Laboratory phase-contrast tomography for imaging of zebraﬁsh

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Laboratory phase-contrast tomography

for imaging of zebrafish

WILLIAM VÅGBERG

Master of Science Thesis

Biomedical and X-Ray Physics

Department of Applied Physics

KTH – Royal Institute of Technology

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TRITA-FYS 2014:22 ISSN 0280-316X

ISRN KTH/FYS/--14:22--SE

Biomedical and X-Ray Physics KTH/Albanova SE-106 09 Stockholm This Thesis summarizes the Diploma work by William Vågberg for the Master of Science degree in Engineering Physics. The work was performed during the winter of 2013/2014 under the supervision of Daniel Larsson at Biomedical and X-Ray Physics, KTH – Royal Institute of Technology in Stockholm, Sweden.

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Abstract

Zebrafish (Danio rerio) are often used as laboratory animals in medi-cal studies, because of the similaritiy in their early development with that of human embryos, and their easy handling. Phase-contrast x-ray imaging of ze-brafish and other laboratory animals is of high interest, due to the penetrating power of x-rays and the potential for high spatial resolution. A resolution in the few micrometer range is, however, difficult to reach using only a compact x-ray source and a detector.

In this work, propagation-based phase-contrast tomography was used to image juvenile zebrafish, resolving muscle structures down to 5-7 µm. This was done with a liquid-metal-jet x-ray source and a Gadox scintillator camera. The zebrafish were 20 days post fertilization, some of them Sapje mutants, used to study Duchenne muscular dystrophy.

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Chapter 1 Introduction

1.1 Historical background

X-rays were discovered in 1895 by Wilhelm Conrad Röntgen, who identified them as rays, since he found that objects exposed to x-rays create shadows behind them [1]. To generate the x-rays, Röntgen used an evacuated glass tube, in which an electrical discharge was generated between two electrodes. He discovered that the x-rays can penetrate through matter, but to an extent that is strongly dependent on the material and its thickness. Furthermore, Röntgen discovered that x-rays could be used to see the bones inside a hand, since they penetrated the soft tissue in a way that visible light is not able to. He therefore introduced a new technique for medical imaging. However, he did not know about the damage that x-rays can cause in biological tissues. For the discovery of x-rays, Röntgen received the first Nobel Prize in Physics, in 1901 [2].

After the discovery, x-ray imaging quickly found its use in hospitals, and the image quality was improved. In the early 1970’s, computed tomography (CT) was introduced as an imaging method. The idea of CT was discovered independently by Allan Cormack and Godfrey Hounsfield. The principle is to image an object from many different angles, and from these projections reconstruct a three-dimensional image of the object. This takes a lot of computational power, which is the reason it could not be developed earlier. In 1979, Cormack and Hounsfield shared the Nobel Prize in Physiology or Medicine [3]. Today, most of the work within x-ray medical imaging focuses of lowering the dose of x-rays delivered to the patient, without degrading the image quality too much. We are well aware of the fact that x-rays can destroy DNA, proteins and other important parts of a living organism.

1.2 Study of zebrafish

The zebrafish (Danio rerio) is a freshwater fish with origin in the Himalayas [4]. An adult zebrafish is a few centimeters long, and has five horizontal blue stripes

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2 CHAPTER 1. INTRODUCTION

on its body. They are easy to handle, have a normal lifetime of two to three years and interact well with other fish, which together with their beautiful stripes makes them popular as aquarium fish. The zebrafish is also commonly used as laboratory animal in scientific research. Its full genome is sequenced and well-understood, and their early development has many similarities to that of mammals. Zebrafish are easy to breed in large numbers, and the embryos are easy to handle and can develop outside their mother. The rapid development of several organ functions already in the larval stage enables high-throughput analysis. Specific proteins can be altered with genetic techniques and several fish strains with disease mutations exist. This animal thus provides a powerful model where effects of gene mutations, observed in human disease, can be examined.

Figure 1.1: An adult female zebrafish. Reprinted from [4].

Duchenne muscular dystrophy and Sapje zebrafish

Duchenne muscular dystrophy (DMD) is a rare recessive mutation in the dystrophin gene, located in the X chromosome, therefore affecting almost only boys [5]. The dystrophin protein, which is no longer fully functional in a patient with DMD, provides structural stability in the muscle tissue. The main symptom is progressive muscle weakness, which will lead to difficulties or even inability to walk. Eventually, DMD may induce abnormal bone development, including spine curvature. The life expectancy for DMD patients is around 25 years.

