Automatic Alignment of 2D Cine Morphological Images Using 4D Flow MRI Data

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Master of Science Thesis in Electrical Engineering

Department of Electrical Engineering, Linköping University, 2016

Automatic alignment of 2D

cine morphological images

using 4D Flow MRI data

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Victoria Härd LiTH-ISY-EX–16/4992–SE Supervisor: Vikas Gupta, PhD

imh, Linköpings universitet Mariana Bustamante, MSc imh_{, Linköpings universitet} Examiner: Professor Tino Ebbers, PhD

imh_{, Linköpings universitet}

Division of Cardiovascular Magnetic Resonance Department of Electrical Engineering

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Abstract

Cardiovascular diseases are among the most common causes of death worldwide. One of the recently developed flow analysis technique called 4D flow magnetic resonance imaging (MRI) allows an early detection of such diseases. Due to the limited resolution and contrast between blood pool and myocardium of 4D flow images, cine MR images are often used for cardiac segmentation. The delin-eated structures are then transferred to the 4D Flow images for cardiovascular flow analysis. Cine MR images are however acquired with multiple breath-holds, which can be challenging for some people, especially, when a cardiovascular dis-ease is present. Consequently, unexpected breathing motion by a patient may lead to misalignments between the acquired cine MR images.

The goal of the thesis is to test the feasibility of an automatic image registration method to correct the misalignment caused by respiratory motion in morpholog-ical 2D cine MR images by using the 4D Flow MR as the reference image. As a registration method relies on a set of optimal parameters to provide desired re-sults, a comprehensive investigation was performed to find such parameters. Different combinations of registration parameters settings were applied on 20 datasets from both healthy volunteers and patients. The best combinations, se-lected on the basis of normalized cross-correlation, were evaluated using the clin-ical gold-standard by employing widely used geometric measures of spatial cor-respondence. The accuracy of the best parameters from geometric evaluation was finally validated by using simulated misalignments.

Using a registration method consisting of only translation improved the results for both datasets from healthy volunteers and patients and the simulated mis-alignment data. For the datasets from healthy volunteers and patients, the regis-tration improved the results from 0.7074 ± 0.1644 to 0.7551 ± 0.0737 in Dice in-dex and from 1.8818 ± 0.9269 to 1.5953 ± 0.5192 for point-to-curve error. These values are a mean value for all the 20 datasets.

The results from geometric evaluation on the data from both healthy volunteers and patients show that the developed correction method is able to improve the alignment of the cine MR images. This allows a reliable segmentation of 4D flow MR images for cardiac flow assessment.

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Acknowledgments

I would like to thank my supervisors, Mariana Bustamante and Vikas Gupta at IMH, Linköpings University, for all the help and feedback during the thesis. It has been nice to always know that you support me. I would also like to thank Alexandru G. Fredriksson for the help with the segmentation of all the data. The result would not have been so good without your help. Also many thanks to my examiner, Tino Ebbers.

I would also like to thank Peter Thulin for always supporting and believing in me.

Linköping, August 2016 Victoria Härd

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Notation

Abbreviation

Abbreviation Meaning

bssfp _{Balanced steady state free precession MRI}

la Long axis

mi Mutual Information

mri Magnetic Resonance Imaging ncc Normalized Cross-Correlation nmi Normalized Mutual Information

sa Short axis

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1

Introduction

This is a master thesis in image processing and has been written at the Faculty of Medical and Health Sciences (IMH), Department of Cardiovascular Medicine, at Linköpings University.

1.1 Background

Cardiovascular diseases are one of the most common causes of death worldwide [2], [9]. Cardiovascular magnetic resonance imaging (MRI) is a commonly used technique to non-invasively study the structure and function of the heart for their early detection. Many of the cardiovascular MR acquisition methods require mul-tiple breath-holds. This can be hard for some patients and thus, motion artefacts are introduced in the acquired images. As a result, the myocardial segmenta-tion performed in these images may lead to reduced certainty in the analysis of 4D Flow images. Manual alignment of these images is time consuming, tedious, and prone to observer bias. An automatic method using image registration tech-niques is therefore desired. Figure 1.1 depicts the extent of spatial misalignments caused by the motion artefacts. Commonly employed measures of spatial corre-spondence are used here. Further details on these measures are provided in the subsequent chapters.

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Figure 1.1:Dice index and point-to-curve errors for the different regions of the heart. A: Apical, B: Basal, M-V: Mid-ventricle.

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1.2 Literature review 3

1.2 Literature review

Carminati et al. attempted to translate each short-axis image in a CMR dataset by optimizing the normalized cross-correlation (NCC) of the pixel intensities at the slice intersection with the long-axis images. The method produced good results but was only tested on a phantom, which could be misleading when it applied on clinical data [5]. In a study made by Elen et al. post-processing is presented based on the constrained optimization of the intensity similarity in the line of in-tersection between the different images. This was a fully automatic approach in which four different cost functions were evaluated to obtain the best possible re-sults. Their analysis showed that using Absolute Difference of Derivative resulted in better misalignment correction [8]. Another article of interest was written by Chandler et al. where rigid registration, with NMI as similarity measure, was used to register slices of the SA image to a high-resolution 3D MR axial cardiac volume. The method was evaluated in a group of volunteers who had moved between breath-holds when the datasets was created, resulting in significant mis-alignment correction [7]. Barajas et al. also developed a method that corrects the displacement artefacts by using Normalized Mutual Information (NMI) as a mea-surement of registration accuracy [2]. More examples of this type of solutions are found in [4], [6], [16], [17] and [20].

All these articles use the intersection line between the short-axis and the long-axis images. On these intersection lines, the intensities are measured and compared. A transformation is then used to correct the moving image so it is as similar to the fixed image as possible. The difference between theses articles and this the-sis is the image that is used as the reference image for the registration. To our knowledge, previous studies have not used 4D Flow MRI images as a reference.

