Vol. 28

Marius Reichardt Multiscale X-ray Structural Analysis of Cardiac Cells and Tissues

Göttingen Series in X-ray Physics

Marius Reichardt

#### Multiscale X-ray Structural Analysis of Cardiac Cells and Tissues

ISBN 978-3-86395-536-6

The cardiac function relies on an intricate molecular and cellular threedimensional (3d) architecture of a complex, dense and co-dependent cellular network. Structural alterations of the cardiac structure can affect its essential function and lead to severe dysfunction of the organ. Cardiovascular diseases are

However, it is not possible to give a generalized answer how the heart is formed. Up to now, cardiac structure as well as physiologic and disease-related tissue alterations of the tissue are mainly investigated by established 2d imaging

This work presents a multiscale and multimodal X-ray imaging approach, which allows to probe the heart structure from the scale of entire intact murine hearts

While the molecular structure of the actomyosin complex is probed by scanning X-ray diffraction, the 3d arrangement of the cellular network is investigated by propagation-based X-ray phase-contrast tomography. In this context, the concept of 3d virtual histology of cardiac tissue by X-ray phase-contrast tomography using laboratory sources as well as highly coherent synchrotron

the main cause of death worldwide with a rising incidence.

methods such as optical microscopy or electron microscopy.

to the molecular organisation of the sarcomer structure.

radiation is being further developed.

ISSN 2191-9860 eISSN 2512-6326 Universitätsverlag Göttingen Universitätsverlag Göttingen

Marius Reichardt Multiscale X-ray Structural Analysis of Cardiac Cells and Tissues

> This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Published in 2022 by Universitätsverlag Göttingen as volume 28 in the series "Göttingen series in X-ray physics" Marius Reichardt

Multiscale X-ray Structural Analysis of Cardiac Cells and Tissues

Göttingen series in X-ray physics Volume 28

Universitätsverlag Göttingen 2022

#### Bibliographic information

The Deutsche Nationalbibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.dnb.de.

Funded by the Max Planck School "Matter to Life" supported by the German Federal Ministry of Education and Research (BMBF) in collaboration with the Max Planck Society and the Cluster of Excellence - EXC 2067/1- 390729940 "Multiscale Bioimaging".

*Address of the author* Marius Reichardt Email<EMAIL_ADDRESS>
Dissertation for the award of the degree "Doctor rerum naturalium" of Georg-August-Universität Göttingen within the doctoral program "IMPRS for Physics of Biological and Complex Systems" der Georg-August University School of Science (GAUSS)

Thesis Advisory Committee Prof. Dr. Tim Salditt, Institute for X-Ray Physics, Georg-August University, Göttingen Prof. Dr. Stefan Luther, Biomedizinische Physik, Max-Planck-Institut für Dynamik und Selbstorganisation, Göttingen Prof. Dr. Wolfram-Hubertus Zimmermann, Institut für Pharmakologie und Toxikologie, Universitätsmedizin, Göttingen

Date of the oral examination: 11.10.2021

This work is protected by German Intellectual Property Right Law. It is also available as an Open Access version through the publisher's homepage and the Göttingen University Catalogue (GUK) at the Göttingen State and University Library (http://www.sub.uni-goettingen.de). The license terms of the online version apply.

Setting and layout: Marius Reichardt Cover image: Marius Reichardt

© 2022 Universitätsverlag Göttingen https://univerlag.uni-goettingen.de ISBN: 978-3-86395-536-6 DOI: https://doi.org/10.17875/gup2022-1907 ISSN: 2191-9860 eISSN: 2512-6326

#### **Preface of the series editors**

The Göttingen series in x-ray physics is intended as a collection of research monographs in x-ray science, carried out at the Institute for X-ray Physics at the Georg-August-Universität in Göttingen, and in the framework of its related research networks and collaborations.

It covers topics ranging from x-ray microscopy, nano-focusing, wave propagation, image reconstruction, tomography, short x-ray pulses to applications of nanoscale x-ray imaging and biomolecular structure analysis.

In most but not all cases, the contributions are based on Ph.D. dissertations. The individual monographs should be enhanced by putting them in the context of related work, often based on a common long term research strategy, and funded by the same research networks. We hope that the series will also help to enhance the visibility of the research carried out here and help others in the field to advance similar projects.

Prof. Dr. Tim Salditt Prof. Dr. Sarah Köster Editors Göttingen June 2014

#### **Preface to the present volume**

Muscle contraction has fascinated biophysics from the beginning on.

As in the time of Hermann von Helmholtz, muscle physiology bridges physics, life sciences and medicine, also today. The refined understanding in particular of heart muscle has to be built on quantitative modelling, which in turn requires multi-scale structural analysis, from the sarcomere to the entire organ.

To this end, the current thesis has advanced X-ray diffraction and phase contrast imaging tools, using state-of-the-art synchrotron and laboratory X-ray setups. The progress achieved has already helped to address the pathophysiology of heart involvement in Covid-19.

Find out how this works in this well-compiled and excellent cumulative thesis, and do not miss the enjoyable historical perspective on a topic close to our heart!

Prof. Dr. Tim Salditt Göttingen, December 2021

#### **Contents**

# **Introduction** 1

As the central part of the circulatory system of the human body, the heart is primarily responsible for the distribution of oxygen and nutrients via the blood throughout the body to enable the essential functions of muscles, the brain and other organs [1]. Through the cardiovascular system, a network of arteries and veins with a total length of almost 100 000 km, the human heart pumps oxygenated blood from the left ventricle through the aorta and smaller arteries in the capillary network. On the capillary level, oxygen and nutrients are released and carbon-dioxide (CO2) and waste materials, such as creatinine (waste product of muscle activity) and urea (by-product of protein and amino acid breakdown) are absorbed. Veins allow the back-transport of the desoxygenated blood to the right atrium of the heart. From the right ventricle the blood is pumped via the lung arteries into the capillary network of the lung. Here, CO2 is released and new oxygen is absorbed. Oxygenated blood is then transported back to the left atrium and the left ventricle, starting the next cycle.

An average human heart is formed by about 10 billion cells, has the size of a fist and a weight of about 300 grams. The contractile force of a heart muscle cell, named cardiomyocyte, is generated by molecular motors. The smallest contractile unit, the *sarcomere*, is formed by an actomyosin complex which reduces its length during an action potential-triggered, ATP consuming reaction. In a resting state, the human heart beats about 60 to 90 times per minute, resulting in approximately 100 000 heart beats per day. Considering an average volume of 70 ml to 80 ml per beat, more than 7 000 liters of blood are pumped through the body each day. The synchronized contraction of the excitable cardiac tissue cells is controlled by the conduction system, which initiates an electric signal in the sinoatrial node and coordinates the propagation of the action potential through the heart. The continuous function of the heart during its entire lifetime is essential for the proper maintenance of all vital organs. Small dysfunctions or abnormalities can cause drastic changes and effects in the human organism. Therefore, it is very important to understand the cardiac structure from the molecular level up to the scale of the entire organ, as well as its function within the body.

The primary aim of this thesis is to develop imaging protocols to probe the entire cy-

toarchitecture of cardiac tissue using X-ray techniques. To this end, the cardiac structure is investigated using a multiscale and multimodal imaging approach. The 3d arrangement of the cellular network of the heart is investigated by propagation-based phase-contrast X-ray tomography, while the molecular structure of the actomyosin complex is probed by scanning X-ray diffraction. In this context, the concept of 3d virtual histology of cardiac tissue by X-ray phase-contrast tomography is being further developed. The data quality in terms of contrast, resolution and structural preservation is investigated for different sample preparation methods and image acquisition schemes. Additionally, novel data analysis pipelines, including structural analysis and feature segmentation, are presented.

This thesis is a cumulative dissertation consisting of an introduction followed by four peer-reviewed manuscripts published in the context of my work [2–5] and a summary and outlook section. The introduction provides background information on the research on cardiac structure, conventional imaging methods as well as X-ray based imaging techniques. In the first publication, laboratory investigations of entire murine hearts are presented, followed by investigations at higher resolution obtained by synchrotron radiation.

In chapter 2 an experimental imaging approach for the investigation of entire murine hearts by propagation-based phase-contrast tomography using a laboratory liquid metal jet source is presented [2]. In this context, the influence of sample preparation, including paraffin embedding, heavy-Z element staining, dehydration of the tissue using ethanol solutions and the Evaporation of Solvent method is compared. Further, the arrangement of the cellular network is reconstructed by a novel approach to identify local structural orientation and degree of alignment based on Fourier-analysis, as well as by an established gradient based method.

The functionality of the algorithm is also confirmed by high resolution datasets acquired at a synchrotron radiation facility, as presented in chapter 3 [3]. In this work, the 3d murine heart structure was analyzed in a multiscale X-ray imaging approach based on three different configurations set up at the *Göttingen Instrument for Nano-Imaging with X-Rays* (GINIX) setup of the P10 beamline (DESY, Hamburg, Germany). Overview scans of entire murine hearts are acquired using a cone beam illumination provided by Kirkpatrick-Baez-mirrors, before region of interest tomograms with higher resolution were acquired in parallel beam geometry. The sub-cellular structure of cardiac biopsies was probed by a cone beam wave guide illumination.

The concepts of image acquisition and reconstruction explained in the previous chap-

ters were then used to investigate histopathological changes of cardiac tissue structure caused by influenza, typical coxsackie virus myocarditis or Covid-19 (see chapter 4) [4]. Overview scans of tissue samples with a cross section of 3.5 mm were acquired at the laboratory liquid metal jet setup and the tissue structure was investigated based on structure tensor analysis. Additionally, the synthesis of new vessels (angiogenesis) was observed in severe cases of Covid-19. To this end, the vascular network of diseased and control samples was segmented by a deep learning based approach and analyzed by graph theory. By the formation of intraluminar pillars, small capillaries bifurcate from an intraluminar intussusception of myofibroblasts, creating a core between the two new vessels. The presence of intraluminar pillars was also observed using high resolution cone beam CT.

Chapter 5 presents a proof-of-concept experiment, describing how the sub-cellular structure of isolated cardiomyocytes can be analyzed by X-ray imaging techniques [5]. The 3d arrangement of myofibrils in a freeze-dried cell as well as the distribution of mitochondria was determined by high resolution X-ray tomography. Additionally, the actin network of the cell was investigated by confocal fluorescence microscopy. Furthermore, X-ray diffraction experiments on isolated cardiomyocytes were performed to probe the actomyosin lattice. Additionally to the structural analysis of freeze-dried and chemically fixed cells, we investigated for the first time isolated cardiomyocytes in living state.

The type of sample preparation, data acquisition and analysis schemes provided in this work can help to investigate cardiac tissue affected by different cardiovascular diseases. Furthermore, it allows for the analysis of the 3d structure of unstained formalinfixed, paraffin-embedded (FFPE) tissue. Thus, the histopathological tissue archives of departments all over the world can be accessed and structural changes due to different diseases (not only in respect to cardiac dysfunction) can be investigated, thereby paving the way for better understanding of the body function.

#### **1.1 Cardiac structure and (dys)function**

Cardiovascular diseases (CVDs) are the main cause of death worldwide with a rising incidence. While CVDs were responsible for less than 10% of the deaths worldwide by the beginning of the 20th century, the number of CVD-related deaths increased to over 30% by 2016 [6–8]. This corresponds to 17.9 million global deaths due to CVDs in one year. The major share of these death (85%) is attributed to heart attacks and

#### strokes [6].

Especially in high-income countries, where injuries, infections and nutritional deficiencies play a minor role, almost 50% of all deaths are related to CVDs [9]. In Germany, the leading cause of death in 2019 were CVDs with more than 330 000 deaths, followed by about 231 000 deaths due to cancer [10].

There are many known causes that increase the risk of developing CVD, such as lack of exercise, unhealthy diet, smoking, harmful use of alcohol as well as genetic reasons. Additionally, the risk for CVDs can be reduced pharmaceutically by drug treatment of diabetes, hypertension and high level blood lipids. However, there is no possibility to eliminate the risk completely as of yet.

The increased survival rate for coronary artery disease and myocardial infarction due to medical progress goes along with a high number of patients suffering from ischemic heart disease, including heart failure and fibrosis. Thereby, the structure of the heart is irreparably damaged in the long term. Hence, treating the cause of CVDs efficiently remains one of the biggest challenges to solve in today's medicine. The life quality as well as the life expectancy of millions of individuals could be improved while costs for the health system could be reduced by a better understanding of the cardiovascular system. To tackle this problem, it is essential to understand the underlying structure of the heart.

Until now, the fundamental physiology of the heart, regardless of the influence of diseases, is not completely understood. The exact arrangement of the complex, dense and codependent cardiac network formed by cells of different types is still unknown [11–13]. Hence, it is not possible to explain the contractile function of the human heart in full detail, yet. Throughout history, many studies on the cardiac anatomy were performed to improve the understanding of cardiac structure and function.

#### **1.1.1 A brief history of cardiac anatomy**

This section presents a summary of the historical development of cardiac anatomy and function over the last 5000 years and is based on the following review articles [14–17].

Figure 1.1 shows a timetable of the understanding of cardiac anatomy over the last centuries.

