Water–fat separation in magnetic resonance imaging and its application in studies of brown adipose tissue

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ACTA UNIVERSITATIS

UPSALIENSIS UPPSALA

Digital Comprehensive Summaries of Uppsala Dissertations

from the Faculty of Medicine

1589

Water–fat separation in magnetic

resonance imaging and its

application in studies of brown

adipose tissue

JONATHAN ANDERSSON

ISSN 1651-6206 ISBN 978-91-513-0718-3

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Dissertation presented at Uppsala University to be publicly examined in Enghoffsalen, Entrance 50, Akademiska sjukhuset, Uppsala, Friday, 13 September 2019 at 13:15 for the degree of Doctor of Philosophy (Faculty of Medicine). The examination will be conducted in Swedish. Faculty examiner: Docent Kerstin Lagerstrand (Department of Medical Physics and Biomedicine, Sahlgrenska University Hospital, Gothenburg, Sweden and Institute of Clinical Sciences, Sahlgrenska Academy, University of Gothenburg, Gothenburg, Sweden).

Abstract

Andersson, J. 2019. Water–fat separation in magnetic resonance imaging and its application in studies of brown adipose tissue. Digital Comprehensive Summaries of Uppsala Dissertations

from the Faculty of Medicine 1589. 65 pp. Uppsala: Acta Universitatis Upsaliensis.

ISBN 978-91-513-0718-3.

Virtually all the magnetic resonance imaging (MRI) signal of a human originates from water and fat molecules. By utilizing the property chemical shift the signal can be separated, creating water- and fat-only images. From these images it is possible to calculate quantitative fat fraction (FF) images, where the value of each voxel is equal to the percentage of its signal originating from fat. In papers I and II methods for water–fat signal separation are presented and evaluated. The method in paper I utilizes a graph-cut to separate the signal and was designed to perform well even for a low signal-to-noise ratio (SNR). The method was shown to perform as well as previous methods at high SNRs, and better at low SNRs.

The method presented in paper II uses convolutional neural networks to perform the signal separation. The method was shown to perform similarly to a previous method using a graph-cut when provided non-undersampled input data. Furthermore, the method was shown to be able to separate the signal using undersampled data. This may allow for accelerated MRI scans in the future.

Brown adipose tissue (BAT) is a thermogenic organ with the main purpose of expending chemical energy to prevent the body temperature from falling too low. Its energy expending capability makes it a potential target for treating overweight/obesity and metabolic dysfunctions, such as type 2 diabetes. The most well-established way of estimating the metabolic potential of BAT is through measuring glucose uptake using 18_{F-fludeoxyglucose (}18_{F-FDG) positron}

emission tomography (PET) during cooling. This technique exposes subjects to potentially harmful ionizing radiation, and alternative methods are desired. One alternative method is measuring the BAT FF using MRI.

In paper III the BAT FF in 7-year olds was shown to be negatively associated with blood serum levels of the bone-specific protein osteocalcin and, after correction for adiposity, thigh muscle volume. This may have implications for how BAT interacts with both bone and muscle tissue.

In paper IV the glucose uptake of BAT during cooling of adult humans was measured using

18_{F-FDG PET. Additionally, their BAT FF was measured using MRI, and their skin temperature}

during cooling near a major BAT depot was measured using infrared thermography (IRT). It was found that both the BAT FF and the temperature measured using IRT correlated with the BAT glucose uptake, meaning these measurements could be potential alternatives to 18_F-FDG

PET in future studies of BAT.

Keywords: brown adipose tissue, magnetic resonance imaging, water–fat signal separation,

graph-cut, positron emission tomography, 18_{F-fludeoxyglucose, infrared thermography,}

machine learning, artificial neural networks, deep learning, convolutional neural networks

Jonathan Andersson, Department of Surgical Sciences, Akademiska sjukhuset, Uppsala University, SE-75185 Uppsala, Sweden.

ISBN 978-91-513-0718-3

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List of papers

This thesis is based on the following papers, which are referred to in the text by their Roman numerals.

I Andersson J, Ahlström H, and Kullberg J. Water-fat separation incorporating spatial smoothing is robust to noise. Magnetic Resonance Imaging, 50:78–83, 2018.

II Andersson J, Ahlström H, and Kullberg J. Separation of water and fat signal in whole-body gradient echo scans using convolutional neural networks. Magnetic Resonance in Medicine, 82(3):1177–1186, 2019. III Andersson J, Roswall J, Kjellberg E, Ahlström H, Dahlgren J, and

Kullberg J. MRI estimates of brown adipose tissue in children – Associations to adiposity, osteocalcin, and thigh muscle volume. Magnetic Resonance Imaging, 58:135–142, 2019.

IV Andersson J, Lundström E, Engström M, Lubberink M, Ahlström H, and Kullberg J. Estimating the cold-induced brown adipose tissue glucose uptake rate measured by18F-FDG PET using infrared thermography and water-fat separated MRI. Accepted in Scientific Reports.

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Related work

The author has also contributed to the following papers:

1. Bucci M, Huovinen V, Guzzardi MA, Koskinen S, Raiko JR, Lipponen H, Ahsan S, Badeau RM, Honka M-J, Koffert J, Savisto N, Salonen MK, Andersson J, Kullberg J, Sandboge S, Iozzo P, Eriksson JG, and Nuutila P. Resistance training improves skeletal muscle insulin sensitivity in elderly offspring of overweight and obese mothers. Diabetologia, 59(1):77–86, 2016.

2. Honka M-J, Bucci M, Andersson J, Huovinen V, Guzzardi MA, Sandboge S, Savisto N, Salonen MK, Badeau RM, Parkkola R, Kullberg J, Iozzo P, Eriksson JG, and Nuutila P. Resistance training enhances insulin suppression of endogenous glucose production in elderly women. Journal of Applied Physiology, 120(6):633–639, 2016. 3. Motiani P, Teuho J, Saari T, Virtanen KA, Honkala SM, Middelbeek

RJ, Goodyear LJ, Eskola O, Andersson J, Löyttyniemi E,

Hannukainen JC, and Nuutila P. Exercise training alters lipoprotein particles independent of brown adipose tissue metabolic activity. Obesity Science & Practice, 5(3):258–272, 2019.

4. Kjellberg E, Roswall J, Andersson J, Bergman S, Karlsson A-K, Svensson P-A, Kullberg J, and Dahlgren J. Metabolic risk factors associated with visceral and subcutaneous adipose tissue in a

sex-specific manner in seven-year-olds. Obesity, 27(6):982–988, 2019. 5. Lundström E, Ljungberg J, Andersson J, Manell H, Strand R,

Forslund A, Bergsten P, Weghuber D, Mörwald K, Zsoldos F,

Widhalm K, Meissnitzer M, Ahlström H, and Kullberg J. Brown adipose tissue estimated with the magnetic resonance imaging fat fraction is associated with glucose metabolism in adolescents. Pediatric Obesity, 14(9):e12531, 2019.

6. Lundström E, Andersson J, Engström M, Lubberink M, Strand R, Ahlström H, and Kullberg J. PET/MRI of glucose uptake, lipid content and perfusion in human brown adipose tissue. Manuscript.

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1. Introduction

This thesis includes work on two related subjects. The separation of water and fat signal in magnetic resonance imaging (MRI), and the study of brown adipose tissue (BAT).

