Fiber architecture of the post-mortem rat heart obtained ... · ﬂber architecture, but a detailed picture of ﬂber architecture in regions such as the base or the ventricle fusion

Fiber architecture of the

post-mortem rat heart obtained

with Diffusion Tensor Imaging

MSc-thesisD.J. Hautemann

August 2007BMTE 07.29

Supervisors:

dr. ir. Peter Bovendeerddr. ir. Gustav Strijkersprof. dr. ir. Frans van de Vosse

Biomedical NMR & Cardiovascular BiomechanicsDepartment of Biomedical EngineeringEindhoven University of Technology

Abstract

The global mechanical performance of the heart is the result of the cooperative action of themuscle cells in the wall. In order to understand how each part of the wall contributes tototal pump function, local mechanics are of interest, e.g. the distribution of myofiber stressand strain throughout the cardiac wall. Since myocardial tissue organization is one of themain determinants of this behavior, a thorough understanding of the cardiac morphology isneeded.

Currently, it is investigated through Finite Element (FE) modeling whether cardiac fiberarchitecture can be predicted from models of cardiac adaptation. Knowledge of region-specificfiber orientation is needed to test the model predictions. Diffusion Tensor Magnetic ResonanceImaging (DTI) is a technique capable of measuring cardiac fiber architecture non-invasivelyin the intact post-mortem heart and has been used studying fiber architecture for the lastdecade. However, a detailed picture of region-specific fiber architecture is still lacking.

The aim of this study was to give insight in the region-specific nature of ventricular fiberarchitecture with a special interest to the base region and the fusion sites of the left and rightventricle. Cardiac fiber architecture of the rat heart was measured with DTI and tools weredeveloped for data quantification. Fiber architecture was investigated qualitatively throughtractography and quantitatively through the analysis of fiber angle distributions.

An in situ perfusion fixation protocol of the rat heart was developed, that resulted ina suitable heart specimen. The use of isotropic imaging resolution enabled the study ofregion-specific fiber architecture. Transmural fiber orientation was found resembling a fan-like pattern, as reported in literature. In-plane fiber architecture showed different feather-likepatterns, being in agreement with some and in conflict with other reports in literature. Theshape of the transmural helix angle course was found to be region-specific; in the septumand free wall it showed a steady decreasing slope from subendocardial region to epicardialwall, while at the anterior and posterior fusion sites (FSA and FSP) the courses were nonmonotonous, with bumps in the midwall region.

In addition, by focussing on the zero-out-of-plane (ZOOP) band, defined as the region inwhich fibers are in plane with a short axis slice, it was found that the fusion of both ventricleswas more distinct at the FSP than at the FSA. Earlier findings in literature on the transverseangle in the midwall region were confirmed by our results but shown incomplete. In the baseregion a zone of inflection was found through tractography and quantification, confirmingearlier findings in literature through blunt dissection.

In conclusion, the applied preparation method and measurement settings enabled theregion-specific study of cardiac fiber architecture. Visualization of fiber architecture withtractography and the developed quantification method enabled the findings of typical as wellas atypical patterns. Thus, a deeper understanding of the region-specific nature was obtainedin this study.

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Contents

Abstract 2

List of symbols 6

List of abbreviations 8

1 General introduction 101.1 Project aim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111.2 Outline of this study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

2 Background 122.1 Cardiac morphology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

2.1.1 Gross anatomy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.1.2 Constituents and structure of the ventricular myocard . . . . . . . . . 132.1.3 Ultrastructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.1.4 Microstructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.1.5 Macrostructure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.1.6 Myocardial fiber architecture . . . . . . . . . . . . . . . . . . . . . . . 16

2.2 DTI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.2.1 Principles of Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.2.2 Diffusion tensor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282.2.3 DW-MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292.2.4 DTI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302.2.5 DTI of the myocard . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3 Experiment 363.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.2 Materials and methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.2.1 Specimen preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . 363.2.2 DTI acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.2.3 Data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.3.1 Diffusion characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . 413.3.2 Superficial endocardial fiber architecture . . . . . . . . . . . . . . . . . 423.3.3 Fiber architecture in the compacta region . . . . . . . . . . . . . . . . 43

3.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.4.1 DTI acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

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3.4.2 Specimen preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . 523.4.3 Diffusion characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . 533.4.4 Data visualization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533.4.5 Myocardial fiber architecture . . . . . . . . . . . . . . . . . . . . . . . 53

3.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

4 Quantification of fiber architecture 564.1 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

4.1.1 Anatomical coordinate system . . . . . . . . . . . . . . . . . . . . . . 564.1.2 Fiber angle calculations . . . . . . . . . . . . . . . . . . . . . . . . . . 584.1.3 Geometric characteristics . . . . . . . . . . . . . . . . . . . . . . . . . 584.1.4 Presentation of myofiber direction data . . . . . . . . . . . . . . . . . 59

4.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604.2.1 Geometric characteristics . . . . . . . . . . . . . . . . . . . . . . . . . 604.2.2 Fiber angle distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 614.2.3 Base region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

4.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 694.3.1 Cardiac coordinate system . . . . . . . . . . . . . . . . . . . . . . . . . 694.3.2 Quantification near the base . . . . . . . . . . . . . . . . . . . . . . . . 694.3.3 Fiber angle distribution . . . . . . . . . . . . . . . . . . . . . . . . . . 70

4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5 General discussion 74

Acknowledgements 78

A Fiber angle distribution contour plots 84

B Transmural fiber angle courses in the basal region 88

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List of symbols

Symbol Description UnitsADC Apparent diffusion coefficient m2 · s−1

αh Helix angle ◦

αt Transverse angle ◦

b-factor Strength of diffusion weighting s ·m−2

D Diffusion coefficient m2 · s−1

D Diffusion tensor -D Diffusion matrix -D′ Diffusion matrix with respect to eigenvectors -Dav Average diffusion coefficient m2 · s−1

∆ Pulse separation time sδ Pulse duration s~e1 Principal eigenvector -~e2 Secondary eigenvector -~e3 Tertiary eigenvector -e3 Transverse angle ◦

~ec Circumferential direction -~ef Fiber direction -~eip In-plane fiber vector -~el Longitudinal direction -~eoop Out-of-plane fiber vector -~er Radial direction -~ez z-direction -FA Fractional anisotropy -G Gradient strength T ·m−1

Gdiff Diffusion gradient strength T ·m−1

γ Gyromagnetic ratio MHz · T−1

h Normalized transmural wall coordinate -λ1 Principal eigenvalue m2 · s−1

λ2 Secondary eigenvalue m2 · s−1

λ3 Tertiary eigenvalue m2 · s−1

ÃLab Apex-to-base length -

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Symbol Description UnitsN Number of dimensions -R Distance between a point and Zc mR0 Distance between a point on the ZOOP ellipse and Zc mRm Mean midwall radius mS0 Signal intensity without diffusion weighting mSb Signal intensity with diffusion weighing mt Time sT1 Spin-lattice relaxation time sT2 Spin-spin relaxation time stdiff Diffusion time sTE Echo time sTR Repetition time sΦ Rotation angle ◦

Zc Cardiac z-axis direction -

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List of abbreviations

3DSE Three dimensional spin echoA AnteriorCHESS Chemical shift selectiveDAI Diffusion anisotropic indexDTI Diffusion Tensor magnetic resonance imagingDT-MRI Diffusion Tensor magnetic resonance imagingDW-MRI Diffusion weighted magnetic resonance imagingFE Finite elementFLASH Fast low angle shot gradient echoFOV Field of viewFSA anterior ventricular fusion siteFSP posterior ventricular fusion siteFW Free wallIP In planeIPM Inter Papillary MuscleLV left ventricleOOP Out of planeP PosteriorPBS Phosphate buffered salinePFA ParaformaldehydePP Perpendicular to the planeRF Radio frequenceRV right ventricleS SeptumTCI trabeculata compacta interfaceVOI Volume of interestVMB Ventricular myocardial bandZOOP Zero-out-of-plane

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Chapter 1

General introduction

The function of the heart is to provide blood flow to the circulatory system, so that the cellsin the body are supplied with oxygen and nutrients, and waste products can be retrieved fromthem. The global mechanical performance of the heart is the result of the cooperative action ofthe muscle cells in the wall. Function of the cell depends on the moment of electrical activation,the availability of oxygen and nutrients, and its mechanical environment. In cardiac research,the main topics of research are the spatial distribution of metabolical, electrophysiologicaland mechanical behavior of the heart.

Global pump work is directly related to myofiber work. The stress generated in themyofibers is responsible for the pressure rise in the ventricles. Once ventricular pressureexceeds end-diastolic aortic and pulmonary pressure, blood is ejected into the aorta andpulmonary artery, respectively. The amount of blood ejected is directly related to sarcomereshortening. Generally, global left ventricular (LV) pump function is characterized by a systolicpressure of about 16 kPa and an ejection fraction of the cavity by 60% [25].

In order to understand how each part of the wall contributes to total pump functionunder normal and pathological conditions such as ischemia, or with conduction disorders,local mechanics are of interest, e.g. the distribution of myofiber stress and strain throughoutthe cardiac wall.

Because of the difficulties associated with the experimental analysis of local ventricularmechanics, mathematical Finite Element (FE) models have been developed to investigatethe factors that govern the local mechanical behavior of the individual muscle cells and theconnective tissue that surrounds the cells. An example of such a model is the one developedby Bovendeerd et al. With this model, the cardiac cycle can be simulated.

The initial FE model consisted of the LV only, modeled as a thick-walled ellipsoid. It wasfound that the choice of fiber direction strongly affects the distribution of stress and strain[7] [8] [46]. The next step was to extend the model to obtain both the LV and right ventricle(RV). A first attempt has been made by Kerckhoffs et al. with a fairly realistic shape of theheart. However, fiber orientation was not realistic, partly because of the lack of experimentaldata in the RV free wall, the base of the heart and the area of connection between the RVand LV wall [25]. Currently, in the PhD-project of Wilco Kroon, it is investigated whethercardiac fiber architecture can be predicted from models of cardiac adaptation. In this project,knowledge of region-specific fiber orientation is needed to test the model predictions.

Since myocardial tissue organization is one of the main determinants of this behavior, athorough understanding of the cardiac morphology is needed. Cardiac fiber architecture has

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Project aim General introduction

been investigated by many researchers, and cardiac models have been equipped with theirfindings. However, knowledge of fiber architecture is still incomplete. During the last twentyyears a technique called Diffusion Tensor Magnetic Resonance Imaging (DT-MRI or DTI)has been developed. DTI is capable of measuring cardiac fiber architecture non-invasively inthe intact post-mortem heart. For the last decade, it has been used in the study of cardiacfiber architecture, but a detailed picture of fiber architecture in regions such as the base orthe ventricle fusion sites is still lacking.

1.1 Project aim

The goal was to give insight in the region-specific nature of ventricular fiber architecture witha special interest to the base region and the fusion sites of the left and right ventricle. Tothis end, cardiac fiber architecture was measured with DTI and tools were developed for dataquantification.

1.2 Outline of this study

Because interpretation of data measured with DTI needs a thorough understanding of tissuestructure, this is the primary topic of Chapter 2. In addition, qualitative and quantitativeknowledge of fiber architecture is evaluated. The subject of the second part in Chapter 2is DTI. It will be explained how self-diffusion is measured, how three-dimensional diffusioninformation is obtained in a diffusion tensor, how it correlates with fiber orientation and howanisotropic parameters are retrieved from it. Furthermore, it will be explained how the dif-fusion tensor can be used to visualize the orientation of the fibers with tractography. Also,optimal preparation of a heart specimen before measurement is addressed. In Chapter 3, theresults of the measurements of fiber architecture in the rat heart are discussed qualitatively.Chapter 4 provides a quantitative analysis of the fiber architecture of the rat heart. Finally,Chapter 5 contains a general discussion on the reported findings in the region-specific natureof fiber architecture and on the developed tools for quantification. Furthermore, recommen-dations can be found here for future research of fiber architecture and the development oftools.

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Chapter 2

Background

The organization of myocardial tissue has been a topic of research for many centuries. Manyresearchers have contributed to describing the heart structure on different levels. Gross mor-phology, microstructure and ultrastructure are relatively well understood levels of organiza-tion. However, in between the level of gross anatomy and cardiac microstructure lies the levelof (myo-)fiber architecture. Observing the ventricular myocard at this scale, it is known thatfibers are arranged in layers of about four cells thick (e.g.laminar structures or myolaminae),but it is still not completely clear how the cardiac myofibers are oriented, connected andorganized in the whole heart.

Several concepts on this level of tissue organization have been developed, each of whichhas its own implications on the wall mechanics. These different concepts have been reviewedrecently by Gilbert et al. [15].

In order to be able to measure tissue anisotropy with DTI and interpret its results, anunderstanding of the structural organization of the tissue of interest is needed as well as someknowledge of the principles of diffusion, how it can be measured with MRI and how resultscan be visualized. Thus, the goal of this chapter is to provide enough background on the topicof fiber architecture and its measurement technique DTI in order to understand the resultsfound in Chapter 3 and 4.

The first part of this chapter deals with the structure of ventricular myocardial tissue atdifferent levels. Research of fiber architecture has been done with different techniques, eachyielding different insights. Some concepts developed are discussed as well as previously foundquantitative results of fiber architecture, obtained with DTI or other techniques.

In the second part of this chapter, it is explained how fiber architecture can be mea-sured with DTI. To explain this technique, basic principles of the diffusion process will beaddressed. After that, the Diffusion-Weighted Spin-Echo sequence is explained. Next, it isexplained how a diffusion tensor is derived, containing 3D structural information. Then it isexplained how the diffusion tensor can be interpreted in order to derive fiber architecture, e.g.fiber orientation and anisotropic indices. Also, tractography or ”fiber tracking” is explained,which provides a means of visualizing 3D anisotropic structures. In addition, some issues areconsidered dealing with the preparation of a suitable heart specimen for measurement withDTI.

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Cardiac morphology Background

2.1 Cardiac morphology

2.1.1 Gross anatomy

The heart is a muscular organ that consists of 4 cavities, two atria which collect blood from twosources and two ventricles which pump blood into two sinks. The right atrium collects bloodfrom the systemic circulation from where it flows through the Tricuspid valve into the rightventricle (RV) which pumps blood through the Pulmonary valve into the respiratory system.Blood from the respiratory system is collected in the left atrium from where it flows throughthe Mitral valve into the left ventricle (LV) from where it is pumped through the Aortic valveinto the systemic circulation. The LV wall is thicker than the RV wall which is not strange,considering the fact that the systemic circulation is larger than the respiratory circulationand therefore gives more resistance to the outflowing blood. The atria are separated from theventricles by the base. The point or ”tip” of the heart farthest away from the base is calledthe Apex. At about 1/3 apex-to-base distance away from the base lies the equator.

