Creating hemodynamic atlas of aorta

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Creating hemodynamic atlas of aorta

Author: Pierre-Loïc Felter Supervisor: Merih Cibis Examiner: Petter Dyverfeldt LiU-IMT-TFK-A-M–17/–SE

A thesis submitted in fulfillment of the requirements

for the double degree in Biomedical Engineering and Electrical Engineering in the

Cardiovascular Magnetic Resonance Group Department of Medical and Health Sciences - IMH

Linköping University

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Linköping University

Abstract

Cardiovascular Magnetic Resonance Group Department of Medical and Health Sciences - IMH

Biomedical Engineering and Electrical Engineering Creating hemodynamic atlas of aorta

by Pierre-Loïc Felter

Turbulent blood flow is involved in the pathogenesis of several cardiovascular diseases. While it is known that turbulence is present in patients with obstructive disease in the major vessels, the magnitude and impact of turbulence in the normal heart and aorta is still relatively unexplored. Besides, existing analysis method of the blood flow is a labour intensive process and requires excessive amount of time.

A method to automatically create hemodynamic atlases has been developed, using 4D Flow magnetic resonance imaging (MRI), a powerful tool to measure blood flow characteristics. The resulting atlases show the expected blood flow characteristics in the aorta for a group of similar subjects.

Application of the method in healthy young and healthy old has shown significant differences in kinetic energy and turbulent kinetic energy in the aortic flow.

Résumé

L’écoulement turbulent du sang dans le coeur et les grandes artères est impliqué dans l’apparition de maladies cardiovasculaires. Tandis que la présence d’un écoule-ment turbulent a été montré chez les patients ayant des maladies obstructives des grands vaisseaux sanguins, l’existence et l’impact des turbulences dans l’aorte et le coeur sains sont des aspects encore relativement peu connus. De plus, les méthodes actuelles d’analyse de l’écoulement sanguin sont des processus longs et très coûteux en temps.

Une méthode permettant la création d’atlas hémodynamiques a été développée dans le cadre de ce projet. Elle utilise une technique avancée d’imagerie par réso-nance magnétique appelée "4D Flow MRI", permettant la mesure des propriétés de l’écoulement sanguin. Les atlas hémodynamiques issus de la méthode développée montrent les propriétés "normales" attendues de l’écoulement sanguin dans l’aorte.

L’utilisation de cette méthode chez les sujets sains, jeunes et âgés, montre des différences importantes en énergie cinétique et énergie cinétique turbulente dans l’écoulement du sang dans l’aorte.

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group aiming to gain incremental insight into the cardiovascular system in health and disease by development and application of novel imaging methods for quantification of blood flow, wall motion, and tissue characterization. Part of Linköping University and located at the University Hospital in Linköping, the research group works in close collaboration with the Center for Medical Image Science and Visualization (CMIV). The research group works on extending the diversity of magnetic resonance imag-ing and usimag-ing it to study blood flow patterns, turbulence intensity, myocardial defor-mation, and tissue characterization, but makes also use of other imaging modalities like ultrasound and computer tomography.[1]

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and help all the way through, even at a distance over the latter part of the project. I would also like to thank Petter Dyverfeldt for offering me the opportunity to work within the CMR group on a very interesting and stimulating project, and for advising me at key steps of the thesis.

A great thank to the wonderful and international team of the laboratory for valuable discussions and pleasant lunch and coffee breaks, you undoubtedly have contributed to the educational and enjoyable time I have had.

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List of Figures

2.1 Anatomy of the human heart and aorta. . . 4

2.2 Spin, magnetic moment and net magnetization . . . 5

2.3 Precession and T1/T2 correspondences. . . 6

2.4 Examples of different registration methods. . . 9

3.1 Flowchart of the process to obtain the atlas . . . 12

3.2 Temporal alignment graph. . . 13

4.1 Flow atlas in young and old subjects . . . 18

4.2 KE atlas and standard deviation in young and old subjects . . . 20

4.3 TKE atlas and standard deviation in young and old subjects . . . 22

4.4 p-value map of KE data between young and old subject groups . . . . 23

4.5 p-value map of TKE data between young and old subject groups . . . 24

List of Tables

3.1 Study population statistics . . . 15

4.1 Statistics over subjects and geometry at time-frame 8. . . 17

4.2 Proportion of significantly different voxels over the geometry, per data type. . . 24

List of Abbreviations

KE Kinetic Energy

MRI Magnetic Resonance Imaging

PC-CMR Phase Contrast Cardiac Magnetic Resonance

PC-MRCA Phase-Contrast Magnetic Resonance CardioAngiography TKE Turbulent Kinetic Energy

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Chapter 1

Introduction

1.1 Formulation of the problem

Cardiovascular diseases are the world’s biggest killer and have remained the leading cause of death for at least 15 years [2]. It has been shown that several arterial diseases are characterized by abnormalities in the vessel geometry, concomitant with altered hemodynamics [3]. More specifically, increasing evidence has shown that turbulent blood flow is involved in the pathogenesis of several cardiovascular diseases [4][5].

