Quantification of myocardial perfusion using contrast agent enhanced first pass magnetic resonance imaging

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Dissertations in Forestry and Natural Sciences

DISSERTATIONS | MINNA HUSSO | QUANTIFICATION OF MYOCARDIAL PERFUSION USING CONTRAST... | No 384

PUBLICATIONS OF

THE UNIVERSITY OF EASTERN FINLAND

MINNA HUSSO

Quantification of myocardial

perfusion using contrast agent

enhanced first pass

magnetic resonance imaging

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PUBLICATIONS OF THE UNIVERSITY OF EASTERN FINLAND DISSERTATIONS IN FORESTRY AND NATURAL SCIENCES

N:o 384

Minna Husso

QUANTIFICATION OF MYOCARDIAL PERFUSION USING CONTRAST AGENT

ENHANCED FIRST PASS MAGNETIC RESONANCE IMAGING

ACADEMIC DISSERTATION

To be presented by the permission of the Faculty of Science and Forestry for public examination in the Auditorium MD100 in Mediteknia, Kuopio, on September 25 ,^th 2020, at 12 o’clock.

University of Eastern Finland Department of Applied Physics

Kuopio 2020

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Grano Oy Jyväskylä, 2020

Editors: Pertti Pasanen, Raine Kortet, Jukka Tuomela, and Matti Tedre

Distribution:

University of Eastern Finland Library / Sales of publications julkaisumyynti@uef.fi

http://www.uef.fi/kirjasto

ISBN: 978-952-61-3456-7 (print) ISSNL: 1798-5668

ISSN: 1798-5668 ISBN: 978-952-61-3457-4 (pdf)

ISSNL: 1798-5668 ISSN: 1798-5676

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Author’s address: University of Eastern Finland Kuopio University Hospital Diagnostic Imaging Center P.O.Box 100

70029 KYS FINLAND

email: minna.husso@kuh.fi Supervisors: Professor Juha Töyräs

University of Eastern Finland Department of Applied Physics P.O.Box 1627

70211 KUOPIO FINLAND

email: juha.toyras@uef.fi Professor Hannu Manninen University of Eastern Finland Department of Clinical Medicine P.O.Box 1627

70211 KUOPIO FINLAND

email: hannu.manninen@kuh.fi Petri Sipola, MD, Ph.D.

Kuopio University Hospital Diagnostic Imaging Center P.O.Box 100

70029 KYS FINLAND

email: petri.sipola@kuh.fi Pauli Vainio, Ph.Lic.

Kuopio University Hospital Diagnostic Imaging Center P.O.Box 100

70029 KYS FINLAND

email: vainiopauli@gmail.com

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Reviewers: Assistant Professor Sebastian Weingärtner Delft University of Technology

Faculty of Applied Sciences Lorentzweg 1

Delft Netherlands

email: S.Weingartner@tudelft.nl

Deputy Head of Department Amedeo Chiribiri King’s College

Department of Cardiovascular Imaging

School of Biomedical Engineering and Imaging Sciences London

United Kingdom

email: amedeo.chiribiri@kcl.ac.uk

Opponent: Professor Hannu Eskola

Tampere University

Faculty of Medicine and Health Technology Kalevantie 4

Tampere Finland

email: hannu.eskola@tuni.fi

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Minna Husso

Quantification of myocardial perfusion using contrast agent enhanced first pass magnetic resonance imaging

Kuopio: University of Eastern Finland, 2020 Publications of the University of Eastern Finland Dissertations in Forestry and Natural Sciences n:o 384

ABSTRACT

Coronary artery disease (CAD) is the most common cause of death globally, with more than 100 million people suffering from it. Accurate quantification of myocardial blood flow (MBF) is important in diagnostics of CAD, and offers important information about the severity and progression of cardiac disease, response to ther- apy and prognosis. Contrast agent enhanced first-pass MRI (CMR) is a promising method for estimatingMBF, because its availability is good, and it does not expose patients to ionizing radiation. This method necessitates monitoring the concentration of contrast agent in blood and myocardium and is based on the assumption that the MRI signal increases linearly with the contrast agent concentration. How- ever, with high contrast agent concentrations this linearity is no more valid. High concentrations may occur in blood pool, where the arterial input function (AIF) for determination of MBFis obtained. Distortion in AIF leads to errors in determined MBFvalues. Another drawback is related to image artefacts, which are regrettably common in MR imaging. The image artefacts may spoil the MRI signal from myocardium, and therefore impede the accurate estimation of MBF.

In this thesis, a novel method – modified dual bolus method - to correct the high concentration arterial input function (AIF) for determination of MBF was introduced. It was tested with 16 patients in studyIand five pigs in studyIIby com- paring the values of K^trans and MBF with corresponding values determined with the traditional dual bolus method and PET. To solve problems caused by image artefacts, the feasibility of three machine learning methods, support vector machine (SVM), random forest (RF) and linear regression (LR), to estimate the values ofMBF from tissue impulse response was investigated in studyIII. In this analysis, also the artefacted myocardial tissue MRI signals were included. In addition, the capability of SVM and RF methods to recognize the artefacted tissue impulse responses was studied. The performance of these methods were tested with five pigs in rest and stress. The estimated values ofMBFwere compared with the corresponding values ofMBFdetermined with PET.

Strong correlation in K^trans values determined with modified dual bolus and traditional dual bolus methods was found in studyI, except in cases when heart rate varied significantly during MR imaging. In studyII, strong correlation in the values of MBF between modified dual bolus method and PET was seen. The modified dual bolus method was found to give more reliable estimates of MFB than the traditional dual bolus method, especially when the heart rate varied during MRI.

In studyIII, SVM was found to produce the most accurate estimates of MBF. RF method managed also well, but performance of LR method was modest. SVM and RF were able to estimate the values ofMBFcorrectly also for the artefacted areas of myocardium. SVM recognized the artefacted tissue impulse responses most reliably.

To conclude, the modified dual bolus method and SVM and RF machine learning

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methods improve the reliability in determination of MBF. SVM is also well suited for detecting the artefacted MRI data.

National Library of Medicine Classification: WG 106, WG 141.5.M2, WG 280, WN 160, WN 185

Medical Subject Headings: Diagnostic Imaging; Magnetic Resonance Imaging; Regional Blood Flow; Myocardium; Coronary Circulation; Contrast Media; Positron-Emission To- mography; Machine Learning; Coronary Artery Disease/diagnosis

Yleinen suomalainen ontologia: kuvantaminen; magneettikuvaus; sydän; verenkierto;

sepelvaltimo; varjoainetutkimus; kontrasti; positroniemissiotomografia; koneoppiminen; se- pelvaltimotauti; diagnoosi

Keywords:Magnetic resonance imaging, Myocardial perfusion, Modified dual bolus, Positron emission tomography, Machine learning

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To my great family

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ACKNOWLEDGEMENTS

This study was carried out during the years 2008-2020 in Department of Clinical Radiology at the Kuopio University Hospital and in Department of Applied Physics at the University of Eastern Finland.

