Instituto de F´ısica Gleb Wataghin
Leonardo Augusto Ulbrich Bueno
Constru¸c˜
ao e Caracteriza¸c˜
ao de um Sistema ´
Optico para Imageamento de
Fluxo Sangu´ıneo
Construction and Characterization of an
Optical System for Blood Flow Imaging
Campinas 2019
Construction and Characterization of an
Optical System for Blood Flow Imaging
Constru¸c˜
ao e Caracteriza¸c˜
ao de um Sistema ´
Optico para
Imageamento de Fluxo Sangu´ıneo
Dissertation presented to the Instituto de F´ısica ”Gleb Wataghin” of the University of Campinas in partial fulfillment of the requirements for the degree of Mas-ter, in the area of Applied Physics.
Disserta¸c˜ao apresentada ao Instituto de F´ısica ”Gleb Wataghin” da Universidade Estadual de Campinas como parte dos requisitos exigidos para a obten¸c˜ao do t´ıtulo de Mestre em F´ısica, na ´area de F´ısica Aplicada.
Supervisor/Orientador: Prof. Dr. Rickson Coelho Mesquita
Este trabalho corresponde `a vers˜ao final da disserta¸c˜ao de-fendida pelo aluno Leonardo Augusto Ulbrich Bueno, e orientada pelo Prof. Dr. Rickson Coelho Mesquita
Campinas 2019
Biblioteca do Instituto de Física Gleb Wataghin Lucimeire de Oliveira Silva da Rocha - CRB 8/9174
Bueno, Leonardo Augusto Ulbrich,
B862c BueConstruction and characterization of an optical system for blood flow imaging / Leonardo Augusto Ulbrich Bueno. – Campinas, SP : [s.n.], 2019.
BueOrientador: Rickson Coelho Mesquita.
BueDissertação (mestrado) – Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin.
Bue1. Fluxo sanguíneo. 2. Imagem. 3. Espectroscopia ótica de difusão. 4. Espectroscopia no infravermelho próximo. 5. Tomografia ótica por contraste speckle. I. Mesquita, Rickson Coelho, 1982-. II. Universidade Estadual de Campinas. Instituto de Física Gleb Wataghin. III. Título.
Informações para Biblioteca Digital
Título em outro idioma: Construção e caracterização de um sistema óptico para
imageamento de fluxo sanguíneo
Palavras-chave em inglês:
Blood flow Imaging
Diffuse optical spectroscopy Near infrared spectroscopy
Speckle contrast optical tomography
Área de concentração: Física Aplicada Titulação: Mestre em Física
Banca examinadora:
Rickson Coelho Mesquita [Orientador] George Cunha Cardoso
Sandro Guedes de Oliveira
Data de defesa: 20-02-2019
Programa de Pós-Graduação: Física
Identificação e informações acadêmicas do(a) aluno(a)
- ORCID do autor: https://orcid.org/0000-0003-4735-3180
- Currículo Lattes do autor: http://lattes.cnpq.br/9321122490237742
MEMBROS DA COMISSÃO JULGADORA DA DISSERTAÇÃO DE MESTRADO DE LEONARDO AUUSTO ULBRICH BUENO – RA 190928 APRESENTADA E APROVADA AO INSTITUTO DE FÍSICA “GLEB WATAGHIN”, DA UNIVERSIDADE ESTADUAL DE CAMPINAS, EM 20 / 02 / 2019.
COMISSÃO JULGADORA:
- Prof. Dr. Rickson Coelho Mesquita – Orientador – DRCC/IFGW/UNICAMP
- Prof. Dr. George Cunha Cardoso – FFCLRP/USP
- Prof. Dr. Sandro Guedes de Oliveira – DRCC/IFGW/UNICAMP
OBS.: Informo que as assinaturas dos respectivos professores membros da banca
constam na ata de defesa já juntada no processo vida acadêmica do aluno.
CAMPINAS
2019
S´o tenho a agradecer por esses ´ultimos dois anos e meio! Ca´ı de paraquedas na UNICAMP com o intuito de trabalhar com o assunto que me envolvi durante toda a minha gradua¸c˜ao e, na verdade, ganhei muito mais do que experiˆencia profissional. Vivenciei diversas experiˆencias e amizades que queria levar para o resto da vida e, como forma de agradecimento, deixo aqui um recado para os que cruzaram meu caminho durante esse per´ıodo.
