Research Collection

Master Thesis

Hypoxia measurements with near-infrared optical tomographyand fluorescence molecular tomography: a comparison study

Author(s): Wyser, Dominik

Publication Date: 2014

Permanent Link: https://doi.org/10.3929/ethz-a-010428889

Rights / License: In Copyright - Non-Commercial Use Permitted

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ETH Library

Master Thesis

Advisors: Supervisor:Prof. Robert Riener Dr. Juan Mata PaviaProf. Martin Wolf

Hypoxia measurements withnear-infrared optical

tomography andfluorescence molecular

tomography:a comparison study

Dominik Wyser

(April - November 2014)

Symbols

Symbols

CO2Hb(r) Concentration of oxy-hemoglobin in tissue

CHHb(r) Concentration of deoxy-hemoglobin in tissue

µa,0 Homogeneous absorption coefficient

δµa(r) Heterogeneous absorption coefficient (tumor)

µa(r) Total absorption coefficient (homogeneous & heterogeneous)

µs Scattering coefficient

µ′s Reduced scattering coefficient

k Extinction coefficient

U(r) Total light field in medium

U0(r) Homogeneous light field in medium

r Position in medium

rs Position of source

rd Position of detector

φ(rs, rd) Imaginary and real phase diffference between total field and homogeneous field

λ Wavelength

Acronyms and Abbreviations

ETH Eidgenoessische Technische Hochschule

BORL Biomedical Optical Research Lab

AIC Animal Imaging Center

SMS Sensory Motor Systems Lab

NIROT Near-Infrared Optical Tomography

FMT Fluorescence Molecular Tomography

HIF Hypoxia Inducible Factor

HRE Hypoxia Response Element

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Abstract

The hypoxic state of tumors influences strongly the survival rate of patients. Studiesrevealed that the survival rate is about 40% lower for patients suffering from hypoxictumors than for patients suffering from normoxic tumors. However, there is no es-tablished method to measure tumor oxygenation in clinical practice. Fluorescencemolecular tomography (FMT) measures the emission of a fluorescence protein, thatis produced under hypoxic conditions and expresses the amount of hypoxia induciblefactors (HIF) in the blood. However, this method is almost entirely used for pre-clinical research with small animals, since only one fluorescence protein is allowedfor the use with humans. Near-infrared optical tomography (NIROT) measures theabsorption of hemoglobin in blood, from which the oxygen saturation in tissue canbe obtained. The objective of this thesis was to compare measurements performedwith FMT and NIROT to gain knowledge about how the measurements of thesetwo methods correspond to better understand the behavior of tumors under hy-poxic conditions. The first combined FMT and NIROT setup, to our knowledge, ispresented in this thesis. A novel NIROT reconstruction algorithm employing wave-length normalization was implemented and tested. The wavelength normalizationreduces the constraints of the algorithm on the accuracy of the model that is beingsimulated. Hypoxia measurements on two mice, both containing a subcutaneoustumor, have been performed. The obtained results validated the novel algorithmand hypoxia measurements by NIROT and FMT could be compared. The resultsshowed a good correspondence of the hypoxia measurements for these two meth-ods. We were able to show that both methods are able to determine accurately thelocation of hypoxic tissue and that the two methods can be used complimentary,since in FMT hypoxia is determined in terms of HIF concentration in the cell andin NIROT hypoxia is expressed in terms of oxygen saturation.

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Contents

Symbols i

Abstract iii

1 Introduction 11.1 NIROT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 FMT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.3 Project description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2 NIROT reconstruction algorithm 72.1 Diffusion equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.1.1 Homogeneous medium . . . . . . . . . . . . . . . . . . . . . . 82.1.2 Heterogeneous medium . . . . . . . . . . . . . . . . . . . . . 8

2.2 NIROT reconstruction with wavelength normalization . . . . . . . . 122.3 Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.3.1 Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . 162.3.2 Contrast comparison . . . . . . . . . . . . . . . . . . . . . . . 182.3.3 Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . 23

2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

3 Combined FMT and NIROT setup 253.1 Experimental setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.2 Laser characterization . . . . . . . . . . . . . . . . . . . . . . . . . . 26

3.2.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273.2.2 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 27

3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

4 Experimental measurements with mice 334.1 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 364.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

5 Conclusion and Outlook 39

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Chapter 1

Introduction

Patients suffering from hypoxic tumors have a much lower life expectancy thanthose with normoxic tumors, as shown by Vaupel [1], where it was found that thesurvival rate two years after diagnosis is approximately 40% lower for patients withhypoxic tumors than for patients with normoxic tumors. Thus, it is of greatestinterest to physicians to know the hypoxic state of a tumor in order to give anaccurate prognosis and to choose the appropriate therapy.

In this thesis two methods - both capable of detecting hypoxia in tissue - were used:Fluorescence Molecular Tomography (FMT) and Near-Infrared Optical Tomogra-phy (NIROT). Both techniques take advantage of the ability of near-infrared lightto be able to deeply penetrate tissue [2].

Figure 1.1: Absorption spectrum of the four main absorbing chromophores in bio-logical tissue, i.e. oxy-hemoglobin (O2Hb), deoxy-hemoglobin (HHb), water (H2O)and lipid.

In figure 1.1 the absorption coefficients of oxy- and deoxy-hemoglobin, water andlipid are shown. Between 650 nm and 900 nm an optical window exists, in whichthe the absorption of these four substances is low and light is able to penetrate up

1

Chapter 1. Introduction 2

to several centimeters into tissue [2]. At wavelengths below 650 nm the absorptionof oxy- and deoxy-hemoglobin increases rapidly and light is quickly absorbed, whileabove 950 nm water has a high absorption coefficient.

The absorption of oxy- and deoxy-hemoglobin in this near-infrared window is muchhigher than for the other substances. By measuring at two or more different wave-lengths, it is possible to calculate the concentration of the two chromophores oxy-and deoxy-hemoglobin[3]. From the calculated oxy- and deoxy-hemoglobin concen-trations CO2Hb/CHHb the oxygen saturation StO2 in tissue can be determined.

StO2 =CO2Hb

CO2Hb + CHHb(1.1)

The possibility to reconstruct the oxygen saturation of tissue by measuring thehemoglobin concentration is used by NIROT. In NIROT, hypoxia is therefore de-termined by means of oxygen saturation.

The same optical window is also used in FMT. The tissue is illuminated with near-infrared light and the emission of fluorescence proteins is measured. The emissionof the fluorescence proteins is dependent on the amount of hypoxia inducible factors(HIF) in the tissue; HIFs prevent the cells from necrosis and are present in tissuesuffering from hypoxia. In the case of FMT, hypoxia is expressed by means of theamount of HIFs in the tissue.

1.1 NIROT

The propagation of near-infrared light in tissue is very diffuse and the photons arerepeatedly scattered before reaching the detector. As a consequence the scatteringin the medium is much larger than the absorption and that the photons completelylose their directionality already after a small distance of about 1 mm[4] [5]. In figure1.2, an example of a weakly and a strongly scattering medium is shown.

(a) (b)

Figure 1.2: Light propagation in tissue. (a) Highly absorbing medium: scattering� absorption. (b) Highly scattering (diffuse) medium: scattering � absorption.Stuker et al.[6] c© 2011 IEEE

Depending on the oxygen saturation the tissue has different absorption curves. Infigure 1.3 seven specific absorption curves at seven different oxygenation levels are

3 1.2. FMT

shown. The curves are a linear combination of the absorption of oxy- and deoxy-hemoglobin, as can be seen in figure 1.1. Since a tumor often has a lower oxygensaturation and a higher vascularity than the surrounding tissue, the absorption oflight in the tumor tissue is higher, and thus more light is absorbed. The propagationof light is affected by the tumor and an altered light field at the surface of the objectcan be observed.

Figure 1.3: Absorption coefficient of hemoglobin for different oxygen saturationlevels

In this project the transmission mode was applied for NIROT measurements sincethe measurements are more robust because no reflected light hits the camera. Also,the sensors do not saturate quickly in transmission mode, since the light first hasto travel through the tissue and smaller intensities are measured. The measuredlight, however, contains more relevant information about the tumor, what results inhigher distinct contrast. By sequential scanning of the medium surface the depthof the tumor can be reconstructed, since the tissue is illuminated from differentsource positions, i.e. different angles. By knowing the position of the sources, a3-dimensional model of the tissue can be created.

The implementation of the algorithm for the reconstruction of a tumor in the tissuewas one of the objectives in this thesis. The code was implemented in Matlab.

1.2 FMT

FMT is an established method for preclinical research of molecular processes insmall animals [7][8][9]. Fluorescence describes the effect of light emission of certainmolecules, after the absorption of photons at shorter wavelengths [10]. In figure 1.4the emission and excitation spectra of a fluorescence protein are shown. In biologicaltissue naturally weak fluorescent proteins are produced due to spontaneous photonemissions (SPE) during oxidative metabolic reactions, which generate a weak auto-luminescence [11]. However, this autoluminescence can not indicate on the location

Chapter 1. Introduction 4

of a tumor in the tissue. As a consequence, artificial fluorescence proteins have tobe used.

