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(1)Faculty of Physics and Applied Computer Science. Doctoral thesis. mgr inz˙ . Artur Dawid Surówka. Development of analytical approaches for molecular and fully quantitative elemental micro-imaging of brain tissue with X-ray and infrared radiation Supervisor: dr hab. inz˙ . Magdalena Szczerbowska-Boruchowska. Krakow, October, 2016.

(2) Declaration of the author of this dissertation: Aware of legal responsibility for making untrue statements I hereby declare that I have written this dissertation myself and all the contents of the dissertation have been obtained by legal means.. ˙ Artur Dawid Surówka 14/10/2016, mgr inz.. Declaration of the thesis Supervisor: This dissertation is ready to be reviewed.. ˙ Magdalena Szczerbowska-Boruchowska 14/10/2016, Dr hab inz.. 2.

(3) Acknowledgements 1. First, I would like to express my sincerest gratitude to my supervisor and advisor Dr hab. inz˙ . Magdalena Szczerbowska-Boruchowska for a great collaboration, continuous support of my research, Her patience, and constant motivation. Her exceptional involvement helped me all the time to progress the work undertaken. 2. Also, I am grateful to Prof. Peter Gardner and His group at the University of Manchester for an exciting collaboration during my ERASMUS+ internship and further scientific visits. It was, and is always, a great pleasure for me to work with Them. I would like to thank for many scientific discussions, advice, and support. I am grateful to Dr Mike Pilling for assistance during infrared measurements and Dr Alex Henderson for hints on data analysis. I would like to thank Julie Brooks, Stephen Casabella, Zack Zhang, James Doherty, and Adam Keen for a collaboration and excellent time spent in Manchester. I would also like to thank Dr Herve Boutin from Wolfson Molecular Imaging Centre at the University of Manchester for our cooperation and to Dr Irma Berrueta-Razo (Manchester Institute of Biotechnology) for staining brain specimens. 3. I am using this opportunity to thank Prof. Tim Salditt and His group from the Institute for X-ray Physics at the University of G˝ottingen for a fruitful and exciting collaboration, which is always a great pleasure for me. I would like to thank Him for many excellent ideas, advice, support, and assistance during our beamtime. I would like to thank Mareike T˝opperwien and Martin Krenkel for showing me what phase contrast means. I am also very grateful to Marten Bernhardt for help with the data analysis, and other colleagues from G˝ottingen for help and fantastic time spent together. 4. I would like to thank our collaborators at Jagiellonian University Medical College without whom this work would never be undertaken. I am thankful to Prof. Dariusz Adamek and Mrs Edyta Radwanska from Chair of Pathology for introducing me to modern neurobiology, for many stimulating discussions and new fresh ideas for research. I would like to make thanks to Dr Agata Ziomber for our excellent collaboration, support and the time spent together on the preparation of brain samples. I would thank Prof. Anna Krygowska-Wajs for our cooperation. 5. I am tremendously grateful to all my Department colleagues. I would like to make thanks to Prof. Marek Lankosz for being my advisor at the beginning of my Ph.D. training. I am very grateful to Dr Pawel Wrobel, Dr Joanna Dudala and Dr Beata Ostachowicz for our constant collaboration and many exciting projects completed. 6. Last but not least, I would like to thank my parents, sister, brothers and friends for ongoing support, understanding and all the help I received. 3.

(4) This thesis was prepared in LATEX.. 4.

(5) Streszczenie pracy Celem. przedstawionej. pracy. doktorskiej. było. opracowanie. procedur. metodologicznych dla współcześnie stosowanych technik fizycznych, które w znaczącym. stopniu. mogą. biologicznych.. Szczególny. wspomagać. nacisk. badania. położono. na. biofizyczne. układów. mikroobrazowanie. składu. chemicznego tkanki ośrodkowego układu nerwowego człowieka z wykorzystaniem dwóch technik spektroskopowych: rentgenowskiej mikroanalizy fluorescencyjnej (ang. X-ray fluorescence - XRF) i mikrospektroskopii w podczerwieni z transformacją Fouriera (ang. Fourier transform infrared micro-spectroscopy - FTIR). Pierwsza z metod, umożliwiająca określenie składu pierwiastkowego, jest szczególnie czuła na różnice w masie powierzchniowej próbki, co powszechnie stanowi znaczące utrudnienie w przypadku badań ilościowych cienkich skrawków tkanek. Tym samym, jednym z podstawowym. zadań. niniejszej. rozprawy. doktorskiej. było. opracowanie. metodologii pozwalających na realizację tego typu prac, poprzez przeprowadzenie eksperymentów spektroskopowych, umożliwiających jednoczesną lub prawie jednoczesną rejestrację sygnału czułego na różnice w masie powierzchniowej struktur badanych próbek tkanki. W tym celu zaproponowano dwa podejścia. W pierwszym z nich zastosowano korektę efektów masy powierzchniowej w oparciu o względną intensywność promieniowania X rozproszonego niekoherentnie rozproszenie Comptona - dla tkanki istoty czarnej mózgu. Niewątpliwą zaletą tego rozwiązania jest fakt równoczesnej rejestracji promieniowania rozproszonego wraz z sygnałem. fluorescencyjnym.. Metoda. ta. pozwoliła. na. wyznaczenie. mas. powierzchniowych struktur tkanki istoty czarnej: ciał komórek nerwowych jak również otaczającego je neuropilu. Ponadto, zademonstrowano potencjalną użyteczność pół-ilościowych metod korekty wykorzystujących sygnał transmisyjny linii Si-Kα pochodzący z membran stosowanych jako podkładki dla skrawków tkanki.. Drugie. z zastosowanych. podejść. metodologicznych. polegało. na. przeprowadzeniu badań z wykorzystaniem obrazowania rentgenowskim kontrastem fazowym,. użytym. do. wyznaczenia. wielkości. proporcjonalnej. do. masy. powierzchniowej próbki. Prace te pokazały, że efekt masy powierzchniowej ma istotny. wpływ. na. obrazy. dystrybucji. pierwiastków. w. projekcjach. dwuwymiarowych. W celu eliminacji takiego efektu zaproponowano procedurę korekty na potrzeby pół-ilościowego obrazowania topografii pierwiastków w tkance na przykładzie istoty czarnej mózgu. W celu pogłębienia informacji nad własnościami. strukturalnymi. tkanki. istoty. czarnej. mózgu,. obrazowanie. pierwiastkowe zostało połączone z eksperymentem przy użyciu skaningowej. 5.

(6) mikroskopii z wykorzystaniem promieniowania X (ang. scanning transmission X-ray microscopy - STXM) z jednoczesną akwizycją sygnału niskokątowego rozpraszania fotonów X (ang. Small Angle X-ray scattering - SAXS). Ponadto, w ramach przeprowadzonych badań wykonane zostały pionierskie analizy topografii próbek biologicznych przygotowywanych według rutynowo używanej metody opierającej się na ich suszeniu w niskiej temperaturze (tzw. ang. freeze-drying). Pozwoliło to na ocenę realnej grubości skrawków tkanki po procesie suszenia. Równolegle prowadzono drugi nurt badań z wykorzystaniem spektroskopii w podczerwieni.. Celem. prac. była. identyfikacja. potencjalnych. efektów. przeszkadzających, związanych z niejednorodnością tkanki ośrodkowego układu nerwowego człowieka, jak również rozwój procedur analitycznych na potrzeby dokładnej oceny struktury drugorzędowej białek i składu lipidowego tkanek. W toku badań określono zasadnicze efekty związane z rozproszeniem Mie i artefaktami fal stojących, które okazały się być istotnym utrudnieniem w przypadku badań struktur tkankowych o znacząco wysokim współczynniku załamania. Stwierdzono, że w obrębie tkanki istoty czarnej mózgu efekt ten był szczególnie duży w neuronach, a w obszarze neuropilu był w pełni pomijalny. W pracy skupiono się ponadto, na ocenie użyteczności dwóch metod analizy danych: fitowania widm absorpcyjnych i sztucznych sieci neuronowych. Pierwsza z metod została użyta do oceny zmian w strukturze drugorzędowej białek w przypadku obrazowania lokalnego rozkładu tych molekuł wokół blaszek starczych w modelu zwierzęcym choroby Alzheimera i badaniach nad modelem wczesnej formy choroby Parkinsona. Druga z metod pozwoliła na ocenę różnic w strukturze drugorzędowej białek w przypadku nowotworów mózgu pochodzenia glejowego. Ukoronowaniem analiz przeprowadzonych w ramach niniejszej pracy doktorskiej. była. ocena. użyteczności. stworzonych. narzędzi. analitycznych. na potrzeby badań składu pierwiastkowego i molekularnego tkanki istoty czarnej, przeprowadzonych dla dużej liczby mózgów starczych. Zrealizowane. badania. wskazują. na. znaczące. utrudnienia. analityczne,. wynikające z niejednorodności strukturalnej próbek pochodzenia biologicznego, co ma istotny wpływ na ilościowe i pół-ilościowe wyniki badań spektroskopowych z wykorzystaniem promieniowania X i podczerwonego. Zaproponowane w ramach rozprawy doktorskiej rozwiązania metodologiczne poszerzają stosowalność ww. technik analitycznych na potrzeby potencjalnych badań biofizycznych, mających na celu zarówno zrozumienie mechanizmów fizjologicznego starzenia mózgu jak również chorób ośrodkowego układu nerwowego.. 6.