The ventricles are separated by the intra-ventricular septum which anatomically belongs tothe LV. The LV can be geometrically described as a truncated thick-walled ellipsoid. Lookingcloser at the LV wall different layers or regions can be distinguished. The outer boundary ofthe free wall is called the epicardial wall and is smooth. The endocardial wall is irregular withtrabeculae, or invaginations, protruding into the wall up to 30% of its thickness. In additionto the trabeculae, papillary muscles originate from the endocardial wall which support theleaflets of the mitral valve through the chordae tendineae [9]. This endocardial layer is alsoreferred to as the trabecular layer. The dense muscular midwall layer is called the compactaregion. The intermittent region is referred to as the trabeculata-compacta interface (TCI)[39].

2.1.2 Constituents and structure of the ventricular myocard

The building block of the heart muscle is the cardiac myocyte. These cells fill about 80% of theventricular myocard volume [29]. Other constituents are blood vessels supplying oxygen andnutrients to the myocytes, and the collagenous extracellular network, in which myocytes arepositioned in a manner that is complex and is the topic of this project, the fiber architecture.

2.1.3 Ultrastructure

Contraction of a myocardial fiber takes place on an ultrastructural level. In short, myocytescontain contractile elements called sarcomeres, which consist of a parallel three-dimensionalarray of thin actin and thick myosin filaments. Sarcomeres can be viewed as short cylindersof about 2 µm long, terminated by Z-discs (Figure 2.1). In between two subsequent Z-discs,the myosin filaments are suspended by titin filaments. From each Z-disc, actin filamentsextend in between the myosin filaments, in a hexagonal pattern. Sarcomere are coupled inseries through the Z-discs. The discs are connected to the cell membrane where they formthe insertion places for the collagen struts that connect adjacent myocytes.

Contraction of the myofibers occurs upon depolarization of the myofiber cell membrane.This process, called excitation-contraction coupling involves spreading of the action potentialto the sarcoplasmatic reticulium (SR) through the T tubuli. From the SR, Calcium ionsare released into the intrafibrillar space, where they bind to the actin filaments and exposemyosin binding sites. Then, myosin binds to actin through myosin heads. Depending on the

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mechanical boundary conditions, either fiber shortening or stress development occurs, or acombination of the two. After about 200 ms, the myosin heads release from the actin bindingsites, using energy supplied by ATP.

Figure 2.1: The major components of a cardiac muscle sarcomere, the smallest contractile unit, areshown. It consists of thin actin (green) and thick myosin (red) filaments. In between two subsequentZ-discs, the myosin filaments are suspended by titin (light blue) filaments. Furthermore, band patternsindicated in the figure can also be noticed with a view at microstructural level (see Figure 2.2) [17].

2.1.4 Microstructure

The shape of the cardiac myocyte itself can be thought of as a rod 12-20 µm in diameterand 60-100 µm long. A train of such rods could form a single fiber, but mostly the myocytesshow terminal anastomoses, or branching, forming Y junctions with more than one othercell. The myocytial interconnections occur through intercalated discs. Therefore if a cardiacfiber would be tracked, many pathways may be found [39]. This is in great contrast withthe long and discrete skeletal muscle fibers, which are built of multinucleated myotubes.Therefore, mapping fiber direction from origin to insertion will result in a single fiber path.This difference is illustrated in Figure 2.2.

Each myocyte is wrapped in a prominent sheath of endomysium which supports the Z-band and basal laminae.

The term myofiber direction is denoted by Gilbert et al. [15] as the net axial direction ofmyocytes at a specific cardiac location. The orientation of these myofibers is referred to asfiber architecture.

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Figure 2.2: Microstructure of skeletal (a-b) and cardiac (c-d) muscle. The most profound differenceis that skeletal myocytes are organized as discrete fiber bundles of fiber, while cardiac myocytes showterminal anastomoses, forming y junctions with more than one cell.

2.1.5 Macrostructure

Not only are myocytes interconnected, they are also organized in groups of about four cellsthick, surrounded by a perimisial weave. These groups are referred to as myolaminae andare depicted in Figure 2.3. The perimysium unites the myolaminae as units, from within,via collagen struts linking adjacent myocytes (120-150 nm), and exteriorly as a weave ofconnective tissue. Long perimysial collagenous tendons link connective tissue of adjacentmyolaminae [15]. Interconnections between myolaminae were found sparse with about 7 to13 branches per mm depending on the location in the LV myocard [29].

(a) (b)

Figure 2.3: Micrographs of myolaminae. (a) Is a tangential surface of myocardial tissue showinglayered organization of myocytes, branching of layers (arrow), and collagen fibers between adjacentmyolaminae. Scale bar, 100 µm. (b) shows a transverse surface of the specimen. Perimysial connectivetissue weave surrounding the myolaminae is evident and covers surface cappilaries (c). Scale bar, 25µm. [29]

The myolaminae are organized in the myocard in such a way that in between them gaps

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may occur, which are called cleavage planes [15]. This had already been found earlier byHort et al. as stated by Streeter [39]. It was found that these gaps were systematicallyordered anastomosis-poor sections in the myocard. A feather-like pattern or ”pinnation”was found. In the apical half, they were found pointing clockwise when looking towards thebase. In the basal half the pinnation figures were reversed looking towards the base, pointingcounter-clockwise. In literature, the term ”sheet” is used to describe the planar features ofthe myocardial wall, both the myolaminae and the cleavage planes between myolaminae [10].

2.1.6 Myocardial fiber architecture

Quantification of myofiber orientation

As reported by Streeter [39], Hort was the first to quantify fiber orientation. Streeter quan-tified fiber architecture by introducing the helix and transverse angle. The helix angle (αh)spans the local circumferential direction (~ec) and the projection of the myofiber orientation(~ef )on the plane parallel to the wall. The transverse angle (αt) spans the local circumferentialdirection (~ec) and the projection of the myofiber orientation (~ef ) on the plane perpendicularto the local longitudinal direction (~eip), depicted in Figure 2.4.

Figure 2.4: Definitions of helix (αh) and transverse (αt) fiber angles. The fiber angles at a point Pare defined from projection of the fiber direction (~ef ) on planes spanned by the local transmural (~er),longitudinal (~el) and circumferential (~ec) direction.

In order to obtain these fiber angles, an anatomical coordinate system must be obtainedon which fiber vectors can be projected. Furthermore, the location of the fiber vectors mustbe defined. Streeter et al. used a local wall bound coordinate system for angle calculations,depicted in Figure 2.5(a). the longitudinal direction ~el was tangent to the local epicardialsurface, thus not necessarily parallel to the cardiac z-axis. The radial direction ~er was definedperpendicular to the epicardial wall surface. The circumferential direction ~ec was definedtangent to the epicardial wall and perpendicular to the cardiac z-axis. The longitudinaldirection ~el was perpendicular to both ~er and ~ec, and thus not necessarily parallel to thecardiac z-axis. The transmural position was taken relative to LV wall thickness which wasmeasured from an average endocardial location to the epicardium. Because of the irregularitiesfound in the shape of the endocardial cardiac wall, defining the transmural position in sucha way is difficult.

Geerts et al. developed a local cylindrical coordinate system based on characteristicsfound in the myofiber field found in the study of the post mortem goat heart with DTI [14],

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depicted in Figure 2.5(b). Myofibers in the transversal slice corresponding with an out-of-plane component smaller than ±0.1 rad were used for fitting a circle and obtaining the localcircumferential direction ~ec, tangent to the midwall circle. The local longitudinal direction~el was aligned with the centers fitted through ZOOP circles in 5 adjoining transversal cross-sections. ~er was defined perpendicular to ~el and ~ec. The location in the LV compacte regionwhere αh was found to change sign was defined as the midwall position. Transmural positionsof myofiber vectors were normalized with respect to the distance between the midwall positionand the center of the circle fit.

(a) (b)

Figure 2.5: (a) Shows the local cardiac coordinate system introduced by Streeter et al. [39]. (b)Shows the local cylindrical coordinate system (R, Φ, Zc) developed by Geerts et al. and how it is orientedrelative to the rectangular magnet coordinate system (Xm, Ym, Zm). The axis Zm is aligned with thecenters of the nearby short axis transversal-sections. The angle Φ = 0 indicates the anterior connectionof the RV free wall to the LV. In the right figure the pixels corresponding to myofibers with an out-of-plane component smaller than ±0.1 π rad are indicated by the gray area. ~el was defined to be in Zc

direction. ~ec and ~er were defined as the tangential and perpendicular with respect to the circle fittedthrough the gray area in (b)[14] [9].

The development of the local cylindrical coordinate system solved the problem of definingthe transmural position of myofibers, but because coordinate system directions differ betweenthe method of Geerts and Streeter, different fiber angle values will be calculated. Especiallyoutside the equatorial region, ~el and ~er directions will differ between the two coordinatesystems and fiber angles cannot be compared directly.

As reported by Geerts, Rijcken et al. investigated the magnitude of difference in fiberangle values due to the use of the different coordinate systems. The relationship between thetransverse angles calculated from the local cylindrical coordinate system αt,cyl and from thelocal wall bound coordinate system αt,wall was found to be

αt,wall = arctan(tan(αt,cyl) cos(β)), (2.1)

where β is the angle between local longitudinal direction and the local long LV axis.It was found that at the equator both coordinate systems coincide and fiber angle data are

directly comparable. Outside the equatorial slice, midwall αt values were reported to differin the order of 2◦ in the most apical slice and in the order of 1◦ in the most basal slice.

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Measurement techniques of myofiber orientation

A review of the history of investigating fiber architecture can be found in [39]. The earlieststudies of fiber architecture were based on visual inspection of the myocard. Later on, bluntdissection was used, which gave insight in fiber architecture in a qualitative manner. Byboiling a heart in slightly acidic water , the collagen can be degradated and muscular pathwayscan be studied as described by Schmid et al. [35]. By scraping of superficial fibers fiberarchitecture can be investigated.

Quantitative measurement was traditionally performed with micrometric studies. Blocksof myocardial tissue were taken out of the myocard and histology was performed on slicestaken from the blocks. The data reported display a large variation, as is a consequence of thelimited accuracy of the two dimensional technique. Furthermore, it is possible to find in-planefiber orientation in a slice, but a possible out-of-plane component will remain unknown.

During the last decade, DTI has been used frequently in the study of fiber architectureof the heart as well as many other anisotropic biological tissues. As compared to histologi-cal techniques, the main advantage is that it is non-invasive so that true three-dimensionalmyofiber direction vectors are measured in the intact heart in a well established magneticcoordinate system. Furthermore, digital reconstruction is relatively simple and far less timeconsuming. Different studies validated DTI derived fiber orientation with traditional his-tological techniques. Chen et al. found the mean angular deviations in fiber angles to be8.4◦ ± 1.6◦ with histology and 6.1◦ ± 1.6◦ with DTI. Jiang et al. estimated fiber orientationmeasurement accuracy of 5.5◦ in fixed mouse hearts with DTI[23].

Therefore, DTI is a very useful technique to investigate the region-specific nature of themyocardial fiber architecture.

The highest imaging resolution possible to obtain with DTI is in the order of 100 µm3

which means a net myofiber orientation is measured rather than the orientation of singlefibers. Resolution obtained with histological techniques is found higher which makes thelatter more suitable for fundamental structural research. Because the structural organizationof tissue under observation is a determinant of the signal measured with DTI as explainedin the second part of this chapter, the tissue structure at ultra-, micro-, and macrostructurallevel should be well known. DTI is not capable of obtaining this, but histological techniquesare available and have been used in validating fiber architecture results measured with DTI.

Qualitative fiber architecture

Within the myocard, myofibers have been found oriented in a characteristic helical patternillustrated in Figure 2.6, which is similar across various animal species [9].

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Figure 2.6: Biventricular muscle bandafter removal of the most apical parts ofthe myocardial mass [35].

Greenbaum et al. investigated the fiber architecture of the human heart of which imagesare depicted in Figure 2.7 [16]. It was found that in the midwall region of the left ventriclefibers were circumferential, best developed towards the base and in the upper part of theseptum. Near the apex of the left ventricle and in the mid-wall of the right ventricle suchfibers were sparse. Subendocardial region consisted of longitudinally directed fibers, formingthe trabeculae and the papillary muscles, while fibers deep to and between the trabeculaecoursed more obliquely. Short-axis views near the left ventricular apex, at 50 % of the wayup the ventricular mass, showed clockwise spiral fibers in the subepicardial layer, and anti-clockwise spiral fibers in the subendocardial layer. At 75 % of the way up the ventricularmass, circumferential fibers were found to be well-developed. Longitudinal fibers could befound located in some parts of the outer epicardial region. At 90 % of the way up the ven-tricular mass, clockwise spiral fibers appeared in the subepicardial layer. Few circumferentialfibers were seen in the left ventricle wall, but they appeared in the septum. The bulk of thewall consisted of spiral fibers.

19


Figure 2.7: Three transversal views of the myocard showing a slice near the apex (left), 50 % of theway up the ventricular mass (middle), and 90 % of the way up the ventricular mass (right), summariz-ing the findings of Greenbaum et al. [16]. They have cut histological sections throughout the ventricularmass (upper images) and quantitated fiber orientation relative to the ventricular equator (lower im-ages). The longitudinal epicardial layer is shown in green, while the longitudinal subendocardial layersare colored yellow. The circular fibers are shown in purple. Fibers spiralling counterclockwise areshown in red and clockwise spiralling fibers in blue. As can be seen, there are multiple helical patternsto be seen in transversal sections taken across the ventricular mass, albeit without discrete fibrouspartitions producing any ”muscle bundles” [3].

The in-plane pattern of clockwise and counterclockwise fibers found by Greenbaum et al.as can be seen in Figure 2.7 was also noted by Streeter et al. [40] and Hort (as reported byStreeter) [39]. However, the phenomenon was called ”Pinnation” and ascribed to the cleavageplanes visible as gaps in the myocard, depicted in Figure 2.8. Streeter et al. stated that thepinnation patterns were not to be confused with myofiber direction. It was reported, that onlyat sufficient magnification, where it was possible to ensure the identification of myofilaments,it was possible to make the distinction. Furthermore, it was found that αt remained smalleverywhere in the wall, retained its sign across the compacta, and changed sign across theequator.

20


Figure 2.8: Transverse section removed from the free wall at the equator. Streeter et al. statedthat pinnate gaps, which are depicted in an exaggerated manner, must not be confused with transversecomponents of fiber orientation. Where fibers are oriented out-of-plane, the transverse angle, denoted inthe picture as α3, is discernible only at sufficient magnification to ensure identification of myofilaments.[40]

Torrent-Guasp et al. developed the concept of the unique Ventricular myocardial band(VMB) depicted in Figure 2.9. After boiling the myocard in acidic water and making someincision in the remaining muscle, it was found possible to unroll the heart into a singlemyocardial band. The two ends of the single myocardial band originate from and are insertedinto the aortic and pulmonary artery roots, respectively. The aortic part builds up the leftventricular wall, while the pulmonary artery part encircles and builds up the right ventricle.However, the VMB concept is currently opposed strongly by Lunkenheimer et al. who statethat this unique band is obtained due to the invasive dissection technique destroying theessential spatially netted nature of the ventricular myocardium.

Figure 2.9: Cartoon showing the unique myocardial ventricular band concept developed by Torrent-Guasp in which the muscle is a single band originating and inserted into the aortic and pulmonaryroots [2].

