The effects of internal refractive index variation in near-infrared optical tomography: a finite element modelling approach

Diagnostic efficacy of systemic immune-inflammation biomarkers in benign prostatic hyperplasia using receiver operating characteristic and artificial neural network

Benign prostatic hyperplasia (BPH) is a chronic, progressive disease characterized by mesenchymal cell-predominance and stromal and glandular cell-hyperproliferation. Although, the precise cause of BPH is unknown, it is believed to be associated with hormonal changes in aging men. Despite androgens and ageing are likely to play a role in the development of BPH, the pathophysiology of BPH remains uncertain. This paper aims to evaluate the diagnostic efficacy of platelet-to-lymphocyte ratio (PLR), neutrophil-lymphocyte ratio (NLR) and systemic immune-inflammation index in in diagnosing BPH. A single-center-randomized-retrospective study was carried out at Alzahraa university hospital between January 2022 and November 2022 on 80 participants (40 non-BPH subjects and 40 patients with symptomatic enlarged prostate) who visited the outpatient clinic or admitted to the urology department. The BPH cases were evaluated by digital rectal examination (DRE), International Prostate Symptom Score (IPSS), prostate size, prostate specific antigen (PSA), TRUS biopsy in elevated PSA > 4 ng/ml, PLR, NLR and systemic immune inflammatory (SII). The diagnosing efficiency of the selected parameters was evaluated using Receiver Operating Characteristic (ROC) and Artificial Neural Network (ANN) showing excellent discrimination with 100% accuracy and AUC = 1 in the ROC curves. Moreover, the accuracy rate of the ANN exceeds 99%. Conclusion: PLR, NLR and SII can be significantly employed for diagnosing BPH.

Influence of Tumor Volume on the Fluence Rate Within Human Breast Model Using Continuous-Wave Diffuse Optical Imaging: A Simulation Study

Objective: This article investigates the effect of varying breast tumor size on the fluence rate distribution within a breast model during the diffuse optical imaging procedure. Background: Early detection of breast cancer is of significant importance owing to its wide spread among women worldwide. Mastectomy surgery became very common due to the late detection of breast cancers by the conventional diagnostic methods such as X-ray mammography and magnetic resonance imaging. On the contrary, optical imaging techniques provide a safe and more sensitive methodology, which is suitable for the early detection criteria. Methods: The implementation was performed based on simulating multiple detectors placed on the outer surface of a human breast model to compute the optical fluence rate after probing the breast (normal and different tumor sizes) with laser irradiation. Different laser wavelengths ranging from the red to near-infrared rays spectral range were examined to determine the optimum fluence rate that shows the highest capability to differentiate between normal and cancerous breasts. A three-dimensional breast model was created using the COMSOL multiphysics package where the optical fluence rate was estimated based on the finite-element solution of the diffusion equation. Results: To evaluate the efficiency of the suggested technique for identifying cancers and discriminate them from normal breast at various wavelengths (600-1000 nm) and several tumor sizes. Conclusions: The obtained results reveal different fluence rate distributions in the breast with different radius tumors, especially at 600 nm due to the significant differences in the scattering coefficient between malignancies and healthy tissue.

Detectability of low-oxygenated regions in human muscle tissue using near-infrared spectroscopy and phantom models

The present work aims to describe the detectability limits of hypoxic regions in human muscle under moderate thicknesses of adipose tissue to serve as a groundwork for the development of a wearable device to prevent pressure injuries. The optimal source-detector distances, detection limits, and the spatial resolution of hypoxic volumes in the human muscle are calculated using finite element method-based computer simulations conducted on 3-layer tissue models. Silicone phantoms matching the simulation geometries were manufactured, and their measurement results were compared to the simulations. The simulations showed good agreement with the performed experiments. Our results show detectability of hypoxic volumes under adipose tissue thicknesses of up to 1.5 cm. The maximum tissue depth, at which hypoxic volumes could be detected was 2.8 cm. The smallest detectable hypoxic volume in our study was 1.2 cm³. We thus show the detectability of hypoxic volumes in sizes consistent with those of early-stage pressure injury formation and, consequently, the feasibility of a device to prevent pressure injuries.

L1-norm based nonlinear reconstruction improves quantitative accuracy of spectral diffuse optical tomography

Spectrally constrained diffuse optical tomography (SCDOT) is known to improve reconstruction in diffuse optical imaging; constraining the reconstruction by coupling the optical properties across multiple wavelengths suppresses artefacts in the resulting reconstructed images. In other work, L1-norm regularization has been shown to improve certain types of image reconstruction problems as its sparsity-promoting properties render it robust against noise and enable the preservation of edges in images, but because the L1-norm is non-differentiable, it is not always simple to implement. In this work, we show how to incorporate L1 regularization into SCDOT. Three popular algorithms for L1 regularization are assessed for application in SCDOT: iteratively reweighted least square algorithm (IRLS), alternating directional method of multipliers (ADMM), and fast iterative shrinkage-thresholding algorithm (FISTA). We introduce an objective procedure for determining the regularization parameter in these algorithms and compare their performance in simulated experiments, and in real data acquired from a tissue phantom. Our results show that L1 regularization consistently outperforms Tikhonov regularization in this application, particularly in the presence of noise.