1.3 Aim

The goal of this thesis is to implement and validate an automatic method for correction of misalignments in Balanced steady state free precession MR images, often introduced due to breathing motion. We propose a technique that uses, already existing registration techniques in order to align short-axis 4D Flow and balanced images. The method that produces the best result will be evaluated in a group of dataset acquired from both healthy volunteers and patients.

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1.4 Outline

The outline of this document is the following:

Chapter 2provides theoretical background to the thesis.

Chapter 3describes the methods that were used during the thesis. Chapter 4presents the results if proposed methods evaluation.

Chapter 5discusses the results and motivates all the choices that have been made. Also some future work is presented here.

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2

Theoretical background

2.1 Magnetic resonance imaging

MRI is a medical imaging technique based on the principle of nuclear spin and magnetic field. In a human body, there are a large number of hydrogen atoms that can be affected by a magnetic field. During image acquisition, the changes in magnetic field leads to the alignment of hydrogen atoms inside the body. Because of the different number of hydrogen atoms in the various tissue types, the mag-netization varies accordingly. This variation is then used to distinguish between different types of tissues. To measure it, a radio wave with the same frequency as the resonant frequency is sent into the body. The radio frequency pulse causes transversal magnetization which is orthogonal to the magnetic field. The fre-quency is then turned off and the magnetization is measured in the orthogonal plane. Measurement from this result, together with the density of hydrogen in the tissue, results in an MR-image in which the differences between the tissues can be observed [23].

2.2 Anatomy of the heart

The heart is a muscular organ, placed in the middle thoracic cavity, between both the lungs. It is a part of the circulatory system and provides the whole body with blood. The heart is divided into four different chambers: two ventricles and two atria. Between the ventricles and atria there are valves that prevent the back-flow of the blood. Blood with low oxygen enters the right atrium, and goes through the tricuspid valve to the right ventricle. From the right ventricle, it enters the pulmonary circulation where it receives oxygen and releases carbon dioxid. The blood that has been oxygenated returns to the left atrium [9].

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Figure 2.1:Anatomy of the heart [11].

In this image, the upper chambers are the atria and the lower are the ventri-cles. In addition, oxygenated and deoxygenated blood are shown in red and blue colors, respectively [9].

2.3 4D Flow MRI

4D Flow MRI is a 3D+time image or more specifically, a three-dimensional dataset acquired in a time-resolved, ECG-gated manner, with velocity encoding in all three spatial directions [18]. Using 4D Flow MRI, it is possible to measure and visualize the blood flow patterns within an acquired 3D volume [18], [21]. This 3D volume is composed of isotropic or nearly isotropic voxels and allows for vi-sualization at any location within it. Additionally, the 4D Flow MRI is acquired using navigator gating without the need for a hold. Consequently, breath-hold motion errors are not present in these images. So with these benefits, a slice that represents the short axis view can be extracted from this 3D volume and then be used as a reference image during motion correction. One disadvantage of 4D Flow MRI is its resolution. Even though its voxels have the same size in all directions, the in-plane resolution of the image is lower when compared to the balanced images.

2.4 Balanced steady state free precession MRI

The cine MR images are acquired using the balanced steady state free precession (bSSFP) technique [19], which usually requires several breath-holds. Typically, 11-16 slices are obtained to encompass the entire heart.

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2.5 Image registration 7

This images have higher in-plane resolution than the 4D Flow MRI images but may have slice thickness up to 10 mm. In addition, the through plane resolution is much lower than for a 4D Flow MRI image and motion artefacts due to respi-ratory motion introduce slice misalignments. These images can be reconstructed in different ways to analyse the heart from various views. The most commonly used reconstructed views are explained in the following text.

2.4.1 Short axis view

Short axis (SA) view, of the heart that shows the left and right ventricles. This view is chosen so that it is perpendicular to the mitral valve plane. Therefore, it is also called the orthogonal view. An image of the SA view can be seen in Figure 2.2a [3].

2.4.2 Long axis view

Long axis (LA) view, shows two, three or four of the heart’s chambers. It is a projection parallel to the ventricular axis. An image of the LA view can be seen in Figure 2.2b [3].

(a)Short axis view. (b)Long axis view. Figure 2.2:SA and LA view of the heart in balanced SSFP images.

2.5 Image registration

Image registration has been used extensively to compare images acquired at dif-ferent time points or using difdif-ferent imaging techniques. The aim is to find a mapping function that best describes the global movement between the different images. Therefore, a model that matches the movement between the images is created, and the solution that fits all the image-points as good as possible is se-lected and used on the images [22].

It requires at least 2 images: a fixed and a moving image, see Figure 2.3. The moving image (Im) is the misaligned image that needs to be aligned to the fixed

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image (If), also called as the reference image. Both images need to have the same size, but their spatial domains can be different. These images will be compared to each other and a mapping function will be found. This mapping function de-scribes the displacement field for each of the points in the two images. It can be defined as

T (x) = x + u(x) (2.1)

where T(x) is the transformation and u(x) is the displacement. x represents the different pixels in the images. The problem is to find the transformation that makes Im(T(x)) spatially aligned to If(x). [15]

This is illustrated in Figure 2.3, where the image registration is between the fixed image to the left, and the moving image to the right. T is the transformation between them.

Figure 2.3: Image registration between the fixed image and the moved im-age.

A program that can solve this type of registration problem is a program called Elastix. In this program, different algorithms are implemented and can be ap-plied on images [14]. By create different combinations of theses algorithms, a best combination can be find and be used in the registration. In Figure 2.4, a general registration method is shown.

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Figure 2.4:Block scheme of a typical registration [10].

Figure 2.4 shows how the reference and target images are sent in to the reg-istration. In this thesis, the reference image will be called the fixed image and the target image will be called the moving image. The registration starts mea-suring the similarity between the fixed and the moving image. Then it tunes the transform matrices accordingly based on the optimization strategies. When the registration is finished, the moving image is supposed to be aligned with the fixed image when the obtained transformation is applied. All the different steps, similarity metric, optimization and spatial transformation are described in detail below [15].

2.5.1 Similarity metric

The first component of a registration is the similarity metric. The metrics defines the quality of alignment between the two images. In this thesis, two different metrics are used and are described below: Normalized mutual information and Mutual information [15].