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1.3. OBJECTIVES 3

1.3 Objectives

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Chapter 2 Background

2.1 X-ray properties

X-rays belong to the electromagnetic spectrum, just as visible light. However, x-rays have a much shorter wavelength. The x-x-rays that were used in this thesis are called hard x-rays, and have a wavelength on the order of 0.1 nm, see figure2.1.

Wavelength and energy

Electromagnetic radiation is quantized into photons. The wavelength λ corresponds to a photon energy

E = hc

λ (2.1)

where h is Planck’s constant and c is the speed of light. In x-ray physics, the energy is for convenience measured in electron volts (eV) instead of the SI unit joule (J). One electron volt is the energy an electron receives as it is accelerated across a 1 V potential (1 eV ≈ 1.6 · 10−19 J). Typical photon energies for hard x-rays are on the order of 10 keV. The corresponding frequency

f = c

λ (2.2)

is above many atomic resonance frequencies, which makes the x-rays able to pene-trate materials.

Refractive index

The refractive index depends on both material and wavelength. Since x-ray fre-quencies are close to atomic resonance frefre-quencies, it is the atomic composition that determines the refractive index, rather than the chemical composition. The refractive index is normally written in the form

n = 1 − δ + iβ (2.3)

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6 CHAPTER 2. BACKGROUND

1 eV 10 eV 100 eV 1 keV 10 keV 100 keV 1 MeV

Soft x-rays V isible 1 µm 100 nm 10 nm 1 nm 100 pm 10 pm 1 pm Wavelength Gamma rays Ultraviolet

Infrared Hard x-rays

Photon energy

Figure 2.1: The electromagnetic spectrum from infrared to gamma rays.

where δ and β are small positive numbers. δ corresponds to the phase shift in-troduced by propagating in a material instead of vacuum, and β corresponds to attenuation. When passing a distance z through a medium with refractive index n, the transmitted wave will look like

U = U0eiknz= U0eikze−ikδze−kβz (2.4) where U0eikz is the vacuum propagation, with an acquired phase shift φ = −kδz and attenuation ˜µ = µz = 2kβz, where µ is the attenuation coefficient.

Wave propagation

Electromagnetic radiation propagates as waves. To a linear approximation, and ignoring polarization, the wave is described by the wave equation

∇2_{U −}n2 c2

∂2_U

∂t2 = 0. (2.5)

This is however, in many cases a much too complicated representation. In order to simplify this, several approximations can be made. There is a lot of literature describing these approximations, for example Hecht [8], or Saleh & Teich [9]. One very common approximation is the Fresnel diffraction integral. It is stated

fz(x, y) = ieikz λz Z Z ∞ ∞ f0(X, Y )eiπ{(x−X) 2_{+(y−Y )}2_}/λz dXdY (2.6)

where f0 is the known electromagnetic field in a plane z = 0 and fzis the

electro-magnetic field that we want to compute, in a plane at distance z from the plane where the field is known. The Fresnel diffraction integral is an approximation from the Huygens-Fresnel principle. For the approximation to be valid, we require that r = |r| ≈ z. Geometrically, that means that r, the propagation direction of the light, has to be roughly parallel to the z-axis, as shown in figure2.2. Both gray areas must then be small compared to the distance z.

Further, we can see that equation (2.6) is a convolution integral. If we make a two-dimensional Fourier transform, F (u, v) = F [f (x, y)], equation (2.6) then turns into a much simpler form:

Fz(u, v) = eikzF0(u, v)e−iπλz(u 2_+v2₎

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2.1. X-RAY PROPERTIES 7

X

Y

x

y

z

r

Figure 2.2: The geometry for Fresnel diffraction. Light comes from a small aperture in

the XY -plane, and diffracts to create a pattern in the xy-plane.

This is one of the key equations in the image processing of phase-contrast images, and is used to derive the phase-retrieval algorithms described in section2.3.