Cortical Activation Patterns Correlate with Speech Understanding After Cochlear Implantation

OBJECTIVES

Cochlear implants are a standard therapy for deafness, yet the ability of implanted patients to understand speech varies widely. To better understand this variability in outcomes, the authors used functional near-infrared spectroscopy to image activity within regions of the auditory cortex and compare the results to behavioral measures of speech perception.

DESIGN

The authors studied 32 deaf adults hearing through cochlear implants and 35 normal-hearing controls. The authors used functional near-infrared spectroscopy to measure responses within the lateral temporal lobe and the superior temporal gyrus to speech stimuli of varying intelligibility. The speech stimuli included normal speech, channelized speech (vocoded into 20 frequency bands), and scrambled speech (the 20 frequency bands were shuffled in random order). The authors also used environmental sounds as a control stimulus. Behavioral measures consisted of the speech reception threshold, consonant-nucleus-consonant words, and AzBio sentence tests measured in quiet.

RESULTS

Both control and implanted participants with good speech perception exhibited greater cortical activations to natural speech than to unintelligible speech. In contrast, implanted participants with poor speech perception had large, indistinguishable cortical activations to all stimuli. The ratio of cortical activation to normal speech to that of scrambled speech directly correlated with the consonant-nucleus-consonant words and AzBio sentences scores. This pattern of cortical activation was not correlated with auditory threshold, age, side of implantation, or time after implantation. Turning off the implant reduced the cortical activations in all implanted participants.

CONCLUSIONS

Together, these data indicate that the responses the authors measured within the lateral temporal lobe and the superior temporal gyrus correlate with behavioral measures of speech perception, demonstrating a neural basis for the variability in speech understanding outcomes after cochlear implantation.

A radiative transfer equation-based image-reconstruction method incorporating boundary conditions for diffuse optical imaging

Developing reconstruction methods for diffuse optical imaging requires accurate modeling of photon propagation, including boundary conditions arising due to refractive index mismatch as photons propagate from the tissue to air. For this purpose, we developed an analytical Neumann-series radiative transport equation (RTE)-based approach. Each Neumann series term models different scattering, absorption, and boundary-reflection events. The reflection is modeled using the Fresnel equation. We use this approach to design a gradient-descent-based analytical reconstruction algorithm for a three-dimensional (3D) setup of a diffuse optical imaging (DOI) system. The algorithm was implemented for a three-dimensional DOI system consisting of a laser source, cuboidal scattering medium (refractive index > 1), and a pixelated detector at one cuboid face. In simulation experiments, the refractive index of the scattering medium was varied to test the robustness of the reconstruction algorithm over a wide range of refractive index mismatches. The experiments were repeated over multiple noise realizations. Results showed that by using the proposed algorithm, the photon propagation was modeled more accurately. These results demonstrated the importance of modeling boundary conditions in the photon-propagation model.

Modified reciprocity relation for the time-dependent diffusion equation

The classical reciprocity relation of radiative transfer fails for two points placed in regions having different indices of refraction. A modified reciprocity relation that involves the relative refractive index between the two points considered was previously derived for the continuous wave (cw) radiative transfer equation and for the cw diffusion equation (DE) [J. Opt. Soc. Am. A14, 486 (1997)]. In this paper, we extend these findings to the time-dependent DE and we discuss some implications to diffuse optical tomography.

Effects of refractive index mismatch in optical CT imaging of polymer gel dosimeters

PURPOSE

Proposing an image reconstruction technique, algebraic reconstruction technique-refraction correction (ART-rc). The proposed method takes care of refractive index mismatches present in gel dosimeter scanner at the boundary, and also corrects for the interior ray refraction. Polymer gel dosimeters with high dose regions have higher refractive index and optical density compared to the background medium, these changes in refractive index at high dose results in interior ray bending.

METHODS

The inclusion of the effects of refraction is an important step in reconstruction of optical density in gel dosimeters. The proposed ray tracing algorithm models the interior multiple refraction at the inhomogeneities. Jacob's ray tracing algorithm has been modified to calculate the pathlengths of the ray that traverses through the higher dose regions. The algorithm computes the length of the ray in each pixel along its path and is used as the weight matrix. Algebraic reconstruction technique and pixel based reconstruction algorithms are used for solving the reconstruction problem. The proposed method is tested with numerical phantoms for various noise levels. The experimental dosimetric results are also presented.