Figure 1.4: Spectrum of a sample fluorescence molecule. Blue: Excitation spectrumin which the photons are absorbed. Red: Emission spectrum in which the pho-tons are reemitted. https://www.chroma.com/sites/default/files/uploads/

3_GenericFluor-2.png

Three different groups of fluorescent agents exist: (1) unspecific, (2) targeted and(3) activated [12]. The unspecific agents, e.g. indocyanine green (ICG), do not bindto specific molecules, but rather circulate arbitrarily in the bloodstream. Due toperfusion those agents are concentrated in highly blood-supplied regions, e.g. tu-mors. The targeted and activated agents contain antibodies, which bind to specifictargets. While the targeted agents always fluoresce when they are irradiated, theactivated agents must first bind to a target molecule. Therefore, with targeted andactivated agents the distribution of specific molecules in the blood, e.g. the hypoxiainducible factors (HIF), can be measured.

In this thesis a targeted agent was used. In blood of hypoxic tissue more HIFs arepresent, because they are not degraded. The HIFs regulate a number of enzymes,which trigger mechanisms for the cell survival in hypoxic conditions. The HIFsthen bind to hypoxia response elements (HRE), which are promoters on the DNAin the cell. Binding of these two substances initiates the binding of the fluorescenceprotein. In FMT hypoxia is expressed by the binding of HIF to HRE. Since thefluorescence emission is measured, no quantitative statement is possible about howhypoxi the tumor is. [12].

FMT measurements are normally performed with a continuous wave laser source.Since the excitation and the emission of the fluorescence proteins are at differentwavelengths (see figure 1.4), the light distribution at both wavelengths can be de-tected by filtering the light with a bandpass filter. Therefore, two measurementsmust be performed, one for the excitation when the photons are absorbed by thefluorescence molecule and one for the emission when the photons are re-emitted dueto relaxation of the electrons in the molecule. Here, the reflection mode was appliedwhere reflected light does not disturb the measurements since filters are applied.Also, a measurement takes less time to conduct than in transmission mode.

The reconstruction algorithm for FMT was provided by the Animal Imaging Center(AIC) at ETH Zurich and is based on the work of Jorge Ripoll. F. Stuker presentsthe algorithm in detail in his dissertation [6].

5 1.3. Project description

1.3 Project description

Since both methods allow the detection of hypoxia in biological tissue, it is ofgreatest interest to correlate these two methods. To our knowledge, there did notexist a study comparing hypoxia measurements performed with NIROT and FMT.The objective of this thesis was therefore the performance of FMT and NIROTmeasurements and the comparison of the results. To reach this objective threesubtasks had to be fulfilled:

• Implement a reconstruction algorithm for NIROT with wavelength normal-ization

• Integrate a new tunable supercontinuum laser in an FMT setup and adapt itfor NIROT

• Perform hypoxia measurements on mice with FMT and NIROT.

All three subtasks were necessary to reach the final objective of this project. Themost work was invested in the development of the novel reconstruction method forNIROT. Subsequently, the three tasks will be discussed in more detail.

Implement a reconstruction algorithm for NIROT with wavelength nor-malization

A novel NIROT reconstruction approach was implemented and tested. The new al-gorithm made use of the principle of wavelength normalization, for which the objectwas illuminated at four instead of two wavelengths. For that the standard Rytovsolution was extended with a second measurement and the simulated term of thehomogeneous light field in the phase of the tumor removed.

Chapter 2 introduces this novel algorithm. At the beginning of this chapter thecalculation of the light distribution in a slab and the standard Rytov solution arepresented (chapter 2.1). The equations of the novel algorithm are derived in chapter2.2 and in chapter 2.3 a parameter study as well as a 3-dimensional reconstructionare shown.

Integrate a new tunable supercontinuum laser in an FMT setup andadapt it for NIROT

Various hybrid systems including FMT or NIRS have been developed in the past:FMT/MRI [13], FMT/PET [14], FMT/CT [15], NIRS/MRI [16], NIRS/PET [17].Although FMT and NIROT are based on a very similar instrumentation, the twomethods have never been combined in one setup so far.

To perform measurements with both methods, a hybrid NIROT/FMT setup hadto be implemented during this project. An FMT setup was provided by the AIC,which was adapted for our purposes. This mainly included the integration of a newtunable supercontiuum laser, which is able to emit near-infrared light at a tunablewavelength.

In chapter 3.1 the structure of the existing setup is presented and the new super-continuum laser compared with another device, which is available at the lab.

Chapter 1. Introduction 6

Perform hypoxia measurements on mice with FMT and NIROT

After the completion of the first two tasks, measurements were performed on mice.Two nude mice, both suffering from a hypoxic, subcutaneous tumor in the rightflank, were used as specimen.

The objective was to investigate the correspondence between NIROT and FMT.Since both methods promise to measure hypoxia similar results must be expected.It has to be considered that with FMT no quantitative measurements of hypoxiacan be made and, therefore, only the topography of the results were compared.

This thesis should be a first step to the exact definition of hypoxia, since until todaya qualitative definition of hypoxia does not exist. By measuring hypoxia by HIFexpression as well as oxygen saturation, a method for the qualitative definition ofhypoxia may be found.

In chapter 4 measurements obtained with two mice are presented and discussed indetail.

Based on these results in the last chapter 5 a conclusion and an outlook will begiven.

Chapter 2

NIROT reconstructionalgorithm

The theory of the novel NIROT reconstruction algorithm with wavelength normal-ization is presented in this chapter. The first part of this chapter presents theforward simulation of the light distribution in a highly scattering medium. In thesecond part, the equations of the novel approach are derived and the novel algo-rithm given. At the end of this chapter, a feasibility check of the novel algorithm isperformed.

The subsequent theory is mainly based on the PhD thesis of Maureen A. O’Leary,where the basics of Diffuse Optical Tomography (DOT) is explained in detail [4].

2.1 Diffusion equation

The light propagation in tissue at near-infrared wavelengths is diffusely and it canbe modeled accurately with the diffusion equation [4] [18]:

∂U

∂t+ νµaU(r, t) +∇ · J(r, t) = q0(r, t). (2.1)

U(r, t) describes the photon density [#photons)mm3 ], J the photon current density [#photons)mm∗s ]

and q0(r, t) the source term from the laser [#photons)mm3∗s ]. The term v is defined as thespeed of light in the medium and µa is the absorption coefficient in the medium. r isthe 3-dimensional position in the tissue. This equation is valid for the assumption,that the distance between the source and detector is much greater than the photonmean free path.

The photon mean free path is the distance that light penetrates into a diffusemedium before its photons begin to be scattered [19]. It follows that the origin ofthe light source can not be assumed at the surface of the object, but must be shiftedsome millimeters inside the medium. The mean free path length is defined as thereciprocal of the scattering coefficient µs:

mfp = 1/µs. (2.2)

The scattering coefficient µs can be expressed by the reduced scattering coefficientµs′ . The reduced scattering coefficient describes how often a photon is scatteredalong a dimensional unit [cm−1]. The reduced scattering coefficient and the scat-tering coefficient are connected by the anisotropy factor g:

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Chapter 2. NIROT reconstruction algorithm 8

µ′s = µs(1− g), (2.3)

where g is assumed to be equal to 0.9 [4]. The anisotropy factor is an indicator ofhow much of the incident light is scattered.

2.1.1 Homogeneous medium

In this section the diffusion equation 2.1 is solved for a homogeneous medium. Thetissue is assumed to have the same absorption and scattering coefficient at eachposition.

The photon current density ∇J in equation 2.1 can be substituted by using Fick’slaw:

∇J(r, t) = ∇ · (D∇U(r)), (2.4)

where D is the diffusion coefficient and includes the reduced scattering coefficientµs′ :

D =ν

3µ′s. (2.5)

Since the measurements are performed in the continuous wave mode, the time de-pendency of all terms fall away. Therefore, the term ∂U

∂t becomes zero and thesource term can be written time-independently:

∂U

∂t= 0, (2.6)

q0(r, t) = Aδ(r). (2.7)

A is the intensity of the emitted light from the laser source, δ(r) is the dirac function.