21


Schmid et al. studied the fiber architecture at the base through blunt dissection (Fig-ure 2.10) [35]. Insertions into the basal valve ring (around the mitral and tricuspid valve)were found sparce. Instead, the basal subvalvular edge was found to be a zone of fiber inflec-tion where the subendocardial fiber layers are in continuity with the subepicardial layers.

Figure 2.10: Base of both ventricles, viewed towards apex. The LV is on the left of the image.The atrio-ventricular valves are partially removed such that the myocardial edges of the ventricularwalls appear. It can be observed that the basal LV fibers are crossing over from epicard to endocardin a clockwise manner. R notes the ”roof” of the RV which crosses over from the free wall to thetriangle between the aortic and pulmonary artery valve ring and inserts along the ”chorda pulmo-tricuspidalis”(C) [35].

Quantitative fiber architecture

Post-mortem quantification of fiber architecture has been performed in mammals such as theguinea pig [22] , human [16], dog [38], macaque [33], rabbit [48], goat [14], rat [11], mice [6][23], swine [34] and several other species. Measurement of in vivo fiber architecture in thehuman heart has been reported by Wu et al. [49].

Region-specific research of fiber architecture was performed by Geerts et al. in the goatheart [14] and by Chen et al. in the rat heart [11].

Helix angle A typical transmural slope of αh has been found in many studies across speciesin the septal and free wall regions of the heart near the equator. Measured transmural αh

courses typically range from +60◦ at endocard to −60◦ at epicard, although a large variationexists between measurements. Typical transmural αh graphs can be found in figure 2.11showing a selection of transmural data through histological sectioning collected by Bovendeerdand DTI data obtained by Geerts et al. [9]

22


Figure 2.11: Transmural distribution of αh as reported by Bovendeerd [9]. Left: Data obtainedthrough histological sectioning in dog heart (♦, ◦, macaque heart (4), and human heart (+,×,−).Right: Transmural αh courses in the inter-papillary muscle region (in the free wall) of the LV from 5goat hearts obtained with DTI; symbols indicate different hearts; adapted from [14].

Geerts et al. measured transmural αh courses in the anterior (A), septal (S), posterior(P) and free wall (or lateral) (FW) regions 20◦ wide in an equatorial slice. The measuredαh was found to be within the range of data reported in literature. Chen et al. investigatedtransmural αh (and αt) courses in four regions 90◦ wide of which the results can be found inFigure 2.12. Transmural αh courses found by both studies compare well reasonably well asthey both found steady decreasing slopes in the subendocardial region to epicardial wall. Butas Geerts observed a plateau of high values at the endocard, Chen did not. However, chenexcluded angle data from the invaginated endocardial region upon visual inspection, whichcan explain the difference between the two studies. It was reported by Chen, that αh shiftedlinearly from +80◦ at the endocardium to −50◦ at the epicardium.

In addition, transmural variations of αh (and αt) of whole transversal slice at apical,midventricular and basal levels were investigated.

Both studies did not report significant differences in helix angle data between regions orbetween transversal slices.

23


Figure 2.12: Fiber architecture in normal rat hearts. A: representative map of inclination angle,also called helix angle (αh); B: transmural variations of αh at Anterior, Lateral (or Free Wall), Inferior(or Posterior) and septum regions at midventricular level; C: transmural variations of inclination angleof the whole transversal slice at basal, midventricular and apical levels; D: representative map of αt;E: transmural variations of αt at Anterior, Lateral (or Free Wall), Inferior (or Posterior) and Septumregions at midventricular level; F: transmural variations of αt angle of the whole transversal sliceat basal, midventricular and apical levels; In the αh map, red color at the endocardium represents aright-handed helix, and blue color at epicardium represents a left-handed helix. [11]

24


Transverse angle From bovine heart dissections by Torrent-Guasp, Streeter et al. esti-mated αt to be −8.4◦ ± 1.0◦. Furthermore, they reported that a typical value for αt wasestimated to be −3◦ for the whole transmural path. Furthermore, as stated in a previoussection, αt tended to remain small in the whole wall, retaining its sign across the compacta,and changing sign across the equator.

A finding in agreement with observations of Streeter was done by Geerts et al. whomeasured mean midwall αt in the free wall region of the LV. A mean αt course was foundvarying from −12◦± 4◦ near the apex, to +9◦± 4◦ near the base of the heart and is depictedin Figure 2.13. The change of sign was reported to occur in the region between equator andbase [14].

Figure 2.13: αt course fromapex to base. Solid lines in-dicate average course, dashedlines indicate 95% confidenceintervals for predicted values[14].

Chen et al. found that the average αt was within a ±20◦ range of variation. It wasconcluded that the large variation at the subendocardial region was attributable to the irreg-ularities of the subendocardium, e.g. the presence of papillary muscles and trabeculations. Itwas concluded that myocardial fibers were oriented circumferentially within the transversalplane. (See Figure 2.12) [11] Region-specific differences were not reported, but the graphsfound in Figure 2.12(F) do suggest regional differences in transmural αt distribution. In thesubendocardial wall region transmural αt courses show increased values in the basal slice anddecreased values in the apical slice, with respect to the course taken from the midventricularslice. In the subepicardial region, graphs can be seen resembling each other.

Summarizing remarks

Concerning the topic of cardiac fiber architecture, much is known but there is still informationlacking. Myofibers have been found oriented in a characteristic helical pattern, which is similaracross various animal species. At the very edge of the base, a zone of fiber inflection was foundwhere the subendocardial fiber layers are in continuity with the subepicardial layers. Insertioninto the basal vale ring were found sparse. At the ventricular fusion sites, it remains unclearhow myofibers are oriented.

In order to compare quantitative results from literature, the choice of anatomical coordi-nate system used for fiber angle calculations as well as the definition of transmural positionmust be considered. Measured transmural αh courses typically show a steady slope rangingfrom +60◦ at the subendocardium to −60◦ at the subepicardium, although a large variation

25

DTI Background

between measurements exists. Region-specific differences in αh remain unclear. Data on thedistribution of αt is less comprehensive. It remains disputed how in-plane fibers are orientedin the LV compacta. Streeter et al. reported, that αt remained small everywhere in thewall, retained its sign across the compacta, and changed sign across the equator. This hasbeen partly confirmed by findings of Geerts et al. They reported that the mean αt in themidwall region of the LV free wall varied from varied from −12±4◦ near the apex, to +9±4◦

near the base of the heart, changing sign between equator and base of the heart. Resultsshown by Chen et al. also seem to indicate such a change of sign, and although unreported,the presented data also suggest αt does vary across the compacta at apical and basal levels.While Greenbaum reported of clockwise spiralling fibers in the subepicardial layer, circum-ferential fibers in the midwall region and anti-clockwise spiral fibers in the subendocardiallayer, Streeter et al. also found such a pattern but ascribed it to pinnation gaps, not to beconfused with fiber orientation. In correspondence with the findings of Greenbaum et al.,Lunkenheimer et al. reported that myofiber direction was found intruding at angles up to 35◦

relative to the epicardium.Quantitative data in atypical regions such as the ventricular fusion sites and the base is

still very much lacking.

2.2 DTI

In this part of the chapter, the principles of diffusion are explained first. Then it is explainedhow a 3x3 diffusion tensor can describe three dimensional diffusion. Next the measurement ofdiffusion with MR is explained and how the diffusion tensor can be obtained. After that, therole of diffusion time in DTI measurements is discussed as well as how diffusion anisotropicindices (DAIs) are of interest in evaluating measurement quality and anisotropic tissue prop-erties. Furthermore, the visualization technique of tractography is addressed. Finally, it isdescribed how a heart specimen may be prepared for the DTI measurement

2.2.1 Principles of Diffusion

Diffusion is the random translational (or Brownian) motion of molecules or ions that is drivenby internal thermal energy [32].

In an isotropic medium, the flux of particles J at position r is directly proportional to theconcentration gradient ∇c(r, t):

J(r, t) = −D∇c(r, t), (2.2)

where D is the diffusion coefficient and c(r, t) is the solute concentration. Conservation ofmass is expressed by

∂c(r, t)/∂t = −∇ · J(r, t) (2.3)

Combining (2.2) and (2.3) leads to Fick’s second law of diffusion:

∂c(r, t)/∂t = D∇2 · c(r, t) (2.4)

D is assumed to be essentially independent of the solute concentration, which is presumedto be low. A probability P (ro |r, t) can be introduced. This probability describes the chance

26

DTI Background

that a molecule, initially located at position ro at t = 0, will be at location r at time t. Forordinary isotropic diffusion, P (ro |r, t) also obeys equation (2.4) leading to

∂P (ro |r, t)/∂t = D∇2 · P (ro |r, t) (2.5)

When the concentration gradient is zero, no net diffusive transport exists. Nevertheless, thediffusion process continues as self-diffusion and no longer involves net solute transport. Inthe case of unbounded diffusion and for starting condition P (ro |r, 0) = δ(ro − r) (indicatingthat as t → 0, c = 0 everywhere except at the origin r = 0) and the boundary conditionP (ro |r, t) → 0 for r →∞, the solution of (2.5) yields the dependence of the probability P onthe displacement:

P (ro |r, t) = (4πDt)−3/2 exp[−(r− ro)2/4Dt

](2.6)

This probability distribution function has a Gaussian shape. In the one-dimensional case theGaussian probabilty density function is written as

P (x, t) = (4πDt)−1/2 exp[−x2/4Dt

](2.7)

The second moment of the Gaussian curve is the variance, which is the expected averagedisplacement and is equal to 2Dt.

Since self-diffusion is a random process and displacements are isotropically probable, thenet or mean molecular displacement (r− ro) is zero. Therefore, displacements associated witha multi-dimensional diffusion process are calculated from (2.6) as average square displacements(variance), which gives the Einstein-Smoluchowski equation:

⟨(ro − r)2

⟩= 2NDt (2.8)

where N is the number of dimensions and t the diffusion time, also denoted as tdiff . Diffusioncoefficient D has units m2s−1 and expresses the particle flux, J, through a unit area per unittime. The magnitude of D depends on particle size, the solvent and temperature. The self-diffusion coefficient of free water for different temperatures has been measured by Mills andranges for the temperatures of 1 ◦C to 45 ◦C from 1.113 to 3.575×10−9 ·m2 · s−1 [31].

The self-diffusion process may be visualized by an ellipsoid which shows the root meansquared displacement in each direction. For the case of a homogeneous solution like bulkwater, self-diffusion is unrestricted and the displacement during tdiff is equal in every directionresulting in a sphere with radius

√(6Dtdiff ) along each axis.

In biological tissues, self-diffusion may be hindered by many of the tissue constituents,like membranes, intra- and extracellular structures and molecules [27]. This hindrance willhave two effects on the diffusion process. First of all, barriers will decrease the total amountof diffusion taking place. Therefore, the measured diffusion coefficient, or apparent diffusioncoefficient, ADC, will be lower than the intrinsic diffusion coefficient of free water. Thevolume of the ellipsoid will be reduced. Second, the manner in which the constituents areorganized will give direction to the diffusion process, e.g. diffusion will occur anisotropically.The spatial organization of diffusion hindereing constituents will determine the shape of theellipsoid.

27

DTI Background

2.2.2 Diffusion tensor

In the case of 3D anisotropic diffusion, one scalar is not enough to mathematically describediffusion fully. Instead, the diffusion scalar D in Fick’s law may be replaced by a secondorder symmetrical tensor D. With respect to a cartesian basis {~ex, ~ey, ~ez}, D has components{Dxx, ..., Dzz}, that can be stored in a diffusion matrix D.

D =

Dxx Dxy Dxz

Dyx Dyy Dyz

Dzx Dzy Dzz

, (2.9)

where each element of D is the coefficient describing particle flux in one direction due theself-diffusion gradient in the other direction. Furthermore, D is symmetric so that Dxy = Dyx,Dxz = Dzx and Dyz = Dzy.

A tensor can also be written with respect to a basis of eigenvectors ~ei, determined by thecondition

D~ei = λi~ei, (2.10)

where ~ei represents the eigenvectors ~e1, ~e2 and ~e3. and λ1, λ2 and λ3 are the correspondingeigenvalues. Also they are the diagonal elements of the Diffusion matrix tensor D′, thatresults after writing tensor D with respect to the basis of eigenvectors {~e1, ~e2, ~e3}.

D′ =

λ1 0 00 λ2 00 0 λ3

(2.11)

The eigenvalues can be found by solving the characteristic equation

det(D− λI) = 0, (2.12)

which gives

λ3 + I1λ2 + I2λ + I3 = 0, (2.13)

where I1, I2 and I3 are the first, second and third rotationally invariant of D, which can bewritten as

I1 = trD = trD = λ1 + λ2 + λ3 (2.14)

I2 = tr2D− tr(D2

)= λ1λ2 + λ2λ3 + λ3λ1 (2.15)

I3 = detD = λ1λ2λ3 (2.16)

By solving these three equations the three eigenvalues are obtained and it becomes possibleto describe the magnitude of water self-diffusion in a three dimensional anisotropical environ-ment. In this report, we arrange the eigenvalues such that λ1 ≥ λ2 ≥ λ3.

Many indices based on the three rotationally invariant eigenvalues are used to describethe 3D diffusion process [28]. The average diffusion coefficient Dav, is given by

Dav =λ1 + λ2 + λ3

3(2.17)

28

DTI Background

often referred to as the ADC. Many diffusion anisotropic indices (DAIs) have been used inresearch of tissue anisotropy. The most widely used DAI is the fractional anisotropy, FA,given by

FA =

√3

[(λ1 −Dav)

2 + (λ2 −Dav)2 + (λ3 −Dav)

2]

√2

(λ2

1 + λ22 + λ2

3

)2(2.18)

ranging from zero (isotropic) to one (anisotropic). Because λ1 ≥ λ2 ≥ λ3, there is a possibilityof sorting errors to occur. (e.g. when eigenvalues are close to each other, because of tissueproperties, or a low signal to noise ratio). Eigenvalue ratios λ1/λ2 , λ1/λ3 and λ1/λ3 can beused to invesigate the possibility of this effect to occur.

2.2.3 DW-MRI

The self-diffusion of water may be studied by means of Diffusion Weighted Magnetic Reso-nance (DW-MRI) using the pulsed field gradient technique introduced by Stejskal and Tanner[37]. They incorporated a pair of diffusion-sensitizing linear magnetic field gradients into aHahn Spin-Echo sequence symmetrically around the 180◦ pulse, as depicted in Figure 2.14The technique was further developed for spatial mapping by Taylor and Bushell [42].

The Spin-echo sequence works as follows: When the 90◦ excitation pulse of the DW-MRIsequence is applied, spins will be flipped into the transverse plane. After the pulse, a readoutgradient is applied which causes the spins to disperse. After a while, 1/2 TE, a 180◦ pulse isapplied which flips the spins in the transverse plane. After TE an echo will be produced witha read out gradient. With the obtained signal a T2- weighted image may be constructed.