RESULTS

The results show that the proposed scheme ART-rc is able to reconstruct optical density inside the dosimeter better than the results obtained using filtered backprojection and conventional algebraic reconstruction approaches. The quantitative improvement using ART-rc is evaluated using gamma-index. The refraction errors due to regions of different refractive indices are discussed. The effects of modeling of interior refraction in the dose region are presented.

CONCLUSIONS

The errors propagated due to multiple refraction effects have been modeled and the improvements in reconstruction using proposed model is presented. The refractive index of the dosimeter has a mismatch with the surrounding medium (for dry air or water scanning). The algorithm reconstructs the dose profiles by estimating refractive indices of multiple inhomogeneities having different refractive indices and optical densities embedded in the dosimeter. This is achieved by tracking the path of the ray that traverses through the dosimeter. Extensive simulation studies have been carried out and results are found to be matching that of experimental results.

Solution of Radiative Transfer Equation with a Continuous and Stochastic Varying Refractive Index by Legendre Transform Method

The present paper gives a new computational framework within which radiative transfer in a varying refractive index biological tissue can be studied. In our previous works, Legendre transform was used as an innovative view to handle the angular derivative terms in the case of uniform refractive index spherical medium. In biomedical optics, our analysis can be considered as a forward problem solution in a diffuse optical tomography imaging scheme. We consider a rectangular biological tissue-like domain with spatially varying refractive index submitted to a near infrared continuous light source. Interaction of radiation with the biological material into the medium is handled by a radiative transfer model. In the studied situation, the model displays two angular redistribution terms that are treated with Legendre integral transform. The model is used to study a possible detection of abnormalities in a general biological tissue. The effect of the embedded nonhomogeneous objects on the transmitted signal is studied. Particularly, detection of targets of localized heterogeneous inclusions within the tissue is discussed. Results show that models accounting for variation of refractive index can yield useful predictions about the target and the location of abnormal inclusions within the tissue.

Virtual source method for diffuse optical imaging

The Green's function for diffusive wave propagation can be obtained by utilizing the representation theorems of the convolution type and the correlation type. In this work, the Green's function is retrieved by making use of the Robin boundary condition and the representation theorems for diffusive media. The diffusive Green's function between two detectors for photon flux is calculated by combining detector readings due to point light sources and utilizing virtual light sources at the detector positions in optical tomography. Two dimensional simulations for a circular region with eight sources and eight detectors located on the boundary are performed using a finite element method to demonstrate the feasibility of virtual sources. The most important potential application would be the replacement of noisy measurements with synthetic measurements that are provided by the virtual sources. This becomes an important issue in small animal and human studies. In addition, the same method may also be used to reduce the imaging time.

A near-infrared spectroscopy computational model for cerebral hemodynamics

Near infrared spectroscopy (NIRS) is a technique used to detect and measure changes in the concentrations of oxygenated hemoglobin, deoxygenated hemoglobin, and water in tissues based on the differential absorption, scattering, and refraction of the near infrared light. In this imaging technique, the optical properties of tissues are reconstructed from the measurements obtained from the sensors located on the boundary. A computational method for the rapid noninvasive detection ∕ quantification of cerebral hemorrhage is described using the above procedure. CFD Research Corporation's finite volume computational biology code was used to numerically mimic the NIRS procedure by (i) noninvasively 'numerically penetrating' the brain tissues and (ii) reconstructing the optical properties the presence of water, oxygenated, and deoxygenated blood. These numerical noninvasive measurements are then used to predict the extent and severity of the brain hemorrhage. The paper also discusses ideas to obtain the location and the severity of a localized injury. Two-dimensional and three-dimensional simulations are performed as a proof of concept for the numerical formulation being feasible for the above mentioned detection/quantification. The results demonstrate that this numerical NIRS formulation can be used as a noninvasive technique for both qualitative and quantitative evaluation of cerebral hemodynamics.

Three-dimensional Neumann-series approach to model light transport in nonuniform media

We present the implementation, validation, and performance of a three-dimensional (3D) Neumann-series approach to model photon propagation in nonuniform media using the radiative transport equation (RTE). The RTE is implemented for nonuniform scattering media in a spherical harmonic basis for a diffuse-optical-imaging setup. The method is parallelizable and implemented on a computing system consisting of NVIDIA Tesla C2050 graphics processing units (GPUs). The GPU implementation provides a speedup of up to two orders of magnitude over non-GPU implementation, which leads to good computational efficiency for the Neumann-series method. The results using the method are compared with the results obtained using the Monte Carlo simulations for various small-geometry phantoms, and good agreement is observed. We observe that the Neumann-series approach gives accurate results in many cases where the diffusion approximation is not accurate.