Aos meus colegas que estiveram por perto com certeza pela maior parte do tempo no Laborat´orio de ´Optica Biom´edica: meu orientador Rickson Coelho Mesquita por todo o conhecimento, li¸c˜oes de vida e confian¸ca depositada. Meus queridos colegas Luiz, Andr´es, Edwin, S´ergio, Rodrigo, Gioz˜ao, Gio, Arnaldo e Alex. Cada um de vocˆes merece seu lugar em meu cora¸c˜ao.
Viver em Campinas n˜ao teria sido a mesma experiˆencia sem a presen¸ca de algumas pessoas muito especiais. Pelas trips, discuss˜oes, militˆancias e obviamente as milhares de cervejas (para podermos seguir em frente) gostaria de mandar um salve para Murilo, Pedroca, Jeg, Taina, Chic˜ao, Gabi, Danilo, Raul, Nat, Man´e, Jo˜ao e ´e claro ao meu terapeuta, Guto, que me ajudou a manter a cabe¸ca na linha!
S˜ao Paulo obviamente n˜ao ficou para tr´as. Voltei sempre que pude (quase todo final de semana na verdade), pois l´a sempre tive v´ınculos muito fortes. Aos colegas da USP um grande abra¸co e seguimos todos na luta (da obten¸c˜ao de t´ıtulos kkk): Thomas, Pedro, Vit˜ao, Phelps, Bull, Carica, Brun˜ao, Gabriel, Mi, Lais e Guizera. Foi l´a tamb´em que conheci uma pessoa que com certeza mudou a minha vida. Um agradecimento especial para Mayara Palmieri pelos quase cinco anos de ensinamentos de vida e momentos especiais vivenciados. A vida cruzou nossos caminhos em um momento de forma¸c˜ao de car´ater e por isso s´o tenho a agradecer pela pessoa que ajudou a formar. A vocˆes (vocˆe e meninos) serei eternamente grato.
Aos meus eternos amigos da vida Cika, Pietro e Andrei. Desde crian¸ca juntos seja l´a qual a distˆancia que nos separa. Um dia vamos morar todos juntos na praia! Pelos infinitos rolˆes todos os finais de semana desde a oitava s´erie queria agradecer a cada um dos meus amigos de Cotia (98). A semana n˜ao passaria t˜ao r´apido se n˜ao fosse pra vˆe-los: Bru, Carrijo v´eio, De, Gut˜ao, Ranny, Gui, Ski, Luli, Firo, Luquinha, Bˆe, Zero, Flavinho e Felipe. Eu amo cada um vocˆes!
`
a fam´ılia Steinhauser. Clara, vocˆe esteve ao meu lado durante o que era pra ter sido o per´ıodo mais estressante da vida e sinceramente foi muito leve! Conversar com vocˆe todos os dias e saber que te veria em breve (muitas vezes na praia) ajudou a fazer desse ano o mais delicioso de todos! Um especial obrigado e n˜ao vejo a hora de te ver de novo :)
Por fim aqueles que sempre estiveram ao meu lado em qualquer situa¸c˜ao: M˜ae, Tio Flavio e V´o Rosa por todo o carinho, confian¸ca apoio emocional e financeiro. Vocˆes s˜ao o n´ucleo da minha vida. Ao meu pai, Adri e Gui pelos infinitos alegres momentos na praia, todo o carinho e apoio. Para a av´o muito mais do que fofa Maria Am´alia e meus queridos Tios Marco, Junior e Cida. Meus irm˜aos Gabriel, Bruna, Lˆe, Vitinho, Laura e Rod. N˜ao tenho palavras para agradecer a companhia de vocˆes. Primo: estou chegando!