In order to measure diffusion a pair of diffusion sensitizing gradients is added around the180◦ pulse which are equal in magnitude. The first gradient, called the dephasing gradient,is applied before the 180◦ pulse, phase labeling the dephasing spins. The second gradient, orrephasing pulse is applied after the 180◦ pulse in order to establish phase coherence. Againat TE, spins will have refocused to form an echo. In the absence of diffusion, spins will notmove out of position and an echo with maximum signal intensity will occur. But in the caseof diffusion, water molecules will move out of their phase labeled positions during the timeseparation (∆) between the two diffusion sensitizing gradients. Therefore, diffusion causesphase dispersion, which results in a signal intensity loss of the echo [18]. Because self diffusionis an isotropic process, the net phase change is zero.

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DTI Background

Figure 2.14: Diffusion sensitized Spin Echo sequence. The effect of diffusion gradients on staticand diffusing spins.

The relationship between signal intensity loss, system settings and diffusion time, ∆, hasbeen derived by Price et al. [32] and is given by

S(G)/S(0) = e−γ2G2Dδ2∆ (2.19)

S(0) is the signal intensity without diffusion weighting. S(G) is the diffusion sensitized signalintensity. In practice, also diffusion displacement during the diffusion-sensitizing gradientpulses needs to be considered. In the case of rectangular pulse gradients the equation iswritten as

S(G)/S(0) = e−γ2G2Dδ2(∆−δ/3), (2.20)

where δ is the pulse duration and (∆ − δ/3) is usually referred to as tdiff . This equation isalso written as

S(b)/S(0) = e−bD or ln(S(b)/S(0)) = −bD (2.21)

b is called the b-factor or b-value. It indicates the strength of the diffusion weighting that isapplied. Up to this point D represented a scalar value for the ADC of water.

2.2.4 DTI

The symmetrical diffusion tensor, given in (2.9), contains 6 different values. In order toobtain this tensor fully, a total of at least seven measurements must be performed; one

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DTI Background

unweighted measurement, S0, in combination with at least 6 diffusion weighted measurements,Si (i = 1, . . . , n) with gradients gi = (xi, yi, zi) applied in 6 different directions.

Dxx

Dyy

Dzz

Dxy

Dyz

Dxz

=

x21 y2

1 z21 x1y1 y1z1 x1z1

......

......

......

x2i y2

i z2i xiyi yizi xizi

......

......

......

x2n y2

n z2n xnyn ynzn xnzn

−1

− 1b1

ln S1S0

...− 1

biln Si

S0...

− 1bn

ln SnS0

(2.22)

Jones et al. investigated different measurement schemes and recommended different setsof gradient unit vectors for estimating the ADC and the diffusion tensor matrix. Optimaldirections for the latter for measurement schemes containing six or ten different diffusiongradient directions are given in Table 2.1.

Table 2.1: Recommended arrangement of unit gradient vectors for estimating the diffusion tensormatrix [24].

2.2.5 DTI of the myocard

As explained, DTI offers the capability to investigate tissue anisotropy. In validation studiesperformed on muscular tissues, it has been found that the principal eigenvector of the diffu-sion tensor is statistically similar to the myofiber direction found with histological techniques.Cleveland et al. found this in skeletal frog muscle [12]. Accuracy of myocardial fiber orienta-tion measurement with DTI has been reported to be between 5◦ and 11◦ in different studies.[23] [11] [45]. Also, correlation between sheet orientation and the other two eigenvectors hasbeen reported in literature with the secondary eigenvector correlated to sheet direction andthe tertiary eigenvector correlated to sheet normal direction [45].

DTI has also been used to reconstruct fiber architecture, such as in the rabbit heart[36].

Diffusion time considerations

The diffusion signal measured with DTI is directly related to the diffusion time applied inthe measurement. A short diffusion time will result in measuring short average squared

31

DTI Background

displacements. If these distances are short enough, hindrance will not occur enough andtissue anisotropy will not be observed. This is the reason why one should have knowledgeof the tissue structure. On the other hand, a long diffusion time will result in a decreasedsignal to noise ratio because of T2 relaxation. Thus, the optimal length of tdiff is a trade-offbetween adequate average squared displacements and T2 relaxation. A typical tdiff appliedis 12 ms. Assuming a self-diffusion coefficient of 2.0 ×10−9 ·m2 · s−1 at room temperatureof 20 ◦C the corresponding average squared displacement is 12 µm according to (2.8). Withrespect to cardiac tissue dimensions described earlier in this chapter, this tdiff seems suitablefor diffusing water molecules to run into intracellular constituents and cell membranes of themyocytes.

Kim et al. studied the dependence of the eigenvalues of the diffusion tensor on diffusiontime. It was found that the value for λ1 did not change as tdiff was increased from 32 msto 400 ms. However the other two eigenvalues did decrease in this range [26]. This findingcould indicate full hindrance is already achieved at a short diffusion time in the principal fiberdirection and that the other two directions need a longer time. This could be explained by thelarger dimensions of the anisotropic structures and that larger average squared displacementsmust occur for anisotropy to be observed.

Sorting errors

One of the problems that may occur in trying to determine true fiber orientation, is thepossibility of sorting errors to occur [15] [20]. Recall that in measuring the diffusion tensor,eigenvalues are automatically sorted. If the magnitudes are close to one another, it is pos-sible that the sorting errors occur. In order to investigate this potential problem, differenteigenvalue ratios can be calculated and evaluated.

Tractography

Tractography, or fiber tracking, is a visualization technique developed to study tissue anisotropyin a three dimensional qualitative manner. Basically, pathways through the measured vectorfield are followed and visualized with fibers [5] [4]. A value of FA or other DAIs may be usedas a stopping criterium for fiber pathways.

There are several reports that can be found having performed fiber tracking on the my-ocard. The report of Helm et al. illustrated the helical patterns in the myocard through fibertracking of DTI data [19].

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DTI Background

Figure 2.15: DTI based ventricular reconstruction illustrating helical fiber patterns [19].

Specimen preperation

Until now, performing DTI at high resolution was only possible on excised post-mortemhearts. If one would simple excise a heart post-mortem, it will be in a state of rigor mortis.The geometry and fiber architecture will be different from that of an in vivo heart underphysiological conditions.

Actually, many rigor mortis hearts have been used in studies of fiber architecture withor without DTI. Thick walls and small cavity volumes indicate this, which can be noticedquickly. Also, fiber orientation is influenced by rigor mortis, which is not observed so easy.

It is possible to prevent this by arresting the heart with a cardioplegic solution. Basically,a hypothermic saline solution can be used for this, such as St. Thomas solution or Tyrode’ssolution. An overview of cardioplegia, their constituents and their influence on cardiac physi-ology can be found in a literature review performed by van den Akker [47]. In the DTI studieof mice, phosphate buffered saline (PBS) was used for in situ cardiac arrest [6]. Cardioplegiamay prevent a state of rigor mortis, however, some swelling of the cardiac wall still may occur.For further preparation in fixing the shape of the geometry of the heart and conserving it, afixative, such as formaldehyde (or formalin) may be used. Formaldehyde cross-links proteinamino groups with methylene bridges to render tissues metabolically inactive and structurallystable [43]. While this preserves microstructural organization within a tissue, it necessarilyalters chemical and physical environments that contribute to MRI contrast mechanisms. Thisis significant because DW-MRI is widely employed to image chemically fixed biological sam-ples. It was reported by Thelwall et al. that formaldehyde reduces water proton T2 and ADCsignificantly. Holmes et al. also found that formalin decreased T2 significantly (55 ms) inmyocardial tissue in comparison with myocardial tissue contained in a crystalloid buffer (90ms) [21]. Sun et al. investigated different DAIs in live and formalin-fixed mouse brains. Itwas found that the ADC decreased two or three fold. However, it was found that the relativeindices studied were equivalent [41].

Thus, fixation should be performed in order to fix the shape of the heart, but it may not

33

DTI Background

be entirely beneficial for specimen preparation. It should be reduced to a minimum for anoptimal acquisition of the diffusion tensor.

34

DTI Background

35

Chapter 3

Experiment

3.1 Introduction

In this chapter, it is explained how the region-specific nature of fiber architecture was ob-tained and analyzed in the post-mortem rat heart. First, the heart specimen was preparedand excised. Then, the DTI measurement was performed in order to obtain cardiac fiberarchitecture data. In addition, a high resolution T1-weighted measurement was performedfor additional information about architecture. Data were then processed and quality of thedata was evaluated using different diffusion characteristics. Several visualization techniqueswere then used to study the fiber architecture in a qualitative manner, in order to investigatethe architecture at various locations of the heart, focussing on the fusion sites and the baseregion. Finally, results were compared with findings reported in literature.

3.2 Materials and methods

3.2.1 Specimen preparation

A 15 month old mature Lewis Rat weighing 300 grams, used in unrelated neurobrain activityexperiments, was obtained from the department of Biomedical NMR. After sedation of therat with isoflurane (Schering-Plough, Animal Health, Maarssen, The Netherlands), a skinincision was made from the abdomen to the xiphoid process and the skin and peritoneumwere cut loose. The vena cava inferior was cut just below the liver and closed both at theproximal and distal ends. Two needles were inserted apically in both the left and rightventricle. The ventricles were perfused with a heparinized phosphate buffered saline solution(PBS) of 4 ◦C under hydrostatic pressure of approximately 1 kPa, in order to cleanse thecirculation from blood, prevent clotting and establish cardioplegic arrest. The proximal endof the vena cava was opened and closed manually to drain blood and PBS and to preventcardiac shock taking place. After a few minutes the perfusate was changed to a 4% phosphatebuffered paraformaldehyde (PFA) solution for a short fixation of 3 minutes. The heart wasthen excised and rinsed in PBS and the aorta was retrogradely perfused to get rid of bloodresidues and excess formalin. The heart was stored in PBS in a refrigerator at 4 ◦C for oneday until the measurement took place.

Before measurement, the heart was taken out of the storage solution, dipped and driedthoroughly to get rid of excess water and was mounted on a polycarbonate container filled

36

Materials and methods Experiment

with Fomblin (Fens Chemicals, Goes, The Netherlands), a low dielectric perfluoropolyetherfor susceptibility matching.

3.2.2 DTI acquisition

MR setup

The experiments were conducted on a 6.3 T MRI scanner (Oxford Instruments Superconduc-tivity, Eynsham, Oxon, England) with a horizontal 12 cm bore, equipped with 400 mT/mgradients interfaced with a Bruker imaging console (Bruker BioSpec, Germany). The heartwas placed inside a 32 mm diameter quadrature birdcage coil (Rapid Biomedical, Rimpar,Germany). For DTI a three-dimensional diffusion-weighted spin echo (3DSE) sequence wasused consisting of one frequency encoding and two phase encoding directions, depicted in Fig-ure 3.1. Spoiler gradients were applied around the 180◦ pulse in order to remove unwantedtransverse magnetization causing a striping artefact in the non-diffusion weighted images.Furthermore, fat suppression was carried out with CHESS (CHemical Shift Selective). TheRF pulse had a duration of 2.6 ms, a Gaussian shape, a bandwidth of 1050 Hz and a 3.8ppm offset.

Figure 3.1: 3D Diffusion-Weighted Spin Echo sequence.

Hermite pulse shapes were used for 90◦ and 180◦ RF pulses. Diffusion weighted mea-surements were recorded with diffusion gradients applied along ten non-collinear directionsoptimized for tensor acquisition according to Jones et al. (See Chapter 2, Table 2.1) alongwith one reference measurement without diffusion weighting. Scan parameters were: field ofview (FOV) = 28 × 14 × 14 mm3, matrix size = 128 × 64 × 64, echo time (TE) = 25 ms,repetition time (TR) = 1070 ms, resulting in an isotropic resolution of 219 µm3 and a totalscan time of about 13.5 hrs. The diffusion weighting parameters were: gradient separationtime (∆) 14 ms, gradient duration (δ) 6 ms, resulting in a tdiff of 12 ms (see 2.20). The mea-surement took place at room temparature, approximately 20◦C, corresponding with a waterself-diffusion coefficient of 2.0×10−9 ·m2 · s−1, resulting in averaged squared displacements of

37


12 µm. Gradient strength (Gdiff ) was adjusted to obtain b-values around 900 s ·mm−2. Theeffective b-values for the diffusion weighted scan directions were, 906, 906, 899, 920, 939, 924,903, 923, 913, and 950 s ·mm−2. The b−value for the unweighted image was 6 s ·mm−2 (closeto 0). Spoiler gradients were applied at 50% maximum gradient strength and had a durationof 1.5 ms. These gradients also contribute to diffusion weighting. The b-value, caused by alldiffusion-weighting contributors, was calculated automatically by the Paravision 4.0 softwareon the imaging console, taking care that all imaging and spoiler gradients were accounted forin the calculation of the b− value.

In addition to the DTI measurement, high resolution T1 data were obtained with 3DFLASH (Fast Low Angle Shot Gradient Echo). Scan parameters were α = 40◦, TE =5.743ms, TR = 50 ms, number of averages was 16 resulting in a total scan time of 2.75 hrs. Matrixsize was 256 × 128 × 128, FOV was 28 × 14 × 14 mm resulting in an isotropic resolution of109 µm3 (twice DTI resolution).

Finally, in another heart specimen, T1 and T2 relaxation times were measured.

Scan procedure

In order to prevent imaging artifacts, such as wrap around or B1 inhomogeneities, the heartwas placed accurately in the RF coil center. After fixation in the magnet bore, tuningand matching of the impedance of the coil was performed manually. In order to acquirea homogenous B0 field, shimming was done automatically. The next step was to plan themeasurement with the use of scout images. A 5x5x5 tripilot multiscan was used to definethe size of the volume of interest (VOI) and to align the read-out direction with the cardiacz-axis. The imaging volume was chosen as small as possible, containing as much heart filledspace as possible.

After the scans were completed, DTI-data were processed by the Paravision 4.0 Softwareon the console reconstructing diffusion tensor components as well as eigenvalues, eigenvectors,the apparent diffusion coefficient, ADC (2.17), fractional anisotropy, FA (2.18), T2-weightedimages and Diffusion-weighted T2 images (DWI). Recall from Chapter 2, that the ADC isthe measured amount of diffusion and FA is a normalized diffusion anisotropic index rangingfrom zero (isotropic) to one (anisotropic), a widely used measure in literature. For each voxel,a total of 22 quantities were computed. These could then be read out for further processingand analysis using Mathematica (Wolfram Research, Inc.) or fiber tracking software.

3.2.3 Data analysis

DTI data analysis was performed with Mathematica (Wolfram Research, Inc.). The datasetcreated by the imaging console contained more than 11 million data points (22×128×64×64).In order to reduce the amount of data, they were thresholded based on a percentage ofmaximum T2 intensity, filtering out noise, effectively reducing the amount of data. Withadditional thresholding of T2 intensity and ADC data (filtering out water residues), a maskof the myocard was created.

Data Quality

Quality of the DTI data was evaluated with the ADC and FA. The susceptibility to sortingerrors was evaluated with eigenvalue ratios λ1/λ2, λ2/λ3 and λ1/λ3.