Simulating photon-transport in uniform media using the radiative transport equation: a study using the Neumann-series approach

We present the implementation, validation, and performance of a Neumann-series approach for simulating light propagation at optical wavelengths in uniform media using the radiative transport equation (RTE). The RTE is solved for an anisotropic-scattering medium in a spherical harmonic basis for a diffuse-optical-imaging setup. The main objectives of this paper are threefold: to present the theory behind the Neumann-series form for the RTE, to design and develop the mathematical methods and the software to implement the Neumann series for a diffuse-optical-imaging setup, and, finally, to perform an exhaustive study of the accuracy, practical limitations, and computational efficiency of the Neumann-series method. Through our results, we demonstrate that the Neumann-series approach can be used to model light propagation in uniform media with small geometries at optical wavelengths.

Effect of tissue fluid on accurate determination of the complex refractive index of animal tissue

We investigate the effect of tissue fluid on the measurement of complex refractive index (RI) of animal tissue. A new model is proposed and verified through experimental results of simulation samples made of glycerol and methyl-red-doped poly(methyl methacrylate). Coupled with polarized optical reflectance measurements performed on several kinds of animal muscle tissues, RIs were resolved using the new model. We find that the tissue fluid existing at the prism-sample interface is unavoidable. We also find that with a change of proportion of the tissue fluid, the RI of muscle tissue can still be measured using the new model.

Quantitative modeling of Cerenkov light production efficiency from medical radionuclides

There has been recent and growing interest in applying Cerenkov radiation (CR) for biological applications. Knowledge of the production efficiency and other characteristics of the CR produced by various radionuclides would help in accessing the feasibility of proposed applications and guide the choice of radionuclides. To generate this information we developed models of CR production efficiency based on the Frank-Tamm equation and models of CR distribution based on Monte-Carlo simulations of photon and β particle transport. All models were validated against direct measurements using multiple radionuclides and then applied to a number of radionuclides commonly used in biomedical applications. We show that two radionuclides, Ac-225 and In-111, which have been reported to produce CR in water, do not in fact produce CR directly. We also propose a simple means of using this information to calibrate high sensitivity luminescence imaging systems and show evidence suggesting that this calibration may be more accurate than methods in routine current use.

Refractive index measurement of acute rat brain tissue slices using optical coherence tomography

An optical coherence tomography (OCT) system employing a microelectromechanical system (MEMS) mirror was used to measure the refractive index (RI) of anatomically different regions in acute brain tissue slices, in which viability was maintained. RI was measured in white-matter and grey-matter regions, including the cerebral cortex, putamen, hippocampus, thalamus and corpus callosum. The RI in the corpus callosum was found to be ~4% higher than the RIs in other regions. Changes in RI with tissue deformation were also measured in the cerebral cortex and corpus callosum under uniform compression (20-80% strain). For 80% strain, measured RIs increased nonlinearly by up to 70% and 90% in the cerebral cortex and corpus callosum respectively. Knowledge of RI in heterogeneous tissues can be used to correct distorted optical images caused by RI variations between different regions. Also deformation-dependent changes in RI can be applied to OCT elastography or to mechanical tests based on optical imaging such as indentation tests.

Neuroimaging with near-infrared spectroscopy demonstrates speech-evoked activity in the auditory cortex of deaf children following cochlear implantation

Cochlear implants (CI) are commonly used to treat deafness in young children. While many factors influence the ability of a deaf child who is hearing through a CI to develop speech and language skills, an important factor is that the CI has to stimulate the auditory cortex. Obtaining behavioral measurements from young children with CIs can often be unreliable. While a variety of noninvasive techniques can be used for detecting cortical activity in response to auditory stimuli, many have critical limitations when applied to the pediatric CI population. We tested the ability of near-infrared spectroscopy (NIRS) to detect cortical responses to speech stimuli in pediatric CI users. Neuronal activity leads to changes in blood oxy- and deoxy-hemoglobin concentrations that can be detected by measuring the transmission of near-infrared light through the tissue. To verify the efficacy of NIRS, we first compared auditory cortex responses measured with NIRS and fMRI in normal-hearing adults. We then examined four different participant cohorts with NIRS alone. Speech-evoked cortical activity was observed in 100% of normal-hearing adults (11 of 11), 82% of normal-hearing children (9 of 11), 78% of deaf children who have used a CI > 4 months (28 of 36), and 78% of deaf children who completed NIRS testing on the day of CI initial activation (7 of 9). Therefore, NIRS can measure cortical responses in pediatric CI users, and has the potential to be a powerful adjunct to current CI assessment tools.

