Computational and theoretical models in diffuse imaging

Topi Kuutela

Computational and theoretical models in diffuse imaging

Julkaisun otsikon käännös: Laskennallisia ja teoreettisia menetelmiä diffuusiin kuvantamiseen

Topi Kuutela

Tutkimustuotos: Doctoral Thesis › Collection of Articles

Abstrakti

Tässä työssä tutkitaan diffuusiin kuvantamiseen liittyvien parametrinestimointiongelmien ominaisuuksia. Sekä impedanssitomografia että diffuusi optinen tomografia ovat elliptisiin osittaisdifferentiaaliyhtälöihin liittyviä heikosti aseteltuja käänteisongelmia, joissa kappaleen sisäpuolisia fysikaalisia suureita pyritään määrittämään sen ulkopuolisilla mittauksilla. Työssä tarkastellut kuvantamismenetelmät ovat heikon asettelunsa johdosta erityisen herkkiä mallinnusvirheille. Tässä väitöskirjassa esitellään laskennallisia ja teoreettisia malleja, joiden avulla virhettä tutkittavien tomografiamenetelmien tuottamissa rekonstruktioissa voidaan vähentää. Impedanssitomografian logaritminen suora kuvaus on työkalu, jolla voidaan helpottaa parametrinestimointiongelman linearisointia. Tämän työn ensimmäisessä osassa todistetaan logaritmisen suoran kuvauksen Fréchet-derivoituvuus ja tarkastellaan derivaataan säännöllisyyttä. Fréchet-derivaatta osoittautuu yllättäen säännöllisemmäksi kuin itse logaritminen suora kuvaus. Työn toisen teoreettisen osan muodostavat laajennukset impedanssitomografian sarjareversioon. Sarjareversiolla voidaan johtaa korkeamman asteen suppenemisnopeuden numeerisia ratkaisumenetelmiä, joiden käyttö edellyttää ainoastaan suunnattujen derivaattojen määrittämistä, mikä on laskennallisesti helppoa impedanssitomografian suoralle kuvaukselle. Tässä työssä sarjareversio yleistetään sekä kappaleen sisäisen johtavuuden että kontakti-impedanssien samanaikaiseen ratkaisemiseen. Lisäksi molempien suureiden parametrisaatio yleistetään vapaamuotoiseksi. Yksi suurimmista virhelähteistä impedanssitomografiassa on elektrodien geometrinen paikkavirhe. Väitöskirjassa esitellään laskennallisesti yksinkertainen menetelmä elektrodien paikkavirheen huomioimiseksi rekonstruktiossa ja tutkitaan numeerisesti menetelmän toimivuutta. Menetelmä perustuu silotetun täydellisen elektrodimallin laajennukseen, jossa elektrodien kontakti-impedansseja ei oleteta vakioksi, vaan ne määritellään funktiona mitattavan kappaleen reunalla. Menetelmän toimivuus osoitetaan esittelemällä kokeellisiin mittauksiin pohjautuvia kaksiulotteisia rekonstruktioita ja lisäksi kolmiulotteisilla numeerisilla kokeilla sarjareversiotutkimuksen yhteydessä. Työn viimeisessä osassa tutkitaan taajuusalueen diffuusin optisen tomografian herkkyyttä anatomiselle vaihtelulle. Vaihtelun tutkimiseen käytetään 166 vastasyntyneen segmentoituja päämalleja, joissa mittaus mallinetaan kahdella tyypillisimmällä laskentamenetelmällä: diffuusioapproksimaatiolla ja Markovin ketju Monte Carlo -simulaatiolla. Lisäksi artikkelissa esitellään uusi menetelmä aivo-selkäydinnesteen jakamiseksi kahteen fysiologisesti perusteltuun tyyppiin, joista ensimmäinen esiintyy kallon ja aivojen välissä ja toinen aivojen uurteissa.