First, I would like to express my whole-hearted gratitude to all my supervisors for their guidance during this Ph.D. thesis. I am grateful to my principal supervi- sor Professor Juha Töyräs, Ph.D., for his professional guidance and enthusiasm. His tireless encouragement: ‘Don’t worry, this will be good!’ were invaluable words during difficult times. I thank Professor Hannu Manninen MD., Ph.D. for his valuable advice and the opportunity to perform this study in the Department of Radiology.

Petri Sipola MD., Ph.D. I thank for guiding me to the world of MRI of heart. His clinical aspect has been real richness in this group. I thank Pauli Vainio Ph.Lic. for his deep knowledge concerning clinical MRI and its applications.

I wish to thank all the co-authors for their contributions in the publications.

Especially I thank Mikko Nissi Ph.D. for his invaluable help with Matlab-codes and deeper understanding of imaging sequences. Isaac Afara Ph.D. I thank for showing me the fascinating world of machine learning. I thank Professor Juha Hartikainen for giving me the opportunity to be involvement in research of different kind of myocardial diseases. Taru Kuittinen MD, Ph.D. I thank for her valuable help and endless optimism concerning our first manuscript. She has shown me the value of hard work and persistence. My thanks go to Simo Saarakkala Ph.D. his open- minded advice concerning our first manuscript. I owe my deepest thanks to Paavo Halonen MD, Antti Kuivanen MD and Miikka Tarkia Ph.D. for their invaluable help with pigs. My special thanks go to Virva Saunavaara and Jarmo Teuho for their help with PET-MRI imaging in Turku PET Centre. Professors Seppo Ylä-Herttuala MD, Ph.D. and Juhani Knuuti MD, PH.D. I thank for giving me the possibility to work with their great research group. I also thank them for giving me the resources, which made this work possible.

I thank radiographers Aarno Klemola and Jari Räisänen for their special help in performing heart MRI study to NHL patients.

I want to express my sincere thanks to the official reviewers of this thesis, As- sistant Professor Sebastian Weingärtner, Ph.D., and Deputy Head of Department Amedeo Chiribiri MD, Ph.D., for their professional review and constructive criti- cism.

I owe my warmest thanks to my colleagues Mervi Könönen, Hanna Matikka, Siru Kaartinen and Sami Väänänen in KYS Radiology. You have always done the business, also on behalf of me, when I have been out of office working with my thesis.

I would like to thank the staff of Department of Clinical Radiology. I am proud to be one of this wonderful team.

I also wish to thank to Mauri and Sirkka Wiljasalo fund, Radiological Society of Finland grant, Kuopio University Hospital (VTR-grant) and Kuopio University Hospital Research Foundation for financial support of my work.

My warmest thanks go to my schoolteachers Arja and Pauli Hakalahti and Heikki Nousiainen. They lit my passion to physics. They also gave me the basic tools to survive in the world of science.

I thank my parents, Kaarina and Tuomo for caring and supporting me when I was child. Giving a good example themselves, they taught me the importance of diligence. This is one of the most important skills that helped me to carry through

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this work. I thank my dear brothers Matti and Antti for growing up with me. We were always together – in work and fun. I also thank the families of Matti and Antti for delighting my life.

I thank my beloved children Elina, Maria, Viljami and Anna for reminding me what really is import in my life. Being your mother has been the most wonderful, interesting, challenging and rewarding project of my life. I also thank Jukka-Pekka, Aapo, Kalle, Eemeli and Helmi for being members of our great family. I thank my grandchildren Joonatan and Eveliina for lighting my life. It is a great privilege to be a proud grandmother of yours!

My greatest and deepest thanks go to beloved Jouni for his tireless care, support and understanding during this project. You are the bedrock of my life. Thank you for standing - and building and renovating - with me.

Kuopio, August 10, 2020 Minna Husso

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LIST OF PUBLICATIONS

This thesis consists of the present review of the author’s work in the field of quantification of myocardial perfusion with MRI and the following selection of the author’s publications:

I M. Husso, P. Sipola, T. Kuittinen, H. Manninen, P. Vainio, J. Hartikainen, S.

Saarakkala, J. Töyräs and J. Kuikka, "Assessment of myocardial perfusion with MRI using a modified dual bolus method,"Physiol. Meas.35, 533–547 (2014).

II M. Husso, M. Nissi, A. Kuivanen, P. Halonen, M. Tarkia, J. Teuho, V. Saunavaara, P. Vainio, P. Sipola, H. Manninen, S. Ylä-Herttuala, J. Knuuti and J. Töyräs,

"Quantification of porcine myocardial perfusion with modified dual bolus MRI – a prospective study with a PET reference,"BMC Med Imaging1, 19, 58 (2019).

III M. Husso, I. Afara, M. Nissi, A. Kuivanen, P. Halonen, M. Tarkia, J. Teuho, V. Saunavaara, P. Vainio, P. Sipola, H. Manninen, S. Ylä-Herttuala, J. Knuuti and J. Töyräs, "Quantification of myocardial blood flow by machine learning analysis of modified dual bolus MRI examination," submitted to Annals of Biomedical Engineering.

Throughout the thesis, these papers will be referred to by Roman numerals.

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AUTHOR’S CONTRIBUTION

The publications selected in this dissertation are original research papers on quantification of myocardial perfusion using magnetic resonance imaging. In all the papers, the author participated in the study design, analysed the images and was the principal author.

In paperI, the author performed all the patient MRI studies and carried out all the data analysis.

In paperII, the author performed part of the animal MRI studies, and carried out all the data analysis of MRI studies.

In paperIII, the author performed part of the animal MRI studies, and carried out part of the data analysis of MRI studies.

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1 Introduction

Heart is organ, which is responsible for circulating blood in the human body. This muscle pump has to work tirelessly throughout life. To fulfil this task, heart muscle - myocardium - must have good delivery of oxygen through coronary arteries. How- ever, coronary arteries may obstruct, causing limited myocardial blood flow, due to several reasons. Constricted coronary arteries are not able to deliver blood efficiently into the myocardium, and myocardium suffers lack of oxygen i.e. ischemia. This may cause dyspnea and chest pain, especially during physical stress, and physical performance may be reduced [1]. Finally, when constriction of coronary artery is serious, the result is life-threatening heart attack i.e. infarct.

In Finland cardiovascular diseases are the single most important cause of death.

There were more than 60 000 myocardial infarcts and minor manifestation of coronary artery disease in 2014. About 21% of these individuals were still in working age [2].

