Three-dimensional optical tomography: resolution in small-object imaging

Wavelength dependence of sensitivity in spectral diffuse optical imaging: effect of normalization on image reconstruction

Near Infrared Diffuse Optical Tomography has the potential to be used as a non-invasive imaging tool for biological tissue specifically for the diagnosis and characterization of breast cancer. Most model based reconstruction algorithms rely on calculating and inverting a large Jacobian matrix. Although this method is flexible for a wide range of complex problems, it usually results in large image artifacts from hypersensitivity around the detectors. In this work a Jacobian normalization technique is presented which takes into account the varying magnitude of different optical parameters creating a more uniform update within a spectral image reconstruction model. Using simulated data the Jacobian normalization method is used to reconstructed images of absolute chromophore and scattering parameters which are qualitatively and quantitatively as compared to conventional methods. The hypersensitivity resulting in boundary artifacts are shown to be minimized with only a small additional computational cost.

Methodology development for three-dimensional MR-guided near infrared spectroscopy of breast tumors

Combined Magnetic Resonance (MR) and Near Infrared Spectroscopy (NIRS) has been proposed as a unique method to quantify hemodynamics, water content, and cellular size and packing density of breast tumors, as these tissue constituents can be quantified with increased resolution and overlaid on the structural features identified by the MR. However, the choices in how to reconstruct and visualize this information can have a dramatic impact on the feasibility of implementing this modality in the clinic. This is especially true in 3 dimensions, as there is often limited optical sampling of the breast tissue, and methods need to accurately reflect the tissue composition. In this paper, the implementation and display of fully 3D MR image-guided NIRS is outlined and demonstrated using in vivo data from three healthy women and a volunteer undergoing neoadjuvant chemotherapy. Additionally, a display feature presented here scales the transparency of the optical images to the sensitivity of the measurements, providing a logical way to incorporate partial volume sets of optical images onto the MR volume. These concepts are demonstrated with 3D data sets using Volview software online.

Wavelength band optimization in spectral near-infrared optical tomography improves accuracy while reducing data acquisition and computational burden

Multispectral near-infrared (NIR) tomographic imaging has the potential to provide information about molecules absorbing light in tissue, as well as subcellular structures scattering light, based on transmission measurements. However, the choice of possible wavelengths used is crucial for the accurate separation of these parameters, as well as for diminishing crosstalk between the contributing chromophores. While multispectral systems are often restricted by the wavelengths of laser diodes available, continuous-wave broadband systems exist that have the advantage of providing broadband NIR spectroscopy data, albeit without the benefit of the temporal data. In this work, the use of large spectral NIR datasets is analyzed, and an objective function to find optimal spectral ranges (windows) is examined. The optimally identified wavelength bands derived from this method are tested using both simulations and experimental data. It is found that the proposed method achieves images as qualitatively accurate as using the full spectrum, but improves crosstalk between parameters. Additionally, the judicious use of these spectral windows reduces the amount of data needed for full spectral tomographic imaging by 50%, therefore increasing computation time dramatically.

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.

Image-guided Raman spectroscopic recovery of canine cortical bone contrast in situ

Raman scattering provides valuable biochemical and molecular markers for studying bone tissue composition with use in predicting fracture risk in osteoporosis. Raman tomography can image through a few centimeters of tissue but is limited by low spatial resolution. X-ray computed tomography (CT) imaging can provide high-resolution image-guidance of the Raman spectroscopic characterization, which enhances the quantitative recovery of the Raman signals, and this technique provides additional information to standard imaging methods. This hypothesis was tested in data measured from Teflon tissue phantoms and from a canine limb. Image-guided Raman spectroscopy (IG-RS) of the canine limb using CT images of the tissue to guide the recovery recovered a contrast of 145:1 between the cortical bone and background. Considerably less contrast was found without the CT image to guide recovery. This study presents the first known IG-RS results from tissue and indicates that intrinsically high contrasts (on the order of a hundred fold) are available.

Implementation of a computationally efficient least-squares algorithm for highly under-determined three-dimensional diffuse optical tomography problems

Three-dimensional (3D) diffuse optical tomography is known to be a nonlinear, ill-posed and sometimes under-determined problem, where regularization is added to the minimization to allow convergence to a unique solution. In this work, a generalized least-squares (GLS) minimization method was implemented, which employs weight matrices for both data-model misfit and optical properties to include their variances and covariances, using a computationally efficient scheme. This allows inversion of a matrix that is of a dimension dictated by the number of measurements, instead of by the number of imaging parameters. This increases the computation speed up to four times per iteration in most of the under-determined 3D imaging problems. An analytic derivation, using the Sherman-Morrison-Woodbury identity, is shown for this efficient alternative form and it is proven to be equivalent, not only analytically, but also numerically. Equivalent alternative forms for other minimization methods, like Levenberg-Marquardt (LM) and Tikhonov, are also derived. Three-dimensional reconstruction results indicate that the poor recovery of quantitatively accurate values in 3D optical images can also be a characteristic of the reconstruction algorithm, along with the target size. Interestingly, usage of GLS reconstruction methods reduces error in the periphery of the image, as expected, and improves by 20% the ability to quantify local interior regions in terms of the recovered optical contrast, as compared to LM methods. Characterization of detector photo-multiplier tubes noise has enabled the use of the GLS method for reconstructing experimental data and showed a promise for better quantification of target in 3D optical imaging. Use of these new alternative forms becomes effective when the ratio of the number of imaging property parameters exceeds the number of measurements by a factor greater than 2.