Julkaisun otsikon käännös	Laskennallisia ja teoreettisia menetelmiä diffuusiin kuvantamiseen
Alkuperäiskieli	Englanti
Pätevyys	Tohtorintutkinto
Myöntävä instituutio	Aalto-yliopisto
Valvoja/neuvonantaja	Hyvönen, Nuutti, Vastuuprofessori Hyvönen, Nuutti, Ohjaaja
Kustantaja	Aalto University
Painoksen ISBN	978-952-64-1144-6
Sähköinen ISBN	978-952-64-1145-3
Tila	Julkaistu - 2023
OKM-julkaisutyyppi	G5 Artikkeliväitöskirja

Tutkimusalat

käänteisongelmat
parametriestimointi
suora mallinnus
impedanssitomografia
diffuusi optinen tomografia
täydellinen elektrodimalli
mallinnusvirheet
sarjareversio

Pääsy asiakirjaan

http://urn.fi/URN:ISBN:978-952-64-1145-3

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@phdthesis{9f26fc9fa01143dca930c35918364b26,

title = "Computational and theoretical models in diffuse imaging",

abstract = "In this thesis, aspects of parameter estimation problems associated with diffuse imaging modalities are studied. Both considered modalities, electrical impedance tomography (EIT) and diffuse optical tomography (DOT), correspond to ill-posed inverse problems governed by elliptic partial differential equations, with the goal of reconstructing a material parameter field inside an examined body from measurements on the surface of the body. The ill-posedness of these problems is particularly evident in their sensitivity to modeling errors. This thesis studies computational and theoretical models with which some of the reconstruction artifacts can be reduced. The logarithmic forward map of EIT has been previously introduced to facilitate the use of linearization in the parameter estimation problem. The first theoretical contribution of this thesis is proving the Fr{\'e}chet differentiability of the logarithmic forward map, and establishing its regularity. Curiously the Fr{\'e}chet derivative is found to be more regular than the logarithmic forward map itself. The second theoretical contribution consists of extensions to the series reversion technique in EIT. Numerical methods with higher order convergence rates can be constructed via series reversion using only directional derivatives, which are cheap to compute for the forward map of EIT. In this thesis, the series reversion method is extended to simultaneously cover the domain conductivity and the electrode contact reconstructions and to also allow arbitrary parametrizations for the reconstructed quantities. The error in electrode locations is known to be one of the most significant error sources for EIT reconstruction problems. A computationally simple method to compensate for the electrode location error in the reconstruction process is presented and numerically evaluated in this thesis. The method is based on an extension to the smoothened complete electrode model in which the contact conductivity between the electrodes and the measured domain is not considered a constant but instead a function on the boundary. The viability of this method is demonstrated by two-dimensional reconstructions based on real-world measurements and by three-dimensional numerical experiments as a part of the study on the generalized series reversion. Finally, this thesis includes a careful evaluation of the effect of anatomical variation in frequency-domain DOT. The variation is studied numerically using 166 segmented neonatal head anatomies with the two commonly used computational models for DOT, the diffusion approximation and Markov chain Monte Carlo. Furthermore, a new segmentation method is presented to separate cerebrospinal fluid into two physiologically plausible types, one present in between the skull and the brain while the other found in the sulci of the brain.",

keywords = "inverse problem, parameter estimation problem, forward modeling, electrical impedance tomography, diffuse optical tomography, complete electrode model, modeling errors, series reversion, k{\"a}{\"a}nteisongelmat, parametriestimointi, suora mallinnus, impedanssitomografia, diffuusi optinen tomografia, t{\"a}ydellinen elektrodimalli, mallinnusvirheet, sarjareversio, inverse problem, parameter estimation problem, forward modeling, electrical impedance tomography, diffuse optical tomography, complete electrode model, modeling errors, series reversion",

