 160 to 296 surface measurements of emission light at 830 nm in response to incident 785-nm excitation light modulated at 100 MHz. Measurement error of acquired fluence at fluorescent emission wavelengths is shown to be highly variable. Convergence and quality of image reconstructions are improved by Bayesian conditioning incorporating (i) experimentally determined measurement error variance, (ii) recursively updated estimates of parameter uncertainty, and (iii) dynamic zonation. The results demonstrate that, to employ NIR fluorescence-enhanced optical imaging for large volumes, reconstruction approaches must account for the large range of signal-to-noise ratio associated with the measurements.

A “Random Chemistry” Algorithm for Identifying Collections of Multiple Contingencies That Initiate Cascading Failure

This paper describes a stochastic “Random Chemistry” (RC) algorithm to identify large collections of multiple (n-k) contingencies that initiate large cascading failures in a simulated power system. The method requires only O(log (n)) simulations per contingency identified, which is orders of magnitude faster than random search of this combinatorial space. We applied the method to a model of cascading failure in a power network with n=2896 branches and identify 148243 unique, minimal n-k branch contingencies (2 ≤ k ≤ 5) that cause large cascades, many of which would be missed by using pre-contingency flows, linearized line outage distribution factors, or performance indices as screening factors. Within each n-k collection, the frequency with which individual branches appear follows a power-law (or nearly so) distribution, indicating that a relatively small number of components contribute disproportionately to system vulnerability. The paper discusses various ways that RC generated collections of dangerous contingencies could be used in power systems planning and operations.

Simultaneous estimation of transmissivity values and zonation

The extended Kalmanfilter (EKF) has long been recognized as a powerful, yet computationally intensive, methodology for stochastic parameter estimation. Three improvements to traditional algorithms are presented and applied to heterogeneous transmissivity estimation. First, the costly EKF covariance updates are replaced by more efficient approximations. Second, the zonation structure of the distributed parameterfield being estimated is dynamically determined and refined using a partitional clustering algorithm. Third, a new method of mergingfirst and second moments of randomfields that have heterogeneous statistics is introduced. We apply this method, called random field union, as an alternative to conventional randomfield averaging for the systematic shrinking of covariance matrices as the dimensionality of the parameter space is reduced. The effects of these three improvements are examined. In applications to steady state groundwaterflow test problems, we show that thefirst and second improvements reduce the computational time requirements dramatically, while the second and third can improve the accuracy and stability of the results. The resulting integrated method is successfully applied to a larger, more realistic calibration test case under steady and cyclostationary flow conditions (similar to regular seasonalfluctuations). Whenflow is steady, the method can be viewed as iterative; whenflow is transient, the method is fully recursive.

Efficient three-dimensional data inversion: Soil characterization and moisture Monitoring from cross-well ground-penetrating radar at a Vermont Test Site

We extend our methodology for three-dimensional parameter structure and value estimation and apply it to a Vermont test site. Ground-penetrating radar (GPR) cross-well travel times are inverted for estimation of heterogeneous GPR soil velocities before and after a controlled release of salt water in the unsaturated zone. The method, which is based on an approximation of the extended Kaiman filter in conjunction with data-driven zonation, automatically estimates not only distributed zone values but also the number of zones, zone geometry, and zone covariance. Resultant GPR velocity estimates are shown to reduce travel time estimation errors and to be consistent with independent cone penetrometer measurements at all five walls at the site. Comparison of velocity estimates before and after forced injection of salt water is used to detect and visualize soil moisture patterns in three dimensions. By varying the “cluster tolerance criterion” in the data-driven zonation process, the user can obtain a desired resolution of heterogeneity (number of zones used) in the resultant model.

Diagnostic imaging of breast cancer using fluorescence-enhanced optical tomography: phantom studies

Molecular targeting with exogenous near-infrared excitable fluorescent agents using time-dependent imaging techniques may enable diagnostic imaging of breast cancer and prognostic imaging of sentinel lymph nodes within the breast. However, prior to the administration of unproven contrast agents, phantom studies on clinically relevant volumes are essential to assess the benefits of fluorescence-enhanced optical imaging in humans. Diagnostic 3-D fluorescence-enhanced optical tomography is demonstrated using 0.5 to 1 cm(3) single and multiple targets differentiated from their surroundings by indocyanine green (micromolar) in a breast-shaped phantom (10-cm diameter). Fluorescence measurements of referenced ac intensity and phase shift were acquired in response to point illumination measurement geometry using a homodyned intensified charge-coupled device system modulated at 100 MHz. Bayesian reconstructions show artifact-free 3-D images (3857 unknowns) from 3-D boundary surface measurements (126 to 439). In a reflectance geometry appropriate for prognostic imaging of lymph node involvement, fluorescence measurements were likewise acquired from the surface of a semi-infinite phantom (8x8x8 cm(3)) in response to area illumination (12 cm(2)) by excitation light. Tomographic 3-D reconstructions (24,123 unknowns) were recovered from 2-D boundary surface measurements (3194) using the modified truncated Newtons method. These studies represent the first 3-D tomographic images from physiologically relevant geometries for breast imaging.

