Alexander D. Klose

Gradient-based iterative image reconstruction scheme for time-resolved optical tomography

Currently available tomographic image reconstruction schemes for optical tomography (OT) are mostly based on the limiting assumptions of small perturbations and a priori knowledge of the optical properties of a reference medium. Furthermore, these algorithms usually require the inversion of large, full, ill-conditioned Jacobian matrixes. In this work a gradient-based iterative image reconstruction (GIIR) method is presented that promises to overcome current limitations. The code consists of three major parts: (1) A finite-difference, time-resolved, diffusion forward model is used to predict detector readings based on the spatial distribution of optical properties; (2) An objective function that describes the difference between predicted and measured data; (3) An updating method that uses the gradient of the objective function in a line minimization scheme to provide subsequent guesses of the spatial distribution of the optical properties for the forward model. The reconstruction of these properties is completed, once a minimum of this objective function is found. After a presentation of the mathematical background, two- and three-dimensional reconstruction of simple heterogeneous media as well as the clinically relevant example of ventricular bleeding in the brain are discussed. Numerical studies suggest that intraventricular hemorrhages can be detected using the GIIR technique, even in the presence of a heterogeneous background.

Iterative reconstruction scheme for optical tomography based on the equation of radiative transfer.

We report on the development of an iterative image reconstruction scheme for optical tomography that is based on the equation of radiative transfer. Unlike the commonly applied diffusion approximation, the equation of radiative transfer accurately describes the photon propagation in turbid media without any limiting assumptions regarding the optical properties. The reconstruction scheme consists of three major parts: (1) a forward model that predicts the detector readings based on solutions of the time-independent radiative transfer equation, (2) an objective function that provides a measure of the differences between the detected and the predicted data, and (3) an updating scheme that uses the gradient of the objective function to perform a line minimization to get new guesses of the optical properties. The gradient is obtained by employing an adjoint differentiation scheme, which makes use of the structure of the finite-difference discrete-ordinate formulation of the transport forward model. Based on the new guess of the optical properties a new forward calculation is performed to get new detector predictions. The reconstruction process is completed when the minimum of the objective function is found within a defined error. To illustrate the performance of the code we present initial reconstruction results based on simulated data.

Sagittal laser optical tomography for imaging of rheumatoid finger joints.

We present a novel optical tomographic imaging system that was designed to determine two-dimensional spatial distribution of optical properties in a sagittal plane through finger joints. The system incorporates a single laser diode and a single silicon photodetector into a scanning device that records spatially resolved light intensities as they are transmitted through a finger. These data are input to a model-based iterative image reconstruction (MOBIIR) scheme, which uses the equation of radiative transfer (ERT) as a forward model for light propagation through tissue. We have used this system to obtain tomographic images of six proximal interphalangeal finger joints from two patients with rheumatoid arthritis. The optical images were compared to clinical symptoms and ultrasound images.

First clinical evaluation of sagittal laser optical tomography for detection of synovitis in arthritic finger joints

Objective: To identify classifiers in images obtained with sagittal laser optical tomography (SLOT) that can be used to distinguish between joints affected and not affected by synovitis. Methods: 78 SLOT images of proximal interphalangeal joints II–IV from 13 patients with rheumatoid arthritis were compared with ultrasound (US) images and clinical examination (CE). SLOT images showing the spatial distribution of scattering and absorption coefficients within the joint cavity were generated. The means and standard errors for seven different classifiers (operator score and six quantitative measurements) were determined from SLOT images using CE and US as diagnostic references. For classifiers showing significant differences between affected and non-affected joints, sensitivities and specificities for various cut off parameters were obtained by receiver operating characteristic (ROC) analysis. Results: For five classifiers used to characterise SLOT images the mean between affected and unaffected joints was statistically significant using US as diagnostic reference, but statistically significant for only one classifier with CE as reference. In general, high absorption and scattering coefficients in and around the joint cavity are indicative of synovitis. ROC analysis showed that the minimal absorption classifier yields the largest area under the curve (0.777; sensitivity and specificity 0.705 each) with US as diagnostic reference. Conclusion: Classifiers in SLOT images have been identified that show statistically significant differences between joints with and without synovitis. It is possible to classify a joint as inflamed with SLOT, without the need for a reference measurement. Furthermore, SLOT based diagnosis of synovitis agrees better with US diagnosis than CE.

Fluorescence tomography with simulated data based on the equation of radiative transfer.

The quantification of a nonuniform quantum yield or fluorophore absorption distribution is of major interest in molecular imaging of biological tissue. We introduce what is believed to be the first fluorescence image reconstruction algorithm based on the equation of radiative transfer that recovers the spatial distribution of light-emitting fluorophores inside a highly scattering medium from measurements made on the surface of the medium. We obtain images of either the quantum yield or the fluorophore absorption.

Quasi-Newton methods in optical tomographic image reconstruction

Optical tomography (OT) recovers the cross-sectional distribution of optical parameters inside a highly scattering medium from information contained in measurements that are performed on the boundaries of the medium. The image reconstruction problem in OT can be considered as a large-scale optimization problem, in which an appropriately defined objective function needs to be minimized. In the simplest case, the objective function is the least-square error norm between the measured and the predicted data. In biomedical applications that apply near-infrared light as the probing tool the predictions are obtained from a model of light propagation in tissue. Gradient techniques are commonly used as optimization methods, which employ the gradient of the objective function with respect to the optical parameters to find the minimum. Conjugate gradient (CG) techniques that use information about the first derivative of the objective function have shown some good results in the past. However, this approach is frequently characterized by low convergence rates. To alleviate this problem we have implemented and studied so-called quasi-Newton (QN) methods, which use approximations to the second derivative. The performance of the QN and CG methods are compared by utilizing both synthetic and experimental data.