(7) Research published in JCR journals the thesis was based on1 [P1] A.D. Surowka, D. Adamek, E. Radwanska, and M. Szczerbowska-Boruchowska. Variability of protein and lipid composition of human substantia nigra in aging: Fourier transform infrared microspectroscopy study. Neurochemistry International, 76:12–22, oct 2014 (IF: 3.092). [P2] A. D. Surowka, A. Krygowska-Wajs, A. Ziomber, P. Thor, A. A. Chrobak, and M. Szczerbowska-Boruchowska. Peripheral Vagus Nerve Stimulation Significantly Affects Lipid Composition and Protein Secondary Structure Within Dopamine-Related Brain Regions in Rats. NeuroMolecular Medicine, 17(2):178–191, jun 2015 (IF: 3.678). [P3] A.D. Surowka, D. Adamek, and M. Szczerbowska-Boruchowska. The combination of artificial neural networks and synchrotron radiation-based infrared micro-spectroscopy for a study on the protein composition of human glial tumors. The Analyst, 140(7):2428– 2438, 2015 (IF: 4.107). [P4] A.D.. Surowka, P. Wrobel, D. Adamek, E. Radwanska, and M. Szczerbowska-. Boruchowska. Synchrotron radiation based X-ray fluorescence shows changes in the elemental composition of the human substantia nigra in aged brains.. Metallomics,. 7(11):1522–1531, 2015 (IF: 3.585). [P5] A.D.. Surowka, P. Wrobel, D. Adamek, E. Radwanska, and M. Szczerbowska-. Boruchowska. Novel approaches for the mass thickness effect’s correction in the quantitative elemental imaging using Synchrotron X-Ray Fluorescence of the human substantia nigra tissue. Spectrochimica Acta part B, 123:47–58, 2016 (IF: 3.585). [P6] A.D. Surowka, M. Töpperwien, M. Bernhardt, J.D. Nicolas, M. Osterhoff, T. Salditt, D. Adamek, and M. Szczerbowska-Boruchowska. Combined in-situ imaging of structural organization and elemental composition of substantia nigra neurons in the elderly Talanta, 161:368–376, 2016 (IF: 4.025). [P7] A.D. Surowka, M. Pilling, A. Henderson, H. Boutin, L. Christie, M. SzczerbowskaBoruchowska, P. Gardner. FTIR imaging of the molecular burden around Aβ deposits in an early-stage 3-Tg-APP-PSP1-TAU mouse model of Alzheimer’s disease. Analyst, 142(1):156-168, 2016 (IF: 4.033).. 1. Electronic versions of the respective papers were attached to this thesis.. 7.

(8) Other research published in JCR-listed journals [O1] A.D. Surowka, D. Adamek, E. Radwanska, M. Lankosz, and M. SzczerbowskaBoruchowska. A Methodological approach to the characterization of brain gliomas, by means of semi-automatic morphometric analysis. Image Analysis & Stereology, may 2014 (IF: 0.971). [O2] J. Dudala, M. Bialas, A.D. Surowka, M. Bereza-Buziak, A. Hubalewska-Dydejczyk, A. Budzynski, M. Pedziwiatr, M. Kolodziej, K. Wehbe, and M. Lankosz. Biomolecular characterization of adrenal gland tumors by means of SR-FTIR. The Analyst, 140(7):2101– 6, apr 2015 (IF: 4.107). [O3] P.M. Wrobel, S. Bala, M. Golasik, T. Librowski, B. Ostachowicz, W. Piekoszewski, A.D. Surowka, and M. Lankosz. Combined micro-XRF and TXRF methodology for quantitative elemental imaging of tissue samples (accepted for publication in Talanta). [O4] A. Ziomber, A.D. Surowka, P .Wrobel, and M. Szczerbowska-Boruchowska, Influence of transcranial Direct Current Stimulation on the elemental composition of brain structures in obese rats - the EDXRF study (submitted for publication in X-ray Spectrometry).. Research published in non-JCR journals [N1] T. Zalecki, A. Gorecka-Mazur, W. Pietraszko, A.D. Surowka, P. Novak, M. Moskala, and A. Krygowska-Wajs. Visual feedback training using WII Fit improves balance in Parkinson’s disease. Folia medica Cracoviensia, 53(1):65–78, 2013. [N2] W. Pietraszko, A. Furgala, A. Gorecka-Mazur, P. Thor, M. Moskala, J. Polak, A. D. Surowka, and A. Krygowska-Wajs. Efficacy of deep brain stimulation of the subthalamic nucleus on autonomic dysfunction in patients with Parkinson’s disease. Folia medica Cracoviensia, 53(2):15–22, 2013.. 8.

(9) Contents I. Introduction. 13. 1. Sources of limitations to spectroscopic methods based on X-ray and infraded radiation. 2. 13. How X-ray and infrared radiation facilitate biochemical/biophysical studies on neurodegeneration?. 14. 3. Aims of the thesis. 16. 4. Structure the thesis. 18. II Methods to account for the problem of sample morphology in quantitative elemental imaging by SRXRF 19 5. Introduction. 19. 6. Theory. 19. 6.1. Interaction of X-rays with matter . . . . . . . . . . . . . . . . . . . . . . . . . .. 19. 6.2. Rayleigh scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 21. 6.3. Compton scattering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 21. 6.4. Photo-absorption - foundations of X-ray fluorescence spectroscopy . . . . . .. 22. 6.5. Phase shift . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 25. 6.6. Considerations on sample thickness in XRF . . . . . . . . . . . . . . . . . . . .. 30. 6.7. Quantitative XRF with thin specimens . . . . . . . . . . . . . . . . . . . . . . .. 32. 7. Experimental part. 33. 7.1. Preparation of specimens for the experiments with the use of X-rays . . . . .. 33. 7.2. Topography measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 35. 7.3. How sample morphology affects spectral data by XRF and how to get rid of it? 37 7.3.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 37. 7.3.2. Experimental conditions for the XRF studies . . . . . . . . . . . . . . .. 38. 7.3.3. Data quantification by the external standard method . . . . . . . . . .. 40. 7.3.4. Analysis of homogeneity of Si3 N4 membranes . . . . . . . . . . . . . .. 43. 7.3.5. Analysis of X-rays’ transmission through SN samples . . . . . . . . . .. 46. 7.3.6. Compton-based correction against the mass thickness effect . . . . . .. 48. 9.