Several methods have been used to evaluate myocardial perfusion(MBF)for diagnosis and follow-up of treatment in cardiovascular diseases. In catheter coronary angiography the severity and location of constriction can be accurately seen in X-ray images. It is possible to dilate the stenosed segment of the artery by balloon angio- plasty during the diagnostic study. That is the great advantage of this method [3].

The disadvantages of this method are invasiveness and exposure of patient to ionizing radiation.

Single photon emission tomography (SPECT) has been used to visualize the regional distribution of blood flow in myocardium. The local perfusion defects, i.e.

ischemic areas, can be discerned from surrounding healthy myocardium [4]. The injection of radioactive tracer is possible to perform also during physiologic stress.

This procedure gives valuable knowledge about the performance of heart during stress and rest, which is the strength of this method [5]. However, it is impossible to detect the areas with lowered perfusion if the perfusion is globally decreased. This is the main weakness of this method, along exposing patient to ionizing radiation.

Positron emission tomography (PET) offers possibility for determination of absolute, i.e. quantitative perfusion [6]. Because of that, PET is considered as the gold standard in determination of myocardial perfusion [7]. PET examination is possible to carry out in rest or during pharmacological stress, which enables evaluation of degree of difficulty of the ischemia. In PET short-lived radioisotopes are often used, which necessitates having a cyclotron on site. This impairs the availability of this method, which is its main weakness, along exposing patient to ionizing radiation.

Computed tomography (CT) is a new method for quantification of myocardial perfusion [8]. The main advantages of CT are its superior spatial and temporal resolution and good availability. A major disadvantage of this method is the high radiation dose [9].

The most recent method for quantification ofMBFis myocardial contrast echocardiography (MCE). This bed side method is inexpensive and widely available, but unfortunately weak inter- and itraobservability and tendency for poor image quality restricts its wider use [10, 11].

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During last decades, contrast agent enhanced first pass magnetic resonance imaging (MRI-FP) has become a potential method in evaluation of myocardial perfusion [12]. This method enables the quantification of myocardial perfusion [13] simultaneously with evaluation of the anatomy, function and tissue characteristics of heart [14,15] without exposing the patient to ionizing radiation. It is possible to con- duct MRI-FP study during pharmacologically induced physiological stress, which gives valuable information about severity of ischemia. Currently, MRI is relatively well available, as well.

Despite of these great advantages, MRI bears few challenges. The quantification of myocardial blood flow necessitates a reliable method to determine the arterial input function, which is measured from blood. This is difficult, because high concentration of contrast agent causes distortion in MR signal of blood during the first pass [16]. If this distortion cannot be corrected, the determined values of myocardial blood flow will be overestimated. The first aim of this thesis was to introduce a new, improved method, modified dual bolus method, to correct the arterial input function. The other challenge of MRI based evaluation ofMBFis that the MR signal is noisy and sensitive to artefacts [17]. These may cause distortion to intensity of MR signal recorded from myocardium, and lead to incorrect values ofMBF. The second aim of this thesis was to apply machine learning analysis to improve the reliability of the determination ofMBF.

In this work, the modified dual bolus method was tested with five pigs and sixteen human patients. The random forest model was tested with five domestic pigs. The human patients were examined with MRI. The pigs were examined with MRI and PET, which was used as a golden standard method in determination of MBF.

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2 Heart and coronary artery disease

Heart is a hollow muscle pump consisting of four chambers and located between the lungs in the thoracic cavity. This rhythmically pumping organ is sized about its owners fist. Together with network of arteries and veins heart comprises the vascular system, which is in responsible for blood circulation. Every day, the average heart beats about 100 000 times and pumps over 4000 litres of blood.

2.1 ANATOMY AND FUNCTION OF HEART

The walls of the heart are composed of cardiac muscle, called myocardium. The heart is divided by septa into right and left halves. Further, the halves are subdi- vided into two cavities, the atrium, and the ventricle [18]. The blood flow between atrium and ventricle is controlled by valves. Valves between right ventricle and pulmonary trunk, as well as between left ventricle and aorta, prevent the reflux of blood into ventricles [19] (figure 2.1).

Figure 2.1: Structure of heart. Right and left atrium and ventricles and valves between them. The great vessels, vena cava, aorta, pulmonary arteries and veins, and their connection to heart. Circulation of blood is illustrated using white arrows.

The blood returns from the systemic circulation through vena cava to the right atrium, and from there through the valve to the right ventricle. After that, the blood is ejected from the right ventricle through the pulmonary valve to the lungs. The pulmonary veins return the oxygenated blood from the lungs to the left atrium, and from there through the mitral valve to the left ventricle. Finally, blood is pumped through the aortic valve to the aorta and back to the systemic circulation [18, 19].

The left ventricular free wall and the interventricular septum are much thicker than

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the right ventricular wall (figure 2.1). This is logical since the left ventricle pumps blood to the systemic circulation where the pressure is considerably higher than in the pulmonary circulation, which arises from right ventricular outflow.

Continuous workload consumes a lot of oxygen. The oxygen supply of myocardium is taken care by two coronary arteries, which begin from the base of the ascending aorta. Coronary arteries run along the outer surface of the heart.

The right coronary artery goes in the right portion of the coronary sulcus (re- cess between right atrium and ventricle) down, towards the apex of the heart as the posterior descending branch. Most of the circulation of free wall of the right ventricle arises from this posterior descending branch. Another branch of right coronary artery, diverges and follows the anteroinferior border of the heart. This marginal branch supplies branches to both surfaces of the right ventricle (Figure 2.2). It also gives small branches to the right atrium and to the part of the left ventricle which adjoins the posterior longitudinal sulcus [18, 20].

Figure 2.2:Coronary arteries of the heart.

The left coronary artery, being larger than the right, branches into anterior descending and circumflex branches. The anterior descending branch goes down towards the anterior longitudinal sulcus. It proceeds down along the longitudinal sulcus, and descends to the notch of cardiac apex. The anterior descending branch gives branches to both ventricles. Most of the blood supply to the interventricular septum is provided by the left anterior descending coronary artery and its many branches. The circumflex branch follows the left part of the coronary sulcus, running first to the left and then to the right towards the posterior longitudinal sulcus, where it meets the marginal branch of right coronary. The circumflex branch gives branches to the left atrium and ventricle (Figure 2.2). There are free anastomoses between the muscular branches of the two coronary arteries inside the myocardium [18, 20].

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2.2 CORONARY ARTERY DISEASE

Coronary artery disease is caused by progressive constriction of coronary arteries due to atherosclerotis process. The most important risk factors for CAD are hyper- tension, hypercholesterolaemia, diabetes, sedentary lifestyle, obesity, smoking and genetic factors [21]. During development of CAD, lipids accumulate into the vascular walls and maturing into atheromatic plaque, gradually obstructing the lumen of the artery. The progress of atherosclerosis can be classified into different types, i.e.

stages [22].