UV-induced modification of stress distribution in optical fibers and its contribution to Bragg grating birefringence

This paper discusses the importance of stress-induced contributions to the photo-induced birefringence observed in fiber Bragg gratings. Optical tomography measurements are performed in exposed and unexposed fibers to extract the stress profiles induced by UV-writing of fiber Bragg gratings for various exposure levels. A photoelastic analysis and a high-order isoparametric finite elements method are then used to calculate the birefringence caused by stress profile modifications. The results are compared to the birefringence directly measured by spectral analysis of a chirped fiber grating with multiple phase-shifts. We can therefore estimate the fraction of the photo-induced birefringence due to stress-induced anisotropy following UV exposure.

Calibration of the second-order nonlinear optical susceptibility of surface and bulk of glass

A two-beam second-harmonic generation technique is developed to calibrate the magnitude of the second-order nonlinear optical susceptibility components of surface and bulk (multipolar origin) of isotropic materials. The values obtained for fused silica calibrated against ChiXXX of crystalline quartz are chi parallel parallel perpendicular = 7.9(4), chi perpendicular parallel parallel (+)gamma = 3.8(4), parallel perpendicular perpendicular perpendicular(+)gamma = 59(4), and delta' = 7.8(4) in units of 10(-22) m(2)/V. Similar values are obtained for BK7 glass. An alternative way of calibration against ChiXYZ of quartz is demonstrated. The technique could also be extended to characterize the susceptibility tensor of crystals as a convenient alternative to the Maker-fringe technique.

Polarization dependence of non-linear gain compression factor in semiconductor optical amplifier

We investigate the power and the polarization dependence of the intraband dynamics in a bulk semiconductor optical amplifier using both a 2.5-ps pump-probe experimental set-up in contra-propagation and a theoretical model. Our model is based on the rate equations and takes into account the polarization dependence of the gain. By comparing experimental and computational results we are able to highlight the dependences of the intraband dynamics and to extract the non-linear gain compression factor as a function of both pulse energy and polarization of the injected pulses.

Simple and robust image-based autofocusing for digital microscopy

A simple image-based autofocusing scheme for digital microscopy is demonstrated that uses as few as two intermediate images to bring the sample into focus. The algorithm is adapted to a commercial inverted microscope and used to automate brightfield and fluorescence imaging of histopathology tissue sections.

Silicon cross-connect filters using microring resonator coupled multimode-interference-based waveguide crossings

We report silicon cross-connect filters using microring resonator coupled multimode-interference (MMI) based waveguide crossings. Our experiments reveal that the MMI-based cross-connect filters impose lower crosstalk at the crossing than the conventional cross-connect filters using plain crossings, while offering a nearly symmetric resonance line shape in the drop-port transmission. As a proof-of-concept for cross-connection applications, we demonstrate on a silicon-on-insulator substrate (i) a 4-channel 1 x 4 linear-cascaded MMI-based cross-connect filter, and (ii) a 2-channel 2 x 2 array-cascaded MMI-based cross-connect filter.

Blazed high-efficiency x-ray diffraction via transmission through arrays of nanometer-scale mirrors

Diffraction gratings are ubiquitous wavelength dispersive elements for photons as well as for subatomic particles, atoms, and large molecules. They serve as enabling devices for spectroscopy, microscopy, and interferometry in numerous applications across the physical sciences. Transmission gratings are required in applications that demand high alignment and figure error tolerances, low weight and size, or a straight-through zero-order beam. However, photons or particles are often strongly absorbed upon transmission, e.g., in the increasingly important extreme ultraviolet (EUV) and soft x-ray band, leading to low diffraction efficiency. We demonstrate the performance of a critical-angle transmission (CAT) grating in the EUV and soft x-ray band that for the first time combines the advantages of transmission gratings with the superior broadband efficiency of blazed reflection gratings via reflection from nanofabricated periodic arrays of atomically smooth nanometer-thin silicon mirrors at angles below the critical angle for total external reflection. The efficiency of the CAT grating design is not limited to photons, but also opens the door to new, sensitive, and compact experiments and applications in atom and neutron optics, as well as for the efficient diffraction of electrons, ions, or molecules.

Birefringence and optical power confinement in horizontal multi-slot waveguides made of Si and SiO2

Through simulations and measurements, we show that in multi-slot thin film waveguides, the TM polarized modes can be confined mostly in the low refractive index layers of the waveguide. The structure consisted of alternating layers of a-Si and SiO(2), in the thickness range between 3 and 40 nm, for which the slots were the SiO(2) layers. Simulations were performed using the transfer matrix method and experiments using the m-line technique at 1.55 mum. The dependence of the birefringence and of the power confinement in the slots was studied as a function of the waveguide thickness, the Si and SiO(2) layer thicknesses, and the SiO(2) / Si layer thickness ratio. We find a large birefringence-a refractive index difference between TE and TM modes-as large as 0.8. For TM polarized modes, up to ~ 85% of the total power in the fundamental mode can be confined in the slots.

High-power, femtosecond, thermal-lens-shaped Yb:KGW oscillator

Thermal lens shaping for astigmatism compensation is extended to a high-power, diode-pumped, Yb:KGW laser by employing a gain crystal geometry designed for efficient polarized pumping. The 63MHz oscillator is soliton mode-locked with the aid of a saturable Bragg reflector to yield 250fs (347fs) pulses at an output power of 3.5W (5W). Frequency doubling of the 250fs pulses with an intrinsic efficiency >60% provides 1.65W of average green power.

Interaction of transverse modes in a single-frequency few-mode fiber amplifier caused by local gain saturation

We report on the behavior of modal polarization states in a single-frequency, ytterbium-doped, few-mode fiber amplifier. Experimental data show that the polarization of the individual transverse modes depends on the pump power and that the modes tend towards orthogonally polarized states with increasing gain. The observations can be explained by local gain saturation that favors the amplification of differently polarized modes.