For constant µa and D values the diffusion equation 2.1 can then be rewritten as:

(∇2 − k2)U(r, t) = Aδ(r), (2.8)

where

k =

√νµaD

. (2.9)

The solution to this Helmholtz equation is a standard physical problem and has thefollowing form in an infinite medium:

U0(r) = Ae−kr

4πDr. (2.10)

2.1.2 Heterogeneous medium

Tumors have different optical properties than their surrounding tissue. It is possi-ble to write the total tissue absorption µa(r) as a combination of the backgroundabsorption coefficient µ0

a and the contribution to the absorption coefficient of thedifferent structures embedded in it δµa(r):

µa(r) = µ0a + δµa(r). (2.11)

Different approaches exist to calculate the light distribution in a heterogeneousmedium. The two methods discussed by O’Leary [4] in chapter 4 are the Born and

9 2.1. Diffusion equation

the Rytov approximations. For continuous wave applications these methods arevery similar. During this thesis, the Rytov approximation is applied, because it isan exponential approach, which is necessary for the success of the novel reconstruc-tion algorithm.

With Rytov approximation the total light intensity U(r) can be written as a com-bination of the homogeneous field U0(r) and the perturbation of the tumor φ(r) onit:

U(r, rs) = U0(r, rs)eφ(r). (2.12)

The detailed derivation of the Rytov solution for continous-wave measurements canbe found in the dissertation of O’Leary [4] in chapter 4.3. With the assumption that∇φ(r, rs))

2 << O(r) the solution of the heterogeneous problem has the subsequentform:

φ(r, rs) = − 1

U0(r, rs)

∫G(r− rd)O(r)U0(r, rd)d

3r, (2.13)

where

O(r) =νδµa(r)

D. (2.14)

rs is the position of the source, rd is the position of the detector and G(r − rd) isthe Green’s Function. In an infinite medium the Green’s function is defined as:

G(r− rd) =eik|r−rd|

4π|r− rd|. (2.15)

After discretization of equation 2.13, when the medium is divided into n voxels, weobtain an equation system in which the light measurements at the surface of themedium (left side of equation) and the optical properties of the tissue are connected:

φ(rsi, rdi) =

n∑j=1

G(r − rdi)O(rj)U0(rsi, rj)h3, (2.16)

where h3 is the volume of a voxel. The right side of this equation can be expressed asa weight matrix W and an array δµa(r), which are our unknown tissue properties:

φ(rs1, rd1)...

φ(rs2, rdm)...

φ(rsl, rdm)

=

W11 · · · W1n

.... . .

...W(l∗m)1 · · · W(l∗m)n

δµa(r1)

...δµa(rn)

, (2.17)

where

Wij =G(rdi, rj)U0(rsi, rj)vh

3

U0(rdi, rsi)D. (2.18)

The equation system 2.17 will be referred to in its simpler form in the next chapters:

φ(rs, rd) = Wδµa(r). (2.19)

The term on the left side φ(rs, rd) is a combination of the measured total fieldU(rs, rd) and the simulation of the homogeneous field U0(rs, rd)

φ(rs, rd) = ln(U(rs, rd))− ln(U0(rs, rd)). (2.20)

Chapter 2. NIROT reconstruction algorithm 10

Light distribution in bounded media

The light distribution in a finite medium is obtained by adding boundary conditionsto the solution of an infinite medium. Equation 2.10 and 2.17 are expanded withthe boundary conditions at the surface. In this section, first the solution for a semi-infinite medium and afterwards for a slab is given. The semi-infinite medium hasone boundary in positive z-direction, while the slab is restricted in both z-directions(see figure 2.1).

(a) (b)

Figure 2.1: Source positions for different geometries. (a) Semi-infinite medium: theblack point indicates the original light source, the white point is the virtual source.(b) Slab: The black point in the slab is the original light source. The originallight source is mirrored by the white points closest to it. The virtual sources areagain mirrored on the opposite surface (black points), etc.. d is the thickness of themedium. Adapted from Patterson et al. [18]

Patterson et al. [18] presented an approach to model the light distribution inbounded objects. The idea is to control the photon flux at the surface of theobject. The photon flux is changed by creating virtual light sources. The virtuallight sources are the mirror image of the original light sources at the surface. Whena source is mirrored one to one, a photon flux of zero is created at the surface. This,however, would indicate that only total internal reflection according to Snell’s Lawis present. Since this is not consistent with the reality, the position of the virtualsource has to be shifted slightly away from from the surface to generate a photonflux out of the medium.

In the case of the semi-infinite medium two light sources exist, the original source atposition rs and the imaginary source at position rim. In figure 2.1 the black pointindicates the original source and the white point indicates the mirrored, virtual

11 2.1. Diffusion equation

source. The solution for this semi-infinite medium is written as a superposition ofthe two light sources:

U0(r) =Ae−k|r−rs|

4πD|r − rs|+

Ae−k|r−rim|

4πD|r − rim|. (2.21)

The approach for a slab functions in a similar way as for the semi-infinite medium.The original source has to be mirrored at both surfaces. The two virtual sources,however, influence the photon flux at their opposite surface. Therefore, they needto be mirrored again at the opposite surface (see figure 2.1 (b)). The new virtualsources again disturb the flux at the opposite surface. This mirroring process needsto be repeated infinite times. The light distribution in a slab can be written as:

U0(r) =A

4πD

∞∑i=1

e−k|r−ri|

|r − ri|, (2.22)

where ri is a variable defining the position of the original and all mirrored sources.In practice, the contribution of multiple mirrored sources is negligible small, and,thus, a repetition rate of the mirroring process of 10 times was implemented.

Chapter 2. NIROT reconstruction algorithm 12

2.2 NIROT reconstruction with wavelength nor-malization

Many factors can disturb the homogeneous light propagation in a real object. Forexample, the shape of the object may be uneven or the background tissue can beinhomogeneous due to internal organs. Furthermore, the instrumentation may in-duce noise and inaccuracies in the measurements. Since there are many unknownsin a real medium, it is impossible to accurately simulate the homogeneous lightdistribution.

(a) (b)

(c) (d)

(e)

Figure 2.2: Comparison between a homogeneous and heterogeneous medium. (a)Homogeneous slab. (b) Heterogeneous slab with tumor. (c) Homogeneous lightfield. (d) Total light field. (e) Cross section through the light fields in (c) and (d)showing the intensities of the homogeneous and total field along the medium.

In figure 2.2 a simulation of two different slabs is shown; one slab has homogeneous(a) and one heterogeneous (b) tissue properties. For both media the light distribu-tion at the surface are simulated in (c) and (d). The light fields resemble each otherstrongly. By taking a cross section of the light fields in (c) and (d), a comparison

13 2.2. NIROT reconstruction with wavelength normalization

between them is presented in (e). The blue and red curve indicate the homogeneousand total light intensity along the surface of the slab. In figure 2.2 (e) the differencebetween the total and homogeneous fields is highlighted; the difference for that caseis approximately 7%.

Because the difference between homogeneous and total field is small and the ac-curate simulation of the homogeneous light field impossible, a NIROT algorithmwas deduced which gets rid of the simulated term ln(U0(rs, rd)). An expressioncontaining only measured data should be obtained.

In the novel NIROT algorithm two datasets φλ1 and φλ2, i.e. two measurements attwo wavelengths, with identical homogeneous fields are subtracted. If the homoge-noeus fields are identical the terms ln(Uλ10 (r)) and ln(Uλ20 (r)) can be eliminated.An expression, which only consists of measured data, remains:

φλ1−λ2(r) = φλ1(r)− φλ2(r)

=[ln(Uλ1(r))− ln(Uλ10 (r))

]−[ln(Uλ2(r))− ln(Uλ20 (r))

]= ln(Uλ1(r))− ln(Uλ2(r))

= ln

(Uλ1(r)

Uλ2(r)

).

(2.23)

Since one measurement is divided by the other, this approach is called NIROT re-construction with wavelength normalization.

In order to obtain two datasets with identical homogeneous fields, the extinctioncoefficient k at the two measured wavelengths must be identical. The light distribu-tion in tissue depends exponentially on the wavenumber k: U(r) ∝ e−kr. Therefore,the light distribution is wavelength-dependent on k. Equation 2.9 can be expressedby the absorption coefficient µa and the scattering coefficient µs at two wavelengths.The absorption coefficient is measured at the wavelength and the scattering coeffi-cient is available from previous studies.

kλ1 = kλ2 (2.24)

µλ1a µλ1s = µλ2a µ

λ2s (2.25)

In figure 2.3 an example is given on the selection of the correct wavelength. Twoabsorption curves are shown; one for the background tissue (green) and one forhypoxic tissue (red). Assuming that the tumor has a much smaller oxygen satura-tion than the healthy tissue, an oxygenation of 75% for the healthy tissue and anoxygenation of 25% for the hypoxic tissue is chosen. In this example it is clearlyvisible that there are several wavelengths at which the extinction coefficient k isthe same, since there are four intersection points between the green curve and theblue line. When illuminating at the wavelengths of the first two intersection points,which is in the optical window between 650 nm and 900 nm (see figure 1.1), thehomogeneous light fields are identical. In this case the equation 2.23 is true and thesimulated light fields are eliminated. As the tumor has a different absorption curvethan the background tissue, the ratio between the two measurements will providea contrast that is exclusively produced by the tumor.