Normalized mutual information

The normalized mutual information, NMI, is a common method used for both mono-modal and multi-modality registration. A mono-modal image set captured on the same device and the images have the same or similar brightness range. A multi-modal image set is instead captured on different devices and therefore the brightness range for the images is different.

To understand NMI, marginal entropy and joint entropy must first be presented. Marginal entropy is defined as the probability that a random variable has a spe-cific value. By knowing the entropy for one of the image intensity distribution, the other intensity distributions can be predicted. The entropy becomes zero if the two images are homogeneous and that means that there is no uncertainty about the intensity. Entropy is instead high if the images are inhomogeneous. Marginal entropy is calculated as shown in Equation 2.2.

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H(X) = −X

a

PX(a)logPX(a) (2.2)

where X is a random variable and PX is the probability that X has value a.

Joint entropy is instead computed between two random variables using Equation 2.3.

H(X, Y ) = −X

a,b

PXY (a, b)logPXY (a, b) (2.3)

Here, X and Y are two variables and PXY is the probability that both X and Y

have the value a and b. All this can also be shown in a Venn diagram. Then it can be easier to see how H(X) and H(X, Y ) are related to each other [15].

Figure 2.5:A Venn diagram that shows the marginal entropy H(X), the joint entropy H(X,Y) and the mutual information I(X,Y). [24].

By taking this two entropies, NMI can be defined as shown in Equation 2.4. F and M are the two different images that should be compared and the calculations are done for all the pixels in the image and then a mean value of all the pixels is computed.

N MI(M, F) = H(M) + H(F)

H(M, F) (2.4)

where H(M) and H(F) are the marginal entropies and H(M,F) a joint entropy of the data.

Mutual Information

For the Mutual Information, MI, there should only be a relation between the probability distributions of the intensities. This type of measure is good for image registration because it can handle both mono-modal and multi-modal images. MI measures the marginal and joint/conditional entropies between the two images and is very similar to NMI [15].

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2.5 Image registration 11 MI(IF, IM) = X m∈LM X f ∈LF p(f , m)log2 p(f , m) pF(f )pM(m) ! (2.5) where p(f , m) is the joint probability distribution of F and M. pF(f ) and pM(m)

are the marginal probability distribution of F and M respectively.

2.5.2 Optimization

The optimizer controls the spatial correspondence between two images: in this case between the fixed image and the moving image. The optimizer decides when to stop the iterations and converge. Two different optimizers were used in this the-sis. Standard gradient descent, (SGD) and Adaptive stochastic gradient descent, (ASGD). Both are methods that find the local minimum and in this case, find which combination of parameters produces the best result. That is, the result that minimizes the difference between the images. The optimizer will stop when the result is found, or after a specified maximum number of iterations. ASGD is a more advanced version of SGD and is less sensitive to the other parameter settings in the registration [13]. ASGD will adapt the step to the steepness of the error curve and SGD will always take steps of equal lenght. As a result, ASGD is often faster in finding the minimum but it can be difficult to determine how reliable it is [15].

2.5.3 Spatial transformation

Spatial transformation is decides which type of deformations the mapping func-tion can handle. In this thesis, translafunc-tion and rigid transformafunc-tion are used [15].

Translation

Translation between two images allows only movement in straight direction. The image cannot change size or be rotated. The mapping function for translation is defined in Equation 2.6

Tµ(x) = x + t (2.6)

where x is the image and t is a translation matrix or vector [15].

Rigid transform

Rigid transform consists of rotation and translation between the two images. Scal-ing cannot be changed when this transformation is used. The mappScal-ing function for the rigid transform is defined in Equation 2.7

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where R is the rotation matrix that contains Euler angles. For 2D, one angle is needed and for 3D, three angles need to be selected. t is the translation and c is the centre point of the rotation [15].

2.5.4 Other parameters

There are a few more parameters in the registration that can be chosen and will affect the result for the registration. They are described in the following text [15].

Image samplers

Image samplers describe different methods to select pixels in the images. The Equations 2.2 to 2.5 all have a sum over all pixels in the image, which will be time consuming. By reducing the amount of pixels, the registration can be faster, even though some information may be lost. In general, the registration can han-dle fewer pixels and only the time will be positively affected. In this thesis, four different types of pixel selection methods have been evaluated.

The first methods uses all the pixels in the image. This results in long execu-tion times but no informaexecu-tion loss. The second method defines a regular grid on the fixed image from which a number of pixels are selected. The third and fourth method is to select the pixels at random in the image. All the pixels have the same probability to be selected and only a part of the total are chosen. In the fourth method it is also possible to select values between two pixels [15].

Interpolation

Interpolation is used to estimate values that are between two pixels. When the registration has been applied, the image has probably been moved to a place where its values might be undefined. This means that if the new position is a non-position, a new value for that position must be calculated. Interpolation can vary in both speed and quality. In this thesis, three different interpolation methods were used. Nearest neighbour interpolation, linear interpolation and B-spline interpolation [15].

Nearest neighbour is a fast method that can result in lower quality images. The method takes the nearest pixel’s intensity value, and selects that value as the new pixel’s intensity. Linear interpolation looks at the surrounding pixels and takes a weighted value of these values. It has the potential to produce high quality images. However, it is slower than the nearest neighbour technique. B-spline is a method that can produce higher quality results, but takes longer time to pro-duce. There are different orders of b-spline. The zero and first order represent the nearest neighbour and linear interpolation [15].

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Data complexity

The complexity of an image describes how much information is contained on the image. An image with low complexity is very smooth and it can also be down sampled, which means that the sampling factor has been decreased from the orig-inal. If the complexity of an image is low, the amount of data contained in it will be smaller, and the time required to apply registration to it will be less. In this thesis, three different types of data complexity reduction techniques have been used: Gaussian pyramid, Gaussian scale pyramid and Shrinking pyramid. When using a Gaussian pyramid, both down sampling and smoothing on the image are applied. This will produce an image with low complexity. Gaussian scale pyra-mid applies only smoothing and Shrinking pyrapyra-mid uses down sampling [15]. The techniques that use down sampling should not be utilized in combination with random or random coordinates (as discussed in image sampling section). However, by applying down sampling on an image or using a grid, the registra-tion will save time [15].