Measurement of internal tissue optical properties at ultraviolet and visible wavelengths: Development and implementation of a fiberoptic-based system

A novel, multi-wavelength, fiberoptic system was constructed, evaluated and implemented to determine internal tissue optical properties at ultraviolet A (UVA) and visible (VIS) wavelengths. Inverse modeling was performed with a neural network to estimate absorption and reduced scattering coefficients based on spatially-resolved reflectance distributions. The model was calibrated with simulated reflectance datasets generated using a condensed Monte Carlo approach with absorption coefficients up to 85 cm(-1) and reduced scattering coefficients up to 118 cm(-1). After theoretical and experimental evaluations of the system, optical properties of porcine bladder, colon, esophagus, oral mucosa, and liver were measured at 325, 375, 405, 445 and 532 nm. These data provide evidence that as wavelengths decrease into the UVA, the dominant tissue chromophore shifts from hemoglobin to structural proteins such as collagen. This system provides a high level of accuracy over a wide range of optical properties, and should be particularly useful for in situ characterization of highly attenuating biological tissues in the UVA-VIS.

Low jitter Q-switched fiber laser using optically driven surface-normal saturable absorber modulator

A technique for stabilizing the repetition frequency of a passively Q-switched laser is presented using an optically driven surface-normal semiconductor modulator. A method is capable of significant reduction of the timing jitter in a passively Q-switched laser by optical triggering the saturable absorber semiconductor reflector. The experimental demonstration using passively Q-switched ytterbium-doped fiber laser shows the jitter reduction by factor of 1.66??10(3) from 50 mus down to 30 ns.

Fluorescence tomography characterization for sub-surface imaging with protoporphyrin IX

Optical imaging of fluorescent objects embedded in a tissue simulating medium was characterized using non-contact based approaches to fluorescence remittance imaging (FRI) and sub-surface fluorescence diffuse optical tomography (FDOT). Using Protoporphyrin IX as a fluorescent agent, experiments were performed on tissue phantoms comprised of typical in-vivo tumor to normal tissue contrast ratios, ranging from 3.5:1 up to 10:1. It was found that tomographic imaging was able to recover interior inclusions with high contrast relative to the background; however, simple planar fluorescence imaging provided a superior contrast to noise ratio. Overall, FRI performed optimally when the object was located on or close to the surface and, perhaps most importantly, FDOT was able to recover specific depth information about the location of embedded regions. The results indicate that an optimal system for localizing embedded fluorescent regions should combine fluorescence reflectance imaging for high sensitivity and sub-surface tomography for depth detection, thereby allowing more accurate localization in all three directions within the tissue.

Aberration reduction and unique light focusing in a photonic crystal negative refractive lens

Light focusing characteristics of a negative refractive lens fabricated out of a silicon-on-insulator photonic crystal (PC) slab are investigated theoretically and experimentally. It focuses in the near infrared, but the focal spot is degraded by a lens aberration. To reduce the aberration, we designed a composite PC that gives rise to a narrower focal spot. In addition, two unique functions of this lens are demonstrated: refocusing outside of the PC and parallel focusing, enabling image transfer and real image formation, respectively. These results prove the feasibility of an in-plane free space optical network based on negative refraction.

Magnetic resonance-coupled fluorescence tomography scanner for molecular imaging of tissue

A multichannel spectrally resolved optical tomography system to image molecular targets in small animals from within a clinical MRI is described. Long source/detector fibers operate in contact mode and couple light from the tissue surface in the magnet bore to 16 spectrometers, each containing two optical gratings optimized for the near infrared wavelength range. High sensitivity, cooled charge coupled devices connected to each spectrograph provide detection of the spectrally resolved signal, with exposure times that are automated for acquisition at each fiber. The design allows spectral fitting of the remission light, thereby separating the fluorescence signal from the nonspecific background, which improves the accuracy and sensitivity when imaging low fluorophore concentrations. Images of fluorescence yield are recovered using a nonlinear reconstruction approach based on the diffusion approximation of photon propagation in tissue. The tissue morphology derived from the MR images serves as an imaging template to guide the optical reconstruction algorithm. Sensitivity studies show that recovered values of indocyanine green fluorescence yield are linear to concentrations of 1 nM in a 70 mm diameter homogeneous phantom, and detection is feasible to near 10 pM. Phantom data also demonstrate imaging capabilities of imperfect fluorophore uptake in tissue volumes of clinically relevant sizes. A unique rodent MR coil provides optical fiber access for simultaneous optical and MR data acquisition of small animals. A pilot murine study using an orthotopic glioma tumor model demonstrates optical-MRI imaging of an epidermal growth factor receptor targeted fluorescent probe in vivo.

A simulation study of the variability of indocyanine green kinetics and using structural a priori information in dynamic contrast enhanced diffuse optical tomography (DCE-DOT)

We investigated (1) the variability of indocyanine green kinetics (ICG) between different cases in the existence of random noise, changing the size of the imaging region, the location and the size of the inclusion, (2) the use of structural a priori information to reduce the variability. We performed two-dimensional simulation studies for this purpose. In the simulations, we used a two-compartmental model to describe the ICG transport and obtained pharmacokinetic parameters. The transfer constant and the rate constant showed a wide variation, i.e. 60% and 95%, respectively, when random Gaussian noise with a standard deviation of 1% in amplitude and 0.4 degrees in phase was added to data. Moreover, recovered peak ICG concentration and time to reach the peak concentration was different within different cases. When structural a priori information was used in the reconstructions, the variations in the transfer and the rate constant were reduced to 29%, 15%, respectively. As a result, although the recovered peak concentration was still case dependent, the variability of the shape of the kinetic curve was reduced.