Devo tamb´em me lembrar da UNICAMP, mais especificamente do Instituo de F´ısica “Gleb Wataghin”, por fornecer toda a infra-estrutura necess´aria para a realiza¸c˜ao desse projeto de mestrado. Por fim, gostaria de agradecer ao CNPq pelo apoio financeiro, sem o qual este t´ıtulo n˜ao teria sido obtido. This study was financed in part by the Coordena¸c˜ao de Aperfei¸coamento de Pessoal de N´ıvel Superior - Brasil (CAPES) - Finance Code 001 Process number: 142990/2016-7
Constru¸c˜ao e Caracteriza¸c˜ao de um Sistema ´Optico para Imageamento de Fluxo Sangu´ıneo
Leonardo Augusto Ulbrich Bueno Rickson Coelho Mesquita
O fluxo de sangue mostrou desempenhar um papel vital em diversas doen¸cas e, portanto, tem sido associado como um potencial biomarcador para a progress˜ao de doen¸cas e efic´acia de tratamentos. Independentemente, t´ecnicas ´opticas no infravermelho pr´oximo demonstraram ser uma poderosa ferramenta n˜ao invasiva para o estudo da hemodinˆamica. Neste tipo de ilumina¸c˜ao, o tecido biol´ogico ´e considerado como um meio turvo (no qual o espalhamento predomina sobre a absor¸c˜ao) e assim a propaga¸c˜ao da luz no tecido profundo pode ser mod-elada por um processo de Difus˜ao de F´otons. Medidas espectrosc´opicas do fluxo sangu´ıneo em tecidos profundos foram previamente validadas com Espectroscopia de Correla¸c˜ao Difusa (DCS), uma t´ecnica atualmente empregada em nosso laborat´orio para estudos em humanos. A fim de expandir e implementar uma t´ecnica ´optica para imagens de pequenos animais, neste trabalho focamos nossa aten¸c˜ao na constru¸c˜ao e caracteriza¸c˜ao de um instrumento ´
optico h´ıbrido capaz de produzir imagens de fluxo sangu´ıneo com Laser Speckle Imaging (LSI) e Speckle Contrast Optical Tomograpy (SCOT). Os fenˆomenos de speckle surgem do espalhamento m´ultiplo da luz coerente que percorre os meios difusivos, como o tecido biol´ogico. O padr˜ao de interferˆencia observado (padr˜ao de speckle) pode ser estatisticamente descrito por uma distribui¸c˜ao exponencial da intensidade da luz associada ao movimento das part´ıculas que espalham luz no meio. O Laser Speckle Imaging consiste na aquisi¸c˜ao de imagens do padr˜ao de speckle e na estimativa de mapas de fluxo a partir do c´alculo do contraste de speckle, resultando em imagens de fluxo bidimensionais. Embora o LSI tenha se mostrado uma t´ecnica poderosa, r´apida e barata, n˜ao permite a quantifica¸c˜ao das velocidades das part´ıculas espalhadoras e fornece apenas medidas em tecidos superficiais. O SCOT, por outro lado, combina as principais caracter´ısticas do DCS e do LSI para fornecer imagens tridimensionais e quantitativas do fluxo.
Como o SCOT compartilha uma instrumenta¸c˜ao semelhante `a de LSI, desenvolvemos e car-acterizamos uma instrumenta¸c˜ao h´ıbrida que executa LSI e SCOT separadamente. Ambas as t´ecnicas foram validadas com experimentos realizados em meios controlados.
Construction and Characterization of an Optical System for Blood Flow Imaging
Leonardo Augusto Ulbrich Bueno Rickson Coelho Mesquita
Blood flow has shown to play a vital role in several diseases and therefore has been associated as a potential target biomarker for disease progression and treatment efficacy. Independently, optical techniques in the near infrared have shown to be a powerful non-invasive tool for studying hemodynamics. Under this type of illumination biological tissue is considered as a turbid medium (in which scattering predominates over absorption) and so light propagation in deep tissue can be modeled by a Photon Diffusion process. Spectroscopic measurements of blood flow in deep tissue have been previously validated with Diffuse Correlation Spec-troscopy (DCS), a technique currently employed in our laboratory for human studies. In order to expand and implement an optical technique for small animal imaging, in this work we have focused our attention to the construction and characterization of a hybrid optical instrument capable of imaging blood flow with Laser Speckle Imaging (LSI) and Speckle Con-trast Optical Tomography (SCOT) techniques. Speckle phenomena arises from the multiple scattering of coherent light when traveling through diffusive media such as biological tissue. The observed interference pattern (Speckle Pattern) can be statistically described by an ex-ponential distribution of light intensity associated with the movement of scattering particles that compose the medium. Laser Speckle Imaging consists on acquiring Speckle Pattern im-ages and estimating flow maps from the Speckle Contrast resulting in two-dimensional flow images. Although LSI has shown to be a powerful, fast and inexpensive technique it lacks on quantification of scattering particle velocities and provides measurements on superficial tissue only. SCOT, on the other hand, combines the main features of DCS and LSI to provide quantitative three-dimensional images of flow. Since SCOT shares similar instrumentation to that of LSI, we developed and characterized a hybrid instrumentation that performs both LSI and SCOT separately. Both techniques were validated with pilot liquid phantom experiments described in this dissertation.
