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

Effects of atlas-based anatomy on modelled light transport in the neonatal head

Objective.Diffuse optical tomography (DOT) provides a relatively convenient method for imaging haemodynamic changes related to neuronal activity on the cerebral cortex. Due to practical challenges in obtaining anatomical images of neonates, an anatomical framework is often created from an age-appropriate atlas model, which is individualized to the subject based on measurements of the head geometry. This work studies the approximation error arising from using an atlas instead of the neonate's own anatomical model.Approach.We consider numerical simulations of frequency-domain (FD) DOT using two approaches, Monte Carlo simulations and diffusion approximation via finite element method, and observe the variation in (1) the logarithm of amplitude and phase shift measurements, and (2) the corresponding inner head sensitivities (Jacobians), due to varying segmented anatomy. Varying segmentations are sampled by registering 165 atlas models from a neonatal database to the head geometry of one individual selected as the reference model. Prior to the registration, we refine the segmentation of the cerebrospinal fluid (CSF) by separating the CSF into two physiologically plausible layers.Main results.In absolute measurements, a considerable change in the grey matter or extracerebral tissue absorption coefficient was found detectable over the anatomical variation. In difference measurements, a small local 10%-increase in brain absorption was clearly detectable in the simulated measurements over the approximation error in the Jacobians, despite the wide range of brain maturation among the registered models.Significance.Individual-level atlas models could potentially be selected within several weeks in gestational age in DOT difference imaging, if an exactly age-appropriate atlas is not available. The approximation error method could potentially be implemented to improve the accuracy of atlas-based imaging. The presented CSF segmentation algorithm could be useful also in other model-based imaging modalities. The computation of FD Jacobians is now available in the widely-used Monte Carlo eXtreme software.

Modeling of Errors Due to Uncertainties in Ultrasound Sensor Locations in Photoacoustic Tomography

Photoacoustic tomography is an imaging modality based on the photoacoustic effect caused by the absorption of an externally introduced light pulse. In the inverse problem of photoacoustic tomography, the initial pressure generated through the photoacoustic effect is estimated from a measured photoacoustic time-series utilizing a forward model for ultrasound propagation. Due to the ill-posedness of the inverse problem, errors in the forward model or measurements can result in significant errors in the solution of the inverse problem. In this work, we study modeling of errors caused by uncertainties in ultrasound sensor locations in photoacoustic tomography using a Bayesian framework. The approach is evaluated with simulated and experimental data. The results indicate that the inverse problem of photoacoustic tomography is sensitive even to small uncertainties in sensor locations. Furthermore, these uncertainties can lead to significant errors in the estimates and reduction of the quality of the photoacoustic images. In this work, we show that the errors due to uncertainties in ultrasound sensor locations can be modeled and compensated using Bayesian approximation error modeling.

Time-domain diffuse optical tomography utilizing truncated Fourier series approximation

Diffuse optical tomography (DOT) uses near infrared light for in vivo imaging of spatially varying optical parameters in biological tissues. It is known that time-resolved measurements provide the richest information on soft tissues, among other measurement types in DOT such as steady-state and intensity-modulated measurements. Therefore, several integral-transform-based moments of the time-resolved DOT measurements have been considered to estimate spatially distributed optical parameters. However, the use of such moments can result in low-contrast images and cross-talks between the reconstructed optical parameters, limiting their accuracy. In this work, we propose to utilize a truncated Fourier series approximation in time-resolved DOT. Using this approximation, we obtained optical parameter estimates with accuracy comparable to using whole time-resolved data that uses low computational time and resources. The truncated Fourier series approximation based estimates also displayed good contrast and minimal parameter cross-talk, and the estimates further improved in accuracy when multiple Fourier frequencies were used.

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.

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.

An Automated Preprocessing Method for Diffuse Optical Tomography to Improve Breast Cancer Diagnosis

The ultrasound-guided diffuse optical tomography is a noninvasive imaging technique for breast cancer diagnosis and treatment monitoring. The technique uses a handheld probe capable of providing measurements of multiple wavelengths in a few seconds. These measurements are used to estimate optical absorptions of lesions and calculate the total hemoglobin concentration. Any measurement errors caused by low signal to noise ratio data and/or movements during data acquisition would reduce the accuracy of reconstructed total hemoglobin concentration. In this article, we introduce an automated preprocessing method that combines data collected from multiple sets of lesion measurements of 4 optical wavelengths to detect and correct outliers in the perturbation. Two new measures of correlation between each pair of wavelength measurements and a wavelength consistency index of all reconstructed absorption maps are introduced. For phantom and patients' data without evidence of measurement errors, the correlation coefficient between each pair of wavelength measurements was above 0.6. However, for patients with measurement errors, the correlation coefficient was much lower. After applying the correction method to 18 patients' data with measurement errors, the correlation has improved and the wavelength consistency index is in the same range as the cases without wavelength-dependent measurement errors. The results show an improvement in classification of malignant and benign lesions.

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.

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.