1
|
Hirvi P, Kuutela T, Fang Q, Hannukainen A, Hyvönen N, Nissilä I. Effects of atlas-based anatomy on modelled light transport in the neonatal head. Phys Med Biol 2023; 68:135019. [PMID: 37167982 PMCID: PMC10460200 DOI: 10.1088/1361-6560/acd48c] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/08/2022] [Revised: 04/21/2023] [Accepted: 05/11/2023] [Indexed: 05/13/2023]
Abstract
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.
Collapse
Affiliation(s)
- Pauliina Hirvi
- Aalto University, Department of
Mathematics and Systems Analysis, PO Box 11100, FI-00076 AALTO,
Finland
| | - Topi Kuutela
- Aalto University, Department of
Mathematics and Systems Analysis, PO Box 11100, FI-00076 AALTO,
Finland
| | - Qianqian Fang
- Northeastern University, Department of
Bioengineering, 360 Huntington Ave, Boston, MA 02115, United States of
America
| | - Antti Hannukainen
- Aalto University, Department of
Mathematics and Systems Analysis, PO Box 11100, FI-00076 AALTO,
Finland
| | - Nuutti Hyvönen
- Aalto University, Department of
Mathematics and Systems Analysis, PO Box 11100, FI-00076 AALTO,
Finland
| | - Ilkka Nissilä
- Aalto University, Department of
Neuroscience and Biomedical Engineering, PO Box 12200, FI-00076 AALTO,
Finland
| |
Collapse
|
2
|
Mozumder M, Hauptmann A, Nissila I, Arridge SR, Tarvainen T. A Model-Based Iterative Learning Approach for Diffuse Optical Tomography. IEEE TRANSACTIONS ON MEDICAL IMAGING 2022; 41:1289-1299. [PMID: 34914584 DOI: 10.1109/tmi.2021.3136461] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Diffuse optical tomography (DOT) utilises near-infrared light for imaging spatially distributed optical parameters, typically the absorption and scattering coefficients. The image reconstruction problem of DOT is an ill-posed inverse problem, due to the non-linear light propagation in tissues and limited boundary measurements. The ill-posedness means that the image reconstruction is sensitive to measurement and modelling errors. The Bayesian approach for the inverse problem of DOT offers the possibility of incorporating prior information about the unknowns, rendering the problem less ill-posed. It also allows marginalisation of modelling errors utilising the so-called Bayesian approximation error method. A more recent trend in image reconstruction techniques is the use of deep learning, which has shown promising results in various applications from image processing to tomographic reconstructions. In this work, we study the non-linear DOT inverse problem of estimating the (absolute) absorption and scattering coefficients utilising a 'model-based' learning approach, essentially intertwining learned components with the model equations of DOT. The proposed approach was validated with 2D simulations and 3D experimental data. We demonstrated improved absorption and scattering estimates for targets with a mix of smooth and sharp image features, implying that the proposed approach could learn image features that are difficult to model using standard Gaussian priors. Furthermore, it was shown that the approach can be utilised in compensating for modelling errors due to coarse discretisation enabling computationally efficient solutions. Overall, the approach provided improved computation times compared to a standard Gauss-Newton iteration.
Collapse
|
3
|
Sahlstrom T, Pulkkinen A, Tick J, Leskinen J, Tarvainen T. Modeling of Errors Due to Uncertainties in Ultrasound Sensor Locations in Photoacoustic Tomography. IEEE TRANSACTIONS ON MEDICAL IMAGING 2020; 39:2140-2150. [PMID: 31940525 DOI: 10.1109/tmi.2020.2966297] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/10/2023]
Abstract
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.
Collapse
|
4
|
Tick J, Pulkkinen A, Tarvainen T. Modelling of errors due to speed of sound variations in photoacoustic tomography using a Bayesian framework. Biomed Phys Eng Express 2019; 6:015003. [PMID: 33438591 DOI: 10.1088/2057-1976/ab57d1] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
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.