Generation of x-rays

There are several ways of generating x-rays. The most common way is to use an electron impact source, which is also the kind of source used in this thesis. In such a source, electrons are accelerated at high voltages, and focused to a target, which is typically made of metal. X-rays are generated through two processes [10]. First, by characteristic line emission, where the electrons collide with one of the inner electrons in one of the atoms in the target, and knocks the electron out of its orbit. When one of the outer electrons falls down to a lower level to fill the vacancy, the atom emits radiation of one of its discrete characteristic energies. Second, x-rays can be emitted through bremsstrahlung. That is, when the high-energetic incoming electrons decelerate inside the target, they emit x-rays at a continuous spectrum.

Another way to generate x-rays is to use synchrotrons. In a synchrotron, elec-trons travel at highly relativistic velocities around a large accelerator ring. When the electrons pass through a magnetic field they emit x-rays. Synchrotrons have much higher brightness than laboratory microfocus sources, but are on the other hand not as accessible, since they are large national or international facilities.

Detection of x-rays

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2-dimensional detector arrays, it is common to use a scintillator material, which emits visible light when an x-ray photon is absorbed. The scintillator is mounted in front of a charge-coupled device (CCD), that detects the visible light.

2.2 Phase-contrast imaging

As mentioned in section 2.1, a wave both attenuates and acquires a phase shift when propagating through an object. Both these effects can be used to image the object.

Absorption contrast

The absorption contrast imaging method is the method that has been used in medical applications since the discovery of x-rays. It builds on the principle that some materials absorb x-rays more efficiently than others. Using only a source and a detector, the object can be imaged by detecting where the x-rays are absorbed by the object, since this gives a shadow of the object on the detector [11].

Phase contrast

When a wave propagates through an object, absorption is not the only effect. The wave will also be distorted, since the wavefront will propagate at different speed in materials with different refractive index. The distorted wavefront will cause a redistribution of the intensity, if the wave gets some distance to propagate, see figure2.3.

Object

Incoming wave

D

et

ec

tor

−→

Propagation distance

− →

Figure 2.3: Phase contrast from an object. The bright and dark fringes will make edges

prominent. The effect is only seen if the light is given a propagation distance, and requires a high resolution detector to separate the fringes.

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2.3. THE PHASE PROBLEM AND PHASE RETRIEVAL 9

The principle is the same for x-rays. However, the effect depends on differences in refractive indices. Since refractive indices for all materials are close to unity in the x-ray regime, these differences are small. To utilize the phase contrast, an x-ray source with small spot and a high-resolution detector must be used. This is analogous to the diffraction described in section2.1.

2.3 The phase problem and phase retrieval

When detecting x-rays, the detector measures the intensity (absolute square of the amplitude) at each pixel. But the wave also has a phase, which is not measured. The change in phase over the detector contains information about the direction of the wave, which together with the amplitude makes up the full wave. If the full wave is known at the detector, the distortion of the wave caused by the object can be calculated and reveal information about the object. To solve the problem that the phase is unknown, one has to use the intensity distribution and some known information about the object to estimate the phase. To get a comprehensible reconstructed tomogram, the phase-contrast images must be processed to become images that correspond to the projected thickness of the object. This process is called phase retrieval.

Phase retrieval algorithms and assumptions

In order to estimate the phase of the wave accurately, we need to use some in-formation about the setup and the object. There are several methods to do this, both iterative and non-iterative [12]. For tomography, the datasets are large, so non-iterative methods are used since iterative methods are very time consuming. The methods are based on assumptions on the wave propagation and also on the object.

By passing through the object, the wave will acquire a phase shift and lose some intensity due to absorption and scattering, as described in equation (2.4). The distortion of the wave directly after the object, as function of the transverse coordinates x and y, is

f0(x, y) = eiφ(x,y)− ˜µ(x,y)/2 (2.8) Our first assumption about the object is that it is weakly interacting. In that case, φ and ˜µ will be small, and we can Taylor expand as

f0(x, y) ≈ 1 + iφ(x, y) − ˜µ(x, y)/2. (2.9) The wave propagation is well described under the Fresnel approximation, since the direction of propagation of all radiation is close to the z-axis. So if we Fourier transform, and use equation (2.7), we get the field at a plane z as

Fz(u, v) = eikzF0(u, v)e−iπλz(u 2_+v2₎

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which will give the intensity at the plane z as Iz(u, v) =F h |fz(x, y)| 2i = FhF−1_[F z(u, v)] 2i = =F F −1h_F

0(u, v)e−iπλz(u 2_+v2₎i

2

=

=FhF−1[(d(u, v) + iΦ(u, v) − m(u, v))(cos χ − i sin χ)]

2_{i ∼}

= ∼

=d(u, v) + 2Φ(u, v) sin χ − 2m(u, v) cos χ (2.11) to first order approximation in φ and ˜µ, where χ = πλz(u2+v2), d is the Dirac delta function and Φ and m are the Fourier transforms of φ and ˜µ/2 respectively [13].