A boundary element approach for image-guided near-infrared absorption and scatter estimation

Multimodality NIR spectroscopy systems offer the possibility of region-based vascular and molecular characterization of tissue in vivo. However, computationally efficient 3D image reconstruction algorithms specific to these image-guided systems currently do not exist. Image reconstruction is often based on finite-element methods (FEMs), which require volume discretization. Here, a boundary element method (BEM) is presented using only surface discretization to recover the optical properties in an image-guided setting. The reconstruction of optical properties using BEM was evaluated in a domain containing a 30 mm inclusion embedded in two layer media with different noise levels and initial estimates. For 5% noise in measurements, and background starting values for reconstruction, the optical properties were recovered to within a mean error of 6.8%. When compared with FEM for this case, BEM showed a 28% improvement in computational time. BEM was also applied to experimental data collected from a gelatin phantom with a 25 mm inclusion and could recover the true absorption to within 6% of expected values using less time for computation compared with FEM. When applied to a patient-specific breast mesh generated using MRI, with a 2 cm ductal carcinoma, BEM showed successful recovery of optical properties with less than 5% error in absorption and 1% error in scattering, using measurements with 1% noise. With simpler and faster meshing schemes required for surface grids as compared with volume grids, BEM offers a powerful and potentially more feasible alternative for high-resolution 3D image-guided NIR spectroscopy.

Fast intersections on nested tetrahedrons (FINT): An algorithm for adaptive finite element based distributed parameter estimation

A variety of biomedical imaging techniques such as optical and fluorescence tomography, electrical impedance tomography, and ultrasound imaging can be cast as inverse problems, wherein image reconstruction involves the estimation of spatially distributed parameter(s) of the PDE system describing the physics of the imaging process. Finite element discretization of imaged domain with tetrahedral elements is a popular way of solving the forward and inverse imaging problems on complicated geometries. A dual-adaptive mesh-based approach wherein, one mesh is used for solving the forward imaging problem and the other mesh used for iteratively estimating the unknown distributed parameter, can result in high resolution image reconstruction at minimum computation effort, if both the meshes are allowed to adapt independently. Till date, no efficient method has been reported to identify and resolve intersection between tetrahedrons in independently refined or coarsened dual meshes. Herein, we report a fast and robust algorithm to identify and resolve intersection of tetrahedrons within nested dual meshes generated by 8-similar subtetrahedron subdivision scheme. The algorithm exploits finite element weight functions and gives rise to a set of weight functions on each vertex of disjoint tetrahedron pieces that completely cover up the intersection region of two tetrahedrons. The procedure enables fully adaptive tetrahedral finite elements by supporting independent refinement and coarsening of each individual mesh while preserving fast identification and resolution of intersection. The computational efficiency of the algorithm is demonstrated by diffuse photon density wave solutions obtained from a single- and a dual-mesh, and by reconstructing a fluorescent inclusion in simulated phantom from boundary frequency domain fluorescence measurements.

Receiver operating characteristic and location analysis of simulated near-infrared tomography images

Receiver operating characteristic (ROC) analysis was performed on simulated near-infrared tomography images, using both human observer and contrast-to-noise ratio (CNR) computational assessment, for application in breast cancer imaging. In the analysis, a nonparametric approach was applied for estimating the ROC curves. Human observer detection of objects had superior capability to localize the presence of heterogeneities when the objects were small with high contrast, with a minimum detectable threshold of CNR near 3.0 to 3.3 in the images. Human observers were able to detect heterogeneities in the images below a size limit of 4 mm, yet could not accurately find the location of these objects when they were below 10 mm diameter. For large objects, the lower limit of a detectable contrast limit was near 10% increase relative to the background. The results also indicate that iterations of the nonlinear reconstruction algorithm beyond 4 did not significantly improve the human detection ability, and degraded the overall localization ability for the objects in the image, predominantly by increasing the noise in the background. Interobserver variance performance in detecting objects in these images was low, suggesting that because of the low spatial resolution, detection tasks with NIR tomography is likely consistent between human observers.

Fully adaptive finite element based tomography using tetrahedral dual-meshing for fluorescence enhanced optical imaging in tissue

We have developed fluorescence enhanced optical tomography based upon fully adaptive finite element method (FEM) using tetrahedral dual-meshing wherein one of the two meshes discretizes the forward variables and the other discretizes the unknown parameters to be estimated. We used the 8-subtetrahedron subdivision scheme to create the nested dualmesh in which each are independently refined. However, two tetrahedrons from the two different meshes pose an intersection problem that needs to be resolved in order to find the common regions that the forward variables (the fluorescent diffuse photon fluence fields) and the parameter estimates (the fluorescent absorption coefficients) can be mutually assigned. Using an efficient intersection algorithm in the nested tetrahedral environments previously developed by the authors, we demonstrate fully adaptive tomography using a posteriori error estimates. Performing the iterative reconstructions using the simulated boundary measurement data, we demonstrate that small fluorescent targets embedded in the breast simulating phantom in point illumination/detection geometry can be resolved at reasonable computational cost.

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.

Validation of luminescent source reconstruction using single-view spectrally resolved bioluminescence images

We characterize the capabilities and limitations of the Living Image Software 3D Analysis package (Xenogen, Alameda, California) in the reconstruction of calibrated light sources. Sources shallower than the mean free path of light propagation suffered reconstruction inaccuracy. For sources deeper than the mean free path, the average error in depth and intensity reconstruction was less than 4% and 12%, respectively, for homogeneous tissue. The reconstruction of luminescent beads implanted within an optically heterogeneous mouse abdomen proved less accurate. The ability to distinguish multiple sources decreased with increasing source depth. A number of factors influence the accuracy of light source reconstruction.

