Scattering of diffuse photon density waves by spherical inhomogeneities within turbid media: analytic solution and applications

Non-invasive monitoring of blood oxygenation in human placentas via concurrent diffuse optical spectroscopy and ultrasound imaging

Direct assessment of blood oxygenation in the human placenta can provide information about placental function. However, the monitoring of placental oxygenation involves invasive sampling or imaging techniques that are poorly suited for bedside use. Here we show that placental oxygen haemodynamics can be non-invasively probed in real time and up to 4.2 cm below the body surface via concurrent frequency-domain diffuse optical spectroscopy and ultrasound imaging. We developed a multimodal instrument to facilitate the assessment of the properties of the anterior placenta by leveraging image-reconstruction algorithms that integrate ultrasound information about the morphology of tissue layers with optical information on haemodynamics. In a pilot investigation involving placentas with normal function (15 women) or abnormal function (9 women) from pregnancies in the third trimester, we found no significant differences in baseline haemoglobin properties, but statistically significant differences in the haemodynamic responses to maternal hyperoxia. Our findings suggest that the non-invasive monitoring of placental oxygenation may aid the early detection of placenta-related adverse pregnancy outcomes and maternal vascular malperfusion.

High-density diffuse optical tomography for imaging human brain function

This review describes the unique opportunities and challenges for noninvasive optical mapping of human brain function. Diffuse optical methods offer safe, portable, and radiation free alternatives to traditional technologies like positron emission tomography or functional magnetic resonance imaging (fMRI). Recent developments in high-density diffuse optical tomography (HD-DOT) have demonstrated capabilities for mapping human cortical brain function over an extended field of view with image quality approaching that of fMRI. In this review, we cover fundamental principles of the diffusion of near infrared light in biological tissue. We discuss the challenges involved in the HD-DOT system design and implementation that must be overcome to acquire the signal-to-noise necessary to measure and locate brain function at the depth of the cortex. We discuss strategies for validation of the sensitivity, specificity, and reliability of HD-DOT acquired maps of cortical brain function. We then provide a brief overview of some clinical applications of HD-DOT. Though diffuse optical measurements of neurophysiology have existed for several decades, tremendous opportunity remains to advance optical imaging of brain function to address a crucial niche in basic and clinical neuroscience: that of bedside and minimally constrained high fidelity imaging of brain function.

Controlling Disorder by Electric-Field-Directed Reconfiguration of Nanowires To Tune Random Lasing

Top-down fabrication is commonly used to provide positioning control of optical structures; yet, it places stringent limitations on component materials, and oftentimes, dynamic reconfigurability is challenging to realize. Here, we present a reconfigurable nanoparticle platform that can integrate heterogeneous particle assembly of different shapes, sizes, and chemical compositions. We demonstrate dynamic control of disorder in this platform and use it to tune random laser emission characteristics for a suspension of titanium dioxide nanowires in a dye solution. Using an alternating current electric field, we control the nanowire orientation to dynamically engineer the collective scattering of the sample. Our theoretical model indicates that a change of up to 22% in scattering coefficient can be achieved for the experimentally determined nanowire length distribution upon alignment. Dependence of light confinement on anisotropic particle alignment provides a means to reversibly tune random laser characteristics; a nearly 20-fold increase in lasing intensity was observed with aligned particle orientation. We illustrate the generality of the approach by demonstrating enhanced lasing for aligned nanowires of other materials including gold, mixed gold/dielectric, and vanadium oxide.

Hybrid Brain-Computer Interface Techniques for Improved Classification Accuracy and Increased Number of Commands: A Review

In this article, non-invasive hybrid brain-computer interface (hBCI) technologies for improving classification accuracy and increasing the number of commands are reviewed. Hybridization combining more than two modalities is a new trend in brain imaging and prosthesis control. Electroencephalography (EEG), due to its easy use and fast temporal resolution, is most widely utilized in combination with other brain/non-brain signal acquisition modalities, for instance, functional near infrared spectroscopy (fNIRS), electromyography (EMG), electrooculography (EOG), and eye tracker. Three main purposes of hybridization are to increase the number of control commands, improve classification accuracy and reduce the signal detection time. Currently, such combinations of EEG + fNIRS and EEG + EOG are most commonly employed. Four principal components (i.e., hardware, paradigm, classifiers, and features) relevant to accuracy improvement are discussed. In the case of brain signals, motor imagination/movement tasks are combined with cognitive tasks to increase active brain-computer interface (BCI) accuracy. Active and reactive tasks sometimes are combined: motor imagination with steady-state evoked visual potentials (SSVEP) and motor imagination with P300. In the case of reactive tasks, SSVEP is most widely combined with P300 to increase the number of commands. Passive BCIs, however, are rare. After discussing the hardware and strategies involved in the development of hBCI, the second part examines the approaches used to increase the number of control commands and to enhance classification accuracy. The future prospects and the extension of hBCI in real-time applications for daily life scenarios are provided.

High-density speckle contrast optical tomography (SCOT) for three dimensional tomographic imaging of the small animal brain

High-density speckle contrast optical tomography (SCOT) utilizing tens of thousands of source-detector pairs, was developed for in vivo imaging of blood flow in small animals. The reduction in cerebral blood flow (CBF) due to local ischemic stroke in a mouse brain was transcanially imaged and reconstructed in three dimensions. The reconstructed volume was then compared with corresponding magnetic resonance images demonstrating that the volume of reduced CBF agrees with the infarct zone at twenty-four hours.

