Diffuse Optical Tomography Method Research Articles

A Semi-smooth Newton Method for Diffuse Optical Tomography with L1-Norm and Total Variation Regularization

This study introduces a novel multi-measurement Diffuse Optical Tomography reconstruction method that employs both L1-norm and Total Variation regularization, solved by the semi-smooth Newton method. By integrating L1-norm regularization to address sparsity and TV regularization to preserve edges and structural details, our approach effectively combats the ill-posed nature of DOT reconstructions. The results demonstrate that our approach reduces the required iterations while simultaneously maintaining or enhancing reconstruction accuracy and robustness to noise.

Non-line-of-sight imaging in the presence of scattering media using phasor fields.

Non-line-of-sight (NLOS) imaging aims to reconstruct partially or completely occluded scenes. Recent approaches have demonstrated high-quality reconstructions of complex scenes with arbitrary reflectance, occlusions, and significant multi-path effects. However, previous works focused on surface scattering only, which reduces the generality in more challenging scenarios such as scenes submerged in scattering media. In this work, we investigate current state-of-the-art NLOS imaging methods based on phasor fields to reconstruct scenes submerged in scattering media. We empirically analyze the capability of phasor fields in reconstructing complex synthetic scenes submerged in thick scattering media. We also apply the method to real scenes, showing that it performs similarly to recent diffuse optical tomography methods.

Nonconvex and nonsmooth total variation regularization method for diffuse optical tomography based on RTE * *Submitted Funding: this work is supported by the National Natural Science Foundation of China (Grant No. 11701159).

Diffuse optical tomography with near-infrared light is a promising technique for noninvasive study of the functional characters of human tissues. Mathematically, it is a seriously ill-posed parameter identification problem. For the purpose of better providing both segmentation and piecewise constant approximation of the underlying solution, nonconvex nonsmooth total variation based regularization functional is considered in this paper. We first give a theoretical study on the well-posedness of solutions corresponding to this minimization problem in the Banach space of piecewise constant functions. Moreover, our theoretical results show that the minimizers corresponding to a sequence nonconvex nonsmooth potential functions which converge to the 0–1 functions, can be used to approximate the solution to the weak Mumford–Shah regularization. Then from the numerical side, we propose a double graduated nonconvex Gauss–Newton algorithm to solve this nonconvex nonsmooth regularization. All illustrations and numerical experiments give a flavor of the possibilities offered by the minimizers of the proposed algorithm.

Influence of contrast-reversing frequency on the amplitude and spatial distribution of visual cortex hemodynamic responses

Visual stimulation is one of the most commonly used paradigms for cerebral cortex function investigation. Experiments typically involve presenting to a volunteer a black-and-white checkerboard with contrast-reversing at a frequency of 4 to 16 Hz. The aim of the present study was to investigate the influence of the flickering frequency on the amplitude of changes in the concentration of oxygenated and deoxygenated hemoglobin. The hemoglobin concentrations were assessed with the use of a high resolution diffuse optical tomography method. Spatial distributions of changes in hemoglobin concentrations overlaying the visual cortex are shown for various stimuli frequencies. Moreover, the hemoglobin concentration changes obtained for different source-detector separations (from 1.5 to 5.4 cm) are presented. Our results demonstrate that the flickering frequency had a statistically significant effect on the induced oxyhemoglobin changes (p < 0,001). The amplitude of oxy hemoglobin concentration changes at a frequency of 8 Hz was higher in comparison with that measured at 4 Hz :[median(25th-75thpercentiles) 1.24 (0.94-1.71) vs. 0.92(0.73-1.28)µM, p < 0.001]; 12 Hz:[1.24 (0.94-1.71) vs. 1.04 (0.78-1.32) µM, p < 0.001]; and 16 Hz:[1.24 (0.94-1.71) vs. 1.15(0.87-1.48) µM, p < 0.001]. No significant differences were observed between the size of an area of activation for various frequencies. The demonstrated superiority of 8 Hz over other frequencies can advance understanding of visual stimulations and help guide future fNIRS protocols.

An Automated Preprocessing Method for Diffuse Optical Tomography to Improve Breast Cancer Diagnosis.

