Segmentation-Guided MRS Analysis of Brain Tumor Patients · 2017. 2. 5. · Faculty of Medicine...

Faculty of MedicineBiomedical Engineering

Master of Science Thesis

Segmentation-Guided MRS Analysis of BrainTumor Patients

by

Martin Pletscher

of Schleitheim SH

SupervisorsMSc Nuno Pedrosa de Barros

MSc Raphael Meier

InstitutionsInstitute for Surgical Technology & Biomechanics, University of Bern

Institute of Diagnostic and Interventional Neuroradiology, Inselspital, BernUniversity Hospital, University of Bern

ExaminersProf. Dr. Mauricio Reyes

PD Dr. Johannes Slotboom

Bern, December 2016

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Abstract

Magnetic resonance imaging (MRI) is considered the method of choice for glioblas-toma multiforme diagnosis and follow-up. MRI provides structural information andplays a crucial role in progression monitoring, treatment planning, and analysis ofbrain tumors. Two-dimensional measurement of tumor diameters is considered thegold standard for neuro-oncologic therapy response assessment as of today. In recentyears magnetic resonance spectroscopy (MRS) is used increasingly to gain additionalinformation on a metabolic level to improve tumor diagnosis. The additional informa-tion comes at the cost of a considerable amount of experience needed by clinicians totranslate spectral information into histopathological tissue information. Therefore, theaim of this work was to investigate a tissue segmentation method to help facilitate theuse of MRS in neuro-oncologic glioblastoma assessment by automating the translationprocess.

The 22 pre-operative data sets from patients with histologically confirmed glioblas-toma multiforme contained four MRI sequences (T1, T2, T1c, and FLAIR) and 1HMRSI scan data (2D-PRESS, CHESS, TE=135ms, TR=1500ms) acquired at a nativeresolution of 12x12 and interpolated to 32x32 voxels. The data sets were acquired on1.5T Siemens scanners (Area, Avanto). The measurements were performed conformingto local and national ethical regulations: all patients gave their informed consent touse the data for scientific purposes.

In the first step of the proposed method, 17 randomly selected data sets werepre-processed with jMRUI’s Spectrim plugin (residual water removal HLSVD, quality-filtering, frequency-shift correction, and auto-phasing). After QUEST quantificationa feature set of metabolite-ratios Cho/Cr, NAA/Cho, NAA/Cr, (Lip1.3+Lac)/Cr,(Lip1.3+Lac)/NAA, (Lip1.3+Lac)/Cho was extracted from the 17 data sets. Thefeature set was then clustered by the x-means algorithm. The clustering revealed ninecharacteristic sources (Necrosis 1, Necrosis 2, Necrosis + Active Tumor, Active Tumor,Active Tumor + Infiltration, Infiltration, Normal WM1, Normal WM2, and NormalGM) which were labeled and ordered by an experienced spectroscopist. In the secondstep, the nine sources were used to segment the remaining five test data sets whichwere excluded from the clustering. The result of the segmentation was visualized as amap with colors ranging from red (malignant) to blue (healthy) for each type of tissuefound. Additionally, a visual and statistical comparison to a structural segmentationof the same data sets, generated by the Brain Tumor Image Analysis (BraTumIA)software, was performed.

The resulting segmentation maps show a good visual resemblance of the structuralsegmentation. A quantitative analysis with the Dice similarity coefficient yielded amean spatial overlap of 0.62 ± 0.29 for the malignant regions and 0.71 ± 0.20 forhealthy regions, both areas excluding the Infiltration and Edema classes. Only lowcorrespondence of 0.22± 0.14 was found between Infiltration and Edema.

We conclude that the proposed method has the potential to enhance the clinical useof MRS in neuro-oncologic glioblastoma assessment. It facilitates and largely automa-tizes the translation of spectral information into histopathological tissue information.In future research, the method could be applied to other types of brain tumors to gaina better understanding of the differences between those.

Acknowledgements

First and foremost, I would like to thank Nuno Pedrosa de Barros. With his help, I wasable to enter the field of MRS research. He was always available to answer my questionsand comment on my progress. It was a very exciting and challenging time, and I was giventhe opportunity to learn and research at the edge of human knowledge. Also, I would liketo thank Nuno for providing me with the opportunity to build a phantom and do real MRSacquisitions and tests with it. I would also like to thank PD Dr. Johannes Slotboom forhis strong support, trust and guidance. Moreover, it was always a pleasure sitting togetherwith Hans and Nuno and discussing new results or analyze parts of the pipeline. I alsowould like to thank Hans for providing the patient data sets that made this work possibleand for his support with deep experience in MRS from which this work profited greatly.

Secondly, I would like to thank Raphael Meier for his helpful feedback and the inspiringideas for this project. Also, I would like to thank him in particular for providing theBraTumIA segmentation of the patient data sets. I would also like to thank Prof. Dr.Mauricio Reyes for enabling this project, his valuable inputs, his strong support, and thetrust I always felt.

A special thanks goes to the Support Center for Advanced Neuroimaging (SCAN). Itwas a pleasure to be at the SCAN and meeting the inspiring people working in this group.We had so many interesting discussion during lunch. Thank you all.

Finally, a warm thanks goes to my significant other Rahel Ryser for her unwaveringsupport and patience during this project.

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Ich erkläre hiermit, dass ich diese Arbeit selbständig verfasst und keine anderen als dieangegebenen Hilfsmittel benutzt habe. Alle Stellen, die wörtlich oder sinngemäss aus Quellenentnommen wurden, habe ich als solche kenntlich gemacht. Mir ist bekannt, dass andernfallsder Senat gemäss dem Gesetz über die Universität zum Entzug des auf Grund dieser Arbeitverliehenen Titels berechtigt ist.

Bern, December 6th 2016

Martin Pletscher

Contents

Contents ix

List of Figures xi

List of Tables xii

1 Introduction 11.1 Medical perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1.1 Diagnosis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Technical perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.3 Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.4 Related work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81.5 Aim & structure of the thesis . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Magnetic resonance spectroscopy 112.1 Nuclear magnetic resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2 Shimming . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.3 Chemical shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.4 Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.4.1 Spin echo . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.4.2 PRESS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4.3 STEAM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.5 Chemical shift imaging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.6 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

3 Phantom 173.1 Materials & methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.1.1 Scanning protocols . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4 Clustering 214.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4.1.1 Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

4.2.1 Pre-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224.2.2 Quantification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 244.2.3 Selection profile correction . . . . . . . . . . . . . . . . . . . . . . . . 244.2.4 Feature extraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

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x CONTENTS

4.2.5 X-means clustering . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264.2.6 Ordering and labeling . . . . . . . . . . . . . . . . . . . . . . . . . . 274.2.7 Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5 Segmentation 355.1 Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

5.2.1 Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355.2.2 Segmentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365.2.3 BraTumIA segmentation pre-processing . . . . . . . . . . . . . . . . 365.2.4 Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

6 Discussion and Conclusions 436.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 436.2 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

7 Outlook 45

Bibliography 47

List of Figures

1.1 BraTumIA showcase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 RANO measurement visualization . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 In vivo spectrum of a healthy human brain . . . . . . . . . . . . . . . . . . . . 41.4 Spectroscopy showcase . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2.1 B0 field strength and magnetic quantum numbers . . . . . . . . . . . . . . . . . 122.2 Evolution of macro magnetization in magnetic resonance spectroscopy (MRS)

one puls sequence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3 Pulse and gradient sequences for PRESS . . . . . . . . . . . . . . . . . . . . . . 142.4 Pulse and gradient sequences for STEAM . . . . . . . . . . . . . . . . . . . . . 152.5 Pulse and gradient sequences for a basic chemical shift imaging sequence . . . . 152.6 k-space and Fourier reconstructed CSI spectra grid . . . . . . . . . . . . . . . . 16

3.1 Cube model and photo for comparison . . . . . . . . . . . . . . . . . . . . . . . 183.2 Metabolite maps of different native scan resolutions . . . . . . . . . . . . . . . 193.3 Susceptibility-weighted Image showing field inhomogeneity . . . . . . . . . . . . 20

4.1 Method pipeline diagram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234.2 Selection profile correction in phantom acquisition . . . . . . . . . . . . . . . . 254.3 X-means clustering step by step . . . . . . . . . . . . . . . . . . . . . . . . . . . 274.4 Phantom validation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.5 Feature evaluation statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.6 Quantification visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.7 Ordered source spectra found by clustering training data . . . . . . . . . . . . . 33

5.1 Comparison between BraTumIA segmentation and MRSI segmentation for thebest test case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

5.2 Comparison of the test data sets and the associated BraTumIA segmentation. . 385.3 Combined contingency matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385.4 Comparison between BraTumIA segmentation and MRSI segmentation with DSC 40

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List of Tables

3.1 Metabolite solutions for the cube phantom . . . . . . . . . . . . . . . . . . . . 173.2 Resolutions of test scans and recorded acquisition time . . . . . . . . . . . . . . 20

4.1 Feature set composition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 254.2 Parameters for the x-means algorithm . . . . . . . . . . . . . . . . . . . . . . . 284.3 LOOCV statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

5.1 DSC for BraTumIA and MRSI class group correspondence . . . . . . . . . . . . 39

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Abbreviations

AIC Akaike Information Criterion

ANN Artificial Neural Network

ATP Adenosine Triphosphate

BIC Bayesian Information Criterion

BraTumIA Brain Tumor Image Analysis

CCA Canonical Correlation Analysis

CSF Cerebrospinal Fluid

CSI Chemical Shift Imaging

CT Computed Tomography

DFT Discreet Fourier Transform

DNA Deoxyribonucleic Acid

DSC Dice Similarity Coefficient

FFT Fast Fourier Transform

FID Free Induction Decay

fMRI functional MRI

GBM Glioblastoma Multiforme

GM Gray Matter

LOOCV Leave-one-out Cross-validation

MRI Magnetic Resonance Imaging

MRS Magnetic Resonance Spectroscopy

MRSI Magnetic Resonance Spectroscopy Imaging

NAA N-acetylaspartate

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xiv ABBREVIATIONS

NIfTI Neuroimaging Informatics Technology Initiative

NMR Nuclear Magnetic Resonance

PEPSI Proton Echo-Planar Spectroscopic Imaging

PRESS Point RESolved Spectroscopy

RANO Response Assessment in Neuro-Oncology Criteria

RF Radio Frequency Oscillating Magnetic Field

SNR Signal-to-Noise Ratio

SPICE SPectroscopic Imaging by exploiting spatiospectral CorrElation

STEAM STimulated Echo Acquisition Mode

SVM Support Vector Machine

SVS Single Voxel Spectroscopy

SWI Susceptibility-Weighted Imaging

VOI Volume of Interest

WHO World Health Organization

WM White Matter

Chapter 1

Introduction

This first chapter introduces the reader to the topics: brain tumor history, tumor mechanics,diagnosis, and treatment. In a second part, it will state the hypothesis of this work andthe related work that was performed by other researchers. The purpose of this chapter isto explain the motivation of the work and its aim.