1.1 Magnetic resonance imaging

Magnetic resonance imaging is a medical imaging method capable of gen-erating anatomical and functional tomographic images of the human body. Unlike other tomographic methods capable of imaging the entire body, such as positron emission tomography (PET), computed tomography (CT), or sin-gle photon emission computed tomography (SPECT), MRI does not expose the subject to potentially harmful ionizing radiation. The image generation is done by exciting atomic nuclei in the body by using external magnetic fields. After excitation the atomic nuclei will induce electric currents in nearby re-ceiver coils. The currents are measured and used to create tomographic im-ages. Normally1H nuclei are imaged, since other nuclei give a very poor or no signal. During typical scanning conditions, the vast majority of the signal in the human body will originate from water or fat molecules.

The external magnetic fields can be programmed to perform different MRI sequences. Some sequences, such as gradient echo sequences, produces a se-ries of images at different time points after the initial excitation. These images can be used to separate the signal originating from water and the signal origi-nating from fat. This is done by utilizing the property chemical shift, i.e. small differences in the resonance frequency of the nuclei depending on factors such as which molecule a nucleus is a part of and its position within the molecule, together called its chemical environment. The chemical shift between the nu-clei in water and the nunu-clei in fat cause different relative phases between the corresponding signals at different times after excitation. These relative phases can be used to perform the signal separation, thereby producing water and fat signal images. These images can in turn be used to calculate quantitative fat fraction images, i.e. the percentage of the signal coming from fat molecules. Additionally, for gradient echo sequences it is possible to calculate the rate at which the signal decays after the initial excitation, the so called effective transverse relaxation rate (R*2).

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1.2 Brown adipose tissue

In mammals, adipose tissue (AT) can be subdivided into two types, white (WAT) and brown adipose tissue (BAT). The vast majority of all AT in adult humans consists of WAT, which main function is energy storage. In contrast, the main function of BAT is heat generation through energy consumption.

It was recently discovered that adult humans can have metabolically sig-nificant amounts of BAT [1, 2, 3, 4]. It is possible that the BAT’s ability to expend energy could be used to combat overweight, obesity, or metabolic dys-functions, such as type 2 diabetes [1, 2, 3, 5]. This potential has lead to a significant research interest in the tissue, since these conditions and diseases pose a major risk to the public health.

To be able to measure the effect of any pharmacological or other type in-tervention of has on the BAT metabolism methods for estimating its metabolic activity are needed. Currently the most well-established method is using18 F-fluorodeoxyglucose (18F-FDG) PET. This method however has the drawback of exposing the subjects to potentially harmful radiation, and is also expen-sive and difficult to perform. Alternative methods include e.g. MRI, including measuring the FF and R*2of BAT, or estimating the BAT metabolic activity by measuring the skin temperature near the BAT depots using attachable temper-ature probes or infrared thermography (IRT).

1.3 Aims of the thesis

The overall aim of this thesis is to present and evaluate methods for perform-ing water–fat signal separation in MRI and to employ and evaluate water–fat signal separated MRI for studies of BAT. Study specific aims of this thesis can be found in chapter 7.

1.4 Structure of the thesis

This thesis is based on four research papers, summarized in chapter 7. Paper I describes a method for water–fat signal separation using a graph-cut that is robust to noise. Paper II describes a method for water–fat signal separation using convolutional neural networks that can perform the separation using un-dersampled data. In paper III water–fat separated MRI is used to study BAT and its associations to different measures of adiposity, hormones, and thigh muscle volume in a cross-sectional study of 7-year old children. In paper IV it is evaluated how well water–fat separated MRI and IRT measurements can predict BAT metabolic activity, using18F-FDG PET as a reference method.

The framing text serves to provide a context for these papers. Chapter 2 goes through the basics of magnetic resonance imaging and water–fat signal separation. Chapter 3 gives an introduction to positron emission tomography

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and how it can be used to calculate images of the glucose uptake rate. Chapter 4 contains a short description on how infrared thermography can measure the temperature of an object. Chapter 5 gives a short overview of both white and brown adipose tissue, and goes through some imaging methods that may be used for studying brown adipose tissue. Chapter 6 goes through the basics of artificial neural networks, including a description of convolutional neural networks. Chapter 8 offers a summary discussion of the work in this thesis. In chapter 9 a short summary of the thesis in Swedish is given.

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2. Magnetic resonance imaging

MRI uses the phenomenon known as nuclear magnetic resonance (NMR) to produce images. Resonance is the phenomenon where a system starts to os-cillate with a large amplitude when a force is applied at or near one of the natural frequencies of the system. Resonance can be desirable, such as when pushing a swing repeatably at the right time to make it go higher and faster, or unwanted, such as when walking with a cup of coffee, moving it back- and forwards in such a way that it starts to slosh and eventually spill. In NMR an external magnetic field cause the atomic nuclei under investigation to have a net magnetic moment. Energy is deposited by use of an oscillating magnetic field, causing the magnetic moment to oscillate. This oscillating magnetic mo-ment induces electric currents in nearby receiver coils. The currents are mea-sured, and within MRI these measurements are used to create images of the object under investigation. MRI can be used to study human subjects, and has found great use within diagnostic medicine and biomedical research. There is no evidence that an MRI scan is harmful as long as standard precautions are taken. Standard precautions include use of hearing protection, avoiding excessive heating of the subject, and not scanning persons with certain types of implants.

2.1 Basics of nuclear magnetic resonance

The physics of NMR is based on the quantum mechanical property of spin. Spin can be thought of as an intrinsic form of angular momentum that is present in certain particles. All isotopes with an even number of neutrons and an even number of protons have a spin equal to zero and can not be mea-sured using NMR. However, all other isotopes have a nucleus with a non-zero spin and a magnetic moment aligned with their spin. These isotopes can be measured using NMR. Since only particles with a non-zero spin can be inves-tigated using NMR they are sometimes referred to as ’spins’.

Although there are individual differences, the atomic percent in a human body is approximately 62% for hydrogen, 24% for oxygen, 12% for carbon, and small amounts of other elements. Unfortunately only approximately 1.1% of all carbon nuclei and 0.04% of all oxygen nuclei occurring naturally in a human body have a non-zero spin. However, approximately 99.98% of all hy-drogen in the human body are1H, which has a non-zero spin, and additionally this isotope provides a strong signal per nuclei [6]. Due to this, virtually all

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MRI is of1H. The1H nuclei are often referred to as protons, as they consist of single protons.

In the absence of an external magnetic field the spins of an object will be randomly aligned, and therefore have no net magnetization. When a static external magnetic field (B0) is applied, the spins will tend to align with it. However, for the temperature of a human body and the magnetic field strength of a clinical scanner (typically 1.5, 3, or 7 T) the total net magnetization will only be a few parts per million (ppm) of what it would have been, had the spins been perfectly aligned with the external field. This is due to thermal motion moving the magnetic moments out of alignment. The steady state net magnetization (M0) can be estimated using the first order approximation of the Boltzmann distribution described in Eq.2.1.

M0≈ NS ¯h2γ2 4kBT

B0 (2.1)

Ns is the number of spins, ¯h is the reduced Planck constant, γ is the gyro-magnetic ratio, kB is the Boltzmann constant, and T is the temperature. The value of γ is dependent on the type of particle that is being measured, in the case of1H γ/2π = 42.6 MHz/T.

In NMR, the magnetic moments of the individual particles are never mea-sured, only the net magnetization of large ensembles of particles. This means that quantum mechanical phenomena such as wave function collapse are not of concern, and for the most part NMR can be treated using classical physics [7].

The total net magnetization (M) of an ensemble of particles is proportional to the total angular momentum of the particles caused by their spins (A), as described in Eq.2.2.