In a real object the same behavior can be observed. The healthy tissue has aswell a higher absorption coefficient than the tumor and a contrast can be expectedwhen the ratio of two measurements is calculated. The absorption coefficient of the

Chapter 2. NIROT reconstruction algorithm 14

Figure 2.3: Extinction coefficient for healthy (green) and tumor tissue (red). In thisexample the healthy tissue was given an oxygenation of 75% and the tumor tissue of25%. The oxygenation of the healthy tissue is obtained in previous measurements.When fixing one wavelength at 850 nm the second wavelength can be obtained bydrawing a horizontal line (blue line); in this case it is 678 nm. The homogeneousfields at these two wavelengths would be identical. Since the tumor has a differentabsorption curve, the ratio total fields are different.

healthy tissue can be determined by comparing a measurement, where the tumordoes not influence the measured light field, with the simulation of the homogeneouslight field. By varying the extinction coefficient k the error between measurementand simulation can be minimized and the homogeneous tissue properties derivedwith an a priori defined scattering coefficient. The absorption curve of the hypoxictissue is the unknown which must be calculated with the reconstruction algorithm.

Based on the subtraction in equation 2.23 a new equation system can be established:

φλ1−λ2(r) = Wλ1δµλ1a (r)−Wλ2δµλ2a (r). (2.26)

The weight matrices Wλ1 and Wλ2 are not identical, since they depend on µa andµs, which vary with the wavelength. In order to calculate the concentration of oxy-and deoxy-hemoglobin, equation 2.23 needs to be transformed. The substitution

δµa(r) = εHHb ∗ δCHHb(r) + εO2Hb ∗ δCO2Hb(r) (2.27)

is applied, where εO2Hb and εHHb are the molar absorption coefficients of oxy- anddeoxy-hemoglobin and CO2Hb and CHHb are their corresponding concentrations.

The previous equations can each be expressed in matrix form as:

δµa,n×1(r) =[EHHb,n×n EO2Hb,n×n

] [ δCHHb,n×1(r)δCO2Hb,n×1(r)

], (2.28)

where

EHHb =

εHHb 0 · · · 0

0 εHHb · · · 0...

.... . .

...0 0 · · · εHHb

(2.29)

15 2.2. NIROT reconstruction with wavelength normalization

and

EO2Hb =

εO2Hb 0 · · · 0

0 εO2Hb · · · 0...

.... . .

...0 0 · · · εO2Hb

. (2.30)

With the substitution 2.28 the original equation 2.26 can be rewritten as:

φλ1−λ2(r) = Wλ1[Eλ1HHb Eλ1O2Hb

] [ δCHHb(r)δCO2Hb(r)

]−Wλ2

[Eλ2HHb Eλ2O2Hb

] [ δCHHb(r)δCO2Hb(r)

] . (2.31)

The final equation for one dataset, which comprises two wavelengths, is obtained:

φλ1−λ2(r) =[

Wλ1−λ2HHb Wλ1−λ2

O2Hb

] [ δCHHb(r)δCO2Hb(r)

], (2.32)

where

Wλ1−λ2HHb = Wλ1Eλ1HHb −Wλ2Eλ2HHb (2.33)

and

Wλ1−λ2O2Hb

= Wλ1Eλ1O2Hb −Wλ2Eλ2O2Hb. (2.34)

Since two independent equation systems are required for the correct reconstructionof the unknown hemoglobin concentrations in the tissue, a second dataset needs tobe added: φλ1−λ2(r)

φλ3−λ4(r)

=

Wλ1−λ2HHb Wλ1−λ2

O2Hb

Wλ3−λ4HHb Wλ3−λ4

O2Hb

δCHHb(r)

δCO2Hb(r)

. (2.35)

The first dataset uses measurements at wavelenths λ1 and λ2, the second datasetat wavelenths λ3 and λ4 . The solution to this ill-posed problem can be found bycalculating the inverse solution with a standard least squares approach. During thisthesis a normal least squares approach is used [20].

Chapter 2. NIROT reconstruction algorithm 16

2.3 Simulation

Before measurements with real mice were performed, a small validity check on thenovel NIROT reconstruction algorithm was conducted. Because no publicationsexisted about this novel algorithm, it was checked if this approach delivers sensibleresults and further work can be invested in the development of this algorithm.

In this section, first the properties of mouse tissue are defined by means of a lit-erature research. Also, important points of the simulation are discussed. In aparameter study the influence of different parameter on the contrast were investi-gated. To check the validity of the algorithm a 3-dimensional reconstruction of asphere in a slab was conducted.

2.3.1 Characteristics

Previously, the results of the literature research are presented and important pointsof the simulation discussed.

Scattering Coefficient

Krainov et al. [21] studied the optical properties of mice. Figure 2.4 shows thereduced scattering coefficient of internal organs of nude mice measured in theirstudy. The curve depicts a mixture of internal organs, containing muscles, thebowel and the liver. A decent wavelength-dependent decay of the reduced scatteringcoefficient can be observed; the coefficient drops from about 8 cm−1 at 700 nm toabout 7 cm−1 at 1100 nm. A linear fit was calculated in order to obtain the reducedscattering coefficient at any given wavelength within this range:

µs = 8cm−1 − (8cm−1 − 7cm−1)

(1100nm− 700nm)∗ (λ− 700nm)

= 8cm−1 − 0.0025 ∗ (λ− 700)cm−1,

(2.36)

where λ is the wavelength at which the measurement is performed.

Figure 2.4: Reduced scattering coefficient of internal organs of mice. Adapted fromKrainov et al. [21]

17 2.3. Simulation

Absorption Coefficient

No significant difference between the absorption curve of oxy- and deoxy-hemoglobinfor mice or humans exists [22]. Consequently, the well-studied absorption curve ofhumans was used (data available from the BORL).

The units of the molar absorption coefficient εO2Hb/εHHb are given in 1mM∗mm

(see figure 1.1). As we are interested in the absolute absorption coefficient µa(units: 1

mm ), the oxy- and deoxy-hemoglobin concentrations CO2Hb/CHHb have tobe multiplied with the specific absorption coefficients εO2Hb/εHHb:

µa = εHHb ∗ CHHb + εO2Hb ∗ CO2Hb (2.37)

The amount of hemoglobin in blood was assumed to be constant, as it only changesslightly from animal to animal. The total hemoglobin concentration in blood isnormally given in g

L and has to be transformed to mmolL . An average value of

hemoglobin in blood of 150 gL and a molar mass of hemoglobin of 64.4 g

mmol wasused [23]. The hemoglobin in blood has therefore a constant value equal to 2.33mmolL .

Blood Concentration

It was assumed that the blood distribution in a mouse is homogeneous and, thus,only the tumor has a different blood concentration.

Since a mouse body contains in average about 6% blood, this value was taken asthe homogeneous blood concentration CHB [23]. According to Bernsen et al. [24] theconcentration of blood in a glioma may vary between 7% and 14%. This implies thatthe blood concentration of the tumor may be nearly identical to the surroundingtissue, but as well be twice as high. An initial value of 10% for the tumor bloodconcentration CTH was chosen and a variation between 6% and 14% applied.

Oxygen Saturation

A lack of a golden standard for measuring the oxygenation in biological tissue wasobserved, because different methods were applied to measure hypoxia in tumors[25][26][27][28]. The values strongly fluctuated depending on the used instrumen-tation. Adapting the suggestion of Steen et. al. [25], who measured the tissueoxygenation with NIRS, an average value of 75% was chosen for the oxygenation ofthe healthy tissue StO2H (see the orange curve in figure 1.3).1

Large fluctuations of the tumor tissue oxygenation were found, ranging from 10%[1] to 64% [25]. As initial condition, a tumor oxygenation StO2T of 50% was chosen.The variation on the tumor oxygenation used in our simulation ranged from 10%to 70%.

Medium geometry

The thickness of the slab was set to 2 cm, which approximately corresponds to thethickness of a mouse trunk. The region of interest on the slab was restricted to asquare with a size of 2 cm × 2 cm.

1The oxygenation is sometimes given in mmHg, which is transformed to a percentage withthe help of the hemoglobin oxygen dissociation curve [29]. An online calculator can be foundonhttp://www-users.med.cornell.edu/ spon/picu/calc/o2satcal.htm

Chapter 2. NIROT reconstruction algorithm 18

Tumor geometry

A subcutaneous tumor close to the surface was simulated. Therefore, a sphericalobject with tumor properties was located in the center of the 2 cm × 2 cm squareat a depth close to the surface. The tumor had an initial size of 5 mm and a depthof 5 mm. The tumor radius rz was varied between 1 mm and 4 mm and the depthzT between 5 mm and 10 mm.

Segmentation

The region of interest was divided into 25×25×12 voxels. A higher segmentation,e.g. 64×64×32 voxels, would have been possible, but pre-runs showed no significantimprovement on the accuracy of the reconstructed values. The computation timewas significantly shorter with a smaller segmentation, but this compromised theaccuracy of the reconstructed shape.