1.1 Medical perspective

According to the American Cancer Society [27, 28, 29], the word cancer was introducedby the Greek physician Hippocrates around 400 BC by the terms carcinos and carcinoma.These terms describe non-ulcer forming and ulcer forming tumors. In Greek, these terms re-fer to a crab. It is believed that Hippocrates referred to the finger like spreading projectionsof a tumor that look like a crab. Around 50 BC, the Roman physician Celsus translatedit finally into the Latin term cancer. The next era of advancement in cancer knowledgearrived in the 18th century when famous Scottish surgeon John Hunter suggested removingcancers surgically. He defined a tumor as surgically removable if it had not invaded nearbytissues. In the 19th century, the scientific oncology was born with the help of the modernmicroscope. It allowed a precise analysis and diagnosis of tissues removed in surgical proce-dures. These new analysis methods led to many speculative theories about cancer causes.However, only in the early 20th century, Katsusaburo Yamagiwa and Koichi Ichikawa atTokyo University [67], were able to induce cancer artificially to animals by applying coaltar to rabbit skin. However, only after the discovery of the exact chemical structure of de-oxyribonucleic acid (DNA) by the middle of the 20th century [56], it became clear that alldiscovered carcinogenic chemicals and radiation caused DNA damage. Therefore it becameaccepted knowledge that DNA damage was the main cause of cancer.

Over centuries, the only cancer treatment available was surgical removal of tumors.Only after the discovery of X-rays, radiation therapy became available and was used totreat tumors. Chemotherapy was originally discovered during World War II. The frequentlyused war agent mustard gas proved to be deadly to enemy soldiers as well as efficient indestroying cancer cells. During the development of even deadlier war agents, the US Armydiscovered that a compound called nitrogen mustard worked well against lymph node cancercalled lymphoma. This discovery led to the development of a long series of similar but moreefficient compounds to treat cancer.

These three methods are still used today as the main treatment methods. Nevertheless,they have been improved greatly over the years to be more specific and do less damage tohealthy tissue surrounding tumors.

1

2 CHAPTER 1. INTRODUCTION

The world health organization (WHO) categorizes brain tumors into four grades [34].G1: well differentiated (low grade), G2: Moderately differentiated (intermediate grade),G3: Poorly differentiated (high grade), G4: Undifferentiated (high grade), and GX: Gradecannot be assessed (undetermined grade).

Tumors are abnormal growth of tissue due to mutated cells that can have a higherproliferation rate than surrounding tissues. Tumors can be non-cancerous (benign) as longas the mass does not infiltrate nearby tissue or spread to other parts of the body. When themutation gets unstable, the tumor can become malignant and begin to infiltrate surroundingtissue and spread into the bloodstream. Tumor cells that enter the bloodstream can formcell masses in other organs which are then called secondary tumors or metastases.

In this work, the focus lies on a specific malignant brain tumor, the glioblastoma multi-forme (GBM) (see Figure 1.1 for an example). Historically the term glioblastoma multiformewas introduced in 1926 by Percival Bailey and Harvey Cushing [3] based on the premisethat the tumor originates from mutated glial cells. GBM’s are classified as grade IV by theWHO grading scheme. It is the most common and aggressive form of brain tumor. In 2010,22’000 cases were diagnosed in the United States of America. The average patient survivaltime is 14.6 months [24]. The five-year survival rate only reaches 5.1 %.

Risk Factors for GBM’s include male sex (slightly more common in men) [48], age (over50 years old), history of low-grade astrocytoma, lead exposure [64], ionizing radiation [1],andmalaria [39]. Moreover, several genetic disorders such as Neurofibromatosis, Tuberous scle-rosis, Li-Fraumeni syndrome, and Turcot syndrome. In summary, all forms of DNA damageincrease the risk of tumor manifestation.

Figure 1.1. (Left) FLAIR-weighted image. (Right) FLAIR-weighted image with BraTumIAsegmentation overlay. The colors indicate (red) necrosis, (green) edema, (yellow) contrastenhancing tumor, and (blue) non-enhancing tumor.

1.1. MEDICAL PERSPECTIVE 3

1.1.1 Diagnosis

The current clinical standard for neuro-oncologic tumor assessment is the response assess-ment in neuro-oncology criteria (RANO) [65] that depends on two-dimensional measure-ments in magnetic resonance imaging (MRI) images with different sequences. The acquiredsequences are Pre-contrast T1, T2 or FLAIR, and Post-contrast T1. Based on this sequencesthe tumor is measured by the largest two-dimensional diameters in multiple lesions. In Fig-ure 1.2 a visualization of the measurement technique is shown. In contrast to the olderMcdonald Criteria [43], the RANO procedure does not depend entirely on contrast enhanc-ing parts of a tumor. It also takes changes in T2/FLAIR signals into account. In some casesbrain tumors are assessed with other imaging techniques as computed tomography (CT) orfunctional MRI (fMRI). A more technological approach that emerged, is the BraTumIA [45]software, developed at the University of Bern. This software is currently only used in clin-ical research. However, it can fully-automatically segment brain tumors and differentiatefour different compartments (Necrosis, Edema, Non-Enhancing Tumor, and Enhancing Tu-mor). This segmentation will allow to not only calculate the total tumor volume but alsothe volume of the different compartments individually. See Figure 1.1 for an example of aBraTumIA segmentation.

Figure 1.2. Calculate products of maximal diameters and add them together toyield the sum of products of diameters (SPD). Image source: http://www.iconplc.com/jp/our-services/imaging/central-imaging-core-lab-/regulatory-expertise/IMI-RANO-Critieria-Booklet-Nov-2011.pdf (12/02/2016)

MRS was first used for in vivo brain analysis in 1989 by Frahm et al. [21]. Beforethat MRS was used since the 1950s in organic chemistry to decode the molecular structureof compounds. Over the years many neuro-oncologist have started to use MRS as anadditional diagnosis method. The main advantage of MRS is that it provides localizedchemical information non-invasively. In order to interpret MR spectra of the brain, it isnecessary to understand the biological relevance of the metabolites that can be detected.Figure 1.3 shows the total of detectable metabolites with a 1.5 T MR scanner. In thefollowing sections, the biologic role and the diagnostic value of important metabolites forthis work are explained.

N-Acetylaspartate (NAA)

The N-acetylaspartate (NAA) peak is visible around 2.0 ppm in a healthy brain spectrum.NAA is synthesized in the mitochondria of neurons and transported along the axons. It isa derivative of aspartic acid. Therefore, NAA can be used as a neuronal marker becausea high concentration shows that neurons are intact and working correctly. Normal healthy

http://www.iconplc.com/jp/our-services/imaging/central-imaging-core-lab-/regulatory-expertise/IMI-RANO-Critieria-Booklet-Nov-2011.pdf




Figure 1.3. In vivo spectrum of a healthy human brain [41]. The peaks are labeled with thecorresponding metabolite and the chemical structure. Healthy brain tissue contains no lipidsand lactate.

brain tissue shows a uniform distribution of NAA except in the cerebrospinal fluid (CSF)where almost no metabolites are detected.

Choline (Cho)

The main choline resonance can be found around 3.2 ppm. In regions that contain patholog-ical alterations, the membrane turnover can increase drastically. This results in a massiveincrease of MRS visible products such as phosphatydilcholine and glycerophosphoryl choline.Therefore, an abnormal increase in choline signal can indicate irregular cell activity.

Creatine (Cr)

The main creatine resonance can be found around 3 ppm. Creatine plays a crucial role in thesynthesis of adenosine triphosphate (ATP), the main energy molecule in cell metabolism.Therefore it is an important marker for neuronal activity.

1.1. MEDICAL PERSPECTIVE 5

Lipids (Lip)

There are two main resonance frequencies for lipids in the brain: at 0.9 ppm and 1.3 ppm.Lipids are normally bound to the cell membrane and can therefore not be detected byMRS. However, in necrotic tissue due to unnatural cell death, the lipids dissolve from themembrane and move freely. Therefore, lipids seen in a spectrum are a good marker fornecrotic tissue.

Lactate (Lac)

The main lactate peak is seen as a doublet at 1.33 ppm. It can be distinguished from the1.3 ppm lipid peak by the inverted phase at TE=135 ms (see Chapter 2). Lactate is notdetectable in the healthy brain tissue. However, in oxygen-starved tissue, the cells switchto anaerobic glycolysis to produce energy. Therefore, the cells produce a detectable amountof lactate. Lactate is an indicator of pathological activity.

Figure 1.4. Patient with GBM. (A) MRS spectrum from healthy brain region. (B) Spectrumfrom a tumor voxel showing a high ratio between choline and creatine and almost no NAA.(C) T1 MR image and (D) color-rendered MRS metabolite map showing variations in thecholine levels within the scan slice. Image source: http://www.massgeneral.org/imaging/news/radrounds/july_2012/ (12/02/2016)

Horska et al. [33] stated that early in the development of MRS, it was realized that

http://www.massgeneral.org/imaging/news/radrounds/july_2012/

http://www.massgeneral.org/imaging/news/radrounds/july_2012/


tumor tissue shows different spectra from normal healthy brain tissue [7, 36]. The mainfinding was that nearly all brain tumors show a lower NAA level and often an increased levelof choline. Therefore a high Cho/NAA ratio can indicate the presence of tumor tissue. Theanalysis of MRS is also often done by comparison of tumor regions with the contralateralside of the brain.

In Figure 1.4 four representative images from a clinical viewer software are shown. Fig-ure 1.4A shows the spectrum from a voxel in a healthy brain region. It shows roughly equalcreatine and choline levels and approximately twice as much NAA. These ratios are typicalfor healthy brain tissue. Figure 1.4B shows a voxel from the border of the visible GBM.This spectrum shows a high ratio between choline and creatine and almost no NAA. Sucha spectrum is interpreted to be active tumor tissue. Finally, in Figure 1.4D a interpolatedand color-coded choline map is shown. With such a map an experienced spectroscopist canidentify areas of interest very quickly.

1.2 Technical perspective

In MRS, tumors show abnormal spectra or more precisely, abnormal metabolite values.MRS can be used for absolute quantification using certain sequences and preprocessingmethods. Nevertheless, in magnetic resonance spectroscopy imaging (MRSI) it is often notpossible to retrieve the metabolite concentrations and, consequently, metabolite ratios areused for interpretation of the spectra. From a technical perspective, the question arises ifit is possible to find an algorithm that can discriminate between healthy and malignantregions or even better, many different healthy and malignant regions. However, to be ableto discriminate between the tissues, the characteristic spectroscopy features of each tissuetype have to be identified. Such an identification can be done by clustering a set of spectrafrom a group of GBM patient data sets. Once the tissue types have been identified in theclustered data set, they can be used to segment data sets from patients that have not beenincluded in the clustering. Clustering the whole spectra would be a possible strategy but theavailable data set did not provide absolute quantification and therefore, metabolite-ratioswere used. A set of metabolite-ratios was extracted for each voxel. Moreover, given thedifference in spatial resolution between MRSI and conventional MRI, the MRSI data setswere interpolated.