Collapse
Affiliation(s)
- Jenni Tick
- Department of Applied Physics, University of Eastern Finland, PO Box 1627, 70211 Kuopio, Finland
| | | | | |
Collapse
|
5
|
Rimpiläinen V, Koulouri A, Lucka F, Kaipio JP, Wolters CH. Improved EEG source localization with Bayesian uncertainty modelling of unknown skull conductivity. Neuroimage 2018; 188:252-260. [PMID: 30529398 DOI: 10.1016/j.neuroimage.2018.11.058] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2018] [Accepted: 11/30/2018] [Indexed: 10/27/2022] Open
Abstract
Electroencephalography (EEG) source imaging is an ill-posed inverse problem that requires accurate conductivity modelling of the head tissues, especially the skull. Unfortunately, the conductivity values are difficult to determine in vivo. In this paper, we show that the exact knowledge of the skull conductivity is not always necessary when the Bayesian approximation error (BAE) approach is exploited. In BAE, we first postulate a probability distribution for the skull conductivity that describes our (lack of) knowledge on its value, and model the effects of this uncertainty on EEG recordings with the help of an additive error term in the observation model. Before the Bayesian inference, the likelihood is marginalized over this error term. Thus, in the inversion we estimate only our primary unknown, the source distribution. We quantified the improvements in the source localization when the proposed Bayesian modelling was used in the presence of different skull conductivity errors and levels of measurement noise. Based on the results, BAE was able to improve the source localization accuracy, particularly when the unknown (true) skull conductivity was much lower than the expected standard conductivity value. The source locations that gained the highest improvements were shallow and originally exhibited the largest localization errors. In our case study, the benefits of BAE became negligible when the signal-to-noise ratio dropped to 20 dB.
Collapse
Affiliation(s)
- Ville Rimpiläinen
- Department of Physics, University of Bath, Claverton Down, Bath, BA2 7AY, United Kingdom; Institute for Biomagnetism and Biosignalanalysis, University of Münster, Malmedyweg 15, D-48149, Münster, Germany.
| | - Alexandra Koulouri
- Laboratory of Mathematics, Tampere University of Technology, P. O. Box 692, 33101, Tampere, Finland; Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, 541 24, Greece
| | - Felix Lucka
- Computational Imaging, Centrum Wiskunde & Informatica, Science Park 123, 1098 XG, Amsterdam, the Netherlands; Centre for Medical Image Computing, University College London, Gower Street, London, WC1E 6BT, United Kingdom
| | - Jari P Kaipio
- Department of Mathematics, University of Auckland, Private Bag 92019, Auckland, 1142, New Zealand; Department of Applied Physics, University of Eastern Finland, FI-90211, Kuopio, Finland
| | - Carsten H Wolters
- Institute for Biomagnetism and Biosignalanalysis, University of Münster, Malmedyweg 15, D-48149, Münster, Germany
| |
Collapse
|
6
|
Abstract
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.
Collapse
|
7
|
Nissinen A, Kaipio JP, Vauhkonen M, Kolehmainen V. Contrast enhancement in EIT imaging of the brain. Physiol Meas 2015; 37:1-24. [PMID: 26642274 DOI: 10.1088/0967-3334/37/1/1] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
Abstract
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.
Collapse
Affiliation(s)
- A Nissinen
- Department of Applied Physics, University of Eastern Finland, PO Box 1627, FIN-70211 Kuopio, Finland
| | | | | | | |
Collapse
|
8
|
Mozumder M, Tarvainen T, Seppänen A, Nissilä I, Arridge SR, Kolehmainen V. Nonlinear approach to difference imaging in diffuse optical tomography. JOURNAL OF BIOMEDICAL OPTICS 2015; 20:105001. [PMID: 26440615 DOI: 10.1117/1.jbo.20.10.105001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/03/2015] [Accepted: 09/02/2015] [Indexed: 06/05/2023]
Abstract
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.