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Data Visualization

A mask of the myocard was created based on high resolution T1-weighted data and used tocreate 3D surface rendered images (Amira) for inspection of superficial fiber architecture atthe endocard in both ventricles. Inspection of fiber architecture in the compacta region ofthe myocard was initially presented with combined out-of-plane (OOP) contour plots andin-plane (IP) vector plots. In addition, tractography was performed for a deeper qualitativeunderstanding of fiber architecture throughout the myocard. (DTI-tool, Biomedical Imagingand Modeling Division, Technische Universiteit Eindhoven). The FA was used as a stoppageindex. Fibers were only constructed if the FA was above 0.20.

Initially, typical fiber architecture is presented, such as found at the endocard and epicard,or in the compacta region at the equator. Next, the focus was on evaluating atypical fiberarchitecture at locations such as the compacta outside of the equator, the fusion sites, andthe base region.

Other specimens

A total of eight DTI data sets were acquired with isotropic voxel dimensions. A total of sixdifferent rat hearts were used for this. The location of needle insertion for perfusion fixation,the perfusate, imaging resolution as well as measurement time were varied. An overview ofthese specimens can be found in Figure 3.2 and Table 3.1. The most suitable heart specimenfound for quantification of fiber architecture in Chapter 4 and the quantitative results inthis chapter, was specimen ”Ia”. The choice of quantification was mainly based on the easeof ZOOP segmentation in the construction of an anatomical coordinate system (which isdiscussed later on in Paragraph 4.1.1). For tractographic purposes, heart specimen ”Vb”was found most suitable upon visual inspection. Heart specimen ”IV” was used to create 3Dsurface rendered images, as the T1-weighted measurement of this specimen was done with thehighest isotropic resolution of 50 µm.

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Specimen Perfusion Perfusate Isotropic TR Measurement Number oflocation resolution (µm3) (s) Time (hrs) directions

Ia LV&RV PBS 219 1070 13:23 10Ib LV&RV PBS 159 1070 19:10 6II LV Tyrode’s 234 1070 13:23 10III Vena Cava PBS 196 1000 28:09 10IV LV Tyrode’s 200 1070 20:55 10Va LV Tyrode’s 213 1070 13:18 6Vb LV Tyrode’s 200 850 16:37 10VI Vena Cava Tyrode’s 213 1070 13:18 6

Table 3.1: Overview of different heart specimens measured depicted on Figure 3.2. Specimen Ia wasused for quantification purposes. Specimen IV was used for 3D surface rendering images. Specimen Vb,the same heart as Va but with the atria removed, was used for fiber tracking. All hearts were scannedbefore two days after excision, except for II and IV. All hearts were stored at 4◦C in PBS, except forII, stored in formalin solution. Heart specimen VI was used for measuring T1 and T2 relaxation times.

Figure 3.2: Overview of different heart specimens measured. Table 3.1 contains an overview ofspecimen preparation parameters. Specimen Ia was used for quantification purposes. Specimen IV for3D surface rendering images. Specimen Vb, that was the same heart asa Va but with the atria removed,was used for fiber tracking.

More specimens were scanned, rat and slaughterhouse rabbit hearts, but not with isotropicresolution or without a proper geometry because of another container that was too smallpressing the RV against the septum. Also, the rabbit hearts were excised approximately 20minutes after death, most likely in state of rigor mortis. Thus these specimens were foundless suitable to be used for studying fiber architecture.

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3.3 Results

T1 and T2 relaxation times were found to be approximately 1600 and 70 ms, respectively.After noise filtering and segmentation based on T2-weighted and ADC data, DTI data was

reduced from 500,000 to approximately 115,000 points. T2-weighted data and the mask of theheart are depicted in figure 3.3. Holes in the wall, such as can be seen located in the septumin figure 3.3, are the result of the needle penetrations used in the perfusion-fixation. Dataabove the heart (above slice 103) and below the apex (below slice 10) were not evaluated.

(a) (b) (c)

Figure 3.3: a T2-weighted image(a), its mask(b) and a high resolution T1-weighted(c) image of anequatorial transversal slice (number 50), viewed towards the base.

3.3.1 Diffusion characteristics

The mean values for λ1, λ2 and λ3 for the whole heart were found to be 1.06 ± 0.20, 0.71± 0.20 and 0.48 ± 0.21× 10−9 ·m2 · s−1, respectively. Maps of the principal eigenvalues aredepicted in Figure 3.4.

0

2.5

(a)

0

2.5

(b)

0

2.5

(c)

Figure 3.4: λ1(a), λ2(b) and λ3(c) maps of an equatorial transversal slice (number 50), viewedtowards the base. Color scale: Eigenvalue ×10−9 ·m2 · s−1. For the whole heart, the mean λ1, λ2 andλ3 were found to be 1.06 ± 0.20, 0.71 ± 0.20 and 0.48 ± 0.21 ×10−9 ·m2 · s−1, respectively.

The susceptibility of the tensor data to sorting errors was evaluated with eigenvalue ratiosfor the range of slice 13 to 76 (apex to above the base). The mean λ1/λ2 and λ2/λ3 and

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λ1/λ3 were found to be 1.60 ± 0.10, 1.58 ± 0.53 and 2.55 ± 0.90, respectively. Maps of theseratios are shown in figure 3.5. λ1/λ3 (Figure 3.5c) has the highest value indicating that therisk of sorting errors is lowest for λ1 and λ3.

1

>2

(a)

1

>2

(b)

1

>2

(c)

Figure 3.5: λ1/λ2 (a), λ2/λ3 (b) and λ1/λ3 (c) ratio maps for an equatorial transversal slice(number 50), viewed towards the base. The whole heart mean values for λ1/λ2, λ2/λ3 and λ1/λ3 werefound to be 1.60 ± 0.10, 1.58 ± 0.53 and 2.55 ± 0.90, respectively.

Maps of the ADC and FA are shown in Figure 3.6. For the whole heart, the mean ADCwas found to be 0.75 ± 0.17 ×10−9 · m2 · s−1 and the mean FA was found to be 0.38 ±0.12. Upon close inspection of Figure 3.6, several voxels were found showing a higher ADCand a lower FA, located at coronary positions. Overall, the ADC was found more evenlydistributed over the wall than the FA. Especially at the endocardial Inter Papillary Muscleregion (IPM) values were found to be decreased.

0

2.5

(a)

0

1

(b)

Figure 3.6: ADC (a) and FA (b) short-axis plots of an equatorial slice (number 50), viewed towardsthe base. For the whole heart, the mean ADC and FA were found to be 0.75 ± 0.17 10−9 m2 · s−1

and 0.38 ± 0.12, respectively. Color scale: ADC ×10−9 ·m2 · s−1.

3.3.2 Superficial endocardial fiber architecture

A 3D surface rendering of high resolution T1-weighted data of the endocard in both ventriclescan be found in Figure 3.7. In the LV, the septum appears smooth, while at the free wall,invaginations can be seen, as superficial fibers run from apex to base with a counterclockwisetwist, as viewed from the septum. In the RV endocard several superficial myocardial bundles

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can be seen emerging at the RV free wall apex and fusing with the LV at the Anterior fusionsite (FSA) in the basal region.

Figure 3.7: 3D surface rendered images of T1-weighted data. Notice the smooth LV Septum (o)(a)in contrast with the invaginated LV Free Wall (x)(b). At the FSA several bundles of fibers emerge atthe RV apex and insert into the LV (v)(c).

3.3.3 Fiber architecture in the compacta region

Fiber architecture in the myocardial compacta region is visualized in three transversal slices,one at the equator, located at 1/3 apex-to-base length (Lab) away from the base (Figure 3.8),one located at 1/3 Lab away from the apex, and one near the base in (Figure 3.9) with acombination of out-of-plane (OOP) contour plots and in-plane (IP) vectors. In the equatorialslice, in the midwall region, principal fiber direction is predominantly tangent to the wall.A dark blue band can be seen indicating that fibers stay in plane. The width of this zeroout of plane (ZOOP) band varies and is smallest at the septum and largest at the posteriorfusion site. In subendocardial and subepicardial wall regions fiber directions stick out of thetransversal plane. At the LV endocardial free wall, there are two distinct fiber bundles runningin perpendicular direction (red). Another bundle at the endocard near the posterior fusionsite (green) is directed obliquely, inserting into the LV at the FSP. At this insertion point nearthe base, the typical blue ZOOP band found in most of the transversal planes, is interrupted.(See also Figure 3.15 and Appendix A Figure A.1, slices 56 through 68.) In the slices at thebase and in the apical half of the heart, fibers in the midwall region also can be seen runningin circumferential direction tangent to the epicardial wall. At the basal slice, endocardial fibervectors can be seen pointing towards the endocardium in a clockwise manner, while epicardialvectors are oriented anti-clockwise. The opposite occurs in the apical slice; endocardial fibervectors can be seen pointing anti-clockwise to the endocard, while epicardial vectors pointcan be found pointing to the epicard in clockwise direction.

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Figure 3.8: Visualization of fiber architecture with a combination of out-of-plane (OOP) componentmaps and in-plane (IP) vectors at the equator (slice 52). Blue indicates the principal fiber directionsoriented in-plane (IP). Red indicates fiber directions perpendicular to the plane (PP). PP fibers arefound in the subepi and endocardial wall regions. IP fibers (blue) are found in the midwall regionencircling the LV. Furthermore 2 PP bundels (red) can be seen located at the LV endocard. Anotheroblique fiber (green) can be seen at the posterior LV endocard. In-plane vectors show that fibers predom-inantly run in circumferential direction, parallel to the epicardial wall. Only the most inner endocardialfibers show small in-plane vectors, but it is hard to find them not being parallel to the wall.

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Results Experiment

Figure 3.9: Visualization of fiber architecture with a combination of Out-of-plane (OOP) componentmaps and in plane (IP) vectors. Two transversal slices are viewed from the base, located at 1/3Lab(slice 33)(top), and at the base(slice 71)(bottom). the locations of the slices are indicated in theoverview on the right. Blue indicates principal fiber direction is in plane (IP). Red indicates fiberdirection perpendicular to the plane (PP). In both figures fibers can be seen running in-plane in themidwall region encircling the LV. Subepi- and endocardial fibers direction is more perpendicular thethe transversal plane. In-plane vectors show directions are pointed to the endocardial wall in anti-clockwise, and pointed towards the epicardial wall in clockwise direction in the basal slice. In the apicalslice this pattern can be seen reversed.

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Results Experiment

Figure 3.10 shows fibers tracked from seed points located along a line running from theLV Free Wall, through the Septum, to the RV Free Wall. A fan-like pattern can be observedin all three wall regions.

Figure 3.10: Tracking of fibers seeded along a line between the LV Free wall and the RV Free Wall.A fan-like pattern can be observed in all three regions.

In subendocardial/subepicardial regions outside the equatorial plane, fibers tend to crossover between midwall and endocard/epicard with opposite directions illustrated by the in-plane vectors in Figure 3.9. In the basal region the cross over directions are opposite to thedirection found in the apical regions. In the equatorial plane, most of the fiber directionstend to stay tangent to the cardiac wall. Figure 3.11 shows fibers tracked for a short distancefrom seed points located in the transversal plane. A feather-like pattern can be observed withfibers in the midwall running in circumferential direction and fibers outside of this regioncrossing over to the endocard and epicard in opposite directions.

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Results Experiment

Figure 3.11: Short distance tracking of fibers seeded in transversal planes, viewed towards the base.The color-coding scheme used is the same as in Figure 3.8 with in-plane fibers shown in blue, obliquefibers in green and fibers perpendicular to the plane in red. Four transversal slices are shown located at30% (slice 32)(a), 50% (slice 48)(b), 70% (slice 64)(c) and at 90% (slice 80)(d) apex-to-base length.a) Shows fibers spiralling from endocard to the midwall predominantly in a clockwise direction. b)shows clockwise (at the FSA) as well as anti-clockwise fibers (at the FSP) in the subendocardial region.c) and d) show predominantly anti-clockwise spiralling fibers in the endocardial region. In the midwallregion fibers run circumferentially in all slices. In the subepicardial region, fibers are spiralling frommidwall towards the epicard in a predominantly anti-clockwise manner (a) or in a predominantlyclockwise manner(c-d). In the slice close to the equator (b) epicardial fibers are running predominantlytangent to the epicard. By focussing on the ZOOP fibers, different patterns can be seen at the fusionsites. The FSP region shows a split in the ZOOP band while in the FSA region, there seem to be manyZOOP fibers crossing from the LV to RV along different routes.

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Results Experiment

Epicard

Figure 3.12b illustrates the possibility of tracking fibers throughout the heart from pointsseeded in a single transversal plane. Figure 3.13 shows superficial fibers at the epicard visu-alized by tracking fibers from seed points in several planes throughout the heart. From theseimages it clearly appears that at the LV Free Wall, epicardial fiber direction is more longitudi-nally oriented, while fibers at the RV epicardial surface run more transversally. Furthermore,a spiralling pattern can be observed at the apex in Figure 3.13d.

(a) (b)

Figure 3.12: OOP map of a longitudinal slice, viewd from the free wall (a). Focussing on thezero out of plane (ZOOP) component as it runs from apex to base, a clear difference can be seen inits pattern at both fusion sites. In the FSP region, there appears to be a clear split in the ZOOPcomponent, while many different ZOOP component pathways appear in the FSA region. b) Shows animage of fibers tracked from seeding points in an equatorial transversal slice (number 52). The value0f 0.20 was used as a stoppage index. It can be seen how fiber pathways are tracked throughout themyocardium. The colorcoding is the same as found in Figure 3.8.

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(a) (b)

(c) (d)

Figure 3.13: Whole heart fiber tracking. Images are of the epicard viewed towards the free wall(a), posterior (b), anterior (c) and apex (d). Color coding is the same as presented in the OOPcontour maps. (Blue fibers are parallel, green fibers are oblique and red fibers are perpendicular to thetransversal plane.

Fusion Sites

The fiber architecture found at both fusion sites differs from each other as can be seen inFigure 3.11 when focussing on the zero out of plane (ZOOP) component. At the FSP there

49

Results Experiment

appears to be a split between septum and RV free wall that is more distinct than the splitat the FSA. The OOP contour map of longitudinal slices shown in Figure 3.12 illustratesthat this phenomenon can also be observed when focussing on the ZOOP component in alongitudinal slice of the heart.

Base region

As epicardial fibers spiralling upwards to the base approach the very edge of it, they start tocross over to the endocard where they spiral down again. This zone of inflection is illustratedin Figure 3.14. From the images in Figure 3.13 it can be seen how fibers in the base regiondo not stick out of the wall.

Figure 3.14: View of fibers tracked at the base of the heart. A zone of inflection can be seen in theLV free wall region as fibers cross over from epicard to endocard in a clockwise manner.

Throughout the heart, a typical ZOOP band encircling the LV was found. At the point

50

Discussion Experiment

where a muscle bundle from the LV endocard is inserted into the LV myocard, this ZOOPband is interrupted, as explained before. Several images of transversal OOP maps in thebasal region can be found in Figure 3.15 illustrating how fiber architecture varies in the basalregion.

