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

A Data Self-Calibration Method Based on High-Density Parallel Plate Diffuse Optical Tomography for Breast Cancer Imaging

When performing the diffuse optical tomography (DOT) of the breast, the mismatch between the forward model and the experimental conditions will significantly hinder the reconstruction accuracy. Therefore, the reference measurement is commonly used to calibrate the measured data before the reconstruction. However, it is complicated to customize corresponding reference phantoms based on the breast shape and background optical parameters of different subjects in clinical trials. Furthermore, although high-density (HD) DOT configuration has been proven to improve imaging quality, a large number of source-detector (SD) pairs also increase the difficulty of multi-channel correction. To enhance the applicability of the breast DOT, a data self-calibration method based on an HD parallel-plate DOT system is proposed in this paper to replace the conventional relative measurement on a reference phantom. The reference predicted data can be constructed directly from the measurement data with the support of the HD-DOT system, which has nearly a hundred sets of measurements at each SD distance. The proposed scheme has been validated by Monte Carlo (MC) simulation, breast-size phantom experiments, and clinical trials, exhibiting the feasibility in ensuring the quality of the DOT reconstruction while effectively reducing the complexity associated with relative measurements on reference phantoms.

Indocyanine Green-Camptothecin Co-Loaded Perfluorocarbon Double-Layer Nanocomposite: A Versatile Nanotheranostics for Photochemotherapy and FDOT Diagnosis of Breast Cancer

Breast cancer remains the most frequently diagnosed cancer and is the leading cause of neoplastic disease burden for females worldwide, suggesting that effective therapeutic and/or diagnostic strategies are still urgently needed. In this study, a type of indocyanine green (ICG) and camptothecin (CPT) co-loaded perfluorocarbon double-layer nanocomposite named ICPNC was developed for detection and photochemotherapy of breast cancer. The ICPNCs were designed to be surface modifiable for on-demand cell targeting and can serve as contrast agents for fluorescence diffuse optical tomography (FDOT). Upon near infrared (NIR) irradiation, the ICPNCs can generate a significantly increased production of singlet oxygen compared to free ICG, and offer a comparable cytotoxicity with reduced chemo-drug dosage. Based on the results of animal study, we further demonstrated that the ICPNCs ([ICG]/[CPT] = 40-/7.5-μM) in association with 1-min NIR irradiation (808 nm, 6 W/cm²) can provide an exceptional anticancer effect to the MDA-MB-231 tumor-bearing mice whereby the tumor size was significantly reduced by 80% with neither organ damage nor systemic toxicity after a 21-day treatment. Given a number of aforementioned merits, we anticipate that the developed ICPNC is a versatile theranostic nanoagent which is highly promising to be used in the clinic.

Reducing image artifact in diffuse optical tomography by iterative perturbation correction based on multiwavelength measurements

Ultrasound (US) guided diffuse optical tomography has demonstrated great potential for breast cancer diagnosis, treatment monitoring, and chemotherapy response prediction. Optical measurements of four different wavelengths are used to reconstruct unknown optical absorption maps, which are then used to calculate the hemoglobin concentration distribution of the US visible lesion. Reconstructed absorption maps are prone to image artifacts from outliers in measurement data from tissue heterogeneity, bad coupling between tissue and light guides, and motion by patient or operator. We propose an automated iterative perturbation correction algorithm to reduce image artifacts based on the structural similarity index (SSIM) of absorption maps of four optical wavelengths. The initial image is estimated from the truncated pseudoinverse solution. The SSIM was calculated for each wavelength to assess its similarity with other wavelengths. An absorption map is repeatedly reconstructed and projected back into measurement space to quantify projection error. Outlier measurements with highest projection errors are iteratively removed until all wavelength images are structurally similar with SSIM values greater than a threshold. Clinical data demonstrate statistically significant improvement in image artifact reduction.

Nonquadratic penalization improves near-infrared diffuse optical tomography

A new approach that can easily incorporate any generic penalty function into the diffuse optical tomographic image reconstruction is introduced to show the utility of nonquadratic penalty functions. The penalty functions that were used include quadratic (ℓ2), absolute (ℓ1), Cauchy, and Geman-McClure. The regularization parameter in each of these cases was obtained automatically by using the generalized cross-validation method. The reconstruction results were systematically compared with each other via utilization of quantitative metrics, such as relative error and Pearson correlation. The reconstruction results indicate that, while the quadratic penalty may be able to provide better separation between two closely spaced targets, its contrast recovery capability is limited, and the sparseness promoting penalties, such as ℓ1, Cauchy, and Geman-McClure have better utility in reconstructing high-contrast and complex-shaped targets, with the Geman-McClure penalty being the most optimal one.