First reports about the anatomy of the human heart date back to ancient Egypt around 3000 BC. Figure 1.1A shows a hieroglyph representing the heart with the main ves-

**Fig. 1.1: Historic timetable of cardiac anatomy.** (A) Hieroglyphic representation from the ancient Egyptians [17]. (B) Drawing of the cardiac anatomy by Aristotle [15]. (C) Sketch of the heart by Leonardo da Vinci [15]. (D) Cardiac model by Richard Lower [18]. (E) Text book figure of Henry Gray's anatomy [16]. (F) Concept of a "Triebwerk" by Ludolf Krehl [18]. (G) Jane Sands Robb's model of the heart [18]. (H) Cardiac fiber model of Alfred Benninghoff and Kurt Goerttler [18]. (I) Model of the helical ventricular band by Francisco Torrent-Guasp [18].

sels attached to the top of the organ. Already back then, the heart was considered the central organic motor of the body. Egyptians believed the heart was responsible for the transport of blood, air, urine and feces, as well as allocated human intelligence, emotions and desire. Knowledge of the heart structure and function was still in its infancy and mostly obtained from the mummification process and veterinary dissections. However, it enabled medical progress such as for example pulse-monitoring of patients in the 17th century BC by correlating the heart rate to a water clock.

Next important information on human anatomy was delivered by the Greeks. After Homer claimed the heart to be the source of bravery and human courage, noteworthy historical figures such as Asclepios and Alcmaeon (a student of Pythagoras) started to study the heart from an anatomical viewpoint. Around 460 BC an anatomical series of 70 books without any philosophical speculations, the Hippocratic Corpus, was published by Hippocrates from the school of Cos. In the book titled "On the Heart", the macroscopic structure of the heart was described for the first time as a strong muscle. The interventricular septum, semilunar valves and morphological differences between the thick-walled left ventricle and thinner right ventricle were described. Furthermore, the atria were mentioned for the first time, though their function was misinterpreted as "ears" to capture air.

The next update on the cardiac anatomy was made by Aristotle around 350 BC, who believed the heart to be formed by three chambers. He described the right and left ventricle as well as a medial chamber, which can be related to the left atrium. Since the right atrium is directly connected to the venae cavae, he did not consider it to be a part of the heart. Within the right chamber, he identified sinews, later known as "chordae tendinae", connected to the papillary muscles. He pictured that all chambers were connected to the lung via "ducts" and that there was a connection between the left and right ventricle. The idea of oxygen exchange in the lung and of a closed blood circuit did not exist yet. Instead, the Greeks believed that the brain was the origin of all blood vessels and that arteries narrow to become nerve fibers. This idea was refuted around 300 BC by Erasistus, who identified a connection between arteries and veins. He defined the heart as a double pump which distributes blood through the right ventricle into the veins and pneuma (air and vital spirits) through the left ventricle into the arteries.

In the Roman era around 130 AD, Claudius Galen discovered that arteries contain blood. Further, he recognized fibers with different orientations (long, sectional and diagonal) within the heart wall. However, he did not classify the heart as a muscle since heart function is autonomously and cannot be moved voluntarily. He believed that the heart is formed by two chambers. The left ventricle contained air and was connected to the right ventricle by a diaphragm permeable for blood, allowing it to flow in an ebb-flow motion from right to left ventricle through invisible holes in the septum.

This assumption was state of the art in the western world until the 16th century, when Leonardo da Vinci described the anatomy of the heart as we know it today: a four chambered organ with two ventricles and one atrium on top of each ventricle including the auricular appendages. He described the heart as a pump and identified the spiral blood flow in the aorta near the aortic valve, but he could not conclude the directed circular flow of the blood. He supported Galen's assumption that the ventricles are communicating by invisible pores and misjudged that the heart has the purpose to produce "vital heat" by friction of the blood.

Matteo Realdo Colombo is credited to be the first who implied that air and blood mix in the lung and the heart valves allow an unidirectional blood flow. Here, it is worth noting that the idea of separated ventricles as well as an oxygen exchange in the pulmonary circulation was already discovered in the 13th century in the Islamic area by Ibn-Al-Nafis.

During the 17th century, research on cardiac function and anatomy continued. In Richard Lowers work "Tractatus de Corde", he described the heart as a four-chambered fibrous muscular organ. He also described the contraction of myocardial fibers resulting in the blood flow from the heart to the lungs and back. In the first half of the 19th century, Wilhelm His and Johann Evangelist Purkinje discovered the conduction system of the heart, which enables a controlled contraction of the cardiac muscle cells. Further, sub-cellular structures such as muscle fibers, striated myofibrils and the cellular membrane (sarcolemma) were identified by Bowman in 1840 [19].

In the middle of the 19th century, it was assumed that all discoveries of the human anatomy had been made. In this era many textbooks were published by renowned physicians all over the world such as Jakob Henle ("Handbuch der systematischen Anatomie des Menschen"), Xavier Bichat ("Anatomie Generale") and Henry Gray and Henry Vandyke Carter ("Grays Anatomy"). Nevertheless, due to ongoing research and new discoveries the textbooks had to be updated constantly. In October 2020, the 42th edition of "Grays Anatomy" was released. Concerning the cardiac anatomy, most of the open questions were related to the cardiac function and structural changes caused by CVDs. For example, in 1891 Ludolf Krehl introduced the idea of a circumferential

arrangement of cardiomyocytes in the middle layers of the left ventricle wall, called "Triebwerk", to provide a driving force for ventricular contraction. Following the idea of a fiber-like alignment of cardiomyocytes, many other models were published in the 20th century. The lower part of Fig. 1.1 shows the models of Jane Sands Robb (1942), Alfred Benninghoff and Kurt Goerttler (1980) as well as a more recent model of the "helical ventricular myocardial band" by Francisco Torrent-Guasp [18].

Most of these models indicate that the muscle cells are arranged in a helical manner, emerging from the apex spinning up to the base [18, 20] or also as a nested set of warped "pretzels" [21]. So far, no model of the cardiac structure can explain its contractile function in full detail. Another more recent approach is to describe the heart as a complex network of cardiomyocytes which are arranged in a mesh of extra cellular matrix [13, 22, 23]. A short summary of the current state of cardiac anatomy is given in the next section.

#### **1.1.2 Current state of cardiac anatomy**

The cardiac function relies on an intricate, hierarchical molecular and cellular architecture. On the molecular scale actomyosin complexes form sarcomeric units, which are arranged in elongated myofibrils within a single cardiomyocyte. Chains of myocytes are embedded in connective tissue and form aggregation within a complex cellular mesh supported by an extra-cellular matrix (ECM). The specific composition and alignment of this network represents the foundation of the life-sustaining heart function [11, 13].

A sketch of the cardiomyocyte blueprint is shown in Fig. 1.2. On the nanoscale, the contractile force of the heart is generated by molecular motors composed of an actomyosin complex. The smallest contractile unit is called *sarcomere* [25–27]. An average sarcomere of a human cardiomyocyte has a length of about 2.2 µm in the relaxed state and is composed of thick myosin filaments and thin filaments formed by actin, troponin and tropomyosin. The structure of single actin and myosin filaments is well understood. While the thick filaments are a composite of multiple myosin molecules arranged in a helical manner with a distance of 14.3 nm between their head groups and a periodicity of 42.9 nm, the thin filaments are composed of a single filamentous actin (f-actin) strand. F-actin is a double helix of single actin molecules with an intermolecular distance of 0.55 nm and a periodicity of 35.75 nm. One sarcomere reaches from one Z-disc to the next one. The area around the Z-discs contains thin filaments and is called I-band [19, 28, 29]. The myosin rods are located in the A-band. The

**Fig. 1.2: Sketch of the cardiomyocyte structure.** (A) A sarcomere is composed of thin filamentous actin and thick myosin filaments.  They exhibit a periodicity of 42.9 nm and a distance of 14.3 nm between their head groups. Thin filaments, composed of actin, troponin and tropomyosin, form a double helix with an intermolecular distance of 0.55 nm and a periodicity of 35.75 nm. Sarcomeres are mirror symmetrical structures connected by Z-discs. The area around the Z-discs (A-band) is composed of actin filaments, which overlap with myosin on the side facing the center. The area containing thick filaments is called I-band. In the center of the sarcomere, where only myosin is present (H-zone), the thick filaments are connected by the M-line which also forms the mirror axis. The cross section of the hexagonal sarcomere lattice has a 2:1 actin-to-myosin-filament ratio and is described by the distances *d* (1*,*1) and *d* (1*,*0) . Figures adapted from [24]. (B) Sketch of the cardiomyocyte network. The contractile function of individual cardiomyocytes is provided by chains of sarcomeres called myofibrils. Energy is provided by mitochondria. Further, cardiomyocytes contain a nucleus, a Golgi apparatus and microtubules. The cardiomyocytes are connected via intercalated discs, gap junctions and desmosomes and surrounded by extracellular matrix containing the capillary network. Adapted from [5].

naming of the areas is related to its imaging properties: A for anisotropic and I for isotropic scattering of polarized light. The center of the A-band, where no thick and thin filaments overlap, is called H-zone, corresponding to the German word "Hellerscheibe" (clear disc). The dense line connecting the thick filaments is named M-line ("Mittelscheibe", middle disc).

Each myosin filament is surrounded by six thin actin filaments and each thin filament by three myosin filaments, resulting in a hexagonal sarcomere lattice with 2:1 actinto-myosin-filament ratio. The inter-filament lattice can be described by the distances *d* (1*,*1) and *d* (1*,*0) .

The contraction process is caused by an action potential-triggered, ATP consuming, isothermal reaction with an efficiency of almost 50% [30]. The process of shortening of the sarcomere can be explained by the sliding filament theory [19, 31]. In a rowinglike motion the actin filaments slide over the myosin filaments, pulling the Z-discs toward the center of the sarcomere. The link between electrical excitation triggered by the action potential and muscle contraction is given by the release of calcium (Ca2+) ions.

The sarcomeres form long chains, connected by Z-discs, called myofibrils [32]. About 80% of the volume load of a single cardiomyocyte with a length of about 100 µm to 150 µm is filled with myofibrils. The dimensions of the cardiomyocyte is defined by the cell membrane, called sarcolemma. Besides covering the cell, it contributes to the excitation and contraction process due to its electroconductivity and elasticity. Next to myofibrils, a cardiomyocyte contains mitochondria, which are located in close proximity to the myofibrils and provide ATP, a nucleus, containing the DNA, the rough endoplasmic reticulum and sarcoplasmic reticulum for ion storage [33]. The decaytime of the ions channels located in the sarcolemma is in the range of hours. Therefore, microtubules serve as "highways" from the Golgi apparatus to the membrane and enable directed transport of the channels [33].

Cardiomyocytes tend to form long myocyte chains which are connected by intercalated discs at the longitudinal side of the cell. A lateral connection of the cells is provided by gap junctions. These connections allow the flow of the action potential caused by a depolarizing current from one cell to another. Inter-cellular stability is increased by desmosomes, linking neighboring cells [34]. Aggregations of cardiomyocyte chains are embedded in connective tissue, the extracellular matrix, including elastic and collagenous fibers and a capillary network supporting the cells with oxygen and nutrients.

The heart muscle tissue, called the myocardium, is formed by a complex network of cardiomyocyte aggregations, which are arranged in several layers and enable the contractile function of the heart. The outer surface of the heart is covered by a thin layer of tissue, named pericardium, which acts as a protective film. On the inside of the ventricles, another layer of tissue, the endocardium, separates the myocytes from the blood pool. A sketch of the gross cardiac anatomy is shown in Fig. 1.3.

The intrinsic electrophysiological system controls the cardiac contraction cycle. Starting at the sinoatrial node, which is located in the wall of the right atrium, an electrical signal excites the atria by the Bachman's bundle causing the contraction of cardiac

**Fig. 1.3: Cardiac anatomy.** The heart consists of four chambers (two atria and two ventricles separated by the interventricular septum). Through the pulmonary veins oxygenated blood is transported to the left atrium and ventricle and is distributed through the aorta into the body. Desoxygenated blood is then pumped back through the venae cavae to the right atrium and ventricle of the heart and back to the lungs through the pulmonary arteries. The cardiac valves prevent a backflow of the blood. The cardiac conduction system is indicated in yellow. The sinoatrial and the atrioventricular node control the time gating of the contraction cycle, while the Bachman's and His bundle as well as the Purkinje fibers act as conduction pathways. The direction of action potential propagation is indicated by the white arrows. Adapted from [35].

muscle cells of both atria. This process is named atrial systole. After the signal reaches the atrioventricular node it propagates along the ventricular impulse-conducting system including the bundle of His and the Purkinje fibers to the base of the heart, triggering the ventricular systole. A backflow of the blood during diastole, cardiac muscle relaxation, is prevented by the cardiac valves.

During the continuous contraction cycle, different pressures, strains and electrical stimuli occur in each chamber of the heart. Therefore, the basic function of the heart cannot be provided by a unified type of cell but requires a variety of different cardiac cells types. One can differentiate atrial cardiomyocytes, ventricular cardiomyocytes, fibroblasts, endothelial cells, pericytes, smooth muscle cells, immune cells, adipocytes, mesothelial cells and neuronal cells. Each cell group has its own functionality and specialized structure [11, 36].

These cell types can also be separated in populations by gene expression. For example, there are at least five different types of ventricular cardiomyocytes with different proportions in the left and right ventricle. Furthermore, the composition of the ventricular cardiomyocytes not only differs locally but is also gender-specific [11].