Figure 3.15: Several OOP contour plots of transversal slices in the basal region. Notice how thetypical ZOOP band gets interrupted in several slices as they are located closer to the base. Furthermore,it can be noticed how the ZOOP band starts to emerge at the endocardial free wall region as slice numberrises.

3.4 Discussion

The DTI method described here was used to measure diffusion tensor images of the rat heartwith an isotropic resolution of 219 µm in 13.5 hrs. High resolution T1-weighted data wereobtained from another heart specimen with isotropic resolution of 50 µm in a total scan timeof 8 hrs.

3.4.1 DTI acquisition

Imaging with an additional phase encoding gradient instead of the slice selection gradientincreases the duration of the measurement but also makes it possible to image at higherisotropic resolution [18]. Furthermore, every time a measurement is performed, the echo con-tains more signal, coming from the whole VOI and not just only a certain slice. Additionally,the use of thin slices which need a high slice selection gradient leads to additional unwanteddiffusion weighting which has to be corrected for. This correction is not perfect and thereforethis leads to artefacts.

The use of isotropic resolution in this study revealed region-specific fiber architecture.The FSA region is a good example. When the imaging voxel dimensions are not the same,the largest length will determine the amount of detail that can be observed. In literature,many examples of DTI measurements can be found performed without isotropic resolution [14]

51


[19] [20] [11] [45]. Mostly short-axis resolution is higher than long-axis resolution. This willcontribute to smoothening the image, averaging out and covering up region-specific details.

Other reports do report of isotropic resolution, but in many cases, this is obtained in apost-processing step through zero-filling (or zero-padding)[6] or other techniques [23]. Again,this will average out and cover up region-specific details.

The diffusion time used in the DTI measurements was 12 ms. According to equation 2.8this is in accordance with a distance of about 12 µm. In the light of the structural dimensionsof the myocardial muscle tissue, this is in the order of myocytial membrane distances. TEused was 25 ms. Since T2 was measured to be approximately 70 ms, it is possible to use longerdiffusion times possibly incorporating the hindrance of larger structures in the macrostructurallevel into the diffusion weighting scheme.

Imaging resolutions were in the range of 159 to 213 µm3. It should be possible to use aresolution of 100 µm3, however, for the whole rat heart, measurement time will increase andsignal to noise will decrease since smaller voxels will generate less signal.

3.4.2 Specimen preparation

The preparation was carried out in order to obtain a heart with optimal geometry and archi-tecture resembling an in vivo heart at diastole. In addition, the fiber architecture of a heartspecimen not arrested under optimal conditions showing a thick swelled ventricular myocardwas studied because this was found beneficial.

Perfusion fixation was carried out simultaneously through both ventricles with a hypother-mic heparinized phosphate buffered saline solution as used by Bouts et al. [6]. Several othercardioplegic solutions can be found in literature such as Tyrode’s solution. Using this partic-ular solution, it was not possible to find differences in the state of the arrested heart. SincePBS is easier to prepare, it was found more suitable to use.

The location of perfusion was varied in different hearts. Perfusion through the vena cavawas found very difficult to perform, and resulted in very thick myocard walls. Perfusionthrough the LV apex alone, resulted in less thickening of the myocard, but the best result wasobtained by simultaneous perfusion fixation through the left and right ventricle. Althoughthis left both ventricles with insertion holes in the myocard at the apex and in the lowerseptum, the RV cavity volume was found largest, making it relatively easy to distinguish LVand RV and most suitable for reconstruction of cardiac geometry [25]. Short fixation wasnecessary to fix and preserve the geometry of the heart at the time of cardiac arrest. Theduration of fixation was kept at a minimum (few minutes) because of its reducing effect onADC as investigated by Sun et al. [41] and possibly on T2 as investigated by Thelwall etal. [43]. A deterring effect on tissue anisotropy has not been found by Sun and colleagues.However, from our unreported observations, formalin seemed to have a negative effect on DTIimage quality.

In order to prevent ongoing fixation, the heart was flushed retrogradely with the cardio-plegic solution, before it was stored at 4 ◦C. With this method it was still possible to obtainDTI data of reasonable quality after a month of storage. The two hearts measured after anmonth of storage in PBS or formalin can be found in Table 3.1 and Figure 3.2.

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3.4.3 Diffusion characteristics

Values for ADC and FA found in literature are in the range of 0.6− 1.3 ×10−9 ·m2 · s−1 and0.2− 0.4, respectively [6] [23] [11] [14]. Values found for ADC (0.75 ± 0.17 ×10−9 ·m2 · s−1)and FA (0.38 ± 0.12) in this study were in the range of values found in literature. The riskof sorting errors involving the principal eigenvector, was found to be low, indicating that thegeometric relation between myofiber direction and the first eigenvector of the diffusion tensoris strong.

3.4.4 Data visualization

The study of fiber architecture throughout the ventricular wall was carried out through dif-ferent visualization methods. Surface rendering of high resolution T1-weighted data revealedsuperficial endocardial fiber architecture. DTI data were visualized with out of plane con-tour plots in combination with in-plane vectors and gave insight in fiber architecture in thecompacta region of the myocard. Further analysis of the DTI data was performed throughtractography, giving additional insight in fiber architecture. It was shown possible to trackfiber pathways throughout the heart from seeding points located in a single slice (See Fig-ure 3.12b). It should be noted that the short fibers tracked in Figure 3.11 contain a 3Deffect.

3.4.5 Myocardial fiber architecture

Typical as well as atypical patterns for ventricular fiber architecture have been found. In theLV, the septal wall appeared smooth, while the free wall appeared invaginated. The visibilityof invaginations of the trabecular layer depended on the manner of cardiac arrest. In manycases, arrested hearts found in literature used for fiber architecture studies, were reported to bein a state of rigor mortis [39] [16] [14], indicating thick walls, making it difficult or impossibleto distinguish the trabecular layer from the compacta region (e.g. the TCI). The myocardialcompacta region showed typical patterns at the equator, with fibers running predominantlyin circumferential direction, tangent to the cardiac wall. In transversal planes outside ofthe equator, a feather-like pattern (Figure 3.11) was observed, with midwall fibers runningin circumferential direction and subendo and subepicardial fibers crossing over. Fibers didnot stick out of the wall, as was clearly shown by tractography results. This feather-likepattern is in conflict with reports from literature, stating that fibers cross over at midwall[39], but in agreement with findings by Greenbaum et al. [16] who found spiralling fibers inthe subendo and subepicardial regions, and Lunkenheimer et al. [30] who reported of in-planefiber orientations at angle with the epicardial wall.

The fan-like pattern (Figure 3.10) was found throughout the wall and is in correspon-dence with that reported in literature [39], stating that fibers gradually change directionover a transmural course, running tangent to the transversal plane at midwall, and oblique orperpendicular to the transversal plane at the endocard and epicard, but in opposite directions.

Fusion Sites

At the fusion sites where fiber architecture is very complex, it has been demonstrated byfocussing on the ZOOP component, there are many fiber pathways in the FSA region observedrunning from LV to RV, while at the FSP a clearer split can be observed. This has been

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Conclusion Experiment

visualised within different transversal slices and in a longitudinal image. To the best of ourknowledge, this finding has not been reported in literature. The reason for this could be thatlongitudinal resolution used in DTI acquisitions, frequently is lower than in-plane resolution,so that these region-specific details are averaged out.

Furthermore, at the FSA distinct fibers have been observed running through the RVlumen. The extent of this RV trabecular layer is again dependent on the state of the arrestedheart. In a swelled myocardium, RV and LV trabeculae could easily be mistaken in a DTIimage for compacta wall parts.

Base

At the edge of the base, a zone of inflection was found by Schmid et al. [35] This has beenconfirmed by our fiber tracking results as the image of basal fibers obtained in Figure 3.14is very well comparable with the fiber architecture obtained by Schmid et al. [35] throughblunt dissection (Figure 2.10).

As one approaches the base, going through a stack of transversal slices, the characteristicZOOP band in the LV compacta gets interrupted near the FSP. This could make it difficult toestablish an anatomical coordinate system based on the ZOOP charactersistic as developedby Geerts et al. [14]. Furthermore, as observed the basal plane is not perpendicular to thecardiac z-axis. The upper base of the RV lies higher than the LV base. This geometricalobservation could be specific for rat hearts.

3.5 Conclusion

Insight has been given in the region-specific nature of ventricular fiber architecture. Byapplying different visualization techniques typical patterns reported in literature have beenfound, as well as atypical patterns. For a deeper understanding of the region-specific natureof cardiac fiber architecture and for making it possible to incorporate fiber architecture in anFE model, further quantification is needed, which is the subject of the next chapter.

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55

Chapter 4

Quantification of fiber architecture

A clearer understanding of the region-specific nature of cardiac fiber architecture was obtainedin Chapter 3 through visualization of the diffusion tensor. Quantification of the data, which isthe subject of this chapter, will provide additional knowledge. Furthermore, it enables imple-mentation of the measured architecture in a region-specific FE model. First, an anatomicalcoordinate system was constructed based on the zero out of plane (ZOOP) characteristic ofthe myocardial fiber field. Next, fiber architecture was quantified with the transverse andhelix angle. Fiber architecture was evaluated in several regions in transversal slices located atthree different longitudinal positions, in the basal half, at the equator and in the apical halfof the heart in order to find region-specific characteristics. In addition, the geometry of theexamined heart was characterized with different parameters, such as wall volume to cavityvolume ratio and midwall radius.

4.1 Methods

4.1.1 Anatomical coordinate system

In order to quantify the principal fiber direction with fiber angles an anatomical coordinatesystem needs to be defined. Geerts et al. proposed to use characteristics of the myofiberfield as a starting point in the definition of an anatomical coordinate system [14]. Themethod used in this report is quite similar. Based on the out-of-plane component (OOP)contour plot, the zero-out-of-plane (ZOOP) component was segmented in each transversalslice. In order to improve segmentation, the OOP images were enhanced with edge-preservingnoise suppression. Segmentation of the ZOOP component (Figure 4.1) was performed forevery transversal slice by finding the center of mass of the hearts mask and finding theminimum OOP value along lines radiating from this center point. Instead of a circle fit usedby Geerts, an ellipse fit was used here and the ellipse tangent and normal vectors foundwere the circumferential (~ec) and radial (~er) direction of the anatomical coordinate system,respectively [1].

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Methods Quantification of fiber architecture

Figure 4.1: ZOOP segmentation. a) shows lines radiating from the center point of mass in thetransversal plane. The minimum value along these lines is found in the image, enhanced with an edgepreserving noise suppression. b) Shows the ZOOP points found along the radiating lines.

The fitting procedure resulted in quadratic curve equation constants from which ellipseparameters could be derived, such as ellipse center point, axis lengths and rotation angle ofthe ellipse. Figure 4.2 shows the result of the fitting procedure. Through extrapolation ofthe transversal ZOOP ellipse parameters to each point in the plane, ~ec and ~er were definedfor all points in the transversal plane.

Figure 4.2: Result of the ZOOP ellipse fitting procedure in 5 transversal planes with slice number24(a),37(b), 52(c), 66(d) and 72(e).

The DTI measurement of the heart was carefully planned so that ~ez of the measurementdata and ~el in the anatomical coordinate system were parallel. In short, the direction of ~el

for each point in the dataset was the same. ~ec and ~er directions for each point depended onthe ZOOP ellipse segmentation.

57


4.1.2 Fiber angle calculations

Both transverse angle αt and helix angle αh used for quantification of the fiber architectureare depicted in figure 4.3 [9].

Figure 4.3: Definition of the helix (αh) and transverse (αt) fiber angles. The fiber angles at a pointP are defined from projection of the fiber direction ~ef on planes spanned by the local transmural ~er,longitudinal ~el and circumferential ~ec direction.

The transverse angle αt was defined as the angle between the projection of the principaleigenvector onto the transversal plane (~eip), and ~ec. It was calculated with

αt = arccos(

~ec · ~eip

‖~ec‖ ‖~eip‖)

(4.1)

The helix angle αh was defined as the angle taken between the projection of the principaleigenvector on the plane spanned by ~el and ~ec. It was calculated by

αh = arctan( ‖~eoop‖

cos (αt) ‖~eip‖)

(4.2)

When calculating these angles, the orientation of the vectors must be considered in findingthe right orientation of the angles. This was done by considering the sign of the inner productbetween ~er and ~eip, for αt calculation, and the sign of the outer product between ~er and the~eip for αh calculation.

4.1.3 Geometric characteristics

Several parameters characterizing the geometry of the heart, such as total wall volume, totalcavity volume, and the ratio between them were determined. Furthermore, the mean leftventricular Rm, defined as the mean distance of the ZOOP ellipse to the center of the ellipse,was determined in each transversal plane from apex to base. Furthermore, the apex-to-baselength (ÃLab) was determined with the base of the heart defined as the slice nearest to theoutflow tract but not showing it and the apex defined located in the first slice containingtissue. The equator was defined lying at a distance of 1/3 apex-to-base length from the baseof the heart.

58


4.1.4 Presentation of myofiber direction data

Because of the large amount of data, in the order of 100,000 voxels, a selection of the datawas made, to find region-specific characteristics of the fiber architecture.

In order to investigate differences between apical, equatorial and basal planes, fiber angledata from three transversal slices, located towards the apex (slice 37 at 0.4 ÃLab), at the equator(slice 52 at 0.66 ÃLab) and towards the base (slice 66 at 0.91 ÃLab) were presented with colorcoded contour plots showing maps of the fiber angles in the range of −90◦ and +90◦.

Helix angle

In addition, transmural fiber angle courses were determined in sectors 20◦ wide, represent-ing four different regions, Anterior (A), Septum (S), Posterior (P) and Free Wall (FW) asillustrated in figure 4.4.

Figure 4.4: Locations of the twelve LV sectors used for obtaining transmural αh angle fiber courses.A: Anterior, FW: Free Wall, P: Posterior, S: Septum. In addition, the segmented ZOOP ellipse andthe datapoints are depicted as well.

Each point in a transversal slice corresponded to a point on the ZOOP ellipse segmentedin that slice. The mean distance of this point to the center of the ellipse, R0, was used tonormalize the transmural position, R:

h =R−R0

R0(4.3)

with h the normalized transmural coordinate. The slopes of fiber courses for αh in theseregions were determined using a linear fit to the transmural data for the LV compacta, definedas −0.2 < h < 0.2 to exclude the invaginations of the trabeculae compacta interface andpapillary muscle. The range of fiber angle values found along the transmural courses wasdetermined by considering the maximal and minimal values in the LV and in the RV. Thenormalized transmural coordinate h was considered in distinguishing between the two ventriclewalls.

Transverse angle

Because variations of αt were small, especially in the midwall region, additional contour plotswere presented with αt mapped within a range of −20◦ to +20◦ in order to find region-specific

59

Results Quantification of fiber architecture

characteristics. Furthermore, the average midwall αt was determined in the free wall, definedas the LV region between both RV fusion sites, for each transversal slice, from apex to base.Data in the range of −0.05 < h < 0.05 were used in this calculation.

Fiber architecture towards the base

In order to investigate fiber architecture in the basal half of the heart, contour plots as wellas transmural fiber angle courses in the FW region were plotted for several transversal slicesclose to the base. Both αh and αt angle courses were analyzed. The slopes of the transmuralfiber courses were determined using a linear fit to the transmural data for the LV compacta,similar as described in the previous section.