Model-resolution based regularization improves near infrared diffuse optical tomography

Diffuse optical tomographic imaging is known to be an ill-posed problem, and a penalty/regularization term is used in image reconstruction (inverse problem) to overcome this limitation. Two schemes that are prevalent are spatially varying (exponential) and constant (standard) regularizations/penalties. A scheme that is also spatially varying but uses the model information is introduced based on the model-resolution matrix. This scheme, along with exponential and standard regularization schemes, is evaluated objectively based on model-resolution and data-resolution matrices. This objective analysis showed that resolution characteristics are better for spatially varying penalties compared to standard regularization; and among spatially varying regularization schemes, the model-resolution based regularization fares well in providing improved data-resolution and model-resolution characteristics. The verification of the same is achieved by performing numerical experiments in reconstructing 1% noisy data involving simple two- and three-dimensional imaging domains.

An adaptive regularization parameter choice strategy for multispectral bioluminescence tomography

PURPOSE

Bioluminescence tomography (BLT) provides an effective tool for monitoring physiological and pathological activities in vivo. However, the measured data in bioluminescence imaging are corrupted by noise. Therefore, regularization methods are commonly used to find a regularized solution. Nevertheless, for the quality of the reconstructed bioluminescent source obtained by regularization methods, the choice of the regularization parameters is crucial. To date, the selection of regularization parameters remains challenging. With regards to the above problems, the authors proposed a BLT reconstruction algorithm with an adaptive parameter choice rule.

METHODS

The proposed reconstruction algorithm uses a diffusion equation for modeling the bioluminescent photon transport. The diffusion equation is solved with a finite element method. Computed tomography (CT) images provide anatomical information regarding the geometry of the small animal and its internal organs. To reduce the ill-posedness of BLT, spectral information and the optimal permissible source region are employed. Then, the relationship between the unknown source distribution and multiview and multispectral boundary measurements is established based on the finite element method and the optimal permissible source region. Since the measured data are noisy, the BLT reconstruction is formulated as l(2) data fidelity and a general regularization term. When choosing the regularization parameters for BLT, an efficient model function approach is proposed, which does not require knowledge of the noise level. This approach only requests the computation of the residual and regularized solution norm. With this knowledge, we construct the model function to approximate the objective function, and the regularization parameter is updated iteratively.

RESULTS

First, the micro-CT based mouse phantom was used for simulation verification. Simulation experiments were used to illustrate why multispectral data were used rather than monochromatic data. Furthermore, the study conducted using an adaptive regularization parameter demonstrated our ability to accurately localize the bioluminescent source. With the adaptively estimated regularization parameter, the reconstructed center position of the source was (20.37, 31.05, 12.95) mm, and the distance to the real source was 0.63 mm. The results of the dual-source experiments further showed that our algorithm could localize the bioluminescent sources accurately. The authors then presented experimental evidence that the proposed algorithm exhibited its calculated efficiency over the heuristic method. The effectiveness of the new algorithm was also confirmed by comparing it with the L-curve method. Furthermore, various initial speculations regarding the regularization parameter were used to illustrate the convergence of our algorithm. Finally, in vivo mouse experiment further illustrates the effectiveness of the proposed algorithm.

CONCLUSIONS

Utilizing numerical, physical phantom and in vivo examples, we demonstrated that the bioluminescent sources could be reconstructed accurately with automatic regularization parameters. The proposed algorithm exhibited superior performance than both the heuristic regularization parameter choice method and L-curve method based on the computational speed and localization error.

Implementation of edge-preserving regularization for frequency-domain diffuse optical tomography

In this study, we first propose the use of edge-preserving regularization in optimizing an ill-conditioned problem in the reconstruction procedure for diffuse optical tomography to prevent unwanted edge smoothing, which usually degrades the attributes of images for distinguishing tumors from background tissues when using Tikhonov regularization. In the edge-preserving regularization method presented here, a potential function with edge-preserving properties is introduced as a regularized term in an objective function. With the minimization of this proposed objective function, an iterative method to solve this optimization problem is presented in which half-quadratic regularization is introduced to simplify the minimization task. Both numerical and experimental data are employed to justify the proposed technique. The reconstruction results indicate that edge-preserving regularization provides a superior performance over Tikhonov regularization.

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.

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

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

Multistage inversion algorithm for biological tissue imaging

A new inversion method for diffuse optical tomography is proposed. This is a multistage algorithm, that uses a signal subspace-based method to simplify the inverse problem and proposes a guided iterative inversion process to improve the imaging. First, subspace-based analysis is used to determine the voxels that definitely belong to the background and exclude them from further consideration. Then, the pseudo-inverse technique is applied for reconstruction. In the final stage, the reconstruction is improved iteratively by finding and excluding more voxels belonging to background. The method reduces the ill-posedness of the image reconstruction problem iteratively such that good imaging results are obtained for multiple heterogeneities having complicated geometries even in the presence of 3% additive white noise.

Ultimate spatial resolution with Diffuse Optical Tomography

We evaluate the ultimate transverse spatial resolution that can be expected in Diffuse Optical Tomography, in the configuration of projection imaging. We show how such a performance can be approached using time-resolved measurements and reasonable assumptions, in the context of a linearized diffusion model.