1.1 Resolution and sampling depth domain of various imaging techniques used for measuring blood flow. Figure adapted from [5]. . . 18 2.1 Absorption coefficients of main blood in the optical window: i ) water; ii )
oxyhemoglobin and iii ) deoxyhemoglobin. Adapted from [16]. . . 23 2.2 Light propagation under diffusive regime inside a turbid medium. Light
prop-agates spherically and the intensity vanishes for longer distances from the source. Photons are also scattered back to illumination surface and can be collected by a detector. Adapted from [16]. . . 24 2.3 Variables described by the Radiative Transport Theory. The radiance
repre-sents the power per unit area per unit solid angle traveling in bΩ direction at time t and position r. The amount of radiant power transported across an element of area dσ in directions confined to an element of solid angle dΩ is calculated from equation 2.1. Figure obtained from [18]. . . 25 2.4 The light radiance L(r + dr, bΩ, t + dt, λ) emerging from an infinitesimal volume
differs from the incident radiance L(r, bΩ, t, λ) due to light-tissue interactions. The absorbed portion is µa(r, bΩ, t, λ)L(r, bΩ, t, λ)|dr| and the portion scattered
by tissue in bΩ direction is p(r, bΩ0, bΩ, t, λ)L(r, bΩ, t, λ)|dr|. The term |dr| denotes the magnitude of vector dr (|dr| = vdt) where v = c/n is the speed of light in the considered volume element. Adapted from [18]. . . 26 2.5 Representation of a photon (red dot) taking two random walks with length
`tr. Each random walk consists of many scattering events that occur after a
2.6 Illustration of a common Diffuse Correlation Spectroscopy experiment scheme. A NIR coherent laser beam is shined on a sample on a point-like manner and a photon counter receives the rapid (µs scale) light intensity fluctuations obtained at a distance away from the source. A correlator is fed with the measurement and calculates the light intensity auto-correlation function. A non-linear fit relating the measured intensity auto-correlation and the elec-tric field auto-correlation function obtained from the Photon Diffusion Theory allows spectroscopic measurements of blood flow dynamics. Figure obtained from [16]. . . 38 3.1 Simulation of Speckle Patterns with an exposure time of 1, 5 and 25 ms
conducted by [37]. . . 41 3.2 Light intensity negative exponential probability function profile on a fully
de-veloped Speckle Pattern. Note that the origin on x axis correspond to null values of light intensity. It is more likely to measure a dark spot (intensity values below the mean) than bright spots. Figure obtained from [39]. . . 43 3.3 Illustration of a Laser Speckle Imaging setup. A coherent NIR source
ilumi-nates the object in a full-field manner. The speckle pattern is recorded by a CCD for calculation of contrast images. . . 45 3.4 Raw speckle pattern (left) with its computed speckle contrast (right) showing
clear distinction between regions with increased flow (dark areas in the right image). The images show a cortical surface of 5 × 4 mm2 area. Adapted from
[41]. . . 46 3.5 Scheme of the optical tray built in our laboratory. A coherent NIR light
source has its intensity lowered by a Neutral Density Filter and is amplified and collimated by a microscope objective to provide wide-field illumination of a biological sample. . . 48 3.6 Logitech webcam sofware user interface that allows the control of some
param-eters related to the employed detector. Although the exposure time is available for manual set it does not provide the user exact value in a milli-second scale. 49 3.7 Labview Vision Acquisition user interface allowing the same parameters to be
adjusted on a scale to that corresponding to Logitech Webcam Software. . . 50 3.8 A typical light intensity image obtained from our detector when static
scat-tering media is shined with coherent NIR source. Currently, Speckle Pattern images are obtained with a 20x20mm field-of-view distributed on a 1080x1080 pixel grid, with each pixel corresponding to approximately 0.02mm. The yel-low bar corresponds to 2.5mm. . . 51 3.9 Spatial sampling of a speckle pattern on a CCD camera. A total of four pixels
were needed to record a single speckle on this pictorial representation obtained from [51]. . . 51
3.10 The characterization of our detection system is shown at the left-side with pixel (blue dots) and speckle (red dots) sizes represented as a function of camera-sample distance. The ideal situation for Speckle experiments would be to have the same values for pixel and speckle sizes. A change in our system’s f-stops would provide this situation as indicated on the right-hand side of the image. The solid black vertical line represents the current optimal object-camera distance for sampling small animal. . . 52 3.11 Current Laser Speckle Imaging system consisting of an optical tray (light