The entire human heart is formed by about 10 billion cells, which interact in a complex, dense and codependent network. Even though the gross anatomy is well described, the multiscale structure and its functionality is still not completely understood [11–13].

So far, it is not possible to give a generalized answer how the entire (healthy) heart is formed. Considering diversity between individuals or structural changes due to aging or CVDs such as e. g. myocardial infarction or hypertension for an individual patient, the problem is even more complex to understand. The question how exactly the action potential propagates through the entire organ of a patient, triggering the time-gated contraction of the heart remains unsolved.

To improve the understanding of the cardiac structure and function, computational modeling of the heart is conducted [37]. It is possible to model, analyze and control cardiac dynamics based on the coupling of nonlinear (chaotic) systems such as the electrical wave propagation in cardiac tissue [38, 39]. These simulations can for instance help to understand the cause and effects of cardiac arrhythmia. The fundamental mechanisms such as the propagation of the action potential, as well as the mechanical response, highly depend on the material properties of the cardiac cells. While defects like scar tissue (caused by aging or myocardial infarctions) disturb the propagation, the speed of propagation is higher along the orientation of the cardiomyocytes [40, 41]. In order to overcome the challenge of upscaling cardiac models from the sub-cellular and cellular level to the tissue and organ scale, it is mandatory to link the models to experimental data [42–44]. For instance, the cardiac dynamics of a beating (pig) heart mounted on a Langendorff perfusion system was analyzed using fluorescence imaging of the calcium wave propagation and four-dimensional ultrasound imaging. The reconstruction of the 3d structural dynamics as well as the calcium wave propagation along the surface of the heart revealed scroll waves which are considered to be the organizing center of cardiac arrhythmia [45].

Another approach to support the computational modeling of cardiac function is the combination with diffusion tensor MRI [37, 46]. Since the propagation of the electrochemical signal within the heart depends on the orientation of the cardiomyocytes, the vectorfield obtained by diffusion tensor MRI is of high value for computational simulations [47]. In addition to electro-mechanical simulations of the heart based on its 3d structure, it is also possible to perform computational modeling of blood flow and pressure distribution within the heart [37].

There are a variety of models to describe the cardiac function on multiple scales. However, it is still unclear how exactly the cardiac cells are arranged within the heart to enable the contractile function in full detail.

From the current state of research one can conclude that it is essential to understand the structure of the heart to improve the computational modeling and the general understanding of a complex organ as the heart. Therefore, imaging of cardiac tissue is and has always been one of the fundamental conditions for progress in cardiac research.

#### **1.2 Conventional imaging of heart tissue**

#### **1.2.1 Histology**

Historically, the observation of the heart structure started by documenting visual impressions gained from evisceration of animals or autopsies. With progress in the manufacture of optics and the invention of the microscope in the 17th century, it was possible to investigate structures in the micrometer range [48]. During this time, Marcello Malpighi was the first who identified small capillaries in the lungs of bats and established the process of oxygen uptake [49]. This procedure, later called histology (from Greek: *histos*, tissue and *logos*, study), revealed its full potential during the 19th

century, when fixation techniques and staining protocols were developed. Those lead to increased contrast for specific tissue structures and made it possible to characterize healthy as well as diseased tissue by light microscopic analysis [50].

Today, conventional histology is the goldstandard in clinical practice worldwide. In a standardized procedure, the dissected tissue is chemically fixed by a liquid fixing agent, such as formaldehyde. In a diffusion-based process, the tissue gets slowly penetrated by the fixative, which cross-links proteins to stop the disintegration of the tissue. The fixed sample is then dehydrated using an ethanol series with increasing concentrations and cleared by xylene in order to be transferred to melted paraffin wax. After the entire sample is infiltrated by liquid paraffin, it is poured out into a block with an attached cassette [50, 51]. Samples embedded in paraffin wax blocks are very stable and make up the majority of archived tissue stored in pathology departments all over the world. In a further step, thin slices with a thickness of a few µm are cut from the paraffin blocks using a microtome. These slices have to be transferred to microscopy glass slides, where they are deparaffinized, before histological staining. Depending on the aim of the investigation, a variety of different histological staining procedures, such as Hematoxilin and Eosin (HE) stain, Masson-Trichrome stain or antibody-based immunohistological staining can be performed [52]. The stained sections can then be sealed to increase their durability. At the end of this labor-intensive and time-consuming process, a pathologist can analyze the tissue structure by light microscopy at different magnification, to identify morphological changes [53]. Based on his diagnosis, the pathology of the sample can be classified and if applicable further treatment such as drug treatment, surgery or radiation be prescribed.

However, conventional histology has three major disadvantages when analyzing the 3d tissue structure. Since the procedure is based on the microscopic analysis of thin slices of paraffin embedded tissue, histology is a *destructive*, *two-dimensional* technique with *limited, anisotropic resolution*.

In order to analyze an entire organ, hundreds to thousands of paraffin slices need to be prepared, analyzed under the microscope and stitched together. Since artefacts of the paraffin embedding (such as shrinking of the tissue), tissue deformations or even destruction while cutting, and inhomogeneities of the histological staining procedure cannot be excluded, it is very challenging to visualize an entire organ using conventional histology. Nevertheless, there are some datasets available [54, 55]. For example, entire human brains were analyzed in a multiscale approach by MRI and histology [56]. Microscopy images with a pixelsize of 4 µm of 25 µm thick, stained

slices were acquired and co-registered with the low resolution MRI data. To reduce redundancies, the workload and the amount of data only every 10th or 20th section was analyzed, depending on the brain region and its cell density.

There are comparable histological investigations of the heart in animal models, but there is no human investigation with such high detail so far [57, 58]. An exemplary histological slice of a murine heart is shown in Fig. 1.4A. For human heart tissue, it is more common to take photographs of short-axis sections with a thickness of a few mm and record micrographs of stained sections of paraffin biopsies taken from regions of interest of embedded tissue afterwards [59–61].

So far, histology as a 2d technique seems to be the best combination of resolution and identification of (sub-)cellular structures. However, the resolution of conventional histology in combination with light microscopy is also limited. According to Ernst Karl Abbe, the resolution *d* of an optical system is diffraction limited [62]. In the lateral plane it is given by

$$d = \frac{\lambda}{2n\sin(\alpha)}\tag{1.1}$$

with numerical aperture NA = *n* sin(*α*) and wavelength *λ*. For visible light the lateral Abbe limit is in the range of 200 nm. The axial resolution limit for (*d* = 2*λn* NA2 ) is larger, though it does not play a role for histological investigations since the resolution is limited by the slice thickness and the distance between consecutive slices, stained with the same histological dye. Hence, the resolution of histological investigations is anisotropic.

Furthermore, when analyzing cardiac structures such as the actomyosin complex, the diffraction limit of visible light microscopy is about one order of magnitude too high to resolve the single protein bundles.

Other light microscopy techniques such as high resolution episcopic (reflection) microscopy or polarized light microscopy enable a different contrast. However, their limitations in terms of resolution and invasive sample preparation are congruent with conventional histology [63–66].

In order to analyze molecular structures, different imaging modalities which allow for higher resolution are necessary. In the following, two of those techniques, electron microscopy and fluorescence (super resolution) microscopy, are briefly described.

#### **1.2.2 Electron microscopy**

One option to image (biological) structures at higher resolution is electron microscopy. Due to a smaller wavelength of the accelerated electrons compared to visible light, a higher resolution can be reached (see Eq.(1.1)). This technique is already well established in cardiac research and is especially well suited to analyze the structure of mitochondria and sarcomeric structures at high resolution [36, 67]. Additionally, molecular structures can be labeled by gold nanoparticles coupled to antibodies. Figure 1.4C shows an electron micrograph of cardiomyocytes of a wild type mouse, where the attachment sites of desmin filaments (of the intermediate filament family of cytoskeletal proteins) were immuno-gold-labeled [68].

Since the penetration depth of the electrons through the tissue, usually stained by heavy elements such as uranium and tungsten, is very small, the axial resolution is limited by the slice thickness. Thus, the samples have to be sectioned to slices with a thickness in the range of a few nm. Similar to conventional histology, the third dimension can be accessed by labor-intensive and artefact sensitive serial sectioning [69, 70]. For instance, in 2018 the 3d structure of two neighboring cardiomyocytes was acquired from 1019 serial sections of 50 nm thickness [71]. Electron microscopy is a technique which is more commonly used to analyze the 2d ultrastructure of cells and tissue and to support results obtained from techniques with a lower resolution and larger field of view such as conventional histology or (confocal) fluorescence microscopy [36, 68, 72].

#### **1.2.3 Fluorescence imaging**

With fluorescence imaging it is possible to image specific protein complexes of labeled (biological) specimens. Fluorescent dyes absorb electromagnetic radiation and consequently emit light with a certain wavelength. This consequence also allows the same sample to be stained with multiple dyes at various binding sites of different protein complexes. By point wise scanning of the sample with a focused excitation laser, slices of stained tissue can be analyzed.

Figure 1.4B shows an example of a fluorescence micrograph of cardiomyocytes. In this case nuclei (blue) and desmin (green) were labeled with different fluorescent dyes.

The resolution of these measurements is also limited by diffraction, thus molecular structures such as the actomyosin lattice cannot be resolved. The resolution limitation by Abbe was overcome by the invention of *stimulated emission depletion* (STED)

**Fig. 1.4: Conventional imaging of cardiac tissue.** (A) Histological HE stain of a wild type mouse. (B) Fluorescence imaging using an immunostaining with a desmin antibody. (C) Electron micrograph of cardiomyocytes of a wild type mouse. In this case, attachment sites of desmin filaments were immuno-gold-labeled using antibodies. Adapted from [68] (D) SPECT image of two human hearts in stress (top) and resting (bottom) state [73]. (E) Cardiovascular MRI perfusion analysis of two human hearts in stress (top) and resting (bottom) state using a gadolinium contrast agent [73]. (F) An exemplary slice of a coronary CT angiography. A coronary artery stenosis is marked by a white arrow. Scale bars: A: 1 mm, B: 5 µm, C: 0.25 µm, D and E: 2 mm. Adapted from [74]

microscopy by Stephan Hell and Jan Wichmann in 1994 [75]. The excited fluorescent molecules can be switched off again by stimulated emission using a second, doughnut shaped laser pulse. The time gated depletion of the point of illumination and the detection of the emitted light not depleted allows "super resolution" to be achieved. Recently, this invention was further developed by a combination of STED and single molecule localization microscopy such as *stochastic optical reconstruction microscopy* (STORM). The novel technique called *minimal photon fluxes* (MINFLUX) allows to analyze single molecules in 3d with a resolution in the range of a few nm while also reducing the problem of photobleaching [76, 77]. MINFLUX uses a doughnut shaped excitation laser and is based on stochastic assumptions, the dose can be reduced and

theoretically an image can be recorded without the excitation of the dyes. In terms of cardiovascular research super resolution microscopy is very promising regarding the investigation of structures within the cells such as the function of single mitochondria, ion channels, membranes or the sarcomeric structure [72, 78, 79]. Research in the field of fluorescent imaging is still ongoing. On the biochemical side, new dyes are being developed while on the imaging side a large research field is continuously working on improvements of image quality. This is not only relevant in terms of nanoscale imaging, since new developments of fluorescent dyes also enable functional time resolved *in vitro* imaging of hydrated cells or tissue. For instance, Ca2+ sensitive dyes allow to perform surface imaging of calcium waves propagating over the heart [45].

Note, that the advantage of fluorescence imaging techniques to label specific structures is also one of its disadvantages. It requires staining with suitable fluorescent dyes and only labeled structures can be identified, while unlabeled tissue appears dark in the images. Furthermore, 3d imaging using light microscopy is challenging since the penetration depth of visible light through the sample is limited by self absorption and light scattering. Hence, to analyze larger volumes, serial sectioning of the tissue is mandatory. One possibility to reduce the self absorption and scattering of the emitted photons within the sample is tissue clearing [80–82]. During this process the refractive index of a chemically fixed tissue is homogenized so that it turns transparent for visible light. The preparation usually includes decalcification, decolorization, delipidation, dehydration and clearing of the sample. In combination with fluorescent staining and light sheet microscopy, larger volumes in the range of the size of murine brain, a zebra fish or even an entire mouse can be analyzed [81–84]. However, this technique is also limited by diffraction and has an anisotropic resolution due to the properties of the excitation laser. Furthermore, the molecular and cellular organization in tissues is affected during the preparation process. The delipidation has an especially large effect on the tissue structure. Additionally to the clearing of the tissue, the uniform injection of fluorescent dyes e. g. by immunostaining, is very challenging especially for dense 3d biological material such as murine cardiac tissue [82, 85, 86]. One possibility to image entire hearts by light sheet microscopy is the combination of transgenic modification with the cardiomyocytes. By the expression of green fluorescent protein (GFP), originally found in jellyfish *Aequorea victoria*, or by the expression of *TdTomato* the problem of the tissue penetration can be overcome [85, 86].

In order to analyze larger and denser structures such as an entire human heart or even the full body of a patient, different imaging techniques are used in clinical routine.

#### **1.2.4 Clinical 3d imaging**

Conventional techniques used to clinical imaging of cardiac tissue include echocardiography, positron emission tomography (PET), single-photon emission computed tomography (SPECT), (diffusion tensor) magnetic resonance imaging (d)MRI, as well as absorption-based computed X-ray tomography (CT) and angiography. For all of these clinical techniques, a unifying principle is the injection of contrast agents into a peripheral vein [63, 74, 87].