Heterodyne frequency-domain multispectral diffuse optical tomography of breast cancer in the parallel-plane transmission geometry

PURPOSE

The authors introduce a state-of-the-art all-optical clinical diffuse optical tomography (DOT) imaging instrument which collects spatially dense, multispectral, frequency-domain breast data in the parallel-plate geometry.

METHODS

The instrument utilizes a CCD-based heterodyne detection scheme that permits massively parallel detection of diffuse photon density wave amplitude and phase for a large number of source-detector pairs (10(6)). The stand-alone clinical DOT instrument thus offers high spatial resolution with reduced crosstalk between absorption and scattering. Other novel features include a fringe profilometry system for breast boundary segmentation, real-time data normalization, and a patient bed design which permits both axial and sagittal breast measurements.

RESULTS

The authors validated the instrument using tissue simulating phantoms with two different chromophore-containing targets and one scattering target. The authors also demonstrated the instrument in a case study breast cancer patient; the reconstructed 3D image of endogenous chromophores and scattering gave tumor localization in agreement with MRI.

CONCLUSIONS

Imaging with a novel parallel-plate DOT breast imager that employs highly parallel, high-resolution CCD detection in the frequency-domain was demonstrated.

An accelerated photo-magnetic imaging reconstruction algorithm based on an analytical forward solution and a fast Jacobian assembly method

We previously introduced photo-magnetic imaging (PMI), an imaging technique that illuminates the medium under investigation with near-infrared light and measures the induced temperature increase using magnetic resonance thermometry (MRT). Using a multiphysics solver combining photon migration and heat diffusion, PMI models the spatiotemporal distribution of temperature variation and recovers high resolution optical absorption images using these temperature maps. In this paper, we present a new fast non-iterative reconstruction algorithm for PMI. This new algorithm uses analytic methods during the resolution of the forward problem and the assembly of the sensitivity matrix. We validate our new analytic-based algorithm with the first generation finite element method (FEM) based reconstruction algorithm previously developed by our team. The validation is performed using, first synthetic data and afterwards, real MRT measured temperature maps. Our new method accelerates the reconstruction process 30-fold when compared to a single iteration of the FEM-based algorithm.

Measurement of the surface effect of a small scattering object in a highly scattering medium by use of diffuse photon-pairs density wave

The surface effect close to the boundary of a small light-scattering object in a highly scattering medium is experimentally demonstrated. This is the first attempt to measure the surface effect of a small spherical scattering object in 1% intralipid solution by use of developed diffuse photon-pairs density wave (DPPDW) in terms of the amplitude and phase detection. Theoretically, the surface effect of a small scattering object in turbid media is localized close to the boundary according to the perturbation theory, concerning an inhomogeneous distribution of the diffusion coefficient in the frequency-domain diffusion equation. Hence, an improvement of the spatial resolution of the image via an inverse algorithm, which relates to detection sensitivity of localization to the boundary of the image object in a multiple scattering medium, is anticipated. In this study, we demonstrate that DPPDW is able to sense the surface effect of a 2-mm spherical scattering object in 1% intralipid solution, with high sensitivity. Subsequently, an improvement of spatial resolution of imaging in turbid media by using DPPDW in comparison with conventional diffuse photon density wave (DPDW) using inverse algorithm is discussed.

Comprehensive analytical model for CW laser induced heat in turbid media

In this work, we present a new analytical approach to model continuous wave laser induced temperature in highly homogeneous turbid media. First, the diffusion equation is used to model light transport and a comprehensive solution is derived analytically by obtaining a special Greens' function. Next, the time-dependent bio-heat equation is used to describe the induced heat increase and propagation within the medium. The bio-heat equation is solved analytically utilizing the separation of variables technique. Our theoretical model is successfully validated using numerical simulations and experimental studies with agarose phantoms and ex-vivo chicken breast samples. The encouraging results show that our method can be implemented as a simulation tool to determine important laser parameters that govern the magnitude of temperature rise within homogenous biological tissue or organs.

Diffuse photon density wave measurements and Monte Carlo simulations

Diffuse photon density wave (DPDW) methodology is widely used in a number of biomedical applications. Here, we present results of Monte Carlo simulations that employ an effective numerical procedure based upon a description of radiative transfer in terms of the Bethe–Salpeter equation. A multifrequency noncontact DPDW system was used to measure aqueous solutions of intralipid at a wide range of source–detector separation distances, at which the diffusion approximation of the radiative transfer equation is generally considered to be invalid. We find that the signal–noise ratio is larger for the considered algorithm in comparison with the conventional Monte Carlo approach. Experimental data are compared to the Monte Carlo simulations using several values of scattering anisotropy and to the diffusion approximation. Both the Monte Carlo simulations and diffusion approximation were in very good agreement with the experimental data for a wide range of source–detector separations. In addition, measurements with different wavelengths were performed to estimate the size and scattering anisotropy of scatterers.