Comprehensive investigation of three-dimensional diffuse optical tomography with depth compensation algorithm

A depth compensation algorithm (DCA) can effectively improve the depth localization of diffuse optical tomography (DOT) by compensating the exponentially decreased sensitivity in the deep tissue. In this study, DCA is investigated based on computer simulations, tissue phantom experiments, and human brain imaging. The simulations show that DCA can largely improve the spatial resolution of DOT in addition to the depth localization, and DCA is also effective for multispectral DOT with a wide range of optical properties in the background tissue. The laboratory phantom experiment demonstrates that DCA can effectively differentiate two embedded objects at different depths in the medium. DCA is further validated by human brain imaging using a finger-tapping task. To our knowledge, this is the first demonstration to show that DCA is capable of accurately localizing cortical activations in the human brain in three dimensions.

Topographic localization of brain activation in diffuse optical imaging using spherical wavelets

Diffuse optical imaging is a non-invasive technique that uses near-infrared light to measure changes in brain activity through an array of sensors placed on the surface of the head. Compared to functional MRI, optical imaging has the advantage of being portable while offering the ability to record functional changes in both oxy- and deoxy-hemoglobin within the brain at a high temporal resolution. However, the reconstruction of accurate spatial images of brain activity from optical measurements represents an ill-posed and underdetermined problem that requires regularization. These reconstructions benefit from incorporating prior information about the underlying spatial structure and function of the brain. In this work, we describe a novel image reconstruction approach which uses surface-based wavelets derived from structural MRI to incorporate high-resolution anatomical and structural prior information about the brain. This surface-based approach is used to approximate brain activation patterns through the reconstruction and presentation of topographical (two-dimensional) maps of brain activation directly onto the folded surface of the cortex. The set of wavelet coefficients is directly estimated by a truncated singular-value decomposition based pseudo-inversion of the wavelet projection of the optical forward model. We use a reconstruction metric based on Shannon entropy which quantifies the sparse loading of the wavelet coefficients and is used to determine the optimal truncation and regularization of this inverse model. In this work, examples of the performance of this model are illustrated for several cases of numerical simulation and experimental data with comparison to functional magnetic resonance imaging.

Numerical modelling and image reconstruction in diffuse optical tomography

The development of diffuse optical tomography as a functional imaging modality has relied largely on the use of model-based image reconstruction. The recovery of optical parameters from boundary measurements of light propagation within tissue is inherently a difficult one, because the problem is nonlinear, ill-posed and ill-conditioned. Additionally, although the measured near-infrared signals of light transmission through tissue provide high imaging contrast, the reconstructed images suffer from poor spatial resolution due to the diffuse propagation of light in biological tissue. The application of model-based image reconstruction is reviewed in this paper, together with a numerical modelling approach to light propagation in tissue as well as generalized image reconstruction using boundary data. A comprehensive review and details of the basis for using spatial and structural prior information are also discussed, whereby the use of spectral and dual-modality systems can improve contrast and spatial resolution.

Early-photon fluorescence tomography: spatial resolution improvements and noise stability considerations

In vivo tissue imaging using near-infrared light suffers from low spatial resolution and poor contrast recovery because of highly scattered photon transport. For diffuse optical tomography (DOT) and fluorescence molecular tomography (FMT), the resolution is limited to about 5-10% of the diameter of the tissue being imaged, which puts it in the range of performance seen in nuclear medicine. This paper introduces the mathematical formalism explaining why the resolution of FMT can be significantly improved when using instruments acquiring fast time-domain optical signals. This is achieved through singular-value analysis of the time-gated inverse problem based on weakly diffused photons. Simulations relevant to mouse imaging are presented showing that, in stark contrast to steady-state imaging, early time-gated intensities (within 200 ps or 400 ps) can in principle be used to resolve small fluorescent targets (radii from 1.5 to 2.5 mm) separated by less than 1.5 mm.

Near infrared optical tomography using NIRFAST: Algorithm for numerical model and image reconstruction

Diffuse optical tomography, also known as near infrared tomography, has been under investigation, for non-invasive functional imaging of tissue, specifically for the detection and characterization of breast cancer or other soft tissue lesions. Much work has been carried out for accurate modeling and image reconstruction from clinical data. NIRFAST, a modeling and image reconstruction package has been developed, which is capable of single wavelength and multi-wavelength optical or functional imaging from measured data. The theory behind the modeling techniques as well as the image reconstruction algorithms is presented here, and 2D and 3D examples are presented to demonstrate its capabilities. The results show that 3D modeling can be combined with measured data from multiple wavelengths to reconstruct chromophore concentrations within the tissue. Additionally it is possible to recover scattering spectra, resulting from the dominant Mie-type scatter present in tissue. Overall, this paper gives a comprehensive over view of the modeling techniques used in diffuse optical tomographic imaging, in the context of NIRFAST software package.

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.