Stage 1. First, low density lipoprotein (LDL) accumulates in the intimal layer thickening it [23]. This is called as xanthomata or fatty streak (figure 2.3 a), which can either progress into a mature coronary plaque or regress over time [24].

Figure 2.3:Progress of coronary artery disease.

Stage 2. The intimal layer of arteria continues to thicken. The fatty streaks collect macrophages, which phagocytose the lipid droplets. Then macrophages transform to foam cells (figure 2.3 b), which is the first visible presentation of atherosclerosis [25].

Stage 3. Pathological thickening of intima leads to its transformation into an actual fibroatheroma by promotion of atherosclerotic macrophages [26]. The fibroatheroma matures further, calcification increases, and lesion protrudes into artery lumen (figure 2.3 c).

Stage 4. The core of lesion has grown large, and its fibrous cap has become thinner because of the loss of smooth muscle cells, extracellular matrix and inflam- matory processes. Hemorrhage and/or calcification are often present in the plaque core (figure 2.3 d). These kind of lesions are most likely to rupture [22]. In this stage, the patients often have angina pectoris [27].

Stage 5. The thin cap of fibroatheroma has now ruptured (figure 2.3 e). When the hemostatic material of the lesion core communicates with blood, it results in the formation of a thrombus [22, 24]. If the thrombus is occlusive, it may cause infarction, or even sudden death. In case of non-occlusive thrombus, the symptom is unstable angina pectoris [27].

Coronary artery disease is treated according to duration of disease and degree of severity in the following order: change of lifestyle, medication, and finally percutaneous coronary intervention or bypass operation.

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3 Conventional methods for assessment of myocardial perfusion

3.1 CORONARY ANGIOGRAPHY

Coronary angiography is considered as the gold standard of coronary imaging [28, 29]. For coronary angiography a flexible diagnostic catheter is navigated from radial or femoral artery puncture to coronary artery ostium during fluoroscopic guidance.

X-ray angiography is performed by injecting radio-opaque iodine contrast agent to the artery. While detecting an obstrution, it is also possible to traverse it with a thin guide wire and dilate with a balloon catheter or place a metal stent, if needed (Percutaneous coronary intervention, PCI). PCI has been found effective specially to relieve the symptoms of angina pectoris with stable coronary artery disease [30].

Determining which lesions require revascularization is important. This is possible by intravascular methods. Fractional flow reserve (FFR) predicts whether percutaneous intervention will benefit a patient. FFRshows how far maximal myocardial blood flow is limited from epicardial stenosis [31]. To measure FFR a wire, equipped with pressure sensor, is inserted beyond the stenotic lesion. Then, maximal hyperemia is achieved pharmacologically, and the mean pressure is measured simultaneously from aorta (Pa) and coronary beyond the lesion (Pb). FFR-index is the ratio of measured pressures (Pb/Pa) [28, 32, 33]. FFR-index lower than 0.75 indicates ischemia-producing stenosis, and should thus be revascularizated [32].

Another tool for characterization of plaques is intravascular ultrasound (IVUS).

A small ultrasound transducer is mounted on the tip of a catheter, which is inserted at the level of a stenotic lesion in the coronary artery. Then the transducer is pulled through the stenotic lesion and reflected and backscattered ultrasound is used to form a high resolution image of the lesion [29]. Typically plaque rupture, thrombus, positive remodeling, attenuated plaque, spotty calcification, and thin-cap fibroatheroma can be separated [34]. IVUS has been found to be useful in assessing vascular geometry and morphology, and quantitative composition of atherosclerotic plaque before the PCI [29, 34, 35].

While coronary angiography, IVUS and especially optical coherence tomography (OCT) produce images of coronary arteries with high temporal and spatial resolution, they do not give any information about the perfusion in myocardial tissue.

3.2 POSITRON EMISSION TOMOGRAPHY (PET)

Positron emission tomography (PET) is considered as the gold standard in imaging of myocardial perfusion. PET is based on using a radioactive tracer injected as a bolus into circulation. From blood the tracer diffuses through capillary wall into the myocardium. The distribution of radioactive tracer is imaged dynamically using a PET scanner. Therefore, PET enables the determination of absolute, i.e. quantitative perfusion with spatial resolution of 5 mm [6, 36]. Quantitative perfusion (expressed inml/min/g) enhances the ability to detect significant myocardial disease. It is also

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useful in the assessment of coronary microvascular dysfunction [37].

Several radioactive tracers are in use for determination of myocardial perfusion.

Well validated radiowater, H215O is a perfect tracer for determination of quantitative myocardial perfusion. It is metabolically inert, freely diffusible agent, and independent of the metabolic state of the myocardium. The extraction fraction of H₂¹⁵O is not dependent on flow rate, which is a significant benefit [36,38–40]. While H₂¹⁵O is superior as myocardial perfusion tracer, the use of it requires specific conditions. The half-life of ¹⁵O is short, 2.4 min, and the production of ¹⁵O requires cyclotron on-site. Because of these two facts the straight pipeline from cyclotron to PET camera is necessary. These arrangements are costly, and often challenging to build.

13N-ammonia is another well validated tracer for myocardial perfusion. The extraction of¹³N-ammonia is not complete, and flow-dependent correction at high perfusion is needed [36, 38]. The half-life of¹³N is 9.8 min, which requires the use of cyclotron on-site. However, the specific pipeline for transfer of the tracer is not needed like with¹⁵O.

82Rb is the most commonly used radiotracer in cardiac PET imaging, and it has been found reliable tracer to measure myocardial perfusion [41]. ⁸²Rb is available from a ⁸²Sr/⁸²Rb generator and cyclotron is therefore not needed. The half-life of ⁸²Rb is very short, 75 s [38]. However, the extraction of ⁸²Rb is nonlinear, and strongly dependent on flow. Because of that, correction is needed [36, 41, 42].

18F-Flupiridaz is the newest tracer for determination of myocardial perfusion [36, 38]. The main advantage of this tracer is its long half-life, 110 min. This enables transfer from cyclotron to another imaging centre. The extraction is linear but flow- dependent, which needs to be corrected for. However, this tracer has shown promise in myocardial PET imaging [43].

Current PET scanners are equipped with a CT component. These hybrid PET/CT devices offer almost simultaneous anatomical and functional information within a single scanning session [44]. Also, CT provides information about the attenuation of radiation. This information can be used to correct the PET imaging data, which improves the reliability of the PET study.