source, neutral density filters and microscope objective), imaging sample and webcam detector. . . 53 3.12 Micro-fluidic channels used for liquid phantom Laser Speckle Imaging
exper-iments. There are a total of fourteen rectangular channels with 400µm side length which are 4.5mm apart. The flow was controlled by a pump and deliv-ered from 0.5 to 4.5ml/min with 0.5ml/min step increase. . . 54 3.13 Example of a single Speckle Pattern image taken from static (left side) and
dynamic (right-side) situations of an experiment conducted on a micro-fluidic channel as described in Section 3.5. The yellow bar corresponds to 2.5mm. . 55 3.14 Example of a single Speckle Pattern image taken from static (left side) and
dynamic (right-side) situations of an experiment conducted on a micro-fluidic channel as described in Section 3.5. The yellow bar corresponds to 2.5mm. . 55 3.15 Speckle Contrast mean from a 2 × 2 pixels region inside the central channel
represented in Figure 3.14 as a function of flow. The error bar corresponds to the standard deviation. As expected, Speckle Contrast values decrease with increased flow. . . 56 3.16 Speckle Pattern examples of exposed micro-fluidic channels (right-hand side)
and 5mm submerged channel (right-hand side). Blurring is clearly visible on exposed image and is lost with depth increase. Each square has 5mm side length. . . 57 3.17 Laser Speckle Imaging results on a 5 mm2 area of a micro-fluidic channel.
Every situation had the same flow velocity controlled by a syringe pump. The channel depth was adjusted in order to demonstrate LSI limitation of conducting superficial measurements only. . . 58 4.1 Illustration of Speckle Contrast Optical Tomography system consisting of a
point-like NIR coherent source, a galvo mirror used for surface scanning and a CCD to measure light intensity with post-processing conducted on a computer. Figure adapted from [52]. . . 60 4.2 Computed Speckle Contrast versus source-detector separation according to the
4.3 Examples of flow reconstructions conducted with SCOT technique. The figure on the left-side represented a shear flow reconstruction by [12] whereas the right-side image consists of a Brownian-motion modeled flow by [13]. . . 63 4.4 Laser Galvo system built in our laboratory corresponding to two stepper
mo-tors connected to golden surface mirrors for xy beam scanning on a surface. Each motor has its movement controlled by an Arduino which is synchronized with detector data capturing using a home-made Labview environment. . . . 64 4.5 Sequence representing a SCOT experiment. A first step consists on
determin-ing the center of mass of raw intensity images to determine the source-detector (S-D) separations. Speckle Contrast is calculated according to equation 3.4 on nine 5x5 pixel windows surrounding each of the defined detectors and the mean value is assigned to the central pixel. A nonlinear least square minimiza-tion is conducted on K vs. S-D data to obtain boundary Diffusion Coefficient. This information is used on NIRFAST for tomographic procedure. . . 65 4.6 Raw intensity image example on a SCOT experiment with light source (blue
star) and user-defined detectors (yellow circles) represented for a single illu-mination spot. The yellow bar corresponds to 5mm. . . 65 4.7 Pictorial representation of a SCOT experiment. The light path differs for each
of the defined detectors and the penetration depth is increased with Source-detector separation. Tomographic procedure consists on isolating individual contributions of each sample volume to the measured Speckle Contrast. . . . 66 4.8 The left-hand side shows the flow reconstruction of a 6×4×4mm3heterogeneity
phantom submerged 2mm on a homogeneous highly-scattering media. The image on the right side corresponds to a real picture of the phantom with size 7 × 7 × 30mm3. . . . 69
A.1 Semi-infinite geometry representation. The Photon Diffusion Equation was solved using the Methods of Images. Adapted from [18]. . . 84 B.1 Representation of a single photon scattering event. . . 86 B.2 Representation of a multiple scattering regimen. Adapted from [16]. . . 88
Agradecimentos Resumo Abstract List of Figures Contents 1 Introduction 17 1.1 Dissertation Organization . . . 19
2 Theoretical Aspects of Light Propagation in Tissue 21 2.1 Light-Matter Interaction . . . 21
2.2 NIR Light Propagation Modeling in Turbid Media . . . 23
2.2.1 Radiative Transport Theory . . . 23
2.2.2 Photon Diffusion Equation . . . 31
2.3 Diffuse Correlation Spectroscopy (DCS) . . . 34
2.3.1 Experimental Methods of DCS . . . 35