Wavelength Selection

Two matching wavelengths were selected for which the homogeneous light fieldswere equal. We decided to fix one wavelength at a constant value and to adjust theother wavelength.

In order to obtain a high contrast the tumor must absorb much light at one wave-length and few light at the the other one. A large heterogeneous absorption co-efficient for one wavelength and a small coefficient for the other wavelength aremeasured, when the fixed wavelength ranges between 830 nm and 900 nm and thevariable wavelength is chosen below 750 nm [30].

Since the efficiency of the camera drops at longer wavelengths, the two fixed wave-lengths were chosen at 830 nm and 850 nm. For oxygen saturations below 50%no intersection point can be found for wavelengths below the isosbestic point and,thus, the oxygen saturation of the healthy tissue must never drop below 50%.

During the parameter study, additionally the results at two other fixed wavelengths,at 750 nm and 798 nm, were studied in order to compare the contrast obtained atthese wavelengths.

2.3.2 Contrast comparison

An overview on the investigated parameters can be found in table 2.1. The influenceof different parameters on the contrast is shown in the subsequent section.

Parameter Initial case VariationFixed wavelength λf [nm] 850 750, 798, 850Concentration of blood in homogeneous medium CHB [%] 6 -Concentration of blood in tumor CTB [%] 10 6-14Oxygenation of blood in homogeneous medium StHO2

[%] 75 -

Oxygenation of blood in tumor StTO2[%] 50 10-70

Radius of tumor rT [mm] 2 1-4Depth of tumor zT [mm] 5 5, 10Scattering coefficient at 700 nm µs[1/mm] 80 -Scattering coefficient at 1100 nm µs[1/mm] 70 -

Table 2.1: Definition of parameters

19 2.3. Simulation

Initial Case

In the figures 2.5/2.6 (a) and (b) the light fields on a homogeneous and heteroge-neous slab are shown. The light fields were obtained by locating each detector onsame position as the source at the opposite side of the slab and by measuring onlythe the intensity of the opposed source. A strong resemblance between the twolight fields can be observed for both wavelengths. In (c) a cross-section throughthe middle of the fields (a) and (b) are shown and the small difference between thelight intensities seen. The ratio of the two curves in (d) results in a contrast whichshows the influence of the tumor. In figure 2.5 (d) the perturbation of the tumoron the homogeneous field is 10% and in figure 2.6 (d) it is 4%.

(a) (b)

(c) (d)

Figure 2.5: Comparison of the homogeneous and total light field at 678 nm. (a)Homogeneous light field U0. (b) Total light field U . (c) Cross section through thelight fields in (a) and (b). (d) Contrast at 678 nm, defined as U/U0.

In figure 2.7 the ratio of the curves 2.5 (d) and 2.6 (d) is shown. This curve indicatesthe contrast between the total field at 678 nm and the total field at 850 nm andis required for the novel reconstruction algorithm according to equation 2.23. Amaximum contrast of 7% can be derived from this figure. This value lies is exactlybetween the results of the single wavelength measurements of 4% and 10%. Since nosimulation is needed to obtain this contrast, this novel NIROT algorithm promisesaccurate results.

Chapter 2. NIROT reconstruction algorithm 20

(a) (b)

(c) (d)

Figure 2.6: Comparison of the homogeneous and total light field at 850 nm. (a)Homogeneous light field U0. (b) Total light field U . (c) Cross section through thelight fields in (a) and (b). (d) Contrast at 850 nm, defined as U/U0.

Figure 2.7: Ratio of the total fields Uλ1/Uλ2. The total fields are simulated at 678nm and 850 nm and have identical homogeneous fields.

Parameter variation

The variation of four tumor parameters was evaluated: the oxygen saturation, theblood concentration, the tumor size and the tumor depth. The maximum con-trast for the different cases was calculated. The maximum contrast is defined asthe maximum difference of the contrast, e.g. the maximum range in figure 2.7 (7%).

21 2.3. Simulation

In figure 2.8 the maximum contrast for different tumor oxygen saturations is shown.The contrast decreases with increased oxygen levels. While for a small tumor oxy-genation of 10% a contrast of up to 18% can be expected, the contrast falls below2% for a tumor oxygenation of 70%. No contrast would be received for a tumoroxygenation of 75%, because then the healthy tissue and the tumor have exactlythe same oxygen saturation. The highest contrast is obtained at 850 nm; the valuesat 798 nm are two times smaller and at 750 nm even three times. This behavior isconsistent with the theory, because the difference between the absorption coefficientat the variable wavelength and the absorption at the fixed wavelength is the largestat 850 nm.

Figure 2.8: Maximum contrast value for different tumor oxygenations

Figure 2.9 shows the contrast dependent on different hemoglobin concentrations.The trend can be seen that the contrast increases with a higher tumor vascularity.It can again be observed the results at 850 nm are better than at 750 nm and 798nm.

Figure 2.9: Maximum contrast value for different tumor blood concentrations

In figure 2.10 the variation of the tumor size is shown for two depths. In (a) thesimulation is performed at a tumor depth of 5 mm and in (b) at a depth of 10 mm.

Chapter 2. NIROT reconstruction algorithm 22

The contrast in (a) is higher than in (b), because the effect of the tumor is smallerdue to the diffuse light propagation. The maximum contrast at zT =10 mm is 25%smaller than at zT =5 mm. Also, it can be seen that the contrast grows exponen-tially with increased tumor size. While nearly no contrast can be measured at aradius of 1mm, the contrast skyrockets for higher radii to a maximum contrast ofnearly 40%. The measurements at 750 nm and 798 nm again deliver worse resultsthan at 850 nm.

(a) zT = -5 mm (b) zT = -10 mm

Figure 2.10: Maximum contrast value for different tumor radii. (a) The tumor islocated in a depth of zT=-5mm. (b) The tumor is located in a depth of zT=-10mm.

23 2.4. Conclusion

2.3.3 Reconstruction

A validation check of the novel reconstruction algorithm was implemented. A spherein a slab was simulated: first the forward simulation of the light distribution in aslab was performed, afterwards the inverse problem was solved with the novel recon-struction algorithm. In the forward simulation the light distribution in the slab wascalculated for four wavelengths (see equation 2.35). A segmentation of 18×18×15voxels and 5×5 source points were used to decrease the computational effort. Thetissue properties from table 2.1 were used; only a changed radius of 2.5 mm was im-plemented. The inverse problem was solved with a standard least squares approach.

In figure 2.11 the reconstruction of the oxy- and deoxy-hemoglobin in the slab ispresented according to equation 2.35. Since the influence of the tumor is of interest,the absorption of the background tissue is neglected during this reconstruction andonly the hemoglobin difference between the tumor and the healthy tissue. The greenspheres represent the exact simulation of the tumor. They have an oxy- and deoxy-hemoglobin concentration of -0.116 mmol/L and 0.815 mmol/L respectively. Thered and blue spheres inside the green ones represent the reconstructed hemoglobinconcentrations δCO2Hb and δCHHb.

The shape of the reconstruction match very accurately with the forward simulation.The reconstruction has a spherical shape and sharp boundaries. The algorithm has,however, the slight tendency to be superficial. The magnitude of the reconstructionis in the same range as the exact values, an error between 10% -20% was observed.

(a) (b)

Figure 2.11: Reconstruction of the oxy- and deoxy-hemoglobin in the tumor. Theconcentrations are given in mmol

L .

2.4 Conclusion

In this chapter the novel NIROT reconstruction algorithm with wavelength normal-ization was presented. The algorithm enables an easier NIROT reconstruction, sincethe homogeneous simulation of the tissue can be eliminated. Different influences onthe expected contrast of the novel algorithm were investigated. The simulation of asphere in a slab revealed a good performance of this approach, since it was possibleto reconstruct the shape of the simulated sphere accurately and since the values

Chapter 2. NIROT reconstruction algorithm 24

showed an error of 10% - 20%.

Further improvements to increase the accuracy of the reconstruction could be im-plemented in the future. For example advanced inversion techniques might be used,e.g. subspace-preconditioned least squares [31], or measurements with more sourcepoints performed.

Chapter 3

Combined FMT and NIROTsetup

After the implementation of the novel NIROT algorithm a setup has been imple-mented, which was able to perform both NIROT and FMT measurements. Anexisting FMT setup was adapted for this purpose. At the beginning of this chap-ter the experimental setup will be presented. The functionality of supercontinuumlasers is introduced and a new laser system characterized in this chapter.

3.1 Experimental setup

Figure 3.1: Schematic view of the FMT setup. Stuker et al. [?]