This means that different spatial frequencies in the object will have different visibility in the image, governed by the factors sin χ and cos χ for phase contrast and absorption contrast respectively. To get the true image of the object, we want all spatial frequencies to have the same visibility. To start with, a normalization in regular space removes the term d(u, v) in Fourier space:

ˆ

Iz(u, v) ∼= 2Φ(u, v) sin χ − 2m(u, v) cos χ (2.12)

Furthermore, we can make a material assumption on the object, to be able to distinguish the phase and absorption terms. Such an assumption could be to assume that the attenuation coefficient is zero (µ = 0), removing the last term, making the phase shift from the object

Φµ=0(u, v) ∼=

ˆ Iz(u, v)

2 sin χ . (2.13)

Another approach is to assume that the absorption is proportional to phase shift (µ ∝ δ), which is equivalent to assuming that the object consists of only one material, with varying density and thickness. This gives that

m(u, v) Φ(u, v) = −

β

δ = constant (2.14)

which gives us the phase as

Φµ∝δ(u, v) ∼=

ˆ Iz(u, v)

sin χ +β_δ cos χ. (2.15)

From now on, this method is referred to as the Fourier method.

Both these approximations are problematic at the frequencies where the denom-inator goes to zero. This can be solved by using a noise filter [12], or by choosing another method. The method derived by Paganin et al. gives the result [14]

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2.4. TOMOGRAPHY 11

This is very similar to equation (2.15) for small χ, and the denominator is always nonzero. However, small χ implies that the Fresnel number is large, a2_{/λz 1,} where a is the smallest diameter of the structures in the object we want to resolve. All the methods above give an approximation for the phase of the wave. The phase φ(x, y) is proportional to the projected thickness of the object, which is what is needed for tomography.

2.4 Tomography

The principle of tomography is to generate a 3D image of the object. To do this, the object is imaged from many different angles. Using a computer the images can be reconstructed as a 3D image.

Reconstruction algorithm and requirements

The reconstruction algorithm is based on the Fourier transform. The most basic case is for a parallel incoming x-ray. Consider only one slice of our sample, with the normal along the rotational axis and perpendicular to the beam. In that case, there exists a simple relationship between the Fourier transforms of the projections and the two-dimensional Fourier transform of the slice. This relation is called the Fourier slice theorem, and will be summarized here. A more rigorous explanation can be found in the book by Kak & Slaney [15].

Let the slice be positioned in a (x, y)-coordinate system, and let θ be the angle from the x -axis. A projectional image taken along the y -axis, will measure

P0(x) = Z

f (x, y)dy. (2.17)

In an absorption contrast image, f (x, y) is the attenuation in the sample, and P0(x) is the measurement on the detector array. In phase contrast, P0(x) is instead the projected thickness, computed from the phase retrieval method, and f (x, y) is the density. Now consider the Fourier transforms of f (x, y) and P0(x):

F (u, v) = Z Z

f (x, y)e−2πi(ux+vy)dxdy (2.18) S0(w) = Z P0(x)e−2πiwxdx (2.19) We see that F (u, 0) = Z Z

f (x, y)e−2πiuxdxdy = Z

P0(x)e−2πiuxdx (2.20)

which is the Fourier transform of the projection. This works similarly if we rotate our sample and change the coordinate system to

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At an angle θ, the corresponding projection is Pθ(t) =

Z

f (t, s)ds (2.22)

with the Fourier transform Sθ(w) =

Z

Pθ(t)e−2πiwtdt =

Z Z

f (x, y)e2πiw(x cos θ+y sin θ)dxdy (2.23) which is a radial line of the two-dimensional Fourier transform. That means, that we can sample the two-dimensional Fourier transform by taking projection images, as shown in figure 2.4. By rotating the object 180◦, we can get the full two-dimensional Fourier transform, and thus get an image of the slice by applying the inverse transform. Intensity on detector

θ

Slice of an object

θ

f

y

f

x 2D Fourier transform of slice 1D Fourier transform of projected thickness

Figure 2.4: The Fourier slice theorem used in tomography. The intensity gives the

projected thickness, whose Fourier transform is a slice of the two-dimensional Fourier transform of the object slice. By making many projections at different angles θ, we can sample the full Fourier transform of the object slice.