An extended analytical approach for diffuse optical imaging

In this work, we introduce an analytical method to solve the diffusion equation in a cylindrical geometry. This method is based on an integral approach to derive the Green's function for specific boundary conditions. Using our approach, we obtain comprehensive analytical solutions with the Robin boundary condition for diffuse optical imaging in both two and three dimensions. The solutions are expressed in terms of the optical properties of tissue and the amplitude and position of the light source. Our method not only works well inside the tissue but provides very accurate results near the tissue boundaries as well. The results obtained by our method are first compared with those obtained by a conventional analytical method then validated using numerical simulations. Our new analytical method allows not only implementation of any boundary condition for a specific problem but also fast simulation of light propagation making it very suitable for iterative image reconstruction algorithms.

Multigrid-based reconstruction algorithm for quantitative photoacoustic tomography

This paper proposes a multigrid inversion framework for quantitative photoacoustic tomography reconstruction. The forward model of optical fluence distribution and the inverse problem are solved at multiple resolutions. A fixed-point iteration scheme is formulated for each resolution and used as a cost function. The simulated and experimental results for quantitative photoacoustic tomography reconstruction show that the proposed multigrid inversion can dramatically reduce the required number of iterations for the optimization process without loss of reliability in the results.

Analytical model of optical fluence inside multiple cylindrical inhomogeneities embedded in an otherwise homogeneous turbid medium for quantitative photoacoustic imaging

We present an analytical model of optical fluence for multiple cylindrical inhomogeneities embedded in an otherwise homogeneous turbid medium. The model is based on the diffusion equation and represents the optical fluence distribution inside and outside inhomogeneities as a series of modified Bessel functions. We take into account the interplay between cylindrical inhomogeneities by introducing new boundary conditions on the surface of inhomogeneities. The model is compared with the numerical solution of the diffusion equation with NIRFAST software. The fluences inside the inhomogeneities obtained by the two methods are in close agreement. This permits the use of the model as a forward model for quantitative photoacoustic imaging.

Analytical reconstruction of the bioluminescent source with priors

Bioluminescence imaging has been a popular tool in small animal imaging. During the last decade, the efforts have focused on the development of tomographic systems. However, due to the difficulties in the nature of inverse source problem, multi-modal systems have been the center of attention for the last couple of years. These systems provide complementary information such that the difficulties of the inverse source problem could be overcome using the a priori information obtained. Motivated by these advances in multi-modal systems, this work presents a novel analytical reconstruction of the bioluminescent source. It is shown that if source strength is known a priori then source position could be calculated or vice versa, if source location is known a priori, source strength could be calculated as well as the photon fluence rate. The determination of the source location can be achieved by another imaging system such as X-ray computed tomography. Therefore, in bioluminescence tomography together with an imaging system can be utilized as a multi-modal system. In this work, conventional finite element based simulations are also performed and the numerical results are compared with the analytical ones. It turns out to be that the analytical results are in a good accordance with the numerical results.

Forward solvers for photon migration in the presence of highly and totally absorbing objects embedded inside diffusive media

In this paper, after a critical review of the literature, we present two forward solvers and a new methodology for description of photon migration in the presence of totally absorbing inclusions embedded in diffusive media in both time and CW domains. The first forward solver is a heuristic approach based on a higher order perturbation theory applied to the diffusion equation (DE) [denoted eighth-order perturbation theory (EOPT)]. The second forward solver [denoted eighth-order perturbation theory with the equivalence relation (EOPTER) ] is obtained by combining the EOPT solver with the adoption of the equivalence relation (ER) [J. Biomed. Opt.18, 066014 (2013)]. These forward solvers can possibly overcome some evident limitations of previous approaches like the theory behind the so-called banana-shape regions or exact analytical solutions of the DE in the presence of highly or totally absorbing inclusions. We also propose the ER to reformulate the problem of a totally absorbing inclusion in terms of another inclusion having a finite absorption contrast and a re-scaled volume. For instance, we have shown how this approach can indeed be used to simulate black inclusions with the Born approximation. By means of comparisons with the results of Monte Carlo simulations, we have shown that the EOPTER solver can model totally absorbing inclusions with an error smaller than about 10%, whereas the EOPT solver shows an error smaller than about 20%, showing a performance largely better than that observed with solvers proposed previously.

Phantoms for diffuse optical imaging based on totally absorbing objects, part 2: experimental implementation

We present the experimental implementation and validation of a phantom for diffuse optical imaging based on totally absorbing objects for which, in the previous paper [J. Biomed. Opt.18(6), 066014, (2013)], we have provided the basic theory. Totally absorbing objects have been manufactured as black polyvinyl chloride (PVC) cylinders and the phantom is a water dilution of intralipid-20% as the diffusive medium and India ink as the absorber, filled into a black scattering cell made of PVC. By means of time-domain measurements and of Monte Carlo simulations, we have shown the reliability, the accuracy, and the robustness of such a phantom in mimicking typical absorbing perturbations of diffuse optical imaging. In particular, we show that such a phantom can be used to generate any absorption perturbation by changing the volume and position of the totally absorbing inclusion.