PET and SPECT, as imaging techniques based on radioactive tracers, are well suited to characterize cardiac function and can help identify coronary artery diseases, hypertrophic cardiomyopathies and abnormalities in heart wall motion. Figure 1.4D shows SPECT images of two human hearts in a stressed (top) and resting (bottom) state. Such images are used to quantify the extent of left ventricular myocardial ischaemia [74]. However, their spatial resolution is in the cm to mm range and thus too low to characterize the cardiac structure in detail.

Echocardiography, a non invasive imaging technique without ionizing radiation, is based on ultrasonography and uses microbubbles as contrast agent to visualize the blood flow. Echocardiography can be performed at the bedside of the patient, however compared to other imaging techniques presented, it is noisy and yields many artefacts. Further, it is not reproducible and most importantly for the structural analysis of the cardiac muscle structure it only yields intravascular contrast for the blood flow but not for cardiomyocytes. Thus, it is not suited to study the cytoarchitecture of the heart.

MRI, as a technique which is well suited to image the dynamics of hydrogen nuclei, enables an excellent contrast for soft tissue. Due to the high anisotropy of the cardiomyocyte organization within the heart, the cardiac structure can be estimated by diffusion tensor MRI, which represents a suitable option to characterize orientation of the cardiomyocyte arrangement indirectly in *in vivo* and *ex vivo* experiments [88, 89]. The signal can be enhanced by gadolinium-based contrast agents. MRI is commonly used to characterize myocardial ischemia with a high sensitivity and specificity [90]. The recent development of real time MRI also allows the study of blood flow during cardiac contraction. Exemplary data of MRI acquisitions of two hearts in a stressed and resting state is shown in Fig. 1.4E. Such data provides myocardial blood flow values [74]. After all, clinical MRI is well suited to study the cardiac structure, including the cardiomyocyte orientation, and can also reveal the dynamics of the cardiac blood flow. However, the resolution depends on the strength of the magnetic field and is typically allocated in the (sub-)millimeter range. Even *ex vivo* studies of cardiac structure using MRI can reach resolutions down do 50 µm, but cannot achieve sub-cellular resolution, yet [63, 91].

Conventional CT and radiography is a cost efficient, widely available imaging technique used for multiple clinical applications [74, 92, 93]. It is based on the attenuation of X-rays and provides a good contrast for highly absorbing materials such as teeth or bone, but also enables several cardiovascular examinations. For example, ischemic heart disease can be detected using coronary angiography. In the procedure a iodinebased contrast dye is injected into the coronary artery through a catheter. The spread of the agent in the blood is detected by a series of 2d radiography images. In this way, blockages in the coronary arteries caused by plaque buildup can be identified. A coronary angiography is recommended by European guidelines to detect ischemic heart disease of patients with a low to intermediate clinical likelihood. The 3d morphology of the heart can be investigated by chest CT in combination with the injection of contrast agents. A slice of a coronary CT angiography indicating a coronary artery stenosis is shown in Fig. 1.4F. Cardiac CT is used to quantify stenosis and plaques in 3d at high resolution e. g. by calcium scoring. Furthermore, in combination with vasodilators (medications that dilate blood vessels) myocardial CT perfusion imaging can be performed. It allows to identify defects of the myocardium.

The disadvantage of conventional CT is the comparatively weak contrast for soft unstained tissue and the delivered radiation dose, which also limits the temporal resolution of the medical image acquisition [94]. An average coronary computed tomography angiography with a resolution of about 0.5 to 0.7 mm delivers a dose of approximately 8.7 millisievert to the patient. This equals about 3 years of background radiation [95, 96]. For comparison, the dose limitation for occupationally exposed persons is 20 millisieverts in a calendar year in all European countries [97]. Furthermore, scatter artefacts of absorbing structures reduce the quality of soft tissue recordings. However, even for *ex vivo* experiments, in which the radiation dose can be increased, the absorption contrast for soft tissue is very weak [63].

In summary, imaging of cardiac function and structure in the clinical routine is subject to more stringent conditions on the imaging technology compared to pre-clinical research. Since data acquisition is performed *in vivo*, motion artefacts and penetration depth of the imaging modality as well as the delivered dose plays an important role. The clinical methods are well suited to identify and characterize cardiomyopathies, but neither the resolution nor the contrast of the given modalities is high enough to resolve sub-cellular structures of *in vivo* human cardiac tissue. Even under *ex vivo*

conditions and when using small animal models, imaging the entire cardiac architecture remains challenging. To uncover the myocyte arrangement, a destruction free, multiscale imaging approach, reaching from an entire organ down to sub-cellular resolution is required. A possible solution is given by recent progress in X-ray imaging techniques and especially by the advent of X-ray phase-contrast CT, introduced in the next section.

#### **1.3 X-ray phase-contrast CT**

X-ray imaging of human tissue goes back to its discovery by Wilhelm Conrad Röntgen in 1895, when he noticed a glow on a nearby phosphor screen caused by an invisible ray [98]. On 22 December 1895 he acquired an X-ray radiograph of his wife's hand. In the slightly unsharp projection on photosensitive film, shown in Fig. 1.5A, one can identify her hand bones and a large ring, despite the contrast for soft tissue being quite low. Given that it took approximately 30 to 45 minutes to acquire the image, it is quite impressive how little motion artefacts are visible.

Due to further development of X-ray sources and detectors, patients do not need to be this patient anymore. The first conventional CT scanners developed in 1971 by the group of Sir Godfrey Hounsfield required about 25 to 30 minutes to acquire an entire tomogram. Today, an average CT scan can be recorded within a quarter of a second. The reason for these improvements is related to the progress in X-ray generation and detection of X-ray radiation [99, 100].

#### **1.3.1 X-ray generation and detection**

While the basic principle of X-ray generation in X-ray tubes based on electron impact has not changed in the last 125 years, the efficiency of modern X-ray sources and X-ray detection techniques has increased. A schematic X-ray tomography setup is shown in Fig. 1.5B. In a conventional X-ray tube electrons emitted by a cathode, are accelerated onto an anode material (usually tungsten, molybdenum or copper), where their kinetic energy is transferred into heat and electromagnetic radiation [102]. The emitted energy spectrum of the X-rays can be traced back to two physical processes: *Bremsstrahlung* and the *characteristic emission* of the anode material. The *Bremsstrahlung* X-rays are named after the German word for braking and emerge from the kinetic energy loss of the electrons passing through the anode material. The de-

**Fig. 1.5: Principles of X-ray imaging.** (A) One of the first X-ray images was acquired in 1895 on a photographic plate showing the hand of Anna Bertha Röntgen [101]. (B) Sketch of a cone beam X-ray tomography setup. X-rays are generated by electrons, which are emitted by a cathode and accelerated onto an anode material. Projections of a sample are acquired by an X-ray detector. (C) Interaction of an electromagnetic wave with matter. When passing through an object, the amplitude of the incoming wavefront is reduced. Furthermore, the phase of the wave is shifted compared to a reference wave propagating in vacuum.

celeration of the scattered electrons in the external electric field of the anode nuclei results in a continuous X-ray emission spectrum. Photons emitted by excited atoms of the anode material contribute to the *characteristic spectrum*. The generated X-rays are emitted in all directions, thus a conventional X-ray source is a 4*π* radiator.

Since only about 1% of the electron energy is transformed into radiation, an overheat-

ing or even melting of the anode material is the most important limiting factor when increasing the power. In order to reduce skin dose, the amount of X-ray used for clinical imaging is further reduced by radiation shielding and collimation of the beam as well as trimming of the X-ray energy spectrum. In the end, only a fraction of about 0.03% of the energy is used for image acquisition [102]. The power of an X-ray source can be characterized by the brightness defined as source photons (ph) per solid angle and per source area (ph mrad*−*2 mm*−*2 ).

#### **Development of laboratory X-ray sources**

The first X-ray tubes used by Röntgen were initially designed to study energetic electron beams. These tubes were invented around 1875 by William Crookes and unintentionally radiated X-rays with photon energies below 30 keV as a byproduct. The Crookes tubes could not be actively cooled and the photon emission was very low since the electrons were emitted from ionized gas near the cathode and thus the tubes were not well evacuated.

In 1913, the first high vacuum X-ray tubes designed by Coolidge were produced. This next generation of X-ray tubes emitted electrons from a heated cathode filament which were then accelerated onto a solid anode target which could be cooled actively by water. The progress in the generation of a stable vacuum enabled higher electron energies and flux.

A further increase in heat dissipation and photon flux was achieved by the invention of the rotating anode tube [103]. By rotating the anode, the source spot moves over the anode surface. Thus, the heat is distributed over a larger area of the anode material, which still reaches up to 2500°C despite active water cooling. Another approach based on the same principle is the rotating frame anode, which rotates inside the housing assembly. This design allows for a direct contact of the anode with oil and enables high cooling rates. These designs enables a relatively high photon flux and are used as the gold standard for most clinical applications [100, 102].

The reason the source spot can not be expanded limitless, thus enabling a limitless increase in flux, is the effect of source blurring. The resolution which can be achieved by a cone beam X-ray system depends on the configuration of the imaging setup sketched in Fig. 1.5B. The geometric magnification *M* = x01+x12 x01 can be enlarged by increasing the sample-to-detector-distances x12 or decreasing the source-to-sample distances *x*01. Thus, the effective pixelsize *px*eff = *px M* is reduced. However, the shadow created by the extended source spot *s* increases for higher magnifications. In order to optimize

the resolution of the setup, the width of the point spread function of the system *σ*sys should not be larger than the detector pixel size. *σ*sys can be determined by [104]

$$
\sigma\_{\rm sys} = \sqrt{\left(s\frac{M-1}{M}\right)^2 + \left(\frac{px}{M}\right)^2}.
$$

Note that while the effective spot size of the source is reduced by larger source-todetector distances x02, the photon flux in the detector plane is reduced. For high resolution imaging of samples with a high contrast, the effect of source blurring is one of the most limiting factors for the resolution.

The problem was tackled with the development of micro- and nano-focus sources. By using magnetic lenses the accelerated electrons can be focused onto a small source spot with a diameter of a few µm or hundreds of nm. One can differentiate between three types of microfocus sources, characterized by the design of the anode [105, 106]:

The first design of microfocus sources is based on a reflection target. It is similar to the conventional Coolidge tube, but the (effective) source spot is minimized by focusing the electrons and tilting the anode. In this way, the source spot can be reduced to an effective size of 5-20 µm and be operated at 4-8 W (10 µm spot size).

To further decrease the source spot size, a transmission target can be used. It is built from a thin-film of anode material deposited on a diamond window to stabilize the anode [105, 107]. By this design, the source spot expansion through electron avalanches inside the anode material is limited. Hence, nanofocus sources are based on transmission targets. To further improve the capability of electron focusing, the electron source spot of the cathode has to be minimized. One possibility is the use of a lanthanum hexaboride (LaB6) filament as cathode material which allows to emit electrons based on the electric field instead of the common electrical heating of a tungsten coil. The sharp tip LaB6 cathode reduces the electron source spot and enables to focus the electrons to source spots down to 100 nm.

The maximum power of these two designs based on solid target materials is again limited by heat transfer. To overcome this problem and to increase the power of a microfocus source, an X-ray generator based on a liquid metal anode can be used. Instead of the solid target, the anode is made of a metal alloy, such as Galinstan (86.5% Ga, 21.5% In, 10% Sn) which is liquid at room temperature. This alloy is pumped with high pressure through a nozzle into the vacuum tube and forms a metal jet anode. The advantage of this setup is the heat dissipation, due to the steady renewing of the anode material. These sources can be operated at a power of more than 100 Watt (10

µm spot size). With this setup a brightness of 1010 ph mrad*−*2 mm*−*2 for the *Kα* line of Gallium was measured [108].

#### **Developments in X-ray detection**

Another reason for the faster image acquisition compared to the era of Röntgen is the development of new X-ray detection techniques [100, 109]. Instead of photosensitive glass plates or X-ray films, X-ray radiation is nowadays usually detected by digital Xray detectors. From today's perspective, the X-ray detection technology can be divided into direct and indirect detection. In an indirect system a composition of different components serves to slow down or stop the photons to create an initial signal which then can be amplified or converted to another form of energy before being detected. In a direct detector the signal is created and imaged in the same component, such as in a photographic plate.

For 3d imaging, digital processing of the data is required. Usually, an indirect, scintillatorbased detection systems is used for this purpose[109]. It is based on the luminescence of a scintillator material, which can be excited by ionizing radiation. The emitted light in the visible range is then collected by a lens or fiber optic and recorded by a photodiode, which converts the photon energy to an electronic signal. Thus, a digital image can be saved.

The spatial resolution, dynamic range, noise contributions and the read-out time of the X-ray detector depend on the absorption and emission spectrum and the thickness of the scintillation-screen as well as the magnification of the coupled optical imaging system and the sensitivity and pixel size of the photodiode [110]. Usually, a photodiode based on a metal-oxide-semiconductor, such as a Charge-Coupled Device (CCD) or Complementary Metal-Oxide Semiconductor (CMOS) is used [111]. In 2009 Willard Boyle and George E. Smith were honored with the Nobel Prize for the invention of the CCD [112].