However, the magnitude and impact of turbulence in the healthy heart and aorta is still relatively unexplored. Determining the normal blood flow and turbulence level in the aorta would enhance the understanding of the changes in the flow patterns in the presence of cardiovascular diseases. Previous catheter-based measurements have been performed [6], but are limited by the method. It is indeed invasive, therefore interfering with the flow that is being assessed, and one-directional only.

Accurately measuring pulsatile blood flow in a non-invasive way is enabled by advanced magnetic resonance imaging (MRI) techniques, such as four-dimensional phase-contrast cardiac magnetic resonance imaging (known as ”4D Flow CMR”). 4D Flow CMR is a tool for performing studies of flowing tissues like blood [7].

Increasing number of studies have used 4D Flow CMR to enhance the existing knowledge on intra-cardiac flow and its influence on cardiovascular physiology and pathophysiology [3][8][9]. However, the conventional analysis method for 4D Flow CMR is a labour intensive process and requires excessive amount of time. Alterna-tive methods which enable analysis of multiple subjects in an automated manner is therefore required.

1.2 Aim of the thesis

The aim of this thesis is to develop a method to automatically create atlases of the blood flow from several similar individual aortas. A hemodynamic atlas is defined as a map of expected values for flow-related quantity, and is actually the average of the values over several subjects. Hence, they are an efficient way to study a large population and target the differences between several subject groups. Cibis et al. [10] demonstrated that hemodynamic atlases can be accurately obtained using 4D Flow CMR images.

The focus will be on automatically registering and averaging several data-sets to create an atlas. This atlas will show the expected blood flow patterns in a specific patient group, as well as the standard deviation and statistical differences between groups.

Following the implementation of the method, the thesis will also concentrate on analyzing the flow and turbulence in healthy young and healthy old subjects.

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Chapter 2

Background

2.1 The cardiovascular system

The cardiovascular system is responsible for transporting oxygen, nutrients, hor-mones, and cellular waste products throughout the body. It consists of three in-terrelated components: blood, the heart, and blood vessels (see figure 2.1a). There are three main types of blood vessels, named arteries, capillaries and veins. Arteries carry blood away from the heart to other organs, and veins from the organs back to the heart. Capillaries connect arteries and veins, and allow exchanges of substances between the blood and body tissues thanks to their thin walls. The heart periodically pulses blood through the entire body. In each cardiac cycle, the atria and ventricles alternately contract (systole) and relax (diastole). [11]

2.1.1 The aorta

The aorta is the largest artery of the body, with a diameter of 2–3 cm. It emerges from the left ventricle of the heart, and contains the aortic valve at its beginning. It can be separated into two sections: thoracic aorta and abdominal aorta. The upper part of the thoracic aorta can also be divided into ascending aorta and arch of the aorta (see figure2.1b).

The aorta gives off distributing arteries that lead to various organs. For instance, the right and left coronary arteries arise from the ascending aorta just superior to the aortic valve [11].

The aortic flow is dictated by the succession of systole and diastole of the left ventricle.

2.1.2 Arterial diseases and deformation

The blood flow is dictated by the shape of the aorta, and can be altered by certain cardiovascular diseases [3].

One common cardiovascular disease affecting the flow is atherosclerosis. Atheroscle-rosis is a disease in which plaque builds up within the arterial wall. Plaque is made up of fat, cholesterol, calcium, and other substances found in the blood. Over time, plaque hardens and can lead to stenosis [14]. The term stenosis refers to an abnormal narrowing or constriction of a duct or opening [11]. Regarding blood vessels, it can result in a reduction of flow capacity distal to the stenosis. Areas with great inclina-tion of developing atherosclerosis are branch points and bifurcainclina-tions of artery [5][15]. Atherosclerosis can lead to serious problems, including heart attack, stroke, or even death.

Abdominal aortic aneurysm is another type of cardiovascular disease, affecting the abdominal aorta anatomical shape and its blood flow, and can be life-threatening in the case of complications.

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4 Chapter 2. Background

(a) Heart with direction of the blood flow. Figure from [12]

(b) Aorta. Figure modified from [13]

Figure 2.1: Anatomy of the human heart and aorta.