Spectrally resolved bioluminescence tomography using the reciprocity approach

Spectrally resolved bioluminescence optical tomography is an approach to recover images of, for example, Luciferase activity within a volume using multiwavelength emission data from internal bioluminescence sources. The underlying problem of uniqueness associated with nonspectrally resolved intensity-based bioluminescence tomography is demonstrated and it is shown that using a non-negative constraint inverse algorithm, an accurate solution for the source distribution can be calculated from the measured data. Reconstructed images of bioluminescence are presented using both simulated complex and heterogeneous small animal models as well as real multiwavelength data from a tissue-simulating phantom. The location of the internal bioluminescence source using experimental data is obtained with 0.5 mm accuracy and it is shown that small (2.5 mm diameter) sources of up to 12.5 mm deep, within a complex mouse model, can be resolved accurately using a single view data collection strategy. Finally, using the reciprocity approach for image reconstruction, a dramatic improvement in computational time is shown without loss to image accuracy with both experimental and simulated data, potentially reducing computing time from 402 to 3.75 h.

Improving image quality of diffuse optical tomography with a projection-error-based adaptive regularization method

Diffuse optical tomography (DOT) reconstructs the images of internal optical parameter distribution using noninvasive boundary measurements. The image reconstruction procedure is known to be an ill-posed problem. In order to solve such a problem, a regularization technique is needed to constrain the solution space. In this study, a projection-error-based adaptive regularization (PAR) technique is proposed to improve the reconstructed image quality. Simulations are performed using a diffusion approximation model and the simulated results demonstrate that the PAR technique can improve reconstruction precision of object more effectively. The method is demonstrated to have low sensitivity to noise at various noise levels. Moreover, with the PAR method, the detectability of an object located both at the center and near the peripheral regions has been increased largely.

An approximate numerical technique for characterizing optical pulse propagation in inhomogeneous biological tissue

An approximate numerical technique for modeling optical pulse propagation through weakly scattering biological tissue is developed by solving the photon transport equation in biological tissue that includes varying refractive index and varying scattering/absorption coefficients. The proposed technique involves first tracing the ray paths defined by the refractive index profile of the medium by solving the eikonal equation using a Runge-Kutta integration algorithm. The photon transport equation is solved only along these ray paths, minimizing the overall computational burden of the resulting algorithm. The main advantage of the current algorithm is that it enables to discretise the pulse propagation space adaptively by taking optical depth into account. Therefore, computational efficiency can be increased without compromising the accuracy of the algorithm.

Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography

Diffuse optical tomography (DOT) involves estimation of tissue optical properties using noninvasive boundary measurements. The image reconstruction procedure is a nonlinear, ill-posed, and ill-determined problem, so overcoming these difficulties requires regularization of the solution. While the methods developed for solving the DOT image reconstruction procedure have a long history, there is less direct evidence on the optimal regularization methods, or exploring a common theoretical framework for techniques which uses least-squares (LS) minimization. A generalized least-squares (GLS) method is discussed here, which takes into account the variances and covariances among the individual data points and optical properties in the image into a structured weight matrix. It is shown that most of the least-squares techniques applied in DOT can be considered as special cases of this more generalized LS approach. The performance of three minimization techniques using the same implementation scheme is compared using test problems with increasing noise level and increasing complexity within the imaging field. Techniques that use spatial-prior information as constraints can be also incorporated into the GLS formalism. It is also illustrated that inclusion of spatial priors reduces the image error by at least a factor of 2. The improvement of GLS minimization is even more apparent when the noise level in the data is high (as high as 10%), indicating that the benefits of this approach are important for reconstruction of data in a routine setting where the data variance can be known based upon the signal to noise properties of the instruments.

Diffuse light propagation in a turbid medium with varying refractive index: Monte Carlo modeling in a spherically symmetrical geometry

We report on the development of Monte Carlo software that can model media with spatially varying scattering coefficient, absorption, and refractive index. The varying refractive index is implemented by calculating curved photon paths in the medium. The results of the numerical simulations are compared with analytical solutions obtained using the diffusion approximation. The model under investigation is a scattering medium that contains a spherically symmetrical inclusion (inhomogeneity) created by variation in optical properties and having no sharp boundaries. The following steady-state cases are considered: (a) a nonabsorbing medium with a spherically symmetrical varying refractive index, (b) an inclusion with varying absorption and scattering coefficients and constant refractive index, and (c) an inclusion with varying absorption, scattering, and refractive index. In the latter case it is shown that the interplay between the absorption coefficient and the refractive index may create the effect of a hidden inclusion.

Analytical solution for light propagation in a two-layer tissue structure with a tilted interface for breast imaging

Reflectance measurement of breast tissue is influenced by the underlying chest wall, which is often tilted as seen by the detection probe. We develop an analytical solution of light propagation in a two-layer tissue structure with tilted interface and refractive index difference between the layers. We validate the analytical solution with Monte Carlo simulations and phantom experiments, and a good agreement is seen. The influence of varying the tilting angle of the interface on the reflectance is discussed for two types of layered structures. Further, we apply the developed analytical solution to obtain the optical properties of breast tissue and chest wall from clinical data. Inverse calculation using the developed solution applied to the data obtained from Monte Carlo simulations shows that the optical properties of both layers are obtained with higher accuracy as compared to using a simple two-layer model ignoring the interface tilt. This is expected to improve the accuracy in estimating the optical properties of breast tissue, thus enhancing the accuracy of optical tomography of breast tumors.