Clustering is commonly known as the task of grouping data points such that data insidea group is more similar to each other than to data in other groups. The selection of theclustering algorithm depends mainly on the kind of data to cluster. Many clustering modelshave been developed in the past and can roughly be classified into hierarchical methods,partitioning methods, distribution models, and density models [4]. Hierarchical methodsassume that the data points follow a hierarchical structure. Distribution methods assumethat groups of data points belong to the same statistical distribution. Density modelsassume that areas of similar density can be found in a set of data points. The partitioningmethod assumes that a cluster of data points can be represented by the mean of its points,a so-called centroid. The most popular clustering algorithm used for data partitioning bycentroids is the k-means algorithm [32]. In this work the x-means algorithm is used, anextended k-means algorithm with automatic estimation of the number of clusters.

Segmentation refers to the procedure of combining neighboring voxels into a connectedregion. There are many approaches to how this can be achieved. Commonly used are pixel-,edge- and region-based methods. Pixel-based methods decide for each pixel individually towhich group it belongs. Edge-based methods search the data set for lines or curves thatseparate groups of pixels. Finding lines or edges is usually achieved by calculating first or

1.3. HYPOTHESIS 7

second order derivatives in one or more directions. Areas of high values in second orderderivative denote an area of high spatial frequencies and therefore indicate a line or curveof some sort. The problem is that most lines or curves are not forming closed contours.Therefore, additional algorithms have to be used to close the contours to form connectedareas. Region-based methods try to find regions directly. For example region growing [52],active contour models [10], or level sets [49] can be used to find connected regions of interest.

Feature set refers to a set of information that describes a voxel and its neighborhood.Feature sets can contain different types of features such as spectral-, shape-, or texturefeatures. What features to use for a given data set is usually the most complex part of thesegmentation method. Feature sets of advanced methods can reach to hundreds of featuresdescribing a single voxel and its neighborhood. Spectral features describe the properties of asingle voxel such as intensity or color. Shape features describe the shape of the neighborhoodof a feature.

Interpolation is commonly known as a method of constructing new data points betweenknown data points. It is an estimation of the location between two known data points. Overthe years many mathematical methods have been developed for this estimation [20]. Thebest-known interpolation methods are nearest neighbor interpolation, bilinear interpolation,cubic spline interpolation, and the Sinc interpolation. Nearest neighbor interpolation is themost basic form of interpolation. It just looks at the directly adjacent data points andsearches for the one that has the nearest value. This value is then used for the new datapoint. Bilinear interpolation is already a more sophisticated approach. It does not just takethe value of the nearest neighbor but calculates a linearly interpolated value from all theadjacent data points. Cubic spline interpolation uses the same approach but with a cubicspline interpolation instead of linear interpolation and with a 3×3 neighborhood. The Sincinterpolation (Whittaker-Shannon interpolation) can be considered one of the best forms ofinterpolation. It does not just interpolate from the adjacent data points but from all datapoints in the data set. A normalized Sinc function with the center over the new data pointis created. For each point in the data set, the function value is used to calculate the newvalue.

In this work, the information from each voxel is more complex than simple intensityvalues. Therefore, we can not directly work with basic segmentation methods mentionedearlier. However, from each voxel a set of features are extracted and based on this featuresthe clustering and the segmentation will be done. The feature set has to resemble theinformation used by spectroscopist. Therefore, a set of metabolite-ratios that describeseach voxel was used.

1.3 Hypothesis

If we look at MRS data sets of different patients with GBM’s we can observe that voxelsinside tumors have characteristic spectra that can be found in many data sets. Consequently,an experienced spectroscopist can identify different regions of a tumor or possible infiltrationinto surrounding tissue.

First hypothesis

We hypothesize that it should be possible to find a set of characteristic source spectra in alarge amount of MRS data from GBM patients. We expect to find a set of sources with asmooth transition between malignant and healthy spectra without forcing a certain numberof sources. The clustering method will be validated by clustering a phantom scan data setthat provides a controlled environment with an expected amount of sources.


Second hypothesis

Based on the set of source spectra found in a training data set, the segmentation of aseparate test data set will be done. We hypothesize that the segmentation shows a goodcorrespondence to the structural MRI segmentation of the same data sets. This hypothesiswill be validated by comparing the resulting MRSI segmentation visually and quantitatively,by a spatial overlap analysis with the Dice similarity coefficient (DSC), to a structuralsegmentation of the same data sets by the BraTumIA software.

1.4 Related work

In 2000 De Edelenyi et al. [12] proposed a new method to display MRSI information in aneasy readable format. The method used segmentation to assign a histopathological class toeach voxel of a MRS image. This approach is since then known as nosologic imaging. Overthe last years, many approaches have been seen to assign histopathological information toMRSI data. These approaches can roughly be divided into three major groups. One groupuses artificially generated model spectra that represent a known histopathological tissuetype. The second group combined MRSI data with MRI data to improve the segmentationand also the resolution, and the last group used unsupervised and supervised learningmethods and blind source selection approaches to achieve a segmentation without priorinformation.

Tate et al. [62] conducted research on automated classification of short echo time in vivoMRS spectra from two different institutions and different scanners at 1.5 T. The conclusionof this project was that there are no statistically significant differences in intensities betweenmanufacturers or acquisition protocols with different TE and other parameters.

A work of Stadlbauer et al. [60] from 2004 proposed a method that used the assumedGaussian distribution of Cho/NAA values to achieve a tumor segmentation via histogramthresholding. They concluded that the method could improve the delineation of tumorborders compared to MRI diagnosis.

In 2005 Laudadio et al. [38] proposed a method that used canonical correlation analysis(CCA) to compare MRSI spectra and simulated model spectra to achieve a histopathologicalclassification of prostate tumors. They conclude that CCA is a robust and accurate methodfor the correlation of measured spectra with simulated model spectra. In 2008 Laudadio etal. [37] further investigated their method on MRSI data set of heterogeneous brain tumors.They concluded that CCA outperforms ordinary correlation when used on heterogeneousMRSI data. De Vos and Laudadio [13] also conducted research on combining MRSI and MRIdata for the histopathological classification of tumor voxels. In their 2007 work they usedCCA on a feature set that incorporates information from MRSI and MRI. They concludedthat CCA on feature vectors outperformed CCA on whole spectra.

Other approaches for segmentation with combined data were conducted by Bonekamp etal. [5], Devos et al. [14], and Luts et al. [42]. These approaches rely heavily on segmentationof MRI images. As the idea of this work is to focus entirely on MRS data only, we do notfurther investigate combined methods.

One of the oldest approaches for the supervised segmentation is based on artificial neuralnetwork (ANN) by Usenius et al. [63]. In 1996 they proposed a method to discriminatebetween benign and malignant gliomas with a ANN trained on metabolite phenotypes.They concluded that the accuracy of their approach was 82 %.

Newer approaches to machine learning based segmentation of MRSI data are for exam-ple the work by Gonzales-Navarro et al. [22] in 2009. They investigated the problem ofdimensionality reduction and feature selection. The conclusion of the work was that the

1.5. AIM & STRUCTURE OF THE THESIS 9

reduction of used spectral frequencies preserves the discrimination capability of a classifierand improves the computational performance. Another work by Dimou at al. [16] proposeda supervised method using paired support vector machine (SVM) kernels to discriminatebetween healthy and malignant tissue voxels. They compared the classification to man-ual segmentations by radiologists and physicists. In conclusion, their method achieved anoverall accuracy of 88 %.

One of the more recent unsupervised learning approaches is from Li et al. [40]. In theirwork of 2013, they proposed a blind source selection method using hierarchical nonnegativematrix factorization to find a set of sources for histopathological tissue types. In contrastto the other methods which generate nosologic images [12, 60, 38] their approach does notassign a single class of histopathological information to a voxel. They rather use a mix ofprimary colors to show the amount of contribution of each source to the voxel.

The work by Wright et al. [66] from 2009 used an unsupervised learning method calledindependent component analysis (ICA) to find linear combinations of model tissue data.Their method is assumed to be able to detect three classes of tissues. Tumor core, infiltrativegrowth, and normal brain tissue. A study was conducted to compare the results to diffusiontensor imaging (DTI) of the same data sets. They conclude that both techniques providemarkers that represent infiltrative growth and are complementary.

1.5 Aim & structure of the thesis

The aim of this thesis is to automatically find groups of tissue types with a smooth transitionbetween healthy and malignant in a set of training data, without forcing a certain numberof tissue types to be searched. This approach is novel in the sense that in all previouswork, it was always assumed that a certain number of sources should be found. The foundhistopathological tissue sources will then be used to classify the test data sets that wereexcluded from the training. A spatial overlap analysis is performed to validate the foundsources. As there is no ground truth available, the resulting segmentation is compared to astructural segmentation by BraTumIA of the same data sets.

This work is structured as follows: Chapter 2 will introduce the reader to the basicprinciples of nuclear magnetic resonance (NMR) and MRS to build a foundation of under-standing for the forthcoming chapters. In the third chapter the reader is introduced to thetest phantom, how it was built, and the scan sequences that were acquired to test differ-ent scan resolutions. The results of the visual comparison are shown and discussed. Thefourth chapter approaches the first hypothesis and shows the pipeline that was developedfor the clustering of MRS data set. First, the reader is introduced to the materials usedand to the theory behind the clustering algorithm. After that, each step of the pipeline isexplained, and the validation of the method with the phantom data sets is shown. In thelast section of the chapter, the results of the clustering are shown and discussed. In thefifth chapter, the second hypothesis is approached. The segmentation of the test data setsand comparison with BraTumIA segmentation. After explaining the steps that are differentfrom the clustering pipeline, the segmentation results are shown and discussed. At the endof the chapter the comparison with the BraTumIA segmentation and the correlation of thefound sources are analyzed. In the final chapter, the method in its entirety is discussedand compared to other research done in the field of MRS segmentation. Additionally, anoutlook for future research based on the results and the discussion is proposed.

Chapter 2

Magnetic resonance spectroscopy

In this chapter the reader is introduced to the concepts of NMR and MRS. The first sectiondescribes the basic physics principles of NMR. In the second part the chemical shift and theacquisition of MRS are described. The last part introduces a few basic MRS sequences aswell as chemical shift imaging. This chapter is a summary of learning resources [53, 44, 47]collected for this work.

2.1 Nuclear magnetic resonance

The concept of NMR was first introduced by Wolfgang Pauli in 1924 and further developedby Paul Dirac in 1928. It is based on the quantum-physical spin of elementary particles.In a given volume and in the absence of an exterior magnetic field the spins of all particleshave a random direction. Therefore, the net magnetization sums up to zero. However, afterapplying an external magnetic field B0 in the z-axis the spins align along the magnetic fieldlines. The spins of 1H protons can have two different magnetic quantum numbers: −1/2and +1/2. In the case that the magnetic field B0 6= 0 more spins are precessing at the −1/2level. This causes a macroscopic magnetization that can be measured.