The ultrasound-guided diffuse optical tomography is a noninvasive imaging technique for breast cancer diagnosis and treatment monitoring. The technique uses a handheld probe capable of providing measurements of multiple wavelengths in a few seconds. These measurements are used to estimate optical absorptions of lesions and calculate the total hemoglobin concentration. Any measurement errors caused by low signal to noise ratio data and/or movements during data acquisition would reduce the accuracy of reconstructed total hemoglobin concentration. In this article, we introduce an automated preprocessing method that combines data collected from multiple sets of lesion measurements of 4 optical wavelengths to detect and correct outliers in the perturbation. Two new measures of correlation between each pair of wavelength measurements and a wavelength consistency index of all reconstructed absorption maps are introduced. For phantom and patients’ data without evidence of measurement errors, the correlation coefficient between each pair of wavelength measurements was above 0.6. However, for patients with measurement errors, the correlation coefficient was much lower. After applying the correction method to 18 patients’ data with measurement errors, the correlation has improved and the wavelength consistency index is in the same range as the cases without wavelength-dependent measurement errors. The results show an improvement in classification of malignant and benign lesions.

A reconstruction method for diffuse optical tomography by grouping of source-detector configuration

Image reconstruction for diffusion optical tomography often involves repeatedly solving the forward problem, wherein the diffusion equation is typically utilized to describe the light propagation. However, the diffusion equation may not be valid in regions of either high absorption or low scatter. In this paper, a new method is proposed to improve the forward model. This method is based on the modelling error between the Monte Carlo method and the diffusion equation. To further improve the efficiency of image reconstruction, we propose the grouping strategy of source-detector configuration. Simulation results demonstrate that the proposed method can significantly speed up the reconstruction process with the high reconstruction quality.

Next-generation Raman tomography instrument for non-invasive in vivo bone imaging.

Combining diffuse optical tomography methods with Raman spectroscopy of tissue provides the ability for in vivo measurements of chemical and molecular characteristics, which have the potential for being useful in diagnostic imaging. In this study a system for Raman tomography was developed and tested. A third generation microCT coupled system was developed to combine 10 detection fibers and 5 excitation fibers with laser line filtering and a Cytop reference signal. Phantom measurements of hydroxyapatite concentrations from 50 to 300 mg/ml had a linear response. Fiber placement and experiment design was optimized using cadaver animals with live animal measurements acquired to validate the systems capabilities. Promising results from the initial animal experiments presented here, pave the way for a study of longitudinal measurements during fracture healing and the scaling of the Raman tomography system towards human measurements.

A Homotopy Perturbation Method for Diffuse Optical Tomography Based on Radiative Transfer Equation

A Homotopy Perturbation Method for Diffuse Optical Tomography Based on Radiative Transfer Equation

Optical Property of Indocyanine Green in a Tissue Model

The fluorescence temporal profile has been studied at the symmetrical point of the target in tissue phantom by a time-resolved fluorescence diffuse optical tomography method. Indocyanine green served as the fluorescence target. The results showed that the geometrical symmetry of the fluorescence peak intensity ratio was broken due to target position. By using this parameter, an unknown target location could be identified for fluorescence targeting and further reconstruction of the fluorescence image in a tissue model.

A parallel strategy and performance analysis of the EM-like reconstruction method for diffuse optical tomography

The EM-like reconstruction method for steady state diffuse optical tomography is a propagation back-propagation method and its sequential implementation requires excessively longer computation time. Hence we apply a parallel strategy to the reconstruction method. We divide the groups of boundary measurements into several nonoverlapping subsets and each subset of boundary measurements are handled by selected processing element. We take two-dimensional numerical experiments on a single Symmetric Multi-Processing system to test the performance of the parallel strategy. The computation time of the parallel implementation indicates that high performance of computation can be obtained. Besides, the more groups of boundary measurements are used for the reconstruction, the higher speed-up and parallel efficiency can be achieved. Due to the usage of memory, the curve of speed-up with respect to different numbers of processing elements appears a wave pattern while the curve of efficiency with respect to different numbers of processing elements decreases rapidly. Thus, for three-dimensional reconstruction problem, we can execute the parallel reconstruction scheme on a cluster which aligns multiple workstations by a network.