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3

Method

3.1 Experimental setup

The thesis work was evaluated on data from healthy volunteers and patients.

3.1.1 Datasets used

The proposed method was evaluated in 20 subjects including 10 healthy volun-teers and 10 patients with heart failure of different ethologies. These was divided in 8 female and 2 male for the healthy volunteers and 2 female and 8 male for the patients respectively. The age for these person are 65 ± 4 year for healthy volunteers and 65 ± 6 year for patients. The healthy volunteers had no history of prior or current cardiovascular disease or cardiac medication. The patients were enrolled from the Department of Cardiology, Linköping University Hospi-tal. Exclusion criteria for the patients were: significant ventricular arrhythmia, heart rate lower than 40 bpm or greater than 100 bpm, cardiovascular shunt, and more than mild to moderate valvular disorder. The research was performed in line with the Helsinki declaration and was approved by the regional ethics board. All subjects gave written informed consent.

The MRI examinations were performed on a clinical 3T Philips Ingenia scanner (Philips Healthcare, Best, the Netherlands). All subjects were injected with a Gadolinium based contrast agent (Magnevist, Bayer Schering Pharma AG) prior to the acquisition for a late-enhancement study.

Cine MR images were acquired using a balanced Steady-State Free Precession (bSSFP) protocol at end-respiratory breath-holds, resulting in 30 time frames over the cardiac cycle. A short-axis stack with resolution of 1 x 1 mm, and slice thickness of 8 mm was acquired. Two-, three-, and four-chamber long-axis views

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were also obtained with resolution of 1 x 1 mm.

4D Flow MRI examinations were performed during free-breathing, using a navi-gator gated gradient-echo pulse sequence with interleaved three-directional flow-encoding and retrospective vector cardiogram controlled cardiac gating. Scan parameters included: Candy cane view adjusted to cover both ventricles, velocity encoding (VENC) 120 cm/s, flip angle 10 degrees, echo time 2.6 ms, repetition time 4.4 ms, parallel imaging (SENSE) speed up factor 3 (AP direction), k-space segmentation factor 3, acquired temporal resolution of 52.8 ms, spatial resolu-tion 2.7 x 2.7 x 2.8 mm3, and elliptical k-space acquisiresolu-tion. The typical scan time was 7-8 min excluding and 10-15 min including the navigator gating.

Two acquisitions from each dataset: 4D Flow MRI and bSSFP cine MRI SA stack. The 4D Flow image will be the fixed image and the bSSFP cine MRI SA stack will become the moving image when registration is applied. In order to apply regis-tration on these images, they must be prepared so that they represent the same area of the heart. Therefore, the 4D Flow volume was interpolated in the location and direction of each plane in the bSSFP SA stack. In Figure 3.1, the original image from both bSSFP SA stack and 4D Flow are shown. All images are from slice 7, a slice in the middle of the stack.

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Figure 3.1:Original images for different datasets. Top row: bSSFP cine MRI SA stack. Bottom row: same slice but on the 4D Flow MRI.

As can be seen in the images, the resolution is not the same and the interpo-lated slices of the 4D Flow volume contain sections where the two images did not intersect. To solve this problem cropping was used.

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3.2 Automatic image cropping 17

3.2 Automatic image cropping

The original images present a challenge for the registration. To remove the sec-tions, where the bSSFP cine MRI SA stack and 4D Flow images do not intersect, the fixed and moving were pre-processed using a cropping method. Cropping is applied on the images and only the registration; the cropped areas are restored before the final transformation (from registration) is applied to the moving im-age. The cropping allows the registration to focus on the most important parts of the image, such as the heart.

It is worth noting that the cropping must ensure the inclusion of both the left and the right ventricle in the images that are being registered. To ensure that, the middle point of the cropping depends on the position of the heart, and therefore it will be in different points for each dataset. To find the location of the heart, a cropping in the middle area of the original image was used. Figure 3.2 shows the resulting images after cropping the centre of the image.

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Figure 3.2:A smaller image that are used to find the centre of the heart. These images are then converted to binary images by using Otsu´s method, which performs clustering-based image thresholding. The method calculates the optimum threshold for the image in order to separate it into different values. A binary image consists only of pixels that have intensity value 0 or 1. That gives an image that only is black and white and can be seen in Figure 3.3.

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Assumptions that are drawn from this image are that the biggest area will belong to the heart and the other areas will be removed. In figure 3.4, only the biggest area is left.

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Figure 3.4:Binary images when only the biggest area are left.

After that, the centre of mass of that area is calculated. This point is then used as the center of the cropping and converts to a point in the original image. From this point, automatic cropping can be applied. It consist of a square box that is 80x60. In Figure 3.5, it can be seen that the datasets have different centres and therefore the cropping will look different for each datasets.

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Figure 3.5:Point in the middle of the biggest area found in the binary image. The final results from the cropping are shown in Figure 3.6. These images are then the images that are used in the registration.

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3.3 Evaluation 19

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Figure 3.6:Final images for different datasets. The first row shows the cine MR image and the second the same slice in the 4D Flow MRI.

3.3 Evaluation

Different evaluation methods were used to decide which of all the combination of parameters generated the best results. By taking all the measurements from the methods, a final result can be presented. Three different types of evaluation methods were used: geometric measure based evaluation, intensity based evalua-tion, and evaluation through simulated misalignments.

3.3.1 Geometric measure based evaluation

Geometricmeasure based evaluation is independent of the intensity in the objects. It uses contours, which are created by segmenting different parts in the area of interest. In this case, the segmentation was done manually on the endocardium and epicardium in the left ventricle, on both the cine MR and the 4D Flow MR images. The segmentations were done by a clinician with 5 years of experience in cardiovascular imaging. The clinical drew the contours manually in the cine MR images, and then transferred the same contours in the 4D Flow image.