3.3 SINGLE PHOTON EMISSION COMPUTED TOMOGRAPHY (SPECT) Single photon emission tomography (SPECT) has been used for decades to visualize the regional distribution of myocardial perfusion. Radioactive tracer is administered into patient’s circulation, and after a while, tracer has accumulated to myocardium with relation to perfusion at that moment. Distribution of radioactive tracer can be imaged using a gamma camera, and the final images can be reconstructed three-dimensionally with spatial resolution of 10 mm. SPECT images are analysed qualitatively: The perfusion defects are detected based on comparison with the surrounding healthy tissue. However, this is the main weakness of this method:

in case of balanced ischemia, i.e. globally decreased myocardial perfusion, the qualitative analysis does not enable detecting the decreased perfusion [45, 46]. However, perfusion defect is a strong prognostive indicator of cardiac events [47].

Myocardial perfusion SPECT can be performed in a ECG-gated manner. In this method, the RR-period of one heart beat is divided into shorter periods. The imaging data is acquired in these periods, and reconstructed after imaging. Gated myocardial SPECT enables measurement of left ventricular ejection fraction (LVEF),

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segmental wall motion, and absolute left ventricle volume [48].

The most common radioactive tracers used in myocardial perfusion SPECT are

201Tl and^99mTc. ²¹⁰Tl has relatively low energy of the predominant photo peak, 68

± 10% keV, and long half-life, 73 hours. Correspondingly, photo peak of^99mTc is 141 keV and half-life 6 hours, which decreases significantly the radiation dose of a patient. Moreover, the cellular uptake of those tracers is different. ²⁰¹Tl uptake is associated with active Na+, K+ ATPase transport system. Because of that, only the active myocardium does accumulate the tracer, and is visible in images. ^99mTc uptake is related to the transmembrane potential, and is thus passive. Therefore, the areas, with circulation are visualized [49]. However, both tracers have been found reliable for measurement of myocardial perfusion, LVEF, segmential wall motion and left ventricle volume [49, 50].

3.4 COMPUTED TOMOGRAPHY

Recent technological advancements have made computed tomography (CT) potential method for diagnostics of cardiovascular diseases. Sufficient coverage of detector and fast rotation time make possible the fast imaging with high spatial resolution.

CT angiography (CTA), has become a reliable modality for the exclusion of coronary artery disease [51, 52]. CTA imaging allows robust qualitative and quantitative assessment of atherosclerotic plaques. Detecting the morphological differences between the stable and unstable plaques might provide a tool to classify these lesions, which would be useful for the identification of the risk of heart attack [51, 53].

While CTA is widely used, the assessment of myocardial perfusion with CT is a very new technique. CT provides number of protocols for evaluation of myocardial perfusion in qualitative, semi-quantitative or quantitative manner [54]. In a single-phase method, the contrast agent is injected into circulation, and after that CT imaging of whole heart is performed. This method provides a snapshot image of iodine contrast distribution at a particular moment. Local perfusion defects can be observed similarly as with SPECT. Dual energy CT (DECT) is a separate single-phase CT technique that enables quantifying iodine concentration, providing semi-quantitative measurements of myocardial blood supply [9, 55].

In the dynamic method X-ray positive contrast agent is injected intravenously, and dynamic CT is performed simultaneously. Thus, the distribution of contrast agent as a function of time can be determined, and the changes in signal intensity over time. Especially, determination of quantitative perfusion of left ventricle has been found reliable [56, 57]. However, the different tracer kinetic methods give significantly different values, which has to be taken into consideration when determining the thresholds for diagnostic purposes [58,59]. The radiation dose of patient is considered high in the dynamic method. Also, the radiation dose of stress-rest protocol is about 10 mSv. However, the optimal use of radiation dose reducing techniques, for example variable tube current and variable temporal sampling reduce the dose [60, 61]. At the moment there is lack of solid scientific evidence about the clinical feasibility and diagnostic accuracy of the dynamic CT method. Because of that, it is not in wide clinical use. Currently, the combination of coronary CTA and CT myocardial perfusion imaging is considered as effective procedure in detection of coronary artery disease (CAD) [9, 62].

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3.5 ULTRASOUND

The most recent method for quantification of MBF is myocardial contrast echocardiography (MCE). This method was first introduced by Wei et al [63], and validated by Vogel et al [64]. In this method, the contrast agent contains gas-filled microbubbles, which interact to acoustic waves producing a detectable signal. Contrast agent is administered intravenously as a continuous infusion. When the contrast agent concentration has achieved a steady state, all the microbubbles are destroyed using a specific ultrasound pulse. Immediately after that, the dynamic imaging is used to detect the reappearance of contrast agent into the blood and tissue. Therefore, the changes in signal intensity over time can be determined to assess the quantitative values of MBF. MCE has been shown to provide a good correlation with PET-derivedMBFin humans [63, 64]. MCE has also been used for determination of coronary flow reserve (CFR) [65,66] and coronary flow velocity reserve (CFVR) [67].

The main advantages of MCE are the good availability and low costs. Also, the lack of ionizing radiation is benefit of this method. However, many limitations hinder the wider clinical use of MCE. First, echocardiography is operator dependent. Second, the image quality may be impaired by obesity, respiratory motion, and parenchy- mal lung diseases. Destruction of the microbubbles in the near field can also cause swirling artefacts affecting the determinedMBFvalues [10, 11].

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4 Physics of cardiac MRI

4.1 SIGNAL EQUATIONS AND RELAXATION PROCESSES

MRI-imaging is based on nuclear magnetic resonance. Nuclei having odd number of nucleons have a feature called spin angular momentum, which interacts with external magnetic field(B₀). The most common nucleus is hydrogen nucleus¹H, which is a single proton. In the external magnetic field, the energy level of ¹H is quantized (spin up and spin down). The energy states of spins can be manipulated to higher energy level involving the application of a pulse of radio frequency (RF) energy. The spins rapidly return to their original lower energy state, loosing the extra energy via spin lattice relaxation. The resultant vector (M), which describes the sum of magnetic moments of spins, will generate a changing magnetic field that induces a measurable signal. The MRI image is formed from this signal using the Fourier transform.

The external magnetic field,B0causes a change inM[68]:

dM

dt =γM×B0, (4.1)

whereγ= gyromagnetic ratio (=2.675×10⁸rad^-1 T^-1 for¹H).

In static B₀ theMmoves circularly about B₀. This motion is called precession.