One of the factors of aorta alteration is age. It has been shown that the normal aging process brings many changes to the aorta [16]. Van Ooij et al. [8] also revealed that significant correlation exists between age and blood flow velocity at systole (event of the cardiac cycle where blood is ejected into the aorta).

2.2 Magnetic Resonance Imaging

Nuclear magnetic resonance imaging (MRI) is a technique based on spin-physics and stands on the science of nuclear magnetic resonance (NMR). It is used in medicine to obtain pictures of the anatomy and the physiological processes in the body. This non-invasive method has seen great improvements during the last decades.

MRI produces high-contrast, high-resolution images of two-dimensional slices as well as three-dimensional volumes. The fact that MRI does not involve x-rays is an advantage, compared to other techniques such as Computed Tomography (CT). In addition, MRI has proven to be a highly versatile imaging technique, and is capable of producing a variety of chemical and physical data, in addition to detailed spatial images. More specifically, MRI is able to quantify flow-related quantities such as velocity.

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2.2.1 Physics

Spin and magnetic moment of a single particle

MRI is based on the physical phenomenon called spin, a fundamental property of nature. Spin, in the same way as mass, does not arise from more basic mechanisms. Particles such as electrons, protons, neutrons and atomic nuclei possess spin. Most MRI scanners records the signal from the hydrogen (H) nuclei, which is made of one single proton, and is principally found in water and fat molecules. Magnetic resonance of the hydrogen nuclei (or proton) is therefore well suited for the study of the human body.

The object of interest (molecule, atom or subatomic particle) can be seen as a magnetic dipole. As such, it possess a magnetic moment (µ), which is a vector quantity describing its tendency to interact with an external magnetic field. Spin and a particular form of the magnetic moment are colinear and directly proportional to one another. The constant connecting them is called the gyromagnetic ratio (γ), and is given in M Hz/T esla. The value of the gyromagnetic ratio varies by atomic species. Spin and magnetic moment of the atom of hydrogen are illustrated in figure 2.2a.

(a) Spin and magnetic moment of the atom of hydrogen, proportionally connected by the gyromagnetic ratio

γ.

(b) Net magnetization (M ), the averaged sum of many individual quantum spins, can be treated as a regular vector in classical physics.

Figure 2.2: Spin, magnetic moment and net magnetization

Courtesy of Allen D. Elster, MRIquestions.com

Net Magnetization

During an MRI experiment, the magnetic signal is not received from individual nuclei, but from millions to billions in the aggregate. Thus, rather than studying individual nuclear spins, it is preferable to think about the sum of their magnetic properties averaged together. This quantity is called the net magnetization and is denoted M . This principle is illustrated in figure2.2b.

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In the absence of external magnetic field, the spins align randomly and the net magnetization is the null vector.

External magnetic field and precession

The influence of an external magnetic field, denoted B0, causes a net magnetization

aligned with the magnetic field.

At the same time, this external magnetic field causes the particles with spin to precess around the direction of the field. Precession of individual particles occurs at a specific frequency ν (the Larmor frequency), which is proportional to the strength of the magnetic field B0 and the gyromagnetic ratio γ. This is embodied in the Larmor

relationship, given by ν = γB0[Hz]. This phenomenon is illustrated in figure 2.3a.

(a) Precession of one particle in an

external magnetic field. (b) Correspondences between approximate values of T1 and T2 at 1.5T and the type of

tissue. Figure 2.3: Precession and T1/T2 correspondences.

Courtesy of Allen D. Elster, MRIquestions.com

Unlike individual particles, the net magnetization does not precess at equilibrium. It will start precessing once put out of equilibrium by a transverse magnetic field B1,

oscillating at the Larmor frequency (radio frequency pulse or RF-pulse). This second magnetic field is actually an external injection of energy. This is called Nuclear Magnetic Resonance (NMR): a short-term, induced phenomenon, involving energy exchange between precessing spins and their environment. When the applied RF-pulse is switched off, the net magnetization returns to equilibrium while the absorbed energy is re-emitted. This phenomenon is called relaxation. The return of the vector

M back aligned to the field B0produces a time-varying signal known as free induction decay (FID). Coils are placed to convert the magnetization into a current. It is the MR-signal.

This MR-signal, sampled during the relaxation process, can be described with the help of two time constants T1 and T2 (first defined by Bloch, 1946 [18]). Those constants give insight about the nature of the matter, as shown in figure2.3b. 2.2.2 Imaging principles

Since the scanned matter is a three-dimensional volume, it is convenient to split it up into smaller cubic volumes that are called voxels. Voxels within a 2D plane are called pixels. This part describes how to acquire and localize the source of the MR-signal emitted by the matter on a 2D plane, and thus form an image.