3 Speckle-based Imaging of Blood Flow 40 3.1 Speckle Pattern . . . 41
3.2 Speckle Statistics . . . 42
3.3 Laser Speckle Imaging (LSI) . . . 44
3.4 Design of a Laser Speckle Imaging System . . . 47
3.4.1 Light Source . . . 47
3.5 Laser Speckle Imaging Experiments . . . 52
3.5.1 Phantom Preparation and Experimental Protocol . . . 53
3.5.2 Flow Sensitivity Experiments . . . 53
3.5.3 Depth Sensitivity Experiments of the LSI . . . 57
4 Speckle Contrast Optical Tomography (SCOT) 59 4.1 Construction and Characterization of a SCOT system . . . 63
4.2 Speckle Contrast Optical Tomography Pilot Experiment . . . 68
5 Summary and Perspectives 70 A Solutions for the Photon Diffusion Equation 80 A.1 The Green’s Functions Solution . . . 80
A.2 Infinite Media . . . 82
A.3 Semi-Infinite Media . . . 83
B Correlation Diffuse Equation 85 B.1 Dynamic Light Scattering in the Single-Scattering Limit . . . 85
B.2 Multiple Scattering Limit . . . 87
C SCOT Scripts 93 C.1 Experimental Speckle Contrast Calculation . . . 93
C.2 Theoretical Speckle Contrast Calculation . . . 102
C.3 Smear Correction . . . 105
C.4 Minimization Algorithm . . . 107
C.5 Theoretical Auto-correlation Calculation . . . 115
Chapter 1
Introduction
Great attention has been paid over the last decades on the development of medical instru-mentation capable of providing physicians quantitative measurements that allow early and accurate detection of a disease as well as information that might be helpful on a treatment scenario. There currently is a vast universe of techniques that are used on a daily routine for patient care and provide a huge spectra of information.
Tissue hemodynamics (i.e., blood characteristics over time) has been one of the main targets for quantitative physiological assessment by several groups. Blood flow, for example, has shown to play a vital role on several diseases such as spinal cord ischemia and ischemic stroke, and has also been used as an indicator of treatment efficacy [1–4]. The potential of blood flow as a biomarker led to the development of several techniques to measure this quantity in different spatial domains (Figure 1.1). Imaging modalities such as Magnetic Resonance Imaging (MRI), Computed Tomography (CT), Positron Emission Tomography (PET) and ultrasound (US) have been extensively advanced over the last years to acquire information on blood flow. Every technique has its own restrictions and limitations, and the physical principles behind each method varies widely.
Figure 1.1: Resolution and sampling depth domain of various imaging techniques used for measuring blood flow. Figure adapted from [5].
Currently, the assessment and monitoring of blood flow at the micro-circulatory level provide the highest resolution on preserved tissue specimens, whereas imaging of living deep tissues can be done with the use of clinical methods at the cost of a lower resolution and specificity. Therefore, resolving vessels at a micro-circulation resolution requires the use of more complex and costly protocols [6].
More recently, optical techniques have shown to be a powerful tool for studying micro-circulation physiology with a portable, fast and inexpensive setup suitable for performing continuous non-invasive measurements at the bedside. Spectroscopic measurements of blood flow in macroscopic tissue have been previously reported by our group [1–4, 7–9] using a home-made Diffuse Correlation Spectroscopy (DCS) system that is now on clinical trials at the Clinics Hospital of the University of Campinas (UNICAMP). The main disadvantage of DCS and its tomographic attempt (Diffuse Correlation Tomography - DCT) is the low signal-to-noise (SNR) ratio which arises due to the fact that the measured quantity, light intensity auto-correlation, has to be computed for each Speckle independently using single or few-mode fibers. SNR increases as the square root of number of Speckles and so obtaining significant benefits would require the employment of large number of detectors which is not
feasible for the required dense sampling of DCT applications [10]. An alternative suggested by the literature was to employ large arrays of detectors to capture the intensity fluctuations of many Speckles simultaneously using a photon-counting CCD and then computing the intensity auto-correlation. This attempt has been made and is not yet feasible for biomedical applications as the decay of intensity auto-correlation function is much faster (µs) than frame rates of current camera technology (ms) [11]. Although spectroscopic measurements of relative blood flow provide physicians information on this potential bio-marker, it lacks on spatial resolution which might be interesting for localizing flow heterogeneity in tissue.