The frequency of precession is called Larmor frequency (ω0), which depends on amplitude ofB0[69] as follows

ω0=γB0. (4.2)

When external energy, in a form of radio frequency pulse (excitation pulse) is targeted to spins, the orientation ofMis deviated from its equilibrium state. Imme- diately after the excitation pulse has ended,Mstarts to return back to its equilibrium state. This time-dependent change ofMis described by Bloch equations [68, 70]

dMx

dt =ω0My− ^M^x

T₂ (4.3)

dMy

dt =−ω₀Mx− ^M^y

T2 (4.4)

dMz

dt = ^M⁰−Mz

T₁ , (4.5)

where Mx,My and Mz are the components ofM.T1and T2are the relaxation time constants of longitudinal and transverse relaxation. The equations 4.3-4.4 can be solved as follows

Mx(t) = [Mx(0)cosω0t+My(0)sinω0t]e⁻^T^t² (4.6) My(t) = [My(₀)cosω₀t+Mx(₀)sinω₀t]e⁻^T^t² (4.7)

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Mz(t) = [Mz(0)e⁻^T^t¹ +M₀[1−e⁻^T^t¹]. (4.8) T₁relaxation, i.e. longitudinal relaxation, describes the energy exchange between a spin and its surroundings, i.e. lattice. The time constantT₁characterizes the rate of the energy change, and the decay of transverse magnetization (Mz) towards the equilibrium state. T2 relaxation, i.e. transverse relaxation, describes the interaction between spins, and loss of transverse magnetization (Mxy). T1 and T2 relaxations occur simultaneously. The amplitude of the measured signal depends on many parameters, and can be written as follows, [69]

S=ρ×e⁻^TE^T² ×[1−e⁻^TR^T¹], (4.9) where (ρ) is spin density, TE is the time to echo and TR is time to repetition. These pulse sequence parameters are described later.

4.2 SATURATION RECOVERY SEQUENCE FOR CARDIAC IMAGING

The quest for determining myocardial perfusion in quantitative manner places several requirements on the MR imaging sequence utilized. First, the temporal resolution must be adequate: at least one image per RR-interval. Second, the images should have maximalT₁-contrast to detect the changes in contrast agent concentration. Third, the spatial resolution should be sufficient to detect the myocardial ischemia. Fourth, images should be free of artefacts, caused for example by the move- ment of beating heart, by breathing, or by inhomogeneities of magnetic field [71,72].

Spoiled gradient echo saturation recovery (SR) sequence meets these requirements the best. In the beginning of SR sequence, a 90^◦preparation pulse is applied.

This turnsMinto xy-plane. Then,Mis allowed to relax during the saturation recovery time (ST). During ST, the longitudinal relaxation happens in each tissue component according to their individualT1relaxation times. After the ST, an excitation pulse (α < 90^◦) is performed, and signal is acquired. New α-pulse is performed before every phase encoding, which are repeated until the whole image matrix has been acquired (Figure 4.1). However, before the newα-pulse, the residual transverse magnetization is eliminated using a high-amplitude spoiler gradient pulse [73]. As soon as the image of one slice is ready, imaging of the next slice begins with a 90^◦ preparation pulse. The time between the excitation pulses is called the repetition time (TR) [73, 74].

The American Heart Association (AHA) recommend that to ensure the coverage of left ventricle imaging, three short axis images should be acquired from basal, mid and apical regions [75]. To achieve this within a single RR-interval, the imaging sequence has to be accelerated. First, the excitation flip angle (α) must set low, typically 30^◦ or less. In that case, the longitudinal magnetization disappears soon allowing the TR to be reduced to shorter than 10 ms. This is necessary to be able to acquire several short axis images during one RR-interval. Time between echoes (TE) must be also set very short, 1-3 ms [74]. Saturation time is typically set to be around 100 ms [71]. Longer saturation time would maximize the T1-contrast, but would also take up too much of the RR-interval and thus limit the coverage or spatial resolution, or the maximum heart rate compatible with the acquisition of one image per RR-interval.

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Figure 4.1: The chart of spoiled gradient echo SR sequence. Three slices are imaged during one RR-interval. After saturation preparation pulse (90^◦) follows the saturation time (TS), and thereafter multiple excitation RF-pulses (α^◦). Echo signals are acquired after theα-pulses. TS is the time between the preparation pulse and effective slice time.

The spoiled gradient echo SR sequence is the most widely used sequence for determination of quantitative myocardial perfusion. However, there are also other sequences, such as inversion recovery (IR) turboflash sequence, which has been used successfully for semiquantitative determination ofMBF[76,77]. The drawback of IR sequence is its poor time resolution and tendency to yield negative signal intensities from certain tissues. Also, when an IR sequence is used, contrast becomes dependent on the RR cycle, making the subsequent postprocessing very challenging and causing variable signal in case of arrhythmias. These features cause trouble in quantification of MBF. Balanced steady state free precession (bSSFP), and hybrid echo planar (Hybrid EPI) sequences are also used for myocardial perfusion imaging.

The main advantages of bSSFP sequence are its speed and high signal to noise ratio due to combined signal of several consecutive excitations. However, this sequence is very sensitive to field inhomogeneities, and thus prone to image artefacts [72,74]. In hybrid EPI sequence multiple lines of k-space are rapidly acquired after the single alpha pulse. This makes very fast imaging possible. However, the main weakness of hybrid EPI sequence is its low contrast to noise ratio (CNR) compared with spoiled gradient echo SR and bSSFP sequences [71, 78].

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4.3 CONTRAST AGENTS

Contrast of MR image can be enhanced using contrast agents, which are usually administered intravenously. Contrast agents decreaseT₁andT₂relaxation times of the tissue, and cause increase or decrease of measured signal. Thus, presence of contrast agent can be seen as a bright or dark area in an MR image.

Paramagnetic gadolinium (Gd) compounds are the most widely used contrast agents in MRI. It is toxic in its elemental state, but it can be chelated to a ligand such as diethylene-triamine penta-acetic acid (DTPA). After intravenous injection, Gd-DTPA is distributed with blood to all perfused tissues. In most organs it diffuses rapidly from blood into the tissue interstitial space.

Gadolinium has seven unpaired electrons, which form weak local magnetic field.

This local magnetic field speeds up the spin-lattice interaction and energy transfer, which causes the decrease of T1and T2 relaxation times. When discussing on the change of relaxation time caused by a contrast agent, relaxation rate (R) is a practical quantity. Relaxation rate is defined as follows [70, 79]

R1= ¹

T1 (4.10)

R₂= ¹

T2. (4.11)

Further, the change in relaxation rate can be expressed as follows:

∆R= (R⁰−R) =rC, (4.12)

where R’ is deceased relaxation rate, Cis the concentration (mmol/kg) of contrast agent in a tissue, andris relaxivity (mmol⁻¹ s⁻¹). Relaxivity describes the change of relaxation rate as a function of contrast agent concentration. Relaxivity can be measured, and it is dependent on several factors, for example tissue composition and temperature [79, 80].

