Practical fully three-dimensional reconstruction algorithms for diffuse optical tomography.

We have developed an efficient fully three-dimensional (3D) reconstruction algorithm for diffuse optical tomography (DOT). The 3D DOT, a severely ill-posed problem, is tackled through a pseudodynamic (PD) approach wherein an ordinary differential equation representing the evolution of the solution on pseudotime is integrated that bypasses an explicit inversion of the associated, ill-conditioned system matrix. One of the most computationally expensive parts of the iterative DOT algorithm, the reevaluation of the Jacobian in each of the iterations, is avoided by using the adjoint-Broyden update formula to provide low rank updates to the Jacobian. In addition, wherever feasible, we have also made the algorithm efficient by integrating along the quadratic path provided by the perturbation equation containing the Hessian. These algorithms are then proven by reconstruction, using simulated and experimental data and verifying the PD results with those from the popular Gauss-Newton scheme. The major findings of this work are as follows: (i) the PD reconstructions are comparatively artifact free, providing superior absorption coefficient maps in terms of quantitative accuracy and contrast recovery; (ii) the scaling of computation time with the dimension of the measurement set is much less steep with the Jacobian update formula in place than without it; and (iii) an increase in the data dimension, even though it renders the reconstruction problem less ill conditioned and thus provides relatively artifact-free reconstructions, does not necessarily provide better contrast property recovery. For the latter, one should also take care to uniformly distribute the measurement points, avoiding regions close to the source so that the relative strength of the derivatives for measurements away from the source does not become insignificant.

Biodegradable Protein-Stabilized Inorganic Nanoassemblies for Photothermal Radiotherapy of Hepatoma Cells.

Inorganic nanomaterials require optimal engineering to retain their functionality yet can also biodegrade within physiological conditions to avoid chronic accumulation in their native form. In this work, we have developed gelatin-stabilized iron oxide nanoclusters having a primary crystallite size of ∼10 nm and surface-functionalized with indocyanine green (ICG)-bound albumin-stabilized gold nanoclusters (Prot-IONs). The Prot-IONs are designed to undergo disintegration in an acidic microenvironment of tumor in the presence of proteolytic enzymes within 72 h. These nanoassemblies demonstrate bio- and hemocompatibility and show significant photothermal efficiency due to strong near infrared absorption contributed by ICG. The surface gold nanoclusters could efficiently sensitize hepatoma cells to γ-irradiation with substantial cytoskeletal and nuclear damage. Sequential irradiation of Prot-ION-treated cancer cells with near infrared (NIR) laser (λ = 750 nm) and γ-irradiation could cause ∼90% cell death compared to single treatment groups at a lower dose of nanoparticles. The superparamagnetic nature of Prot-IONs imparted significant relaxivity (∼225 mM-1 s-1) for T2-weighted magnetic resonance imaging. Additionally, they could also be engaged as photoacoustic and NIR imaging contrast agents. This work demonstrates bioeliminable inorganic nanoassemblies with significant theranostic potential.

Nontoxic In Vivo Clearable Nanoparticle Clusters for Theranostic Applications.

Disintegrable inorganic nanoclusters (GIONs) with gold seed (GS) coating of an iron oxide core with a primary nanoparticle size less than 6 nm were prepared for theranostic applications. The GIONs possessed a broad near-infrared (NIR) absorbance at ∼750 nm because of plasmon coupling between closely positioned GSs on the iron oxide nanoclusters (ION) surface, in addition to the ∼513 nm peak corresponding to the isolated GS. The NIR laser-triggered photothermal response of GIONs was found to be concentration-dependent with a temperature rise of ∼8.5 and ∼4.5 °C from physiological temperature for 0.5 and 0.25 mg/mL, respectively. The nanoclusters were nonhemolytic and showed compatibility with human umbilical vein endothelial cells up to a concentration of 0.7 mg/mL under physiological conditions. The nanoclusters completely disintegrated at a lysosomal pH of 5.2 within 1 month. With an acute increase of over 400% intracellular reactive oxygen species soon after γ-irradiation and assistance from Fenton reaction-mediated supplemental oxidative stress, GION treatment in conjunction with radiation killed ∼50% of PLC/PRF/5 hepatoma cells. Confocal microscopy images of these cells showed significant cytoskeletal and nuclear damage from radiosensitization with GIONs. The cell viability further decreased to ∼10% when they were sequentially exposed to the NIR laser followed by γ-irradiation. The magnetic and optical properties of the nanoclusters enabled GIONs to possess a T2 relaxivity of ∼223 mM-1 s-1and a concentration-dependent strong photoacoustic signal toward magnetic resonance and optical imaging. GIONs did not incur any organ damage or evoke an acute inflammatory response in healthy C57BL/6 mice. Elemental analysis of various organs indicated differential clearance of gold and iron via both renal and hepatobiliary routes.

Accelerated gradient based diffuse optical tomographic image reconstruction.