M = γA (2.2)

The net magnetization will start to precess around the static magnetic field if they are out of alignment. It is due to the intrinsic momenta of the particles that the net magnetization will precess rather than simply swing. This phenomenon is similar to that of a spinning top, with the magnetic field in place of the gravitational field. The torque (τ) an external magnetic field will exert on the particles due to their magnetic moment is described in Eq.2.3.

τ = M × B (2.3)

The toque will make the angular momentum change according to Eq.2.4. dA

dt = τ (2.4)

Using Eqs.2.2–2.4, it is possible to calculate the rate of change of the net magnetization as in Eq.2.5.

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dM

dt = γM × B (2.5)

2.2 Excitation

As can be told from the cross product in Eq.2.5, the net magnetization will remain static as long as it is aligned to a static external magnetic field. The signal in NMR is generated by the precession of the magnetization around the static field. To get the net magnetization to start to precess, it needs to be moved out of alignment with the static field. This is done by applying an additional magnetic field, B1. B1is perpendicular to B0, and rotating with the resonance frequency (ω) of the relevant spins, described in Eq.2.6.

ω = γ |B0| (2.6)

The resonance frequency is also known as the Larmor frequency. For a normal MR scanner this frequency will be in the radio frequency range, and applying B1 is known as a RF pulse. By letting B1 rotate at the Larmor fre-quency, M will start precessing around B1, while the effect from B0is negated. By convention B0 is aligned with the z-axis, also known as the longitudinal axis, meaning it can be described as in Eq.2.7.

B0=   0 0 B₀   (2.7)

Since M0 is aligned with B0, this means that M0 can be described as in Eq.2.8. M0=   0 0 M0   (2.8)

B1, located in the perpendicular xy-plane, also known as the transversal plane, can then be described as in Eq.2.9.

B1(t) = B1   −sin(−γB0t) cos(−γB0t) 0   (2.9)

If M is initially aligned with B0, and B1 = 0 for t < 0, then M(t) for t > 0 can be calculated using Eq.2.5 as described in Eq.2.10

M(t) = M0   cos(−γB0t)sin(γB1t) sin(−γB0t)sin(γB1t) cos(γB1t)   (2.10)

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If B1 is turned off again at t = τ, the angle γB1τ ≡ α is known as the flip angle. As long as α is not a multiple of 180◦, some of the magnetization will be in the transversal plane. This process is known as excitation. After excitation, the magnetization will rotate according to Eq.2.5. This rotating magnetization will induce currents in nearby coils, which is how the NMR signal is measured. It is possible to measure both the magnitude and the phase of the signal. There is seldom a need for α to exceed 180◦, and for a modern clinical scanner this angle can be achieved in at most a few milliseconds. By using the knowledge presented so far, it would only be possible to measure the spin density (ρ), commonly called the proton density (PD) in the case of1H NMR.

2.3 Relaxation

After excitation, the magnetization will start returning to its steady state, de-scribed in Eq.1. This process is known as relaxation. An extension of Eq.2.5. incorporating the relaxation, called the Bloch equation, is shown in Eq.2.11.

dM

dt = γM × B + (M0− M) ◦ R (2.11)

The Hadamard product, also known as the entrywise product, is denoted by ◦, and R is defined as in Eq.2.12.

R =   1/T2 1/T2 1/T1   (2.12)

By solving Eq.2.11 after the application of a 90◦ pulse it can be seen that the magnetization along the longitudinal axis (Mz) will evolve according to Eq.2.13 and the transversal plane (Mxy) evolve according to Eq.2.14.

Mz(t) = M0(1 − e−t/T1) (2.13)

Mxy(t) = M0e−t/T2 (2.14)

T1 is known as the T1 relaxation time, and is also known the longitudi-nal relaxation or the spin-lattice relaxation. By solving Eq.2.11. it can be seen that T1is the time it takes for the longitudinal magnetization to get 1-1/e (≈63%) of the way to M0 from its value at any arbitrary timepoint after ex-citation. Longitudinal relaxation is caused by the system moving towards its thermal equilibrium, described in Eq.2.1. The move towards thermal equilib-rium means an energy loss from the magnetization to nearby particles, i.e. the lattice, in the form of heat.

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Table 2.1. List of relaxation times (in ms) of1H nuclei in water molecules at 1.5 T Tissue type Approximate T1value Approximate T2value

Adipose tissue 240–250 60–80

Whole blood (deoxygenated) 1,350 50 Whole blood (oxygenated) 1,350 200

Cerebrospinal fluid 4,200–4,500 2,100–2,300 (similar to pure water)

Gray matter of cerebrum 920 100 White matter of cerebrum 780 90

Liver 490 40

Kidney 650 60–75

Muscle 860–900 50

Values from Miller et al. [10].

T2 is known as the T2 relaxation time, and is also known as the transverse relaxation or the spin-spin relaxation. By solving Eq.2.11. it can be seen that T2 is the time it takes for the transversal magnetization to be reduced to 1/e (≈37%) of its value at any arbitrary timepoint after excitation. Longitudi-nal relaxation is caused by stochastic fluctuations in the local magnetic field caused by e.g. thermal motion. This leads to a decoherence of the magnetiza-tion, effectively a smaller net magnetization.

What causes T1relaxation also causes T2relaxation, and T2≤2T1, however a usual practical limit is T2≤T1 [8]. For pure substances both T1 and T2 can be predicted reasonably well using the so called Bloembergen-Purcell-Pound theory [9]. However, in highly heterogeneous substances such as biological tissue it is not possibly to reliably predict the values, instead they have to be measured. Values can vary between individuals and be affected by e.g. different pathologies. The strength of the B0 also affect the values. Typical values for 1H nuclei in water molecules of some tissues at B0 = 1.5 T are presented in Table.2.1.

Two important parameters in NMR sequences not mentioned yet are rep-etition time (TR), which is the time between successive RF pulses used to excite the magnetization, and time to echo (TE), the time from the last excita-tion to a measurement. By having a short TE and TR (typical values <30ms and <800ms, respectively) it is possible to create so called T1-weighed im-ages where the signal intensity of a material will mainly be affected by its T1. In such an image materials with a long T1 will appear darker. By hav-ing a long TE and TR (typical values >80ms and >2000ms, respectively) it is possible to create so called T2-weighed images where the signal intensity of a material will mainly be affected by its T2. In such an image materials with a long T2 will appear brighter. By having a short TE and a long TR (typi-cal values <30ms and >1000ms, respectively) it is possible to create so (typi-called PD-weighed images where the signal intensity of a material will mainly be

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Figure 2.1. PD-, T1-, and T2-weighed axial slices of a brain. Image courtesy of Dr.

Elin Lundström, Uppsala University.

affected by its proton density. In such an image materials with a high pro-ton density will appear brighter. Sequences with a long TE and a short TR are usually not performed since they produce images with a poor contrast between different tissues. Example images are shown in Fig.2.1.

As described above, the T2relaxation is only due to irreversible stochastic processes, such as thermal motion. However, the transverse magnetization will also decrease due to reversible deterministic effects, such as static field inhomogeneities. This will cause certain spins to precess faster than others, resulting in decoherence and an effective transverse relaxation time, T*2, which can be defined as in Eq.2.15.

1 T*2 = 1 T2 + 1 T02 (2.15)

Where T02 is due to deterministic effects. From the definition of T*2, it fol-lows that it is always shorter than T2. This process is however reversible. For example, the spins that will be leading some time after excitation, will instead be lagging after an 180◦pulse. If the pulse is applied at time t=τ, the effect of T02relaxation will be negated at time t=2τ.