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2.4. TOMOGRAPHY 13

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Chapter 3 Methods

3.1 Simulations

To get an idea of what exposure times and setups that would be necessary to achieve a certain resolution, some simulations were made before the more time-consuming experiments. The simulations were also used to decide what kind of plastic tube that would be suitable for the the sample preparation described in the next section. The simulations were done using XRaySimulator, a program based on Matlab, developed especially for phase-contrast imaging. XRaySimulator takes many relevant details into account, such as the geometry of the setup, the spectrum from the source, source shape, detector performance and of course object shape and material. More details about the program are found in [11].

3.2 Sample preparation

The work with the zebrafish was done in collaboration with Karolinska Institutet, Solna, Sweden. The fish were bred at Karolinska Institutet, where they also were sacrificed in accordance with animal protection regulations and research ethics. The sacrificed fish were fixed with paraformaldehyde, to keep their structure stable. After the fixation, the fish were delivered to the Royal Institute of Technology, where all x-ray experiments were performed.

In order to make tomography on the zebrafish, they had to be prepared in a way that they could be imaged from all angles around a rotation axis. It was also required that they were fully immobilized during the full exposure, since displace-ments of only a few micrometers will lower the resolution or introduce reconstruc-tion artefacts. The immobilizareconstruc-tion was done by preparing an agarose gel [16], by solving 3% agarose in phosphate buffered saline (PBS). The mixture was heated to a clear solution, and then slowly cooled to 35◦C before the fish was added. Using a syringe, the agarose containing the fish was inserted in a fairly stiff tube. The tube was then sealed and mounted, see figure3.1.

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16 CHAPTER 3. METHODS

Figure 3.1: A 20 days post fertilization

ze-brafish, prepared in agarose gel and inserted in a polycarbonate tube. The tube was sealed with nail polish, and mounted on the head of a screw with cyanoacrylate glue. The agarose gel keeps the fish stable. The photo was taken two weeks after preparation, and the only vis-ible defect is a small air bubble in the upper part of the tube.

3.3 Experimental setup

The setup for propagation-based phase-contrast imaging is, as explained in the background, very simple. Only x-ray source, object and detector is needed. The geometry of the problem, as shown in figure 3.2, will give a magnified image of the object on the detector, which will be blurred by the source extension. If R1 and R2are the source-object distance and object-detector distance respectively, the magnification of the object is

M = R1+ R2 R1

. (3.1)

The blurring from the source of width s will be (M −1)s. This will also be combined with the blurring caused by the limited resolution of the detector. The propagation distance for the phase contrast, described in section 2.1, will no longer be the geometrical distance between the object and detector, as for plane waves. Instead, the effective propagation distance is

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3.3. EXPERIMENTAL SETUP 17

−→

− →

− → − → − → − → R1 R2 (M− 1)s M a a s

Figure 3.2: The setup for propagation based phase contrast. The three components are

the x-ray source of width s, the object of width a, and the detector.

X-ray source

The source is a liquid-metal-jet x-ray source from Excillum AB, a modified version of the source described in [17]. It is a microfocus source, which means that an electron gun accelerates electrons, that are focused by electron optics into a small spot. The cathode is a Galinstan (gallium-indium-tin alloy) liquid-metal-jet, which provides good heat dissipation, and the regenerative nature of a liquid jet makes it possible to load the cathode with very high power densities. The source was operated at 50 kV peak acceleration voltage, and at 30 W electron gun power. The size of the x-ray emitting spot was 5 × 9 µm full width at half maximum. It was approximately shaped as a Gaussian. The emitted x-rays from the source are from the gallium emission lines at 9.25 keV (Kα) and 10.26 keV (Kβ), but also from

bremsstrahlung and indium and tin emission lines. The spectrum from the source is shown in figure3.3.

Object

The object was prepared as described in the previous section, and mounted onto a Newport translational and rotational stage controlled through LabView. LabView communicated with the detector, so it was possible to make a rotation automatically after each exposure in the tomogram.