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pulse at a given frequency, perpendicular to B0, only spins within a slice (2D plane)

with matching precessing frequency will be able to emit the MR-signal. This process is known as slice-encoding. Within this slice, applying a phase encoding gradient in one direction and a frequency encoding gradient in the remaining direction allows to give each voxel in the slice a unique combination of frequency and phase. Indeed, the phase encoding gradient gives each spin a phase difference depending on its spatial position along the gradient. In a similar way, the frequency encoding gradient modi-fies the spinning frequency of the particles depending on their spatial position along the gradient. This way, the image can be obtained after recording the MR-signal and Fourier transform it to determine each the spatial origin of the each MR-signal. 2.2.3 Phase-Contrast CMR

Phase-Constrast Cardiovascular Magnetic Resonance (also known as PC-CMR or PC-MRAngiography) is a Flow-Imaging technique. It allows to assess the blood flow using a bipolar phase encoding gradient. A bipolar gradient is one in which the gradient is turned on in one direction for a period of time then turned on in the opposite direction for an equivalent amount of time. Therefore, stationary spins experience both gradients, and the effect on their initial phase is non-existent. On the contrary, spins that are moving along the gradient experience different phase shift during the two steps of the bipolar gradient. It results a total phase shift that permits to compute the speed of the spinning particle along the gradient. [19] On a 3D image, flow-encoding is performed in all three spatial directions and resolved relative to all three dimensions of space.

2.2.4 4D Flow CMR

Several MRI modalities were developed in order to put the emphasis on different characteristics of what is being scanned. For instance, four-dimensional flow car-diovascular magnetic resonance (4D Flow CMR) has been developed to attain more comprehensive access to blood flow through the heart and large vessels [7]. This method creates time-resolved three dimensional images (3D images + time = 4D) with flow-encoding, using phase-contrast CMR. Using this image, the flow can be quantified, described and displayed in a variety of ways [7] [9].

As a non-invasive method, 4D Flow CMR is a convenient way to analyze the complex blood flow in the cardiovascular system. It is now commonly used in the field of cardiovascular research. The scanner provides multiple time-resolved images for each patient. Different types of acquired 4D images are (the term 4D image refers to a time-resolved three-dimensional image): a magnitude 4D image, describing the anatomy; three velocity 4D images, describing the velocity in the three spatial direc-tions; and three turbulent kinetic energy (TKE) 4D images, describing the turbulent aspect of the flow.

From the velocity data, the kinetic energy (KE) can be computed as KE =

1

2ρv2dV , with ρ = 1060[kg/m3] being the blood density, dV the unit voxel volume,

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Turbulent Kinetic Energy

Turbulence is a flow regime in fluid dynamics characterized by velocity fluctuations, in contrast to a laminar flow regime, which is characterized by a flow in parallel layers. Turbulent flow goes together with many forms of cardiovascular disease and may contribute to their progression and lead to other hemodynamic changes. The method to compute the turbulent kinetic energy is presented in [20] and [21].

2.3 Image processing and analysis

Image processing and analysis are nowadays completely digital. It allows to per-form very complex processes on the acquired images, such as flow quantification [22], feature tracking [23] or image registration [24].

Image registration

In the medical imaging field, it is often relevant to relate different images within a set to each other. The process of finding a mapping between the pixels in different images is known as image registration. It means that given two images (a reference image and a moving image), image registration aims at estimating a spatial transformation, such that the transformed moving image and the reference image are as similar as possible. This is illustrated in figure2.4. Three transformation models can be identified: rigid, affine and non-rigid transformations. Rigid registration performs a transformation of the moving image only by translation and rotation. Affine registration additionally includes scaling and shearing: it registers parallel lines onto parallel lines. Non-rigid registration performs elastic deformations and local alignment of anatomical features; it is capable of locally warping the image to this end, in other words registering lines onto curves [24].

Some issues come with this very useful tool, however, such as excessive computation time and a lack of established validation methods or metrics. The latter leads to a general skepticism toward the trustworthiness of the estimated transformations in non-rigid image registration [25]. Nonetheless, in medical imaging non-rigid regis-tration is very powerful and permits to register anatomical parts that are different from a subject to another, that is, it reduces the morphological differences between them. This allows more accurate comparison over a large number of subjects, hence the creation of atlases.

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a.

c.

b.

d.