A radio frequency oscillating magnetic field (RF) pulse B1 is applied at a correspondingfrequency called the Larmor frequency v0 given by:

v0 =γB0

2π, (2.1)

where γ is the gyro-magnetic ratio [19] of the 1H proton. If this B1 field is perpendicularto B0, the spin will be bent by a torque and will rotate on a transverse plane in the directionof B1. When the B1 field is turned off, the spins go back to the equilibrium state. Theprecession of the spins in the transverse plane induces electric current in a receiver coilthat can be measured as a signal. This signal is generally referred to as free inductiondecay (FID). Figure 2.2 shows a one pulse MRS sequence experiment that explains how theexcitation and relaxation work and how the acquired signal looks.

2.2 Shimming

In the last section it has been assumed that the B0 field is perfectly homogeneous. In realitythis is impossible due to field distortions cause by the measured object. There are otherfactors that reduce the homogeneity of the field in real applications such as manufacturingimprecision of the coils and ferro-magnetic materials in the vicinity of the coils. Nevertheless,

11

12 CHAPTER 2. MAGNETIC RESONANCE SPECTROSCOPY

Figure 2.1. Differentiation of the magnetic quantum numbers with increasing field strength.(a) Sum of magnetization is null if B0 = 0. (b) The surplus of spins that fall into + 1

2level

increases with increasing B0 field strength and therefore the net magnetization increases.Image from Popa Horia [53]

Figure 2.2. One pulse MRS sequence showing the evolution of the macro magnetization.(a) The application of the B1 RF pulse bends the magnetization vector M(t) into the ro-tation plane. (b) Turning of the B1 pulse leads to a return to the equilibrium state of themagnetization. (c) The measured signal from the receiver coils. Image from Popa Horia [53]

2.3. CHEMICAL SHIFT 13

the most important factor is magnetic field distortion by the human body. Therefore, thehomogeneity of the B0 field has to be measured and corrected by additional so calledshimming coils, before each scan [58]. These coils can produce additional magnetic fields tooptimize B0 homogeneity. Nevertheless, the B0 homogeneity optimization is limited by thenumber of shimming coils and by the algorithms used to create the shimming fields.

2.3 Chemical shift

In this section the two main effects that influence the magnetic resonance frequency ofnuclear spins are described. The nuclear shielding by electron orbitals and the spin-spincoupling.

The nuclear shielding is also called chemical shift [31]. Each atom in a molecule hasseveral electron orbitals and the orbiting electrons generate their own magnetic field. Thismagnetic field acts as a shielding against the B0 field. Therefore, the magnetic field thatinfluences the spin is not exactly B0 but

B = B0(1− σ), (2.2)

where σ is the shielding constant.The shielding constant is specific to each atom in a molecule. In 1H atoms which have

only one s orbital σ is simple. But in atoms with more complex electron orbitals theshielding constant can be much more complex. This shielding causes the spin frequency tobe shifted relative to the reference frequency of the B0 field. This is also the reason whyit is called chemical shift. The frequency shift combined with theoretical knowledge frommolecular chemistry can then be used to identify the present chemical compound and alsothe relative quantity of said compound.

The spin-spin coupling, also called j-coupling [26] represents the interaction of electronsin chemical bonds in molecules. J-coupling can be explained through quantum physics. Butthis would go far beyond the scope of this work. Nevertheless, important to know is that thecoupling causes spectral peaks to split into tuplets, triplets or even higher splits, dependingon how many 1H protons are present in a molecule and the spatial configuration.

2.4 Sequences

In order to not receive a signal from the whole body but from a specific location inside thebody, a localization system has been developed. To select a voxel inside a given volume, alocal variation of the B0 field is created by an additional gradient field G. This gradientfield is composed by a superposition of three linearly varying magnetic fields Gx, Gy, andGz generated by three gradient coils. When to turn on and off the gradient coils is definedby each pulse sequence implemented in the scanner software. The following sections explainthe most common MRS pulse sequences.

2.4.1 Spin echoThe spin echo sequence was originally developed by Hahn [25] in 1950 and has been improvedby Carr and Purcell [9]. The spin echo sequence is the most basic method of repeated FIDacquisition. In the beginning a 90° RF pulse is activated to bend the spin. Then, aftera time T , a 180° pulse is activated to flip the already dephasing spin so that it starts tophase again. This rephasing increases the FID signal until all spins are phased again. Thishappens exactly at 2 · T and the signal is at the peek of its strength. This peek is called


the echo. After 3 · T the dephasing is complete and another 180° pulse can be activated torestart the process. The time between two 180° pulses is called echo time. In MRS short andlong echo times are used. At long echo time (TE > 120ms) metabolites as NAA, creatine,choline and lactate are visible and at a short echo time (TE = 30ms) more metabolitesincluding macro molecules and lipids become visible.

2.4.2 PRESS

Point RESolved Spectroscopy (PRESS) [6] is a pulse sequence that uses two 180° pulses fora three-dimensional localization. Figure 2.3 shows the sequence and the excited volumesof each step. During the initial 90° RF pulse, the Gz gradient field is activated to selectthe slice of interest along the z-axis. With each subsequent 180° RF pulse the Gy and Gzgradients are activated to select slices in the y-and x-axes. This leads to an excited volumeof the intersection of the three slices. The echo originating from the spins in the voxel canthen be measured with the receiver coil.

Figure 2.3. Pulse and gradient sequences for PRESS with visualization of spatial selectionby three slices. Image from Klose [35]

2.4.3 STEAM

STimulated Echo Acquisition Mode (STEAM) [35] uses a different approach. This sequenceuses three 90° RF pulses instead of one 90° and two 180° pulses. The first 90° pulse withactivated Gz gradient field is the same as in PRESS. The interaction of the three 90° pulsesthen creates the so called stimulated echo in the intersection of the three planes. The mainadvantage of the STEAM sequence is the shorter acquisition time needed and a lower energyconsumption. Therefore it is a more efficient sequence but the signals acquired have onlyhalf the amplitudes of those acquired with the PRESS sequence.

2.5. CHEMICAL SHIFT IMAGING 15

Figure 2.4. Pulse and gradient sequences for STEAM. Image from Meier [44]

2.5 Chemical shift imaging

To acquire more than on voxel a technique called chemical shift imaging (CSI) also calledmulti voxel spectroscopy is used. In a CSI acquisition the sequence displayed in Figure 2.5 isused. To acquire voxels in different locations each acquisition is encoded by activating phasegradients in two spatial directions shortly before the readout. This sequence experiment isthe repeated n × n times to acquire a grid of voxels. The two-dimensional space with theaxes Gy and Gx is called the k-space. Each experiment represents a point in the k-spacegrid shown in Figure 2.6. To fill up the complete k-space n × n experiments have to beconducted.

Figure 2.5. Pulse and gradient sequences for a basic chemical shift imaging acquisitionwith water suppression and phase encoding. Localization is achieved with a PRESS sequence.Image from Meier [44]


2.6 Reconstruction

After measuring the signals for each experiment a two-dimensional Fourier transformationof the k-space is calculated to reconstruct a spectrum for each x-and y-coordinate on oneslice.

(a) (b)

Figure 2.6. (a)Visualization of the k-space. (b)Fourier reconstruction of full k-space acqui-sition. Both images from Meier [44]

Chapter 3

Phantom

In this chapter, we will introduce the reader to the phantom built in this work. The phantomwas specifically built to investigate a question arising with the current acquisition technique.The goal was to evaluate the ability of MRSI to detect compartments of different metabolitesolutions depending on the native scan resolution used.

3.1 Materials & methods

The idea was to build a phantom that provides sharp borders between compartments withdifferent metabolite concentrations. This phantom is necessary to investigate the abilityto detect borders with different native scan resolutions. Therefore, the decision was madeto use a stack of two times four quadratic aligned artificial ice cubes bought from a localsupermarket. Therefore, we had a system with three axes. Along each axis, a differentmetabolite was chosen. To achieve a different concentration in each cube, the metaboliteconcentration was doubled along each axis. In Figure 3.1a the numbering scheme and theaxis definition of the cube model are shown. The maximum volume that a cube can hold wasmeasured to be 18 ml. As the cubes were arranged in a structure that allowed each axis tohave a maximum value of two, the cube with the highest axis value was in position (2,2,2).Therefore the basic unit was chosen to be 3 ml. Table 3.1 shows the exact concentrationsof metabolites in the three solutions that were used. For example, cube 1 contains 2× 3 mlcholine solution +2× 3 ml glycine solution +2× 3 ml NAA solution. In the other cubes theremaining volume was filled with distilled water.

The process of building the phantom was started by removing the original filling andflushing the cubes with distilled water. The washing process was repeated several timesto make sure none of the original fluid was remaining. After the cleaning procedure wasfinished, the cubes were filled with the corresponding metabolite solution and closed withadhesive tape. Finally, the cubes were fitted together with adhesive tape to form the three-dimensional structure. Figure 3.1b shows the finalized phantom embedded in the watercontainer.

Table 3.1. Metabolite concentrations in the cube phantom solutions.

Solution Concentration [g/ml]

NAA 9.525 · 10−3Glycine 5.5255 · 10−3Choline 9.775 · 10−3

17

18 CHAPTER 3. PHANTOM

(a) Model of the cube phantom with metabolite axesand cube numbering scheme.

(b) Photo of the cube phantom in the water con-tainer.

Figure 3.1.

3.1.1 Scanning protocols

To investigate the effect of native scan resolution on the detection of compartments inCSI scans, a series of resolution test scans were acquired of the cube phantom. The seriesincluded 8 × 8, 12 × 12, and a maximum resolution scan of 32 × 32 voxels. All scans wereacquired with a standardized protocol (TE=135 ms, TR=1500 ms FOV 80× 80 mm) on aSiemens Avanto 1.5 T MR scanner. The Siemens scanner software does not allow to savenative scan resolutions that are not a power of two. Therefore, all native resolutions wereinterpolated to 32× 32 voxels by the scanner software to create comparable data sets. Alldata sets were pre-processed with the following steps: residual water removal HLSVD [8],automatic quality filtering [50], frequency shift correction [18], and phase correction. Afterpre-processing, all metabolites were quantified with the QUEST algorithm [23]. The jMRUIclinical viewer plugin Spectrim was used to display metabolite maps and visually analyzethe differences.

3.2 Results

In Figure 3.2 the difference between the three native scan resolutions is clearly visible. Theimages show the excited area only. Each row shows a different native scan resolution andeach column a metabolite map. From left to right: choline, glycine, and NAA. Missingvoxels shown in all images were removed by the quality filtering during pre-processing.Table 3.2 shows the measured acquisition times for each native resolution. The acquisitiontime increases linearly with the amount of voxels that are scanned. Due to the interpolationto 32× 32 all data sets contain the same amount of data.