X-ray detector

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18 CHAPTER 3. METHODS 0 10 20 30 40 50 0 1 2 3 4 5 6 7x 10 8

photon energy [keV]

[photons s −1 W −1 sr −1 (0.1% bandwidth) −1 ]

Figure 3.3: The emitted spectrum from the Galinstan x-ray source. The spectrum was

measured with 50 kV peak acceleration voltage, 40 W electron gun power, and 12 cm of air absorption.

modulation transfer function (MTF), which is a measure of the detector spatial frequency response, is shown in figure3.4.

3.4 Phase retrieval

In this project, two phase retrieval methods described in section 2.3 were used. The Paganin method from equation (2.16) and the Fourier method from equa-tion (2.15). The contrast transfer function (CTF), the system response at different spatial frequencies, describes how clearly different spatial frequencies will be seen in the phase-contrast image. In an optimal image, all spatial frequencies are equally visible. The denominators in (2.16) and (2.15) are both approximations to the CTF, and serve the purpose of making all spatial frequencies equally visible.

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3.4. PHASE RETRIEVAL 19 0 2 4 6 8 10 x 104 0 0.2 0.4 0.6 0.8 1 Spatial frequency [m−1]

Modulation transfer function

Figure 3.4: The MTF of the detector from Photonic Science. Data from [18].

0 0.5 1 1.5 2 0

√πλz

_e_ff

u

CTF (a.u.) Paganin method Fourier method

Figure 3.5: The contrast transfer functions from the Paganin method and the Fourier

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20 CHAPTER 3. METHODS

0 0.5 1 1.5 2

0

√πλz

_e_ff

u

CTF & MTF (a.u.)

Original Fourier method CTF Detector MTF

CTF filtered with MTF

filtered CTF with low−pass filter

Figure 3.6: The filtered CTF and its components.

when πλzeffu2 is large, but the Fourier method goes to zero at some frequencies. In order to make the Fourier method CTF even more accurate, the MTF from the detector was included. To deal with the problem of noise amplification when the CTF is close to zero, a Gaussian function was added to the CTF. Since the intensity is divided by the CTF, this acts as a low-pass filter. The resulting CTF is

sin πλzefff2 + β δ cos πλzefff 2 · MTFd(f ) + aef 2_/b2 (3.3) where f2_{= u}2_+v2_{and MTF}

d(f ) is the detector MTF. The constants a and b in the

Gaussian function were chosen arbitrarily, to give low influence at low frequencies and cut off at a suitable frequency depending on the signal-to-noise ratio in the image. The resulting CTF with MTF and Gaussian filter is shown in figure3.6.

3.5 Reconstruction

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3.6. MINIMIZING ARTEFACTS 21

beam is spherical rather than parallel. It also corrects for the tilt angle, if the axis of rotation is not perfectly aligned to the detector columns.

3.6 Minimizing artefacts

Many kinds of artefacts can arise in tomography. To minimize these, careful pre-cautions has to be made. First, the images should be photon noise limited. That is, all other types of noise are small in comparison. This was done by making flat field images to remove static noise, and to set the exposure time such that read-out noise and dark noise was negligible. In tomography, a large number of projections have to be made within the total exposure time. The more projections we make, the shorter the exposure time of each projection. Normally, the quality of the resulting tomogram improves with the number of projections, as long as each projection is photon noise limited. However, looking at the Fourier transforms, there is no point of sampling angles more dense than the resolution limit of the detector.

Another source of artefacts or reduced resolution is object motion. Movement of the object can induce streaks and shading, or blurring of the image. The tolerance for movements is of course lower when imaging with higher resolution. The sample preparation, described in section3.2, kept the fish from moving.

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Chapter 4 Results and discussion

4.1 Simulations

The simulations with XRaySimulator [11] were used to show two things. First, to find out which tubes that are suitable for the sample preparation. The tube should be as stiff as possible, but still have high x-ray transmission. Some tubes with sufficient inner diameter were selected and the transmission was calculated using XRaySimulator. The results are shown in table 4.1. The glass capillary and the polycarbonate tube were chosen, since the glass capillary had the best transmission and the polycarbonate tube was stiffer than the polyetheretherketone tube. When used in experiments, it was found that the glass capillary gave more beam hardening than the plastic tube, and was also more challenging to handle in the sample preparation than the plastic tube. However, compared to casting the zebrafish into epoxy, which was tried first and gave only 18 % transmission, tubes with agarose gel gave much higher transmission, with almost as good stability.