After the registration, the transformation matrix was created from the result and was applied on the contours. The new contours can then be compared to the ground truth, and the difference can be observed. The evaluation methods that are used in this case are the Dice index and the point-to-curve error. In Figure 3.7, it can be seen how the contours look initially in both the bSSFP cine MR image and the 4D Flow image.

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Figure 3.7:Manually delineated contours for both an bSSFP cine MR and an 4D Flow image.

Dice index

Dice index measures percentage of overlap between ground truth and registered contours. Its value is calculated as the intersecting area between the two con-tours, divided by the average area of the individual contours. This can be seen in Equation 3.1.

Dice index = 2|X ∩ Y |

|_{X| + |Y |} (3.1) where X is the ground truth and Y is the registered contour. The range of the Dice index is between 0 and 1, where 1 is a perfect overlap, and 0 indicates no overlap at all [1], [10].

Point-to-curve error

Another measure to test the accuracy of the registration is the point-to-curve er-rors. This error is calculated as the Euclidean distance between the ground truth contour and the registered contour [10].

3.3.2 Intensity based evaluation

Intensity based evaluation compares the similarity in intensities in the whole im-age or in an area of the imim-age after the registration has been performed. During assessment of the result, the evaluation method should not be the same as the one selected during the registration, in order to avoid biases in the evaluation. Because of that, NMI and MI were not used during this step and NCC was se-lected for intensity based comparison.

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3.3 Evaluation 21

Normalized Cross Correlation (NCC)

NCC, is a measure related to the degree of association between two images. To use it, a linear relation between the intensity in the two images has to exist. NCC is defined between -1 to 1, where -1 represents a perfect negative correlation, and 1 a perfect positive correlation. A value of 0 means that the images do not have any correlation at all.

3.3.3 Simulated misalignments

To further evaluate the result from the registration and determine if the method works as expected, simulated misalignments have been applied on one dataset. This dataset has very small misalignments initially. By doing this, the evaluation is easier to do because the expected correction is known. The misalignment is applied with different levels of in order to assess if the method works for all levels of misalignment. To calculate the levels, the mean of the movement for all the datasets was used.

Large simulated misalignments

Large simulated misalignments means that the image has been moved a lot. To know how much a high value is, the mean and standard deviation of all the orig-inal datasets misalignments were determined. These are calculated for all the different slices and this motion was chosen to be the mean plus two standard de-viation. The first and last three slices were not changed. The 4-6 were moved in one direction and the 7-9 in another direction. So the misalignment is between slices 4-9.

Small simulated misalignments

Small simulated misalignments means that the image has been moved little from the original image. This motion was chosen to be the mean value plus one stan-dard derivation and is applied on the same way as the large simulated misalign-ments.

3.3.4 Visualization of the results

Box plots were used to visualize the results. A box plot shows the distribution over the result. The plot consists of a box that includes the median of the result, so 50 percentiles of the result will be in the box. The lower boundary is 25 per-centile of the result and the upper boundary is 75 perper-centile. The line in the box represents the median result. Points that lie further away from the box are called outliers and are the extreme values compare to the other values. The lines that go from the box represent the lowest and highest value of the result that are not outliers [12].

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3.3.5 Region based analysis

The number of slices in SA cine MR images varies in different patients because of the differences in the size of their hearts. As a result, instead of slicewise comparison, a region based comparison was used. The heart was divided into 4 anatomical regions in order to display and analyse the results, as shown in Figure 3.8. Basal (B) Superior Mid-Ventricle (S M-V) Inferior Mid-Ventricle (I M-V) Apical (A)

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4

Results

The results of the evaluation defined in previous chapter are presented here. The results are divided into different sections. First, the results from the best combi-nation of parameters is shown. After that, a comparison of translation and rigid transformations are shown. In the last section, results from the simulated mis-alignments are presented.

4.1 Parameter evaluation

An extensive investigation was performed to find the best possible combination of parameters for the registration. The registration was applied on 20 datasets and 72 parameter combinations were evaluated. Based on the evaluation criteria, the best 8 of them were selected. The selection procedure will be described in de-tail in Chapter 5. The 8 parameter combinations found to be the best are shown in Table 4.1.

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Table 4.1:Best combinations of parameters.

1 2 3 4

Cost function NMI NMI NMI NMI

Interpolation Linear Linear Spline Spline

Transform Rigid/Trans Rigid/Trans Rigid/Trans Rigid/Trans

Optimiser SGD ASGD SGD ASGD

Data complexity G. pyramid G. pyramid G. pyramid G. pyramid

Image sampling Full Full Full Full

5 6 7 8

Cost function MI MI MI MI

Interpolation Linear Linear Spline Spline

Transform Rigid/Trans Rigid/Trans Rigid/Trans Rigid/Trans

Optimiser SGD ASGD SGD ASGD

Data complexity G. pyramid G. pyramid G. pyramid G. pyramid

Image sampling Full Full Full Full

All these 8 combinations have been applied on the entire cohort to compute Dice index and point-to-curve error. These numbers show that the combinations are very similar and therefore the registrations that were less time consuming were chosen. Subsequently for all the tables, plots, and images, the parameter combination number 1 has been used.

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4.2 Registration using translation transformation 25

4.2 Registration using translation transformation

In Figures 4.1 - 4.3, the four images represent slices from different regions of the heart. The overlaid contours depict the movement of bSSFP cine MR images before (red) and after (blue) the registration in comparison to the ground truth (green). Plots of all the contours are presented in Figure 4.4.

(a) (b)

(c) (d)

Figure 4.1:Different slices in a heart with misalignments. a) represent a slice in the apical region, b) and c) is slices in the mid-ventricle region and d) is a slice in the basal region. The overlaid contours depict the movement of cine MR images before (red) and after (blue) the registration in comparison to the ground truth (green).

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(a) (b)

(c) (d)

Figure 4.2:Different slices in a heart with small misalignments. a) represent a slice in the apical region, b) and c) is slices in the mid-ventricle region and d) is a slice in the basal region. The overlaid contours depict the movement of cine MR images before (red) and after (blue) the registration in comparison to the ground truth (green).