Refractive index of carcinogen-induced rat mammary tumours

Near-infrared optical techniques for clinical breast cancer screening in humans are rapidly advancing. Based on the computational inversion of the photon diffusion process through the breast, these techniques rely on optical tissue models for accurate image reconstruction. Recent interest has surfaced regarding the effect of refractive index variations on these reconstructions. Although many data exist regarding the scattering and absorption properties of normal and diseased tissue, no measurements of refractive index appear in the literature. In this paper, we present near-infrared refractive index data acquired from N-methyl-N-nitrosourea-induced rat mammary tumours, which are similar in pathology and disease progression to human ductal carcinoma. Eight animals, including one control, were employed in this study, yielding data from 32 tumours as well as adjacent adipose and connective tissues.

Video-rate near-infrared optical tomography using spectrally encoded parallel light delivery

A novel parallel source implementation approach to near-infrared tomography is demonstrated through spectral encoding of the light delivery. This new technique allows many sources to be input into the tissue at the same time, and a high-resolution spectrometer is used to spatially spread out the signals from each spectrally encoded source. The parallel sampling of all sources at all detection locations renders rapid imaging. Acquisition of complete tomographic data sets at a video rate of 35 frames/s is achieved for imaging of a 6.35 mm diameter inclusion with an absorption coefficient of 0.01 mm(-1) and a reduced scattering coefficient of 1.5 mm(-1) that is moving along a circular path inside a 1% Intralipid solution.

Time-resolved optical mammography using a liquid coupled interface

A method has been devised for generating three-dimensional optical images of the breast using a 32-channel time-resolved system and a liquid-coupled interface. The breast is placed in a hemispherical cup surrounded by sources and detectors, and the remaining space is filled with a fluid with tissue-like optical properties. This approach has three significant benefits. First, cups can accommodate a large range of breast sizes, enabling the entire volume of the breast to be sampled. Second, the coupling of the source and detector optics at the surface is constant and independent of the subject, enabling intensity measurements to be employed in the image reconstruction. Third, the external geometry of the reconstructed volume is known exactly. Images of isolated targets with contrasting absorbing and scattering properties have been acquired, and the performance of the system has been evaluated in terms of the contrast, spatial resolution, and localization accuracy. These parameters were strongly dependent on the location of the targets within the imaged volume. Preliminary images of a healthy human subject are also presented, which reveal subtle heterogeneity, particularly in the distribution of scatter. The ability to detect an absorbing target adjacent to the breast is also demonstrated.

Recent advances in diffuse optical imaging

We review the current state-of-the-art of diffuse optical imaging, which is an emerging technique for functional imaging of biological tissue. It involves generating images using measurements of visible or near-infrared light scattered across large (greater than several centimetres) thicknesses of tissue. We discuss recent advances in experimental methods and instrumentation, and examine new theoretical techniques applied to modelling and image reconstruction. We review recent work on in vivo applications including imaging the breast and brain, and examine future challenges.

Practical and adequate approach to modeling light propagation in an adult head with low-scattering regions by use of diffusion theory

A practical and adequate approach to modeling light propagation in an adult head with a low-scattering cerebrospinal fluid (CSF) region by use of diffusion theory was investigated. The diffusion approximation does not hold in a nonscattering or low-scattering regions. The hybrid radiosity-diffusion method was adopted to model the light propagation in the head with a nonscattering region. In the hybrid method the geometry of the nonscattering region is acquired as a priori information. In reality, low-level scattering occurs in the CSF region and may reduce the error caused by the diffusion approximation. The partial optical path length and the spatial sensitivity profile calculated by the finite-element method agree well with those calculated by the Monte Carlo method in the case in which the transport scattering coefficient of the CSF layer is greater than 0.3 mm(-1). Because it is feasible to assume that the transport scattering coefficient of a CSF layer is 0.3 mm(-1), it is practical to adopt diffusion theory to the modeling of light propagation in an adult head as an alternative to the hybrid method.

