Corrections to linear methods for diffuse optical tomography using approximation error modelling

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.

High Resolution, Deep Imaging Using Confocal Time-of-Flight Diffuse Optical Tomography

Light scattering by tissue severely limits how deep beneath the surface one can image, and the spatial resolution one can obtain from these images. Diffuse optical tomography (DOT) is one of the most powerful techniques for imaging deep within tissue - well beyond the conventional  ∼ 10-15 mean scattering lengths tolerated by ballistic imaging techniques such as confocal and two-photon microscopy. Unfortunately, existing DOT systems are limited, achieving only centimeter-scale resolution. Furthermore, they suffer from slow acquisition times and slow reconstruction speeds making real-time imaging infeasible. We show that time-of-flight diffuse optical tomography (ToF-DOT) and its confocal variant (CToF-DOT), by exploiting the photon travel time information, allow us to achieve millimeter spatial resolution in the highly scattered diffusion regime ( mean free paths). In addition, we demonstrate two additional innovations: focusing on confocal measurements, and multiplexing the illumination sources allow us to significantly reduce the measurement acquisition time. Finally, we rely on a novel convolutional approximation that allows us to develop a fast reconstruction algorithm, achieving a 100× speedup in reconstruction time compared to traditional DOT reconstruction techniques. Together, we believe that these technical advances serve as the first step towards real-time, millimeter resolution, deep tissue imaging using DOT.

Modelling of errors due to speed of sound variations in photoacoustic tomography using a Bayesian framework

Inverse problem of estimating initial pressure in photoacoustic tomography is ill-posed and thus sensitive to errors in modelling and measurements. In practical experiments, accurate knowledge of the speed of sound of the imaged target is commonly not available, and therefore an approximate speed of sound is used in the computational model. This can result in errors in the solution of the inverse problem that can appear as artefacts in the reconstructed images. In this paper, the inverse problem of photoacoustic tomography is approached in a Bayesian framework. Errors due to uncertainties in the speed of sound are modelled using Bayesian approximation error modelling. Estimation of the initial pressure distribution together with information on the reliability of these estimates are considered. The approach was studied using numerical simulations. The results show that uncertainties in the speed of sound can cause significant errors in the solution of the inverse problem. However, modelling of these uncertainties improves the accuracy of the solution.

Image Reconstruction with Reliability Assessment in Quantitative Photoacoustic Tomography

Quantitative photoacoustic tomography is a novel imaging method which aims to reconstruct optical parameters of an imaged target based on initial pressure distribution, which can be obtained from ultrasound measurements. In this paper, a method for reconstructing the optical parameters in a Bayesian framework is presented. In addition, evaluating the credibility of the estimates is studied. Furthermore, a Bayesian approximation error method is utilized to compensate the modeling errors caused by coarse discretization of the forward model. The reconstruction method and the reliability of the credibility estimates are investigated with two-dimensional numerical simulations. The results suggest that the Bayesian approach can be used to obtain accurate estimates of the optical parameters and the credibility estimates of these parameters. Furthermore, the Bayesian approximation error method can be used to compensate for the modeling errors caused by a coarse discretization, which can be used to reduce the computational costs of the reconstruction procedure. In addition, taking the modeling errors into account can increase the reliability of the credibility estimates.

Contrast enhancement in EIT imaging of the brain

We consider electrical impedance tomography (EIT) imaging of the brain. The brain is surrounded by the poorly conducting skull which has low conductivity compared to the brain. The skull layer causes a partial shielding effect which leads to weak sensitivity for the imaging of the brain tissue. In this paper we propose an approach based on the Bayesian approximation error approach, to enhance the contrast in brain imaging. With this approach, both the (uninteresting) geometry and the conductivity of the skull are embedded in the approximation error statistics, which leads to a computationally efficient algorithm that is able to detect features such as internal haemorrhage with significantly increased sensitivity and specificity. We evaluate the approach with simulations and phantom data.

Nonlinear approach to difference imaging in diffuse optical tomography

Difference imaging aims at recovery of the change in the optical properties of a body based on measurements before and after the change. Conventionally, the image reconstruction is based on using difference of the measurements and a linear approximation of the observation model. One of the main benefits of the linearized difference reconstruction is that the approach has a good tolerance to modeling errors, which cancel out partially in the subtraction of the measurements. However, a drawback of the approach is that the difference images are usually only qualitative in nature and their spatial resolution can be weak because they rely on the global linearization of the nonlinear observation model. To overcome the limitations of the linear approach, we investigate a nonlinear approach for difference imaging where the images of the optical parameters before and after the change are reconstructed simultaneously based on the two datasets. We tested the feasibility of the method with simulations and experimental data from a phantom and studied how the approach tolerates modeling errors like domain truncation, optode coupling errors, and domain shape errors.

Bayesian approximation error approach in full-wave ultrasound tomography

In ultrasound tomography, the spatial distribution of the speed of sound in a region of interest is reconstructed based on transient measurements made around the object. The computation of the forward problem (the full-wave solution) within the object is a computationally intensive task and can often be prohibitive for practical purposes. The purpose of this paper is to investigate the feasibility of using approximate forward solvers and the partial recovery from the related errors by employing the Bayesian approximation error approach. In addition to discretization error, we also investigate whether the approach can be used to reduce the reconstruction errors that are due to the adoption of approximate absorbing boundary models. We carry out two numerical studies in which the objective is to reduce the computational times to around 3% of the time that would be required by a numerically accurate forward solver. The results show that the Bayesian approximation error approach improves the reconstructions.