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(a) (b)

(c) (d)

Figure 4.3: Different slices in a heart with very small misalignments. a) represent a slice in the apical region, b) and c) is slices in the mid-ventricle region and d) is a slice in the basal region. The overlaid contours depict the movement of cine MR images before (red) and after (blue) the registration in comparison to the ground truth (green).

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(a) (b)

(c) (d)

(e) (f)

Figure 4.4:Datasets with different levels of misalignment. a) large misalign-ment, c) small misalignment and e) no or very small misalignment. b), d) and f) present the images after the registration for the different datasets.

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4.2.1 Comparison of the datasets and regions of the heart

The data from the entire cohort was registered with the finally selected parame-ters and the quality of registration was evaluated using the Dice index and point-to-curve error. Figure 4.5 and Table 4.2 show the patientwise comparison and Figure 4.6 and Table 4.3 show how the different regions of the heart were affected by the registration.

Comparison between datasets

First a comparison between the different datasets for the two types of calcula-tions. In Figure 4.5a, Dice index and in Figure 4.5b, point-to-curve error. The corresponding numbers from the plots are shown in Table 4.2.

(a)

(b)

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Table 4.2: Minimum, mean and maximum values for Dice index and point-to-curve error for all datasets.

Dataset Dice index Point-to-curve error

Min Mean Max Min Mean Max

1 0.5121 0.6590 0.7411 2.2115 2.3894 2.6763 2 0.5474 0.8229 0.8601 0.8837 1.0177 1.8264 3 0.3932 0.7075 0.7904 1.2297 1.5676 2.8030 4 0 0.8632 0.9183 0.4754 0.7452 4 5 0.4345 0.7217 0.7918 1.4261 1.5258 2.1530 6 0.1755 0.6939 0.8584 0.9031 1.4902 3.2717 7 0.2438 0.4931 0.5957 2.2792 2.5943 3.1949 8 0.4006 0.8071 0.8551 0.8244 0.9849 2.3609 9 0.1039 0.8413 0.9055 0.6945 0.9232 3.5980 10 0.4310 0.8055 0.8911 0.6742 1.2470 2.6072 11 0 0.7215 0.8928 0.9795 1.7386 4 12 0.2626 0.7086 0.8705 1.0319 1.6669 3.1532 13 0.4473 0.7797 0.9109 1.1127 1.7353 3.1497 14 0.3179 0.7290 0.8563 1.0754 1.4270 2.7728 15 0.4601 0.6490 0.6801 2.1569 2.5689 3.5473 16 0.1657 0.6949 0.8021 1.8088 2.2298 3.5360 17 0.3138 0.6509 0.7617 1.5076 1.8476 2.9776 18 0.5369 0.8264 0.8475 1.5331 1.5382 2.3755 19 0.5131 0.7759 0.8335 1.5205 2.1019 2.9391 20 0.5246 0.7865 0.8597 1.3523 1.7551 2.6172

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Comparison between different regions of the heart

Then a comparison between the regions in the heart for the two types of calcu-lations. In Figure 4.6a, Dice index and in Figure 4.6b, point-to-curve error. The corresponding numbers from the plots are shown in Table 4.3.

(a)

(b)

Figure 4.6:Dice index and point-to-curve errors for the different regions of the heart.

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Table 4.3:Minimum and maximum values for Dice index and point-to-curve error for all different regions of the heart. A: Apical, B: Basal, M-V: Mid-ventricle.

Regions of heart

Dice index Point-to-curve error

Min Max Min Max

A 0 0.5474 1.8264 4

Inferior M-V 0.3185 0.8975 0.6742 2.6447 Superior M-V 0.5580 0.9032 0.7411 3.5473

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4.3 Registration using rigid transformation 33

4.3 Registration using rigid transformation

Here are the results from the rigid transformation. In Figures 4.7 - 4.9, the four images represent different slices of the heart. Also plots of all the contours to-gether are presented. These are shown in Figure 4.10.

(a) (b)

(c) (d)

Figure 4.7:Different slices in a heart with misalignments. a) represent a slice in the apical region, b) and c) is slices in the mid-ventricle region and d) is a slice in the basal region. The overlaid contours depict the movement of cine MR images before (red) and after (blue) the registration in comparison to the ground truth (green).

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(a) (b)

(c) (d)

Figure 4.8:Different slices in a heart with small misalignments. a) represent a slice in the apical region, b) and c) is slices in the mid-ventricle region and d) is a slice in the basal region. The overlaid contours depict the movement of cine MR images before (red) and after (blue) the registration in comparison to the ground truth (green).

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(a) (b)

(c) (d)

Figure 4.9: Different slices in a heart with very small misalignments. a) represent a slice in the apical region, b) and c) is slices in the mid-ventricle region and d) is a slice in the basal region. The overlaid contours depict the movement of cine MR images before (red) and after (blue) the registration in comparison to the ground truth (green).

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(a) (b)

(c) (d)

(e) (f)

Figure 4.10: Datasets with different levels of misalignment. a) dataset with large misalignment, c) dataset with small misalignment and e) dataset with no or very small misalignment. b), d) and f) present the images after the registration for the different datasets.

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4.3.1 Comparison of the datasets and regions of the heart

In the same way as presented in the previous section, when using translation transformation during the registration, the Dice index and the point-to-curve er-ror where also used to evaluate the results. Figure 4.11 and Table 4.4 show the patient comparison and Figure 4.12 and Table 4.5 show how the different regions of the heart were affected by the registration.

Comparison between datasets

First a comparison between the different datasets for the two types of calcula-tions. In Figure 4.11a, Dice index and in Figure 4.11b, point-to-curve error. The corresponding numbers from the plots are shown in Table 4.4.

(a)

(b)

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Table 4.4:Minimum and maximum values for Dice index and point-to-curve error for all datasets.