Combined magnetic resonance and bioluminescence imaging of live mice

We perform combined magnetic resonance and bioluminescence imaging of live mice for the purpose of improving the accuracy of bioluminescence tomography. The imaging is performed on three live nude mice in which tritium-powered light sources are surgically implanted. High-resolution magnetic resonance images and multispectral, multiview bioluminescence images are acquired in the same session. An anatomical model is constructed by segmenting the magnetic resonance images for all major tissues. The model is subsequently registered with nonlinear transformations to the 3-D light exittance (exiting intensity) surface map generated from the luminescence images. A Monte Carlo algorithm, along with a set of tissue optical properties obtained from in vivo measurements, is used to solve the forward problem. The measured and simulated light exittance images are found to differ by a factor of up to 2. The greatest cause of this moderate discrepancy is traced to the small errors in source positioning, and to a lesser extent to the optical properties used for the tissues. Discarding the anatomy and using a homogeneous model leads to a marginally worse agreement between the simulated and measured data.

Subsurface diffuse optical tomography can localize absorber and fluorescent objects but recovered image sensitivity is nonlinear with depth

Subsurface tomography with diffuse light has been investigated with a noncontact approach to characterize the performance of absorption and fluorescence imaging. Using both simulations and experiments, the reconstruction of local subsurface heterogeneity is demonstrated, but the recovery of target size and fluorophore concentration is not linear when changes in depth occur, whereas the mean position of the object for experimental fluorescent and absorber targets is accurate to within 0.5 and 1.45 mm when located within the first 10 mm below the surface. Improvements in the linearity of the response with depth appear to remain challenging and may ultimately limit the approach to detection rather than characterization applications. However, increases in tissue curvature and/or the addition of prior information are expected to improve the linearity of the response. The potential for this type of imaging technique to serve as a surgical guide is highlighted.

Diffuse optical imaging and spectroscopy for cancer

Visible light and near infrared light interact with biological tissue by absorption and scattering. Diffuse optical imaging and spectroscopy reconstructs tissue physiologic parameters based on noninvasive measurement of tissue optical properties. This technology can be used to differentiate physiologic and molecular signatures of both malignant and benign tissues, as they relate to the area of cancer research. Major advantages are the use of non-ionizing radiation, real-time continuous data acquisition, low cost, and portability. Limitations include low spatial resolution and limited reproducibility. This paper reviews the currently available state-of-the-art technologies for diffuse optical imaging and spectroscopy and their applications in cancer research.

Magnetic resonance electrical impedance tomography of the breast: a simulation study on basic imaging setup

Magnetic resonance electrical impedance tomography (MREIT) has been developed as a new medical imaging modality providing high-resolution conductivity and current density images. This paper is about MREIT of the breast. To show the feasibility of breast MREIT, we carried numerical simulations and breast phantom experiments. We found that an anomaly with 4 mm diameter can be visualized in a reconstructed conductivity image using 5 mA injection current if the SNR of the corresponding MR magnitude image is at least 150. We propose a desirable electrode configuration and show our first experimental results of the breast MREIT. Developing an RF coil for the breast MREIT, we plan to conduct various experimental studies including tissue phantoms.

Absolute conductivity reconstruction in magnetic induction tomography using a nonlinear method

Magnetic induction tomography (MIT) attempts to image the electrical and magnetic characteristics of a target using impedance measurement data from pairs of excitation and detection coils. This inverse eddy current problem is nonlinear and also severely ill posed so regularization is required for a stable solution. A regularized Gauss-Newton algorithm has been implemented as a nonlinear, iterative inverse solver. In this algorithm, one needs to solve the forward problem and recalculate the Jacobian matrix for each iteration. The forward problem has been solved using an edge based finite element method for magnetic vector potential A and electrical scalar potential V, a so called A, A - V formulation. A theoretical study of the general inverse eddy current problem and a derivation, paying special attention to the boundary conditions, of an adjoint field formula for the Jacobian is given. This efficient formula calculates the change in measured induced voltage due to a small perturbation of the conductivity in a region. This has the advantage that it involves only the inner product of the electric fields when two different coils are excited, and these are convenient computationally. This paper also shows that the sensitivity maps change significantly when the conductivity distribution changes, demonstrating the necessity for a nonlinear reconstruction algorithm. The performance of the inverse solver has been examined and results presented from simulated data with added noise.

Quantitative reconstruction of refractive index distribution and imaging of glucose concentration by using diffusing light

We show that a two-step reconstruction method can be adapted to improve the quantitative accuracy of the refractive index reconstruction in phase-contrast diffuse optical tomography (PCDOT). We also describe the possibility of imaging tissue glucose concentration with PCDOT. In this two-step method, we first use our existing finite-element reconstruction algorithm to recover the position and shape of a target. We then use the position and size of the target as a priori information to reconstruct a single value of the refractive index within the target and background regions using a region reconstruction method. Due to the extremely low contrast available in the refractive index reconstruction, we incorporate a data normalization scheme into the two-step reconstruction to combat the associated low signal-to-noise ratio. Through a series of phantom experiments we find that this two-step reconstruction method can considerably improve the quantitative accuracy of the refractive index reconstruction. The results show that the relative error of the reconstructed refractive index is reduced from 20% to within 1.5%. We also demonstrate the possibility of PCDOT for recovering glucose concentration using these phantom experiments.

