Light Propagation In Tissue Research Articles

Hybrid forward-peaked-scattering-diffusion approximations for light propagation in turbid media with low-scattering regions

Coupled light transport models which use forward-peaked scattering approximations of the radiative transport equation and the diffusion approximation to model light propagation in tissues are introduced. The forward-peaked Fokker–Planck–Eddington approximations are used in those parts of the domain in which the diffusion approximation is not valid, such as close to the source and boundary, and in low-scattering regions. The diffusion approximation is used elsewhere. The models are coupled through boundary conditions and the resulting system of equations is solved using a finite element method. The proposed coupled Fokker–Planck-diffusion and Fokker–Planck–Eddington-diffusion models are tested with simulations, and compared with the radiative transport equation, diffusion approximation and coupled radiative transport-diffusion model. The results show that the new coupled models give almost as accurate results as the radiative transport equation with reduced computational load.

Mesh Simplification Based on Edge Collapsing Could Improve Computational Efficiency in Near Infrared Optical Tomographic Imaging

The diffusion equation-based modeling of near infrared light propagation in tissue is achieved by using finite-element mesh for imaging real-tissue types, such as breast and brain. The finite-element mesh size (number of nodes) dictates the parameter space in the optical tomographic imaging. Most commonly used finite-element meshing algorithms do not provide the flexibility of distinct nodal spacing in different regions of imaging domain to take the sensitivity of the problem into consideration. This study aims to present a computationally efficient mesh simplification method that can be used as a preprocessing step to iterative image reconstruction, where the finite-element mesh is simplified by using an edge collapsing algorithm to reduce the parameter space at regions where the sensitivity of the problem is relatively low. It is shown, using simulations and experimental phantom data for simple meshes/domains, that a significant reduction in parameter space could be achieved without compromising on the reconstructed image quality. The maximum errors observed by using the simplified meshes were less than 0.27% in the forward problem and 5% for inverse problem.

Comparisons of hybrid radiosity-diffusion model and diffusion equation for bioluminescence tomography in cavity cancer detection

Bioluminescence tomography (BLT) has been successfully applied to the detection and therapeutic evaluation of solid cancers. However, the existing BLT reconstruction algorithms are not accurate enough for cavity cancer detection because of neglecting the void problem. Motivated by the ability of the hybrid radiosity-diffusion model (HRDM) in describing the light propagation in cavity organs, an HRDM-based BLT reconstruction algorithm was provided for the specific problem of cavity cancer detection. HRDM has been applied to optical tomography but is limited to simple and regular geometries because of the complexity in coupling the boundary between the scattering and void region. In the provided algorithm, HRDM was first applied to three-dimensional complicated and irregular geometries and then employed as the forward light transport model to describe the bioluminescent light propagation in tissues. Combining HRDM with the sparse reconstruction strategy, the cavity cancer cells labeled with bioluminescent probes can be more accurately reconstructed. Compared with the diffusion equation based reconstruction algorithm, the essentiality and superiority of the HRDM-based algorithm were demonstrated with simulation, phantom and animal studies. An in vivo gastric cancer-bearing nude mouse experiment was conducted, whose results revealed the ability and feasibility of the HRDM-based algorithm in the biomedical application of gastric cancer detection.

Early-photon fluorescence tomography of a heterogeneous mouse model with the telegraph equation

In this study, we investigate the performance of early-photon fluorescence tomography based on a heterogeneous mouse model. The telegraph equation is used to accurately describe the propagation of light in tissues at short times. The optimal time gate for early photons is determined by singular value analysis at first. Then, fluorescent targets located in different organs of the mouse model are investigated. The simulation results demonstrate that the reconstructed tomographic images based on early photons yield improvement in spatial resolution and quantification than the quasi-CW measurements. Meanwhile, compared with the homogeneous model, the use of the heterogeneous model can improve the accuracy of fluorescence distribution and quantification in early-photon fluorescence tomography.