PURPOSE: Fast reconstruction of interior optical parameter distribution using a new approach called Broyden-based model iterative image reconstruction (BMOBIIR) and adjoint Broyden-based MOBIIR (ABMOBIIR) of a tissue and a tissue mimicking phantom from boundary measurement data in diffuse optical tomography (DOT). METHODS: DOT is a nonlinear and ill-posed inverse problem. Newton-based MOBIIR algorithm, which is generally used, requires repeated evaluation of the Jacobian which consumes bulk of the computation time for reconstruction. In this study, we propose a Broyden approach-based accelerated scheme for Jacobian computation and it is combined with conjugate gradient scheme (CGS) for fast reconstruction. The method makes explicit use of secant and adjoint information that can be obtained from forward solution of the diffusion equation. This approach reduces the computational time many fold by approximating the system Jacobian successively through low-rank updates. RESULTS: Simulation studies have been carried out with single as well as multiple inhomogeneities. Algorithms are validated using an experimental study carried out on a pork tissue with fat acting as an inhomogeneity. The results obtained through the proposed BMOBIIR and ABMOBIIR approaches are compared with those of Newton-based MOBIIR algorithm. The mean squared error and execution time are used as metrics for comparing the results of reconstruction. CONCLUSIONS: We have shown through experimental and simulation studies that Broyden-based MOBIIR and adjoint Broyden-based methods are capable of reconstructing single as well as multiple inhomogeneities in tissue and a tissue-mimicking phantom. Broyden MOBIIR and adjoint Broyden MOBIIR methods are computationally simple and they result in much faster implementations because they avoid direct evaluation of Jacobian. The image reconstructions have been carried out with different initial values using Newton, Broyden, and adjoint Broyden approaches. These algorithms work well when the initial guess is close to the true solution. However, when initial guess is far away from true solution, Newton-based MOBIIR gives better reconstructed images. The proposed methods are found to be stable with noisy measurement data.

Pseudodynamic systems approach based on a quadratic approximation of update equations for diffuse optical tomography.

We explore a pseudodynamic form of the quadratic parameter update equation for diffuse optical tomographic reconstruction from noisy data. A few explicit and implicit strategies for obtaining the parameter updates via a semianalytical integration of the pseudodynamic equations are proposed. Despite the ill-posedness of the inverse problem associated with diffuse optical tomography, adoption of the quadratic update scheme combined with the pseudotime integration appears not only to yield higher convergence, but also a muted sensitivity to the regularization parameters, which include the pseudotime step size for integration. These observations are validated through reconstructions with both numerically generated and experimentally acquired data.

Flux density calibration in diffuse optical tomographic systems.

The solution of the forward equation that models the transport of light through a highly scattering tissue material in diffuse optical tomography (DOT) using the finite element method gives flux density (Φ) at the nodal points of the mesh. The experimentally measured flux (Umeasured) on the boundary over a finite surface area in a DOT system has to be corrected to account for the system transfer functions (R) of various building blocks of the measurement system. We present two methods to compensate for the perturbations caused by R and estimate true flux density (Φ) from Umeasuredcal. In the first approach, the measurement data with a homogeneous phantom (Umeasuredhomo) is used to calibrate the measurement system. The second scheme estimates the homogeneous phantom measurement using only the measurement from a heterogeneous phantom, thereby eliminating the necessity of a homogeneous phantom. This is done by statistically averaging the data (Umeasuredhetero) and redistributing it to the corresponding detector positions. The experiments carried out on tissue mimicking phantom with single and multiple inhomogeneities, human hand, and a pork tissue phantom demonstrate the robustness of the approach.

Implementation of a phase array diffuse optical tomographic imager.

Diffuse optical tomography (DOT) using near-infrared (NIR) light is a promising tool for noninvasive imaging of deep tissue. This technique is capable of quantitative reconstructions of absorption coefficient inhomogeneities of tissue. The motivation for reconstructing the optical property variation is that it, and, in particular, the absorption coefficient variation, can be used to diagnose different metabolic and disease states of tissue. In DOT, like any other medical imaging modality, the aim is to produce a reconstruction with good spatial resolution and accuracy from noisy measurements. We study the performance of a phase array system for detection of optical inhomogeneities in tissue. The light transport through a tissue is diffusive in nature and can be modeled using diffusion equation if the optical parameters of the inhomogeneity are close to the optical properties of the background. The amplitude cancellation method that uses dual out-of-phase sources (phase array) can detect and locate small objects in turbid medium. The inverse problem is solved using model based iterative image reconstruction. Diffusion equation is solved using finite element method for providing the forward model for photon transport. The solution of the forward problem is used for computing the Jacobian and the simultaneous equation is solved using conjugate gradient search. The simulation studies have been carried out and the results show that a phase array system can resolve inhomogeneities with sizes of 5 mm when the absorption coefficient of the inhomogeneity is twice that of the background tissue. To validate this result, a prototype model for performing a dual-source system has been developed. Experiments are carried out by inserting an inhomogeneity of high optical absorption coefficient in an otherwise homogeneous phantom while keeping the scattering coefficient same. The high frequency (100 MHz) modulated dual out-of-phase laser source light is propagated through the phantom. The interference of these sources creates an amplitude null and a phase shift of 180 degrees along a plane between the two sources with a homogeneous object. A solid resin phantom with inhomogeneities simulating the tumor is used in our experiment. The amplitude and phase changes are found to be disturbed by the presence of the inhomogeneity in the object. The experimental data (amplitude and the phase measured at the detector) are used for reconstruction. The results show that the method is able to detect multiple inhomogeneities with sizes of 4 mm. The localization error for a 5 mm inhomogeneity is found to be approximately 1 mm.