BIOMEDICAL OPTICAL TOMOGRAPHY USING DYNAMIC PARAMETERIZATION AND BAYESIAN CONDITIONING ON PHOTON MIGRATION MEASUREMENTS

Stochastic reconstruction techniques are developed for mapping the interior optical properties of tissues from exterior frequency-domain photon migration measurements at the air-tissue interface. Parameter fields of absorption cross section, fluorescence lifetime, and quantum efficiency are accurately reconstructed from simulated noisy measurements of phase shift and amplitude modulation by use of a recursive, Bayesian, minimum-variance estimator known as the approximate extended Kalman filter. Parameter field updates are followed by data-driven zonation to improve the accuracy, stability, and computational efficiency of the method by moving the system from an underdetermined toward an overdetermined set of equations. These methods were originally developed by Eppstein and Dougherty [Water Resources Res. 32, 3321 (1996)] for applications in geohydrology. Estimates are constrained to within feasible ranges by modeling of parameters as beta-distributed random variables. No arbitrary smoothing, regularization, or interpolation is required. Results are compared with those determined by use of Newton-Raphson-based inversions. The speed and accuracy of these preliminary Bayesian reconstructions suggest the near-future application of this inversion technology to three-dimensional biomedical imaging with frequency-domain photon migration.

Optimal 3-D traveltime tomography

We propose a practical new method for 3-D traveltime tomography. The method combines an efficient approximation to the extended Kalman filter for rapid, accurate, nonlinear tomography, with the concept of data‐driven zonation, in which the dimensionality and geometry of the parameterization are dynamically determined using cluster analysis and region merging by random field union. The Bayesian filter uses geostatistics as it recursively incorporates measurements in an optimal (minimum‐variance) manner. Geologic knowledge is introduced through a priori estimates of the parameter field and its spatial covariance. Conditional estimates of the parameter number, geometry, value, and covariance are evolved. An initial decomposition of the 3-D domain into 2-D slices, the simplified filter design, and the data‐driven reduction in parameter dimensionality, all contribute to make the method computationally feasible for large 3-D domains. The method is verified by the inversion of crosswell seismic traveltimes to 3-...

Fluorescence-enhanced optical imaging of large phantoms using single and simultaneous dual point illumination geometries

Fluorescence-enhanced optical tomography is typically performed using single point illumination and multiple point collection measurement geometry. Single point illumination is often insufficient to illuminate greater volumes of large phantoms and results in an inadequate fluorescent signal to noise ratio (SNR) for the majority of measurements. In this work, the use of simultaneous multiple point illumination geometry is proposed for acquiring a large number of fluorescent measurements with a sufficiently high SNR. As a feasibility study, dual point excitation sources, which are in-phase, were used in order to acquire surface measurements and perform three-dimensional reconstructions on phantoms of large volume and/or significant penetration depth. Measurements were acquired in the frequency-domain using a modulated intensified CCD imaging system under different experimental conditions of target depth (1.4-2.8 cm deep) with a perfect uptake optical contrast. Three-dimensional reconstructions of the fluorescence absorption from the dual point illumination geometry compare well with the reconstructions from the single point illumination geometry. Targets located up to 2 cm deep were located successfully, establishing the feasibility of reconstructions from simultaneous multiple point excitation sources. With improved excitation light rejection, multiple point illumination geometry may prove useful in reconstructing more challenging domains containing deeply embedded targets. Image quality assessment tools are required to determine the optimal measurement geometry for the largest set off imaging tasks.

A comparison of exact and approximate adjoint sensitivities in fluorescence tomography

Many approaches to fluorescence tomography utilize some form of regularized nonlinear least-squares algorithm for data inversion, thus requiring repeated computation of the Jacobian sensitivity matrix relating changes in observable quantities, such as emission fluence, to changes in underlying optical parameters, such as fluorescence absorption. An exact adjoint formulation of these sensitivities comprises three terms, reflecting the individual contributions of 1) sensitivities of diffusion and decay coefficients at the emission wavelength, 2) sensitivities of diffusion and decay coefficients at the excitation wavelength, and 3) sensitivity of the emission source term. Simplifying linearity assumptions are computationally attractive in that they cause the first and second terms to drop out of the formulation. The relative importance of the three terms is thus explored in order to determine the extent to which these approximations introduce error. Computational experiments show that, while the third term of the sensitivity matrix has the largest magnitude, the second term becomes increasingly significant as target fluorophore concentration or volume increases. Image reconstructions from experimental data confirm that neglecting the second term results in overestimation of sensitivities and consequently overestimation of the value and volume of the fluorescent target, whereas contributions of the first term are so low that they are probably not worth the additional computational costs.