Tube material Inner diameter Wall thickness Transmission

Borosilicate glass 1.0 mm 0.01 mm 56.8 %

Polycarbonate 1.0 mm 0.5 mm 46.7 %

Polyetheretherketone 1.4 mm 0.1 mm 46.7 %

Polyetherimide 0.9 mm 0.7 mm 43.5 %

Table 4.1: The transmission through sample tubes, including that they were filled with

water. The transmission was calculated as the fraction of photons transmitted, with respect to the source spectrum in figure3.3.

Second, tomography of a zebrafish was simulated. The zebrafish was modelled as cylinders made of soft tissue [19] of different size, encapsulated in water. The phase-contrast setup, absorption from the sample tube, x-ray source performance and detector performance were all taken into account. Several simulations were made, to investigate what setup and exposure time would be necessary to see certain

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24 CHAPTER 4. RESULTS AND DISCUSSION

14 µm

10 µm

7 µm 5 µm 3.5 µm

Figure 4.1: A tomography simulation with source-object distance 0.75 m, source-detector

distance 3 m and exposure time 50 hours. With these settings, cylinders of soft tissue with diameters down to around 5 µm are clearly visible.

details. The result from one of the tomography simulations is shown in figure4.1. In this simulation, muscle fibers of diameter down to around 5 µm are visible.

4.2 Tomography of zebrafish

During the work for this master thesis, nine tomography datasets were taken. The zebrafish were all 10-20 days post fertilization (dpf), and were prepared in either epoxy, agarose gel in a glass capillary or agarose gel in a plastic tube.

Many different problems arose, some easier to solve than others. At the end of the method development, the datasets showed high resolution with clear visibility of individual muscle fibres. However, if the fish happened to move, this drastically lowered the resolution, or induced movement artefacts. The sample preparation was therefore critical. The cause for the movement is not known, and needs further investigation. It is however assumed that it takes some time for the fish to settle in an equilibrium position in the agarose gel. Allowing too much time between sample preparation and image acquisition is not a good idea either, since the agarose gel seem to disintegrate gradually after some time.

Imaging a healthy fish

The dataset that turned out to be most successful was a 20 dpf healthy zebrafish, prepared in agarose gel in a polycarbonate tube. This dataset was taken with the parameters in table4.2. Some selected tomography slices are shown in figure4.2. In the sagittal slice in the right part of the figure, the muscle structure can be observed, even down to single muscle fibers. In some parts of the muscle structure the myosepta are resolved. The myosepta are the structures at about 45◦ angle to the muscle fibers, that separates two muscle segments.

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4.2. TOMOGRAPHY OF ZEBRAFISH 25 Sample preparation 2014-03-13 Start of imaging 2014-03-21 Source-object distance 0.36 m Source-detector distance 1.44 m Exposure/projection 94 s Total exposure 63 h Projections 2416 Step angle 0.075◦

Table 4.2: The experimental settings used for the tomography of a 20 dpf healthy zebrafish.

50 µm 100 µm

Figure 4.2: Selected slices of the 20 dpf healthy zebrafish. Both images correspond to

the black line through the other image. Left: axial slice through stomach, swim bladder, notochord and muscle tissue (indicated by arrows from left to right). The big ring around is the interface between agarose gel and the plastic tube. Right: sagittal slice displaying many parts of the zebrafish. The muscle tissue starts at the arrow and continues down through the tail.

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26 CHAPTER 4. RESULTS AND DISCUSSION 20 µm 41 µm 15 µm (a) (b)

Figure 4.3: Close-up of a selection of the muscle structure in the 20 dpf healthy zebrafish.

In (a), there are three bright and three dark fringes within 41 µm, giving that each muscle fiber is less than 7 µm. In (b), there is one bright and two dark fringes within 15 µm, so each muscle fiber is 5 µm.

Imaging Sapje zebrafish

Images were also taken of a Sapje mutated zebrafish. This fish was also prepared in agarose gel in a polycarbonate tube. The dataset was taken with the parameters in table4.3. Some selected slices from the tomography are shown in figure 4.4.