Figure 2.4: The four registration types. The green aorta is registered on the pink aorta. a. Original before registration, b. After translation,

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Chapter 3

Methods and material

3.1 Hemodynamic atlases

In this thesis, an atlas is defined as a map of expected values for a physical quantity, among several subjects. To this end several subject data sets were processed, including registration and averaging. The hemodynamic atlas thus shows the expected blood flow over a region of the cardiovascular system, for a given subject group (healthy young for example). It is an average representation of the group.

This section details the process of creating hemodynamic atlases. Statistical tools were used to analyze the data within a patient group or between two groups. Those are also presented in this section.

3.1.1 Workflow

The exhaustive workflow is presented in figure 3.1. Images acquired by the MRI scanner are first interpolated to the same size. As the subjects do not have the exact same heart cycle, the data sets are aligned temporally. Using image registrations, a 3D average aorta is then created from all the data sets. Flow data are finally registered to this average aorta to obtain the hemodynamic atlas. Specific steps are detailed here after.

All the registrations were done with the Morphon method [26], and using the Forsberg implementation [25]. This in-house software package is implemented in MatLab (MathWorks, Natick, MA) and was ran on a desktop computer (Intel Xeon 12 core processors, 2.50 GHz CPU, and 64GB RAM).

PC-MRCA

4D Phase-Contrast Magnetic Resonance CardioAngiography or (4D) PC-MRCA was first created from 4D Flow CMR data. The process of creating PC-MRCA is detailed in the work of M. Bustamante [27].

PC-MRCA is an improved and time-resolved PC-MRA (phase-contrast MR an-giography). Because PC-MRA and PC-MRCA are created from magnitude and veloc-ity data, they show a better contrast between the cardiovascular system that is being studied and the other tissues constituting the body. PC-MRCA is obtained with reg-istrations between the PC-MRA time frames over the entire cardiac cycle, and thus retains the anatomical changes of the aorta and the heart over the cycle. Because in this study clear and accurate shapes are important for registration, PC-MRCAs were computed for each data set at the very beginning of the workflow.

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12 Chapter 3. Methods and material

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Figure 3.2: Graph showing the time alignment of two patient sets. The red plots (moving) show the blood flow of one set that is aligned on the blue plots (reference). The interpolated blood flow that results from the temporal alignment process is assessed and gives the green plots (aligned). Three black vertical lines show the time frames chosen

as reference points: systole, early and late diastole.

Temporal Alignment

We want to relate the subject data-sets to one another. Thus, the heart cycles of every patients have to be synchronized together ; we call this synchronization process

temporal alignment. From the 4D data of the PC-MRCA, the mid-systolic time frame

as well as those corresponding to the early and late diastole were identified, through an analysis of the measured velocity over the cardiac cycle. The former was defined as the time frame of peak flow over the aortic valve while the latter were defined as the time frames of the two consecutive peak flows observed in the mitral valve. The three identified time frames were used to temporarily align the PC-MRCAs on a chosen reference PC-MRCA. Time frames between early and late diastole and mid-systole were linearly interpolated. The result of temporal alignment was visually inspected by plotting the blood velocity at mitral and aortic valves over time (figure3.2). Creation of an average aorta

In order to perform statistical studies on the set of subjects thereafter, it is convenient to reduce all the different aorta geometries to one average geometry.

To this end, one data set has been selected as reference as mentioned at the previous step. A time frame t was chosen to be the one for which the atlas is to be computed. The same time frame from every other data set was rigidly registered to the reference time frame. The reference time frame was then non-rigidly registered to every other. The data sets had to be related to one another in a way that after registration, the registered images look all the same. Non-rigid registration is thus the right tool for this sake. All registrations were made with the PC-MRCA data. The

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14 Chapter 3. Methods and material

deformation fields computed were averaged and applied to the reference PC-MRCA frame: it resulted a three dimensional data, referred to as the average aorta.

Registration of each individual data set to the average aorta

At the time frame t as mentioned above, PC-MRCA frames from each data set were non-rigidly registered to the average aorta. The deformation fields obtained were applied to their corresponding subject data (magnitude, velocity, TKE).

3.1.2 Statistical tools

All the data registered to the average aorta were averaged within their type (magni-tude, velocity and TKE). This creates the hemodynamic atlas, made up of the average aorta and the averaged velocity, magnitude and TKE data.

Statistical hypothesis test and p-value

Statistical hypothesis tests were performed on different subject groups. This test is to be performed between two groups, and provides information on whether the groups present similar flow data or not. Voxel by voxel comparison of different groups are done by using unpaired t-test and the level of significance was chosen as α = 0.05. Consequently, a p-value lower than 0.05 gives evidence to say that there is a difference in flow between the groups.