In figure 3.1 a schematic view of the FMT setup is shown [6]. The setup wasprovided from the AIC. Four laser sources with four different wavelengths were in-tegrated in the setup. The wavelength was selected with help of the fiber switch.The laser light passed through a collimation and a focal lens and was measured

25

Chapter 3. Combined FMT and NIROT setup 26

by a power meter. The illumination mode, i.e. transmission or reflection mode,was adjusted with the reflecting mirrors and the scan head. With the scan headthe position of the laser source was controlled. The surface of the mouse was se-quentially illuminated in a grid-like pattern. The light penetrated at each sourcepoint into the specimen and distributed diffusely in the medium. Depending on themethod either the re-emitted photons from the fluorescence protein were measured(in FMT) or the absorption of the tissue detected (in NIROT). The light passedthrough a filter wheel, with which in FMT the excitation or emission light was re-moved. The CCD-camera measured for each source point the light distribution onthe surface of the specimen. The recorded data was saved on a desktop computer.The software for performing the measurements was written on Labview, while thedata processing was implemented in Matlab.

The quantum efficiency of the camera1 can be seen in figure 3.2. In the range be-tween 650 nm and 850 nm the efficiency is always above 50% and therefore a goodsignal-to-noise ratio can be expected. For wavelengths above 850 nm the quantumefficiency drops quickly.

For the new reconstruction method the selection of a wavelength in the spectrumbetween 650 nm and 850 nm was required. Tunable supercontinuum lasers providethis property and therefore a new laser system was integrated in the experimentalsetup. In chapter 3.2.1 characteristic measurements of two supercontinuum lasersare presented. Based on these measurements one of the two laser system was ac-quired.

Figure 3.2: Quantum efficiency e of the CCD-camera Andor DV434-BV ftp://

ftp.aerodyne.com/users/Jones/NASA/DV434.pdf

3.2 Laser characterization

Subsequently, an introduction into the functionality of supercontinuum lasers willbe given and the measurements with two supercontinuum systems presented.

1Andor DV434-BV

27 3.2. Laser characterization

3.2.1 Theory

A supercontinuum system consists of two main parts: the supercontinuum lasersource and the acousto-optic tunable filter (AOTF).

Light from a fiber laser (see figure 3.3, blue line) enters a Photonic Crystal Fiber(PCF). The PCF is a dispersive optical fiber with a hollow core [32]. Photoniccrystals inside the fiber refract the light and produce white light by applying non-linear effects, e.g. Raman scattering or soliton based dynamics [33][34]. In the PCFthe spectrum of the light is broadened to several hundred nanometers (red line).One wavelength is selected by filtering the whole spectrum with the help of an theAOTF (green line).

Figure 3.3: Different spectra of the supercontinuum laser system. Blue is thespectrum of the fiber laser (pump source), red the spectrum after the super-continuum laser and green the emission after the AOTF. Adapted from http:

//en.wikipedia.org/wiki/Supercontinuum

In figure 3.4 the principle of an AOTF is presented. Sound waves, which are gen-erated by a tunable piezoelectric transducer (RF signal generator), generate vibra-tions in a quartz crystal [35] [36]. The quartz crystal diffracts the incoming lightfrequency-dependent and splits it into its components. A beam stopper absorbs allwavelengths except the diffracted one.

3.2.2 Measurements

Two supercontinuum systems, each consisting of a laser source and an AOTF, werecompared. One of the systems was developed by NKT Photonics 2, the other sys-tem was manufactured by Fianium3. The specifications of the two systems werenearly identical. The main difference was the higher power, i.e.8 Watt instead of5.5 Watt, of the Fianium system.

2http://www.nktphotonics.com/: NKT EXR-153http://www.fianium.com/: Fianium SC450

Chapter 3. Combined FMT and NIROT setup 28

Figure 3.4: Block diagram of an AOTF-based multispectral imaging instrument.Adapted from Vila-Frances et al. [35]

The data was recorded with a single photon avalanche diode (SPAD), developed byNiclass et al. [37]. The sensor contained a time-to-digital-converter, which measuresthe time of arrival of the photons. From the measured time of arrival a histogramwas created to determine the laser timing characteristics.

Output intensity

In figure 3.5 and 3.6, the intensity distribution of different laser-filter combinationsare shown. The measurements were performed in the spectrum between 650 nmand 900 nm .

Figure 3.5: Intensity between 650 nm and 900 nm after each laser-filer-systemseparately. The legend shows the configuration: laser/filter (mode).

In figure 3.5 the intensity curves for each laser-filter-system on its own are presented(Fianium source/Fianium AOTF, NKT source/NKT AOTF). Since an AOTF hastwo modes, one where the maximum power is applied on the quartz crystal and onewhere the optimum power is applied, there are two curves for each system.

For both modes the intensity of the Fianium system is higher than of the NKTsystem (figure 3.5). A well appears at 760 nm for the maximum mode of the Fianiumsystem. This irregularity is generated by the Fianium AOTF. This behavior would

29 3.2. Laser characterization

not influence our measurements, since the laser needs solely to be operated in theoptimum mode.

Figure 3.6: Intensity between 650 nm and 900 nm after both laser sources coupledwith the same AOTF (Fianium). The legend shows the configuration: laser/filter(mode).

In figure 3.6 the two lasers are compared by using the same AOTF for both lasersources (Fianium source/Fianium AOTF, NKT source/Fianium AOTF). The inten-sity of the Fianium laser is again higher than for the NKT laser (+30% to +100%)and also the wavelike behavior of the Fianium AOTF appears in the maximummode.

50% time jitter

In figure 3.7 the normalized histograms of the two systems separately are shown (Fi-anium source/Fianium AOTF, Fianium source/Fianium AOTF). The histogramshave a very similar shape. From the histograms the 50% time jitter was derivedby calculating the width of the curve at 50% of the maximum value (full width athalf maximum). The 50% time jitter were nearly identical for both systems withan average value of 355 ps for the NKT system and 343 ps for the Fianium system.

Figure 3.7: Histogram of the NKT and Fianium system

Chapter 3. Combined FMT and NIROT setup 30

Time stability

The stability of three laser-features was evaluated: power intensity, 50% time jitterand time of arrival. The measurements were performed over a short (5 min) anda long (90 min) time period. The results were obtained by combining both super-continuum lasers with the same Fianium AOTF (Fianium source/Fianium AOTF,NKT source/Fianium AOTF).

Figure 3.8 (a) reveals fluctuations of the output power of +/- 3% for the NKT laserand of +/-1% for the Fianium laser over a short time. In (b), i.e. the long timespan, the results for both systems are very similar.

(a) (b)

Figure 3.8: Output power stability. (a) Short time span of 5 min. (b) Long timespan of 90 min.

The fluctuations of the 50% time jitter have a range of +/- 15 ps for the NKT and+/- 7 ps for the Fianium laser for the short time span (figure 3.9 (a)). The valuesof the Fianium and NKT lasers have an error of approximately +/- 2.5% and +/-5%, respectively. For the long time span in (b), the Fianium laser again shows aslight superiority.

(a) (b)

Figure 3.9: Time jitter stability. (a) Short time span of 5 min. (b) Long time spanof 90 min.

Except for an outlier in figure 3.10 (a), the time of arrival is very constant for bothlasers. The time of arrival is defined as the time when the maximum amount ofphotons is detected, i.e. the peak of the histogram.

31 3.3. Conclusion

(a) (b)

Figure 3.10: Stability of time of arrival. (a) Short time span of 5 min. (b) Longtime span of 90 min.

Side lobes

Although it is desired to have a sharp emission band after the AOTF, in reality theoutput is a composition of many wavelengths. The spectrum of the emitted lighttypically reveals smaller side lobes next to the main peak.

The measurements at 670 nm and 830 nm in figure 3.11 show similar spectra forboth systems. Both systems have a sharp emission peak at the desired wavelengthand small side lobes of the same magnitude.

(a) (b)

Figure 3.11: Measurements of the output spectra with the NKT and Fianium sys-tems. (a) Spectrum between 640 nm and 700 nm. (b) Spectrum between 800 nmand 860 nm.

3.3 Conclusion

The characterization of the two laser systems revealed two systems with nearlyidentical properties. Both systems showed good stability behaviors over time. Asexpected, the intensity of the Fianium laser was higher in comparison to the NKTlaser. The Fianium AOTF had a slight irregularity in the maximum mode, as inthe spectrum of the intensity a well at 760 nm was measured. The side lobes werenearly identical for both systems, so was the 50% jitter time.

Based on this characterization, the Fianium system was acquired and integrated inthe setup. After the integration of the new laser and some small adaptations, e.g.

Chapter 3. Combined FMT and NIROT setup 32

adjustment of the reflecting mirrors, the setup was able to perform both FMT andNIROT measurements.

Chapter 4

Experimental measurementswith mice

4.1 Measurements

Measurements were performed on two nude mice, both suffering from a hypoxic,subcutaneous tumor on the right flank. The tumors had a size of approximately3 mm and 4 mm. The position of the mouse was not changed between the mea-surements, since the measurements were performed just one after the other. Thesurface of the mice were illuminated in a grid-like pattern with 10×10 source pointsin both methods.