4.2 Results

4.2.1 Geometric characteristics

The mask of the heart contained approximately 115,000 voxels. Adding up the voxels resultedin a total myocardial wall volume of about 1.16 mm3. Apex-to-base length was found to be12.7 mm (slice 13 to 71). The longitudinal position of the equator, defined as 2/3 ÃLab, wasfound lying in slice 52, at 8.3 mm from the apex. The highest transversal slice numbercontaining LV myocard tissue was 81 (1.17 ÃLab). The highest slice number containing RVmyocard was 99 (1.48 ÃLab). Myocardial, LV cavity and RV cavity volumes for almost thewhole apex-to-base length (from slice 13 to slice 70) were found to be 0.79 mm3, 0.30 mm3

and 0.09 mm3, respectively. This resulted in a total cavity/wall volume ratio of approximately0.5. A graph of the mean midwall radius, Rm, can be found in figure 4.5 and is best describedas an elliptical course. It can be seen that the slope is low near the equator, and that itsteepens with Rm changing the most as the curve approaches the apex. The maximum Rm

was found to be 4.9 mm (slice 54).

60


0 1 2 3 4 5 6 7 8 9 10 11 12 13 140

1

2

3

4

5

6

Mean midwall radius

Mid

wal

l rad

ius

(mm

)

Apex-to-Base position (mm)

37 52 66 71

Figure 4.5: The mean midwall radius, Rm, per transversal slice in the LV. Solid red lines indicateaverage course, dotted green lines indicate 95% confidence intervals for predicted values. Positions ofexamined slices in the apical half (37), at the equator (52), in the basal half (66) as well as at the base(71) are indicated.

4.2.2 Fiber angle distribution

ZOOP segmentation was performed for slices 14 to 76, representing a range of 0.02−1.09 ÃLab

(slices 14 through 76). The range of quantification as well as the locations of the transverseslices of which fiber architecture was evaluated is depicted in Figure 4.6. It can be observed inthe images that the absolute αt values are predominantly low except for the subendocardialregion (Figure 4.6(a) and (b)). There, αt values are positive towards the apex and negativetowards the base. Furthermore, more negative αt values can be found near the apex (Fig-ure 4.6(b)). Throughout the LV αh values are found to be positive in the subendocardialregion, close to zero midwall and negative in the subepicardial region. (Figure 4.6(c) and(d)).

61


Figure 4.6: Overview of the range for which quantification was carried out. a) and b) contain αt

data. c) and d) contain αh data. The Color legend can be found in Figure 4.7. Positions of examinedslices in the apical half (37), at the equator (52) and basal half (66) as well as the base (71) areindicated.

Further evaluation of the helix and transverse angle distributions is presented separatelyin the next two paragraphs.

Helix angle

Maps of αh distributions in an apical, equatorial and basal slice are shown in Figure 4.7. Itcan be observed in the equatorial slice (Figure 4.7(b)), that in the LV the largest positivevalues for αh can be found at the endocard. This occurs along the whole septal area (noticethe hole pierced by the perfusion fixation needle) and along the free wall (more profound atthree distinct spots). The lowest negative values can be found at the epicard, especially atthe lateral and posterior sites. In the RV free wall, again the highest positive values are foundat the endocard. The RV septal region exhibits the lowest negative values for αh. Minimalvalues are also found at the epicard, being mostly positive or sometimes slightly negative. Inthe LV midwall region, αh values approach zero.

In all three slices, contributions of longitudinal bundles of fibers can be seen at threelocations at the endocardial free wall. Two of them are more longitudinally oriented andmore encroached in the wall than the other bundle, which can be seen running obliquelyalong endocardial free wall from the lateral apical endocard to the , posterior part of the freewall in the basal slice. Additional αh maps can be found in Appendix A, illustrating theperpendicular and oblique orientations of the fiber bundles along the free wall.

Although αh is distributed in a pattern quite similar in alle three slices, there is oneprofound difference in αh distribution shown in Figure 4.7 which is the interruption of theZOOP band in the basal slice (c). This phenomenon occurs at the site where the superficialfiber bundle crossing over the endocardial free wall enters the myocard near the base.

62


(a) (b) (c)

Figure 4.7: Maps of Helix angle distribution in three transversal slices located in the apical half(slice 37)(a), at the equator (slice 52)(b) and in the basal half (slice 66)(c). Slices are viewed from theapical side.

Figure 4.8 shows transmural courses of the helix angle in 12 different regions of the my-ocard. Steady descending slopes can be found for most αh courses in the free wall and LVseptal sectors (as seen in sectors FW-37, FW-52, S-37, S-52 and S-66). This is not the casefor the graph in the basal FW region. Another characteristic frequently seen at the endocardis a plateau of high angle values (as seen in sectors A-37, FW-37, S-52, P-52, A-66 and S-66).Bumps in the midwall region are found in graphs taken in the Anterior and Posterior sec-tors, adjacent to the fusion sites (as seen in sectors P-37, P-52, A-52, A-66, A-66) except forthe curve in the apical anterior sector (A-37). At the equator, the transmural courses of αh

typically ranged from +80◦ to −40◦ in the anterior sector, from +80◦ to −80◦ in the septalsector, from +80◦ to −60◦ in the posterior sector and from +60◦ to −80◦ in the free wallsector. The ranges in the other sectors can be found in Table 4.2.

63


-0,4 -0,2 0 0,2 0,4 0,6 0,8

-100

-80

-60

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-0,4 -0,2 0 0,2 0,4 0,6 0,8

Normalized transmural position (h)

Equator, slice 52Apical half, slice 37

He

lix

an

gle

(o)

Basal half, slice 66

FW

S

P

A

Figure 4.8: Transmural course of αh in a total of twelve sectors located in the apical half (slice 37),at the equator (slice 52) and in the basal half (slice 66) of the heart. Sector width was 20◦. A 5th

order polynomial fit was applied to the data, showing the average αh course (solid red line) and the 95% confidence intervals for predicted values (dotted green line). See Figure 4.4 for sector locations.

The slopes of the transmural graphs in the compacta region can be found in Table 4.1.The steepest slopes can be found in the septal sectors while the flattest ones are observedin the posterior sectors. From Table 4.1 it can be seen that the steepest transmural αh arefound in the septal regions. The flattest slopes are found in the posterior region. From the

64


Table 4.1: Results of linear fit of transmural graphs in different sectors in the LV compacta region,defined as −0.2 < h < 0.2. In addition, the minimum and maximum transmural coordinate h are givenas well as the range which can be thought of as the normalized maximum wall thickness in a certainsector.

Slice Sector Offset (◦) SD (◦) Slope (◦) SD (◦) minimum h maximum h range h

37 A 4.9 ±1.0 -284 ±10 -0.43 0.16 0.59S 12.5 ±3.0 -278 ±26 -0.22 0.27 0.50P 24.2 ±1.1 -197 ±10 -0.29 0.36 0.65

FW -4.6 ±0.8 -319 ±7 -0.41 0.24 0.6552 A 13.8 ±2.5 -220 ±23 -0.25 0.21 0.46

S -5.1 ±1.3 -487 ±12 -0.28 0.17 0.45P 14.3 ±1.8 -203 ±16 -0.28 0.27 0.55

FW -0.6 ±1.1 -312 ±10 -0.18 0.28 0.4566 A -0.6 ±2.0 -282 ±10 -0.55 0.37 0.92

S 12.1 ±1.1 -342 ±26 -0.29 0.25 0.54P 13.2 ±2.2 -167 ±10 -0.26 0.52 0.78

FW -6.6 ±4.2 -170 ±7 -0.19 0.53 0.72

Table 4.2: Table containing αh values (◦) with maximum values at the endocard, minimum valuesat the epicard and the range of helix angles found in four regions of the wall in three transversal slices.

slice Anterior Septum Posterior Free Wall37 endo 86.6 75.5 77.8 80.0

epi -46.5 -63.3 -78.8 -67.6range 133.1 138.8 156.5 147.1

52 endo 84.3 78.8 81.8 64.5epi -45.7 -83.3 -63.0 -78.4

range 130.0 162.1 144.8 142.966 endo 66.0 72.3 75.6 77.2

epi -63.6 -69.9 -27.8 -60.0range 129.6 142.2 103.4 137.2

65


αh maps found in Appendix A it can be seen that at the LV endocard maximum values varyvery locally. From Table 4.2 it can be found that at the LV endocard maximal αh values varyin the range of +65◦ to +85◦. At the LV epicard a large display of minimum αh values canbe found ranging between −25◦ and −85◦. The highest values for αh at the epicardial surfacein the apical half are found at the FSA and at the RV and in the basal half at the FSP.

In addition, the mean LV αh range per transversal slice is plotted in Figure 4.9 illustratinga maximum transmural range of mean transversal LV αh near the equator and decreasingranges in apical and basal slices.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 1420

40

60

80

100

120

140

16071665237

transmural range of helix angles

Hel

ix a

ngle

rang

e (o )


Figure 4.9: The mean range of helix angles found per transversal slice in the LV. Solid red linesindicate average course, dotted green lines indicate 95% confidence intervals for predicted values. Po-sitions of examined slices in the apical half (37), at the equator (52), the basal half (66) as well as thebase (71) are indicated.

Transverse angle

Maps of αt distributions of an apical, equatorial and basal slice are shown in Figure 4.10 andagain in Figure 4.11 with a shorter angle range. Additional maps can be found in Appendix A.

66


(a) (b) (c)

Figure 4.10: Maps of Transverse angle distribution in three transversal slices located in the apicalhalf (slice 37)(a), at the equator (slice 52)(b) and in the basal half (slice 66)(c). Slices are viewed fromthe apical side.

(a) (b) (c)

Figure 4.11: Same data as in Figure 4.10, with a color scale ranging from −20 to +20◦. The zeroout of plane (ZOOP) ellipse is added in each map.

Differences in αt distribution between the slices presented in Figure 4.10 and Figure 4.11are more profound in comparison with αh distribution differences between slices. By evalu-ating maps of this angle in Figure 4.10 it can be observed that overall absolute values of αt

are lowest at the equator, and highest in other slices outside of the midwall region. In bothapical and basal slices, the values for αt are found approaching zero in the midwall region.In the apical slice, positive angles are found in the subepicardial LV and negative angles inthe subendocardial LV. This pattern is reversed in the basal slice, showing positive angles inthe subendocardial LV and negative angles in the subepicardial region with one exception,the subendocardial region located at the Posterior Septum, where αt values are positive. Therange of αt values observed in the cardiac wall is mostly between +20◦ and −20◦, except forthe outer subendocardial and subepicardial regions. In order to evaluate the distribution ofαt values in more detail, maps are shown again in Figure 4.11, this time with a narrower anglerange. The patterns found in the basal and apical slices are again observed in Figure 4.11(a) and (c). For the equatorial slice, zooming in with a narrower angle range does not resultin an image illustrating the apical or basal patterns Figure 4.11 (b). Values in the equatorialslice were found to be close to zero, only slightly positive or negative. The αt distribution

67


in the equatorial plane (Figure 4.11b) shows values roughly varying between +10◦ and −10◦.Only the outermost subendocardial wall parts show higher (RV and the longitudinal fiberbundle located laterally in the LV) or lower values (most of the LV). In the slices outside theequator, the ZOOP ellipse overlaps roughly with a region of αt values close to zero, exceptfor the subendocardial region located at the posterior septum, where angle values were foundto be larger than +20◦. In the midwall region the αt values were found to be close to zero.αt values in the subendo- and subepicardial region experiences an opposite sign.

Figure 4.12 (a) illustrates how the mean αt in the midwall region of the entire free walldepends on longitudinal position. It was found to be a few degrees negative in the apicalhalf, increasing from approximately −10◦ near the apex to −2.5◦ as the curve passes theequator. As the curve enters the basal half it becomes positive and its slope becomes steeperobtaining a value of approximately +12.5◦ at the base. These data were divided in a subendo-and subepicardial midwall set and their graphs are depicted in Figure 4.12(b). It can beobserved that the subendocardial set is less negative than the subepicardial part in the apicalregion. Close to the equator both curves cross at about −3◦, so that in the basal region thesubepicardial part is higher than the subendocardial part.

0 2 4 6 8 10 12 14 -25

-20

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-5

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Free wall, 0.95 < h <1.05

Tra

nsve

rse

angl

e (

o )

Apex-to-Base position ( mm )

(a)

0 2 4 6 8 10 12 14

-25

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-5

0

5

10

15

20

25

slice 23

slice 37

slice 72slice 52

-0.05 < h <0

0 < h <0.05

Polynomial Fit of subendocardial midwall region

Polynomial Fit of subepicardial midwall region

Polynomial Fit of full midwall region

Free wall, -0.05 < h <0.05

Tra

nsve

rse

an

gle

(o)


(b)

Figure 4.12: Transverse angle course from apex to base for the midwall region. The course for thefull range of −0.05 < h < 0.05 is shown in (a). The solid line indicates the 5th order polynomial fitof the transmural course, the dotted lines indicate 95% confidence intervals for predicted values. (b)shows 5th order polynomial fits of the courses split into the subendocardial and subepicardial region ofthe midwall.

4.2.3 Base region

The dependence of the transmural fiber angle courses on longitudinal position in the basalhalf of the heart is illustrated in Figure 4.13. The data on which the polynomial fits arebased can be found in Appendix B. From evaluating αh graphs it can be seen how mostcurves overlap. Only endocardial αh values in the two slices closest to the edge of the baseare decreased significantly. At the endocard, αh drops from approximately +60◦ to −20◦.

68

Discussion Quantification of fiber architecture

In Figure 4.13 (b) it can be seen that αt transmural courses show a positive slope similar inmagnitude. However, as slices approach the base, the offsets of the graphs are seen lifted.

-60

-40

-20

0

20

40

60

80

5th order Polynomial fits of transmural helix angle course

He

lix A

ng

le (

o)


slice 66

slice 67

slice 68

slice 69

slice 70

slice 71

-0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5

(a)

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5th order Polynomial fits of transmural transverse angle course

Tra

nsve

rse

an

gle

(o)


slice 66

slice 67

slice 68

slice 69

slice 70

slice 71

-0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4 0.5 0.6

(b)

Figure 4.13: 5th order polynomial fits of transmural courses in the free wall region of the helix angle(a) and transverse angle (b) in several transversal planes in the basal half of the heart.

4.3 Discussion

4.3.1 Cardiac coordinate system

In the present study αh and αt were defined with respect to an anatomical coordinate systembased on the midwall ZOOP component in the myocardial fiber field similar to the methodof Geerts et al. [14]. Instead of defining the direction of the long axis (~el) separately in everyslice, it was taken parallel directly to the z-direction (~ez) of the imaging volume. Therefore,careful planning of the experiment is more important. ~ec and ~er were obtained by fitting anellipse through the ZOOP component instead of a circle used by Geerts. Looking at Figure 4.2this seems to be beneficial for angle calculations outside of the equator. Segmentation of themidwall used for fitting an ellipse, itself was also different than the method used by Geertsbut nevertheless was found applicable as Figure 4.2 shows.