The 8 × 8 (Figure 3.2a) native resolution shows, apart from a slight shift of the signalblob in the metabolite axis direction, nearly no distinction between the different metabolitemaps. The 12 × 12 (Figure 3.2b) native resolution shows the increase of the metaboliteconcentration along the metabolite axis. However, only in the form of a continuous areawithout the possibility to distinct the cubes from each other. In the 32× 32 (Figure 3.2c)

3.2. RESULTS 19

native resolution scan, the cube volume with high metabolite values is separable from theborders which show lower metabolite values. The increase in metabolite concentration alongeach axis is shown very clearly.

During the pre-processing of the data sets the quality filtering showed voxels with badquality specifically along the borders of the cubes. Therefore a susceptibility-weightedimaging (SWI) scan was acquired. Figure 3.3 shows the SWI image side by side with a nonphase-corrected interpolation of the choline map. The result shows that the cube borderscreate field inhomogeneity especially the cube in the lower right corner.

(a) 8× 8 native resolution.

(b) 12× 12 native resolution.

(c) 32× 32 native resolution.

Figure 3.2. From left to right: Metabolite maps of choline, glycine, and NAA. From top tobottom 8× 8, 12× 12, and 32× 32 native scan resolution interpolated to 32× 32 voxels.

20 CHAPTER 3. PHANTOM

Table 3.2. Resolutions of test scans and recorded acquisition time.

Resolution Acquisition time

8× 8 2:1112× 12 4:5332× 32 37:42

(a) Susceptibility-Weighted (SWI) Image of the cubephantom.

(b) Fourier interpolated choline map of a 32×32native resolution scan.

Figure 3.3. SWI of the cube phantom showing field inhomogeneity possibly due to micro-bubbles in the plastic mold. The inhomogeneity causes signal cancellation (black lines in (b))in interpolated MRSI data sets when no phase correction is applied.

3.3 Discussion

The visual comparison of the scans showed that a resolution of 8×8 voxels is mostly useless.It shows a large blob of metabolites which are distributed over the whole phantom area.Therefore, no distinction of any structure is possible. A scan at the maximal resolutionof 32 × 32 voxels shows a very good distinction between the cubes. Therefore it would beoptimal regarding resolution. The major drawback is the acquisition time. At 37 minutesper scan, it is not feasible to use in a clinical environment. The 12 × 12 resolution scan isa trade-off between resolution and acquisition time. In less time as one 32× 32 scan wouldtake, two 12×12 CSI scans with different TE and two single voxel spectroscopy (SVS) scanscan be acquired. Regarding the information that can be extracted for the diagnosis, this ismuch more useful than one 32× 32 CSI scan.

The discovered field inhomogeneity created by the cube borders can be explained bymicro air bubbles that were introduced during the molding process. In future phantombuilding projects, the material should be tested before building a full phantom.

Chapter 4

Clustering

In this chapter, the reader is introduced to the method that was developed for the clusteringof MRS data sets. First, the used software and materials are presented, and the initialinspection of the data is described. After that, each step of the pipeline is introduced, andthe validation of the method with the phantom data sets is explained. In the last sectionof the chapter, the results of the clustering are shown and discussed.

4.1 Materials

MRS data sets of 22 patients with diagnosed and histologically confirmed GBMs were used(9 f / 13 m, mean age 66.36 ± 10.86). The acquisition resolution of the images was 12× 12voxels. Each CSI scan was acquired following a standardized protocol (2D-PRESS, CHESS,Siemens Aera and Avanto, 1.5 T, TE=135 ms, and TR=1500 ms) and was interpolated to32 × 32 voxels by the scanner software. The measurements were performed conforming tolocal and national ethical regulations: all patients gave their informed consent to use thedata for scientific purposes.

Originally 33 data sets were available for this work. Thereof, 11 data set had to be dis-carded. The first 5 data sets due to missing MRI modalities for a BraTumIA segmentation.Slice selection profiles needed for the correction step could only be measured for volumeof interest (VOI)s of a maximum of 80 × 80 mm due to the size of the available phantom.Therefore, 6 data sets with overly large VOI had to be discarded.

An initial visual inspection of the 22 data sets showed that slice placement was notalways optimal. In some cases, the slice was even placed completely outside of any visibletumor structures. It is assumed that this placement was done to detect indication forinfiltration. For this work, we assume, the fact that some data sets were mostly containinghealthy tissue samples, introduces a slight bias toward healthy tissue classes. Some datasets with large tumor structures showed very low signal-to-noise ratio (SNR) inside partsof the tumor structure. Therefore, the automatic quality filtering removed these voxels.

4.1.1 Software

The pipeline was implemented in MATLAB, 8.5.0.197613 (version R2015a, 64-bit) fromMathWorks, Inc. (Natick, MA; United States). Additionally, a small Java (JDK 1.8.0_10164-bit) wrapper application was developed to make use of the x-means algorithm imple-mented in the Weka (version 3.7.13) [30] library. The communication between the Java

21

22 CHAPTER 4. CLUSTERING

application and MATLAB was realized via the jMatIO1 library. Pre-processing and quan-tification was done in jMRUI [61] (version 6.0 beta) and its clinical viewer plugin Spectrim(version 1.0 Beta). Statistical analysis was done with R [57] (version 3.3.2 64-bit) andRStudio [59] (version 1.0.44).

4.2 Methods

The proposed method is shown in Figure 4.1 as a pipeline diagram following the yellow lineand consists of the following six steps: The 22 data sets are randomly split into training anda test set. The training set encompassed 17 data sets which were used to find the sourcespectra and the method was tested on the remaining five data sets. The pre-processingconsists of four steps: residual water removal HLSVD, automatic quality filtering, frequencyshift correction, and phase correction. The data sets are quantified to find relative valuesfor metabolites. The metabolite maps are corrected to account for the non-linearity in theselection profile. Metabolite ratios are then calculated for each voxel and stored as a featurematrix. The feature matrix is standardized and normalized and clustered into groups ofsimilar spectra. Each group is merged to form a source spectrum. In the last step, anexperienced spectroscopist orders the set of source spectra from malignant to healthy in amanual processing step. Given that the ordering of the spectra only affects the color scaleused for visualization of the segmentation results, this step was left out of the diagram. Inthe following sections, each processing step and the methods used are explained in greaterdetail.

4.2.1 Pre-processing

The pre-processing consists of the following four steps: residual water removal HLSVD [8],automatic quality filtering [50], frequency shift correction [18], and phase correction.

In the first step, the residual water peak has to be removed because even after watersuppression has been enabled in the scan sequence, the water peak still has an intensityfactor of up to 1000× the metabolite signal. Residual water peak removal is done withthe Hankel Lanczos singular value decomposition algorithm (HLSVD). This algorithm cangenerate model FID signals for water as seen by a MRS acquisition. By subtracting thesemodel FID’s around 4.7 ppm the water signal can be removed.

After the removal of the water peak, the next step is to apply automatic quality filtering.The automatic quality filtering algorithm assesses each voxel separately and determines ifthe quality is sufficient to process further. Voxels with a low quality score are rejectedand not passed on to the next steps. Problems with quality can arise from many differentsources. For example, the magnetic field can be distorted by blood or air in the tissue or bymetallic leftovers from surgical devices. This is often a problem in follow-up studies afterthe tumor has been surgically removed.

The next step is the frequency shift correction. To enable a good quantification, themetabolite peaks of each voxel have to be on the same frequency. Due to physical limitationsin pulse sharpness and field homogeneity, each voxel can have a slight shift of the frequencieswhich has to be corrected. This correction is done by first searching for the choline and NAApeak around the expected ppm in the mean spectra of all voxels. If the peaks have beenfound, the frequency deviation is calculated, and all spectra are shifted by the measureddelta frequency.

1https://sourceforge.net/projects/jmatio/

https://sourceforge.net/projects/jmatio/

4.2. METHODS 23

Figure 4.1. The pipeline diagram shows the two different paths that the data sets took. Theyellow path indicates the clustering of the training data. The blue path shows the segmentationof the test data sets. Green boxes indicate data input or output and gray boxes indicate thedifferent processing steps of the pipeline.


The last pre-processing step is the phase correction. In certain cases MRSI water-suppression can produce regions where the phase of the water signal can abruptly changefrom one voxel to another. This can be prevented by using different water-suppressionsequences or by zero-order phase correction after residual water removal.

4.2.2 Quantification

Quantification of the data sets was performed with QUEST, using models containing thefollowing metabolite peaks: choline, creatine, NAA, lipid 1.3, lactate, lipid 0.9, myo-inositol,glutamate, and glutamine. QUEST uses individual models for each metabolite to calculate acontinuous function that fits the original spectrum. To achieve a good fitting, each functionmodel is individually broadened or narrowed until it fits the peak at its location. As aninitialization, the models were manually placed in a sample spectrum roughly at the rightfrequency. A damping range of [-7,7] was set as a parameter for the algorithm. Additionally,common damping for all models except lipids and lactate was set.

4.2.3 Selection profile correction

In MRS scans of homogeneous phantoms, a selection profile is visible. This profile leadsto the distortion of the otherwise homogeneous signal profile such a phantom acquisitionshould have. Figure 4.2a shows the selection profile of such a phantom acquisition. A clearlynon-homogenous profile is visible in contrast to the expected profile visible in Figure 4.2b.Therefore, it is expected that this selection profile is also contained in patient acquisitionsand introduces a significant bias to the analysis of in vivo MRS data sets.

The correction of the selection profile can be achieved by dividing the in vivo CSI scanby a CSI scan of a homogeneous phantom with the same VOI. A limitation of this correctionapproach is that the correction profile acquired from a certain VOI can not be interpolatedto different VOI sizes. Therefore, for each VOI available in the 22 data sets a correctionprofile had to be acquired.

A disadvantage is that the correction can lead to high values in the border zone by thedivision of normal values from the in vivo data set by very low values in the correctionprofile. This effect leads to border artifacts that would introduce a bias to the clustering.Therefore, the border of all data sets was cropped by one voxel after the selection profilecorrection.

4.2.4 Feature extraction

The feature extraction step calculates a feature vector for each voxel and stores it in a featurematrix. Two main types of features were calculated. Metabolite-to-metabolite ratios andmetabolite-to-noise ratios. The Metabolite-ratios were chosen because metabolite valuesmeasured with MRS are not quantitative, but the ratio between the values reflects theratio between the metabolites. The noise of a voxel is defined as the standard deviationof 200 points towards the tail of the FID. In this region, the signal contains pure noise.Metabolite-to-noise features were chosen after visual analysis of noise maps from differentdata sets. The noise maps showed the noise was higher inside tumor tissue. It is assumedthat metabolite-to-noise features can help to distinguish between malignant and healthytissue. The following four feature sets (see Table 4.1) have been defined and are evaluatedto see which performs best.

4.2. METHODS 25

(a) Metabolite map of a phantom acquisitionshowing a clear profile despite the homogeneousdistribution of metabolites in the solution.