(10) 7.3.7. Semi-quantitative correction methods utilizing the membrane Si-Kα signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 7.4. 58. Combined elemental and structural imaging to address the mass thickness effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 61. 7.4.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 61. 7.4.2. Beamline layout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 61. 7.4.3. Propagation-based X-ray phase contrast imaging experiments . . . . .. 61. 7.4.4. Combined synchrotron X-ray fluorescence and scanning transmission X-ray microscopy experiments . . . . . . . . . . . . . . . . . . . . . . .. 63. 7.4.5. Analysis of SRXRF spectra . . . . . . . . . . . . . . . . . . . . . . . . . .. 64. 7.4.6. Phase retrieval . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 64. 7.4.7. STXM-SAXS experiments . . . . . . . . . . . . . . . . . . . . . . . . . .. 69. III Development of methodologies for data analysis in molecular imaging by FTIR 75 8. Introduction. 75. 9. Theory. 75. 9.1. Interaction of infra-red radiation with the matter . . . . . . . . . . . . . . . . .. 75. 9.2. Normal modes of vibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 78. 9.3. Lambert-Beer Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 78. 9.4. Fourier transform infrared spectrometers . . . . . . . . . . . . . . . . . . . . .. 79. 9.4.1. Michelson-Morley interferometer . . . . . . . . . . . . . . . . . . . . .. 79. 9.4.2. Data processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 80. 9.5. Sampling modalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 84. 9.6. Detectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 85. 9.7. FTIR spectrum of a biological sample . . . . . . . . . . . . . . . . . . . . . . . .. 88. 9.8. Confounding factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 90. 9.8.1. Electric field standing wave artefacts . . . . . . . . . . . . . . . . . . . .. 90. 9.8.2. Non-resonant Mie scattering . . . . . . . . . . . . . . . . . . . . . . . .. 92. 9.8.3. Resonsant Mie scattering . . . . . . . . . . . . . . . . . . . . . . . . . .. 94. 9.8.4. A highlight on data analysis methods used in FTIR spectroscopy . . .. 96. 10 Experimental part. 98. 10.1 Development of methodology for curve fitting of FTIR spectra - a study on molecular effects underlying vagus nerve stimulation . . . . . . . . . . . . . .. 98. 10.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 98. 10.

(11) 10.1.2 The description of the procedure for the vagus nerve stimulation . . .. 99. 10.1.3 Sample preparation protocol . . . . . . . . . . . . . . . . . . . . . . . .. 99. 10.1.4 Procedure for FTIR data acquisition . . . . . . . . . . . . . . . . . . . . 101 10.1.5 Description of the procedure for spectral curve fitting . . . . . . . . . . 101 10.1.6 Identification of physical effects obscuring the spectral data . . . . . . 105 10.1.7 Analysis of data variability . . . . . . . . . . . . . . . . . . . . . . . . . 106 10.1.8 Analysis of lipid and protein composition in brain samples . . . . . . . 109 10.2 Amyloid plaques in early-stage Alzheimer disease - further improvements on spectral curve fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 10.2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 10.2.2 Experimental conditions for FTIR-FPA imaging . . . . . . . . . . . . . 119 10.2.3 Sample preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 10.2.4 Data pre-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122 10.2.5 Improved methodology for spectral band-fitting . . . . . . . . . . . . . 123 10.2.6 Analysis of differences between protein composition of plaques and surrounding tissue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 10.2.7 Spectral parameters to evaluate lipid- and protein-associated burden around the deposits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 10.3 FTIR study on brain gliomas - development of methodology for automatic analysis of protein secondary structure by artificial neural networks . . . . . . 131 10.3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 10.3.2 Sample prepartion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 10.3.3 Spectral measurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . 133. 10.3.4 Optimization and training of artificial neural networks . . . . . . . . . 134 10.3.5 Analysis of average FTIR spectra of human brain gliomas . . . . . . . 138 10.3.6 Statistical data analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 10.3.7 Analysis of secondary structure contents of proteins vs. WHO malignancy grade . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 10.3.8 Application of LDA to foster diagnosis of brain gliomas . . . . . . . . 140. IV Big-scale proof-of-principle studies on effects underlying human brain aging in the substantia nigra tissue by elemental and molecular imaging 143 11 Introduction. 143. 11.

(12) 12 Experimental part. 146. 12.1 Sample preparation for the SRXRF study . . . . . . . . . . . . . . . . . . . . . 146 12.2 Data quantification in the SRXRF study . . . . . . . . . . . . . . . . . . . . . . 146 12.3 Statistical data analysis of the SRXRF data . . . . . . . . . . . . . . . . . . . . . 149 12.4 Comparison of elemental composition in relation to age . . . . . . . . . . . . . 149 12.5 Experimental conditions for FTIR measurements . . . . . . . . . . . . . . . . . 157 12.6 FTIR data pre-processing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 12.7 Statistical data analysis of the FTIR data . . . . . . . . . . . . . . . . . . . . . . 158 12.8 Protein secondary structure of SN tissue in relation to age . . . . . . . . . . . . 159 12.9 Analysis of lipid composition of SN tissue in relation to age . . . . . . . . . . 162 12.10Analysis of lipid/protein ratio in SN tissue in relation to age . . . . . . . . . . 164. V. Conclusions. 165. References. 170. List of Figures. 196. List of Tables. 204. Erratum. 205. 12.

(13) Part I. Introduction 1. Sources of limitations to spectroscopic methods based on X-ray and infraded radiation Over recently, modern spectroscopic methods experienced a tremendous progress both. in spatial resolution and dramatically reduced acquisition time achievable [1]. Specifically, the development of synchrotron radiation facilities and most modern free electron lasers particularly fostered soft matter studies [2–4]. Although, the state-of-the-art instrumentation offers many solutions to tackle scientific problems to study structure [5,6] and ultra-fast dynamics [7], the problem arises whenever a method falls short of providing desirable spectral information due to shortcomings resulting from a biological sample, as such, rather than due to outstanding instrumental issues [8, 9]. One of the main challenges in this field is associated with heterogeneity of thin (sectioned) slices of biological samples in terms of their thickness and density [8]. Also, the commonly used sample preparation protocols (i.e. freeze drying) enhance their structural variability, showing methodological issues should regularly be addressed to keep up the necessary instrumental development, including sample preparation and data pre- and post-processing [10]. In particular, the methods based on hard X-rays and infrared (IR) radiation were found with a lot of confounding effects that are capable of obscuring actual spectral information to be drawn from a biological sample. Synchrotron radiation based X-ray fluorescence (SRXRF) is an excellent example of quantitative elemental imaging method, which is very prone to differences in sample thickness and density [11–15]. The method is based on emission of various lines of characteristic radiation attributable to different elements upon irradiation of a sample with the primary exciting beam of sufficient energy [16]. For a fully theoretical conversion of the intensities of the characteristic lines of chemical elements into their mass fractions in a sample, the fundamental parameters approach is now commonly used. Unfortunately, it comes up with a relatively large number of parameters to be known, which poses a significant limitation whenever a priori knowledge on complex biological specimens is non available [17]. For simplification of the computations, different approximations of this equation were found to lead simplified quantification procedures. One of these, a thin sample approximation, relies on the assumption that its mass per unit area is so small that the self-absorption could be neglected. As a result, the intensity of characteristic radiation scales up with the sample mass per unit area, which is particularly prone to local variation in sample thickness [17]. In this regard, the challenge is to find a measure/normalization to come up with the quantification in terms of 13.

(14) thickness and density independent mass fractions. For doing so, the sample mass per unit area is required as a normalization factor. In turn, modern imaging methods based on midIR radiation, with the wavelengths comparable with the local extent to sample roughness and dimensions of single cells, come up with the data obscured by inherent Mie scattering and electric-field-standing wave artifacts [18, 19]. These phenomena are usually the case when complex histological objects (neurons, plaques) of radically distinct optical properties are to be analyzed [20]. Another group of methodological problems addressed herein was linked to the development of data analysis protocols, designed to master this process to be more accurate. This issue becomes tremendously important whenever tiny spectral signatures provide the information on massive chemical/structural changes in a sample, which could also be affected by the organic matrix effects highlighted as above. For example, the mentioned above IR spectroscopy serves as a very sensitive tool for studying the changes in protein secondary structure, which are tremendously important in the clinical spectroscopy arena for boosting our understanding on the progression of diseases [21]. As an example, the protein secondary structure encoded in Fourier transfer IR (FTIR) spectra is very minute, and many efforts are made to make the data analysis procedures for extracting the relevant proteomic-related information better work on [22]. Also, this issue becomes significantly cumbersome when additional scattering and reflections contribute to the subtle spectroscopic information. Altogether, there is an urgent need to address the problem of the influence of local variation in samples’ structure by understanding, recognizing and mitigating the contributions of these phenomena in the studies of complex biological samples.. 2. How X-ray and infrared radiation facilitate biochemical/biophysical studies on neurodegeneration? Aggregation of neurotoxic proteins: α-synuclein [23], τ protein [24], β-amyloid [25], along. with inherent oxidative stress neurotoxicity and excitotoxicity, are all triggered by redox and non-redox-active elements (Ca, Fe, Cu, Zn). They are considered as major driving forces in neuronal structural burden associated with both human brain aging and dementias [26–29]. In particular, human substantia nigra (SN) neurons seem to be affected at most, due to their higher propensity for apoptosis, which is caused by the built up of genetic mutations due to their post-mitotic character and increased exposure to harmful products of dopamine metabolism [30]. These effects result in the production of cytotoxic reactive oxygen species (ROS), damage to cellular lipids/proteins, increased rate of neuronal loss, and dopamine depletion underpinning Parkinson disease (PD) [30]. These and many other examples figure out the critical role of the interplay between met14.