Weighed images can be useful for diagnosis since they can give excellent contrast between different types of tissue. However, even though the pixel values in weighed images are largely affected by one parameter they are not truly parametric. To create parametric images, i.e. images in which the value of each voxel is the value of some parameter, e.g. T1 or T2, more complex scans need to be performed. While parametric maps are not commonly used in diagnosis, they can be useful within clinical studies.

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2.4 Image generation

So far, it has been described how the signal is generated and sampled, as well as some basic sources of image contrast. However, simply sampling the sig-nal as described above results in no spatial awareness, i.e. no image can be formed, just averaged values over the entire scanned object. To overcome this, additional spatially linearly varying magnetic fields are introduced, called gra-dients. These gradients can be applied independently along the x-, y-, and z-axes. The gradients will cause the strength of the magnetic field to be slightly different over the imaged object, however, the direction of the magnetic field does not change. The difference in magnetic field strength will cause a spa-tially varying resonance frequency, in accordance with Eq.2.6. By varying the strengths of the gradients, it is possible to spatially encode the signal of the object, and after measuring the signal, to decode it to get an image. To under-stand how this works, an example of a one dimensional object along the x-axis is provided.

The object will have a varying spin density along the x-axis, ρ(x), which if measured will provide us with the image that we seek. For simplicity we will assume that no relaxation takes place during the measurements, and that the scanner used is ideal, with no spatial bias in signal sampling or excitation. Simply measuring the object without any spatial gradients will give us, after modulating with the resonance frequency, the constant signal in Eq.2.16.

S=

Z ∞

−∞ρ (x)dx (2.16)

This is simply a scalar value proportional to the number of spins in the ob-ject. To be able to differentiate the signal coming from different x-coordinates, it is possible to introduce a gradient (Gx), giving a spatially varying magnetic field described in Eq.2.17.

B(x) =   0 0 B0+ Gx× x   (2.17)

Measuring the signal with the gradient turned on results in the time-varying signal in Eq.2.18.

S(t) =

Z ∞ −∞ρ (x)e

t Gxx γ i_dx _(2.18)

By doing the variable substitution in Eq.2.19., Eq.2.18. turns into Eq.2.20. kx= −Gxγ t 2π (2.19) S(k) = Z ∞ −∞ρ (x)e −2π i x kx_dx _(2.20)

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S(k) is the Fourier transform of ρ(x), and so ρ(x) can be calculated by applying the inverse Fourier transform as in Eq.2.21.

ρ (x) =

Z ∞ −∞

S(k)e2π i x kxdx (2.21)

The signal is said to be measured in k-space. To measure the entire k-space, an infinite amount of time would be required. This is obviously not possible in practice, and only a truncated part of the k-space is measured, which leads to ringing artifacts in the reconstructed images due to Gibbs phenomenon. It is possible to extend this method of spatial encoding to multiple dimensions simply by adding additional gradients in those directions. In this way it is possible to reconstruct 2D or even 3D images. While it may be possible to sample the k-space continuously in 1D, it is in practice not possible to sample the k-space in its entirety for higher dimensions, not even when limited to a certain range. In practice only certain points of the k-space will be measured, and therefore the discrete inverse Fourier transform is used in place of the continuous to generate images. The signal is most commonly sampled along a Cartesian grid in k-space, in which case it is straightforward to use the Fourier transform. Many other sampling strategies also exist, in which case some additional preprocessing might be needed before the Fourier transform.

2.5 Water–fat signal separation

In section 2.3 the basic sources of image contrast proton density, T1, and T2 were introduced, as well as T*2. There are however other properties that can be exploited to get other types of contrast. One such property is called chemical shift. This property can be used to separate the signal originating from water and fat molecules, and in general also other types of materials, such as silicone. Example water- and fat images are shown in Fig.2.2.

a

b

Figure 2.2.Axial water (a) and fat (b) images of the abdomen of a subject. Chemical shift refers to a small shift in the resonance frequencies of nuclei due to their chemical environment. Specifically, the electron clouds

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surround-Table 2.2. Locations of fat peaks relative to water at body temperature and their relative contribution to the total fat signal in a human body.

Location (ppm) Percent of total fat signal

0.59 3.7 0.49 1.0 -0.50 3.9 -1.95 0.6 -2.46 5.8 -2.68 6.2 -3.10 5.8 -3.40 64.2 -3.80 8.8

Values from Hamilton et al. [11].

ing the nuclei will provide some shielding against the external magnetic field, which will influence their resonance frequencies according to Eq.2.6. The ef-fect is very small, on the order of a few ppm. The protons in water molecules have a single chemical shift, while the protons in fat molecules will have multi-ple distinct chemical shifts depending on their position in the molecule, called peaks. The main fat peak, corresponding to methylene, constituting about 64.2% of the signal from fat, has a resonance frequency about 3.4 ppm lower than water at body temperature. See Table.2.2. for a list of different peak locations and their typical relative contribution to the total fat signal.

The relative contribution can vary somewhat depending on the exact fatty acid composition. By precisely measuring the relative contributions between the different peaks it is possible to calculate the fatty acid composition. Addi-tionally, the chemical shift of water decreases by approximately 0.01 ppm/◦C while the chemical shift of the fat peaks remain relatively stable. This means that if the relative chemical shift between the fat peaks and the water peak can reliable be measured the temperature may be calculated.

After modulating the signal by the resonance frequency of water, the signal for an arbitrary voxel in a spoiled gradient-echo sequence can be described using Eq.2.22. S(t) = (W + F M

∑

m=1 αmei γ B0δmt)e(i ω−R * 2)t+iω0 _(2.22)

Where t is the time since the excitation, W is the proton density of 1H in water molecules, F is the proton density of1H in fat molecules, ω is the off-resonance frequency due to e.g. inhomogeneities of the static external mag-netic field, ω0 is the phase of the signal at t = 0. αmis the normalized ampli-tude of fat peak m, and δmits corresponding chemical shift relative to water, these values are often assumed to be known a priori. However, they can also be estimated to calculate the fatty acid composition. The effective transverse

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relaxation rate, R*2, is defined as 1/T*2. Using this signal model, with five un-known real values; W , F, ω, ω0and R*2, the complex signal would need to be sampled at least at three distinct times after excitation for the values to be cal-culated. However, for t <<T*2the effect of R*2can be neglected, and a decent estimation of the remaining parameters is possible using only measurements at two time-points. The measurements at different time-points are known as echoes.

Often, the main problem when performing the signal separation is finding the value of ω. Once this value is known, efficient methods exist to calculate the remaining values. In case the spacing between the echoes (∆TE) is con-stant, Eq.2.22. is periodic with respect to ω, with a period of Ω = 2π/∆TE. It is possible to create an energy E that measures how well the estimated parame-ters match Eq.2.22. This energy decreases the better the match is and is equal to 0 only for a perfect match. Over the period Ω, it is common to find two distinct local minima of E. One corresponds to the correct solution, and one closely corresponds to a swap of the values of W and F, a so called water–fat swap.

Without noise, and assuming that Eq.2.22. perfectly models the signal, identifying the correct value of ω would be trivial, since E would be equal to 0 only for this value. However, in practice Eq.2.22. is not perfect, and there will be noise. This means that E will most likely not be 0 for the correct value of ω, and there is no guarantee that the smallest minima of E will be for the correct value of ω. In turn, this means that it is not possible to find the correct values of W and F for a single isolated voxel.

However, the inhomogeneity of the static magnetic field is smoothly vary-ing spatially, which means that neighborvary-ing voxels will have similar values of ω . This information can be taken into account when performing separation of the water and the fat signal. Two common classes of methods for taking the smoothness of ω into account are region-growing methods and graph-cuts.