(b) After profile correction the metabolite mapreflects the homogenous distribution of metabo-lites.

Figure 4.2. Visualization of the selection profile correction effect.

Table 4.1. Composition of the four feature sets out of metabolite-, and metabolite-to-noiseratios.

Ratio Set 1 Set 2 Set 3 Set 4

Choline / Creatine x x x xLactate / Choline x xLipids / Choline x x(Lactate + Lipids) / Choline x xNAA / Choline x x x xLactate / Creatine x xLipids / Creatine x x(Lactate + Lipids) / Creatine x xNAA / Creatine x x x xLactate / NAA x xLipids / NAA x x(Lactate + Lipids) / NAA x xCholine / Noise x xCreatine / Noise x xNAA / Noise x xLipids / Noise x xLactate / Noise x x


Feature set 1

The first feature set comprises all possible ratios of the quantified metabolites. The ratiowas calculated such that the most stable metabolite acts as the denominator and the lessstable metabolite as the numerator.

Feature set 2

The second feature set contains the same ratios as the first with added metabolite-to-noiseratios.

Feature set 3

The third feature set is similar to the first, but here lactate and lipid values are combined.

Feature set 4

The fourth and last feature set contains the same features as the third again with addedmetabolite-to-noise ratios.

Feature scaling

After extracting the features for all voxels in the 17 data set the feature matrix is standard-ized so that each value has a zero-mean and a unit-variance with the following function:

x̃ =x− x̄σ

(4.1)

The last step is to normalize the feature matrix with with a standard logistic function thatall values are scaled between [0,1].

f(x) =1

1 + e−x(4.2)

4.2.5 X-means clusteringThe next step after pre-processing is to cluster the feature matrix with the x-means al-gorithm [51]. X-means is an improved k-means algorithm with an efficient estimation forthe optimal number of clusters. As a criterion for cluster number estimation the Bayesianinformation criterion (BIC) is used.

P (xi) =

K∑n=1

P (xi ∈ Dn) · P (xi | xi ∈ Dn) (4.3)

The BIC is the sum of the probabilities that a point xi, in all points K, is an element ofthe cluster Dn multiplied by the probability that the point xi is near the cluster centroid ifit is an element of cluster Dn.

In Figure 4.3 the three main steps of the algorithm are shown. The algorithm is initial-ized with a starting amount of clusters. For the example shown in 4.3 the initial amountof clusters is three. In the second step shown in Figure 4.3a each cluster is separated intoa region, and a local 2-means is applied. As shown in Figure 4.3b, for each region the BICis calculated with and without the split. The new cluster centers are kept as shown inFigure 4.3c if the BIC increases. If not, the new centers are discarded. After the decision

4.2. METHODS 27

Algorithm 1 x-means clusteringinitialize k=3 clusters randomly with k-means and add them to clusterlistwhile clusterlist has elements doremove cluster from clusterlistcalculate local 2-means for clusterif BIC(local 2-means(cluster)) > BIC(cluster) thenadd the two new clusters to clusterlist

end ifend while

has been made for each area, the global BIC is calculated and if it increased further, thenext iteration is started. If the global BIC does not increase further, the loop is terminated,and the clusters are returned as a result. See Algorithm 1 for pseudo code.

Pelleg et al. [51] suggested that the x-means algorithm could be used with other metricsfor cluster number estimation. For example with the Akaike information criterion (AIC).Although, the implementation used in this work only supported the BIC as a metric.

(a) Each cluster is split into twosubclusters by a local 2-means.

(b) For each cluster the BIC iscalculated with and without thesplit.

(c) The new cluster centroids arekept when the BIC increases.

Figure 4.3. From left to right: The three main steps of the x-means algorithm. Imagefrom [51]

Technically the x-means algorithm can work with any form of distance metric. But re-search conducted by Aggarwal et al. [2] about clustering of high dimensional data concludesthat distance metrics such as euclidean distance (L2) or higher-order distance metrics ofthe general form:

Lk(x, y) = (

d∑i=1

‖xi − yi‖k)1/k : x, y ∈ Rd, k ∈ Z, (4.4)

can have a negative impact on the clustering result. This means that a lower numberof k is preferable for high dimensional data clustering. Therefore, as a distance metric, theManhattan distance (L1 distance) was used. The starting parameters for the clustering areshown in Table 4.2.

4.2.6 Ordering and labelingThe resulting source spectra were ordered from malignant to healthy and labeled with thehistopathological class by an experienced spectroscopist. The ordering step is helpful for a


Table 4.2. Parameters for the x-means algorithm.

Parameter Initial value

minClusters 1maxClusters 500k-means iterations 1’000

good visualization of the MRSI segmentation discussed in Chapter 5 but it does not affectthe comparison with the BraTumIA segmentation. The labeling is helpful to understandthe malignancy of the segmented regions.

4.2.7 ExperimentsFor the validation of the clustering method and the evaluation of the different feature sets,two experiments were carried out. The following two sections explain the experiments.

Phantom validation

The validation of the clustering was carried out on the phantom data. The pipeline describedin this chapter had to be slightly altered because the phantom was built with differentmetabolites and no correction profile was available. Therefore both the 12 × 12 and the32× 32 native resolution phantom data sets were clustered without profile slice correctionand the following feature set.

Cho/Gly, Cho/NAA, Gly/Cho, Gly/NAA, NAA/Gly, NAA/Cho, Cho/noise, Gly/noise,NAA/noise

Feature evaluation

For each feature set, a leave-one-out cross-validation (LOOCV) [46] was carried out. InLOOCV, all training sets except for one are used for clustering. The process is repeateduntil every data set has been left out once. In the case of this work the clustering wasdone 17 times. For each LOOCV the standard deviation, variance, mean Davies–Bouldinindex [11], and the mean Dunn index [17] are calculated. Both the Davies-Boulding indexand the Dunn index are a metric for low intra-cluster and high inter-cluster distances. TheDunn index is calculated by the following formula:

D =

min1≤i<j≤n

d(i, j)

max1≤k≤n

d′(k)), (4.5)

where d(i, j) represents the Manhattan distance between the centroids of clusters i and j,and d′(k) is the distance of any element of a cluster to its centroid. A high Dunn index,therefore, represents a better clustering result.

The Davies-Bouldin index can be calculated by the following formula:

DB =1

n

n∑i=1

maxj 6=i

(σi + σjd(ci, cj)

), (4.6)

where σx is the average distance of all elements in the cluster to the cluster centroid cx,and d(ci, cj) is the distance between the cluster centroids ci and cj .

4.3. RESULTS 29

Based on these metrics the feature sets were evaluated and the best is selected for thefinal clustering. Best in this context describes a feature set with low standard deviation,variance, and Davies-Boulding index and a high Dunn-index.

4.3 Results

The evaluation of the clustering on the 12×12 phantom data set yielded five source spectra.Figure 4.4a shows the result sources of the clustering. Source 1 to 4 show a narrow σ band.This indicates that the clusters are composed of very similar spectra with a high SNR. Incontrast, the source 5 shows a very broad σ band which indicates a composition of lesssimilar spectra with a low SNR. As observable in the segmentation output Figure 4.4bthe source spectrum five is predominantly found in the zone outside of the phantom. Incontrast, the sources 1 to 4 define the different compartments of the cube. Despite the factthat the material of phantom introduced heavy field inhomogeneity in the border area, theclustering of the four different compartments was still possible. The only visible drawbackis that the upper left compartment in the 12 × 12 scan shows bleeding into the border ofthe left column of blocks.

The evaluation result of the second phantom data set with a native resolution of 32×32shows an almost identical image. As shown in Figure 4.4c seven sources were found. Inthis case source 1 to 4 are well behaved and sources 5 to 7 show a low similarity and lowSNR composition. As shown in Figure 4.4d the well-behaved sources resemble the phantomcompartments, and the misbehaved sources resemble the border zone and the areas betweenthe cubes. In consequence, the found sources in both low and high-resolution scan, resembleclosely the four expected compartments and the zone outside the phantom.

The evaluation of the four different feature sets is shown in Figure 4.5. The inclusionof the metabolite-to-noise ratio decreases the stability of the clustering notably. The com-bination of lactate and lipids, on the other hand, increases the stability by a large margin.The evaluation showed that feature set 3 has the best overall values (see Table 4.3) in allcalculated metrics. Therefore, the feature set 3 was used to progress further.

Table 4.3. Statistics for the feature evaluation. med. refers to the median of the LOOCVand nr. fc refers to the number of clusters from the full clustering.

Feature set med. nr. fc σ σ2 Dunn-index Davies-Bouldin-index

1 22 21 4.0348 16.2794 1.1930 · 10−4 1062.42 35 37 5.0512 25.5147 3.8349 · 10−4 601.83 9 9 2.4734 6.1176 0.0029 55.54 23 23 4.0275 16.2206 0.0017 456.5

In Figure 4.6 two examples of quantification results are shown. The left side shows asatisfactory quantification where the fitting has been concluded as expected. The resid-ual shows nearly no metabolite signal left. On the right side, the result of an imperfectquantification is shown. The fitting algorithm was not able to fit the lactate peak properly.Therefore, a part of it is left over and visible in the residual signal.

4.4 Discussion

The validation of the phantom data sets shows that the clustering algorithm can find theexpected number of clusters with the basic sets of features and that the found clusters indeed


(a) 5 source spectra (blue) with ±σ band (gray). (b) Segmentation of the cube phantomwith 12 × 12 native resolution. VOI in-terpolated from 16× 16 to 64× 64.

(c) 7 source spectra (blue) with ±σ band (gray). (d) Segmentation of the cube phantomwith 32 × 32 native resolution. VOI in-terpolated from 16× 16 to 64× 64.

Figure 4.4. Results of the phantom validation.

correspond to the expected compartments. The σ band plotted over the source spectra alsoshows that the grouping of noisy and clean spectra works very well. At least in the phantomvalidation. The second validation with the high-resolution scan shows that sources can befound that exist purely inside the border zone between the cubes. We expected to find fourdifferent sources for the borders between the four compartments. However, we found onlythree border sources. In future work this phantom experiment should be repeated with aphantom using a material of better quality. This could also help to answer the questionwhether the border can be seen due to spectra generated by field inhomogeneity or due tolower metabolite signal intensity.