Another species of contrast agents are the super-paramagnetic iron oxide (SPIO) contrast agents, developed to increase T2-contrast. These contrast agents cause shortening of T2-time, and thus loss of signal in T2-weighted images [70]. SPIO- contrast agents are mainly used for liver imaging.

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5 MRI-based methods for assessment of myocardial perfusion

5.1 COMPARTMENT MODEL

Modelling of myocardial perfusion is based on functional spaces of myocardial tissue: blood pool inside the arteries, and extravascular, extracellular space (EES) in tissue. These functional compartments are separated by endothelium, through which the contrast agent i.e. tracer is able to diffuse with the rate determined by volume transfer constantK^trans (Figure 5.1), which is related toMBFandEas follows [81]

K^trans= MBF·E. (5.1)

F

Figure 5.1: Distribution of contrast agent (black dots) from arteria through vessel wall into the myocardium extravascular extracellular space.

Extraction is the proportion of tracer that transfers from the intravascular space into the EES, and is defined as follows:

E= ^C^a−Cv

Ca , (5.2)

where Ca = tracer concentration of arterial blood, andCv= tracer concentration of venous blood. If the permeability of the capillary endotelium is high (E∼=1), the only factor that limits the diffusion from blood pool to EES is MBF (flow-limited situation) [82]. This situation is dominant with low values ofMBF(figure 5.2).

The diffusion of a tracer through endothelium may also be limited by the permeability (permeability-limited situation). In that case, the tracer flows passively from blood into the EES through the microscopic pores or defects in the capillary walls. This situation is dominant with high values of MBF (figure 5.2). Between flow-limited and permeability-limited situations, there is situation in which diffusion of a tracer is limited by bothMBFand permeability. This intermediate situation is dominant with values of MBF that are typical for myocardial perfusion during

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Figure 5.2:Relation between myocardial blood flow (MBF) andK^trans.

stress (figure 5.2) [83]. Because of that, only this MBF- and permeability-limited situation is elaborated in this following.

The change of tracer concentration in tissue can be described as follows [82]:

dCt

dt =K^trans(Cp−^C^t ve

) =K^transCp−kepCt, (5.3) whereCt=tracer concentration in tissue,Cp=tracer concentration in plasma,ve=volume of EES per unit volume of tissue and kep=rate constant (min⁻¹) between EES and blood plasma. With the initial conditions att=0,Cp=Ct=0. The solution of equation 5.3 is:

Ct(t) =K^trans Z _t

0 Cp(τ)e^−k^ep^(t−τ)dτ (5.4)

When the tracer is administered as a short bolus, the tissue impulse response can be described as follows:

h(t) =K^transe^−k^ep^t. (5.5)

Therefore, it is possible to present the equation 5.3 as follows:

Ct(t) = Z

Cp(τ)h(t−τ)dτ (5.6) whereτ=the mean residence time of a tracer. Furthermore, the equation 5.6 can be presented as convolution

Ct(t) =Cp(t)⊗h(t). (5.7) It is possible to determine the tracer concentrations of tissue and blood plasma from MR images. Therefore, K^trans may be determined from tissue impulse re-

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sponse. K^transis related to MBF(equation 5.1). Therefore,K^trans can be considered as a perfusion marker, incorporating valuable clinical information.

Larsson et al first introduced a method to determine K^trans for Gd-DTPA diffusion across the capillary membrane in the human myocardium with magnetic resonance imaging [84]. This method has been widely used [85–87]. K^trans has been compared withMBFdetermined with microspheres [88] and with PET [89]. In these studies K^trans was found to be a good estimate of MBF at rest, but at stressK^trans was found to underestimateMBF.

5.2 DECONVOLUTION METHODS

Determination of tissue impulse response necessitates the use of deconvolution.

However, due to noisy MRI-signal, deconvolution yields mathematically unstable solution. To solve this problem, Fermi-function deconvolution and model independent deconvolution may be applied.

5.2.1 Fermi function deconvolution

Axel et al [90] introduced the Fermi function method for the analysis of brain perfusion by means of computed tomography. This method was later applied and evaluated into the determination of myocardial perfusion [13]. The Fermi method is based on the assumption that the shape of Fermi function reminds the shape of tissue impulse response. The Fermi function is used as a deconvolution constraint with a non-linear linear least square fitting algorithm. The amplitude of tissue impulse response att=0 corresponds to theMBF. Fermi function works well if the analysis contains only the first pass of the tracer. Fermi function constrained deconvolution has been widely used for quantification of myocardial perfusion [91–96].

5.2.2 Model independent deconvolution

Tissue impulse response may be determined also using model independent deconvolution. That method does not assume any spesific shape of tissue impulse response. The model-independent deconvolution is based on central volume princi- ple introduced by Zierler et al [97]. Jerosch-Herold et. al [98] first introduced a model-independent deconvolution method to estimate myocardial perfusion DCE- MRI. In that workh(t)was parametrized as a sum of shifted B-spline functionals.

This method has been used in several studies [99–102], and it has been validated with fluorescent microspheres [98]. Also parametrization ofh(t) using a ’consoli- dated’ set of gamma variate basis functions [103], and iterative minimization [104]

have been used with the model-independent deconvolution method.

Due to noisy MRI data, the solution of the tissue impulse response is oscillat- ing. To avoid this undesired oscillation, the solution of deconvolution needs to be stabilized. The most widely used technique is the Tikhonov regularization technique [105], which has been used in various studies [98–104].

5.3 MACHINE LEARNING METHODS

Machine learning (ML) is an aspect of artificial intelligence (AI) where the aim is to enable computers learn automatically from observations and data based on patterns (features) within a given data set without human intervention or assistance. In the

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beginning of the learning process, a set of training data with known input (independent variables) and output (dependent variable) is fed to a learning algorithm.

The algorithms learn by analysing and identifying patterns in the training data set, eventually enabling computers to take decisions autonomously based on learned features from the trained dataset. The resulting model is an internal representation of the relationship between input and output data. This new model can then be used to predict the output of data from new samples. With the capacity made available by ML, researchers can now take on complex problems that would be difficult – or almost impossible – for humans to solve using traditional analytical techniques.

With recent advances in technology, ML algorithms can now enable computers to search and quickly interpret large amounts of data – text and image data – within a patient’s electronic medical record and detect patterns of certain diseases. There- fore, it can be used, for example, to support disease diagnosis in many medical situations. With the widespread use of clinical decision support systems (DSS) in medicine [106], specialized medical fields with large image datasets, such as radiology, cardiology, and pathology, may strongly benefit from ML. Recently, ML are being adapted for medical image analysis to identify abnormalities, and map out regions that need attention. In the field of medical imaging, ML has so far been applied mainly for fully automated segmentation of images [107, 108]. Several ML algorithms have been introduced to solve different kind of problems. In this study, support vector machine and random forest methods were adopted. For comparison, traditional linear regression was also used.