Reduced-order modeling of light transport in tissue for real-time monitoring of brain hemodynamics using diffuse optical tomography

This paper proposes a new reconstruction method for diffuse optical tomography using reduced-order models of light transport in tissue. The models, which directly map optical tissue parameters to optical flux measurements at the detector locations, are derived based on data generated by numerical simulation of a reference model. The reconstruction algorithm based on the reduced-order models is a few orders of magnitude faster than the one based on a finite element approximation on a fine mesh incorporating a priori anatomical information acquired by magnetic resonance imaging. We demonstrate the accuracy and speed of the approach using a phantom experiment and through numerical simulation of brain activation in a rat's head. The applicability of the approach for real-time monitoring of brain hemodynamics is demonstrated through a hypercapnic experiment. We show that our results agree with the expected physiological changes and with results of a similar experimental study. However, by using our approach, a three-dimensional tomographic reconstruction can be performed in ∼3 s per time point instead of the 1 to 2 h it takes when using the conventional finite element modeling approach.

Acceleration of the EM-like reconstruction method for diffuse optical tomography with ordered-subsets method

Abstract. Diffuse optical tomography (DOT) is an optical imaging modality, which provides the spatial distribution of the optical parameters inside a random medium. A propagation back-propagation method named EM-like reconstruction method for stationary DOT problem has been proposed yet. This method is really time consuming. Hence the ordered-subsets (OS) technique for this reconstruction method is studied in this paper. The boundary measurements of DOT are grouped into nonoverlapping and overlapping ordered sequence of subsets with random partition, sequential partition and periodic partition, respectively. The performance of OS methods is compared with the standard EM-like reconstruction method with two-dimensional and three-dimensional numerical experiments. The numerical experiments indicate that reconstruction of nonoverlapping subsets with periodic partition, overlapping subsets with periodic partition and standard EM-like method provide very similar acceptable reconstruction results. However, reconstruction of nonoverlapping subsets with periodic partition spends a minimum of time to get proper results.

Fast multipole boundary element method for diffuse optical tomography

The forward problem of diffuse optical tomography (DOT) is commonly solved by the finite element method (FEM) currently. However, with the increase of the model scale, the computational complexity of FEM increases significantly; while the boundary element method (BEM) attracts much attention because of its reduction in calculated dimensions. In this paper, the fast multipole boundary element method (FMBEM) for DOT is studied using a model of highly scattering homogenous medium. In FMBEM, by the multipole expansions of kernel functions, the product of matrix coefficient and iterative vector can be equivalent to the recursion of a quadtree; and then a generalized minimal residual method is used to solve the BEM equation iteratively. The calculations of the FMBEM are compared with Monte Carlo simulations. The results show that the calculations of the FMBEM are in good agreement with Monte Carlo simulations. This demonstrates the feasibility of FMBEM in DOT and indicates that the FMBEM has a bright future for large-scale and real-time imaging.

High-density diffuse optical tomography of term infant visual cortex in the nursery

Advancements in antenatal and neonatal medicine over the last few decades have led to significant improvement in the survival rates of sick newborn infants. However, this improvement in survival has not been matched by a reduction in neurodevelopmental morbidities with increasing recognition of the diverse cognitive and behavioral challenges that preterm infants face in childhood. Conventional neuroimaging modalities, such as cranial ultrasound and magnetic resonance imaging, provide an important definition of neuroanatomy with recognition of brain injury. However, they fail to define the functional integrity of the immature brain, particularly during this critical developmental period. Diffuse optical tomography methods have established success in imaging adult brain function; however, few studies exist to demonstrate their feasibility in the neonatal population. We demonstrate the feasibility of using recently developed high-density diffuse optical tomography (HD-DOT) to map functional activation of the visual cortex in healthy term-born infants. The functional images show high contrast-to-noise ratio obtained in seven neonates. These results illustrate the potential for HD-DOT and provide a foundation for investigations of brain function in more vulnerable newborns, such as preterm infants.

Bedside optical imaging of occipital resting-state functional connectivity in neonates

Resting-state networks derived from temporal correlations of spontaneous hemodynamic fluctuations have been extensively used to elucidate the functional organization of the brain in adults and infants. We have previously developed functional connectivity diffuse optical tomography methods in adults, and we now apply these techniques to study functional connectivity in newborn infants at the bedside. We present functional connectivity maps in the occipital cortices obtained from healthy term-born infants and premature infants, including one infant with an occipital stroke. Our results suggest that functional connectivity diffuse optical tomography has potential as a valuable clinical tool for the early detection of functional deficits and for providing prognostic information on future development.