Effects of refractive index on near-infrared tomography of the breast

Near infrared (NIR) optical tomography is an imaging technique in which internal images of optical properties are reconstructed with the boundary measurements of light propagation through the medium. Recent advances in instrumentation and theory have led to the use of this method for the detection and characterization of tumors within the female breast tissue. Most image reconstruction approaches have used the diffusion approximation and have assumed that the refractive index of the breast is constant, with a bulk value of approximately 1.4. We have applied a previously reported modified diffusion approximation, in which the refractive index for different tissues can be modeled. The model was used to generate NIR data from a realistic breast geometry containing a localized anomaly. Using this simulated data, we have reconstructed optical images, both with and without correct knowledge of the refractive-index distribution to show that the modified diffusion approximation can accurately recover the anomaly given a priori knowledge of refractive index. But using a reconstruction algorithm without the use of correct a priori information regarding the refractive-index distribution is shown as recovering the anomaly but with a degraded quality, depending on the degree of refractive index mismatch. The results suggest that provided the refractive index of breast tissue is approximately 1.3-1.4, their exclusion will have minimal effect on the reconstructed images.

Direct bidirectional angle-insensitive imaging of the flow signal intensity in Doppler optical coherence tomography

We introduce a new method, to our knowledge, for direct detection of flow signal intensity by stationary target rejection. In our system, two delay lines are constructed with identical scanning speed and ranging depth. One delay line is used for depth ranging as well as phase modulation, and the other one acts as a full-range retroreflector (FRRR). The signal from this FRRR carries the overall features of local phase modulation, and it is used as the local oscillator for coherent demodulation. With this setup, stationary targets can be rejected at a 4-kHz high-pass cutoff frequency of the filter that follows the demodulator, compared with 20 kHz for conventional fixed-frequency demodulation. This technique features angle insensitivity and provides flow direction as well by implementing standard in-phase and quadrature detection. Besides the direct directional detection of flow signal intensity, flow speed information can be acquired with postprocessing.

Radiative transfer in a turbid medium with a varying refractive index: comment

In the literature one can encounter at least two different radiative transfer equations for media with spatially varying refractive indices. These are the results of Ferwerda [J. Opt. A Pure Appl. Opt. 1, L1 (1999)] and Tualle and Tinet [Opt. Commun. 228, 33 (2003)]. Accordingly, two different diffusion approximations are derived from these two radiative transfer equations. I reconsider the derivation of the radiative transfer equation in a medium with an inhomogeneous refractive index and confirm the result of Tualle and Tinet. In the diffusion approximation, a simple analytical solution has been found for the steady-state illumination of a non-absorbing turbid medium with a varying refractive index.

Do fluorescence decays remitted from tissues accurately reflect intrinsic fluorophore lifetimes?

Fluorescence spectroscopy and imaging methods, including fluorescence lifetime sensing, are being developed for noninvasive tissue diagnostics. The purpose of this study was to identify and quantify those factors affecting the accurate recovery of fluorophore lifetimes from inhomogeneous tissues in vivo. A Monte Carlo code was developed to numerically simulate time-resolved fluorescence measurements on layered epithelial tissues. Simulations were run with experimental parameters matching previously reported clinical studies in the gastrointestinal tract. The results demonstrate that variations in fluorescence decay time as large as those detected clinically between normal and premalignant tissues (approximately 2 ns) could be simulated by variations in tissue morphology or biochemistry, even when intrinsic fluorophore lifetimes were held constant.

Effect of the refractive index mismatch on light propagation through diffusive layered media

The effect of the refractive index mismatch on light propagation through diffusive layers has been investigated. The refractive index mismatch changes the balance of energy inside the medium determining a temporal and spatial redistribution of light. Light penetration through the medium is obstructed (facilitated) by a negative (positive) refractive index step variation. An analytical solution of the time-dependent diffusion equation that accounts for this effect has been obtained. The solution has been validated by comparisons with the results of Monte Carlo simulations. An excellent description of light propagation is given even for a high refractive index mismatch.

Breast deformation modelling for image reconstruction in near infrared optical tomography

Near infrared tomography (NIR) is a novel imaging technique that can be used to reconstruct tissue optical properties from measurements of light propagation through tissue. More specifically NIR measurements over a range of wavelengths can be used to obtain internal images of physiologic parameters and these images can be used to detect and characterize breast tumour. To obtain good NIR measurements, it is essential to have good contact between the optical fibres and the breast which in-turn results in the deformation of the breast due to the soft plasticity of the tissue. In this work, a tissue deformation model of the female breast is presented that will account for the altered shape of the breast during clinical NIR measurements. Using a deformed model of a breast, simulated NIR data were generated and used to reconstruct images of tissue absorption and reduced scatter using several assumptions about the imaging domain. Using either a circular or irregular 2D geometry for image reconstruction produces good localization of the absorbing anomaly, but it leads to degradation of the image quality. By modifying the assumptions about the imaging domain to a 3D conical model, with the correct diameter at the plane of NIR measurement, significantly improves the quality of reconstructed images and helps reduce image artefacts. Finally, assuming a non-deformed breast shape for image reconstruction is shown to lead to poor quality images since the geometry of the breast is greatly altered, whereas using the correct deformed geometry produces the best images.