3.2 Study Population and MR Examination

Twenty male patients with no current cardiovascular disease were included in the study. Two study groups were recruited according to their age: normal young subjects between 21 and 29 years old, and normal old subjects between 66 and 75 years old. Table3.1shows some statistics about the study population.

Time resolved, three-dimensional phase-contrast MRI (4D Flow CMR) data were acquired on a clinical 3T MRI scanner (Philips Ingenia), using a retrospectively cardiac-gated gradient-echo sequence with four-point asymmetric flow encoding. The 4D Flow CMR data were acquired post injection of Gadolinium contrast agent (Mag-nevist, Bayer Schering Pharma AG). Navigator gating was used to suppress respira-tory effects. Scan parameters included: VENC = 100−200cm/s, flip angle 15 degrees, echo-time = 2.5 − 3.1ms, repetition-time = 4.4 − 5.0ms and spatial resolution (voxel size) of 2.2 ∗ 2.2 ∗ 2.5mm3. The acquired temporal resolution was 35 − 40ms and all data were reconstructed into 40 frames using a sliding-window technique with a Gaussian interpolation kernel. Turbulent Kinetic Energy (TKE) data was computed for each subject from magnitude data.

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Healthy young Healthy old p-value Age [years] 24.5 ± 2.9 69.9 ± 3.1 0.000 Height [cm] 182.6 ± 7.3 178.5 ± 7.3 0.082 Weight [kg] 78.6 ± 11.8 79.6 ± 9.9 0.409 SBP [mmHg] 110.2 ± 3.9 122.3 ± 18.7 0.020 DBP [mmHg] 58.6 ± 3.7 74.1 ± 9.2 0.000

Table 3.1: Study population statistics, given as

mean ± standard deviation.

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Chapter 4

Results

This chapter presents the main output of the method. Once the atlases are obtained in young and old subjects, several indicators were computed such as mean value over the geometry (i.e. the segmented shape of the aorta) and p-value maps. All the results are given at time-frame 8, corresponding to the mid-systole.

4.1 Hemodynamic atlases

The table4.1 shows statistics about the mean speed, KE and TKE values averaged over each subject geometry. A p-value analysis was performed between young and old data sets.

Healthy young Healthy old p-value mean velocity [m/s] 0.64 ± 0.10 0.39 ± 0.07 < 0.05 peak velocity [m/s] 1.51 ± 0.27 1.15 ± 0.21 < 0.05 mean KE [J/m3_] _{277.8 ± 90.4} _{102.3 ± 37.4} _{< 0.05} peak KE [J/m3] 1239.4 ± 448.5 727.1 ± 262.5 < 0.05 total KE [mJ ] 53.2 ± 22.9 30.4 ± 14.5 < 0.05 mean TKE [J/m3] 40.2 ± 14.1 18.7 ± 9.4 < 0.05 peak TKE [J/m3] 415.2 ± 132.1 257.6 ± 97.0 < 0.05 total TKE [mJ ] 7.7 ± 3.5 5.6 ± 3.2 0.089

Table 4.1: Statistics over subjects and geometry at time-frame 8. The table presents the mean ± standard deviation of these pre-computed values over the two sets of patients: young and old. The velocity corresponds to the magnitude of the velocity vector. To ensure accuracy of the result despite the change of volumes between the sub-jects, these statistics were computed for each subject over its original aorta geometry, using backward registration to obtain the segmenta-tion. The values were then averaged over the different subjects, within

their respective groups.

The presented results show a significant difference for mean and peak speed, KE and TKE between healthy young and healthy old. Healthy young group values are significantly higher than healthy old group values. It can however be noticed that this difference is less important for the total TKE. The standard deviations are high for all the categories, and especially in the old subjects group. Indeed, the ratio between standard deviation and mean value for the young subjects group is 0.32 in average, whereas it is 0.38 in average for the old subjects group. Student’s test performed on

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18 Chapter 4. Results

these ratios in young and old subjects groups gives a p-value of 0.02, hence showing significant difference (using the common significance level of 0.05).

Flow atlas

The atlases presented in this part are for visualization purposes mainly. Flow vectors are plotted on the average aorta.

Figure 4.1: Flow atlas in young and old subjects. Cross-section, slice 13.

The background shows the average aorta (geometry in black and white); it is a mean of all the subjects’ PC-MRCAs. Superimposed on the background are the velocity vectors of the mean blood flow, average from all the subjects’ flows in the group. Velocity vectors are plotted in two dimensions, anterior-posterior (AP) and foot-head (FH)

directions.