(15) als and molecular changes that underlie age-associated biochemical and structural burden of the neurons in the elderly [27]. However, to compromise sometimes contradictory evidence, and make the findings more integrated, particular attention must be paid to chemical/structural mapping (2D/3D) of the local extent to the neuronal burden. Currently, to probe in-situ the structural-chemical processes with the highest possible sub-cellular spatial resolution, highly brilliant synchrotron sources of coherent X-ray radiation have been offered for the non-invasive analyzes of biological specimens in dynamic mapping and tomography modes [31]. Specifically, combined Small-Angle X-ray Scattering (SAXS) and Scanning Transmission X-ray Microscopy (STXM) allow for determination of both orientation and density of the nano-scale biological scaffolds throughout the analysis of nanodiffraction patterns (NDP) [6, 32]. With the possibility for imaging of the differential phase contrast (DPC) and dark field intensity (DFI) signal, several studies demonstrated it is possible to extract the information on the scattering strength, electron density gradient, radius of gyration, and orientation of molecular assemblies (cytoskeleton, actomyosin fibers) from the NDPs of cells with excellent sub-micron resolution [33]. Unfortunately, far too little attention has been paid to STXM studies of structural properties of SN tissue samples. Besides, there is an increasing body of inquiry on the 2D imaging of bio-metals in SN using SRXRF [27,34]. By using highly collimated 10-20 keV synchrotron (SR) beams of X-rays, the aberration in the level of selected transition metals: Fe, Cu, Zn, Mn, Se was reported in thin 10-20 µm freeze dried autopsy brain specimens [27, 34]. However, due to variation in the sample’s thickness and density, often referred to as the mass thickness effect, the quantification of elemental mass fractions is a challenging task[8]. Spectroscopic micro-imaging methods have been recently proposed to study lipid- and protein-related molecular effects of human brain aging and dementias [35]. In all, there is a need for increasing both the spatial resolution and gaining more insight into molecular and elemental components, and their interaction with pathological triggers to push our understanding of neurodegeneration forwards. In particular, due to the high sensitivity of molecular components to interaction with hard X-ray microprobe [36], the spectroscopic tools based on visible, infra-red and radio-frequency waves were found very attractive. This property is justified by their non-invasive character which is a prerequisite for the studies on the biological soft matter: tissue sections, tissue slices and single cells [21, 37]. Especially, the methods to image (either full field and mesh-scanning tools) large area histological structures have recently gained in importance, as the efforts are made to co-localize the biochemical action of therapeutic drugs/pathologies to brain structures that may trigger the disease [38]. Specifically, of all the spectroscopic tools, circular dichroism [39], nuclear magnetic resonance [40] and FTIR spectroscopy [35] have proven their usefulness in these studies, although the first two methods listed fall short of providing high spatial resolution down to single cells (<10 15.

(16) µm). At the same time, FTIR spectroscopy is gradually paving its way towards more indepth clinical applications in the ’neuro-spectroscopy’ arena. The method has proven its usefulness in numerous imaging studies to investigate in-situ composition of molecular correlates of neurologic malignancies: misfolded α-synuclein [41], β-amyloid in amyloid plaques [42–44] and τ-protein [45], all of which found in the brains affected by PD, AD and ageing [46]. Apart from studies on protein composition, the method was found very useful for in-situ imaging of lipid peroxidation/unsaturation in animal and human-based studies on neurodegeneration and aging [47]. The method has seen enormous progress both regarding spatial resolution available and acquisition time [35]. The first applications were limited to synchrotron imaging experiments with the pixel size up to 10 µm [42]. At now, the most modern benchtop high-magnification imaging systems offer the measurements at the pixel size of 1 µm [48, 49]. Currently, the most advanced imaging systems coupled with detector matrices based on quantum cascade lasers [50, 51] and even ultra-broadband nano-imaging systems have been brought out [52]. Synchrotron radiation sources significantly facilitated the studies by FTIR imaging due to the possibility to reduce the spatial resolution achievable down to the diffraction limit (even the case with thick samples which comes up with a weak signal by using benchtop sources). It has 2-3 orders of magnitude higher brilliance, as compared with conventional Globar sources [53]. However, despite the instrumental progress, there are still serious methodological issues related to the appropriate data treatment to extract the relevant, usually very subtle, chemical information on the molecular changes (i.e. protein secondary structure/lipid-changes) [21, 54–57].. 3. Aims of the thesis At now, the communities are striving for finding new methods for resolving both dy-. namics and structure of neural assemblies. The new techniques that are gradually emerging in the clinical diagnostic arena are FTIR, Raman, UV-VIS and hard X-ray spectroscopies. With high sensitivity, spatial resolution, and fast acquisition time, they are potentially better suited for diagnosis of complex neurodegenerative syndromes, now thought to be triggered at the sub-molecular level. However, their main shortcoming linked to inherent heterogeneity of biological specimens, and its contribution to the relevant clinical information should be properly understood. In this regard, the major goal of this work was to foster the data analysis for further biophysical studies on two important molecular effects that are possibly involved in neurodegeneration (and can potentially be used as new molecular markers of neurologic diseases): oxidative stress neurotoxicity and misfolding of biologically active proteins. To this end, the methodologies based on two different, somehow complementary methods with elemen16.

(17) tal and molecular contrast: synchrotron X-ray fluorescence imaging and Fourier transform infrared spectroscopy, were proposed along with simple tools to get rid of the inherent physical effects that obscure the relevant biophysical/chemical information. This thesis set out with two major tasks. Regarding the use of the SRXRF microprobe, the goal was to demonstrate the influence of local variation in samples’ morphology on quantitative elemental images and to find analytical solutions to get rid of this effect. Specifically, two related projects were undertaken to find possible correction schemes based on: • relative intensity of either incoherently-scattered or transmitted X-ray radiation taken from sole SRXRF spectra; • full-field high-resolution X-ray phase contrast imaging, along with scanning transmission X-ray microscopy experiments proposed as an alternative mean for correction. These projects were to foster error-free quantification of the elements in thin tissue specimens and to utilize other methods to couple quantitative chemical information with structural organization of neural scaffolds for combined biophysical studies on human brain aging and dementias. As for the FTIR micro-imaging of thin brain tissue samples, the research aimed at the development of a house-made code for evaluation of both secondary structure contents of proteins and lipid composition. The research aimed at the development of two distinct unsupervised/supervised chemometric tools: band-fitting and artificial neural networks to define potential protein/lipid label-free diagnostic markers of early-stage neurodegeneration, malignant human brain tumors and those linked to human brain aging. The work was also to test the performance of these tools for the analysis of protein secondary structure by using a set of reference FTIR spectra. The analytical procedures were developed to be suitable for a widespread use for both animal specimens (taken from the rat brains affected by early-stage pathologies of the dopaminergic system and mouse model of Alzheimer diseases) and human autopsy samples. Also, the goal was to identify the morphology-related effects obscuring the relevant spectroscopic information using FTIR and to propose the solutions based on existing state-of-the-art of data processing methods. In particular, the impact of resonant Mie scattering along with possible electric field standing wave artifacts was to be investigated in FTIR transflection and transmission spectra. Also, the goal was study this effect in complex tissue samples where high refraction index (high density/mass thickness) histological structures such as amyloid plaques were present. Finally, the goal was to utilize the developed analytical tools based on SRXRF and FTIR imaging for a ’cross-sectional’ study on molecular and elemental (diagnostic) correlates of human brain aging in autopsy-based SN tissue samples. The research was to seek any high. 17.