Image reconstruction in diffuse optical tomography using the coupled radiative transport–diffusion model

The coupled radiative transport–diffusion model can be used as light transport model in situations in which the diffusion equation is not a valid approximation everywhere in the domain. In the coupled model, light propagation is modelled with the radiative transport equation in sub-domains in which the approximations of the diffusion equation are not valid, such as within low-scattering regions, and the diffusion approximation is used elsewhere in the domain. In this paper, an image reconstruction method for diffuse optical tomography based on using the coupled radiative transport–diffusion model is developed. In the approach, absorption and scattering distributions are estimated by minimising a regularised least-squares error between the measured data and solution of the coupled model. The approach is tested with simulations. Reconstructions from different cases including domains with low-scattering regions are shown. The results show that the coupled radiative transport–diffusion model can be utilised in image reconstruction problem of diffuse optical tomography and that it produces as good quality reconstructions as the full radiative transport equation also in the presence of low-scattering regions.

An EM‐like reconstruction method for diffuse optical tomography

AbstractDiffuse optical tomography (DOT) is an optical imaging modality which provides the spatial distributions of optical parameters inside an object. The forward model of DOT is described by the diffusion approximation of radiative transfer equation, while the DOT is to reconstruct the optical parameters from boundary measurements. In this paper, an EM‐like iterative reconstruction method specifically for the steady state DOT problem is developed. Previous iterative reconstruction methods are mostly based on the assumption that the measurement noise is Gaussian, and are of least‐squares type. In this paper, with the assumption that the boundary measurements have independent and identical Poisson distributions, the inverse problem of DOT is solved by maximizing a log‐likelihood functional with inequality constraints, and then an EM‐like reconstruction algorithm is developed according to the Kuhn–Tucker condition. The proposed algorithm is a variant of the well‐known EM algorithm. The performance of the proposed algorithm is tested with three‐dimensional numerical simulation. Copyright © 2010 John Wiley &amp; Sons, Ltd.

Multistage inversion algorithm for biological tissue imaging

A new inversion method for diffuse optical tomography is proposed. This is a multistage algorithm, that uses a signal subspace-based method to simplify the inverse problem and proposes a guided iterative inversion process to improve the imaging. First, subspace-based analysis is used to determine the voxels that definitely belong to the background and exclude them from further consideration. Then, the pseudo-inverse technique is applied for reconstruction. In the final stage, the reconstruction is improved iteratively by finding and excluding more voxels belonging to background. The method reduces the ill-posedness of the image reconstruction problem iteratively such that good imaging results are obtained for multiple heterogeneities having complicated geometries even in the presence of 3% additive white noise.

A combined reconstruction–classification method for diffuse optical tomography

We present a combined classification and reconstruction algorithm for diffuse optical tomography (DOT). DOT is a nonlinear ill-posed inverse problem. Therefore, some regularization is needed. We present a mixture of Gaussians prior, which regularizes the DOT reconstruction step. During each iteration, the parameters of a mixture model are estimated. These associate each reconstructed pixel with one of several classes based on the current estimate of the optical parameters. This classification is exploited to form a new prior distribution to regularize the reconstruction step and update the optical parameters. The algorithm can be described as an iteration between an optimization scheme with zeroth-order variable mean and variance Tikhonov regularization and an expectation-maximization scheme for estimation of the model parameters. We describe the algorithm in a general Bayesian framework. Results from simulated test cases and phantom measurements show that the algorithm enhances the contrast of the reconstructed images with good spatial accuracy. The probabilistic classifications of each image contain only a few misclassified pixels.

Tumor localization using diffuse optical tomography and linearly constrained minimum variance beamforming

We present a tumor localization method for diffuse optical tomography using linearly constrained minimum variance (LCMV) beamforming. Beamforming is a spatial filtering technique where signals from certain directions can be enhanced while noise and interference from other directions are suppressed. In our method, we tessellate the domain into small voxels and regard each voxel as a possible position of abnormality (e.g., tumor).We then design a spatial filter based on the linearly constrained minimum variance criterion and apply it to each voxel in the domain. The abnormality is localized by observing the peak in the filter output signals. We test our method using simulated 3D examples. We assume a cubic transmission geometry and consider different cases where the abnormality is an absorber, a scatterer, and both. We also give examples showing the resolution of our method and its performance under different perturbation levels and noise levels. Simulation results show that LCMV beamforming can localize the abnormality well with good computational efficiency. It can be used alone for tumor localization and also as an effective preprocessing tool for improving the image reconstruction performances of other inverse methods.