5.3.1 Support vector machines

Support vector machines (SVM), are methods used for classification and regression.

Classification is a procedure where the goal is to distinguish data points that belong to similar categories in a dataset. Classification is based on the concept of decision planes (hyperplanes) that define decision boundaries [109]. A decision plane is one that separates the data points into different groups, i.e. classes. The decision boundaries are margin planes that are parallel with the decision plane. The distance between decision plane and decision boundaries is set to be maximal so that no data points is located between decision boundaries. The vectors that determine the distance between the decision boundaries are called support vectors. A schematic representation of SVM is presented in figure 5.3a. Most classification tasks, however, are not that simple, and often involves more complex structures. In such situation, kernels (figure reffig:SVM1b), are needed for optimal separation of the classes in the data, i.e., correctly classify new objects (test objects). Since the data in these cases are not linearly separable, decision planes may be curved shaped kernels, called soft-margins. The effectiveness of SVM depends on selection of the optimal kernel, the kernel’s parametersγ, and soft margin parameter C. The parameterCcontrols the trade-off between errors of the SVM on training data and margin maximization andγdescribes the shape of kernel.

SVM is also capable of solving regression tasks [110]. In the case of regression, the goal is to seek and optimize the hyperplane to define it as the line that will enable prediction of the continuous value or target value. Unlike SVM for classification, it is desirable for the data points to be as close as possible to the hyperplane. A margin of tolerance (e) is set in approximation to the SVM which is set beforehand (figure 5.4a). Sometimes all the data points may not be contained within the margin of tolerance. The distance between the margin of tolerance and of those data pointsξ

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Hyperplane Support

vector

Decision boundaries

Hyperplane

New sample

kernel

a b

Figure 5.3: Schematic example of classification. a) Linearly separated data. The objects belong either to class Gray or Black. The separating line defines a boundary on the right side of which all objects are Gray and to the left of which all objects are Black. Any new test object (White circle) falling to the right is labeled, i.e., classified, as Gray (or classified as Black should it fall to the left of the separating line). b) Non- linearly separated data. Gray and Black objects are now separated using separating plane instead of line.

(figure 5.4b) can be minimized using cost functions.

0 +

- - - -

-

a b

0 +

-

Figure 5.4: Schematic example of SVM regression. a) The hyperplane and the margins of tolerance (-eand +e) are fitted to data. b) The distance of ’outlier’ data point from the margin of tolerance (ξ) are minimized using cost functions.

5.3.2 Random forest

Random forest is a learning algorithm that can be applied for classification, regression and other tasks. The method operates by constructing a multitude decision trees at training time [111]. The decision trees are built node by node, which represents a classification or decision. Random forests consist of multiple single decision trees each based on a random sample of the training data. A single decision tree is built using a random sample of the complete training data set. Decision trees learn from data to construct a set of “if-then-else” decision rules for classification. A tree is allowed to grow large enough to ensure the proper classification of new data. The training data is then returned to the pool of training data set, and a new decision tree is created using a new random sample of training data set [112]. After a large number of trees are built using this method, each tree "votes" or chooses the class,

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and the class that receives the most votes by a simple majority is the "winner" or predicted class (figure 5.5).

Tree 1 Tree 2 Tree n

Class artefacted

Class non-artefacted

Class artefacted

Majority-voting

Final classification:

artefacted

. . . New sample

Figure 5.5:Graphical description of random forest method classification task. The paths from root to leaf represent classification rules. Every decision node (black or gray circle) has two or more branches. Each branch represents the outcome of the test on an attribute, which is done in the node. The test sample goes through the tree (arrows), and it is tested in every node. Finally, it reaches the leaf node, which represents a class label. Every sample goes trough the all the trees of forest, and all thentrees produce the vote in which class the sample should be classified. The majority number of votes determines the final class of the sample.

Tree 1 Tree 2 Tree n

Prediction 1 Prediction 2 Prediction n

Mean of all predictions

Prediction

. . . New sample

Figure 5.6: Procedure of random forest regression. The test sample goes again through all the n trees. In every node (black or gray circle) the result of the test designates the branch to follow (arrows). In the case of regression, the leaf node represents numerical value which is the prediction for the sample. The actual estimation is the mean of all the n predicted values.

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Overfitting is avoided by restricting the depth of the trees. This ensures also that the trees test only the features that are considered to be the most important.

Because the trees in the forest are different, they focus on the different features, which improves the accuracy of the results.

Random forest method can be also used for regression tasks. In that case, the mean of the results produced by all the trees of the forest is used as prediction (figure 5.6).

5.3.3 Linear regression

Linear regression (LR) is a basic and commonly used type of predictive analysis [113]. LR is used to find linear relationship between target and predictors. The relationship between target and predictors is formed:

y=ax+b, (5.8)

where ais the slope andb is the y-intercept. The basic idea is to obtain a line that best fits the data. This means, that the vertical distance between a data points and the regression line, i.e. residuals, are as small as possible (figure 5.7).

x y

residuals y = ax +b

target

predictor

Figure 5.7:Graphical presentation of the linear regression method.

As soon as LR model (equation 5.8) is created, it can be used to predict values (y) for new samples (x).

5.4 NONLINEAR RELATIONSHIP BETWEEN SIGNAL INTENSITY AND CONTRAST AGENT CONCENTRATION

For determination of h(t), the concentration of tracer in blood (Cp) and in tissue (Ct) must be known as a function of time. Quantification of tracer concentration is based on enhancement in signal intensity of MR image, which is caused by contrast agent. The concentration of contrast agent in the myocardium may be determined using a model, which is based on extraction of kinetics of a tracer [114]. However, the main challenge is to control theT2*-effect [16]. TheT2*-effect is a phenomenon where high concentration of contrast agent causes local disruption in magnetic field.

This leads to shortening of T2-time, and further decrease of signal intensity in T1- weighted images. During the first pass, concentration of contrast agent in blood pool is high. Due to high concentration of contrast agent, theT₂*-effect causes remarkable

Quantification of myocardial perfusion using contrast agent enhanced first pass magnetic resonance imaging

Dissertations in Forestry and Natural Sciences

MINNA HUSSO

Quantification of myocardial

perfusion using contrast agent

enhanced first pass

magnetic resonance imaging

Minna Husso

QUANTIFICATION OF MYOCARDIAL PERFUSION USING CONTRAST AGENT

ENHANCED FIRST PASS MAGNETIC RESONANCE IMAGING

To my great family

TABLE OF CONTENTS

1 Introduction

2 Heart and coronary artery disease

3 Conventional methods for assessment of myocardial perfusion

4 Physics of cardiac MRI

5 MRI-based methods for assessment of myocardial perfusion

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