Collapse
Affiliation(s)
- Meghdoot Mozumder
- University of Eastern Finland, Department of Applied Physics, P.O. Box 1627, Kuopio 70211, Finland
| | - Tanja Tarvainen
- University of Eastern Finland, Department of Applied Physics, P.O. Box 1627, Kuopio 70211, FinlandbUniversity College London, Department of Computer Science, Gower Street, London WC1E 6BT, United Kingdom
| | - Aku Seppänen
- University of Eastern Finland, Department of Applied Physics, P.O. Box 1627, Kuopio 70211, Finland
| | - Ilkka Nissilä
- Aalto University School of Science, Department of Neuroscience and Biomedical Engineering, P.O. Box 12200, Aalto 00076, FinlanddHelsinki University Central Hospital, HUS Medical Imaging Center, BioMag Laboratory, P.O. Box 340, HUS 00029, Finland
| | - Simon R Arridge
- University College London, Department of Computer Science, Gower Street, London WC1E 6BT, United Kingdom
| | - Ville Kolehmainen
- University of Eastern Finland, Department of Applied Physics, P.O. Box 1627, Kuopio 70211, Finland
| |
Collapse
|
9
|
Koponen J, Huttunen T, Tarvainen T, Kaipio JP. Bayesian approximation error approach in full-wave ultrasound tomography. IEEE TRANSACTIONS ON ULTRASONICS, FERROELECTRICS, AND FREQUENCY CONTROL 2014; 61:1627-1637. [PMID: 25265173 DOI: 10.1109/tuffc.2014.006319] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
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.
Collapse
|
10
|
Mozumder M, Tarvainen T, Kaipio JP, Arridge SR, Kolehmainen V. Compensation of modeling errors due to unknown domain boundary in diffuse optical tomography. JOURNAL OF THE OPTICAL SOCIETY OF AMERICA. A, OPTICS, IMAGE SCIENCE, AND VISION 2014; 31:1847-1855. [PMID: 25121542 DOI: 10.1364/josaa.31.001847] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/03/2023]
Abstract
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.
Collapse
|
11
|
Pulkkinen A, Kolehmainen V, P. Kaipio J, T. Cox B, R. Arridge S, Tarvainen T. Approximate marginalization of unknown scattering in quantitative photoacoustic tomography. ACTA ACUST UNITED AC 2014. [DOI: 10.3934/ipi.2014.8.811] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
|
12
|
Tarvainen T, Pulkkinen A, Cox BT, Kaipio JP, Arridge SR. Bayesian Image Reconstruction in Quantitative Photoacoustic Tomography. IEEE TRANSACTIONS ON MEDICAL IMAGING 2013; 32:2287-98. [PMID: 24001987 DOI: 10.1109/tmi.2013.2280281] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/18/2023]
Abstract
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.
Collapse
|
13
|
Mozumder M, Tarvainen T, Arridge SR, Kaipio J, Kolehmainen V. Compensation of optode sensitivity and position errors in diffuse optical tomography using the approximation error approach. BIOMEDICAL OPTICS EXPRESS 2013; 4:2015-31. [PMID: 24156061 PMCID: PMC3799663 DOI: 10.1364/boe.4.002015] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2013] [Revised: 07/25/2013] [Accepted: 08/29/2013] [Indexed: 05/10/2023]
Abstract
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.
Collapse
Affiliation(s)
- Meghdoot Mozumder
- Department of Applied Physics, University of Eastern
Finland P.O. Box 1627, 70211 Kuopio,
Finland
| | - Tanja Tarvainen
- Department of Applied Physics, University of Eastern
Finland P.O. Box 1627, 70211 Kuopio,
Finland
- Department of Computer Science, University College London Gower Street, London WC1E 6BT,
UK
| | - Simon R. Arridge
- Department of Computer Science, University College London Gower Street, London WC1E 6BT,
UK
| | - Jari Kaipio
- Department of Applied Physics, University of Eastern
Finland P.O. Box 1627, 70211 Kuopio,
Finland
- Department of Mathematics, University of Auckland Private Bag 92019, Auckland Mail Centre, Auckland 1142,
New Zealand
| | - Ville Kolehmainen
- Department of Applied Physics, University of Eastern
Finland P.O. Box 1627, 70211 Kuopio,
Finland
| |
Collapse
|
14
|
Mozumder M, Tarvainen T, Arridge SR, Kaipio J, Kolehmainen V. Compensation of optode sensitivity and position errors in diffuse optical tomography using the approximation error approach. BIOMEDICAL OPTICS EXPRESS 2013; 4:2015-2031. [PMID: 24156061 DOI: 10.1364/biomed.2014.bm3a.76] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/02/2013] [Revised: 07/25/2013] [Accepted: 08/29/2013] [Indexed: 05/18/2023]
Abstract
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.