4.3 Comparison of phase retrieval methods

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4.3. COMPARISON OF PHASE RETRIEVAL METHODS 27 Sample preparation 2014-03-06 Start of imaging 2014-03-09 Source-object distance 0.36 m Source-detector distance 1.44 m Exposure/projection 94 s Total exposure 32 h Projections 1216 Step angle 0.15◦

Table 4.3: The experimental settings used for the tomography of a 20 dpf Sapje zebrafish.

50 µm 100 µm

Figure 4.4: Selected slices of the 20 dpf Sapje zebrafish. Both images correspond to the

black line through the other image. Left: axial slice at the beginning of the tail. Right: sagittal slice slightly off center.

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28 CHAPTER 4. RESULTS AND DISCUSSION

Figure 4.5: A comparison between phase retrieval methods. The tomography slices are

reconstructed identically from the same dataset, but with different phase retrieval. Scale-bars are 20 µm. Left: Fourier method phase retrieval. Right: Paganin method phase retrieval.

4.4 Comparison between healthy and sick fish

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Chapter 5 Conclusion

In this work, zebrafish have been imaged with a resolution of down to 5-7 µm in muscle tissue. Muscle tissue provides very low contrast to the surrounding water, making very long exposure times necessary. The long exposure makes stability of the experimental setup critical, where the main difficulty is the sample preparation. The one dataset that showed the best resolution was prepared 8 days before start of image acquisition, instead of 1-3 days, as was the case for the other samples. The possible reasons could be either that the longer waiting time gave better stability, or that some process changed the properties of the fish. One such possiblility could be that osmosis drained water from the muscle fibers, and thus made them give better contrast. To investigate this, more fish must be imaged and perhaps compared in other ways too.

Aside from the sample preparation, the resolution can be optimized by minimiz-ing beam hardenminimiz-ing and other factors that may induce artefacts and by selectminimiz-ing the most suitable phase retrieval method. The highest resolution was reached when deconvolution of the detector point spread function was included in the phase re-trieval. This could in theory be done with the source spot point spread function as well. However, this would require more thorough analysis of the spot shape.

The limiting factors are photon noise, blurring from the finite size of the x-ray spot and the limited detector resolution. Shorter exposure time would be beneficial, since stability of the object would be required for only a shorter time. To reach this, a source with higher power is needed. The resolution would also improve drastically if it was possible to make a smaller x-ray spot in the source, or by using a detector with higher resolution. However, regarding these parameters, the equipment used in this thesis is already among the best available.

Hard x-ray phase-contrast imaging is a good method to make high resolution tomography of zebrafish. Compared to confocal microscopy, which is the stan-dard method to image zebrafish larvae, x-ray phase-contrast imaging does not yet reach the same resolution. However, x-rays have the advantage of longer penetra-tion depth, which makes it possible to look at thicker samples than with confocal

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30 CHAPTER 5. CONCLUSION

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Acknowledgements

This project was carried out in collaboration with a number of people. Without the help from and discussions with others, the results of this project would not have been as fruitful as it turned out to be.

First and foremost, I would like to thank my supervisor Daniel Larsson. Daniel has been a very good supervisor, and helped with many different matters, both the-oretical and practical. His accurate thinking and availability in answering questions has been very important. I look forward to have Daniel as colleague and friend in the future.

Second, I would like to thank Prof. Hans Hertz, the examiner of my thesis and leader of the hard x-ray imaging research group. Hans is a skilled group leader and gives good inspiration for research.

This project was done in collaboration with Mei Li and Prof. Anders Arner who both do research on zebrafish at Karolinska Institutet. Our collaboration has worked very well, and they have helped me with many biological queries.

Many thanks to Ulf Lundström for advice and helpful discussions on phase retrieval and tomographic reconstruction, to Carmen Vogt for help to find gels for the sample preparation, to Jakob Larsson for helpful discussions on detectors and help with LA_{TEX, to Emelie Fogelqvist for proofreading, and to Tunhe Zhou for help} and company in the lab.

I would also like to thank everyone working at Biomedical & X-ray Physics for the friendly and welcoming atmosphere you create, that makes BioX a great place to work. Last but not least, I thank my parents, Lena and Jan, my brother Adrian and my girlfriend Johanna for the love and support you give.

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Laboratory phase-contrast tomography for imaging of zebraﬁsh