Moving on to the feature evaluation part, the four defined feature sets were tested ina LOOCV experiment. One of the main results of the feature evaluation was that themetabolite-to-noise ratios seem to decrease the stability of the clustering. Metabolite-to-noise features were introduced to achieve a measure closer to an absolute value. On the otherhand, noise is also present over the whole VOI of all data sets. This has likely influencedthe clustering such that more data points were between distinct clusters. Moreover, this,in turn, forced a lower intra-cluster similarity. Therefore the algorithm found more clustersin the same data than without metabolite-to-noise features. Additionally, the evaluation

4.4. DISCUSSION 31

Figure 4.5. Metrics and statistics for the feature evaluation. Feature sets 1 and 2 representall possible combinations of the quantified metabolites. In feature sets 3 and 4 lactate andlipid were combined. 2 and 4 represent feature sets with included metabolite-to-noise ratios.

showed a general trend towards a lower cluster number with fewer features. This hadthe exact opposite effect of generating fewer points between clusters and led to a higherintra-cluster similarity. Therefore, a lower amount of cluster splits led to an increased BICvalue. The combination of lactate and lipid values had a positive effect on the stability ofthe clustering. It is assumed that the increase in stability is the result of compensation offitting errors by combining the two metabolites together. The errors resulted possibly fromthe difficulties of resolving the overlapping peaks by the quantification algorithm. Overallthe stability of the clustering defines how many source are found. In this work, the higheststability was chosen and therefore resulted in the lowest number of sources for the test data.

The final clustering of the test data, with feature set 3, yielded nine sources. An experi-enced spectroscopist ordered them from malignant to healthy. The sources show a smoothgradient between malignant and healthy except for the first two Necrosis 1 and Necrosis 2.These two sources look visually very similar. On the other hand, the σ band shows thatthe Necrosis 1 source is composed of spectra that still have many metabolites. Especiallythe high NAA content is surprising which can not be observed in the Necrosis 2 source.However, both have a high lipid + lactate content which is expected in pure necrotic tissue.The Necrosis 1 source is therefore suspected to be an accumulation of quantification fitting


(a) QUEST quantification curveshowing an example of good fit-ting.

(b) Example of imperfect fit-ting.

Figure 4.6. QUEST quantification output visualization. Not all spectra could be quantifiedto a satisfactory degree. Overall, only a small percentage of spectra showed inadequate fitting.

errors where the fitting algorithm could not decide whether to fit choline or creatine. Thepeaks of these metabolites are close to each other, and if the peak maximum is near the noisepeak level, then fitting is difficult. Also, Necrosis 1 shows a broad σ band over the wholeppm range and therefore it is assumed that a lot of low SNR spectra are combined in thissource. The Necrosis 2 source, on the other hand, shows a typical source of necrotic tissuewhich has a small choline signal present. The sources 3 to 5 show a smooth progressionfrom high lipid + lactate content with a high choline to creatine ratio to low lipid + lactatecontent and a low ratio between choline and creatine. The progression from Necrotic +Active Tumor to Active Tumor + Infiltration is very obvious. According to a trained clini-cian, the pure Infiltration source is discussable because depending on the spatial location ofthe CSI grid it could already be a healthy source. Therefore, this source, in particular, hasto be investigated further and possibly correlated with histological data to gain confidencein this source. The two Normal WM source look visually very similar with only NormalWM1 having a slightly broader σ band around the lactate + lipid peak. Therefore, thesetwo sources are candidates to be merged in future work. Also CSF could not be found asa source in MRSI data. This can be explained by two factors. First, to acquire a pureCSF spectra a voxel has to be completely inside the CSF without acquiring signal fromsurrounding tissue. This already is difficult to achieve because in a 12× 12 scan resolutioneach voxel has a size of approximately 13×13×15 mm. To position a scan exactly in a waythat this large volume is entirely inside the CSF can be challenging. Second, CSF spectra

4.4. DISCUSSION 33

Figure 4.7. Source spectra found by clustering the training data. The spectra were ordered byan experienced spectroscopist according to their malignancy. After the ordering, the obtainedsource spectra show a continuous progress from malignant to healthy. The lightblue bandshows ±σ.

contain almost no metabolites. Therefore, the SNR will be low and the spectrum is verylikely removed by quality filtering. Third, due to the interpolation to 32×32, the pure CSFspectrum will get mixed slightly with the spectra of the surrounding voxels. Therefore, itwas expected that no CSF sources could be found.

Consequently, more research has to be conducted to correlate the found sources withhistological data from patients.

Chapter 5

Segmentation

In this chapter, the blue path of the pipeline shown in Figure 4.1 is explained. The firstfour steps are the same as described in Chapter 4. The additional steps interpolation,segmentation, comparison, and the used materials are explained in the following sections.

5.1 Materials

The nine source feature vectors of the sources found in Chapter 4 were used to classifythe test data sets. For the validation of the segmentation method a MRI segmentation per-formed by BraTumIA [2], calculated from multispectral scans (T1, T1-contrast, T2-contrast,and FLAIR) that were acquired alongside the MRS scans, was used. Each BraTumIA out-put data set was received in neuroimaging informatics technology initiative (NIfTI) formatwith an approximate resolution of 512× 512× 46 voxels.

To enable a comparison between MRSI segmentation and BraTumIA segmentation aninterpolation of the MRSI and a down scaling of the BraTumIA segmentation was done.

5.2 Methods

After completing step 1 to 3 of the method pipeline, a feature matrix x × y × vx, with xand y beeing the size of the VOI of the data set, and vx being the length of the extractedfeature vector, was created. The same features, as explained in Chapter 4, were extractedand stored in the feature matrix.

5.2.1 Interpolation

In the next step, the feature matrix had to be interpolated from 16× 16 to 64× 64 voxels.The interpolation was performed with zero padding also called spectral interpolation.

To do one step of zero padding interpolation, the two-dimensional signal which representsintensity variations in space, or in our case metabolite ratios, has to be transformed intothe time domain with an inverse Fourier transformation. The resulting time domain imagehas to be shifted to align low frequencies in the middle of the image and padded with zerosto double the size of the image. After that, the time domain image has to be transformedback to the intensity domain with a forward Fourier transform. The following pair of two-dimensional discreet Fourier transform (DFT) is therefore required:

35

36 CHAPTER 5. SEGMENTATION

F (u, v) =1

MN

M−1∑x=0

N−1∑y=0

f(x, y)e−j2π(ux/M+vy/N) (5.1)

f(x, y) =1

MN

M−1∑u=0

N−1∑v=0

F (u, v)ej2π(ux/M+vy/N) (5.2)

Luckily, a two-dimensional DFT is separable into the following multiplication of twoone-dimensional DFTs.

F (u, v) =1

N

N−1∑x=0

e−j2πux/NN−1∑y=0

f(x, y)e−j2πvy/N (5.3)

These can then be calculated with the fast Fourier transform (FFT) algorithm availablein MATLAB.

5.2.2 Segmentation

The next step is the segmentation of the test data. The class cx of each voxel x in the dataset is determined by the following formula:

cx = arg minid(vx, vi), (5.4)

where vx is the feature vector of the assessed voxel, vi is the mean feature vector of thesource i, and d(vx, vi) is the Manhattan distance (L1 distance) between the two vectors.The number of the source with the minimum of all distances is assigned as the class cx.

The class values are then stored as an image and displayed with a color map. The colormap was specifically structured to display malignant classes as different shades of red andhealthy as different shades of blue. Between the two, white was inserted to represent theinfiltration class.

5.2.3 BraTumIA segmentation pre-processing

The BraTumIA segmentation output is a three-dimensional data set with an approximateresolution of 512 × 512 × 45 voxels. Therefore, it has to be reduced in dimensionalityand resolution to be comparable to the two-dimensional MRS slice with an approximateresolution of 64× 64× 1 voxels. To achieve this reduction, a winner takes all approach wasused. For each MRS voxel the cardinality of all classes for all BraTumIA voxels inside oneMRSI voxel was calculated and the class with the maximum cardinality was then used asthe BraTumIA label for the MRSI voxel. This approach achieved both the dimensionalityand resolution reduction in one step.

The following formula describes the calculation of the voxel class C ∈ {1, 2, ..., 7}:

vx = maxi∈C|ci| . (5.5)

where vx is the MRSI voxel and |ci| is the cardinality of class ci for all MRI voxels insidethe MRSI voxel.

5.3. RESULTS 37

5.2.4 ComparisonTo compare the results of the MRSI segmentation quantitatively the DSC [15] was used.The DSC, also known as the Sørensen-index, is a simple and useful measure of the similarityof two samples [69], here used to measure the spatial overlap between two segmented regions.The values range between 0 and 1, where 1 is a perfect spatial overlap and 0 is no overlapat all. The DSC can be calculated by the following formula:

DSC =2|X ∩ Y ||X|+ |Y |

, (5.6)

where |X| and |Y | are the number of voxels in each region and |X ∩ Y | is the number ofoverlapping voxels.

5.3 Results

Figure 5.1 shows the MRSI segmentation result of test data set 5 in comparison to the MRIsegmentation. The two segmentations, and respective colormaps correspond visually verywell. No correspondence was found for the BraTumIA edema class. On the other hand, theMRSI segmentation shows a large zone of infiltration (white color) surrounding the activetumor zone. Necrosis 1 was found in unexpected locations around the zone where qualityfiltering removed bad quality voxels.

Figure 5.1. Comparison between BraTumIA segmentation and MRSI segmentation of thetest data set 5. (Left) BraTumIA segmentation image. (Right) MRSI segmentation image.Color bars show the tissue labels for each class.

The other four segmentations displayed in Figure 5.2a show more diverse results. Testdata set 1 shows a similar good correspondence as data set 5, besides the MRSI segmentationshowing two regions of discarded voxels. Data sets 2 and 4 show that the BraTumIA classEdema did not find a correspondence in MRSI segmentation. In data set 2 the large edemaregion could not be segmented due to a large area of discarded voxels in the area. Finally,in data set 3, the MRSI segmentation could not find classes more malignant than ActiveTumor due to slice placement outside of the actual tumor.

Figure 5.3 shows the contingency matrix with probabilities that a MRSI class voxel isfound at the same spatial location as a BraTumIA class voxel. For example, the probabilitythat a Necrosis 1 voxel is found at the same spatial location as a CSF voxel is 0.556. Thetable shows a good probability that Necrosis 2 is found at the same location as Necrosis


(a) MRSI segmentation results for the other 4 test sets

(b) MRI segmentations of the same data sets performed by BraTumIA

Figure 5.2. Comparison of the test data sets and the associated BraTumIA segmentation.From left to right: Test data sets 1 to 4

in the BraTumIA segmentation. Another high probability is seen with Active Tumor andEnhancing Tumor. Necrosis + Active Tumor has a probability of 0.428 to appear on thesame spatial location as Enhancing Tumor but also an almost similar probability of 0.419to Necrosis. Noticeable is that all healthy MRSI classes (Normal WM1, Normal WM2,Normal GM) have a probability over 0.5 to be found at the same location as a voxel of theWM class of BraTumIA.