Phantoms for diffuse optical imaging based on totally absorbing objects, part 1: Basic concepts

The design of inhomogeneous phantoms for diffuse optical imaging purposes using totally absorbing objects embedded in a diffusive medium is proposed and validated. From time-resolved and continuous-wave Monte Carlo simulations, it is shown that a given or desired perturbation strength caused by a realistic absorbing inhomogeneity of a certain absorption and volume can be approximately mimicked by a small totally absorbing object of a so-called equivalent black volume (equivalence relation). This concept can be useful in two ways. First, it can be exploited to design realistic inhomogeneous phantoms with different perturbation strengths simply using a set of black objects with different volumes. Further, it permits one to grade physiological or pathological changes on a reproducible scale of perturbation strengths given as equivalent black volumes, thus facilitating the performance assessment of clinical instruments. A set of plots and interpolating functions to derive the equivalent black volume corresponding to a given absorption change is provided. The application of the equivalent black volume concept for grading different optical perturbations is demonstrated for some examples.

In vivo frequency domain optoacoustic tomography

Optoacoustic imaging has been primarily implemented in the time domain, i.e., using ultrashort nanosecond laser pulses for illumination. Alternatively, frequency domain optoacoustic imaging can be performed when employing amplitude modulated light sources. We present herein a tomographic implementation of optoacoustic imaging using a linear frequency modulated laser source. The method developed demonstrated the ability to produce tomographic images of optical absorbing phantoms and in vivo images, by enabling visualization of the mouse tail following ICG injection.

Galactosyl human serum albumin-NMP1 conjugate: a near infrared (NIR)-activatable fluorescence imaging agent to detect peritoneal ovarian cancer metastases

Patient survival depends on the completeness of resection of peritoneal ovarian cancer metastases (POCM), and therefore, it is important to develop methods to enhance detection. Previous probe designs based on activatable galactosyl human serum albumin (hGSA)-fluorophore pairs, which target lectin receptors expressed on POCM, have used only visible range dyes conjugated to hGSA. However, imaging probes emitting fluorescence in the NIR range are advantageous because NIR photons have deeper in vivo tissue penetration and result in lower background autofluorescence than those emitting in the visible range. A NIR-activatable hGSA fluorophore was synthesized using a bacteriochlorin-based dye, NMP1. NMP1 has two unique absorption peaks, one in the green range and the other in the NIR range, but emits at a NIR peak of 780 nm. NMP1, thus, has two different Stokes shifts that have the potential to allow imaging of POCM both at the peritoneal surface and just below it. hGSA was conjugated with 2 NMP1 molecules to create a self-quenching complex (hGSA-NMP1). The activation ratio of hGSA-NMP1 was measured by the fluorescence intensity before and after exposure to 10% SDS. The activation ratio of hGSA-NMP1 was ~100-fold in vitro. Flow cytometry, fluorescence microscopy, and in vivo spectral fluorescence imaging were carried out to compare hGSA-NMP1 with hGSA-IR800 and hGSA-ICG (two always-on control agents with similar emission to NMP1) in terms of comparative fluorescence signal and the ability to detect POCM in mice models. The sensitivity and specificity of hGSA-NMP1 for POCM implant detection were determined by colocalizing NMP1 emission spectra with red fluorescent protein (RFP) expressed constitutively in SHIN3 tumor implants at different depths below the peritoneal surface. In vitro, SHIN3 cells were easily detectable after 3 h of incubation with hGSA-NMP1. In vivo submillimeter POCM foci were clearly detectable with spectral fluorescence imaging using hGSA-NMP1. Among 555 peritoneal lesions, hGSA-NMP, using NIR and green excitation light, respectively, detect 75% of all lesions and 91% of lesions ~0.8 mm or greater in diameter. Few false positives were encountered. Nodules located at a depth below the small bowel surface were only depicted with hGSA-NMP1. We conclude that hGSA-NMP1 is useful in imaging peritoneal ovarian cancer metastases, located both superficially and deep in the abdominal cavity.

Micro-computed tomography-guided, non-equal voxel Monte Carlo method for reconstruction of fluorescence molecular tomography

The study of dual-modality technology which combines microcomputed tomography (micro-CT) and fluorescence molecular tomography (FMT) has become one of the main focuses in FMT. However, because of the diversity of the optical properties and irregular geometry for small animals, a reconstruction method that can effectively utilize the high-resolution structural information of micro-CT for tissue with arbitrary optical properties is still one of the most challenging problems in FMT. We develop a micro-CT-guided non-equal voxel Monte Carlo method for FMT reconstruction. With the guidance of micro-CT, precise voxel binning can be conducted on the irregular boundary or region of interest. A modified Laplacian regularization method is also proposed to accurately reconstruct the distribution of the fluorescent yield for non-equal space voxels. Simulations and phantom experiments show that this method not only effectively reduces the loss of high-resolution structural information of micro-CT in irregular boundaries and increases the accuracy of the FMT algorithm in both forward and inverse problems, but the method also has a small Jacobian matrix and a short reconstruction time. At last, we performed small animal imaging to validate our method.