author = "Topi Kuutela",

year = "2023",

language = "English",

isbn = "978-952-64-1144-6",

series = "Aalto University publication series DOCTORAL THESES",

publisher = "Aalto University",

number = "17",

address = "Finland",

school = "Aalto University",

}

TY - BOOK

T1 - Computational and theoretical models in diffuse imaging

AU - Kuutela, Topi

PY - 2023

Y1 - 2023

N2 - In this thesis, aspects of parameter estimation problems associated with diffuse imaging modalities are studied. Both considered modalities, electrical impedance tomography (EIT) and diffuse optical tomography (DOT), correspond to ill-posed inverse problems governed by elliptic partial differential equations, with the goal of reconstructing a material parameter field inside an examined body from measurements on the surface of the body. The ill-posedness of these problems is particularly evident in their sensitivity to modeling errors. This thesis studies computational and theoretical models with which some of the reconstruction artifacts can be reduced. The logarithmic forward map of EIT has been previously introduced to facilitate the use of linearization in the parameter estimation problem. The first theoretical contribution of this thesis is proving the Fréchet differentiability of the logarithmic forward map, and establishing its regularity. Curiously the Fréchet derivative is found to be more regular than the logarithmic forward map itself. The second theoretical contribution consists of extensions to the series reversion technique in EIT. Numerical methods with higher order convergence rates can be constructed via series reversion using only directional derivatives, which are cheap to compute for the forward map of EIT. In this thesis, the series reversion method is extended to simultaneously cover the domain conductivity and the electrode contact reconstructions and to also allow arbitrary parametrizations for the reconstructed quantities. The error in electrode locations is known to be one of the most significant error sources for EIT reconstruction problems. A computationally simple method to compensate for the electrode location error in the reconstruction process is presented and numerically evaluated in this thesis. The method is based on an extension to the smoothened complete electrode model in which the contact conductivity between the electrodes and the measured domain is not considered a constant but instead a function on the boundary. The viability of this method is demonstrated by two-dimensional reconstructions based on real-world measurements and by three-dimensional numerical experiments as a part of the study on the generalized series reversion. Finally, this thesis includes a careful evaluation of the effect of anatomical variation in frequency-domain DOT. The variation is studied numerically using 166 segmented neonatal head anatomies with the two commonly used computational models for DOT, the diffusion approximation and Markov chain Monte Carlo. Furthermore, a new segmentation method is presented to separate cerebrospinal fluid into two physiologically plausible types, one present in between the skull and the brain while the other found in the sulci of the brain.

AB - In this thesis, aspects of parameter estimation problems associated with diffuse imaging modalities are studied. Both considered modalities, electrical impedance tomography (EIT) and diffuse optical tomography (DOT), correspond to ill-posed inverse problems governed by elliptic partial differential equations, with the goal of reconstructing a material parameter field inside an examined body from measurements on the surface of the body. The ill-posedness of these problems is particularly evident in their sensitivity to modeling errors. This thesis studies computational and theoretical models with which some of the reconstruction artifacts can be reduced. The logarithmic forward map of EIT has been previously introduced to facilitate the use of linearization in the parameter estimation problem. The first theoretical contribution of this thesis is proving the Fréchet differentiability of the logarithmic forward map, and establishing its regularity. Curiously the Fréchet derivative is found to be more regular than the logarithmic forward map itself. The second theoretical contribution consists of extensions to the series reversion technique in EIT. Numerical methods with higher order convergence rates can be constructed via series reversion using only directional derivatives, which are cheap to compute for the forward map of EIT. In this thesis, the series reversion method is extended to simultaneously cover the domain conductivity and the electrode contact reconstructions and to also allow arbitrary parametrizations for the reconstructed quantities. The error in electrode locations is known to be one of the most significant error sources for EIT reconstruction problems. A computationally simple method to compensate for the electrode location error in the reconstruction process is presented and numerically evaluated in this thesis. The method is based on an extension to the smoothened complete electrode model in which the contact conductivity between the electrodes and the measured domain is not considered a constant but instead a function on the boundary. The viability of this method is demonstrated by two-dimensional reconstructions based on real-world measurements and by three-dimensional numerical experiments as a part of the study on the generalized series reversion. Finally, this thesis includes a careful evaluation of the effect of anatomical variation in frequency-domain DOT. The variation is studied numerically using 166 segmented neonatal head anatomies with the two commonly used computational models for DOT, the diffusion approximation and Markov chain Monte Carlo. Furthermore, a new segmentation method is presented to separate cerebrospinal fluid into two physiologically plausible types, one present in between the skull and the brain while the other found in the sulci of the brain.

KW - inverse problem

KW - parameter estimation problem

KW - forward modeling

KW - electrical impedance tomography

KW - diffuse optical tomography

KW - complete electrode model

KW - modeling errors

KW - series reversion

KW - käänteisongelmat

KW - parametriestimointi

KW - suora mallinnus

KW - impedanssitomografia

KW - diffuusi optinen tomografia

KW - täydellinen elektrodimalli

KW - mallinnusvirheet

KW - sarjareversio

KW - inverse problem

KW - parameter estimation problem

KW - forward modeling

KW - electrical impedance tomography

KW - diffuse optical tomography

KW - complete electrode model

KW - modeling errors

KW - series reversion

M3 - Doctoral Thesis

SN - 978-952-64-1144-6

T3 - Aalto University publication series DOCTORAL THESES

PB - Aalto University

ER -

Computational and theoretical models in diffuse imaging

Abstrakti

Tutkimusalat

Pääsy asiakirjaan

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