The blood flow appears to be parallel to the artery’s wall all the way from the arch of the aorta to the lower part of the abdominal aorta. In old subjects, the flow seems to whirl in the ascending aorta, and it is thus not parallel to the vessel’s wall. Visually, the blood flow appears to be higher in the ascending aorta in old subjects whereas it is higher in the descending aorta (passed the arch) in young subjects.

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slices (number 13) of the KE atlases is presented to provide a view of the flow inside the vessel.

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(a) In young subjects

(b) In old subjects

Figure 4.2: KE atlas and standard deviation map in young and old subjects. Cross-section, slice 13.

KE density was computed per voxel as KE = 1₂ρv2_,

with ρ = 1060[kg/m3_{] being the blood density and v the speed of}

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high where the KE is high.

Turbulent Kinetic Energy atlas

The TKE atlases in figure4.3show the regions of turbulence in the blood flow. The average aorta geometry is made up of 30 slices. One of the middle slices (number 13) of the KE atlases is presented to provide a view of the flow inside the vessel.

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(a) In young subjects

(b) In old subjects

Figure 4.3: TKE atlas and standard deviation map of the atlas in young and old subjects. Cross-section, slice 13. TKE for each subject

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to abdominal organs). The standard deviation map shows high values spread out in the descending aorta and in the suprarenal abdominal aorta, at the artery branches. In old subjects, TKE values appear to be lower than in young subjects almost everywhere, except in the ascending aorta where high TKE values are found. TKE is present in the descending thoracic aorta, but the suprarenal abdominal aorta does not show any high TKE value. Standard deviation is high were TKE is high, except in the suprarenal abdominal aorta where sparse high standard deviations are found.

4.2 P-value maps

The p-value maps in figures 4.4 and 4.5 show the regions of significant differences between young and old subject groups.

Figure 4.4: p-value map resulting from the statistical hypothesis test on KE (level of significance α = 0.05), between young and old subject groups. The grey area shows the limit of the blood vessel, while the red area represents voxels for which the value is significantly different

in young and old subjects.

The results from the statistical hypothesis show significant difference in KE be-tween young and old in the arch of aorta and descending aorta. Only the a the ascending aorta and the subrenal abdominal aorta do not show significant differences in KE.

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Figure 4.5: p-value map resulting from the statistical hypothesis test on TKE (level of significance α = 0.05), between young and old subject groups. The grey area shows the limit of the blood vessel, while the red area represents voxels for which the value is significantly different

in young and old subjects.

The results from the statistical hypothesis show significant difference in TKE between young and old in the thoracic aorta mainly. Sparse regions of significant differences are located close to the wall of the descending aorta, but also spread out in the inner part of the arch of aorta. Voxels in the abdominal aorta do not show any significant difference between the groups, except very close to the branches in the suprarenal abdominal aorta.

Table4.2shows some statistics resulting from the p-value maps.

Percentage (%) of significantly different voxels over geometry

Velocity magnitude HF velocity AP velocity RL velocity KE TKE

66.6 71.1 41.8 43.3 65.3 41.4

Table 4.2: Proportion of significantly different voxels over the geom-etry, per data type. This ratio is computed as

% = number of significantly different voxels over the geometry_{number of voxels forming the geometry} .

Velocity components: HF = Head to Foot, AP = Anterior to Posterior, RL = Right to Left.

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Chapter 5

Discussion

In this work a method to obtain hemodynamic atlases using 4D Flow CMR was presented. The method has some advantages over conventional analysis methods for 4D Flow CMR.

First, the presented method registers anatomical parts ; therefore it reduces the morphological differences between subjects, through the creation of an average aorta geometry. It thus permits the calculation of hemodynamic atlases. The method is automated and requires minimal user interaction. Furthermore, only one segmenta-tion is needed. All the registrasegmenta-tions are performed using the Morphon method, which has for main advantages its robustness and tolerance to gray-scale variation between images. The method enables access to informations that are not easily obtained with common methods. It results for instance the expected hemodynamic values for a spe-cific group of subjects. The resulting atlases can help to define the typical blood flow in a given subjects group (for example healthy old); hence, and by comparing two atlases from two different groups, it helps to determine the difference in flow. In sub-jects with hemodynamic disease, it can give an insight of the causes and consequences of the disease in terms of flow.

5.1 Interpretation of the results

The tendency of the results indicates that the proposed method has great potential for the study of large populations.

The table 4.1shows some interesting results. First of all, it can be noticed that the values match the range of the results from previous studies [3][10]. In the same way, the statistics over the two datasets show significantly higher values for the group of young subjects, thus corroborating the result of these previous studies. Besides, KE being proportional to the square of the velocity, the fact that velocity and KE in healthy young are both higher than velocity and KE in healthy old is coherent. The statistical results show that the TKE is higher in young subjects, which was expected given the higher blood velocity. Indeed, a higher velocity gives a higher Reynolds number, which makes the flow more prone to turbulence. The old subjects group present higher standard deviations than the young subjects group compared to their respective mean value. It means that the old subjects group is more heterogeneous, and it is coherent since old subjects often have more complex aorta geometry than young people [3].

