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 cm3 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 (8×8×8 cm3) in response to area illumination (12 cm2) by excitation light. Tomographic 3-D reconstructions (24,123 unknowns) were recovered from 2-D boundary surface measurements (3194) using the modified truncated Newton's method. These studies represent the first 3-D tomographic images from physiologically relevant geometries for breast imaging.
KEYWORDS: 3D modeling, Optical fibers, Data modeling, Refractive index, Data acquisition, Imaging systems, Cameras, Interfaces, 3D image reconstruction, Tomography
A frequency-domain photon migration (FDPM) imager employing an image-intensified CCD camera for fast data acquisition on a large tissue-mimicking phantom (1087 ml) is described. Fluorescence-enhanced imaging is performed employing frequency-domain techniques at 100 MHz in order to obtain the boundary measurements of phase and amplitude and to recover the interior optical maps using the first principles of light propagation. The effect of refractive-index parameter in the boundary condition of the light propagation model is not significant due to the large phantom volume and its curvilinear nature. Initial experiments were performed under perfect (1:0 contrast) and imperfect (100:1 contrast) uptake cases using indocyanine green as the contrast agent. Preliminary 3D image reconstructions using the approximate extended Kalman filter (AEKF) algorithm are presented.
The approximate extended Kalman filter (AEKF) has been suggested as an appropriate inverse method for reconstructing fluorescent properties in large tissue samples from frequency domain data containing measurement error. The AEKF is an “optimal” estimator, in that it seeks to minimize the predicted error variances of the estimated optical properties in relation to measurement and system errors. However, due to non-linearities in the recursive estimation process, the updates are actually suboptimal. Furthermore, the computational overhead is large for the full AEKF algorithm when applied to large datasets. In this contribution we developed three hybrid forms of the AEKF algorithm that may improve the performance in frequency domain fluorescence tomography. Numerical results of image reconstruction from actual frequency domain emission data show that one hybrid form of the AEKF outperforms the traditional full AEKF in both image quality and computational efficiency for the two cases tested.
In large 3-D finite element optical tomography problems, computation times for forward and adjoint solutions and for calculation of sensitivities can become prohibitive. Parallelization of computer codes can be used to obtain speedups approaching the number of processors employed, but parallel codes and computer systems can be difficult and expensive to develop and maintain. We show that by employing highly vectorized code that takes advantage of pipelining capabilities in the microprocessor we achieve dramatic speedups for forward and adjoint sensitivity calculations on a single processor microcomputer, and that these speedups actually increase as the problem size increases. Our vectorized implementations involve replication of large amounts of data and are thus memory intensive, however we effectively remove memory constraints by using domain decomposition to control the use of virtual memory. We show that global matrix assembly for a large (98,304 element) mesh is speeded up by a factor of 6.5 and adjoint sensitivity calculations of emission fluence with respect to fluorescence absorption are speeded up by a factor of 502 on a single-processor 2.2 GHz Pentium IV.
We present results of ongoing research in 3-D fluorescence tomography on large clinically-relevant tissue-mimicking domains. Finite element predictions of excitation and emission phase shift and amplitude attenuation are compared to experimental data from both column-shaped and breast-shaped tissue mimicking phantoms containing embedded fluorophore; system noise and measurement noise are characterized and utilized in image reconstruction using the Bayesian APPRIZE algorithm.
Research into the near-infrared biomedical optical imaging has produced a multitude of inverse imaging algorithms. Recent experience has shown that when these algorithms are tested with experimental data, they falter due to a mismatch between observed and simulated measurements. When considering measurements for imaging, one must consider both measurement and model error. If data is recorded properly, then measurement error tends to be normally distributed with a mean of zero. Model error can be biased and spatially correlated due to inaccuracies in the diffusion approximation, inaccurate parameter estimates, numerical error, and other factors. This contribution discusses trends in the measurement and model error observed from measurements on a single-pixel, frequency domain photon migration system developed for biomedical optical imaging. In order to reduce the model error bias, an empirical approach was applied to find experimental variables that significantly affect it. This approach reduced the mean of the model error on a test data set and produced a slight smoothing effect on its distribution. Image reconstruction attempts show that the modified data set produces an improved image over the image reconstructed from the raw data set. To our knowledge, this is the first time that model and measurement error information have been incorporated into a three dimensional image reconstruction algorithm.
We present a tomography method for fluorescence and absorption biomedical optical imaging which minimizes the computational burden of three-dimensional image reconstruction and enables data conditioning on the basis of variable and possibly spatially-correlated measurement and system noise. Specifically, we present three-dimensional images reconstructed from (i) synthetic frequency-domain measurements; (ii) finite difference solution to the diffusion equation employing partial current boundary conditions; (iii) a recursive, minimum variance, optimization algorithm employing a Bayesian approximate extended Kalman filter accounting for measurement and system noise; and (iv) a unique, data-driven zonation scheme to dynamically determine parameterization and accelerate convergence. Using a synthetic data set with 0.1¡ standard deviation Gaussian noise added to phase, we demonstrate the ability to image multiple distinct 0.5 cm diameter absorbing/fluorescing heterogeneities within a combined transillumination/reflectance geometry comprising 8 sources and 90 detectors. Reconstruction of absorption maps owing to spatial distribution of fluorophores that were discretized onto a 9x9x9 node grid required just over 4 minutes on a 350 MHz Pentium II computer.
Stochastic methods originally devised for geophysical tomography are adapted to the biomedical optical tomography problem. Frequency domain measurements of modulated NIR light are inverted using a Bayesian approximate extended Kalman filter. Minimum variance updates for the linearized problem are calculated from explicit models of the parameters error covariance, the covariance of the system noise, and the measurement error covariance. The method is not iterative per se, but may be applied iteratively to account for strong nonlinearities. Data-driven zonation is used to dynamically reduce the parameterization for improved efficiency, sensitivity, and stability of the inversion. By modeling the parameters as beta distributed random variables, estimates are kept within feasible limits without ad hoc adjustments. In preliminary studies using synthetic domains we have successfully resolved spatially heterogeneous parameters such as absorption, fluorescence lifetime, and quantum efficiency. The method is shown to be much more accurate and computationally efficient than a more traditional Newton-Raphson method. On a 33 by 33 grid, distributed values of a single unknown parameter can be accurately identified in under 2 minutes on a 350 MHz Pentium.
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