Fluorescence Molecular Tomography: Principles and Potential for Pharmaceutical Research

Fluorescence microscopic imaging is widely used in biomedical research to study molecular and cellular processes in cell culture or tissue samples. This is motivated by the high inherent sensitivity of fluorescence techniques, the spatial resolution that compares favorably with cellular dimensions, the stability of the fluorescent labels used and the sophisticated labeling strategies that have been developed for selectively labeling target molecules. More recently, two and three-dimensional optical imaging methods have also been applied to monitor biological processes in intact biological organisms such as animals or even humans. These whole body optical imaging approaches have to cope with the fact that biological tissue is a highly scattering and absorbing medium. As a consequence, light propagation in tissue is well described by a diffusion approximation and accurate reconstruction of spatial information is demanding. While in vivo optical imaging is a highly sensitive method, the signal is strongly surface weighted, i.e., the signal detected from the same light source will become weaker the deeper it is embedded in tissue, and strongly depends on the optical properties of the surrounding tissue. Derivation of quantitative information, therefore, requires tomographic techniques such as fluorescence molecular tomography (FMT), which maps the three-dimensional distribution of a fluorescent probe or protein concentration. The combination of FMT with a structural imaging method such as X-ray computed tomography (CT) or Magnetic Resonance Imaging (MRI) will allow mapping molecular information on a high definition anatomical reference and enable the use of prior information on tissue's optical properties to enhance both resolution and sensitivity. Today many of the fluorescent assays originally developed for studies in cellular systems have been successfully translated for experimental studies in animals. The opportunity of monitoring molecular processes non-invasively in the intact organism is highly attractive from a diagnostic point of view but even more so for the drug developer, who can use the techniques for proof-of-mechanism and proof-of-efficacy studies. This review shall elucidate the current status and potential of fluorescence tomography including recent advances in multimodality imaging approaches for preclinical and clinical drug development.

Hybrid Small Animal Imaging System Combining Magnetic Resonance Imaging With Fluorescence Tomography Using Single Photon Avalanche Diode Detectors

The high sensitivity of fluorescence imaging enables the detection of molecular processes in living organisms. However, diffuse light propagation in tissue prevents accurate recovery of tomographic information on fluorophore distribution for structures embedded deeper than 0.5 mm. Combining optical with magnetic resonance imaging (MRI) provides an accurate anatomical reference for fluorescence imaging data and thereby enables the correlation of molecular with high quality structural/functional information. We describe an integrated system for small animal imaging incorporating a noncontact fluorescence molecular tomography (FMT) system into an MRI detector. By adopting a free laser beam design geometrical constraints imposed by the use of optical fibers could be avoided allowing for flexible fluorescence excitation schemes. Photon detection based on a single-photon avalanche diode array enabled simultaneous FMT/MRI measurements without interference between modalities. In vitro characterization revealed good spatial accuracy of FMT data and accurate quantification of dye concentrations. Feasibility of FMT/MRI was demonstrated in vivo by simultaneous assessment of protease activity and tumor morphology in murine colon cancer xenografts.

Implementation of the equation of radiative transfer on block-structured grids for modeling light propagation in tissue

We present the first algorithm for solving the equation of radiative transfer (ERT) in the frequency domain (FD) on three-dimensional block-structured Cartesian grids (BSG). This algorithm allows for accurate modeling of light propagation in media of arbitrary shape with air-tissue refractive index mismatch at the boundary at increased speed compared to currently available structured grid algorithms. To accurately model arbitrarily shaped geometries the algorithm generates BSGs that are finely discretized only near physical boundaries and therefore less dense than fine grids. We discretize the FD-ERT using a combination of the upwind-step method and the discrete ordinates (SN) approximation. The source iteration technique is used to obtain the solution. We implement a first order interpolation scheme when traversing between coarse and fine grid regions. Effects of geometry and optical parameters on algorithm performance are evaluated using numerical phantoms (circular, cylindrical, and arbitrary shape) and varying the absorption and scattering coefficients, modulation frequency, and refractive index. The solution on a 3-level BSG is obtained up to 4.2 times faster than the solution on a single fine grid, with minimal increase in numerical error (less than 5%).