In present conventional clinical CT, up to 320 X-ray detectors are arranged in a fixed outer ring of the scanner. Due to the fan-shaped X-ray beam created by the X-ray source, which is rotated around the patient, the duration of the scan could be reduced to less than a second [100].

Novel ideas to increase image quality in clinical applications also include dual-source and dual-energy CT. They allow the acquisition of two images from different angular positions at the same time (to correct for motion artefacts) or with different photon energies to gain more information on the tissue properties [93]. Further developments in

X-ray detection technology include single photon counting detectors, which enable a high signal to noise ratio, zero dark signal and avoid an afterglow which is common for scintillator materials [100, 107]. They are for instance based on a cadmium telluride (CdTe) CMOS technology, which directly convert photons to electrical signals. They allow for fast acquisition, improved resolution and higher contrast. Furthermore, they show less artefacts due to smearing or blurring within the scintillator. Another novel research branch in the detector improvement is dedicated to the development of 2d energy resolving detectors (similar to Silicon Drift Detectors) such as a hybrid silicon pixel detector based on charge integration and analog readout [113–115].

However, for some applications the current efficiency of laboratory X-ray imaging setups is still not sufficient. The temporal and spatial coherence of the illumination is limited by the broad X-ray spectrum and by the extended source spot. Furthermore, the brightness is limited by undirected radiation of the source with limited power. Especially when analyzing small structures with low contrast at high resolution or time resolved processes, laboratory systems reach their limits.

#### **Synchrotron radiation facilities**

One possible solution for increased image quality and acquisition speed is the use of coherent X-ray radiation with a high photon flux created at large scale synchrotron radiation facilities. X-rays are created by the deceleration of electron bundles with relativistic velocities within a magnetic field (bending magnet, wiggler or undulator). Thereby, a high photon flux with a small divergence is obtained. Further, the spectrum can be trimmed by attenuators and monochromators. The photon flux is characterized by its brilliance, defined as brightness per spectral width of the radiation and can reach up to 1025 ph/(s mrad2 mm 2 0.1% BW), more than 10 orders of magnitude higher than a conventional rotating anode source (1012 ph/(s mrad2 mm 2 0.1% BW)) [116, 117].

However, since these large scale synchrotron radiation facilities have high operating costs and limited accessibility, not everyone can be granted the opportunity to carry out an experiment.

After all, the progress in X-ray generation and detection techniques since the Röntgen s discovery is remarkable. Nevertheless, conventional absorption contrast, which is well established in hospitals, yields only a small contrast for soft tissues such as the heart. To improve data quality and increase the signal-to-noise ratio even for laboratory X-ray imaging, the phase-shifting properties of an X-ray wave can be accessed. For soft tissues and hard X-rays the phase information encoded in the dispersion part of the index of refraction is higher by a factor of 100 to 1000 compared to the attenuation [118]. The concept of X-ray phase contrast will be examined in more detail in the next section.

#### **1.3.2 The origin of X-ray phase contrast**

Imaging with X-ray radiation is based on the interactions of electromagnetic waves with matter. These energy dependent interactions occur in terms of photoelectric absorption, scattering or pair production of single photons. The wave interpretation of electromagnetic radiation is well suited to characterize the principles of image formation with X-rays.

The propagation of a plane electromagnetic wave of wavelength *λ* along direction *x* in vacuum can be described by its wave field Ψ*x*

$$
\Psi\_x = e^{-i\frac{2\pi}{\lambda}x} = e^{-ikx},
$$

with wavevector *k* = 2*π*/*λ*. If the wave passes a homogeneous object with a refractive index of *n* = 1 *− δ* + *iβ* and a of thickness ∆*x* the wavefront after an object is given by

$$
\Psi\_{\Delta x} = e^{-ik\Delta x \left(1 - \delta + i\beta\right)},
$$

where *δ* is the dispersion term and *β* the imaginary part of the energy dependent complex refractive index. Thus, it has a phase shifted wavefront of ∆Φ = *−kδ*∆*x* and a reduced amplitude compared to a reference wave propagating in vacuum. The intensity behind the object is given by the absolute square of the wavefront

$$I = \left| \Psi\_x \right|^2 = \Psi\_x \cdot \Psi\_x^\* = \left| e^{-ik\Delta x (1 - \delta + i\beta)} \right|^2 = e^{-2k\Delta x\beta} = e^{-\mu\Delta x},\tag{1.2}$$

describing the Lambert Beer's law with attenuation factor µ = 2*kβ*, used for conventional X-ray imaging and spectroscopy [119]. Since the attenuation depends on the material thickness and its attenuation coefficient, it contains information about the object properties.

As mentioned before, the attenuation of hard X-rays in soft tissue is very weak and depends on the photon energy *E* = *hc λ* , with Planck constant *h* and speed of light *c*. The energy dependence of the absorption *β* is proportional to *E−*4 , while dispersion term *δ* scales with *E−*2 [120]. Hence, the contrast is very low for conventional hard

X-ray radiography. Although the dispersion term *δ* of the refractive index is usually larger than the attenuation *β*, it cannot be detected directly. This phenomenon is known as *phase problem* and will be targeted in the next section.

#### **1.3.3 Solving the phase problem**

The basic idea of phase-contrast imaging goes back to the early 1930s, when Frits Zernike developed phase-contrast microscopy for visible light [121, 122]. In 1953, his work was honored with the Nobel prize. This technique enabled living cells to be imaged, which give too little absorption contrast to be investigated using bright field microscopy. Using a -90° phase shifting ring, the light scattered by the sample interferes with the illumination resulting in a higher contrast for the unstained tissue.

When using hard X-ray radiation, it is much more difficult to make the phase difference visible. Since the interaction of the electromagnetic wave with the material is very weak, conventional lenses and phase rings do not work as efficient as for visible light. There are different approaches to visualize the phase information of X-rays, which can be categorized in three groups [120]:

The first approach was developed in 1965 by Ulrich Bonse and Michael Hart. It is based on a crystal interferometer, creating interference of the scattered wavefront and a reference wave using a beam splitter [123]. This delicate setup has extremely high (sub nm) stability requirements on the setup and its monochromatic illumination [120]. Thus, X-ray phase-contrast imaging remained challenging.

About 30 years later, X-ray imaging modalities based on the first order of spatial derivative were developed. For instance, they are based on crystal analyzers, edge illumination, speckles/diffusors or (phase shifting) gratings [124–130]. These techniques are well suited to detect small changes in phase properties, but are still limited by the optical components needed for imaging formation. For instance, high resolution is challenging since the resolution is limited by the properties of the grating structure and the accuracy of its fabrication [131]. However, even if the dose-efficiency is affected due to absorption of the optical components, diffraction-enhanced X-ray imaging is a good

opportunity for laboratory and also *in vivo* imaging at lower resolution. Especially the grating-based approach established by the groups of Franz Pfeiffer, Timm Weitkamp, Christian David and Atsushi Momose as well as the edge-illumination developed by Alessandro Olivo yield a higher contrast for for soft tissue compared to absorptionbased imaging [132–135]. Thus, are well suited for the application of phase contrast in medical diagnostics.

While the first two approaches are limited by their optical components, in-line holography imaging does not require additional optics between the X-ray source and detector. Thus, there are less requirements on component fabrications and stability of the setup.

The propagation of the wavefront Ψ0 along *x* can be described for small angles using the paraxial approximation by the Fresnel propagator *Dx* [118]

$$D\_x = \exp(ikx)\mathcal{F}^{-1}\exp\left(\frac{-ix\mathbf{k}\_\perp^2}{2k}\right)\mathcal{F}\_+,$$

where *F* denotes the Fourier transform and **k***⊥* the reciprocal vector of the sample plane coordinates. The propagated wavefront Ψ*x* can be approximated as

$$\Psi\_x \approx D\_x \Psi\_0 \dots$$

The principle of in-line or propagation-based phase contrast is sketched in the top part of Fig. 1.6. If the sample is placed immediately in front of the detector, a conventional absorption image (as shown in Eq. (1.2)) is recorded. Thus, in case of a non-absorbing, pure phase object no contrast can be measured. If now the detector is moved further away from the sample and thus the propagation distance of the scattered wave is increased, fringes around the edges of the sample start to appear. The so called "edge enhancement" is caused by interference of scattered photons and can be described by the propagation of the disturbed wavefront. If the sample is placed further away from the detector, the fringes spread and start to overlap until only a fringe pattern, called hologram, is detected.

The imaging regime is characterized by the Fresnel number *F*

$$F = \frac{a^2}{d\lambda},$$

with the characteristic length *a* (pixelsize for X-ray imaging) and propagation distance

*d*. While the edge enhancement or direct contrast regime can be characterized by Fresnel or near field diffraction (*F ≈* 1), the holographic regime can be described by Fraunhofer or far field diffraction (*F ≪* 1).

Figure 1.6 shows the intensity distributions behind a pure phase object (*π*/2-phase shift) as well as for an object with a maximum absorption of 10% for different Fresnel numbers. Additionally, a magnification of the area marked in the absorption image is shown for each propagation distance. The intensity distributions are obtained by projections of a 3d phantom. This phantom was created by the segmentation of the murine heart tissue published in [2]. The voxels of the phantom were assigned with a constant index of refraction. Note that the noise in experimentally measured intensities, acquired by an X-ray detector, is not included in the simulated data shown. The Matlabcode used for this example is shown in Appendix A.1. By the propagation of the wavefront towards smaller Fresnel numbers, the edges of the object are emphasized by phase effects which expand and form stronger, overlapping fringes until the small structures cannot be recognized visually anymore. However, the structural information is still encoded in the measured intensity pattern. While the absorption contrast of the object defines the contrast for large Fresnel numbers, the influence of phase effects increases upon propagation until it dominates the image. Experimentally, phase-contrast imaging is a good technique to analyze samples with a low attenuation coefficient. Since the image formation origins from scattering of photons by electrons, phase-contrast X-ray tomography enables a contrast proportional to electron density.

In order to obtain phase information of the image properties, the intensities measured at the detector plane have to be properly back propagated to reconstruct the phase distribution in the sample plane. This process is called *phase retrieval*. The original technique of holographic imaging goes back to 1948, when Dennis Gabor described interference patterns of electrons and eventually improved electron microscopy [136]. First experiments using X-ray holography measurements were performed at the European Synchrotron Radiation Facility (ESRF) by Snigirev et al. and were published in 1995 [137]. Followup experiments were performed by Cloetens et al. [138]. Only one year later, phase-contrast imaging in combination with laboratory sources was performed by Stephen William Wilkins associated with the Commonwealth Scientific and Industrial Research Organisation (CSIRO) [139].

There is a variety of different phase retrieval approaches, which are based on prior knowledge of the image formation. The lower part of Fig. 1.6 shows a selection of

**Fig. 1.6: Simulation of the propagation and phase retrieval for a heart phantom.** In the top rows, the intensity distributions for a *π*/2-phase shifting object without attenuation (A) and for an object with weak absorption (B) is shown for different Fresnel numbers. For the weakly absorbing object in the contrast regime (marked in green) and the holographic regime (orange), phase retrieval was performed by the SMO, BAC and CTF approach. The respective phase reconstructions are shown in (C). Additionally, the signal along a line marked in the magnified images is plotted for each phase retrieval algorithm.

phase retrieved images for an object with a maximum absorption of 10% after propagation to *F* = 1 and *F* = 10*−*3 obtained by algorithms introduced in the following.

The image formation can be simplified either by the *transport of intensity equation (TIE)* or the *contrast transfer function (CTF)* [118, 140]. The *TIE* states that changes in intensity *∂ ∂x Ix*(*r⊥*) of a paraxial wavefront along infinitesimal propagation distances can be calculated if the intensity and phase information are known

$$\left| \nabla\_{\perp} \boldsymbol{I}\_{x}(\mathbf{r}\_{\perp}) \nabla\_{\perp} \Psi\_{x}(\mathbf{r}\_{\perp}) \right| = -\frac{2\pi}{\lambda} \frac{\partial}{\partial x} \boldsymbol{I}\_{x}(\mathbf{r}\_{\perp}) \,, $$

where *Ix*(**r***⊥*)is the empty beam corrected intensity measured at propagation distance *x* in the plane **r***⊥* = (*y, z*) perpendicular to the optical axis.

Consider a homogeneous object consisting of a single material with a constant refractive index. By replacing the lateral Laplace operator with a Fourier-based pseudo operator, the TIE can be converted into an expression for the phase information of the object obtained from a measurement of the intensity at distance *x*

$$\Phi = \frac{\delta}{2\beta} \cdot \ln \mathcal{F}^{-1} \left[ \frac{\mathcal{F}[I\_x]}{\frac{\delta x}{2k\beta} |\mathbf{k}|^2 + 1} \right]$$

*.*

This phase retrieval approach was first described by Paganin et al. and is named after its initial assumption as *single material object reconstruction (SMO)* [141].

Exemplary reconstructions of the phase SMO phase retrieval are shown in the first row of Fig. 1.6C. While the SMO reconstruction is well suited for the direct contrast regime and a single material object with a low *δ β* ratio, the pseudo differential operator leads to image blurring for higher *δ β* ratios.