(18) and significant correlations between molecular components and mass fractions of chemical elements with age. Last but not least, in the fourth section, the final conclusions arising from the whole research are summarized.. 4. Structure the thesis The thesis was composed of five major parts devoted to in-depth discussion on the. methodological developments in SRXRF and FTIR micro-imaging methods. In the second part, theoretical foundations of SRXRF are presented together with the utilization of this approach for quantification of biologically active elements in thin tissue sections. The commonly used freeze-drying sample preparation used in XRF is presented with pioneer topography measurements of the sample surface. The next section of this part is to discuss two different methods to correct the spectral data against morphology-related issues using Compton scattering, transmission Si-Kα signal, and X-ray phase contrast imaging. Also, potentially new tools for performing combined error-free structural-elemental imaging are presented. In the third part, the theoretical foundations behind FTIR spectroscopy and the respective data analysis procedures are presented. The theoretical discussion is followed by a review of the most important physical phenomena that are capable influencing the spectral data presented in next sections. To start with, a band fitting tool is shown for automatic studies on the molecular effects underlying vagus nerve stimulation in the brains of rats. Next, the optimized and simplified version of this algorithm is presented for a study on protein secondary structure imaging in the animal model of early-stage Alzheimer disease. In the last section, an alternative supervised method for prediction of protein secondary structure components based on artificial neural networks is presented for a study on human brain gliomas. In the fourth part, a big-scale study utilizing the above-described methodologies is undertaken to highlight on the roles chemical major and trace elements along with both lipid and protein components may play in the human brain aging. In the last fifth part, the conclusions arising from this thesis are made, together with overview of the most significant results and outlook.. 18.

(19) Part II. Methods to account for the problem of sample morphology in quantitative elemental imaging by SRXRF 5. Introduction X-ray radiation was discovered in 1895 by Wilhelm Roentgen in Würzburg in Germany.. This milestone paved the way towards its numerous applications in medicine, industry, and science [16]. X-rays’ wavelengths fall within the range from 0.005 nm to 10 nm, while those ranging from 0.2-0.1 nm wavelength are called hard X-rays, and those with higher wavelengths are referred to as soft X-rays [58]. Continuous X-ray spectra are produced if highenergy charged particles (i.e. electrons, protons) lose their kinetic energy in a radiant and thermal manner while passing through Coulomb potentials. The former, result in the emission of so-called bremsstrahlung radiation, whose probability is roughly proportional to q 2 Z 2 T /M02 , where q - the particle charge, Z - the atomic number, T - the particle kinetic energy, M0 - the rest mass of the interacting particle [16]. Although their numerous physical properties (i.e. invisible, not prone to external magnetic and electric fields, propagated in straight trajectories with the speed of light, capable of liberating photoelectrons and recoiling electrons, capable of inducing and modifying biological reactions (damage to DNA)), their possibility to emit a line fluorescence spectrum indicative of the chemical elements, as discovered by Moseley as early as in 1917, underlies the physical foundations of X-ray fluorescence spectroscopy used to study the elemental composition of a different kind of samples including organic and non-organic ones [59].. 6. Theory. 6.1. Interaction of X-rays with matter. The interaction of X-ray with a sample material is due to their absorption and phase shift, as governed by complex refractive index: n = 1 − δ + iβ Where: δ and β decrements describe their phase shift and absorption, respectively.. 19. (1).

(20) In the hard X-ray range, far away from its strong resonances in near IR, UV, and soft Xray, the X-ray refractive index remains slightly lower than one. It is a primary cause of its physical behaviour used to construct dedicated optics [58]. Taken together, the phase variation, propagation and absorption of the electric component of monochromatic X-rays in a homogeneous medium can be described with [16, 60]: E(r, t) = E0 e−i(ωt − k·r) = E0 e−iω(t−r/c) e−i(2πδ/λ)r e−(2πβ/λ)r. (2). Where: E0 - the magnitude of the electric field associated with propagating X-rays; ω the angular velocity; c ≈ 2.99 · 108 (m/s) - speed of light; δ - the phase shift decrement; β - the absorption decrement. One can notice, as the intensity of electromagnetic wave is proportional to |E(r, t)|2 , the only one term responsible for their attenuation is T (x) = e−(2πβ/λ)r , which is often called the transmission function [61]. At the same time, variations due to phase shift do not contribute to the measured intensity signal, which poses a major problem when the information on the phase shift is to be extracted from intensity data [58]. In the case of narrow, para-axial, and monochromatic X-rays, their attenuation in a homogeneous medium is governed by the law: ∗l. I = I0 eµ. (3). Where: I0 - the intensity of the primary incident beam, I - the intensity of the attenuated beam, l - thickness of the absorber (cm), µ∗ - the linear attenuation coefficient (1/cm). Importantly, the linear absorption coefficient is related to the total collision cross section per atom σtot by the following formula: N0 µ∗ = σtot ρ A. . g atoms cm2 · · 3 atom cm g. (4). Where: σtot - total collision cross section; ρ - the medium density; NA - Avogadro’s number (6.02252 × 1023 (atoms/g/atom)). At the same time, the total collision cross section reflects the probability that the X-ray photon will have a specific interaction of some kind, while passing through a sample. In all, it has three major components attributed to the total photoelectric cross-section per atom (τ ), Rayleigh scattering (σR ) and Compton scattering (σC ): σtot = τ + σR + σC .... (5). Importantly, while passing through the medium, these processes are competing. Experimental and theoretical evidence show that the component cross sections are all Z-dependent as follows: σR ≈ Z 2 , σC ≈ Z, τ ≈ Z 4 (low energy) or τ ≈ Z 5 (high energy). 20.

(21) 6.2. Rayleigh scattering. Rayleigh scattering is a sort of elastic interaction of photons with bound atomic electrons, which means the energy of incident X-rays remains unchanged upon the collision. The process is the most efficient for high-Z elements. The Rayleigh scattering differential cross section depends on the observation angle and atomic form factor as follows [62]: cm2 dσR 1 2 2 2 = r0 (1 + cos θ)|F (x, Z)| dΩ 2 atom · sr. (6). Where: θ - the observation angle; r0 ≈ 2.82 · 10−15 m - classical electron radius; the F (x, Z) atomic form factor, which reads |F (x, Z)|2 = Z 2 in the forward direction. The intensity of Rayleigh-scattered photons (at the assumption of randomly distributed directions of incident X-rays) can be described with: 1 IR = I0 2 r. . e2 m0 c2. 2. (1 + cos2 θ). (7). Where: IR - scattering intensity; I0 - intensity of the primary incident beam of X-rays; r - distance to the observation point; θ - scattering angle; e - charge of the electron; m0 - electron’s rest mass. As follows from Eq 7, the intensity of Rayleigh-scattered photons is proportional to the intensity of primary incident beam, which can serve as a means to normalize the data to the beam flux as demonstrated in numerous studies where stability of the beam (synchrotron and laboratory sources) was a concern [8, 16].. 6.3. Compton scattering. Compton scattering is a process whereby X-ray photons lose their kinetic energy upon interaction with weakly bound electrons which are considered to be at rest. By using, the conservation of momentum and energy laws, the energy of a scattered photon reads [63]: E=. E0 1 + γ(1 − cosθ). with. γ=. E0 mo c2. (8). Where: E, E0 - energies of scattered and incident photons, respectively; θ - angular difference between electron’s linear trajectories before and after interaction; h ≈ 6.62 · 10−34 (J · s) Planck’s constant; m0 - electron rest mass. For unpolarized X-ray photons interacting with unbound randomly distributed electrons,. 21.

(22) the Compton scattering differential cross section (number of photons per unit solid angle normalized to the number of incident X-rays) reads: 2 dσKN r02 E E0 E 2 = + − sin θ dΩ 2 E0 E E0. . cm2 electron · sr. (9). Where: r0 classical radius of electron; E, E0 - energies of scattered and incident photons, respectively; θ - angular difference between electron’s linear trajectories before and after interaction. In these conditions, for the atom of atomic number Z, the total Compton scattering cross section simply yields (as long as we consider weakly bound electrons) [16]: σC = ZσKN. (10). For the specimens of non-indefinite thickness, given the sample’s self absorption effects, the intensity of Compton-scattered X-ray photon can be shown as [64]: ICOM =. GI0 σCOM (E0 ) · f (E0 , ECOM , Ψ1 , Ψ2 ) µ(E0 )csc(Ψ1 ) + µ(ECOM )csc(Ψ2 ). (11). With: f (E0 , ECOM , Ψ1 , Ψ2 ) = (1 − exp(−(µ(E0 )csc(Ψ1 ) + µ(ECOM )csc(Ψ2 ))M )). (12). Where: E0 - energy of the primary exciting beam; ECOM - the peak energy of the Compton peak; G - a geometry constant; σCOM - Compton mass scattering coefficient of sample material computed for the energy of the primary exciting monochromatic beam of X-rays; Ψ1 , Ψ2 - the incidence and take-off angles, respectively; µ(E0 ), µ(ECOM ) - the mass attenuation coefficient for the primary exciting radiation as well as for the peak energy of the Compton peak, respectively; I0 - the intensity of the primary exciting beam; M – the mass thickness of a sample. Noticeably, the Compton scattering intensity depends upon sample’s mass thickness (M ), which provided sample mass per unit area is small, is proportional to the sample mass per unit area. This parameter can provide with information on sample’s morphology, and may be used to facilitate quantitative analyzes [8].. 6.4. Photo-absorption - foundations of X-ray fluorescence spectroscopy. Photo-absorption relies on transitions of atomic orbital electrons between permitted energy levels, which is due to ionization of the inner electron shells. The ionization occurs if the X-ray photon has the energy that matches the electron’s binding energy, a prerequisite for 22.