Investigation of a diffuse optical measurements-assisted quantitative photoacoustic tomographic method in reflection geometry

Photoacoustic tomography provides the distribution of absorbed optical energy density, which is the product of optical absorption coefficient and optical fluence distribution. We report the experimental investigation of a novel fitting procedure that quantitatively determines the optical absorption coefficient of chromophores. The experimental setup consisted of a hybrid system of a 64-channel photoacoustic imaging system with a frequency-domain diffused optical measurement system. The fitting procedure included a complete photoacoustic forward model and an analytical solution of a target chromophore using the diffusion approximation. The fitting procedure combines the information from the photoacoustic image and the background information from the diffuse optical measurements to minimize the photoacoustic measurements and forward model data and recover the target absorption coefficient quantitatively. 1-cm-cube phantom absorbers of high and low contrasts were imaged at depths of up to 3.0 cm. The fitted absorption coefficient results were at least 80% of their true values. The sensitivities of this fitting procedure to target location, target radius, and background optical properties were also investigated. We found that this fitting procedure was most sensitive to the accurate determination of the target radius and depth. Blood sample in a thin tube of radius 0.58 mm, simulating a blood vessel, was also studied. The photoacoustic images and fitted absorption coefficients are presented. These results demonstrate the clinical potential of this fitting procedure to quantitatively characterize small lesions in breast imaging.

Contrast-enhanced near-infrared (NIR) optical imaging for subsurface cancer detection

Synergistic efforts in the developments of molecular specific imaging probes and advancements of optical imaging technologies (including the novel instrumentation and imaging algorithms) that lead to a new tool for early disease diagnosis and drug discovery are described.

Parametric level set reconstruction methods for hyperspectral diffuse optical tomography

A parametric level set method (PaLS) is implemented for image reconstruction for hyperspectral diffuse optical tomography (DOT). Chromophore concentrations and diffusion amplitude are recovered using a linearized Born approximation model and employing data from over 100 wavelengths. The images to be recovered are taken to be piecewise constant and a newly introduced, shape-based model is used as the foundation for reconstruction. The PaLS method significantly reduces the number of unknowns relative to more traditional level-set reconstruction methods and has been show to be particularly well suited for ill-posed inverse problems such as the one of interest here. We report on reconstructions for multiple chromophores from simulated and experimental data where the PaLS method provides a more accurate estimation of chromophore concentrations compared to a pixel-based method.

Highly parallel Monte-Carlo simulations of the acousto-optic effect in heterogeneous turbid media

The development of a highly parallel simulation of the acousto-optic effect is detailed. The simulation supports optically heterogeneous simulation domains under insonification by arbitrary monochromatic ultrasound fields. An adjoint method for acousto-optics is proposed to permit point-source/point-detector simulations. The flexibility and efficiency of this simulation code is demonstrated in the development of spatial absorption sensitivity maps which are in broad agreement with current experimental investigations. The simulation code has the potential to provide guidance in the feasibility and optimization of future studies of the acousto-optic technique, and its speed may permit its use as part of an iterative inversion model.

Photon diffusion near the point-of-entry in anisotropically scattering turbid media

From astronomy to cell biology, the manner in which light propagates in turbid media has been of central importance for many decades. However, light propagation near the point-of-entry in turbid media has never been analytically described, until now. Here we report a straightforward and accurate method that overcomes this longstanding, unsolved problem in radiative transport. Our theory properly treats anisotropic photon scattering events and takes the specific form of the phase function into account. As a result, our method correctly predicts the spatially dependent diffuse reflectance of light near the point-of-entry for any arbitrary phase function. We demonstrate that the theory is in excellent agreement with both experimental results and Monte Carlo simulations for several commonly used phase functions.

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.

Hyperspectral image reconstruction for diffuse optical tomography

We explore the development and performance of algorithms for hyperspectral diffuse optical tomography (DOT) for which data from hundreds of wavelengths are collected and used to determine the concentration distribution of chromophores in the medium under investigation. An efficient method is detailed for forming the images using iterative algorithms applied to a linearized Born approximation model assuming the scattering coefficient is spatially constant and known. The L-surface framework is employed to select optimal regularization parameters for the inverse problem. We report image reconstructions using 126 wavelengths with estimation error in simulations as low as 0.05 and mean square error of experimental data of 0.18 and 0.29 for ink and dye concentrations, respectively, an improvement over reconstructions using fewer specifically chosen wavelengths.

Compressed sensing in diffuse optical tomography

Diffuse optical tomography (DOT) allows tomographic (3D), non-invasive reconstructions of tissue optical properties for biomedical applications. Severe under-sampling is a common problem in DOT which leads to image artifacts. A large number of measurements is needed in order to minimize these artifacts. In this work, we introduce a compressed sensing (CS) framework for DOT which enables improved reconstructions with under-sampled data. The CS framework uses a sparsifying basis, ℓ1-regularization and random sampling to reduce the number of measurements that are needed to achieve a certain accuracy. We demonstrate the utility of the CS framework using numerical simulations. The CS results show improved DOT results in comparison to "traditional" linear reconstruction methods based on singular-value decomposition (SVD) with ℓ2-regularization and with regular and random sampling. Furthermore, CS is shown to be more robust against the reduction of measurements in comparison to the other methods. Potential benefits and shortcomings of the CS approach in the context of DOT are discussed.

Mesh-based Monte Carlo method using fast ray-tracing in Plücker coordinates

We describe a fast mesh-based Monte Carlo (MC) photon migration algorithm for static and time-resolved imaging in 3D complex media. Compared with previous works using voxel-based media discretization, a mesh-based approach can be more accurate in modeling targets with curved boundaries or locally refined structures. We implement an efficient ray-tracing technique using Plücker Coordinates. The Barycentric coordinates computed from Plücker-formed ray-tracing enables us to use linear Lagrange basis functions to model both media properties and fluence distribution, leading to further improvement in accuracy. The Plücker-coordinate ray-polygon intersection test can be extended to hexahedral or high-order elements. Excellent agreement is found when comparing mesh-based MC with the analytical diffusion model and 3D voxel-based MC code in both homogeneous and heterogeneous cases. Realistic time-resolved imaging results are observed for a complex human brain anatomy using mesh-based MC. We also include multi-threading support in the software and will port it to a graphics processing unit platform in the near future.