Another approach suited for the direct contrast regime is the *Bronnikov-aided correction (BAC)* [142]. It is a two step reconstruction of the object properties. First the phase information is obtained by the *Modified Bronnikov algorithm (MBA)* which is also based on the *TIE*

$$
\Phi = 2\pi F \mathcal{F}^{-1} \left[ \frac{\mathcal{F}[I\_x - 1]}{|\mathbf{k}|^2 + \alpha} \right],
$$

where *α* is an absorption-dependent regularization parameter to suppress numerical instability caused by the singularity at **k** = 0. For *α* = 4*πβ δ* , the MBA reconstruction scheme delivers the similar results for a weak object as the SMO. In order to restore image sharpness, a second step is applied for the BAC reconstruction. For weakly absorbing materials, the intensity in the object plane can be approximated by the the near-field TIE

$$I = \frac{I\_x}{1 - \frac{x}{k} \nabla^2 \Phi} \cdot \mathbf{t}$$

Using the MBA to approximate the phase of the object and by introducing a regularization parameter *γ ≈ x k* , an effective intensity distribution in the object plane can be calculated. Compared to the SMO, the BAC maintains the sharpness of the reconstructions in the direct contrast regime [143]. However, both algorithms introduced above fail in the holographic regime.

The original approach for holographic phase reconstruction is based on the Fresnel diffraction operator and was proposed by Gabor [144]. By a back propagation of the measured intensity, the phase information in the object plane can be approximated. However, this scheme yields strong artefacts from twin images emerging from the ambiguity of the Fresnel back propagation.

In our group other phase retrieval algorithms for propagation-based X-ray phase retrieval in the holographic regime were developed[94]. For instance, they are based on the TIE for arbitrary propagation distances (Holo TIE) or iterative propagation schemes [145–147].

The most commonly used approach for is based on the CTF and was proposed by Peter Cloetens and coworkers more than 20 years ago [148]. It allows to combine information from projections acquired at different propagation distances. Considering a homogeneous object with a slowly varying phase, the phase distribution in the object plane Φ(**r***⊥*) is given by

$$\Phi(\mathbf{r}\_{\perp}) = F^{-1}\left[\frac{\sum\_{N} (\sin(\chi) + \frac{\beta}{\delta} \cos(\chi)) \cdot F\left[I\_x^N(\mathbf{r}\_{\perp}) - 1\right]}{\sum\_{N} 2(\sin(\chi) + \frac{\beta}{\delta} \cos(\chi))^2 + \alpha(\mathbf{k}\_{\perp})}\right],$$

with natural units *χ* = *λx***k** 2 *⊥* 4*π* for the squared spatial frequencies, a frequency-dependent regularization parameter *α*(**k***⊥*) for regularization of low and high frequencies and *N* indicating the index of the respective distance *x*. The bottom row of Fig.1.6C shows the performance of the CTF in direct contrast regime and the holographic regime for a weakly absorbing object with a strong phase shift measured at a single distance.

Compared to the other two approaches, the CTF is well suited to retrieve the phase information for small Fresnel numbers. Despite it being initially developed to solve the phase problem in the holographic regime, image contrast and details are comparable

to SMO and BAC reconstruction for the direct contrast regime. Image quality can further be improved by using a non-linear approach of the CTF based on a minimization of the Tikhonov functional [149, 150].

Since propagation-based phase contrast is a phenomenon based on interference, it requires spatial and temporal coherence of the illuminating radiation. Some phase retrieval algorithms, such as the CTF and most iterative approaches, only work for highly coherent monochromatic illuminations of single material objects. For others such as BAC and SMO, the restrictions are not so severe and also partially coherent laboratory sources can be used. The advantage of the BAC algorithm compared to the SMO approach was shown for laboratory data by Töpperwien at al. in 2016 [143].

Note, that for cone beam geometries, the geometry of the setup also influences the wave propagation. The Fresnel scaling theorem states that the coordinate system of a cone beam acquisition can be transformed to a parallel geometry by considering an effective propagation distance *x*eff

$$x\_{\text{eff}} = x\_{12}/M\text{ .}$$

Hence, the Fresnel number has to be adjusted with the magnification *F*eff = *F*/*M*.

After image acquisition and phase retrieval, the integrated phase information along the propagation path of the X-ray can be determined. In order to obtain the 3d volume from 2d projections a tomographic reconstruction has to be performed.

#### **1.3.4 Tomographic reconstruction**

The phase retrieved images yield the accumulated phase information along the propagation path of the X-rays. In order to access the 3d structure of the sample, a set of 2d projections at different angular positions has to be acquired.

The process of image acquisition can be mathematically described by the Radon transform developed in 1917 by Johann Radon [151]. In the following we consider one 2d slice of the 3d volume described by *f*(*x, y*) which lies orthogonal to the rotation axis in a setup with a parallel beam geometry. The corresponding pixel line of the detector perpendicular to the rotation axis at rotation angle *θ* can be described by *s* = *x* cos *θ − y* sin *θ*. The integrated phase shift *Pθ* along *s* is given by [152]

$$P\_{\theta} = \int\_{-\infty}^{\infty} \int\_{-\infty}^{\infty} f(x, y) \delta\_D(x \cos \theta - y \sin \theta - s) \mathrm{d}x \, \mathrm{d}y \, \mathrm{d}y$$

where *δD* denotes the Dirac delta distribution.

Based on the inversion of the Radon transform, a 3d volume can be reconstructed slice by slice from the 2d projections. In order to retain image sharpness, a *ram-lak* (high-pass) filter has to be applied in Fourier space [118, 152].

The minimum number of angular positions *Nθ*, which has to be acquired to perform a proper tomographic reconstruction, depends on the number of detector pixels perpendicular to the axis of rotation *Ny* and is given by the Nyquist sampling theorem *Nθ ≥ Ny π* 2 [152].

However, it is also possible to achieve reasonable image quality for sampling rates below Nyquist. For instance, undersampling artefacts in low dose CT can further be reduced by mathematical approaches such as by minimizing the total variation of the estimated image [153], equally sloped tomography [154] or Bayesian statistical reconstructions [155]. Another growing field in artefact reduction of tomographic data is the combination with machine and deep learning networks [156–158].

#### **1.3.5 Virtual histology**

After image acquisition, phase retrieval and tomographic reconstruction, the 3d volume can be further investigated. Compared to conventional absorption-based X-ray imaging, phase-contrast tomography yields a relatively high signal to noise level even for unstained, formalin-fixed, paraffin-embedded (FFPE) tissues and allows the destruction free investigation of 3d tissue structures with an isotropic resolution. Tomographic reconstructions of biological samples can be cut virtually in arbitrary orientations. Thus, the 3d structure can be analyzed to improve the understanding of the tissue properties. Hence, high-resolution X-ray CT is often referred to *virtual histology*, extending conventional histology by a third dimension [159–162]. Furthermore, X-ray phase-contrast tomography of FFPE blocks enables conventional histology after image acquisition. It can be beneficial to know the 3d sample structure within the paraffin block prior to the sectioning process. For instance, knowing the position of a tumor within the tissue facilitates the search via histology for further characterization. Moreover, the paraffin block can be mounted in an optimized orientation [163]. Virtual and conventional histology can be superimposed to improve the understanding of the tomographic data.

Additional data from post processing of the volume, such as segmentation of certain cellular features or the investigation of cell densities, structural orientation or

distances between nuclei in 3d, can reveal new insight on functionality. For example, previously unknown correlations between the orientation of granular cells and the dendrite tree of purkinje cells in the human cerebellum were recently discovered [164].

3d virtual histology is a growing field in neuroscience as well as in research concerning other organs, such as the pancreas [165], the kidneys [166], the vasculature or the skin [167, 168]. Related to the current world wide pandemic, structural changes in lung architecture for severe cases of Covid-19, previously observed by conventional methods [169, 170], were recently also confirmed by propagation-based phase-contrast X-ray tomography [171, 172]. In our work, we performed a segmentation of small capillaries and the hyaline membranes covering the surface of the alveoli and thus hindering the transport of oxygen. Furthermore, characteristic distances from tissue interior to the closest air compartment and the distribution and density of lymphocytes within the tissue were characterized. Parameters like these can help to categorize pathologies in the future.

In order to access the 3d structure, one does not necessarily need to apply for beamtimes at synchrotron radiation facilities. Also partially coherent laboratory sources allow for sufficient image quality to analyze 3d tissue properties [143, 173, 174].

New staining procedures for 3d X-ray analysis are under development to increase image quality. Using high-Z materials such as iodine or phosphotungstic acid (PTA), tissue contrast can be enhanced [175]. However, 3d tissue staining yields the uncertainty of staining artefacts such as unspecific binding or a contrast gradient between the surface and the sample core caused by spatially and temporally anisotropic stain penetration. Protocols for conventional histological stains such as the HE stain were adapted for 3d X-ray imaging [176–178]. This stain is already established and also works for dense tissues such as liver tissue.

The advent of 3d virtual histology has delivered first new insights on the correlation between organ structure and function. Nevertheless, it is still a new technology that needs to be further optimized. The full potential of 3d virtual histology can be exploited by improving image quality and establish novel analysis workflows to characterize the tissue structures.

The next section gives an overview of the current status and recent progress of 3d virtual histology of cardiac tissue.

#### **1.3.6 Virtual histology of cardiac tissue**

Compared to clinical imaging of the heart, which is optimized for diagnostics, virtual histology of cardiac tissue aims to resolve the structure of the heart on the sub-cellular scale for the entire organ. In this context the architecture of the cellular arrangement, its development as well as the influence of CVDs is analyzed [63]. Since the objective of fundamental and preclinical research differs from clinical imaging, the boundary conditions are set differently. First of all, most image acquisition is performed post mortem. Hence, dose delivery is usually not limiting during image acquisition. Furthermore, most investigations are performed on small animal models, such as mice or rabbit, before human studies are performed. In the following, the current state of preclinical cardiac imaging, including the work related to this thesis, is presented.

The first reconstructions of entire small animal hearts using laboratory instruments were obtained with a resolution of down to 30 µm using iodine-based contrast agents [179, 182]. A slice of the tomographic reconstruction is shown in Fig. 1.7A. Furthermore, the cardiac conduction system as well as the influence of congenital heart disease was investigated [179, 183, 184].

In context with this work, the influence of heavy-metal staining agents as well as alternative preparation methods such as tissue dehydration on the cardiac structure was analyzed [2]. Using a liquid metal jet setup, samples were investigated at a resolution of about 5 µm, which was previously not achieved with laboratory X-ray sources. Additionally, the tomographic reconstruction of a murine heart, prepared by the Evaporation of Solvent method, was also probed by a novel approach to identify the cardiomyocyte orientation. The orientation analysis is based on a local Fourier transform of the electron density and was compared to an established gradient-based method, which was previously applied to synchrotron data [185].

In order to achieve higher resolution and contrast (also for hydrated tissue) coherent and brilliant illumination from synchroton radiation facilities is needed. In Fig. 1.7B and C, the gain in image quality is visualized for a PTA stained murine heart recorded by Dullin et. al. [180]. Figure 1.7B shows a reconstruction from an absorption-based laboratory system with a voxelsize of 40 µm. The same heart was also analyzed at the SYRMEP beamline at the Synchrotron Light Source Elettra (Trieste, Italy) using propagation-based phase contrast at a voxelsize of 18 µm (Fig. 1.7C). Due to the higher photon flux and monochromatic illumination, the signal-to-noise ratio was increased and the pixel size reduced.

Further studies of (stained) cardiac tissue were performed on small animal and hu-

**Fig. 1.7: 3d virtual histology of cardiac tissue.** In the top row tomographic reconstructions of small animal hearts stained with heavy Z elements are shown. (A) One of the first laboratory reconstructions of an entire rat heart stained by an iodine solution recorded at a resolution of 30 µm [179]. (B) PTA stained murine heart first analyzed at a laboratory setup at a voxelsize of 40 µm [180]. (C) The same heart analyzed at a synchrotron radiation facility at a voxelsize of 18 µm [180]. The lower part shows tomographic reconstructions of unstained murine hearts aquired at a synchrotron radiation facility [181]. (D) First low resolution scans with a voxelsize of 6.5 µm were acquired. (E) Afterwards, high resolution scans of region of interests were recorded at a voxelsize of 650 nm. Scale bars: A,B,C: 2 mm, D: 3 mm, E: 250 µm.

man hearts using grating interferometry or edge illumination [186–189]. This approach also enables a high contrast for soft tissue, but is limited in resolution by the grating or mask properties.

Propagation-based X-ray phase contrast studies of hydrated cardiac tissue from human and murine hearts allow to study the myofiber network in higher detail [181, 190–194]. The lower part of Fig.1.7 shows an examplary study of a hydrated murine heart by Dejea et. al. [181]. First, the entire heart was scanned at an effective pixel size of 5.8 µm (Fig.1.7D). Afterwards, high resolution tomograms with a voxelsize of 0.65 µm were acquired in regions of interest (see Fig.1.7E). In this study, the vascularity and collagen network was segmented and the myocyte orientation was calculated. In order to facilitate the identification of the collagen, the segmentation was performed based on a tomographic reconstruction without phase retrieval and compared to histological microscopy images afterwards. The bright spaces between the cardiomyocytes are claimed to be a collagen matrix supporting the myocyte network. However, there is a risk that edge enhancement artefacts of the reconstruction were mistakenly claimed to be collagen. In order to confirm conclusions from tomographic reconstructions of sub-cellular structure, artefacts from incorrect or missing phase reconstruction have to be excluded. A solution to this issue is a proper phase retrieval using iterative phase retrieval algorithms. Furthermore, tomographic reconstructions at smaller voxelsizes can be used to confirm the assumptions.