Since the data analysis is performed offline, the oxygen saturation of the healthytissue is not available during the measurements. Multiple measurements at differentwavelengths were performed to find the wavelength pair for which the exctinctioncoefficient is identical. In order to find the matching pairs two wavelengths werefixed at 830 nm and 850 nm, while between 670 nm and 720 nm multiple mea-surements were performed at steps of 10 nm. The extinction coefficient of eachwavelength and the matching wavelengths were then determined offline.

In figure 4.1 (a) and (b) NIROT measurements are shown. First, two single-wavelength measurements at 700nm and 830 nm are presented for both mice. Theimages show the light distributions Uλ1 and Uλ2 on the surface of the mice. Thesespecific wavelengths were selected by calculating the extinction coefficient k for thehealthy tissue and assigning a variable wavelength (700 nm) to a fixed wavelength(830 nm). In the right images in figure 4.1 the ratio of the two total light fieldsUλ1/Uλ2 was calculated (see equation 2.23). This process was done for the fixedwavelengths of 830 nm and 850 nm; so two datasets were obtained.

In the right image in figure 4.1 (a) and (b) the effect of the homogeneous lightfield is reduced. The variation of the light field is much smaller for the ratio of thelight fields , i.e. the right images, than for the single wavelength measurements, i.e.the left and center images. A contrast between healthy tissue and tumor can beobserved for all three images. However, while at single wavelengths a very high con-trast between healthy tissue and tumor was obtained, the contrast is much smallerfor the ratio of the two wavelengths. This behavior can be explained by a hightumor vascularity and only a weak tumor hypoxia. In this case the tumor has ahigh contrast at single wavelengths, because much hemoglobin is concentrated inthe tumor, but only a low contrast in the ratio, because then the influence of the

33

Chapter 4. Experimental measurements with mice 34

(a)

(b)

Figure 4.1: NIROT measurements with mice. (a) Mouse with small tumor.(b) Mouse with large tumor. Left: Measurement of light field Uλ1 performed at 700nm. Center: Measurement of light field Uλ2 performed at 850 nm. Right: Ratio ofthe total light fields Uλ1/Uλ2.

hypoxia acts stronger. Furthermore, a crosstalk with the fluorescence protein wasobserved during the NIROT measurements. The crosstalk was detected by analyz-ing the wavelength-dependency of the contrast between tumor and healthy tissue.

The infrared fluorescence protein (iRFP), which is a targeted agent, was utilizedin this thesis [38]. A virus was injected into the bloodstream of the mouse. Thevirus comprises a strand of DNA which contains the information on how to producefluorescence proteins. The virus infects the mouse cell and viral DNA containingthe information on fluorescence protein production is integrated into the mouse. Infigure 4.2 the absorption (blue curve) and emission spectra (red curve) of iRFP areshown. The absorption spectrum peaks exactly at the same wavelengths at whichthe measurements are performed, i.e. at 690 nm.

The crosstalk with iRFP was integrated in the equations by extending the equationsystem 2.35 with the reconstruction of the concentration of iRFP. Therefore, threedatasets with measurements at six wavelengths were used. The extended equationsystem with the concentration of iRFP CiRFP has the following form:

φλ1−λ2(r)φλ3−λ4(r)φλ5−λ6(r)

=

Wλ1−λ2HHb Wλ1−λ2

O2HbWλ1−λ2

iRFP

Wλ3−λ4HHb Wλ3−λ4

O2HbWλ3−λ4

iRFP

Wλ5−λ6HHb Wλ5−λ6

O2HbWλ5−λ6

iRFP

δCHHb(r)δCO2Hb(r)δCiRFP (r)

. (4.1)

In figure 4.3 FMT measurements are shown for one source point. In the left imagesthe excitation measurements at 690 nm are presented. The emission of the fluores-

35 4.1. Measurements

Figure 4.2: Excitation spectrum and emission spectrum of iRFP

cence protein was filtered out. In the right images the emission of the fluorescenceprotein is shown. This emission measurements were obtained by applying a filterat 690 nm. In the right images the position of the tumor can be easily observed.

(a)

(b)

Figure 4.3: FMT measurements with mice. (a) Mouse with small tumor. (b) Mousewith large tumor. Left: Excitation measurement. Right: Emission measurement.

It must be considered that no reference values of the oxygen saturation in the tumorwere measured. Other methods are either inaccurate or inadequate. All optical re-construction methods, e.g. NIROT with Nirfast, would not deliver exact values ofthe tumor oxygenation. Measurements with electrodes, e.g. Eppendorf microelec-trodes, are also inaccurate and for the blood gas analysis the sacrifice of the micewould be necessary [39].

Chapter 4. Experimental measurements with mice 36

4.2 Results

The NIROT and FMT methods were compared optically by analyzing the corre-spondence of the reconstructed tumor topography. The performance of the novelNIROT algorithm with wavelength normalization was evaluated with the help ofthe same images.

(a) FMT (b) NIROT

Figure 4.4: Reconstruction of the mouse with the small tumor

(a) z = 0 mm (b) z = -1 mm (c) z = -2 mm (d) z = -3 mm

(e) z = 0 mm (f) z = -1 mm (g) z = -2 mm (h) z = -3 mm

Figure 4.5: Depth resolution of the mouse with the small tumor. (a)-(d) FMTreconstruction. (e)-(h) NIROT reconstruction.

In figure 4.4 the results of the first mouse with the smaller tumor are shown. Thefigures show a 2-dimensional map of the reconstructed tumor. In figure (a) theFMT reconstruction is presented, where the emission of the fluorescence protein isdetermined. The units of the reconstruction are arbitrary units (a.u.). In the rightimage the NIROT reconstruction is shown. With NIROT an oxygen saturation of

37 4.2. Results

69% for the healthy tissue an of 37% for the tumor were obtained.

A strong correspondence between the two methods can be observed for the firstmouse. The reconstructed tumor location match perfectly for both methods infigure 4.4. Both methods were able to detect independently that only one half ofthe tumor was hypoxic. Realistic results were obtained with the new NIROT re-construction algorithm. A tumor oxygenation of 37% is in a realistic range and isconsistent with previous observations that the tumor is not strongly hypoxic.

The comparison of the depth resolutions in figure 4.5 also reveals a strong corre-spondence between the two methods. Both methods reconstructed the tumor atthe same location at z=-1mm. The NIROT reconstruction had a depth of 1 mmand was therefore too superficial, whereas the FMT reconstruction had a depth of3-4 mm. This superficiality is a known issue in NIROT [40] and is difficult to solve.

(a) FMT (b) NIROT

Figure 4.6: Reconstruction of the second mouse with the large tumor

(a) z = 0 mm (b) z = -1 mm (c) z = -2 mm (d) z = -3 mm

(e) z = 0 mm (f) z = -1 mm (g) z = -2 mm (h) z = -3 mm

Figure 4.7: Depth resolution of the mouse with the large tumor. (a)-(d) FMTreconstruction. (e)-(h) NIROT reconstruction.

Chapter 4. Experimental measurements with mice 38

Similar results were found for the reconstruction of the second mouse. Again, a goodcorrespondence between the two methods in figure 4.6 was observed. However, thecorrespondence was not as good as for the first mouse. Artifacts occurred duringthe measurement and disturbed the correct FMT reconstruction. The artifacts arevisible in figure 4.6 (a) in form of the two yellow points.

The NIROT reconstruction resulted in oxygen saturations with a real magnitudefor the healthy tissue of 71% and the tumor tissue of 49%. The reconstructioncoincided with the original location of the tumor.

Figure 4.7 emphasizes the same as seen before. In the first layer (a) the two disturb-ing artifacts are clearly visible. In deeper layers, the reconstruction becomes morerealistic. However, the reconstruction was still negatively influenced by the artifactssince its shape was too local. In reality, the fluorescence emission of the tumor wasmuch broader, which was observed when looking at the raw data. The depth reso-lution of the NIROT reconstruction showed again a shallow reconstruction with adepth of 2 mm. The depth of the real tumor was about 4 mm.

4.3 Conclusion

We were able to show that a correspondence between FMT and NIROT existed forboth mice. The reconstructions of the first mouse matched the physiologal shape ofthe tumor perfectly. For the second mouse a strong correspondence was observedas well, although the results of the second mouse were disturbed by artifacts whichoccurred during the measurements.

Surprisingly, the FMT measurements, which are performed in reflection mode, havea higher depth than the NIROT measurements, which are performed in transmissionmode. These results are counterintuitive, since measurement in transmission modecontain more depth informations. This discrepancy can be explained by the NIROTinversion algorithm, which was realized with a simple least squares approach. Withmore sophisticated algorithms better results could be expected. Also, a higheramount of source points and a higher distance between them would increase theaccuracy of the reconstruction.