In vivo bioluminescence tomography with a blocking-off finite-difference SP3 method and MRI/CT coregistration.

PURPOSE Bioluminescence imaging is a research tool for studying gene expression levels in small animal models of human disease. Bioluminescence light, however, is strongly scattered in biological tissue and no direct image of the light-emitting reporter probes location can be obtained. Therefore, the authors have developed a linear image reconstruction method for bioluminescence tomography (BLT) that recovers the three-dimensional spatial bioluminescent source distribution in small animals. METHODS The proposed reconstruction method uses third-order simplified spherical harmonics (SP3) solutions to the equation of radiative transfer for modeling the bioluminescence light propagation in optically nonuniform tissue. The SP3 equations and boundary conditions are solved with a finite-difference (FD) technique on a regular grid. The curved geometry of the animal surface was taken into account with a blocking-off region method for regular grids. Coregistered computed tomography (CT) and magnetic resonance (MR) images provide information regarding the geometry of the skin surface and internal organs. The inverse source problem is defined as an algebraic system of linear equations for the unknown source distribution and is iteratively solved given multiview and multispectral boundary measurements. The average tissue absorption parameters, which are used for the image reconstruction process, were calculated with an evolution strategy (ES) from in vivo measurements using an implanted pointlike source of known location and spectrum. Moreover, anatomical information regarding the location of the internal organs and other tissue structures within the animals body are provided by coregistered MR images. RESULTS First, the authors recovered the wavelength-dependent absorption coefficients (average error of 14%) with the ES under ideal conditions by using a numerical mouse model. Next, they reconstructed the average absorption coefficient of a small animal by using an artificial implanted light source and the validated ES. Last, they conducted two in vivo animal experiments and recovered the spatial location of the implanted light source and the spatial distribution of a bioluminescent reporter system located in the kidneys. The source reconstruction results were coregistered to CT and MR images. They further found that accurate bioluminescence image reconstructions could be obtained when segmenting a voidlike cyst with low-scattering and absorption parameters, whereas inaccurate image reconstructions were obtained when assuming a uniform optical parameter distribution instead. The image reconstructions were completed within 23 min on a 3 GHz Intel processor. CONCLUSIONS The authors demonstrated on in vivo examples that the combination of anatomical coregistration, accurate optical tissue properties, multispectral acquisition, and a blocking-off FD-SP3 solution of the radiative transfer model significantly improves the accuracy of the BLT reconstructions.

α–Intercalated cells defend the urinary system from bacterial infection

α-Intercalated cells (A-ICs) within the collecting duct of the kidney are critical for acid-base homeostasis. Here, we have shown that A-ICs also serve as both sentinels and effectors in the defense against urinary infections. In a murine urinary tract infection model, A-ICs bound uropathogenic E. coli and responded by acidifying the urine and secreting the bacteriostatic protein lipocalin 2 (LCN2; also known as NGAL). A-IC-dependent LCN2 secretion required TLR4, as mice expressing an LPS-insensitive form of TLR4 expressed reduced levels of LCN2. The presence of LCN2 in urine was both necessary and sufficient to control the urinary tract infection through iron sequestration, even in the harsh condition of urine acidification. In mice lacking A-ICs, both urinary LCN2 and urinary acidification were reduced, and consequently bacterial clearance was limited. Together these results indicate that A-ICs, which are known to regulate acid-base metabolism, are also critical for urinary defense against pathogenic bacteria. They respond to both cystitis and pyelonephritis by delivering bacteriostatic chemical agents to the lower urinary system.

Light transport in biological tissue using three-dimensional frequency-domain simplified spherical harmonics equations.

The accuracy of the commonly used diffusion approximation as used in diffuse optical tomography is known to be limited in cases involving strong absorption and in these situations a higher ordered approximation is necessary. In this study, a light transport model has been developed based upon the three-dimensional frequency-domain simplified spherical harmonics (SP(N)) approximation for orders up to N = 7. The SP(N) data are tested against a semi-infinite multi-layered Monte Carlo model. It has been shown that the SP(N) approximation for higher orders (N >1) provides an increase in accuracy over the diffusion equation specifically near sources and at boundaries of regions with increased optical absorption. It is demonstrated that the error of fluence calculated near the sources between the diffusion approximation and the SP(N) model (N = 7) can be as large as 60%, therefore limiting the use of the diffusion approximation for small animal imaging and in situations where optical changes near sources are critical for tomographic reconstructions.

Transport-theory-based stochastic image reconstruction of bioluminescent sources

A stochastic image reconstruction methodology is proposed for solving the highly ill-posed inverse bioluminescent source problem in light-scattering media. The unknown source distribution is expressed in terms of a set of linearly independent source basis functions. The bioluminescent boundary flux originating from each source basis function is computed prior to image reconstruction by solving the equation of radiative transfer. The misfit between the measured and the predicted boundary flux is described by an error function, which is iteratively minimized by stochastically sampling the global parameter space of all basis functions. Selection and alteration mechanisms, which can be guided by evolutionary principles found in nature, lead to new stochastic samples of source distributions for the next iteration cycle. A least-squares-error solution, representing the sought image of the unknown source distribution, is obtained after convergence. Numerical experiments demonstrate the feasibility of reconstructing bioluminescent source distributions in tissuelike media.