Figure 5.3. Probability table derived from the contingency table of all segmentationscombined. This table shows the probability that a voxel from a certain MRSI class wasfound at the same spatial location where a voxel of a certain BraTumIA class was foundp(voxel ∈ bratumiaClass|voxel ∈ mrsiClass). (GM=grey-matter; WM=white-matter; NETum.=non-enhanching tumor; E Tum.=enhancing tumor)

Figure 5.4 shows the comparison of tissue groups with the DSC visualized by fusionimages. The classes of MRSI and BraTumIA were split in three groups: malignant, healthyand a group that includes the Infiltration class from MRSI and the Edema class fromBraTumIA. In Figure 5.4a the malignant classes of both segmentation method are compared.The analysis yields a high similarity, with a DSC over 0.8, for the data set 1 and 5. Dataset 2, and 4 have a slightly lower similarity with a DSC over 0.6. The comparison of data

5.4. DISCUSSION 39

Table 5.1. DSC for MRSI and BraTumIA class group correspondence for test data sets.

CorrespondenceMRSI to BraTumIA

1 2 3 4 5 Mean σ

Malignant to Malignant 0.83 0.65 0.14 0.65 0.84 0.62 0.29Infiltration to Edema 0.08 0.17 0.12 0.30 0.42 0.22 0.14Healthy to Healthy 0.70 0.75 0.89 0.39 0.87 0.72 0.20Normal GM to GM 0.05 0.10 0.19 0.00 0.03 0.06 0.07

set 3 yields a very low DSC of 0.14 due to a large area in the upper middle originating fromMRSI segmentation. Noticeable is that all images show smaller or larger MRSI regions inthe upper middle region.

Figure 5.4b shows the comparison of the MRSI Infiltration and the BraTumIA Edemaclass. Except for data set 5 the similarity is generally very low. In data set 5 a part ofedema is corresponding to infiltration. In Figure 5.4c the healthy classes are compared.

Finally a comparison of MRSI GM and BraTumIA GM classes is displayed in Figure 5.4d.The correspondence is very low.

5.4 Discussion

The visual correspondence of the malignant tissue in the two segmentation methods is goodin most cases except for case 3. Case 5 showed the best visual correspondence.

Case 1 has visually an equally high correspondence as case 5, but inside the tumor zone,some voxels have been discarded by quality filtering. The removed voxels correspond tonecrotic tissue in the BraTumIA segmentation. Calcifications and deposits of hemosiderindue to intra-tumor bleedings are the main causes. These effects can introduce field distor-tions which lead to low SNR in the acquired voxels.

Case 2 shows a good correspondence on the left side but is inconclusive on the right side.A large part of the voxels classified as edema by BraTumIA were removed by the qualityfiltering. Apart from the removed voxels also the right side shows no further malignantvoxels. This can be explained by the fact that the quality filtering would remove morevoxels, but it is thresholded such that fewer spectra were discarded and more data wasavailable to work with, at the risk of having bad quality spectra in the data set. Thereforethe voxels around the discarded areas could contain bad quality spectra and be possiblyfalsely classified as healthy tissue.

Case 3 is special in such a way that the slice was positioned outside of any visible tumorstructures. Therefore the BraTumIA segmentation also contains only very few voxels withmalignant classes. Nevertheless, the MRSI segmentation indicates a large area of Infiltrationin the same region and also a small inner area of Active Tumor tissue. The Active Tumortissue shows a slight correspondence to the areas of enhancing tumor detected in the MRIsegmentation.

In case 4 the Infiltration class (white) spreads over the complete VOI which raises thequestion again if the Infiltration source can be differentiated from a healthy source in allspatial locations of the brain. In other cases, the Infiltration class is mainly found in an areasurrounding the more malignant red areas. This seems to make sense as it could indicatetissue that is already infiltrated by mutating tumor cells but can not be detected in a MRIsegmentation. To answer this question, more research has to be conducted.

To return to the discussion of Chapter 4 about the sources Normal WM1 and Normal


(a) Fusion images of malignant classes from both classification systems.

(b) Fusion images of MRSI Infiltration and BraTumIA Edema class.

(c) Fusion images of healthy classes from both classification systems.

(d) Fusion images of MRSI Normal gray matter (GM) and BraTumIA GM class.

Figure 5.4. Comparison of groups of MRSI classes to groups of BraTumIA classes. Fromleft to right, test data set 1 to 5. Numbers on top of the images show the DSC. (White) Areawhere both classification systems are similar. (Magenta) Area where only MRSI classifiedvoxels. (Green) Area where only BraTumIA classified voxels.

5.4. DISCUSSION 41

WM2. These sources were suspected to be very similar and possibly resembling the sametissue type. The probability table shows that Normal WM1 and Normal WM2 have almostthe same probability to be matched with the BraTumIA class for white matter (WM).Also, Normal GM shows almost the same probability to be WM. And the probability ofNormal GM beeing BraTumIA GM is even lower than Normal WM2 being BraTumIA GM.Figure 5.4d shows a direct comparison between MRSI GM and BraTumIA GM. Visuallyand quantitatively no correspondence could be found between the two classes. Thereforewe can conclude two things from this analysis. Normal WM1 and Normal WM2 could bemerged together into one source, and MRSI segmentation is not able to distinct betweenWM and GM tissue. This could be explained with the low acquisition resolution of MRSIand the interpolation that had to be done. As shown by the phantom experiment describedin Chapter 3, a resolution of 12 × 12 is probably too low to detect the difference betweenWM and GM. Noticeable is also that the healthy tissue types in the BraTumIA trainigdata are segmented by an algorithm (FSL FAST) and not by manual segmentation as arethe malignant tissue types. Therefore, the quality of the BraTumIA segmentation of thehealthy areas is assumed to be less accurate. Another point discussed in Chapter 4 wasthat Necrosis 1 could be an accumulation of fitting errors by the quantification step. Thesegmentation showed that Necrosis 1 was only found in border zones or around black areaswhere bad quality spectra were removed. Therefore it is assumed that this assumption iscorrect and fitting errors happened due to low SNR spectra which are very prone to thiskind of errors.

The analysis with the DSC confirms the visual correspondence of the malignant (withoutinfiltration and edema) regions in all data sets. The highest similarity is found in data sets 1and 5. The lowest in data set 4. An entirely different question is whether the segmentationmethod is able to detect an equivalent to the BraTumIA Edema class. The comparison of theMRSI Infiltration class to the BraTumIA Edema class showed a very low correspondence.Therefore, it is assumed that it is not possible to detect edema with MRS. In contrast,the Infiltration class can not be detected in structural MRI analysis. It is assumed thatthe Infiltration class indicates regions where the tissue already contains a small amountof tumor cells. This information could, therefore, be very useful in tumor response andtreatment planning. To validate the existence of the indicated regions a clinical study withtissue biopsy in the indicated region is necessary. Another possibility would be to investigatethese regions with different imaging techniques like perfusion imaging.

Chapter 6

Discussion and Conclusions

6.1 Discussion

Our first hypothesis stated that we expect to find an unknown number of characteristicsources for tissue types in MRS data from GBM patients. We approached the task of findingthe sources with the x-means clustering algorithm. Different feature sets were investigated,and a cluster analysis with the Dunn-index and DB-index showed that the set of all possiblecombinations of metabolite-ratios with combined lactate + lipids performed best regardingstability and source numbers. The resulting sources have been ordered and labeled byan experienced spectroscopist and show a smooth gradient from malignant to healthy. Incontrast to the work of Wright et al. [66] and Li et al. [40] we did not restrict our approachto a certain number of sources. Therefore we were able to find five sources for malignanttissue types and three sources for healthy tissue types. Additionally we were also able tofind a source between the two groups that we believe is similar to what was described byWright et al. as infiltrative growth.

In our second hypothesis we stated that we expect to find a good correspondence ofthe MRSI segmentation to structural MRI segmentation. A spatial overlap analysis to thestructural segmentation performed by BraTumIA showed that our method is able to segmentthe malignant tissue group with a mean DSC of 0.62±0.29 and healthy tissue group with amean DSC of 0.71±0.20. We excluded the MRSI Infiltration class and the BraTumIA Edemaclass from this analysis and compared them directly with the result that we could only finda very low correspondence between the two. Therefore, we assume that the infiltration classfound by the clustering does not resemble the Edema class of BraTumIA nor did we finda correspondence to any of the other malignant classes of BraTumIA. Further analysis ofthe segmentation showed that MRSI is not able to discriminate between different types ofhealthy tissue. We assume that the acquisition resolution is too low for this discrimination.Additionally, we suspect that the interpolation needed for the comparison to the structuralsegmentation further degraded the discrimination ability and amplified the partial volumeeffect.

6.2 Conclusions

In conclusion, we can say that it is possible to segment GBMs with the help of naturallyfound source spectra from a large amount of analyzed MRS data sets. The proposed methodhas the potential to facilitate the clinical use of MRS in GBM diagnostics. It removes theneed for large amounts of experience to translate spectral information into tissue types.

43

44 CHAPTER 6. DISCUSSION AND CONCLUSIONS

Additionally, the method also has the potential to be able to detect tumor infiltration thatis otherwise not visible to clinicians using MRI. However, it is not clear if the infiltrationdetected by the method can be histologically confirmed. Therefore, further research has tobe conducted to investigate this connection.

Chapter 7

Outlook

The automatic segmentation method proposed in this work has the potential to facilitatethe clinical use of MRS and should, therefore, be investigated further. More research isneeded on a variety of topics.

First, clustering of an even larger set of in vivo data could be conducted to verify thesources that have been extracted, and discover other possible sources that could not be foundin this work. Furthermore, segmentation of more data sets with the sources discovered in thiswork could be conducted to further increase the confidence in the correlation to structuralsegmentation by BraTumIA.

Second, another interesting part of this work was the detection of tumor infiltrationwhich is not visible in MRI. This could help clinicians define the area of tumor resection ina more sophisticated way to prevent tumor regrowth. As infiltration can not be detectedin structural imaging another way of investigation has to be found. For example, one couldconduct a study to assess the infiltration by collecting tissue samples from affected areasand analyzing if there is real infiltration visible. Another approach would be to create abrain atlas of spectra from multiple healthy brains and statistically correlate the foundinfiltration source to all possible healthy spectra. This analysis could help to improve thediscrimination between healthy tissue and already infiltrated tissue.

Third, the automatic segmentation method is expected to work seamlessly with modernacquisition methods as proton echo-planar spectroscopic imaging (PEPSI) [54, 55] or SPec-troscopic Imaging by exploiting spatiospectral CorrElation (SPICE) [68] which can improvefourfold on the acquisition resolution. As shown in the tests with the phantom scans, thesegmentation would benefit greatly from higher acquisition resolution. A higher resolutionwould solve problems with the partial volume effect and improve the visibility of elementswith high spatial frequency. Also, the effect of mixed spectra due to interpolation could belowered by using a higher initial resolution.

Fourth, the automatic segmentation method could be implemented in the clinical viewerplugin Spectrim to provide a fast and simple way to translate spectral information intotissue type information and at the same time keeping the ability to inspect the spectralinformation in parallel.

Finally, the clustering method could be applied to other types of brain tumors andmetastasis to explore if it is possible to find a set of characteristic source spectra for eachtumor type. From this experiments, a database of characteristic sources for all types ofbrain tumors could be created. Such a database could then possibly be used to create amethod for automatic brain tumor classification.

45

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