The combination of FMT and NIROT enables the possibility to detect the Warburgeffect in tissue [41]. The Warburg effect describes tissue, which produces HIF undernormoxic conditions. The Warburg effect can be detected when using the twomethods complementary, i.e. with NIROT no hypoxia in the tissue and with FMTfluorescence emission is measured.

Chapter 5

Conclusion and Outlook

A hybrid FMT/NIROT setup was developed by extending an existing experimentalFMT setup. The main adaptation was the integration of a tunable supercontinuumlaser, which enables the selection of an arbitrary wavelength in the near-infraredspectrum. The adapted setup was successfully applied on phantoms and mice.Further improvements would be beneficial, such as the integration of a 3D surfacescanner or the application of time domain measurements, but are not neccessary.

A novel NIROT reconstruction algorithm was successfully implemented and enabledan easier reconstruction without the accurate simulation of the homogeneous lightfield. The algorithm was tested first by a simulation and then validated on two micesuffering from hypoxic tumors. A first feasibility check returned satisfying results.The 2-dimensional shape of the reconstruction matched the location of the tumorperfectly. The magnitude of the oxygen saturation had a reasonable magnitude,but the 3-dimensional reconstruction was slightly superficial. It must be consideredthat a setup is mandatory with which arbitrary wavelengths between 650 nm and900 nm can be selected. Additionally, twice as many measurements need to beperformed than with the standard NIROT approach. The acquisition time was stillin a reasonable range with an acquisition time of approximately 6 minutes for onewavelength.

The results of the hypoxia measurements on mice showed a good correspondencebetween the two methods FMT and NIROT. The reconstruction for the first mousefitted perfectly the physiological shape of the tumor. However, for the second mousethe results did not match as good as expected, since two light artifacts disturbedthe correct FMT reconstruction. It can be stated that a correspondence betweenFMT and NIROT is very likely, but for a definitive statement more measurementsneed to be performed on mice. This thesis represents a first step for an accurate,qualitative definition of hypoxia based on FMT and NIROT.

It would be beneficial to analyze the tissue properties with another method, e.g.blood gas analysis, to receive a different reference value. Also, it should be con-sidered to use another fluorescence protein with an absorption spectrum below 670nm, so that it can not influence the NIROT measurements.

In future experiments it will be of interest to perform translational research, i.e.moving away from experimental organisms such as mice and applying the experi-ments on humans. The knowledge about the hypoxic state of the tumor may be ofgreat interest to physicians, since hypoxia influences the survival rate of patients.Quantitative statements about hypoxia are possible with NIROT, but many chal-

39

Chapter 5. Conclusion and Outlook 40

lenges, e.g. robustness and applicability, need to be overcome first. The researchon humans will become important for FMT as well, since there exist fluorescentproteins, which are going to be allowed for the use in humans in the coming years.

List of Figures

1.1 Absorption spectrum of the four main absorbing chromophores inbiological tissue, i.e. oxy-hemoglobin (O2Hb), deoxy-hemoglobin(HHb), water (H2O) and lipid. . . . . . . . . . . . . . . . . . . . . . 1

1.2 Light propagation in tissue. (a) Highly absorbing medium: scattering� absorption. (b) Highly scattering (diffuse) medium: scattering �absorption. Stuker et al.[6] c© 2011 IEEE . . . . . . . . . . . . . . . 2

1.3 Absorption coefficient of hemoglobin for different oxygen saturationlevels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.4 Spectrum of a sample fluorescence molecule. Blue: Excitation spec-trum in which the photons are absorbed. Red: Emission spectrum inwhich the photons are reemitted. https://www.chroma.com/sites/default/files/uploads/3_GenericFluor-2.png . . . . . . . . . . 4

2.1 Source positions for different geometries. (a) Semi-infinite medium:the black point indicates the original light source, the white pointis the virtual source. (b) Slab: The black point in the slab is theoriginal light source. The original light source is mirrored by thewhite points closest to it. The virtual sources are again mirrored onthe opposite surface (black points), etc.. d is the thickness of themedium. Adapted from Patterson et al. [18] . . . . . . . . . . . . . . 10

2.2 Comparison between a homogeneous and heterogeneous medium. (a)Homogeneous slab. (b) Heterogeneous slab with tumor. (c) Homoge-neous light field. (d) Total light field. (e) Cross section through thelight fields in (c) and (d) showing the intensities of the homogeneousand total field along the medium. . . . . . . . . . . . . . . . . . . . . 12

2.3 Extinction coefficient for healthy (green) and tumor tissue (red). Inthis example the healthy tissue was given an oxygenation of 75% andthe tumor tissue of 25%. The oxygenation of the healthy tissue isobtained in previous measurements. When fixing one wavelength at850 nm the second wavelength can be obtained by drawing a hori-zontal line (blue line); in this case it is 678 nm. The homogeneousfields at these two wavelengths would be identical. Since the tumorhas a different absorption curve, the ratio total fields are different. . 14

2.4 Reduced scattering coefficient of internal organs of mice. Adaptedfrom Krainov et al. [21] . . . . . . . . . . . . . . . . . . . . . . . . . 16

2.5 Comparison of the homogeneous and total light field at 678 nm. (a)Homogeneous light field U0. (b) Total light field U . (c) Cross sectionthrough the light fields in (a) and (b). (d) Contrast at 678 nm,defined as U/U0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

41

List of Figures 42

2.6 Comparison of the homogeneous and total light field at 850 nm. (a)Homogeneous light field U0. (b) Total light field U . (c) Cross sectionthrough the light fields in (a) and (b). (d) Contrast at 850 nm,defined as U/U0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.7 Ratio of the total fields Uλ1/Uλ2. The total fields are simulated at678 nm and 850 nm and have identical homogeneous fields. . . . . . 20

2.8 Maximum contrast value for different tumor oxygenations . . . . . . 212.9 Maximum contrast value for different tumor blood concentrations . . 212.10 Maximum contrast value for different tumor radii. (a) The tumor is

located in a depth of zT=-5mm. (b) The tumor is located in a depthof zT=-10mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

2.11 Reconstruction of the oxy- and deoxy-hemoglobin in the tumor. Theconcentrations are given in mmol

L . . . . . . . . . . . . . . . . . . . . . 23

3.1 Schematic view of the FMT setup. Stuker et al. [?] . . . . . . . . . . 253.2 Quantum efficiency e of the CCD-camera Andor DV434-BV ftp:

//ftp.aerodyne.com/users/Jones/NASA/DV434.pdf . . . . . . . . 263.3 Different spectra of the supercontinuum laser system. Blue is the

spectrum of the fiber laser (pump source), red the spectrum afterthe supercontinuum laser and green the emission after the AOTF.Adapted from http://en.wikipedia.org/wiki/Supercontinuum . . 27

3.4 Block diagram of an AOTF-based multispectral imaging instrument.Adapted from Vila-Frances et al. [35] . . . . . . . . . . . . . . . . . . 28

3.5 Intensity between 650 nm and 900 nm after each laser-filer-systemseparately. The legend shows the configuration: laser/filter (mode). 28

3.6 Intensity between 650 nm and 900 nm after both laser sources coupledwith the same AOTF (Fianium). The legend shows the configuration:laser/filter (mode). . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3.7 Histogram of the NKT and Fianium system . . . . . . . . . . . . . . 293.8 Output power stability. (a) Short time span of 5 min. (b) Long time

span of 90 min. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.9 Time jitter stability. (a) Short time span of 5 min. (b) Long time

span of 90 min. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.10 Stability of time of arrival. (a) Short time span of 5 min. (b) Long

time span of 90 min. . . . . . . . . . . . . . . . . . . . . . . . . . . . 313.11 Measurements of the output spectra with the NKT and Fianium

systems. (a) Spectrum between 640 nm and 700 nm. (b) Spectrumbetween 800 nm and 860 nm. . . . . . . . . . . . . . . . . . . . . . . 31

4.1 NIROT measurements with mice. (a) Mouse with small tumor.(b) Mouse with large tumor. Left: Measurement of light field Uλ1

performed at 700 nm. Center: Measurement of light field Uλ2 per-formed at 850 nm. Right: Ratio of the total light fields Uλ1/Uλ2. . . 34

4.2 Excitation spectrum and emission spectrum of iRFP . . . . . . . . . 354.3 FMT measurements with mice. (a) Mouse with small tumor. (b)

Mouse with large tumor. Left: Excitation measurement. Right:Emission measurement. . . . . . . . . . . . . . . . . . . . . . . . . . 35

4.4 Reconstruction of the mouse with the small tumor . . . . . . . . . . 364.5 Depth resolution of the mouse with the small tumor. (a)-(d) FMT

reconstruction. (e)-(h) NIROT reconstruction. . . . . . . . . . . . . 364.6 Reconstruction of the second mouse with the large tumor . . . . . . 374.7 Depth resolution of the mouse with the large tumor. (a)-(d) FMT

reconstruction. (e)-(h) NIROT reconstruction. . . . . . . . . . . . . 37

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