Datasets Dice index Point-to-curve error

Min Max Min Max

1 0.4169 0.8025 1.7129 4.0397 2 0.0581 0.9079 0.5834 11.4313 3 0.0386 0.7951 1.2424 11.4808 4 0 0.9134 0.4903 7.1796 5 0.0359 0.8260 1.2668 11.6878 6 0.1598 0.8265 1.0542 3.3247 7 0.2402 0.5807 2.4916 4.1559 8 0.0511 0.8655 0.7685 11.1054 9 0 0.9173 0.6022 9.5672 10 0.0855 0.9051 0.5799 7.3408 11 0 0.8731 1.2115 6.3841 12 0.0528 0.8494 1.2995 11.8743 13 0.3546 0.9079 1.1695 5.2347 14 0.2190 0.8221 1.3091 3.6166 15 0.0614 0.5639 2.7222 12.1429 16 0.0561 0.8068 1.7857 4.7002 17 0.0773 0.7780 1.3800 8.0546 18 0.0626 0.6513 2.2277 11.1131 19 0.1117 0.7821 1.9286 9.3545 20 0.1363 0.8399 1.4671 5.2488

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Comparison between different regions of the heart

Then a comparison between the regions in the heart for the two types of calcula-tions. In Figure 4.12a, Dice index and in Figure 4.12b, point-to-curve error. The corresponding numbers from the plots are shown in Table 4.5.

(a)

(b)

Figure 4.12:Dice index and point-to-curve errors for the different regions of the heart.

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Table 4.5:Minimum and maximum values for Dice index and point-to-curve error for all different regions of the heart. A: Apical, B: Basal, M-V: Mid-ventricle.

Regions of heart

Dice index Point-to-curve error

Min Max Min Max

A 0 0.4169 3.3247 12.1429

Inferior M-V 0.1958 0.9051 0.5799 7.2405 Superior M-V 0.3947 0.9173 0.5834 4.5156

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4.4 Comparison between translation and rigid transformation 41

4.4 Comparison between translation and rigid

transformation

To compare the transformations, they were plotted against each other. This has been done for each region and for both Dice index and point-to-curve error. In Figure 4.13, Dice index and in Figure 4.14, point-to-curve error. a),b), c) and d) represent the regions, starting with apical and ending with basal.

(a) (b)

(c) (d)

Figure 4.13: Dice index after using translation and rigid transformation in a) apical region, b) inferior mid-ventricle region, c) superior mid-ventricle region and d) basal region.

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(a) (b)

(c) (d)

Figure 4.14: Point-to-curve errors after using translation and rigid trans-formation in a) Apical region, b) Inferior mid-ventricle region, c) Superior mid-ventricle region and d) Basal region.

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4.5 Simulated misalignments 43

4.5 Simulated misalignments

As previously explained, different levels of misalignment were applied to one dataset. The parameters that produced the best results were used to register this set. The result from this registration are shown in Table 4.6 and Table 4.7. In Figure 4.15, the contours from different datasets are shown before and after the registration.

Table 4.6: Dice index for different levels of simulated misalignments. U and R stand for unregistered and registered images, respectively. In the first column, different levels of misalignments are shown. µ and σ are the mean and standard deviation of the original movement, respectively. The value in the last row does not include the results from the apical region.

Simulated misalignment Regions Mean value A I M-V S M-V B µ + 2 σ U 0.8254 0.4759 0.5985 0.9223 0.6656 R 0.3388 0.9381 0.8853 0.9063 0.9126 µ + σ U_R 0.8254_0.3401 0.6985_0.9034 0.5616_0.9121 0.9223_0.9055 0.8960_0.9099 None U 0.8254 0.8222 0.9239 0.9223 0.8894 R 0.3117 0.8975 0.8973 0.9055 0.9001

Table 4.7:Point-to-curve (in mm) for different levels of simulated misalign-ments. U and R stand for unregistered and registered images, respectively.

µ and σ are the mean and standard deviation of the original movement,

re-spectively. The value in the last row does not include the results from the apical region. Simulated misalignment Regions Mean value A I M-V S M-V B µ + 2 σ U 1.0836 2.6120 2.4973 0.5581 1.8892 R 2.6352 0.3975 0.6963 0.7805 0.6248 µ + σ U 1.0836 2.1084 2.6155 0.5581 0.7451 R 2.6305 0.4145 0.8418 0.6948 0.6656 None U 1.0836 1.2502 0.5504 0.5581 0.7862 R 2.7941 0.7105 0.7411 0.6945 0.7154

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(a) (b)

(c) (d)

(e) (f)

Figure 4.15: Contours for different levels of simulated misalignments. a) large level of misalignment, c) small level of misalignment and e) no mis-alignment. b), d) and f) present the images after the registration.

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5

Discussion

The results show that the misalignments caused by respiratory motion artefacts can be mitigated by the proposed method. In the following text, we discuss how the different components of the proposed registration approach influence the ac-curacy of the resulting alignments.

It was a challenge to use intensity based registration on the types of images used because of the big difference in resolution and intensity between them. One prob-lem that developed from the large difference in resolution was during the evalua-tion of the method. It was hard to compare the two images to each other and also hard to find an intensity based method that worked on both images. However, when using an evaluation method that only depended on the distance and the ge-ometric properties of the images, a better comparison was possible. The results show that the developed correction method is able to improve the alignment of the bSSFP cine MR SA stack. The method was further validated by the results ob-tained on the simulated misalignments, even when presented with small or large errors.

5.1 Cropping

Cropping of the images is an important step because without it, the registration might result in suboptimal alignments. Since both the left and right ventricles are visible in the SA format and present the desired information, the cropping was implemented in this work to ensure those structures. But this cannot be guaranteed for all cases, because of the variations in size and location of the heart across the patient population. It is often hard to find a small heart and hence its centroid, especially in the apical slices. In that case, the automatic cropping may miss the heart. On the other hand, when a patient has a large heart, cropping

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might not include the entire heart. In both of these cases, there is a higher proba-bility of suboptimal registration.

For this work, we used a constant cropping size for the entire cohort with an additional visual check to make sure that the complete heart is included in the cropping. After the registration, the cropped area will be restored and the whole image is moved. To avoid the visualization step, the implemented tool can be improved by using a weight function instead. This function will then adjust the crop based on the size of the heart and the location of the slice to be registered. Another possible improvement would be to use the location of the LA images. A center-line of the left ventricle of the heart can be found and its position can be used as the center for the cropping.

