Diffuse optical tomography by simulated annealing via a spin Hamiltonian.

Diffuse optical tomography (DOT) is an imaging modality that uses near-infrared light. Although iterative numerical schemes are commonly used for its inverse problem, correct solutions are not obtained unless good initial guesses are chosen. We propose a numerical scheme of DOT, which works even when good initial guesses of optical parameters are not available. We use simulated annealing (SA), which is a method of the Markov-chain Monte Carlo. To implement SA for DOT, a spin Hamiltonian is introduced in the cost function, and the Metropolis algorithm or single-component Metropolis-Hastings algorithm is used. By numerical experiments, it is shown that an initial random spin configuration is brought to a converged configuration by SA, and targets in the medium are reconstructed. The proposed numerical method solves the inverse problem for DOT by finding the ground state of a spin Hamiltonian with SA.

Decay behavior and optical parameter identification for spatial-frequency domain imaging by the radiative transport equation.

The decay behavior of specific intensity is studied for spatial-frequency domain imaging (SFDI). It is shown using the radiative transport equation that the decay is given by a superposition of different decay modes, and the decay rates of these modes are determined by spatial frequencies and Case's eigenvalues. This explains why SFDI can focus on shallow regions. The fact that light with nonzero spatial frequency rapidly decays makes it possible to exclusively extract optical properties of the top layer of a layered medium. We determine optical properties of the top layer of a solid phantom. This measurement is verified with different layered media of numerical phantoms.

Fast and robust reconstruction algorithm for fluorescence diffuse optical tomography assuming a cuboid target.

A fast algorithm for fluorescence diffuse optical tomography is proposed. The algorithm is robust against the choice of initial guesses. We estimate the position of a fluorescent target by assuming a cuboid (rectangular parallelepiped) for the fluorophore target. The proposed numerical algorithm is verified by a numerical experiment and an experiment with a meat phantom. The target position is reconstructed with a cuboid from measurements in the time domain. Moreover, the long-time behavior of the emission light is investigated making use of the analytical solution to the diffusion equation.

Polarization oscillations of near-field thermal emission.

We consider the polarization of thermal emission in the near field of various materials, including dielectrics and metallic systems with resonant surface modes. We find that, at thermal equilibrium, the degree of polarization exhibits spatial oscillations with a period of approximately half the optical wavelength, independent of material composition. This result contrasts with that of Setala et al. [Phys. Rev. Lett.88, 123902 (2002)PRLTAO0031-900710.1103/PhysRevLett.88.123902], who find monotonic decay of the degree of polarization for systems in local thermal equilibrium.

Radiative transport and optical tomography with large datasets.

We consider the inverse problem of optical tomography in the radiative transport regime. We report numerical tests of a direct reconstruction method that is suitable for use with large datasets. Reconstructions of experimental data obtained from a noncontact optical tomography system are also reported.

Singular eigenfunctions for the three-dimensional radiative transport equation.

Case's method obtains solutions to the radiative transport equation as superpositions of elementary solutions when the specific intensity depends on one spatial variable. In this paper, we find elementary solutions when the specific intensity depends on three spatial variables in three-dimensional space. By using the reference frame whose z axis lies in the direction of the wave vector, the angular part of each elementary solution becomes the singular eigenfunction for the one-dimensional radiative transport equation. Thus, Case's method is generalized.

Coarse-graining of perplexity for the spatial distribution of molecules.

Biological tissue consists of various molecules. Instead of focusing on a particular molecule, we consider the Shannon entropy which is calculated from the abundance of different molecules at each spot in the tissue. The spatial distribution of the Shannon entropy is of interest. In this paper, we first obtain the heat map of perplexity, whose logarithm is the entropy. To characterize the spatial variety of molecules, we propose a scalar k that is concerned with the coarse-graining of the perplexity heat map. To verify the usefulness of the number, experiments with mass spectrometry imaging were performed for mouse kidneys. We found that k has large values in the renal pelvis area, cortex area, veins, and arteries in the mouse kidney, whereas fractal dimensions fail to distinguish those regions.