Compensation of modeling errors due to unknown domain boundary in diffuse optical tomography

Diffuse optical tomography is a highly unstable problem with respect to modeling and measurement errors. During clinical measurements, the body shape is not always known, and an approximate model domain has to be employed. The use of an incorrect model domain can, however, lead to significant artifacts in the reconstructed images. Recently, the Bayesian approximation error theory has been proposed to handle model-based errors. In this work, the feasibility of the Bayesian approximation error approach to compensate for modeling errors due to unknown body shape is investigated. The approach is tested with simulations. The results show that the Bayesian approximation error method can be used to reduce artifacts in reconstructed images due to unknown domain shape.

Bayesian Image Reconstruction in Quantitative Photoacoustic Tomography

Quantitative photoacoustic tomography is an emerging imaging technique aimed at estimating chromophore concentrations inside tissues from photoacoustic images, which are formed by combining optical information and ultrasonic propagation. This is a hybrid imaging problem in which the solution of one inverse problem acts as the data for another ill-posed inverse problem. In the optical reconstruction of quantitative photoacoustic tomography, the data is obtained as a solution of an acoustic inverse initial value problem. Thus, both the data and the noise are affected by the method applied to solve the acoustic inverse problem. In this paper, the noise of optical data is modelled as Gaussian distributed with mean and covariance approximated by solving several acoustic inverse initial value problems using acoustic noise samples as data. Furthermore, Bayesian approximation error modelling is applied to compensate for the modelling errors in the optical data caused by the acoustic solver. The results show that modelling of the noise statistics and the approximation errors can improve the optical reconstructions.

Compensation of optode sensitivity and position errors in diffuse optical tomography using the approximation error approach

Diffuse optical tomography is highly sensitive to measurement and modeling errors. Errors in the source and detector coupling and positions can cause significant artifacts in the reconstructed images. Recently the approximation error theory has been proposed to handle modeling errors. In this article, we investigate the feasibility of the approximation error approach to compensate for modeling errors due to inaccurately known optode locations and coupling coefficients. The approach is evaluated with simulations. The results show that the approximation error method can be used to recover from artifacts in reconstructed images due to optode coupling and position errors.

Parametric estimation of 3D tubular structures for diffuse optical tomography

We explore the use of diffuse optical tomography (DOT) for the recovery of 3D tubular shapes representing vascular structures in breast tissue. Using a parametric level set method (PaLS) our method incorporates the connectedness of vascular structures in breast tissue to reconstruct shape and absorption values from severely limited data sets. The approach is based on a decomposition of the unknown structure into a series of two dimensional slices. Using a simplified physical model that ignores 3D effects of the complete structure, we develop a novel inter-slice regularization strategy to obtain global regularity. We report on simulated and experimental reconstructions using realistic optical contrasts where our method provides a more accurate estimate compared to an unregularized approach and a pixel based reconstruction.

Compensation of optode sensitivity and position errors in diffuse optical tomography using the approximation error approach

Diffuse optical tomography is highly sensitive to measurement and modeling errors. Errors in the source and detector coupling and positions can cause significant artifacts in the reconstructed images. Recently the approximation error theory has been proposed to handle modeling errors. In this article, we investigate the feasibility of the approximation error approach to compensate for modeling errors due to inaccurately known optode locations and coupling coefficients. The approach is evaluated with simulations. The results show that the approximation error method can be used to recover from artifacts in reconstructed images due to optode coupling and position errors.

Influence of absorption and scattering on the quantification of fluorescence diffuse optical tomography using normalized data

Reconstruction algorithms for imaging fluorescence in near infrared ranges usually normalize fluorescence light with respect to excitation light. Using this approach, we investigated the influence of absorption and scattering heterogeneities on quantification accuracy when assuming a homogeneous model and explored possible reconstruction improvements by using a heterogeneous model. To do so, we created several computer-simulated phantoms: a homogeneous slab phantom (P1), slab phantoms including a region with a two- to six-fold increase in scattering (P2) and in absorption (P3), and an atlas-based mouse phantom that modeled different liver and lung scattering (P4). For P1, reconstruction with the wrong optical properties yielded quantification errors that increased almost linearly with the scattering coefficient while they were mostly negligible regarding the absorption coefficient. This observation agreed with the theoretical results. Taking the quantification of a homogeneous phantom as a reference, relative quantification errors obtained when wrongly assuming homogeneous media were in the range +41 to +94% (P2), 0.1 to -7% (P3), and -39 to +44% (P4). Using a heterogeneous model, the overall error ranged from -7 to 7%. In conclusion, this work demonstrates that assuming homogeneous media leads to noticeable quantification errors that can be improved by adopting heterogeneous models.

Methods in diffuse optical imaging

We describe some modelling and reconstruction methods for optical imaging in the macroscopic and mesoscopic regimes. Beginning with the basic model of radiative transport, we describe the diffusion approximation and its extensions. Some linear and nonlinear problems in diffuse optical imaging are outlined, together with some indications of current trends and future directions.