In region-growing methods, voxels will take on estimates of ω based on their neighbors estimated values. For these methods it is necessary to have one or multiple initial seed voxels, from which the solutions will begin to grow. The initial seed voxels are typically chosen to be in regions where there is a high probability of finding the correct ω, although it is not possible to guarantee that the correct value is chosen. Furthermore, there is no guarantee that the correct value of ω will be estimated in a voxel even if its neighbor has the correct value. If the incorrect value is estimated in any voxel, the error will typically propagate over large regions [12].

In graph-cut methods, a global energy is created by taking into account both the local energy of each voxel, and also the difference of the estimated values of ω between neighboring voxels. These methods avoid the problems of hav-ing to choose initial seed voxels where it is critical to find the correct value of ω, and also decreases the problem of incorrect values spreading over large

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regions. Because of these properties, graph-cut methods are often considered superior to region-growing methods.

Due to e.g. differing coil sensitivities, the calculated water and fat images are not quantitative measurements of local concentrations of water and fat. They are however still of clinical importance, especially the water images, since the fat signal is often considered to be obscuring pathological markers. It is however possible to calculate the fraction of the signal in each voxel coming from fat, the so called fat fraction, which is a quantitative value. While seldom used in clinic practice, it can be useful in clinical studies.

In two of the papers in this thesis methods for separating the water and the fat signal in MRI images are presented and evaluated. In paper I a graph-cut is used when performing the separation and in paper II convolutional neural networks are used.

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3. Positron emission tomography

As the name implies, positron emission tomography (PET) is a tomographic technique based on the phenomenon of positron emission. Positron emis-sion, also known as beta plus decay, is a type of radioactive decay in which a positron is emitted from an atomic nucleus. Any subject studied using PET is exposed to ionizing radiation due to the radioactive decay. It is debated if the dose delivered from a single or a few PET scans is harmful, however, the po-tential risk hinders large-scale population studies. It is well-known that higher amounts of ionizing radiation over a longer time leads to an increased risk of cancer and higher amounts of ionizing radiation over a short time causes acute radiation syndrome. This limits the degree to which this technique may be used to study any single subject, such as in longitudinal studies.

3.1 Radioactive isotopes and tracers

When performing a PET scan of a subject a so called tracer has to be injected into or otherwise enter the body of the subject. Tracers are chemical com-pounds in which one or more of the atoms have been replaced with a short-lived isotope that may decay via positron emission. Short-short-lived in this context means having a half-life in the order of a minute up to the order of hours. Tracers are necessary since the natural rate of beta plus decay in humans and other animals is far too low to be used for imaging.

Since the isotopes are so short-lived they are not abundant in nature. There-fore they have to be artificially created. Some isotopes may be extracted from so called generators. Generators contain artificially created isotopes which may have a half-life on the order of tens or hundreds of days. These so called parent isotopes decay into the isotopes used for PET imaging which are ex-tracted from the generator. A generator may last for for months or even years before a too large part of the parent isotopes have decayed. This can be ad-vantageous since this means that the artificial creation of elements does not need to be done at the site of the PET scanning or require a constant line of supply. However, only certain nuclei may be created in this way, for example gallium-68.

A more common way of generating isotopes is by the use of a cyclotron. For isotopes with half-lives in the order minutes this has to be done in the im-mediate vicinity of the PET scanner right before the scanning starts. However, for isotopes with half-lives in the order of hours the synthesization may be

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done at a site several hours away from the site of the PET scanner. However, in this case frequent, most likely daily, refills of the tracer are needed, since the amount of tracer left decreases exponentially with time. Most isotopes used in PET imaging are created in this way, carbon-11, nitrogen-13, oxygen-15, and fluorine-18.

The radioactive isotopes can be used to create many different tracers. Since different tracers will behave differently in the body they will give differ-ent information on the physiological state of the subject. For example 18 F-fludeoxyglucose (18F-FDG) can be used to measure glucose uptake and15 O-H2O can be used to measure tissue perfusion.

3.2 Compartmental models

Without any modeling a PET image will simple state the number of counts, i.e. the number of radioactive decays, in every voxel. This is a not a good quan-titative measurement since the number of counts in every voxel is dependent both on the administered dose, i.e. how much of the tracer was administered, and also highly dependent of the weight of the subject. One simple way of correcting for this is by calculating the standardized uptake value (SUV) by dividing the number of counts by the administered dose and multiplying it by the subjects weight. While this is a more robust measurement than just using the number of counts, it is still highly variable between subjects due to e.g. differences in body composition, and therefore not suitable as a quantitative measurement.

One way of generating more robust quantitative measurements is through use of so called compartmental models. In a compartmental model the body is divided into different compartments. A compartment is a chemical species in a physical place. Examples include the tracer in the bloodstream or the intra-or extracellular space of some specific tissue. Inside a compartment the tracer is considered to be uniformly distributed, with no internal barriers restricting motion. However, between different compartments tracer movement is re-stricted due to intercompartmental barriers, and will therefore move between compartments at certain restricted rates, if at all.

The most commonly used tracer is 18F-FDG. FDG is a glucose analog, which makes it behave very similar to glucose in the body. However, one im-portant distinction is that FDG is not metabolized in the same way as glucose is, instead it is phosphorylated, which essentially traps it in a cell. This makes FDG advantageous to use as a traces to study glucose metabolism compared to radiolabeled glucose (11C-glucose), since the metabolization of glucose leads to far more complicated pathways for the radioactive isotope.

When using 18F-FDG the body is commonly divided into three different compartments: FDG in blood plasma, unphosphorylated (free) FDG in tis-sue, and phosphorylated (bound) FDG in tissue. This model is called the

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ir-C

P

(t)

C

F

(t)

C

B

(t)

K

1

k

2

k

3

Figure 3.1.A schematic illustration of the irreversible two-tissue compartment model as described by Eqs.3.1 and 3.2.

reversible two-tissue compartment model since there are two types of tissue involved, blood plasma and the tissue that takes up the FDG, and there is an irreversible process, the phosphorylation of FDG. The rate of change of the free FDG in tissue (CF) is described in Eq.3.1 and that of the bound FDG in tissue (CB) is described in Eq.3.2. The model is schematically illustrated in Fig.3.1.

dCF(t)

dt = K1CP(t) − (k2+ k3)CF(T ) (3.1) dCB(t)

dt = k3CF(t) (3.2)

K1is the rate of transportation of the tracer from the plasma to the tissue, k2 the rate of transfer in the opposite direction, and k3the rate at which the FDG is phosphorylated in the tissue. It is possible to solve the system of differential equations described by Eqs.3.1–3.2 as Eq.3.3.

CT(t) = K1k2 k₂+ k3 CP(t) ∗ e−(k2+k3)t+ K1k3 k₂+ k3 ∗Cp(t) (3.3)

In Eq.3.3 ∗ represent the convolution operator, CP is the concentration of FDG in blood plasma, and CT is the total concentration of the tracer in tissue (i.e. CF+CB), i.e. the signal measured in the PET images if the signal of the tracer in the plasma can be considered negligible. CPis typically either mea-sured using arterial blood sampling or estimated from the tracer concentration in the aorta measured from the PET images. With both CT and CP known at multiple time-points it is possible to determine values of the transfer rates to fit Eq.3.3. Once this is done the net uptake rate of FDG (Ki) of the tissue may be calculated as Eq.3.4.