Perturbation theory for the diffusion equation by use of the moments of the generalized temporal point-spread function. III. Frequency-domain and time-domain results

We study the performance of a previously proposed perturbation theory for the diffusion equation in frequency and time domains as they are known in the field of near infrared spectroscopy and diffuse optical tomography. We have derived approximate formulas for calculating higher order self- and mixed path length moments, up to the fourth order, which can be used in general diffusive media regardless of geometry and initial distribution of the optical properties, for studying the effect of absorbing defects. The method of Padé approximants is used to extend the validity of the theory to a wider range of absorption contrasts between defects and background. By using Monte Carlo simulations, we have tested these formulas in the semi-infinite and slab geometries for the cases of single and multiple absorbing defects having sizes of interest (d=4-10 mm, where d is the diameter of the defect). In frequency domain, the discrepancy between the two methods of calculation (Padé approximants and Monte Carlo simulations) was within 10% for absorption contrasts Deltamu(a)<or=0.2 mm(-1) for alternating current data, and usually to within 1 degrees for Deltamu(a)<or=0.1 mm(-1) for phase data. In time domain, the average discrepancy in the temporal range of interest (a few nanoseconds) was 2%-3% for Deltamu(a)<or=0.06 mm(-1). The proposed method is an effective fast forward problem solver: all the time-domain results presented in this work were obtained with a computational time of less than about 15 s with a Pentium IV 1.66 GHz personal computer.

Diffuse Optics for Tissue Monitoring and Tomography

This review describes the diffusion model for light transport in tissues and the medical applications of diffuse light. Diffuse optics is particularly useful for measurement of tissue hemodynamics, wherein quantitative assessment of oxy- and deoxy-hemoglobin concentrations and blood flow are desired. The theoretical basis for near-infrared or diffuse optical spectroscopy (NIRS or DOS, respectively) is developed, and the basic elements of diffuse optical tomography (DOT) are outlined. We also discuss diffuse correlation spectroscopy (DCS), a technique whereby temporal correlation functions of diffusing light are transported through tissue and are used to measure blood flow. Essential instrumentation is described, and representative brain and breast functional imaging and monitoring results illustrate the workings of these new tissue diagnostics.

Solution of the direct problem in turbid media with inclusions using Monte Carlo simulations implemented in graphics processing units: new criterion for processing transmittance data

The study of light propagation in diffusive media requires solving the radiative transfer equation, or eventually, the diffusion approximation. Except for some cases involving simple geometries, the problem with immersed inclusions has not been solved. Also, Monte Carlo (MC) calculations have become a gold standard for simulating photon migration in turbid media, although they have the drawback large processing times. The purpose of this work is two-fold: first, we introduce a new processing criterion to retrieve information about the location and shape of absorbing inclusions based on normalization to the background intensity, when no inhomogeneities are present. Second, we demonstrate the feasibility of including inhomogeneities in MC simulations implemented in graphics processing units, achieving large acceleration factors ( approximately 10(3)), thus providing an important tool for iteratively solving the forward problem to retrieve the optical properties of the inclusion. Results using a cw source are compared with MC outcomes showing very good agreement.

Chitosan-based systems for molecular imaging

Molecular imaging enables the non-invasive assessment of biological and biochemical processes in living subjects. Such technologies therefore have the potential to enhance our understanding of disease and drug activity during preclinical and clinical drug development. Molecular imaging allows a repetitive and non-invasive study of the same living subject using identical or alternative biological imaging assays at different time points, thus harnessing the statistical power of longitudinal studies, and reducing the number of animals required and cost. Chitosan is a hydrophilic and non-antigenic biopolymer and has a low toxicity toward mammalian cells. Hence, it has great potential as a biomaterial because of its excellent biocompatibility. Conjugated to additional materials, chitosan composites result in a new class of biomaterials that possess mechanical, physicochemical and functional properties, which have potential for use in advanced biomedical imaging applications. The present review will discuss the strengths, limitations and challenges of molecular imaging as well as applications of chitosan nanoparticles in the field of molecular imaging.

Higher-order perturbation theory for the diffusion equation in heterogeneous media: application to layered and slab geometries

We apply a previously proposed perturbation theory of the diffusion equation for studying light propagation through heterogeneous media in the presence of absorbing defects. The theory is based on the knowledge of (a) the geometric characteristics of a focal inclusion, (b) the mean optical path length inside the inclusion, and (c) the optical properties of the inclusion. The potential of this method is shown in the layered and slab geometries, where calculations are carried out up to the fourth order. The relative changes of intensity with respect to the unperturbed (heterogeneous) medium are predicted by the theory to within 10% for a wide range of contrasts dDeltamu(a) (up to dDeltamu(a) approximately 0.4-0.8), where d is the effective diameter of the defect and Deltamu(a) the absorption contrast between defect and local background. We also show how the method of Padé approximants can be used to extend the validity of the theory for a larger range of absorption contrasts. Finally, we study the possibility of using the proposed method for calculating the effect of a colocalized scattering and absorbing perturbation.