In a previous proof-of-concept experiment performed by our group, biopsies of cardiac tissue were first scanned at a laboratory setup in parallel beam geometry at a voxelsize of 0.65 µm. Afterwards, high resolution tomograms with a voxelsize of about 190 nm were acquired at the synchrotron in cone beam geometry [195]. Within the scope of this thesis, the cardiac structure is investigated in a multiscale X-ray phase-contrast tomography approach [3]. Three different configurations of the GINIX endstation were used to record projections at different levels of magnification [165, 196]. First, overview scans of entire murine hearts were acquired at 3.25 µm voxelsize. Regions of interest were than analyzed at 0.65 µm voxelsize before a biopsy punch was taken and scanned at a voxelsize of 167.5 nm. Using iterative phase retrieval algorithms the challenge of a proper phase retrieval in the field of virtual histology is overcome. Phase retrieval was performed by a non-linear approach of the CTF.

So far propagation-based X-ray imaging at synchrotron radiation facilities seems to be the best technique to image the 3d cardiac structure in high detail. It enables a high contrast even for unstained tissue, either embedded in paraffin or in solution. Using this approach, studies on the influence of cardiovascular disease in mouse models were performed [181, 197]. Besides differences in fiber orientation, the wall thickness of the myocardium was analyzed and a few single cardiomyocytes were manually segmented. Experiments and analyses of this kind can provide the basis for a deeper understanding of various diseases.

Recently, we investigated cardiac tissue samples of patients who succumbed to Covid-19 by propagation-based phase contrast [4]. Previously, structural changes of the vascularity due to the disease were observed in lung tissue of Covid-19 patients [169–171]. In severe cases of the disease, the body forms new vessels via a process named intussusceptive angiogenesis, possibly to compensate for disturbances of the blood circulation due to microthrombi. By a deep learning based segmentation of the vascular system and graph theory we could show that these changes also occur in cardiac tissue. Furthermore, structural changes on a cellular level were also observed from laboratory recordings and are described by an analysis of the cellular alignment. The high resolution synchrotron reconstructions reveal sub-cellular structures such as myofibrils, nuclei but also "pillars" within small capillaries, which are a hallmark for intususseptive angiogenesis.

On the sub-cellular level, X-ray virtual histology is very challenging. Most of the work presented above was performed at setups which are designed for a minimal voxelsize of 650 nm. The advantage of the comparably large penetration depth for X-rays compared to conventional imaging techniques as fluorescence imaging does not play a role when analyzing single cardiomyocytes. Contrarily, the weak interaction of hard X-ray and soft matter is challenging when analyzing single cardiomyocytes. However, the fact that X-ray tomography can be performed independent of labeling and yields a contrast for the 3d electron distribution, it reveals the unaltered structure of the object. Thus, it can be used to verify or extend studies obtained by other imaging techniques.

Within the scope of this thesis, we performed a proof-of-concept experiment showing that it is possible to reconstruct the 3d electron density distribution of isolated cardiomyocytes using propagation-based X-ray tomography [5]. Using the high resolution cone beam waveguide setup of the GINIX endstation we could image freeze-dried cells at a voxelsize of 45 nm. Furthermore, the actin network of the cell was labeled by a fluorescent dye and imaged using a confocal microscope. In the tomographic reconstruction myofibrils and mitochondria can be identified. The limit in resolution of X-ray phase-contrast tomography of biological samples is not set by Abbe, but rather by the low contrast for soft tissue and by the geometry and stability of the imaging

setup. One possibility to probe molecular structures smaller than mitochondria, such as the actomyosin lattice, is X-ray diffraction presented in the next section.

#### **1.4 X-ray diffraction of muscle tissue**

#### **1.4.1 Development of X-ray diffraction**

X-ray diffraction is an imaging technique known from crystallography, which allows the molecular structure of crystalline samples to be probed [30]. The concept of X-ray diffraction dates back to Bragg's law for constructive interference, which was published in 1913 by Lawrence Bragg and his father William Henry Bragg [198]. In current research, X-ray crystallography is used to encode the structure of protein complexes by analyzing far field diffraction patterns. Recently, the structure of the SARS-CoV-2 virus and its binding properties to different drugs were characterized using Xray diffraction [199]. One of the biggest challenges in conventional X-ray diffraction crystallography of protein structures is the manufacture of protein crystals without changing the gross and local molecular arrangement and the natural function [200, 201]. However, it is also possible to probe the structure of samples which do not have a perfect crystalline structure.

First X-ray diffraction studies of biological materials were performed on samples containing natural protein fibers such as silk, wool, but also nerve, tendons and muscle tissue using laboratory X-ray sources [202, 203]. Moreover, in 1953, the helical desoxyribonucleic acid (DNA) structure was encoded by James Watson and Francis Crick with diffraction data from Rosalind Franklin [204]. Around the same time, Xray diffraction studies on muscle tissue were resumed using rotation anode sources [205, 206].

The orientation dependent scattering properties of muscle tissue were already known from polarized light microscopy before the discovery of X-rays by Röntgen [19]. The naming of the A and I band of the sarcomere goes back to the scattering properties and indicates the diffractive properties of muscle. The presence of myosin rods in the A-band with a constant length was confirmed in the 1860s [207, 208]. However, it took another 100 years until the basic principle of muscle contraction was revealed by a correlative imaging approach involving light microscopy, electron microscopy and X-ray diffraction.

In 1954 X-ray diffraction experiments as well as light and electron microscopy record-

**Fig. 1.8: X-ray diffraction of muscle tissue.** (A) Schematic setup of a scanning Xray diffraction beamline. Monochromatic beam, focusing optics (usually beryllium lenses or a pair of KB mirrors), sample stage, beamstop to block primary beam and detector. (B) Laboratory diffraction pattern, acquisition time 14 hours [215]. (C) Diffraction pattern acquired at DESY synchrotron in 1 hour [215]. (D) X-ray diffraction pattern of a murine calf muscle acquired at Beamline 18 (Advanced Photon Source, Argonne National Laboratory) in 0.375 seconds [216].

ings on frog muscle were performed by Hugh Huxley and Jean Hanson as well as by Andrew Huxley and Rolf Niedergerke. Both groups observed a correlation between the change in length of H-zone and Z-disc movement, supporting the sliding filament theory [19, 209, 210]. Their results were confirmed by follow up studies in the 1960s, which involved electron microscopy and laboratory X-ray diffraction and could prove the existence of cross-bridges between actin and myosin by the globular heads of myosin [211–214]. However, the photon flux of laboratory sources and the data quality of the pattern was too low to carry out dynamic measurements on muscle contraction at that time.

Due to developments in X-ray generation using synchrotron radiation facilities, acquisition times and data quality of diffraction measurements could be improved. In August 1970 the first X-ray diffraction experiment at a synchrotron was performed on an insect flight muscle [217]. The acquisition time at laboratory diffraction setups is in the range of hours to days when analyzing soft tissue samples such as muscle tissue [215]. Figure 1.8B shows a diffraction pattern of a bug flight muscle recorded in 14 hours using a rotation anode source. The same tissue was analyzed at the DESY synchrotron. The corresponding diffraction pattern was acquired in one hour and is shown in Figure 1.8C. The reflections marked with a 10 and 20 corresponds to the *d* (1*,*0) and *d* (2*,*0) myosin-myosin filament distance. They define the equatorial plane. The doublets occur from different lattice planes (e. g. c: *d* (2*,*1) and *d* (3*,*0)). The horizontal reflections (meridional plane) occur from the cross-bridge repeat at the myosin head binding sites and the helical arrangement of cross bridges around the thick filament. Intensity changes of reflections a and b indicate changes of cross-bridges positions.

The first beamline designed for X-ray diffraction started its operation in 1972 inside bunker 2 of DESY in Hamburg. The focused monochromatic beam had a cross section of 200*×*250 µm2 and a flux of 109 ph/s. Compared to a rotating anode source, the flux density was two orders of magnitude higher. However, time-resolved studies of oscillating insect flight muscle remained without the success hoped for [215]. One of the reasons for the failure of the experiment is the small change of the actomyosin lattice spacing for insect flight muscle. In 1981 Huxley could show changes in meridional reflections obtained from contracting frog muscle at the EMBL outstation of the DORIS facility in Hamburg [218]. The advantage of frog muscle studies is the easy dissection process, the possibility to induce a contraction by electrical stimulus and the comparably large variation in actomyosin lattice spacing during contraction. However, compared to insect flight muscles with a highly crystalline structure, the signal of the reflections is comparably weak.

Further improvements in X-ray generation led to higher quality and increased photon flux. Third generation synchrotron radiation enabled to measure the dynamic changes in the diffraction patterns on the millisecond time scales [219, 220]. The gain in image quality is visualized in the lower row of Figure 1.8. Compared to laboratory (B) and first synchrotron results (C), the diffraction pattern of a murine calf muscle recorded in 0.375 seconds at beamline 18 (Advanced Photon Source, Argonne National Laboratory) shows clear reflections with higher detail (D) [216].

In 1990 , the substructure of the actin and myosin rods as well as the ATP binding sites could be decoded by protein crystallography [30]. Furthermore, it was shown by X-ray diffraction that the actin and myosin molecules are not totally rigid, but show variation in length of about 0.3 to 0.5% under tension [221, 222].

#### **1.4.2 Scanning small angle X-ray scattering**

The real space resolution of classical X-ray diffraction is given by the area illuminated by the X-ray beam. Thus, it is not possible to identify local differences in the cellular structure or dynamics at scales smaller than the beam diameter. With recent progress in X-ray focusing capabilities such as Beryllium lenses and KB mirror systems, a new field of application for X-ray diffraction evolved [223–225].

Figure 1.8A shows a sketch of a scanning small angle X-ray scattering (scanning SAXS) setup. Compared to classical X-ray diffraction experiments, the X-ray beam is additionally focused. By lateral movement of the sample through the nano- or micro-focused beam, diffraction patterns are recorded at different positions. Since the diffraction pattern yields the structural information of the illuminated area, local structural parameters can be observed.

For the analysis of muscle tissue, scanning SAXS is a suitable technique to probe the local actomyosin structure. In previous work of our group we investigated the structure of 2d cardiac tissue slices. Besides identification of the local lattice spacing by the peak positions, the total scattered intensity and the degree of myofiber orientation was determined [226, 227]. By the analysis of the local diffraction patterns, differences in structural arrangement were observed for diseased heart tissue compared to a healthy control sample [228].

Furthermore, the structure of isolated biological cells was investigated by former members of our group [229–232]. In combination with fluorescent staining and STED or with X-ray holography, the orientation of single myofibrils can be determined by X-ray diffraction of single cells [233–235]. However, the sample preparation for single cell analysis is challenging. First experiments of isolated cells were performed on freezedried cardiomyocytes mounted on thin silicon nitrite foils. The diffraction patterns obtained in these experiments show a local anisotropy, however they do not show the characteristic peaks [236].

Using a liquid chamber, hydrated chemically fixed cells can be investigated [226]. The diffraction patterns obtained from hydrated cardiomyocytes show a characteristic peak for the actomyosin lattice. Hence, the molecular structure of the sarcomere is better preserved compared to the freeze-dried preparation. While the intra-cellular signal as well as myofiber orientation do not show large deviations, variations of the mean lattice spacing were observed between different cells. Furthermore, the choice of the fixing agent affects the actomysin structure.

In this work, the scanning SAXS analysis was combined with high resolution X-ray tomography. In addition to the investigation of freeze-dried and hydrated cells, the previous work was extended to *in vivo* studies of freshly isolated cardiomyocytes [5]. The combination of X-ray diffraction, fluorescent imaging and phase-contrast tomography allows to probe the molecular structure of the cells, as well as the 3d electron density distribution.

In order to investigate the entire structure of the heart, a multiscale imaging approach ranging from the scale of the entire organ down to the actomyosin arrangement is needed and can be provided by the the work flow developed in this thesis.

## **Fiber orientation in a whole mouse heart reconstructed by laboratory phase-contrast micro-CT** 2

*M. Reichardt, M. Töpperwien, A. Khan, F. Alves, and T. Salditt* Reproduced from Journal of Medical Imaging, 7(2), 023501 (2020).

#### **Abstract**

**Purpose:** Here we present a phase contrast X-ray tomography study of wild type C57BL/6 mouse hearts, as non-destructive approach to the microanatomy on the scale of the entire excised organ. Based on the partial coherence at a home-built phasecontrast µ-CT setup installed at a liquid metal jet (LMJ) source, we exploit phase retrieval and hence achieve superior image quality for heart tissue, almost comparable to previous synchrotron data on the whole organ scale.

**Approach:** In this work, different embedding methods and also heavy metal-based stains have been explored. From the tomographic reconstructions, quantitative structural parameters describing the 3D architecture have been derived, by two different fiber tracking algorithms. The first algorithm is based on the local gradient of the reconstructed electron density. By performing a principal component analysis (PCA) on the local structure-tensor of small sub-volumes the dominant direction inside the volume can be determined. In addition to this approach which is already well established for heart tissue, we have implemented and tested an algorithm which is based on a local 3D Fourier transform.