5.2 Registration parameters

In total, 72 parameter combinations were tested. Eventually, NCC and the pro-cessing time were used to select the best 8 combinations. These combinations can be seen in Table 4.1. It can be observed from this table that they include only one type of image sampling (full) and one type of data complexity (Gaussian pyra-mid). The Gaussian pyramid does both down sampling and smoothing of the image, which results in a low complexity and by using full image sampling, all the pixels in the images are used.

From theses combinations, similarities were found. There was either a small or no difference between the interpolation methods (linear and spline) and between the optimization strategies (SGD and ASGD). This can be explained by the fact that the images being used do not have very high resolution. From this, it can be concluded that a finer interpolation like spline and a more advanced optimiza-tion like ASGD is not needed. The selecoptimiza-tion of the cost funcoptimiza-tion was from the beginning rather straightforward. Due to the difference in the intensity distribu-tion and resoludistribu-tion of the cine and 4D Flow MR images, mutual informadistribu-tion (MI) and its normalized form, normalized mutual information (NMI), were the best candidates. Since NMI brings the MI values to a bounded range (0,1), it offered a better comparison measure for this work.

For transformation, two options were available: rotation and translation. Many of the misalignments that can occur during a scan are caused by the patient breath-ing or movbreath-ing around. These types of misalignments can usually be fixed by using just rotation and translation. Furthermore, the size and shape of the heart will not be affected and affine transformation is not needed. These two different transformations methods, together with the best combination of the remaining parameters were then used in all images and plots that were shown in the result. While using transformations that include both rotation and translation alignment method resulted in some improvements. However, the best results were obtained

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5.3 Geometric accuracy 47

using only translation. That is because of the limiations of movement imposed initially during generation of the ground truth and also because of the typical presentaion of breath-hold motion errors.

5.3 Geometric accuracy

When registration was applied, which can be seen in Figures 4.1 - 4.3 and in Fig-ures 4.7 - 4.9, the bSSFP cine MR image has been moved to a more correct place. That is illustrated by the difference between the red and the blue contours in the figures. It can be seen that the different images have more or less misalignment initially by looking at the distance between the red and the green contours. If the image was perfect from the beginning, the red and the green should be on top of each other and correction should not be needed. But that was not the case in any of the datasets that were analysed.

When only using translation, Figures 4.1 - 4.3, the image was closer to the ground truth for all the cases. This means that the correction has improved the resulting images. For rigid transformation, Figures 4.7 - 4.9, the contours are in some cases further away than initially. The difference observed between these two transfor-mation types can depend on the way that the ground truth was created, since only translation was allowed when manually aligning the bSSFP cine MR SA stack seg-mentation to the 4D Flow MR image. The contour was never rotated and that could be affecting the result.

In Figures 4.5 and 4.11, boxplots of the Dice index and the point-to-curve error were shown for all the datasets that were used. In Table 4.2 and 4.4 the maxi-mum and minimaxi-mum numbers for the plots were shown. Here it can be seen that the data are very different between datasets. Consequently, it is hard for the reg-istration to fix all the problems. Some things that are misleading in this boxplots are when the interpolated plane created from the 4D Flow MRI contains many empty values, since the intersection between this image and the SA slice is small. For this slices, it was hard to decide where the heart was located. The contour will then most likely be missed for that slice, which resulted in low Dice indexes and high point-to-curve errors.

From Figures 4.6 and 4.12, plots of the Dice index and the point-to-curve error are shown for the different regions of the heart. In Table 4.3 and 4.5 the maxi-mum and minimaxi-mum numbers for the plots are shown. Since the datasets have different amounts of slices, different regions were used instead. It can be seen in the plots that the groups do not have the same result. The registration did not work optimally for the first group that corresponds to the apical part of the heart, but obtained better results for the other three. This is because the apex can not always be seen in these images. Additionally, especially in these images, part of the SA slice is often only partially included in the 4D Flow MRI volume.

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A future work to solve this problem could be to apply different types of trans-formations on different parts of the heart. This could improve the correction, and parts of the heart that are more misaligned than others can benefit from a more adaptable method.

5.4 Evaluation of the results

Both intensity and geometric measures based methods can be to evaluate the result. However, because of the large differences in the intensity distribution be-tween the images, intensity based evaluation did not reflect the true similarities between the compared images. Consequently, NCC was just used to reduce the amount of combinations and geometric methods were used for the evaluation of the registration results. A future work related to this is to find an intensity based method that can also be used to further evaluate the final result.

5.5 Simulated misalignments

This evaluation method provided a better idea of the potential of the developed method. In Table 4.6 and Table 4.7, it can be seen that the registration works for both large and small misalignments. The Dice index became higher than before and the point-to-curve errors became lower. In Figure 4.15, it can also be seen that the alignment of the slices was improved. Additionally, improvements in the smoothness of the contours can be seen in Figure 4.15a and 4.15b.

5.6 Implentation details

When the best parameter combination was selected, all the combinations was very similar and therefore the registrations that were less time consuming were se-lected. In this case, there was a difference between 345sec and 771sec in time be-tween the best and worse combination for a specific dataset. The system used for all experiments had following specifications: Intel Core i7-4770 CPU@ 3.4GHz and RAM 8 GB.

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6

Conclusions

In this thesis the feasibility of an automatic image registration method was tested to correct the misalignment in morphological cine MR images by using the 4D Flow MR as the reference image. The results from geometric evaluation on the data from healthy volunteers and patients show that the proposed method is able to mitigate the motion artefacts caused by both large and small respiratory move-ments during image morphological cine MRI acquisitions. As such it has the potential to improve 4D flow MRI segmentation for a reliable assessment of car-diovascular blood flow.

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Automatic Alignment of 2D Cine Morphological Images Using 4D Flow MRI Data

Master of Science Thesis in Electrical Engineering

Department of Electrical Engineering, Linköping University, 2016