Spatial distribution of the Shannon entropy for mass spectrometry imaging.

Mass spectrometry imaging (MSI) allows us to visualize the spatial distribution of molecular components in a sample. A large amount of mass spectrometry data comprehensively provides molecular distributions. In this study, we focus on the information in the obtained data and use the Shannon entropy as a quantity to analyze MSI data. By calculating the Shannon entropy at each pixel on a sample, the spatial distribution of the Shannon entropy is obtained from MSI data. We found that low-entropy pixels in entropy heat maps for kidneys of mice had different structures between two ages (3 months and 31 months). Such changes cannot be visualized by conventional imaging techniques. We further propose a method to find informative molecules. As a demonstration of the proposed scheme, we identified two molecules by setting a region of interest which contained low-entropy pixels and by exploring changes of peaks in the region.

Changes of Mass Spectra Patterns on a Brain Tissue Section Revealed by Deep Learning with Imaging Mass Spectrometry Data.

The characteristic patterns of mass spectra in imaging mass spectrometry (IMS) strongly reflect the tissue environment. However, the boundaries formed where different tissue environments collide have not been visually assessed. In this study, IMS and convolutional neural network (CNN), one of the deep learning methods, were applied to the extraction of characteristic mass spectra patterns from training brain regions on rodents' brain sections. CNN produced classification models with high accuracy and low loss rate in any test data sets of mouse coronal sections measured by desorption electrospray ionization (DESI)-IMS and of mouse and rat sagittal sections by matrix-assisted laser desorption (MALDI)-IMS. On the basis of the extracted mass spectra pattern features, the histologically plausible segmentation and classification score imaging of the brain sections were obtained. The boundary imaging generated from classification scores showed the extreme changes of mass spectra patterns between the tissue environments, with no significant buffer zones for the intermediate state. The CNN-based analysis of IMS data is a useful tool for visually assessing the changes of mass spectra patterns on a tissue section, and it will contribute to a comprehensive view of the tissue environment.

Distribution of the spacing between two adjacent avoided crossings.

We consider the frequency at which avoided crossings appear in an energy-level structure when an external field is applied to a quantum chaotic system. The distribution of the spacing in the parameter between two adjacent avoided crossings is investigated. Using a random matrix model, we find that the distribution of these spacings is well fitted by a power-law distribution for small spacings. The powers are 2 and 3 for the Gaussian orthogonal ensemble and Gaussian unitary ensemble, respectively. We also find that the distributions decay exponentially for large spacings. The distributions in concrete quantum chaotic systems agree with those of the random matrix model.

Diffuse optical tomography in the presence of a chest wall.

Diffuse optical tomography (DOT) has been employed to derive spatial maps of physiologically important chromophores in the human breast, but the fidelity of these images is often compromised by boundary effects such as those due to the chest wall. We explore the image quality in fast, data-intensive analytic and algebraic linear DOT reconstructions of phantoms with subcentimeter target features and large absorptive regions mimicking the chest wall. Experiments demonstrate that the chest wall phantom can introduce severe image artifacts. We then show how these artifacts can be mitigated by exclusion of data affected by the chest wall. We also introduce and demonstrate a linear algebraic reconstruction method well suited for very large data sets in the presence of a chest wall.

Diffusion approximation revisited.

We study the diffusion approximation (DA) to the radiative transport equation (RTE) in infinite homogeneous space. Different definitions of the reduced intensity I(r) that satisfy a simplified RTE (without accounting for scattering) and that are often used in the derivation of the DA are examined. By comparing the results of the DA with exact solutions to the RTE, we come to the conclusion that the best accuracy in the DA is achieved if we choose the definition of the reduced intensity (from a family of possible definitions) that results in I(r)=0. Thus, the separation of the specific intensity into reduced and diffuse components is unnecessary. We also discuss the conditions under which the DA is applicable.