Ki= K1k3 k2+ k3

(3.4) From Kithe glucose uptake rate (GUR) of the tissue can be calculated as in Eq.3.5.

GU R=C glu P Ki

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C_Pglu is the blood plasma glucose concentration, which can easily be mea-sured using a small blood sample and can be assumed to be almost constant during a PET scan if no special intervention is being performed, and LC is the so called lumped constant, a tissue specific constant meant to account for differences between how glucose and18F-FDG behave in the body.

3.3 Image generation

The positrons that are emitted from the decaying isotopes travel a short dis-tance after emission before annihilating with its antiparticle, the electron. The exact distance is random but depends on the isotope and in which type of tis-sue the positron traveled. In the case of18F this distance is seldom more than a couple of millimeters [13].

Upon annihilation two photons, each with an energy of 511 keV, equal to the rest energy of an electron or a positron, are typically created. In rare cases other particles may be created, but this is of no concern in the context of PET imaging. Thanks to the conservation of linear momentum the two photon will travel in almost opposite directions in the frame of reference in which the PET scanner is at rest. A small deviation from perfect opposite directions occur due to the momenta of the particles before annihilation.

The photons are detected by detector elements in the PET scanner. A pho-ton pair from an annihilation event will be detected by detector elements in opposite directions from the location where the annihilation took place since they travel in opposite directions. The detections will take place within at most a few nanoseconds of each other since the photons travel at nearly the speed of light. Since the detections are almost simultaneous it is possible to assign them to the same annihilation event and calculate a line along which the an-nihilation took place, a so called line of response (LOR). By detecting many photon pairs it is possible to use the information to reconstruct an image of the concentration of the radioactive isotope.

When doing the image reconstruction there are some problems that need to be taken into account. One problem is scattering, where photons may change their direction when interacting with matter. If a photon scatters it will no longer travel in opposite direction with its partner, which means no correct LOR may be calculated. Another problem is random coincidences, when two photon will be detected near simultaneously even though they did not originate from the same annihilation event, leading to an incorrect LOR. Photons may be absorbed by the body, meaning they can not be detected, this is known as attenuation. Photons originating deeper in the body are at greater risk at being absorbed since they travel through more matter. This means that areas deeper in the body will be shown having a falsely low concentration of the radioactive isotope. The detector elements of the PET scanner has a dead-time after each detection during which time they may not detect any new photons, meaning

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that some photons and their associated LORs will be missed. All of these issues need to be taken into account to reconstruct high-quality images.

Since the photons do take a few nanoseconds to reach the detectors it is possible to restrict the location of the anhillation event to a segment of the LOR if the detectors have a high time resolution. This is known as time-of-flight PET, and allows for higher quality images.

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4. Infrared thermography

Infrared thermography (IRT) uses infrared radiation to measure temperature. An infrared camera may be used to create images in which the value of each pixel corresponds to a certain temperature. An infrared camera works similar to a normal digital camera, but is sensitive to parts of the electromagnetic radiation in the infrared spectra (wavelengths 700 nm – 1 mm) instead of the visible spectra (wavelengths 400 nm – 700 nm).

Any object with a temperature above absolute zero will emit electromag-netic radiation, so called thermal radiation. Assuming a black body, i.e. an object that absorbs all incoming electromagnetic radiation, the spectral radi-ance per unit wavelength is distributed according to Planck’s law, as described in Eq.4.1. B_λ(λ , T ) =2hc 2 λ5 1 e hc λ kBT−1 (4.1) B_λ is the amount of energy emitted at a certain wavelength, λ , T is the temperature of the object, h is the Planck constant, c the speed of light in the medium, and kB is the Boltzmann constant. An example of the distribution at 34◦C (307.15 K), i.e. approximately human skin temperature, is shown in Fig.4.1.

The wavelength with the greatest emissive power (λmax) can be calculated using Wien’s displacement law, as described in Eq.4.2.

λmax= hc

x 1

kT (4.2)

xis the value which solves the equation (x − 5)ex+ 5 = 0, and is approxi-mately equal to 4.97. By setting T = 307.15 K in Eq.4.2 a value of λmaxequal to approximately 9.4 μm is obtained. It can also be calculated that approx-imately 95% of all the emissive power will be within the span of 5.4–53.0 μm, all of which is well within the infrared spectra. An infrared camera used for estimating temperature should be sensitive to electromagnetic radiation at wavelengths close to the imaged object’s λmax, although the exact sensitivity profile may vary by camera model.

An infrared camera does not typically use the distribution of the electro-magnetic radiation, as described in Eq.4.1, into account when calculating the temperature of an object. Instead, the total radiation effect is measured and used to determine the temperature. The total radiation effect can be found

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0 10 20 30 40 50 60 Wavelength (µm) 0 0.002 0.004 0.006 0.008 0.01 0.012 Spectral radiance (W sr -1 m -2 nm -1 )

Spectral emissive power

Figure 4.1. Spectral emissive power of a black body at 307.15 K.

by integrating Eq.4.1 over all possible wavelengths, resulting in the Stefan– Boltzmann law, which is described in Eq.4.3.

P= σ T4 (4.3)

Pis the total emissive power and σ is the Stefan–Boltzmann constant. Note that Eq.4.3 only holds true for a black body. No black body exists in practice, and for a real object the emissive power is only a fraction of that of a black body. This fraction is known as an object’s emissivity (ε) and depends on the type of material and the wavelength of the radiation. For human skin at physiological temperatures this value is approximately 0.98. The emissivity of an object has to be taken into account when calculating the temperature of an object.

A fraction of the incoming radiation toward an object is reflected off the ob-ject. According to Kirchhoff’s law of thermal radiation this fraction is 1-ε for an object at thermal equilibrium. The power of the incoming thermal radiation is dependent of the temperature of the environment the object is within. By measuring the environmental temperature it is therefore possible to estimate this radiation. Since the total measured radiation is equal to the sum of the emitted and the reflected radiation of an object, it is necessary to take this into account for more accurate temperature measurements.

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Once taking the emissivity and reflected radiation into account it is possible to create temperature images of an object. An example image of a human subject exposed to mild cold is shown in Fig.7.8.

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5. Adipose tissue

In mammals, adipose tissue (AT) can be subdivided into two types, white (WAT) and brown adipose tissue (BAT). The main function of WAT, which is by far the most abundant type in adult humans, is energy storage. WAT also provides mechanical protection and acts as a thermal insulator. In contrast, the main function of BAT is heat generation through energy consumption, and is therefore in a way antagonistic to WAT. In addition to these functions, AT also plays an important role in the endocrine system.

5.1 White adipose tissue

The main function of WAT is uptake, storage, and release of energy. The en-ergy is stored in the form of triglycerides. White adipose tissue is abundant in humans, generally constituting about 19–39% of the body weight for healthy women 7–27% for healthy men [14]. Thanks to the stored energy, an adult human can live about one month without eating, and survive extended periods of starvation when food supplies are limited.

WAT consists mostly of white adipocytes. They mainly consist of a single large lipid droplet containing triglycerides, which gives them their white color [15]. Little metabolism takes place in these adipocytes, and they therefore contain few mitochondria, and are surrounded by a relatively small amount of capillaries.

The WAT can largely be subdivided into two classes, subcutaneous adipose tissue (SAT) and intraabdomial adipose tissue (IAT), often incorrectly called visceral adipose tissue (VAT), which makes up a subset of the IAT. As the name implies, SAT is found under the skin, while IAT is in the abdominal cavity, where it is packed between the organs. The location of SAT, covering most of the body, makes it function as a thermal insulator, and also provides some mechanical protection. The IAT provides further thermal insulation and mechanical protection of the sensitive abdominal organs.