(23) overcoming Coulomb binding potentials and recoiling it away from the atom. In the case, the electrons are ejected from the K shell, whereby the electrons are the most tightly bound, the atom becomes excited. The excess of energy the atom has over its ground state is that of the energy equal to the ejected electron’s binding energy. Once the electron is removed, there remains a vacancy in a selected shell, which is to be filled by any electron from the higher energy level, be it L, M or so. As shown in Fig 1, the transition of the electron from the L and K shell is referred to as the most intensive Kα series (according to the notation developed by Siegbahn) or KL (as recommended by IUPAC). Analogically, the transition between M and K shells underlies the Kβ series. For the clarity, the possible transitions involve even those between M and L shells provided the selection rules, as highlighted below, are held [61].. 0. K. Energy (keV). K α1 K α2. n 1. l 0. j 1/2. (1s). 2 2 2. 0 1 1. 1/2 1/2 3/2. (2s) (2p1/2) (2p3/2). 3 3 3 3 3. 0 1 1 2 2. 1/2 1/2 3/2 3/2 5/2. (3s) (3p1/2) (3p3/2) (3d3/2) (3d5/2). Kβ3 Kβ 1. LI LII LIII Lα1 Lα2 Lβ1 MI MII MIII MIV MV (a). valence electrons. K L. atomic shell. M. Δl=0 and Δj=0, ±1/2. atomic nucleus (b). Figure 1: Energy levels and the most probable transitions observed in XRF.. Far away from the absorption edges, the photoelectric cross-section for the K-shell was devised by Bethe and Heitler in turn of 1953/4 [65, 66]: √ 4 32 2 2 Z 5 m0 c2 τK = πr0 3 (137)4 hν. (13). Where: r0 = classical radius of electron; hν - incident photon’s energy; m0 c2 - electron rest energy; Z - atomic number. 23.

(24) (a). (b). Figure 2: Relation between (a) the fluorescence yield and (a) the Kα line energy vs. the atomic number (own data prepared in Python 2.7 with xraylib library [67]).. From this equation, one can notice the photoelectric cross section scales up with Z 5 , which makes the phenomenon more probable for high-Z elements. At the same time, for lower elements, the competing phenomenon called the Auger effect predominates. The Auger process relies on de-excitation of the atom in a non-radiant manner, with the energy transferred to liberate one of the electrons from the higher sub-shells. The parameter used to describe this mutually competing photo-absorption and Auger effects is called the fluorescence yield defined as [16]: IK (14) nk Where: IK - the total number of characteristic X-ray photons belonging to the K series; nK ωK =. the total number of vacancies in the K shell supposed to be filled up in a radiative manner. As shown in Fig 2a, for a soft matrix element (C, N, O) the fluorescence yield of their Kα radiation is significantly reduced as compared with high-Z elements such as P, S, Cl, etc. Therefore, in the former, the Auger effects predominates. For the latter, the contribution of photo-absorption is significantly higher. Provided we observe the photoelectric effect, the energy that is emitted by the atom is a difference between two energy levels: E1 and E2 , for the shell at which the vacancy was created and for the level the filling electron is coming from, respectively. The next issue is to judge which of these transitions are the most probable. Quantum mechanical theory states that a very limited number of possible transitions is allowed, while the remaining are forbidden (with very low probability). The most probable. 24.

(25) are those to create electric dipole radiation to obey the relations [16]: ∆l = ±1 and ∆j = 0 or ± 1. (15). Where: l - orbital quantum number; j - total momentum angular quantum number. In turn, as proposed by Dirac, the forbidden dipole transitions can appear as multi-pole radiation governed by the following rules: ∆l = 0 or ± 2 and ∆j = 0 or ± 1 or ± 2. (16). Given a number of photons emitted within a specific series, be it K, the square root of their frequency is directly proportional to the atomic number of the element, as discovered by Moseley: ν = c(Z − σ)2. (17). Where: c - a constant; Z - atomic number; σ - the screening constant to describe repulsion due surrounding electrons in the atom. As shown in Fig 2b, the Moseley’s remark allows for a simple identification based upon energy of a specific series of, here, Kα radiation (but another lines may also be used which is the case in identification of light elements spanning from N-Mg where L lines are utilized). In this regard, the fluorescence radiation emitted by chemical elements, as an indicator of their atomic number, is called the characteristic radiation, which lies behind physical foundations of X-ray fluorescence spectroscopy: the analytical method to analyze a sample qualitatively (in terms of elements present in a sample) as well as in a quantitative manner (in terms of the amount of elements present in the analyte) [68–70].. 6.5. Phase shift. While interacting with a sample material, besides absorption, the X-ray beam undergoes a phase shift. Importantly, for the phase aberrations being detectable there is a lot of prerequisites including among others monochromaticity, full/partial coherence, para-axial character of the beam, etc [71]. In contrast to the visible range of electromagnetic spectrum, the interaction of X-rays is relatively weak, which is mirrored by their refractive index n(r) slightly lower than unity [58]. The parameter has two major parts describing the phase shift(1 − δ(r) - due to Thompson scattering) and absorption (β(r)- predominantly as a result of photoelectric effect and Compton scattering), both of which real positive numbers, and is usually expressed by [61]:. 25.

(26) n(r) = 1 − δ(r) + iβ(r) with (hard X-rays) δ ≈ O(10−6 ) and β ≈ O(10−9 ). (18). Where: δ(r) - the decrement; β(r) - the extinction coefficient; r = r(x, y, x) - position of the specimen in the 3D space. Interestingly, one can notice the δ parameter is 1000 times larger than β, which highlights the phase changes contribute to a greater extent to the image formation and are more sensitive to sample structure as compared with conventional absorption images, strongly limited upon the dose of radiation delivered to the sample/patient. This phenomenon is currently utilized in X-ray imaging to gain in the visualization of higher fidelity histological details obtainable by X-ray phase contrast imaging [72]. Since X-rays mainly interact with bound shell electrons of atoms, both δ(r) and β(r) are linked to the electron density of the medium [58]. By assuming X-ray energies are far away from absorption edges (which is the case when hard X-rays of the energies somewhere in between 5-20 keV are utilized for analyzes of biological specimens mainly composed of H, C, N, O, whose absorption energies are out from this range), both the coefficients of the refractive index reflect the sample electron density [73]. More, by assuming a specimen to be analyzed is a multi-elemental one, the real part of the refractive index scales up with the sample density and is given by [58]: P pi Zi 2πre 2πre δ(r) ≈ ρe (r) 2 = 2 ρm (r) P i k k u i p i Ai. (19). Where: δ(r) - the decrement; β(r) - the extinction coefficient; r = r(x, y, x) the sample position; Zi - atomic number of the i-th element in a sample; Ai - atomic mass of i-th element in the sample; ρm (r) - mass density of the sample; ρm (r) - sample electron density; k - wave vector; u ' 1.66 · 10−27 kg - unified atomic mass unit However, in order to extract the phase shift of X-rays the only possible experiments are limited to intensity measurements, meaning the phase information of the propagated wavefield is lost, which is commonly referred to as the phase problem [74]. For showing how the pure intensity and phase images blend with each other, we first assume the incident para-axial monochromatic wave field propagates out along the z axis and is next transmitted through the sample. While interacting, directly downstream the sample position (z = 0), upon absorption, the wave-field drops down, and undergoes a phase shift, which could be described by [71]:. 26.