Collapse
Affiliation(s)
- Meghdoot Mozumder
- Department of Applied Physics, University of Eastern Finland P.O. Box 1627, 70211 Kuopio, Finland
| | | | | | | | | |
Collapse
|
15
|
Adler A, Lionheart WRB. Minimizing EIT image artefacts from mesh variability in finite element models. Physiol Meas 2011; 32:823-34. [DOI: 10.1088/0967-3334/32/7/s07] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
|
16
|
Nissinen A, Kolehmainen VP, Kaipio JP. Compensation of modelling errors due to unknown domain boundary in electrical impedance tomography. IEEE TRANSACTIONS ON MEDICAL IMAGING 2011; 30:231-242. [PMID: 20840893 DOI: 10.1109/tmi.2010.2073716] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
Electrical impedance tomography is a highly unstable problem with respect to measurement and modeling errors. This instability is especially severe when absolute imaging is considered. With clinical measurements, accurate knowledge about the body shape is usually not available, and therefore an approximate model domain has to be used in the computational model. It has earlier been shown that large reconstruction artefacts result if the geometry of the model domain is incorrect. In this paper, we adapt the so-called approximation error approach to compensate for the modeling errors caused by inaccurately known body shape. This approach has previously been shown to be applicable to a variety of modeling errors, such as coarse discretization in the numerical approximation of the forward model and domain truncation. We evaluate the approach with a simulated example of thorax imaging, and also with experimental data from a laboratory setting, with absolute imaging considered in both cases. We show that the related modeling errors can be efficiently compensated for by the approximation error approach. We also show that recovery from simultaneous discretization related errors is feasible, allowing the use of computationally efficient reduced order models.
Collapse
Affiliation(s)
- Antti Nissinen
- Department of Physics and Mathematics, University of Eastern Finland, FIN-70211 Kuopio, Finland
| | | | | |
Collapse
|
17
|
Li M, Zhang Y, Bai J. In Vivo Diffuse Optical Tomography and Fluorescence Molecular Tomography. JOURNAL OF HEALTHCARE ENGINEERING 2010. [DOI: 10.1260/2040-2295.1.3.477] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
|
18
|
Tarvainen T, Kolehmainen V, Kaipio JP, Arridge SR. Corrections to linear methods for diffuse optical tomography using approximation error modelling. BIOMEDICAL OPTICS EXPRESS 2010; 1:209-222. [PMID: 21258459 PMCID: PMC3005182 DOI: 10.1364/boe.1.000209] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/07/2010] [Revised: 07/09/2010] [Accepted: 07/09/2010] [Indexed: 05/25/2023]
Abstract
Linear reconstruction methods in diffuse optical tomography have been found to produce reasonable good images in cases in which the variation in optical properties within the medium is relatively small and a reference measurement with known background optical properties is available. In this paper we examine the correction of errors when using a first order Born approximation with an infinite space Green's function model as the basis for linear reconstruction in diffuse optical tomography, when real data is generated on a finite domain with possibly unknown background optical properties. We consider the relationship between conventional reference measurement correction and approximation error modelling in reconstruction. It is shown that, using the approximation error modelling, linear reconstruction method can be used to produce good quality images also in situations in which the background optical properties are not known and a reference is not available.
Collapse
Affiliation(s)
- Tanja Tarvainen
- Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 1627, 70211 Kuopio, Finland
- Department of Computer Science, University College London, Gower Street, London WC1E 6BT, UK
| | - Ville Kolehmainen
- Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 1627, 70211 Kuopio, Finland
| | - Jari P. Kaipio
- Department of Physics and Mathematics, University of Eastern Finland, P.O. Box 1627, 70211 Kuopio, Finland
- Department of Mathematics, University of Auckland, Private Bag 92019, Auckland Mail Centre, Auckland 1142, New Zealand
| | - Simon R. Arridge
- Department of Computer Science, University College London, Gower Street, London WC1E 6BT, UK
| |
Collapse
|