PDE-Constrained Fluorescence Tomography With the Frequency-Domain Equation of Radiative Transfer

We present the first fluorescence tomography algorithm that is based on a partial differential equation (PDE) constrained approach. PDE methods have been increasingly employed in many numerical applications, as they often lead to faster and more robust solutions of many inverse problems. In particular, we use a sequential quadratic programming (SQP) method, which allows solving the two forward problems in fluorescence tomography (one for the excitation and one for the emission radiances) and one inverse problem (for recovering the spatial distribution of the fluorescent sources) simultaneously by updating both forward and inverse variables in simultaneously at each of iteration of the optimization process. We evaluate the performance of this approach with numerical and experimental data using a transport-theory frequency-domain algorithm as forward model for light propagation in tissue. The results show that the PDE-constrained approach is computationally stable and accelerates the image reconstruction process up to a factor of 15 when compared to commonly employed unconstrained methods.

Approximation of Internal Refractive Index Variation Improves Image Guided Diffuse Optical Tomography of Breast

Effective usage of image guidance by incorporating the refractive index (RI) variation in computational modeling of light propagation in tissue is investigated to assess its impact on optical-property estimation. With the aid of realistic patient breast three-dimensional models, the variation in RI for different regions of tissue under investigation is shown to influence the estimation of optical properties in image-guided diffuse optical tomography (IG-DOT) using numerical simulations. It is also shown that by assuming identical RI for all regions of tissue would lead to erroneous estimation of optical properties. The a priori knowledge of the RI for the segmented regions of tissue in IG-DOT, which is difficult to obtain for the in vivo cases, leads to more accurate estimates of optical properties. Even inclusion of approximated RI values, obtained from the literature, for the regions of tissue resulted in better estimates of optical properties, with values comparable to that of having the correct knowledge of RI for different regions of tissue.

Nonlinear Inversion Schemes for Fluorescence Optical Tomography

Fluorescence optical tomography is a non-invasive imaging modality that employs the absorption and re-emission of light by fluorescent dyes. The aim is to reconstruct the fluorophore distribution in a body from measurements of light intensities at the boundary. Due to the diffusive nature of light propagation in tissue, fluorescence tomography is a nonlinear and severely ill-posed problem, and some sort of regularization is required for a stable solution. In this paper we investigate reconstruction methods based on Tikhonov regularization with nonlinear penalty terms, namely total-variation regularization and a levelset-type method using a nonlinear parameterization of the unknown function. Moreover, we use the full threedimensional nonlinear forward model, which arises from the governing system of partial differential equations. We discuss the numerical realization of the regularization schemes by Newtontype iterations, present some details of the discretization by finite element methods, and outline the efficient implementation of sensitivity systems via adjoint methods. As we will demonstrate in numerical tests, the proposed nonlinear methods provide better reconstructions than standard methods based on linearized forward models and linear penalty terms. We will additionally illustrate, that the careful discretization of the methods derived on the continuous level allows to obtain reliable, mesh independent reconstruction algorithms.

Development of a compensation algorithm for accurate depth localization in diffuse optical tomography

Diffuse optical tomography endures poor depth localization, since its sensitivity decreases severely with increased depth. In this study, we demonstrate a depth compensation algorithm (DCA), which optimally counterbalances the decay nature of light propagation in tissue so as to accurately localize absorbers in deep tissue. The novelty of DCA is to directly modify the sensitivity matrix, rather than the penalty term of regularization. DCA is based on maximum singular values (MSVs) of layered measurement sensitivities; these MSVs are inversely utilized to create a balancing weight matrix for compensating the measurement sensitivity in increased depth. Both computer simulations and laboratory experiments were performed to validate DCA. These results demonstrate that one (or two) 3-cm-deep absorber(s) can be accurately located in both lateral plane and depth within the laboratorial position errors.