(27) u0 (x, y) = T (x, y) · uinc (x, y). (20). Where: T (x, y) - the transmission function describing the interaction of the beam with the sample; uinc (x, y) - the incident wave amplitude; u0 (x, y) - the incident wave upon interaction with the sample. At the same time, T (x, y) reads: T (x, y) = e−B(x,y) · eiφ(x,y). (21). Where: B(x, y) - the change in amplitude distribution; φ(x, y) - the change in phase distribution. Both φ(x, y) and B(x, y) are linked to the real (δ) and imaginary (β) parts of the refractive index, and are given by the following set of integral equations: Z 2π B(x, y) = β(x, y, z)dz λ z Z Z 2π 2π φ(x, y) = (1 − δ(x, y, z))dz = φair − δ(x, y, z)dz λ z λ z. (22) (23). Where: λ - wavelength; δ(x, y, z) - the decrement’s distribution in a sample; β(x, y, z) - the distribution of the extinction parameter in a sample; φair - the phase shift caused by air (when the sample is absent); B(x, y) - the change in amplitude distribution; φ(x, y) - phase shift upon the sample position. The intensity of the beam at the point z = 0 (located just off the sample position), is a product of the attenuated wave’s amplitude multiplied by its complex conjugate (so-called pure absorption contact image): I = |u0 (x, y)|2 = u2inc (x, y)e−2B(x,y). (24). Where: uinc (x, y) - the incident wave amplitude; B(x, y) - the change in the beam’s amplitude distribution. In turn, by assuming the beam passes straight away from z = 0 a finite propagation distance z, and provided the assumption on near-field (Fresnel) diffraction approximation is held, the intensity of the propagated X-rays is a convolution of the complex function, referred to as the complex propagator Pz , with their amplitude at z = 0 in direct space:. 27.

(28) uz (x, y) = (Pz ∗ u0 )x,y 1 x2 + y 2 Px (x, y) = exp iπ iλz λz. (25) (26). Where: Pz (x, y) - the propagator; u0 (x, y) - the amplitude of the wave-field at z = 0; x, y, horizontal and vertical coordinates in the plane perpendicular to the beam direction, respectively; z =. l·D l+D. - effective propagation distance with l source-to-sample, and D sample-to-. detector distances; λ - wavelength. In reciprocal space, the convolution of two function becomes their multiplication, and the above mentioned formula may be simplified to: u˜z (f, g) = P˜z (f, g) · u˜0 (f, g). (27). And: P˜z (f, g) = exp −iπλz(f 2 + g 2 ). . (28). Where: f , g - equivalents of x and y variables in real space, respectively P˜z (f, g) - Fourier transform of the 2D propagator; u˜0 (f, g) - Fourier transform of the intensity image at z = 0. Henceforward, for convenience, the derivation is carried out for one dimension being selected, be it f . As proposed in [75], the intensity of the propagated wavefield is given in reciprocal space as (in analogy to the real space equation: I(x, y) = |u(x, y)|2 ): Z +∞ 2 ∗ −iπλzf I˜z (f ) = (u˜z ∗ u˜z )f = e dηei2πηf T (η)T (η − λzf ). (29). −∞. Where: f - selected spatial frequency in Fourier space; λ - wavelength; z - effective propagation distance; η - an integration variable analogous to x. In order to simplify this complicated equation, a slowly varying phase approximation is applied to the product of the transmission functions presented above. This approximation assumes the variations in the phase shift in the imaged object are not that rapid [76]: |φ(η) − φ(η − λzf )| << 1 → T (η)T (η − λzf ) ≈ 1 + i[φ(η) − φ(η − λzf )]. (30). Where: f - selected spatial frequency in Fourier space; λ - wavelength; z - effective propagation distance; η - integration variable analogous to x. In addition, by assuming a weak absorption by the sample B(x) << 1, using the slowly varying phase approximation presented as above, the following formula can be finally obtained for the intensity of the wave-field propagated by z (reciprocal space) [71]: 28.

(29) ˜ ) − 2 cos(πλzf 2 ) · B(f ˜ ) I˜z (f ) ≈ δD (f ) + 2 sin(πλzf 2 ) · φ(f. (31). Where: f - selected spatial frequency in Fourier space; λ - wavelength; z - effective propa˜ ) - phase distribution in reciprocal space; B(f ˜ )gation distance; δD - Dirac distribution; φ(f amplitude distribution in reciprocal space.. Figure 3: Phase contrast transfer function (PCTF) and amplitude contrast transfer function (ACTF) for a ’weak-contrast’ object.. As follows from Eq 31, in the intensity image, the phase and absorption information are filtered-out by sinus and cosinus functions, respectively. As shown in Fig 3, for z = 0, one can see the intensity distribution provides with the pure absorption (contact image) image. The phase and absorption filtering function are commonly referred to as phase contrast transfer function (PCTF), and absorption contrast transfer function (ACTF), respectively [71]: ACT F = 2 cos(πλzf 2 ). (32). P CT F = 2 sin(πλzf 2 ). (33). Where: λ - wavelength; z - effective propagation distance; f - selected spatial frequency in Fourier space.. 29.

(30) 6.6. Considerations on sample thickness in XRF. In the case the primary exciting beam of X-rays is monochromatic, the intensity of the respective line of characteristic radiation of the Ei energy is defined by the fundamental parameters equation [77]: I(Ei ) =. G(Ei )ai (E0 )I0 (E0 ) · F (α, β, E0 , Ei ) sin(α). F (α, β, E0 , Ei ) =. 1 − exp[−ρd(µ(E0 ) csc(α) + µ(Ei ) csc(β)] µ(E0 ) csc(α) + µ(Ei ) csc(β). ai = Wi τi (E0 )¯ ωi pi (1 −. 1 ) = Wi f (τi , ω ¯ i , pi , ji ) ji. M = ρd. (34) (35). (36). (37). Where: α, β - the effective incidence and take-off angles; I0 (E0 ) - the number of incident photons of energy E0 per second, per srd; (Ei ) - the intrinsic detector for recording a photon of energy Ei ; Wi - the weight fraction of the i-th element; M - sample mass per unit area; d - sample thickness; ρ - sample density; E0 - the energy of the primary exciting beam; Ei the energy of the fluorescent radiation of the i-th element; µ(E0 ), µ(Ei ) - mass absorption coefficient at the E0 , and Ei energies, respectively; ji - absorption jump for the i-th element; pi - transmission probability for the ith element; τi (E0 ) - cross section for photoelectric absorption. One can notice that the self-absorption process must be considered for characteristic radiation while passing through a sample of specific thickness as encoded by the F (α, β, E0 , Ei ) term. Apparently, the intensity depends upon the sample mass per unit area (called the mass thickness), and, as well, the weight fraction of the i-th element, which means the quantification of the elements is possible based on intensities of their characteristic radiation. The quantification of the data with the formula presented above is often refereed to as the fundamental parameters approach. However, a key issue behind this method is to consider whether the absorption effects in a sample are considerable. In that respect, the value of the mass thickness underlies the classification of sample specimens, which is tremendously critical for the method of quantification to be used. Specifically, if it is assumed that the mass thickness is close to zero M → 0, the sample could be considered thin. In this case, the respective formula for computation of the intensity of characteristic x-rays could be computed by using the approximation 1 − e−x ≈ x as [17]: Iithin =. ¯ i , pi , ji )I0 (E0 )Mi G(Ei )ai (E0 )I0 (E0 )M M ·Wi =mi G(Ei )f (τi , ω ======= ∝ Mi sinα sinα 30. (38).

(31) This equation is satisfied provided the absorption effects in a sample are negligible. By assuming the approximated formula works as long as the relative error between the exact equation and its approximation is lower than 5%, one can draw the condition the sample mass per unit area must satisfy to be considered thin: Mthin ≤. 0.1 µ(E0 )cscα + µ(Ei )cscβ. (39). The thin sample approximation underlies a simplified external standard method of data quantification by assuming the fluorescence signal is proportional to the areal mass of a specific element. In turn, the sample is considered thick, provided M → ∞. With this approximation the formula to compute for the intensity of characteristic x-rays becomes [17]: Iithick (Ei ) =. G(Ei )ai (E0 )I0 (E0 ) µ(E0 ) + µ(Ei ) sinα sinβ. (40). The above-present approximation works as long as the sample mass thickness satisfies the following condition:. 6.9 (41) µ(E0 )cscα + µ(Ei )cscβ In the case the sample mass per unit area lies in between the thin and thick sample approxMthick ≥. Thick sample Thick sample. ple am s e t dia. Intermediate sample e. erm. Int. Thin sample Thin sample. (b). (a). Figure 4: (a) Relative fluorescence intensity vs. sample mass per unit area for the selected biologically-active chemical elements; (b) tentative thickness’ range a dried brain gray matter sample falls into (the computations were made at the energy of 17 keV).. imation, it is regarded as intermediate: Mthin < M < Mthick 31. (42).