Quantitation and mapping of tissue optical properties using modulated imaging

We describe the development of a rapid, noncontact imaging method, modulated imaging (MI), for quantitative, wide-field characterization of optical absorption and scattering properties of turbid media. MI utilizes principles of frequency-domain sampling and model-based analysis of the spatial modulation transfer function (s-MTF). We present and compare analytic diffusion and probabilistic Monte Carlo models of diffuse reflectance in the spatial frequency domain. Next, we perform MI measurements on tissue-simulating phantoms exhibiting a wide range of l values (0.5 mm to 3 mm) and (micro(s) (')micro(a)) ratios (8 to 500), reporting an overall accuracy of approximately 6% and 3% in absorption and reduced scattering parameters, respectively. Sampling of only two spatial frequencies, achieved with only three camera images, is found to be sufficient for accurate determination of the optical properties. We then perform MI measurements in an in vivo tissue system, demonstrating spatial mapping of the absorption and scattering optical contrast in a human forearm and dynamic measurements of a forearm during venous occlusion. Last, metrics of spatial resolution are assessed through both simulations and measurements of spatially heterogeneous phantoms.

Investigation of diffuse correlation spectroscopy in multi-layered media including the human head

In this work, diffuse correlation spectroscopy (DCS) is explored in multi-layered geometries. A quantitative comparison of an homogeneous versus a two-layered model efficiencies to recover flow changes is presented. By simulating a realistic human head with MRI anatomical data, we show that the two-layered model allows distinction between changes in superficial layers and brain. We also show that the two-layered model provides a better estimate of the flow change than the homogeneous one. Experimental measurements with a two-layered dynamical phantom confirm the ability of the two-layered analytical model to distinguish flow increase in each layer.

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.

Estimation and statistical bounds for three-dimensional polar shapes in diffuse optical tomography

Voxel-based reconstructions in diffuse optical tomography (DOT) using a quadratic regularization functional tend to produce very smooth images due to the attenuation of high spatial frequencies. This then causes difficulty in estimating the spatial extent and contrast of anomalous regions such as tumors. Given an assumption that the target image is piecewise constant, we can employ a parametric model to estimate the boundaries and contrast of an inhomogeneity directly. In this paper, we describe a method to directly reconstruct such a shape boundary from diffuse optical measurements. We parameterized the object boundary using a spherical harmonic basis, and derived a method to compute sensitivities of measurements with respect to shape parameters. We introduced a centroid constraint to ensure uniqueness of the combined shape/center parameter estimate, and a projected Newton method was utilized to optimize the object center position and shape parameters simultaneously. Using the shape Jacobian, we also computed the Cramér-Rao lower bound on the theoretical estimator accuracy given a particular measurement configuration, object shape, and level of measurement noise. Knowledge of the shape sensitivity matrix and of the measurement noise variance allows us to visualize the shape uncertainty region in three dimensions, giving a confidence region for our shape estimate. We have implemented our shape reconstruction method, using a finite-difference-based forward model to compute the forward and adjoint fields. Reconstruction results are shown for a number of simulated target shapes, and we investigate the problem of model order selection using realistic levels of measurement noise. Assuming a signal-to-noise ratio in the amplitude measurements of 40 dB and a standard deviation in the phase measurements of 0.1 degrees , we are able to estimate an object represented with an eighth-order spherical harmonic model having an absorption contrast of 0.15 cm(-1) and a volume of 4.82 cm(3) with errors of less than 10% in object volume and absorption contrast. We also investigate the robustness of our shape-based reconstruction approach to a violation of the assumption that the medium is purely piecewise constant.

Measurement of diffuse photon-pairs density wave in a multiple-scattering medium

As a continuation of the previously developed theory of a diffuse photon-pairs density wave (DPPDW) [Appl. Opt.44, 1416-1425 (2005)APOPAI0003-693510.1364/AO.44.001416], this research experimentally studies and verifies the DPPDW theory in a heterogeneous multiple-scattering medium. The DPPDW is generated by collecting the scattered linear polarized photon pairs (LPPPs) in the multiple-scattering medium. Theoretically, the common-path propagation of LPPPs not only provides common phase noise rejection mode but also performs coherence technique via heterodyne detection. In addition, the polarization gating and spatial coherence gating of LPPPs would suppress the severe scattered photon in the multiple-scattering medium. In the experiment, the amplitude and phase wavefronts of DPPDWs, which are distorted by a small object embedded in a homogeneous multiple-scattering medium, are measured in one dimension or two dimensions by scanning the source detector pair. The measured distortion of DPPDW wavefronts are detected precisely and are consistent with the theoretical calculation of DPPDW. It implies an improvement on the detection sensitivity of a small object compared with the conventional diffuse photon density wave (DPDW).

Approximations of the measurable quantity in diffuse optical problems: theoretical analysis of model deviations

Photon density and photon flux are widely used to model the measurable quantity in diffuse optical tomography problems. However, it is not these two quantities that are actually measured, but rather the radiance accepted by the detection system. We provide a theoretical analysis of the model deviations related to the choice of the measurable quantity-either photon density or flux. By using the diffusion approximation to the radiative transfer equation and its solution with extrapolated boundary conditions, an exact analytical expression of the measurable quantity has been obtained. This expression has been employed as a reference to assess model deviation when considering the photon density or the photon flux as the measurable quantity. For the case of semi-infinite geometry and for both continuous wave and time domains, we show that the photon density approximates the measurable quantity better than the photon flux. We also demonstrate that the validity of this approximation strongly depends on the optical parameters.