Topographic mapping of subsurface fluorescent structures in tissue using multiwavelength excitation

Different colors of visible light penetrate to varying depths in tissue due to the wavelength dependence of tissue optical absorption and elastic scattering. We exploit this to map the contour of the closest surface of a buried fluorescent object. This uses a novel algorithm based on the diffusion theory description of light propagation in tissue at each excitation wavelength to derive metrics that define the depth of the top surface of the object. The algorithm was validated using a tissue-simulating phantom. It was then demonstrated in vivo by subsurface brain tumor topography in a rodent model, using the fluorescence signal from protoporphyrin IX that is preferentially synthesized within malignant cells following systemic application of aminolevulinic acid. Comparisons to histomorphometry in the brain post mortem show the spatial accuracy of the technique. This method has potential for fluorescence image-guided tumor surgery, as well as other biomedical and nonbiological applications in subsurface sensing.

Simulation of light propagation in tissue for analysis of NIRS signal

Simulation of light propagation in tissue for analysis of NIRS signal

Experimental bioluminescence tomography with fully parallel radiative-transfer-based reconstruction framework

Bioluminescence imaging is a very sensitive imaging modality, used in preclinical molecular imaging. However, in its planar projection form, it is non-quantitative and has poor spatial resolution. In contrast, bioluminescence tomography (BLT) promises to provide three dimensional quantitative source information. Currently, nearly all BLT reconstruction algorithms in use employ the diffusion approximation theory to determine light propagation in tissues. In this process, several approximations and assumptions that are made severely affect the reconstruction quality of BLT. It is therefore necessary to develop novel reconstruction methods using high-order approximation models to the radiative transfer equation (RTE) as well as more complex geometries for the whole-body of small animals. However, these methodologies introduce significant challenges not only in terms of reconstruction speed but also for the overall reconstruction strategy. In this paper, a novel fully-parallel reconstruction framework is proposed which uses a simplified spherical harmonics approximation (SPN). Using this framework, a simple linear relationship between the unknown source distribution and the surface measured photon density can be established. The distributed storage and parallel operations of the finite element-based matrix make SPN-based spectrally resolved reconstruction feasible at the small animal whole body level. Performance optimization of the major steps of the framework remarkably improves reconstruction speed. Experimental reconstructions with mouse-shaped phantoms and real mice show the effectiveness and potential of this framework. This work constitutes an important advance towards developing more precise BLT reconstruction algorithms that utilize high-order approximations, particularly second-order self-adjoint forms to the RTE for in vivo small animal experiments.

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.

Comparison of light scattering models for diffuse optical tomography

We reconstruct images of the absorption and the scattering coefficients for diffuse optical tomography using five different models for light propagation in tissues: (1) the radiative transport equation, (2) the delta-Eddington approximation, (3) the Fokker-Planck approximation, (4) the Fokker-Planck-Eddington approximation and (5) the generalized Fokker-Planck-Eddington approximation. The last four models listed are approximations of the radiative transport equation that take into account forward-peaked scattering analytically. Using simulated data from the numerical solution of radiative transport equation, we solve the inverse problem for the absorption and scattering coefficients using the transport-backtransport method. Through comparison of the numerical results, we show that all of these light scattering models produce good image reconstructions. In addition, we show that these approximations afford considerable computational savings over solving the radiative transport equation. However, all of the models exhibit significant "cross-talk" between absorption and scattering coefficient images. Among the approximations, we have found that the generalized Fokker-Planck-Eddington equation produced the best image reconstructions in comparison with the image reconstructions produced by the radiative transport equation.