It is interesting to notice that even though the total TKE is lower in old subjects (table 4.1), the flow seems less laminar than in young subject (figure 4.1). This difference in TKE value could be explained by a lower blood velocity in old subjects. In addition, it is noticeable that even if the mean TKE for a voxel is significantly different between young and old, the difference in total TKE over the vessel’s geometry is less significant (see table4.1). This is explained by the fact that old subjects often

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26 Chapter 5. Discussion

have a greater aorta than young subjects : the mean value for a voxel is lower, but the volume (therefore the number of voxels) is greater.

Due to the many registrations made before averaging to form an atlas, there is a possibility that the high TKE values found close to the wall of the vessel in young subjects are wrong. Indeed, the computation of TKE close to a wall is prone to wrong values, and the multiple interpolations due to registration can bring even more imprecision at the boundary between blood flow and vessel wall.

From the standard deviation maps, it can be assessed whether the information provided on the atlas is a good representative of the group. For instance, the stan-dard deviation of TKE in healthy young shows that the lower part of the suprarenal abdominal aorta is prone to very different TKE across young subjects. This might be due to different geometries and velocities (as mentioned before, blood velocity can affect turbulence) among young subjects.

Looking at the p-value maps, it can be seen that KE is significantly different be-tween young and old subjects, especially in the arch and descending aorta. Regarding the TKE p-value map, high values close to the wall confirms that TKE is high in this region only in young subjects. Globally, the two p-value maps corroborate the results in table4.1.

The resulting hemodynamic atlases and their standard deviation maps depend on the anatomical registration between the data-sets and on the temporal align-ment. Trying to create an atlas from a set of subjects too different from one another might lead to incoherent results. Normalized mutual information has been used as a measurement to assess the result of registration, but has shown to give substantial misleading results in some cases.

Other attempts to create atlases of hemodynamic parameters based on 4D Flow CMR in large vessels have been made [28][29]. In their study focusing on flow ve-locities and wall shear stress (WSS), Van Ooij et al [3] showed results similar to the present study, i.e. significant correlations between age and systolic velocity. In these mentioned studies, each individual aorta was segmented and aligned using affine reg-istration to a cohort-specific aorta geometry. Even though Van Ooij et al [3] focused on flow velocity and WSS, their method might be applied on other hemodynamic parameters, hence resulting in atlases similar to the present study results. Their method however requires a template, and a segmentation for each dataset. This would become really challenging for a study based on a large number of subjects. Also, registration methods such as rigid and affine can result in a bad or even wrong alignment of anatomical structures, having for consequence a severe smoothing in the averaged images. More advanced methods such as non-rigid registration is expected to be necessary to obtain high quality hemodynamic atlases.

For the present study, 4D Flow CMR data were acquired focused on the aorta. The lack of other anatomical structures (i.e. other organs) penalizes the non-rigid registration, and sometimes leads to bad alignment. A larger field of view would help to obtain more accurate registrations. As a return, increasing the field of view would lead to a lower resolution for the acquired image, making the atlas less accurate.

Besides, the registration process implies interpolation of the values, which acts as a low-pass filter and might have a significant effect on peak values.

5.2 Future work

Several improvements could be made to the developed method, and further exploita-tion could show interesting results.

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subjective. The automatic exclusion of a data-set based on this metric is a suggested improvement.

Besides, the time alignment method used needs improvements, especially for sub-jects with very particular anatomy or heart cycle. It is believed that the method can be improved with a better assessment of the blood flow over the heart cycle with the use of 3D planes placed on the mitral valve, instead of a 3D point (current method). The automatic placement of this plane could be done using the registration results.

The method has only been applied in healthy young and healthy old, and it will be interesting to use it on patients with aortic diseases such as abdominal aortic aneurysm.

5.3 Conclusion

The proposed method has shown to have a great potential in the aim of comparing different subjects groups and defining normal flow characteristics within a subject group. In the present study, differences in kinetic energy and turbulent kinetic energy between young and old subjects were shown to be significant. Future studies should include a larger number of subjects as well as different patient groups. Hemodynamic atlases can help to improve the pathophysiological understanding of a wide range of cardiac diseases, and make easier the comparison between individual subjects or groups of subjects.

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Creating hemodynamic atlas of aorta