Fluorescence molecular imaging

There is a wealth of new fluorescent reporter technologies for tagging of many cellular and subcellular processes in vivo. This imposed contrast is now captured with an increasing number of available imaging methods that offer new ways to visualize and quantify fluorescent markers distributed in tissues. This is an evolving field of imaging sciences that has already achieved major advances but is also facing important challenges. It is nevertheless well poised to significantly impact the ways of biological research, drug discovery, and clinical practice in the years to come. Herein, the most pertinent technologies associated with in vivo noninvasive or minimally invasive fluorescence imaging of tissues are summarized. Focus is given to small-animal imaging. However, while a broad spectrum of fluorescence reporter technologies and imaging methods are outlined, as necessary for biomedical research, and clinical translation as well.

Multiplicative optical tomography of cardiac electrical activity

Cardiac electrical activity can be mapped today through the response of voltage-sensitive dyes; but poor transparency of muscle tissue has enforced shallow-depth imaging. We present a three-dimensional (3D) reconstruction method for electrical activity deep inside the myocardial wall. Our approach is nonlinear and differs substantially from standard diffusive optical tomography. It does not require matrix inversion, data regularization or a priori information concerning the original object. Opposite sides of a slab-shaped preparation are scanned in parallel by detection and illumination points with a constant vector offset between illumination and detection axes (biaxial scanning). Scanning is performed in two perpendicular directions. In each direction, a pair of 2D images is obtained under offsets of opposite signs. These two pairs are the input for a multiplicative reconstruction algorithm, whose output is a 3D image. The overall procedure was successfully tested on computer-generated sources that include points, lines and hemispheres, patterned after actual electrophysiological excitations. The algorithm is computationally efficient and stable with respect to varying noise levels in the raw data.

Review of tissue simulating phantoms for optical spectroscopy, imaging and dosimetry

Optical spectroscopy, imaging, and therapy tissue phantoms must have the scattering and absorption properties that are characteristic of human tissues, and over the past few decades, many useful models have been created. In this work, an overview of their composition and properties is outlined, by separating matrix, scattering, and absorbing materials, and discussing the benefits and weaknesses in each category. Matrix materials typically are water, gelatin, agar, polyester or epoxy and polyurethane resin, room-temperature vulcanizing (RTV) silicone, or polyvinyl alcohol gels. The water and hydrogel materials provide a soft medium that is biologically and biochemically compatible with addition of organic molecules, and are optimal for scientific laboratory studies. Polyester, polyurethane, and silicone phantoms are essentially permanent matrix compositions that are suitable for routine calibration and testing of established systems. The most common three choices for scatters have been: (1.) lipid based emulsions, (2.) titanium or aluminum oxide powders, and (3.) polymer microspheres. The choice of absorbers varies widely from hemoglobin and cells for biological simulation, to molecular dyes and ink as less biological but more stable absorbers. This review is an attempt to indicate which sets of phantoms are optimal for specific applications, and provide links to studies that characterize main phantom material properties and recipes.

Image analysis methods for diffuse optical tomography

Three major analytical tools in imaging science are summarized and demonstrated relative to optical imaging in vivo. Standard resolution testing is optimal when infinite contrast is used and hardware evaluation is the goal. However, deep tissue imaging of absorption or fluorescent contrast agents in vivo often presents a different problem, which requires contrast-detail analysis. This analysis shows that the minimum detectable sizes are in the range of 1/10 the outer diameter, whereas minimum detectable contrast values are in the range of 10 to 20% relative to the continuous background values. This is estimated for objects being in the center of the domain being imaged, and as the heterogeneous region becomes closer to the surface, the lower limit on size and contrast can become arbitrarily low and more dictated by hardware specifications. Finally, if human observer detection of abnormalities in the images is the goal, as is standard in most radiological practice, receiver operating characteristic (ROC) curve and location receiver operating characteristic curve (LROC) are used. Each of these three major areas of image interpretation and analysis are reviewed in the context of medical imaging as well as how they are used to quantify the performance of diffuse optical imaging of tissue.

Basic setup for breast conductivity imaging using magnetic resonance electrical impedance tomography

We present a new medical imaging technique for breast imaging, breast MREIT, in which magnetic resonance electrical impedance tomography (MREIT) is utilized to get high-resolution conductivity and current density images of the breast. In this work, we introduce the basic imaging setup of the breast MREIT technique with an investigation of four different imaging configurations of current-injection electrode positions and pathways through computer simulation studies. Utilizing the preliminary findings of a best breast MREIT configuration, additional numerical simulation studies have been carried out to validate breast MREIT at different levels of SNR. Finally, we have performed an experimental validation with a breast phantom on a 3.0 T MREIT system. The presented results strongly suggest that breast MREIT with careful imaging setups could be a potential imaging technique for human breast which may lead to early detection of breast cancer via improved differentiation of cancerous tissues in high-resolution conductivity images.

Computationally efficient methods for incorporation of spectral priors in 3-d optical tomography

Use of spectral prior in optical tomography has significantly improved accuracy and quality of images, when applied in two-dimensional (2-D) models. However, the size of the problem increases substantially when applied in 3-D. Two methods are presented here that make 3-D spectral imaging computationally feasible. The data-subset approach uses a smaller subset of variable measurement s to reduce the size of the inverse problem. The basic principle consists of using a dynamic criterion to select optimal subset that capture the major changes in the imaging domain. Additionally, the sensitivity matrix is analyzed and made sparse based on a memory requirements (to 8% of full matrix) and provides less tha 2% percent difference in quantification compared to use of full matrices in the image reconstruction.