(32) In order to simulate the relation between the intensity of characteristic radiation and the mass thickness in a real tissue, by using Eq 34, the dimensionless relative intensity was computed as [17]: Ri (Mi ) =. Ii (Ei ) thick Ii (Ei ). = 1 − exp [−M (µ(E0 ) csc(α) + µ(Ei ) csc(β)]. (43). In tissue samples, the elemental composition is usually very complex. To account for this problem, the mass attenuation of the medium is determined as a weighted arithmetic mean of respective mass attenuation coefficients with the weights representing the fraction of each element present in a sample as [16]: µ=. n X. wi · µi. (44). i=1. Where: n - the number of elements in a sample contributing to the total absorption coefficient; wi - the weight fraction of the i-th element; µi - the absorption coefficient of the i-th element. By using Eq 43 and Eq 44 as well as the average composition of the soft matrix of the brain gray matter tissue (taken from [78]), the relative intensity of characteristic radiation vs. sample mass per unit were computed for the primary exciting beam of 17 keV. The results of these calculations are highlighted in Fig 4a-b. From this data, one can infer the selfabsorption phenomenon is indicative of the energy of characteristic radiation, and should always be considered for low energy elements such as P. As a consequence, given a sample thickness, as presented in Fig 4b showing the respective ranges for thin, intermediate and thick samples, although for some the high-Z elements a sample may be considered thin (i.e. from Fe onwards), for another ones (i.e. from Ca downwards) the quantification should take into account absorption effects. This remark makes the whole quantification of chemical elements a very challenging task, which should be preceded by a thorough investigation of the mass thickness of analyzed tissue to decide which mathematical model fits in with the best.. 6.7. Quantitative XRF with thin specimens. Typically, the first step in the XRF data analysis is the spectral curve fitting to determine the net peak areas of Kα (or Lα ) lines of the elements present in a sample [79]. However, these values do not reflect the relative elemental contents, as they depend upon many parameters (please see Eq 34) which significantly varies for various elements. To transform raw numerical values of net peak values into measurable units reflecting their abundances, the quantification procedure is carried out to end up with elemental masses per unit area, or, mass fractions [9]. For this step, either external or internal standards are used [17]. The 32.

(33) former, commonly used in bio spectroscopy of thin/intermediate tissue sections, is a separate sample with certified values of elements [17, 26,79]. However, the latter, usually used in the analysis of liquid specimens, is a solution of known elemental composition that is added to the sample [80]. Since the presented thesis focuses upon the use of external standards, the internal standard method will no be discussed any longer. Provided the specimen may be considered thin, meaning its self-absorption turns out to be negligible, theory shows (cf. Eq 38) the net peak value for the i-th element is directly linked to its mass per unit area. With this assumption satisfied, a simplified method of quantification, commonly referred to as a thin sample approach, can be utilized in the quantification step alongside a dedicated set of external standards [17]. As highlighted in Fig 4, it may happen that all the elements quantified fulfill the stringent requirement of a thin sample, and the quantification can be performed via the simplified method as highlighted above. However, depending on the sample mass per unit area, it may be the case the absorption becomes non-negligible, which is usually the issue for the low-Z part of the XRF spectrum (i.e. P), and the sample becomes intermediate. In other words, for high-Z elements the specimen can be considered thin, but for the low-Z ones, an intermediate sample correction should be taken into account (for brain tissue it is usually the concern for the sample (fresh specimen) thickness ranging from 25 µm upwards). This fact requires a special data treatment by accounting the self-absorption of the characteristic radiation in a sample [81, 82].. 7. Experimental part. 7.1. Preparation of specimens for the experiments with the use of X-rays. For the XRF imaging, the tissue samples are routinely the subject of deep freeze-drying to evaporate water out the specimens. This procedure allows reducing the detection limits by decreasing strong background arising from large stoichiometric amounts of hydrogen. The process is also used to prevent the sample degradation without using any chemical fixation to end up with a specimen in a pristine state [10]. Unfortunately, the commonly used freezedrying enhances the artifacts arising from complex topography of biological specimens [10]. In this research, the problem of sample morphology was addressed by analyzing freeze dried SN specimens [10]. Evidence shows that the tissue is morphologically heterogeneous, and one can distinguish its two major parts: the neuromelanin pigmented neurons (visible in the optical microscope as dark points without any staining - cf. Fig 5) and surrounding neuropil areas with elevated mass density in the former. This effect may influence the final quantification using the XRF technique due to the higher projected mass density in neurons. 33.

(34) [8, 12].. (a). (b). (d) (c). Figure 5: Microscopic image of (a)-(b) unstained and (c)-(d) haematoxylin-stained SN tissue specimen of the same area (scalebar = 50 µm).. In the studies that will follow, the samples were cryosectioned (in -20 o C) onto 10, 15, 20 and 25 µm, thaw-mounted onto either versatile 200 nm-thick silicon nitride (Si3 N4 ) membranes (Silson Ltd. UK) or Utralene films (SPEX, CertiPrep, USA), and freeze-dried in -80 o C [8]. In particular, Si3 N4 substrates come up with low background, and, most importantly, they can be used in other imaging modalities including among others molecular imaging by FTIR [83], which is commonly used in clinical spectroscopy. Also note the membrane Si seems particularly attractive for X-ray measurements, where its transmission can provide with in-depth information on absorption properties of tissue compartments whenever a sample is morphologically heterogeneous, as proposed herein.. 34.

(35) 7.2. Topography measurements. For these studies, topography maps of the SN samples were acquired using a DektakXT (Bruker Corporation) profilometer with a 0.2 µm radius contact stylus sensor. The low stylus force was chosen for measurements (0.5 mg, N-Lite+) in order to prevent any damages to the sample surface. The spatial resolution was set to 1 µm and 0.1 µm in X and Y directions, respectively. The data was finally presented as two-dimensional maps. For computation of the average thickness of a specimen, the curve fitting procedure with the boxcar fitting model was used, and the fitting error was used as a measure of uncertainty. Finally, to ensure that the stylus force would not cause any damage to the sample material, each scan across a sample was repeated six times, and the thickness homogeneity was computed as a percentage coefficient of variation (the standard deviation divided by the mean value) for the average thickness computed. Fig 6 shows the topography measurements of dried SN samples cut onto 10 µm and 20 µm [8, 10]. Topography maps of the SN specimens were recorded by the acquisition of either 2D topography maps (cf. Fig 6a-b) or linear profiles (cf. Fig 6 c-d) across a selected specimen. In all, as shown in Fig 6 c-d, the surface of the samples was found rough with the variations comparable with the reduced thickness of a dried brain slice. Fig 6 c-d demonstrate that although the samples were nominally cut onto 20 µm and 10 µm, the final thickness of a sample got reduced by around 80 %, which is consistent with the average content of water in brain tissue samples. Interestingly, it was relatively difficult to co-localize the morphology variations to the positions of neuron bodies suggesting the drying of the samples may not be density-related. The histogram in Fig 6e highlights the scan-to-scan variation of the measurements. It implies the changes due to the stylus force exerted to the sample surface were negligible (less than 5 %), and more likely due to small shifts between the measured lines rather than as a result of possible damage to the specimens. These topography measurements are tremendously important in the light of the commonly used sample preparation protocol by the freeze-drying of thin biological specimens. It is due to adhesive forces acting between the substrate and the sample make a biological specimen shrink and its surface becomes even more rough. This analysis made possible to determine the reduction in thickness of thin biological specimens upon freeze-drying. It could also be used in further research to approximate the average thickness of similar types of brain tissue samples upon preparation.. 35.

(36) 8.0 (μm) 7.0 6.0 5.0 4.0 3.0. Nominal thickness of 20 (µm). 2.0 1.0 0.0. Nominal thickness of 10 (µm). 2.0 (μm) 1.5 1.0 0.5 0.0 -1.0. (b). -1.5. Dried sample thickness (μm). Dried sample thickness (μm). (a). h~2 (µm). h~4 (µm). (c). (d). Repeat the scan six times. Repeat the scan six times. (e). Figure 6: Topography maps of two selected SN specimens mounted onto Si3 N4 , nominally cut onto: (a) 10 µm; (b) 20 µm; the curve fitted thickness profiles for the samples nominally cut onto (c) 10 µm and (d) 20 µm; the data variability histogram for the set of consecutive topography measurements along the lines depicted as above. Nominal thickness - the thickness of freshly cut samples; Dried sample thickness - the thickness of a sample upon freeze-drying. 36.