**Results:** In this study, we could show that the choice of sample preparation influences the 3D structure of the tissue, not only in terms of contrast, but also with respect to the structural preservation. A heart prepared with the Evaporation Of Solvent method was used to compare both algorithms. The results of structural orientation

were very similar for both approaches. in addition to the determination of the fiber orientation, the degree of filament alignment and local thickness of single muscle fiber bundles was obtained using the Fourier-based approach.

**Conclusions:** Phase contrast X-ray tomography allows to investigate the structure of heart tissue with an isotropic resolution below 10 µm. The fact that this is possible with compact laboratory instrumentation opens up new opportunities for screening samples and to optimize sample preparation, also prior to synchrotron beamtimes. Further, results from the structural analysis can help to understand cardiovascular diseases or can be used to improve computational models of the heart.

#### **2.1 Introduction**

Heart contractility as one of the most important physiological functions relies on an intricate, hierarchical molecular and cellular architecture. The macroscopic structure of the heart and the inner structure of heart muscle is known for more than a hundred years from classical anatomy and histology. However, by the invasive nature of histological sectioning impedes the reconstruction of the detailed three-dimensional (3D) arrangement of cardiomyocytes and myofibrils for the whole organ. Accordingly, the 3D structure of heart muscle is not completely understood and there are many different attempts to describe it, as for example the controvers discussed helical ventricular myocardial band[20] or the idea of a complex 3D mesh of cardiomyocytes surrounded by a fibrous matrix[13, 22]. Verification of these fundamental models requires high resolution imaging of the heart structure. Ultrasound and diffusion tensor magnetic resonance imaging (MRI) are incapable to resolve the cellular structures of the entire heart with a resolution in the range a few micrometer [91]. Conventional absorptionbased X-ray imaging results in low contrast, since the X-ray absorption of heart tissue is relatively small compared to mineralized tissues such as bone. One way to increase contrast is the use of metal-based stains such as iodine[179, 237, 238]. In order to increase contrast for unstained tissue, its phase-shifting properties can be exploited for contrast formation in weakly absorbing objects. For soft tissue the real-valued decrement *δ* of the refractive index *n* = 1 *− δ* + *iβ* is by one to three orders of magnitude larger (depending on tissue composition and X-ray wavelength *λ*) than the imaginary part *β*. Phase-contrast X-ray imaging therefore offers superior image quality and in particular visibility of small features down to cellular and sub-cellular scale, while keeping the penetration depth at the scale of the whole organ. The overall potential

of the method has already been convincingly lined out using synchrotron radiation (SR) with a parallel beam geometry[181, 187, 190, 193, 194, 239]. In prior work, we could show that even sub-cellular features in heart tissue biopsies can be resolved [195] by cone beam phase contrast tomography with SR.

In this work we explore an approach to small animal heart imaging based on compact laboratory instrumentation. Firstly, this offers broader accessibility of the method, including further clinical settings in future. Secondly, high end SR beamtimes can be better prepared if different samples can be screened and sample preparation protocols can be optimized beforehand using laboratory instrumentation. In particular, we show that the image quality and resolution is high enough to deduce the 3D (pseudo- )vector field of heart tissue. Note that the structure of heart poses a multi-scale challenge for structure analysis, based on the different hierarchies: heart, cardiac mesh, aggregation of myocyte chains (aggregated units), connective tissue, myocyte chain, single cardiomyocyte, myofibril and finally the sarcomere as the molecular machine underlying contractility. Here we present phase contrast reconstructions of whole mouse hearts with pixel sizes around five microns. Based on the reconstructed electron density, the orientation of the muscle fiber bundles can be determined. To this end, we compare two different sub-volume-based algorithms. The first algorithm is based on the Fourier transform[191, 240]. Its implementation and validation was one of the main goals of the present work. By analyzing the Fourier space of small subvolumes, the fiber orientation, the degree of filament alignment and also structural information as local thickness of single muscle fiber bundles can be obtained. Results from this algorithm are then compared to a more established approach based on the local gradient of the reconstructed electron density, which was already applied to high resolution synchrotron data[185, 193, 194].

The manuscript is organized as follows. Following the introduction, the procedure of sample preparation, data acquisition, phase reconstruction and tomographic reconstruction is described in Sec. 2.2. The quality of the 3D electron density obtained for the different preparations is than evaluated in terms of resolution, signal-to-noise and preservation of the cardiac structure in Sec. 2.2.3. In Sec. 2.3 the Fourier-transformbased algorithm including the analysis of orientation, degree of alignment and fiber thickness is introduced and compared to the gradient-based approach. In Sec. 2.4 the work is summarized and further possibilities for data analysis and possible applications as well as restrictions of this procedure are pointed out.

#### **2.2 Three-dimensional structure of a whole mouse heart**

#### **2.2.1 Sample preparation**

Fig. 2.1 presents the imaging setup, coordinate system and representative images of the samples. The heart structure of wild type C57BL/6 mice was investigated, using five different preparations, in view of comparing contrast and signal-to-noise ratio:

The whole explanted hearts were washed in phosphate-buffered saline and fixated in 4% formaldehyde solution for 24 hours. The stains were administered in solution by diffusion of the staining agent, with incubation times of 24 hours (iodine) or 7 days (PTA). Afterwards the samples were dehydrated in an increasing series of ethanol. For paraffin embedding the hearts were transferred to xylene and cast in paraffin. Excess paraffin was removed with a scalpel before imaging the sample. The heart embedded in 100% ethanol solution was mounted in a polyimide tube (*Kapton, Professional Plastics, Inc.*) with an inner diameter of 6 mm and a wall thickness of 75 µm. The EOS method was performed following the protocol described in [173].It is based on dehydration of the fixed sample in ethanol, removal of lipids using xylene similar to the classical histology procedure. The major difference is a evaporation of xylene instead of the transfer to liquid paraffin. The evaporation of xylene results in tissue shrinkage but does not alter the gross morphology[173]. The sample was also mounted in a polyimide tube with an inner diameter of 6 mm. An image of the different samples can be seen in Fig. 2.1c.

#### **2.2.2 Data acquisition and phase reconstruction**

Data acquisition was performed at a laboratory liquid metal jet µ-CT (*Excillum Metaljet-D2*) shown in Fig. 2.1a. The X-rays were produced by electrons focused on a liquid Galinstan (68.5% Ga, 21.5% In and 10% Sn) jet with a diameter of approximately 180 µm. For the experiments in this work the electrons were focused down to 10*×*40 µm2

**Fig. 2.1:** (a) Sketch of the laboratory liquid metal jet µ-CT setup with electron beam sketched in blue and X-ray beam in yellow. The emission spectrum can be filtered (i.e. pre-hardened) by metal foils. The sample is placed at a distance x1 behind the source spot and projections are recorded with a flat panel detector at distance x2. (b) Definition of the coordinate system. Point in the heart are parameterized by cylindrical coordinates, i.e. *z* along the long axis positioned in the center of the left ventricle, azimuthal angle *φ*, and radial distance *r*. The fiber orientation are parameterized by the in-plane angle *ψ* and the helical angle *ν*. (c) Image of the different samples. From left to right: unstained, iodine and PTA stained paraffin embedded hearts, polyimide tube for sample mounting, EOS heart. (d) Empty beam-corrected projection acquired at the laboratory setup and the corresponding phase reconstruction.

resulting in an effective spot size of approximately 10*×*10 µm2 . The source was operated with a power of 100 W at an acceleration voltage of 70 keV. For samples with a higher absorption the emission spectrum of Galinstan with a characteristic energy at 9.25 keV (Ga K*α*) was pre-hardened by a metal filter (35 µm Ag, 25 µm Ni) resulting in a peak energy of the K*α* emission line at 24.2 keV[243–245]. The metal filter was installed behind the exit window of the source. The samples were mounted on a motorized triaxial translation and rotation stage (*SmarAct GmbH, PI miCos GmbH*) at a distance *x*1 = 10 - 13 cm behind the source. Two additional translations stages (*PI miCos GmbH*) below the rotation axis allow the positioning of the rotation axis along the optical axis. For image acquisition a flat panel detector with a GsOS:Tbscintillator screen (*Dexela CMOS, PerkinElmer Inc.*) consisting of 1536 *×* 1944 pixels with an isotropic pixel size of *dx* = 75 µm on motorized three directional translation system was placed at a distance of *x*2 = 150 - 180 cm behind the sample. The cone beam geometry of the setup allows to customize zoom and field of view (FOV) by geometric magnification *M* = *x*1+*x*2 *x*1 and leads to effective pixel sizes of *dx*eff = *dx M* = 5.2 - 5.5 µm for the different data sets[140]. Due to a small effective source spot the effects of source blurring are relatively small. Considering the cone beam geometry projections were taken from 1001 equidistant angular positions over 185*◦* for all data set. To increase the signal without saturating the detector, five acquisitions at each position were recorded and averaged. For the metal stained samples, the increased photon absorption of the tissue leads to a decrease in detectable photons at the detector plane. Most notably, low energy photons are absorbed by the sample. To reduce beam-hardening artifacts, the spectrum of the emitted X-rays was pre-hardened by a metal filter and the acquisition time was adapted to keep the photon flux of the empty beam comparable between the measurements. The acquisition and geometric parameters are given in Tab. 2.1, and were chosen in view of magnification/sample size and visibility of phase contrast effects (edge enhancement).

There are different approaches for the phase retrieval of the single projections such as Paganin's Single Material Object approach[141, 246], the contrast transfer function[148] or iterative algorithms[145]. In this work the Bronnikov-aided correction (BAC) was used[142]. The BAC approach provides optimal results for the imaging of weak objects such as soft tissue in the direct contrast regime, in particular at low coherence sources[143]. In addition to the phase shifting properties of an object, BAC also takes the absorption into account. This leads to a reconstruction of the image properties based on coupled (mixed) phase and absorption contrast, without losing resolution due to a blurring of the reconstruction. Fig. 2.1d shows an empty beam-corrected

**Table 2.1:** Acquisition parameters for the tomographic measurements at the laboratory µ-CT setup.

projection from the analysis of the EOS preparation on the left hand side. The corresponding reconstruction in which the edge enhancement was corrected is given on the right hand side of the image. For small propagation distances *x* between the object and the detector, the transport of intensity equation (TIE) can be linearized[118], and the intensity can be written as *Ix* = *I*0(1 *− x*2*π λ ∇*2 *⊥ϕ*). In a first step, the phase *ϕ* of a projection is approximated by the modified Bronnikov algorithm (MBA)[247], based on the TIE inversion of a pure phase object

$$
\phi = \frac{2\pi}{\lambda x} \cdot \mathcal{F}^{-1} \left[ \frac{\mathcal{F} \left[ I\_x - 1 \right]}{|k|^2 + \alpha} \right].
$$

To account for singularities at *k* = 0, an absorption-dependent regularization parameter *α* is introduced to prevent strong artifacts and blurring. These would amplify low spatial frequencies in the image and would inevitably corrupt these Fourier components resulting in strong artifacts and blurring. The assumption of a weak object leads to blurred reconstructions of objects with non-negligible absorption. In order to resharpen the image, a second reconstruction step is applied, in which a weakly absorbing and homogeneous object is assumed and the (effective) intensity distribution at the object plane is reconstructed from the approximated phase *ϕ* via

$$I\_{x\_1} = \frac{I(\Delta x)}{(1 - \gamma \nabla\_{\perp}^2 \phi)},$$

where *γ* is a second *α*-dependent regularization parameter[143]. All parameters for the phase reconstruction of the different samples are shown in Tab. 2.2.

**Table 2.2:** List of the phase retrieval parameters for the Bronnikov-aided correction.

#### **2.2.3 Evaluation of the tomographic reconstructions**

The tomographic reconstruction was performed using the ASTRA toolbox[248]. Additionally, a ring correction[249] was performed. In order to characterize the threedimensional structure of the heart, it is necessary to image the whole organ with sufficient resolution and contrast to identify the direction of the muscle fibers. Therefore, the results are evaluated with respect to resolution, signal-to-noise ratio and preservation of the tissue structure. Orthogonal slices of all tomographic reconstructions of the hearts are shown in Fig. 2.2. Each row of the figure shows a slice of the 3D volume along the long and short axis of the heart. In the lateral slices an area of the inter-ventricular septum is marked in yellow and a zoom of the region is shown on the right. Furthermore, a histogram of all gray values within the 3D volume is given on the right. The values are defined by the tomographic reconstruction of the effective absorption coefficient *µ*

$$
\ln\left(\frac{I(r)}{I\_0}\right) = -\mu N dx\_{\text{eff}},
$$

with the normalized intensity *I*(*r*) *I*0 of the projections and *N* = 1944 the number of horizontal detector pixels. The resolution of the respective data sets was calculated by the Fourier shell correlation (FSC) [250] of two independent reconstructions obtained by splitting the projections in two sets with odd and even angles. The signal-to-noise ratio (SNR) was determined by

$$\text{SNR} = \frac{\overline{\mathbf{A}}\_{\text{signal}} - \overline{\mathbf{A}}\_{\text{noise}}}{\sigma\_{\text{noise}}}$$

where Asignal describes the mean amplitude of 100 voxels from a selected area of tissue of the centered slice with the highest signal, Anoise the mean amplitude of the surrounding medium and *σ*noise its standard derivation. The resolution obtained by

**Table 2.3:** List of the signal-to-noise ratio as well as the resolution obtained at the laboratory µ-CT for different sample preparations.

FSC and the SNR for each preparation is given in Tab. 2.3.