Combining near-infrared tomography and magnetic resonance imaging to study in vivo breast tissue: implementation of a Laplacian-type regularization to incorporate magnetic resonance structure

An imaging system that simultaneously performs near infrared (NIR) tomography and magnetic resonance imaging (MRI) is used to study breast tissue phantoms and a healthy woman in vivo. An NIR image reconstruction that exploits the combined data set is presented that implements the MR structure as a soft-constraint in the NIR property estimation. The algorithm incorporates the MR spatially segmented regions into a regularization matrix that links locations with similar MR properties, and applies a Laplacian-type filter to minimize variation within each region. When prior knowledge of the structure of phantoms is used to guide NIR property estimation, root mean square (rms) image error decreases from 26 to 58%. For a representative in vivo case, images of hemoglobin concentration, oxygen saturation, water fraction, scattering power, and scattering amplitude are derived and the properties of adipose and fibroglandular breast tissue types, identified from MRI, are quantified. Fibroglandular tissue is observed to have more than four times as much water content as adipose tissue, almost twice as much blood volume, and slightly reduced oxygen saturation. This approach is expected to improve recovery of abnormalities within the breast, as the inclusion of structural information increases the accuracy of recovery of embedded heterogeneities, at least in phantom studies.

Diffuse optical tomography of breast cancer during neoadjuvant chemotherapy: a case study with comparison to MRI

We employ diffuse optical tomography (DOT) to track treatment progress in a female subject presenting with locally advanced invasive carcinoma of the breast during neoadjuvant chemotherapy. Three-dimensional images of total hemoglobin concentration and scattering identified the tumor. Our measurements reveal tumor shrinkage during the course of chemotherapy, in reasonable agreement with magnetic resonance images of the same subject. A decrease in total hemoglobin concentration contrast between tumor and normal tissue was also observed over time. The results demonstrate the potential of DOT for measuring physiological parameters of breast lesions during chemotherapy.

Magnetic-resonance-imaging-coupled broadband near-infrared tomography system for small animal brain studies

A novel magnetic-resonance-coupled broadband near-infrared (NIR) tomography system for small animal brain studies is described. Several features of the image formation approach are new in NIR tomography and represent major advances in the path to recovering high-resolution hemoglobin and oxygen saturation images of tissue. The NIR data were broadband and continuous wave and were used along with a second-derivative-based estimation of the path length from water absorption. The path length estimation from water was then used along with the attenuation spectrum to recover absorption and reduced scattering coefficient images at multiple wavelengths and then to recover images of total hemoglobin and oxygen saturation. Going beyond these basics of NIR tomography, software has been developed to allow inclusion of structures derived from MR imaging (MRI) for the external and internal tissue boundaries, thereby improving the accuracy and spatial resolution of the properties in each tissue type. The system has been validated in both tissue-simulating phantoms, with 10% accuracy observed, and in a rat cranium imaging experiment. The latter experiment used variation in inspired oxygen (FiO2) to vary the observed hemoglobin and oxygen saturation images. Quantitative agreement was observed between the changes in deoxyhemoglobin values derived from NIR and the changes predicted with blood-oxygen-level-dependent (BOLD) MRI. This system represents the initial stage in what will likely be a larger role for NIR tomography, coupled to MRI, and illustrates that the technological challenges of using continuous-wave broadband data and inclusion of a priori structural information can be met with careful phantom studies.

Spectrally constrained chromophore and scattering near-infrared tomography provides quantitative and robust reconstruction

A multispectral direct chromophore and scattering reconstruction technique has been implemented for near-infrared frequency-domain tomography in recovering images of total hemoglobin, oxygen saturation, water, and scatter parameters. The method applies the spectral constraint of the chromophores and scattering spectra directly in the reconstruction algorithm, thereby reducing the parameter space of the inversion process. This new method was validated by use of simulated and experimental data, and results show better robustness and stability in the presence of higher levels of noise. The method suppresses artifacts, especially those significant in water and scatter power images, and reduces cross talk between chromophore and scatter parameters. Variation in scattering was followed by this spectral approach successfully in experimental data from 90-mm-diameter cylindrical phantoms, and results show linear variation in scatter amplitude and reduced scattering coefficient (micro(s)'), with total hemoglobin, oxygen saturation, and water remaining constant and quantitatively accurate. Similar experiments were carried out for varying oxygen saturation and total hemoglobin. Accurate quantification was obtained with a mean error of 7.7% for oxygen saturation and 6.2% for total hemoglobin, with minimal cross talk between different parameters.

Excitation patterns in three-dimensional electrical impedance tomography

Electrical impedance tomography (EIT) is a non-invasive technique that aims to reconstruct images of internal electrical properties of a domain, based on electrical measurements on the periphery. Improvements in instrumentation and numerical modeling have led to three-dimensional (3D) imaging. The availability of 3D modeling and imaging raises the question of identifying the best possible excitation patterns that will yield to data, which can be used to produce the best image reconstruction of internal properties. In this work, we describe our 3D finite element model of EIT. Through singular value decomposition as well as examples of reconstructed images, we show that for a homogenous female breast model with four layers of electrodes, a driving pattern where each excitation plane is a sinusoidal pattern out-of-phase with its neighboring plane produces better qualitative images. However, in terms of quantitative imaging an excitation pattern where all electrode layers are in phase produces better results.