Measurement depth and volume in laser Doppler flowmetry

A new method for estimating the measurement depth and volume in laser Doppler flowmetry (LDF) is presented. The method is based on Monte Carlo simulations of light propagation in tissue. The contribution from each individual Doppler shift is calculated and thereby multiple Doppler shifts are handled correctly. Different LDF setups for both probe based (0.0, 0.25, 0.5, and 1.2 mm source–detector separation) and imaging systems (0.5 and 2.0 mm beam diameter) are considered, at the wavelengths 543 nm, 633 nm, and 780 nm. Non-linear speckle pattern effects are accounted for in the imaging system setups. The effects of tissue optical properties, blood concentration, and blood oxygen saturation are evaluated using both homogeneous tissue models and a layered skin model. The results show that the effect on the measurement depth of changing tissue properties is comparable to the effect of changing the system setup, e.g. source–detector separation and wavelength. Skin pigmentation was found to have a negligible effect on the measurement depth. Examples of measurement depths are (values are given for a probe based system with 0.25 mm source–detector separation and an imaging system with a 0.5 mm beam diameter, respectively, both operating at 780 nm): muscle — 0.55/0.79 mm; liver — 0.40/0.53 mm; gray matter — 0.48/0.68 mm; white matter — 0.20/0.20 mm; index finger pulp — 0.41/0.53 mm; forearm skin — 0.53/0.56 mm; heat provoked forearm skin — 0.66/0.67 mm.

Ultrasound-modulated fluorescence based on a fluorophore-quencher-labeled microbubble system

Ultrasound-modulated fluorescence from a fluorophore-quencher-labeled microbubble system driven by a single ultrasound pulse was theoretically quantified by solving a modified Herring equation (for bubble oscillation), a two-energy-level rate equation (for fluorophore excitation), and a diffusion equation (for light propagation in tissue). The efficiency of quenching caused by fluorescence resonance energy transfer (FRET) between the fluorophore and the quencher was modulated when the microbubble oscillates in size driven by the ultrasound pulse. Both intensity- and lifetime-based imaging methods are discussed in three different illumination modes of the excitation light: continuous wave (DC), frequency domain (FD), and time domain (TD). Results show that microbubble expansion opens a time period during which the quenching efficiency is dramatically reduced so that the emitted fluorescence strength and fluorophore lifetime are significantly increased. The modulation efficiency may even reach 100%. In addition, an important finding in this study is that in TD illumination mode, the modulated fluorescence photons may be temporally separated from the unmodulated photons, which makes the modulation efficiency limited only by thermal noise of the measurement system.

Hardware acceleration of a Monte Carlo simulation for photodynamic treatment planning

Monte Carlo (MC) simulations are being used extensively in the field of medical biophysics, particularly for modeling light propagation in tissues. The high computation time for MC limits its use to solving only the forward solutions for a given source geometry, emission profile, and optical interaction coefficients of the tissue. However, applications such as photodynamic therapy treatment planning or image reconstruction in diffuse optical tomography require solving the inverse problem given a desired dose distribution or absorber distribution, respectively. A faster means for performing MC simulations would enable the use of MC-based models for accomplishing such tasks. To explore this possibility, a digital hardware implementation of a MC simulation based on the Monte Carlo for Multi-Layered media (MCML) software was implemented on a development platform with multiple field-programmable gate arrays (FPGAs). The hardware performed the MC simulation on average 80 times faster and was 45 times more energy efficient than the MCML software executed on a 3-GHz Intel Xeon processor. The resulting isofluence lines closely matched those produced by MCML in software, diverging by only less than 0.1 mm for fluence levels as low as 0.00001 cm(-2) in a skin model.

Light propagation in tissues with forward-peaked and large-angle scattering

We study light propagation in tissues using the theory of radiative transport. In particular, we study the case in which there is both forward-peaked and large-angle scattering. Because this combination of the forward-peaked and large-angle scattering makes it difficult to solve the radiative transport equation, we present a method to construct approximations to study this problem. The delta-Eddington and Fokker-Planck approximations are special cases of this general framework. Using this approximation method, we derive two new approximations: the Fokker-Planck-Eddington approximation and the generalized Fokker-Planck-Eddington approximation. By computing the transmittance and reflectance of light by a slab we study the performance of these approximations.