Evaluation of higher-order time-domain perturbation theory of photon diffusion on breast-equivalent phantoms and optical mammograms

Time-domain perturbation theory of photon diffusion up to third order was evaluated for its accuracy in deducing optical properties of breast tumors using simulated and physical phantoms and by analyzing 141 projection mammograms of 87 patients with histology-validated tumors that had been recorded by scanning time-domain optical mammography. The slightly compressed breast was modeled as (partially) homogeneous diffusely scattering infinite slab containing a scattering and absorbing spherical heterogeneity representing the tumor. Photon flux densities were calculated from densities of transmitted photons, assuming extended boundary conditions. Explicit formulas are provided for second-order changes in transmitted photon density due to the presence of absorbers or scatterers. The results on phantoms obtained by perturbation theory carried up to third order were compared with measured temporal point spread functions, with numerical finite-element method (FEM) simulations of transmitted photon flux density, with results obtained from the diffraction of diffuse photon density waves, and from Padé approximants. The breakdown of first-, second-, and third-order perturbation theory is discussed for absorbers and a general expression was derived for the convergence of the Born series in this case. Taking tumor optical properties derived by the diffraction model as reference we conclude that estimates of tumor absorption coefficients by perturbation theory agree with reference values within +/-25% in only 65% (first order), 66% (second order), and 77% (third order) of all mammograms analyzed. In the remaining cases tumor absorption is generally underestimated due to the breakdown of perturbation theory. On average the empirical Padé approximants yield tumor absorption coefficients similar to third-order perturbation theory, yet at noticeable lower computational efforts.

A noninvasive multimodal technique to monitor brain tumor vascularization

Determination of tumor oxygenation at the microvascular level will provide important insight into tumor growth, angiogenesis, necrosis and therapeutic response and will facilitate to develop protocols for studying tumor behavior. The non-ionizing near infrared spectroscopy (NIRS) technique has the potential to differentiate lesion and hemoglobin dynamics; however, it has a limited spatial resolution. On the other hand, magnetic resonance imaging (MRI) has achieved high spatial resolution with excellent tissue discrimination but is more susceptible to limited ability to monitor the hemoglobin dynamics. In the present work, the vascular status and the pathophysiological changes that occur during tumor vascularization are studied in an orthotopic brain tumor model. A noninvasive multimodal approach based on the NIRS technique, namely steady state diffuse optical spectroscopy (SSDOS) along with MRI, is applied for monitoring the concentrations of oxyhemoglobin, deoxyhemoglobin and water within tumor region. The concentrations of oxyhemoglobin, deoxyhemoglobin and water within tumor vasculature are extracted at 15 discrete wavelengths in a spectral window of 675-780 nm. We found a direct correlation between tumor size, intratumoral microvessel density and tumor oxygenation. The relative decrease in tumor oxygenation with growth indicates that though blood vessels infiltrate and proliferate the tumor region, a hypoxic trend is clearly present.

Analytical method for localizing a fluorescent inclusion in a turbid medium

We describe a novel method for localizing a fluorescent inclusion in a homogeneous turbid medium through the use of time-resolved techniques. Based on the calculation of the mean time of the fluorescence curves, the method does not require a priori knowledge of either the fluorescence lifetime or the mean time of the instrument response function since it adopts a differential processing approach. Theoretical expressions were validated and experiments for assessing the accuracy of localization were carried out on liquid optical phantoms with a small fluorescent inclusion. The illumination and detection optical fibers were immersed in the medium to achieve infinite medium geometry as required by the model used. The experimental setup consisted of a time-correlated single-photon counting system. Submillimeter accuracy was achieved for the localization of the inclusion.

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.

Perturbation theory for the diffusion equation by use of the moments of the generalized temporal point-spread function. I. Theory

We approach the perturbative solution to the diffusion equation for the case of absorbing inclusions embedded in a heterogeneous scattering medium by using general properties of the radiative transfer equation and the solution of the Fredholm equation of the second kind given by the Neumann series. The terms of the Neumann series are used to obtain the expression of the moments of the generalized temporal point-spread function derived in transport theory. The moments are calculated independently by using Monte Carlo simulations for validation of the theory. While the mixed moments are correctly derived from the theory by using the solution of the diffusion equation in the geometry of interest, in order to obtain the self moments we should reframe the problem in transport theory and use a suitable solution of the radiative transfer equation for the calculation of the multiple integrals of the corresponding Neumann series. Since the rigorous theory leads to impractical formulas, in order to simplify and speed up the calculation of the self moments, we propose a heuristic method based on the calculation of only a single integral and some scaling parameters. We also propose simple quadrature rules for the calculation of the mixed moments for speeding up the computation of perturbations due to multiple defects. The theory can be developed in the continuous-wave domain, the time domain, and the frequency domain. In a companion paper [J. Opt. Soc. Am. A23, 2119 (2006)] we discuss the conditions of applicability of the theory in practical cases found in diffuse optical imaging of biological tissues.