The ZOOP ellipse was found suitable for obtaining the transmural coordinate of fiberorientation as described by Geerts et al. By using this method, no problems occurred becauseof the irregular shape of the endocardial wall, as did occur in studies by Streeter et al. andChen et al.

4.3.2 Quantification near the base

Quantification of fiber architecture has been performed for almost the whole ventricular mass(Figure 4.6). Quantitative results for the most upper parts of the ventricular wall, the Septumand the RV free wall, were not obtained. The gross morphology of the rat heart could beinherent to this problem. Hearts of other species may exhibit a basal surface that is less

69


oblique to ~el, making it easier to perform quantification in the basal region. Thus, in rats, themethod used for constructing an anatomical coordinate system was not suitable for automaticquantification in the LV upper septum and the RV upper wall. Still, this could be donemanually.

4.3.3 Fiber angle distribution

As discussed in Chapter 2, direct comparison of fiber angle values is not possible if differentanatomical coordinate systems were used in calculating the angle values. But Geerts et al.reported that the angle (β) between the cardiac z-axis and the local longitudinal directioncould be used to enable the comparison of data and estimated β from the apex-to-base courseof Rm. Upon visual inspection of Figure 4.5, we estimated β to be approximately 20◦ at theapical slice (37) and 15◦ at the basal slice (60). At the equator β was estimated to be zero.According to 2.1 differences in αt at the apical and basal slices will be in the order of 1-2◦.as the different anatomical coordinate systems coincide at the equator, fiber angle values aredirectly comparable

Furthermore, upon visual inspection of Figure 4.6, ~ez and the local wall ~el do not differmuch in the free wall region. Therefore, this region seemed appropriate for studying lon-gitudinal variation in transmural fiber angle graphs in the base region, and mean midwalltransverse helix angle with respect to longitudinal position.

Helix angle

The results found for helix angle distribution at the equator compare well to results foundin literature. At the LV endocard the magnitude of maximum αh values was found varyingvery locally in the range of +65◦ to +85◦. At the LV epicard a large display of minimum αh

values was found ranging between −25◦ and −85◦. The highest values for αh at the epicardialsurface in the apical half were found at the FSA and at the RV and in the basal half at theFSP.

The mean LV range per slice (Figure 4.9) was found to be highest at the equator anddecreasing both in apical and basal direction which could be explained by the observationthat β increases as the apex or the base is approached. Thus the differences in values foundat near apical or near basal planes with findings in literature could be ascribed to differentanatomical coordinate systems used for quantification.

Chen et al [11] used a local cylindrical coordinate system similar to Geerts et al. andfound fiber angle distribution of αh angle to shift linearly from +80◦ at ednocardium to−50◦ at epicardium. Their results (Figure 2.12) presented with angle contour maps, at themidventricular position, compare well with the results from the present study. They did notreport of a plateau of high endocardial αh values as found frequently in our results whenregions containing pappilary muscle were evaluated. But the location of the endocard wasreported to be traced upon visual inspection excluding papillary muscle.

From our results region-specificity was found as steady decreasing slopes are present inthe FW and S regions, while at the fusion sites, bumps located in the midwall region startedto occur as our data showed. Furthermore, endocardial plateaus have been shown to existvery locally in the FW. Proper preparation of the heart specimen through in situ perfusion-fixation, limiting swelling due to rigor mortis and preserving the geometrical shape, enabledthis finding. Already in Chapter 3 this was found with volume rendered images, exhibiting

70


an invaginated free wall and a smooth Septum. A possible explanation why Chen et al. andGeerts et al. did not find significant differences in the transmural αh courses, is the swelledmyocard, and not using isotropic imaging resolution.

Transverse angle

The transverse fiber angle distributions quantified in this chapter differ for the apical, equato-rial and basal locations. Quantitative αt distribution is not well comparable with findings ofChen et al. [11]. Chen did not report significant differences found in transmural αt courses,although their published graphs suggest there is a difference in magnitude of αt values inapical, equatorial and basal slices. The variation of mean midwall αt with respect to longitu-dinal position as found by Geerts et al. [14] has been confirmed by our results (Figure 4.12(a), but shown incomplete (b). Geerts assumed transverse angle distribution to be tangentto the cardiac wall at subendo and subepicardial regions, and at maximum offset at midwall.However, our results show midwall values to be at a minimum and subepi and subendocardialvalues larger and opposite to one another. Also the feather-like patterns found in Chapter 3suggest the latter pattern as well as findings reported by Greenbaum et al.

Streeter et al. did find a feather-like pattern in the myocard with microscopic studies athigh magnification, but ascribed this phenomenon to ”pinnation”, already reported by Hortet al. It was stated that the angle of pinnation and αt did not coincide. In Streeters simplifiedmodel, the latter had a value of −3◦ throughout the equatorial compacta section [39]. Now,the question arises if this ”pinnation” of cleavage planes interferes in the measuring of truefiber direction with DTI. Different intra- and extracellular compartments exist, in whichself-diffusion takes place. Thus, in theory the DTI signal contains information on anisotropictissue structures inside as well as outside of the myocytes. Anisotropy in the latter signal maybe a combination of fiber direction and cleavage plane direction. Nevertheless, fiber trackingresults presented in Chapter 3 provided proof of DTI measuring true fiber direction as fibertracts were formed filling up the whole ventricular myocard. This has also been reportedby Schmid et al. [34] who performed tractography in swine myocard and found helical fiberpathway patterns. Furthermore, the measurement of principal fiber direction with DTI hasbeen validated in several studies as discussed in Chapter 2. Still, it remains possible thatpinnation interferes with the measurement of true fiber direction. Also, as it is found thatcleavage planes were not homogenously distributed throughout the cardiac wall, it is possiblethat it interferes with the helix angle and the transverse angle in at different extents. Surfacerendering results in Chapter 3 illustrated superficial fibers emerging and entering the myocard.This clearly suggests a transverse component present in the trabeculata area. Neverthelessit cannot be extrapolated to the compacta region. The basal posterior septal spot exhibitingthe interruption in the ZOOP band also suggests fiber angle is measured correctly with DTI.Again, this region does not account for other parts in the myocardial wall. Since relaxometryresults showed a T2 (Chapter 3) of 70 ms and tdiff of about 25 ms was used. diffusion timecould be lengthened and shortened to investigate its influence on the fiber angles measured,especially αt.

Basal region

Only for the slices nearest to the base, the helix angle in the subendocardial region is loweredfrom approximately +60◦ to −20◦ thereby reducing helix angle range considerably (Fig-

71

Conclusion Quantification of fiber architecture

ure 4.13). The pattern of the transmural helix angle in subepicardial region remains thesame. At the same time it has been observed that transmural transverse angle graphs arelifted when regions closer to the base are examined (Figure b). In other words, at the edge ofthe base, fiber direction starts to be orientated more in-plane and ”crossing over” occurs ina suddenly increasing manner. This finding is in agreement with the zone of inflection foundin Chapter 3 through tractography (see Figure 3.14) and the image of the base obtained bySchmid et al. [34] through blunt dissection (see Figure 2.10. A zone of inflection at the basewas already illustrated in a qualitative manner in Chapter 3 with fiber tracking.

geometric characteristics

The different heart specimens found in Figure 3.2 displayed various wall and cavity sizes. Uponvisual inspection, specimen Ia was found most realistic as it contained a large LV cavity and athin myocardial wall in comparison with the other specimens. The total wall/total cavity ratiofound in the quantified heart (Ia) was found to be 0.5. the ideal heart specimen geometry forFE modeling would resemble a geometry at zero pressure. LV cavity/wall ratio at zero cavitypressure is about 0.30 [25]. However, since perfusion-fixation is possible to perform under acertain pressure, this state is not possible to obtain. In our study a hydrostatic pressure ofabout 1 kPa was found suitable. For FE modeling purposes, the LV cavity/wall ratio shouldbe determined.

4.4 Conclusion

A cardiac coordinate system was semi-automatically implemented making fiber architecturequantification possible for almost the entire ventricular myocard. One should be aware ofthe different geometric characteristics between the ex-vivo heart studied and the in vivoheart. Helix angle data from areas frequently reported on in literature were found to be incorrespondence with results in the present study. As for the transverse angle data, they arein correspondence with Greenbaum et al. and in conflict with Streeter et al. Fiber trackingresults from Chapter 3 do suggest a myocard connected in the principal fiber direction, whichis also in correspondence with Torrent guasp’s VMB. Further research in the LV compactaregion may clearify the role of pinnation in determining myofiber directions with DTI. As forfiber architecture at the base, it was possible to obtain it semi-automatically in the free wall.Results show at the outer part of the base a different helix angle distribution. Transverseangle distribution data showed previous results obtained with DTI were incomplete.

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Conclusion Quantification of fiber architecture

73

Chapter 5

General discussion

In this project, fiber architecture of the post-mortem rat heart was studied with DTI. Theprotocol used for heart preparation is suitable for DTI data acquisition. The 3DSE sequenceand the use of isotropic image resolution enable the region-specific study of fiber architecture.

Region-specific fiber architecture was evaluated by visualizing the data with tractographyand evaluating quantitative results. Tools were developed in order to construct an anatom-ical coordinate system enabling semi-automatic quantification of DTI data for most of theventricular myocard.

fiber architectural findings

From the qualitative and quantitative results it can be concluded that:

• Superficial fiber architecture at the LV endocard is smooth at the septum, and invagi-nated at the free wall.

• In the free wall and septal region, a typical transmural αh graph is found with a maxi-mum value at the endocardial wall, decreasing with a steady slope to a minimum valueat the epicardial wall. At the endocard, plateaus of maximum fiber angle values areobserved very locally, correlating with the location of papillary muscle.

• At the posterior and anterior fusion site regions, the transmural αh courses differ signifi-cantly from courses in the free wall and septum as they were non monotonous, containingbumps in the midwall region.

• Maximum and minimum values of transmural αh courses are very region-specific. Atthe LV endocard maximal vary in the range of +65◦ to +85◦. At the LV epicard a largedisplay of minimum values are found in the range between −25◦ and −85◦. The highestvalues for αh at the epicardial surface in the apical half are found at the FSA and atthe RV and in the basal half they are found at the FSP.

• By viewing fiber orientations in the transversal plane, a feather-like pattern is observedwith fibers in the midwall running at a slight angle with the circumferential directionand fibers outside of this region crossing over to the endocard and epicard in oppositedirections. The mean midwall αt varies from approximately −10◦ near the apex to −2.5◦

as the curve passes through the equator. As the curve enters the basal half it becomespositive and its slope becomes steeper obtaining a value of approximately +12.5◦ at the

74

General discussion

base. The orientation of the feather-like patterns are reversed at apical and basal levels.In the equatorial plane fiber orientations are predominantly circumferential.

• By focussing on the zero-out-of-plane (ZOOP) band, defined as the region in whichfibers are in plane with a short axis slice, it is found that the fusion of both ventriclesis more distinct at the FSP than at the FSA.

• A zone of inflection reported in literature located at the edge of the base, is confirmedby our tractographic results and quantitative results in the free wall region.

Future research and recommendations

Correlation of principal eigenvector with true myofiber direction It is unclear towhat extent cleavage planes interfere with the measurement of true fiber direction with DTIin the LV compacta region. This issue could be clarified by investigating fiber architectureof a tissue block from the LV compacta with DTI and varying tdiff . In theory, longer dif-fusion times will result in hindrance of larger structures to be reflected in the DTI tensor.Maximum isotropic resolution that can be obtained is 100 µm3. Another strategy would beto use contrast agents that are targeted for certain water compartments, locally influencingT2 magnetization. Also, it could be tried to obstruct the extracellular water compartmentby filling it with macromolecules restricting diffusion, making it possible only to measuresignal from within the myocytes and to be sure diffusion is along axial myocytial direction.In addition, histology could be used to validate findings.

Quantification method The current anatomical coordinate system is still ambiguous be-cause the cardiac longitudinal axis was parallel to the manually set z-axis in the imagingvolume. An objective system can be constructed by replacing ~ez by a local ventricular axis asdone by Geerts et al. [14]. The ZOOP ellipse is already used for defining the circumferentialand radial direction in an objective manner.

Implementation of local wall bound coordinate system will improve the comparison of fiberangle distribution outside of the equatorial region with findings from (micrometric) studiesin literature (e.g. Streeter). The method for defining the circumferential direction, based onthe ZOOP ellipse is satisfactory. But the determination of longitudinal and radial directionmust be improved in order to achieve this.

Implementation in the FE model the measured data can be used for the construction ofa cardiac geometry. Through parametrization of region-specific transmural fiber angle coursesit will become possible to incorporate fiber architecture in the FE model, making it regionand patient-specific.

A combined study of cardiac fiber architecture with DTI and deformation with in-vivotagging enables computation of fiber strain, to be used for testing the FE model.

Measured data can be used to test predictions from models of cardiac adaptation.

DW-MRI and tissue deformation the ADC and FA depend on the tissue structure atmicro- and macrostructural level. In vivo DW-MRI has been reported by Gamper et al. [13]and by Tseng et al. [44]. During contraction of the heart, tissue deformation takes place.Structural changes could be investigated with DW-MRI evaluating the ADC and FA during

75

General discussion

the cardiac cycle, at diastole and systole. Also material properties of deforming healthy andinfarcted tissue could be evaluated in vivo.

76

General discussion

77

Acknowledgements

I would like to thank Ward Jennekens, Henk de Feyter and Jaap Jansen for kindly pro-viding rat heart specimens and Jo Habets for performing the perfusion-fixation procedure.Furthermore, I would like to thank Tim Peeters for providing the DTI-tool and keeping itup-to-date.

78

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Appendix A

Fiber angle distribution contourplots

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(a) (b) (c)

(d) (e) (f)

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Figure A.1: Maps of αh distribution at 12 different longitudinal locations in the apical half (a-g),basal half (h-j) and beyond (k,l). Slices are viewed from the apical side.

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(d) (e) (f)

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Figure A.2: Maps of αt distribution at 12 different longitudinal locations in the apical half (a-g),basal half (h-j) and beyond (k,l). Slices are viewed from the apical side.

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Figure A.3: Maps of αt distribution with a shortened angle range at 12 different longitudinallocations in the apical half (a-g), basal half (h-j) and beyond (k,l). Slices are viewed from the apicalside.

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Appendix B

Transmural fiber angle courses inthe basal region

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Figure B.1: Transmural course of αh in the basal FW region (slice 66 to 71). Sector width was20◦. A 5th order polynomial fit was applied to the data, showing the average αh course (solid red line)and the 95 % confidence intervals for predicted values (dotted green line).

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Figure B.2: Transmural course of αt in the basal FW region (slice 66 to 71). Sector width was 20◦.A 5th order polynomial fit was applied to the data, showing the average αh course (solid red line) andthe 95 % confidence intervals for predicted values (dotted green line).

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Documents

Fiber architecture of the post-mortem rat heart obtained ... · ﬂber architecture, but a detailed picture of ﬂber architecture in regions such as the base or the ventricle fusion