In vivo scattering measurement of biological tissue by the use of a pyroelectric polymer transducer

We propose a new method, to our knowledge, for noninvasive scattering measurements of tissues by the use of a pyroelectric polymer transducer, poly(vinylidene fluoride trifluoroethylene) film. In this method, samples are irradiated with nanosecond, low-energy light pulses delivered from an optical fiber, and the pyroelectric signal induced by the diffuse reflectance is measured with a transducer. The signal is then converted into diffuse reflectance by use of a calibration factor. The validity of this method was confirmed by our measuring the scattering coefficient of a white acrylic resin within an accuracy of +/- 15%. We attempted to apply this method to the estimation of scattering coefficients of normal and burned skins in rats in vivo.

Improved quantification of small objects in near-infrared diffuse optical tomography

Diffuse optical tomography allows quantification of hemoglobin, oxygen saturation, and water in tissue, and the fidelity in this quantification is dependent on the accuracy of optical properties determined during image reconstruction. In this study, a three-step algorithm is proposed and validated that uses the standard Newton minimization with Levenberg-Marquardt regularization as the first step. The second step is a modification to the existing algorithm using a two-parameter regularization to allow lower damping in a region of interest as compared to background. This second stage allows the recovery of the actual size of an inclusion. A region-based reconstruction is the final third step, which uses the estimated size and position information from step 2 to yield quantitatively accurate average values for the optical parameters. The algorithm is tested on simulated and experimental data and is found to be insensitive to object contrast and position. The percentage error between the true and the average recovered value for the absorption coefficient in test images is reduced from 47 to 27% for a 10-mm inclusion, from 38 to 13% for a 15-mm anomaly, and from 28 to 5.5% for a 20-mm heterogeneity. Simulated data with absorbing and scattering heterogeneities of 15 mm diam located in different positions show recovery with less than 15% error in absorption and 6% error in reduced scattering coefficients. The algorithm is successfully applied to clinical data from a subject with a breast abnormality to yield quantitatively increased absorption coefficients, which enhances the contrast to 3.8 compared to 1.23 previously.

Characterization of hemoglobin, water, and NIR scattering in breast tissue: analysis of intersubject variability and menstrual cycle changes

Near-infrared imaging was used to quantify typical values of hemoglobin concentration, oxygen saturation, water fraction, scattering power, and scattering amplitude within the breast tissue of volunteer subjects. A systematic study of the menstrual variations in these parameters was carried out by measuring a group of seven premenopausal normal women (aged 41 to 47 years) in the follicular (days 7 to 14 of the cycle) and secretory phases (days 21 to 28) of the cycle, for two complete menstrual cycles. An average increase in hemoglobin concentration of 2.6 microM or 13% of the background breast values was observed in the secretory phase relative to the follicular phase (p<0.0001), but no other average near-infrared parameter changes were significant. While repeatable and systematic changes were observed in all parameters for individual subjects, large intersubject variations were present in all parameters. In a survey of thirty-nine normal subjects, the total hemoglobin varied from 9 to 45 microM, with a systematic correlation observed between total hemoglobin concentration and breast radiographic density. Scattering power and scattering amplitude were also correlated with radiographic density, but oxygen saturation and water fraction were not. Images of breast lesions indicate that total hemoglobin-based contrast can be up to 200% relative to the background in the same breast. Yet, since the background hemoglobin values vary considerably among breasts, the maximum hemoglobin concentrations observed in cancer tumors may vary considerably as well. In light of these observations, it may be important to use hemoglobin contrast values relative to the background for a given breast, rather than absolute hemoglobin contrast when trying to compare the features of breast lesions among subjects.

Imaging changes in blood volume and oxygenation in the newborn infant brain using three-dimensional optical tomography

Induced haemodynamic and blood oxygenation changes occurring within the brain of a ventilated newborn infant have been imaged in three dimensions using optical tomography. Noninvasive measurements of the flight times of transmitted light were acquired during illumination of the brain by laser pulses at wavelengths of 780 nm and 815 nm. The oxygen and carbon dioxide partial pressures were adjusted through alterations to the ventilator settings, resulting in changes to the cerebral blood volume and oxygenation. Three-dimensional images were generated using the physiologically associated differences in the measured data, obviating the need for data calibration using a separate reference measurement. The results exhibit large changes in absorption coefficient at both wavelengths. Images corresponding to differences in concentrations of oxy- and deoxyhaemoglobin are in qualitative agreement with known physiological data.

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.

Interpreting hemoglobin and water concentration, oxygen saturation, and scattering measured in vivo by near-infrared breast tomography

Near-infrared spectroscopic tomography was used to measure the properties of 24 mammographically normal breasts to quantify whole-breast absorption and scattering spectra and to evaluate which tissue composition characteristics can be determined from these spectra. The absorption spectrum of breast tissue allows quantification of (i) total hemoglobin concentration, (ii) hemoglobin oxygen saturation, and (iii) water concentration, whereas the scattering spectrum provides information about the size and number density of cellular components and structural matrix elements. These property data were tested for correlation to demographic information, including subject age, body mass index, breast size, and radiographic density. Total hemoglobin concentration correlated inversely to body mass index, likely because lower body mass indicates proportionately less fat and more glandular tissue, and glandular tissue contains greater vascularity, hence, more total hemoglobin. Optical scattering was correlated to breast diameter, subject age, and radiographic density. In the radiographic density, fatty breasts had low scattering power and extremely dense breasts had higher values. This observation is consistent with low attenuation of conventional x-rays with fat and higher attenuation in glandular tissues. Optically, fatty tissues have large scatterers leading to a low scattering power, whereas glandular or fibrous tissues have more cellular and collagen-based structures that lead to high scattering power. The study presents correlative data supporting the hypothesis that optical measurements of absorption and scattering can provide physiologically relevant information about breast tissue composition. These breast constituents vary significantly between individuals and can be altered because of changes in breast physiology or pathological state.