WAT plays an important role in the endocrine system. A few well stud-ied hormones and cytokines, related to metabolic health, produced by WAT follows. The hormone leptin plays an important role in energy homeosta-sis by regulating energy intake and expenditure. The cytokine interleukin 6 positively correlates with obesity, impaired glucose tolerance, and insulin re-sistance. Concentrations of adiponectin are strongly inversely associated to insulin resistance. There are many other hormones and cytokines produced by WAT, and they influence many other parts of the body in addition to metabolic health [16].

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5.2 Brown adipose tissue

The main function of BAT is thermal generation, which is achieved via so called non-shivering thermogenesis (NST), which stands in contrast to shiv-ering thermogenesis (ST), i.e. non-voluntary contractions of muscles as a re-sponse to cold. As fuel, stored triglycerides, as well as e.g. glucose and free fatty acids that are absorbed from the blood stream, are used by BAT. The estimated total amount of BAT in a normal adult human is relatively small, ranging between approximately 0–200g [1, 2, 3]. However, measuring total BAT content is relatively difficult, and it is entirely possible that all normal adults have at least some BAT, as some studies indicate [17].

It was recently discovered that adult humans can have metabolically sig-nificant amounts of BAT [1, 2, 3, 4]. In one study researchers estimated that fully activated BAT in an adult human could expend energy equivalent to ap-proximately 4.1 kg of adipose tissue over the course of a year, although they believed that it might have been an underestimation [3]. If any pharmaco-logical or other intervention could stimulate the BAT metabolic activity then its energy expenditure might be able to help prevent excessive weight gain [1, 2, 3, 5] since this is often a drawn out process, with a weight increase of a few kg per year. It could also be useful in weight loss interventions and also potentially help combat certain metabolic dysfunctions such as type 2 diabetes [1, 2, 3, 5]. It should however be noted that some researchers believe that the estimated potential energy expenditure of BAT is significantly overestimated [18].

In BAT, so called brown adipocytes are present. In contrast to white adipocytes they contain multiple small droplets containing triglycerides [15]. To be able to generate heat, a good oxygen supply is required, which is accom-plished by a high capillary density. To be able to quickly transform chemical energy into thermal energy, the adipocytes are fitted with a plentitude of mito-chondria. The mitochondria and capillaries are rich in iron, which gives BAT its brown color, from which it derives its name.

In humans there are two types of brown adipocytes, although they do not appear to show any great difference in morphology or function. There are the so called classical brown adipocytes that are found in newborns and infants in the interscapular area [19], which is a depot that diminishes quickly with age. A schematic illustration of this depot can be found in Fig.5.1a. In rodents, these cells have been shown to share the same precursor cells as the myocytes (muscle cells). BAT is especially important in newborns, since NST is not enough to keep them warm.

In human children and adults, so called inducible brown adipocytes, also called brite or beige adipocytes, are typically present, mostly in the cervical-supraclavicular fat depot [19]. A schematic illustration of this depot can be found in Fig.5.1b. They are called inducible because they can be recruited based on the need. Even after recruitment, white adipocytes will remain in

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a

_b

Figure 5.1. Schematic illustrations of the main BAT depots in humans, (a) the inter-scapular depot in an infant and (b) the cervical-supraclavicular depot in an adult, both shown in brown. Image courtesy of Dr. Elin Lundström, Uppsala University.

the depot, leading to a mixture, which has given them the name brite (from brown-in-white) adipocytes. The mixture leads to a less brown appearance, giving them another name, beige adipocytes. These adipocytes are most likely closely related to white adipocytes.

It has been shown that BAT plays an endocrine role in rodents that differ from that of white adipose tissue, and there are indications that the same is true for humans [20]. In paper III a cohort of 7-year olds is studied. MRI mea-sures of the cervical-supraclavicular fat depot are correlated to other meamea-sures, including different hormones.

5.3 Imaging of brown adipose tissue

To characterize human BAT with non-invasive methods is challenging. The goal is often to estimate the BAT’s current or maximal potential for energy expenditure, since increasing these would likely be the target of any pharma-cological or other intervention targeting BAT.

Multiple different imaging methods for estimating the energy expenditure of BAT exist. Some methods may work well without any cooling. However, cooling is often performed to increase the BAT metabolic activity. Either the same cooling may be used for every subject, or the cooling may be individ-ualized to activate the BAT as much as possible without making the subjects shiver. Individualized cooling is probably superior to non-individualized cool-ing since it is fraught with less confoundcool-ing factors. For example, when per-forming non-individualized cooling subjects with more subcutaneous tissue are probably less affected by the cold compared to thinner subjects since they are better insulated, which in turn means that the BAT does not need to

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acti-vate as much to keep the subject from being cooled down [17]. It should be noted that even though it is sometimes assumed that the BAT is maximally activated when a subject is just about to start to shiver [17] this has not been proven. However, subjects are seldom exposed to cold to such a degree that they start to shiver during studies, both since this is taxing on the subject, but also because it interferes with several measuring techniques, such as PET and MRI.

5.3.1 Positron emission tomography

The pioneering methods for estimating BAT metabolic activity in humans used the glucose analog 18F-FDG as the PET tracer [1, 2, 3]. It was shown that the glucose uptake increased in response to cold exposure [1, 3]. 18F-FDG PET is still the most well-established method for estimating BAT metabolic activity. This method works well since BAT will take up glucose from the blood stream while active to use as fuel. In contrast the uptake in WAT is minimal. Alternative PET tracers for estimating BAT metabolic activity using PET include the fatty acid tracer18F-fluoro-thiaheptadecanoic acid [4]. The uptake of18F-FDG in BAT is negligible for most persons under thermoneutral conditions [1, 2], and the same is likely true for18F-fluoro-thiaheptadecanoic acid, therefore the use of cooling is essential if the goal is to measure the BAT metabolic potential. If possible, it is preferable to calculate quantitative measurements such as glucose uptake rate over measurements such as number of counts and SUV.

It is not known precisely in which proportions BAT uses stored triglycerides and circulating glucose and fatty acids to generate heat. This may be depen-dent on numerous factors, such as current availability in the blood stream, and there may also be individual differences. This means that neither glucose nor fatty acid uptake in BAT can be considered a ground truth measurement of the cold-induced BAT metabolism.

It is also possible to measure the perfusion of BAT using certain PET trac-ers. It has been shown that the perfusion of BAT increases in response to cold both using15O-H2O [21] and15O-O2[22] as the tracer. Additionally,15O-O2 has been used to show that the tissue-level metabolic rate of oxygen in BAT increased during mild cold stress [22] and11C-acetate has been used to show a cold-induced activation of oxidative metabolism in BAT [4]. There also exist multiple other tracers that could potentially be used to measure BAT metabolic activity or potential. However, all the tracers have their weaknesses and none gives a precise measurement of BAT metabolic activity or potential.

It should be noted that all methods using PET exposes the subjects to po-tentially harmful ionizing radiation. Additionally PET is quite expensive and difficult to perform, requiring professional healthcare personnel. It should also be noted that while sites that can perform PET with18F-FDG as the tracer are

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relatively common, sites that can use many of the other tracers are less com-mon.

5.3.2 Magnetic resonance imaging

One advantage of MR methods over PET scanning is that the subjects are not exposed to any ionizing radiation. While not trivial to operate, it is possible to learn how to perform a predefined protocol in a matter of hours and no professional healthcare personnel need to oversee the scanning. However, as for PET, examinations are limited to locations with the relevant hardware.

Measurements of FF and T*2 can be of use for characterizing BAT, as well as estimating cold-induced BAT metabolic activity, and this is a fairly well-established method for examining BAT. In paper IV it is explored how well these measurements correlate with the glucose uptake rate of the BAT mea-sured using18F-FDG PET.

The FF and T*2 in BAT is lower than in WAT in humans, likely because of differences in mitochondrial abundance, triglyceride content, and vasculariza-tion [23]. Both the FF [24, 25, 26] and T*2 [24] of BAT have been found to correlate negatively to measurements of cold-induced BAT metabolic activ-ity performed using18F-FDG PET, although some other studies [27, 28] have failed to replicate these results. These measurements have the advantage that they can be performed without any cooling. However, its worth keeping in mind that these measurements are not directly measuring cold-induced BAT metabolic activity.

When comparing different studies measuring the FF it is worth keeping in mind that although the FF is a quantitative measurement it is still partially influenced by the T1- and T2-weighing of a scan. This is because the T1 and T2 of1H nuclei differ depending if they are located in water or fat molecules. Likewise T*2 can vary depending on factors such as the strength of the static external magnetic field.

One alternative MR methods is measuring the BAT temperature using the temperature dependent chemical shift between water and fat. A positive cor-relation between BAT metabolic activity and BAT temperature during cooling or BAT temperature during cooling relative to the temperature before cooling may be expected. One study claims to have observed this correlation [25]. It should however be noted that the measured change in BAT temperature during cooling compared to before cooling was in many cases extreme and proba-bly physiologically unfeasible (ranging between -7 and +9 ◦C). It is notori-ously difficult to accurately measure the temperature of adipose tissue using the chemical shift due to confounding factors [29], and it is not unlikely that the statistically significant correlation in [25] was a fluke.

Additionally, several more MR methods have been used to study BAT al-though none of then are well-established. One potentially promising method

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is measuring apparent diffusion [30]. It is probable that the apparent diffu-sion of molecules in BAT is smaller than in WAT since the smaller droplets in BAT compared to the ones in WAT likely leads to a greater restriction of the molecules movement. It is however difficult to accurately measure the apparent diffusion of BAT due to motion, and additionally the cervical-supraclavicular depot is in an area with severe field inhomogeneities due to susceptibility differences between different tissues and air, which makes it more difficult to perform accurate measurements.

5.3.3 Infrared thermography

One method for measuring BAT activity is measuring the skin temperature of the supraclavicular fossae near the cervical-supraclavicular depot. This can be done using e.g. attachable temperature probes or infrared thermography (IRT). IRT is advantageous compared to PET in that no ionizing radiation is used. It is advantageous compared to both PET and MR in that measurements are very easy to perform and the camera is very cheap compared to a PET or an MR scanner as well as portable. Some kind of cooling is usually performed when doing these measurements.

Several studies have shown positive correlations between the skin temper-ature of the supraclavicular fossae and measurements of cold-induced BAT metabolic activity performed using 18F-FDG PET [26, 31, 32, 33, 34, 35]. There are however some problems with estimating BAT metabolic activity in this way. One problem is that the amount of subcutaneous adipose tissue likely interferes with the measured temperature. Another problem is that although cervical-supraclavicular depot is perhaps the most important BAT depot there are several other depots as well that do not contribute to the temperature of the supraclavicular fossae.

In paper IV it is explored how well temperature of the supraclavicular fossae and a control region, both during and not during cooling, correlate with the glucose uptake rate of the BAT measured using18F-FDG PET.

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6. Artificial neural networks

Artificial neural networks (ANNs) are artificial constructs loosely inspired by the biological neural networks that form the computational part of brains. Like a brain an ANN consist of multiple interconnected simple computational units, called neurons, again inspired by their biological namesake. Similar to a brain, an ANN can be trained to perform certain tasks, which makes them a class of machine learning algorithms.

Each neuron takes as input multiple externally supplied values, e.g. pixel intensities in an image, or internally supplied values, i.e. the output of other neurons in the network and performs a simple non-linear calculation, a so called activation function, producing a scalar output. The activation function will have some tunable parameters, and it is by tuning these parameters that an ANN can learn.

One commonly used basis for the activation function is the so called recti-fied linear unit (ReLU), described in Eq.6.1.

ReLU(x) = (

0, i f x < 0

x, otherwise (6.1)

In an ANN the activation function ( fn) of a neuron n may be as in Eq.6.2.

fn(X) = ReLU (Wn· X + bn) (6.2)

X is the input formatted as a row vector, Wnare weights for the input for each source formatted as a column vector, and bna scalar weight for the neu-ron.

An ANN can typically be divided into multiple layers. The first layer is the so called input layer, which simply is the data fed to the network. These values are then fed to a so called hidden layer, which consists of multiple neurons. The output from a hidden layer is either fed to a subsequent hidden layer or the output layer. The output layer consists of one or multiple neurons, and as its name suggest its output is the output of the ANN. A simple ANN where all layers are fully connected, i.e. the values from every neuron in a layer is used as input to every neuron in the next layer, is schematically shown in Fig.6.1. If an ANN have multiple hidden layers the learning process may be called deep learning. Virtually all modern ANNs have multiple hidden layers which have made the two terms virtually interchangeable.

The weights of an ANN are initially normally either randomized or taken from some other ANN trained to solve a different problem. To be able to tune

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input layer

hidden layer 1 hidden layer 2 hidden layer 3

output layer

Figure 6.1.Schematic representation of a simple ANN. Pink circles symbolizes input values, green circles neurons in the hidden layers, and the blue circle the single neuron of the output layer. The arrows symbolizes values traveling into, within, and out of the ANN.

the parameters of an ANN to solve a problem some training data is needed. The training data consists both of input data to the network and a target output. For example, to train a network to estimate the value of a car the input could be which year the car was built, how much it cost when it was new, and its mileage. In this case, the input data can be relatively easily retrieved, and the target output could be taken from e.g. a used car dealership.

Once training data has been collected a loss function is needed to train the ANN. Given some training data, the network tunes its weight to minimize the loss function. In the simple example above the loss function could be the squared difference between the output of the ANN and the target output. Typically some form of backpropagation is used to perform the tuning. Back-propagation utilizes the chain rule to iteratively update the weights of the ANN using gradient descent.

One class of ANNs that have found great success within image analysis are so called convolutional neural networks (CNN). The organization of the neu-rons in a CNN is inspired by the visual cortex of the brain. The data of an image has important spatial structures, with pixels close to each other often being more highly correlated to each other than pixels further away from each other. A CNN is organized in such a way as to exploit these spatial correla-tions.

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The basic building block of a CNN are convolution matrices, also known as kernels. The weights of the kernels are trainable parameters in a CNN. Each layer in a CNN may consist of multiple channels, also known as feature maps. If the input layer consists of an image, as typically is the case, the feature maps may simply be the different color channels. Each feature map of one layer is convoluted by a kernel, and the sum of the results make up one feature map in the next layer. Multiple sets of kernels may be used to create multiple feature maps in the next layer. Multiple layers performing convolutions are typically used in a CNN. The multiple layers of feature maps correspond to increasingly more complex features, with the first hidden layer identifying e.g. edges, and later layers identifying features corresponding to more complex shapes, such as a face or a car. If the desired output of a CNN is an image, all layers may perform convolutions, however, if e.g. a scalar value is desired the last few layers a usually fully connected.

A CNN may be used for e.g image segmentation or classification. In paper II in this thesis CNNs are used to perform water–fat signal separation of MRI images.