In this work we aimed to develop a low-cost imaging system for blood flow capable of resolving the micro-circulation of small animals. We first developed a Laser Speckle Imaging (LSI) system. Phantom experiments were conducted with our LSI system in order to validate our instrumentation and to show that our current system is capable of imaging superficial blood flow with high spatial resolution. In addition, based on recent publications [12, 13], we made an attempt of imaging deep-tissue flow by extending our previously developed system with an optical technique that merges the ideas behind DCS and LSI known as Speckle Contrast Optical Tomography (SCOT). As LSI and SCOT share similar instrumentation, a hybrid instrument was built allowing the user to perform either SCOT or LSI.
1.1
Dissertation Organization
This dissertation starts with a theoretical approach on a simplification to Maxwell’s Equations that describes the interaction between near-infrared coherent light and a complex turbid medium such as biological tissue. The development of the Photon Diffusion model is shown in Chapter 2. An optical technique capable of measuring blood flow dynamics known as Diffuse Correlation Spectroscopy (DCS) is also explored in Section 2.3 as is of fundamental importance for the understanding of the imaging techniques developed in this work.
Chapter 3 explores theoretical aspects of a speckle-based imaging technique known in the literature as Laser Speckle Imaging (LSI). A system for small animal imaging of blood flow was built and validated as the main objective of this dissertation. Application exam-ples of the technique are also discussed with its potential clinical use and its limitation to acquire information of blood flow in superficial tissues is shown in Section 3.5 with phantom experiment data.
The description of Speckle Contrast Optical Tomography (SCOT), an optical technique that merges the ideas behind DCS and LSI to obtain three-dimensional blood flow images of deep tissue is discussed in chapter 4. As the instrumentation of LSI and SCOT share similar optical components, an attempt of constructing and validating a hybrid system capable of performing both LSI and SCOT is shown in Section 4.1. The algorithms required for imaging processing are also explored in section 4.1.
Final remarks and future perspectives on the development and application of each tech-nique is discussed in Section 5.
Chapter 2
Theoretical Aspects of Light
Propagation in Tissue
2.1
Light-Matter Interaction
Among the different types of light-matter interaction we may find on nature, we will focus this dissertation on the two most important phenomena to consider when working with near-infrared (NIR) light sources applied to phantoms mimicking human tissues: absorption and scattering.
Absorption is the simplest form of interaction between a photon and particles that constitute a medium. It occurs when the energy of the incident photon matches one of the energies of rotational or vibrational modes of the particles, which excites the particle to a higher state. In a macroscopic medium, absorption is usually characterized by the so called absorption coefficient (µa), a statistical measurement of the mean number of absorption
events per unit length (cm−1). This parameter depends on the concentration and the cross-section of the absorber. The cross-cross-section is a function of the incident light wavelength, λ.
When we shine NIR light (700 − 900nm) into biological tissue the main light absorbers are oxy- (HbO) and deoxy-hemoglobin (Hb) molecules present in red blood cells (Figure 2.1).
A more complicated light-matter interaction is scattering. It is described by a change in the incident light propagation direction due to interactions with the particles in the medium. In the near-infrared region, almost all of the scattering events are elastic, therefore there is no change in energy (i.e., λs = λi) but the propagation direction of incoming and outgoing
waves are different. Elastic light scattering in tissue has shown to reveal structural informa-tion about cells and surrounding fluids [14] as scattering events are originated from spatial variations on medium refrective index on the length scale of incident light wavelength [15]. In most situations these variations are directly proportional to the molecule number density and therefore measuring scattering events provide spatial information on the heterogenity of composing molecules.
Scattering processes can be characterized by a scattering coefficient, µs, which similarly
to the previously defined µa is a measurement of the mean number of scattering events per
unit length (cm−1). This coefficient depends on multiple variables: incident light wavelength (λ), relative size of the particles, medium refractive index and also on scattering cross-section. The anisotropy of a medium is described by the anisotropy factor, g, which in turn is related to the mean scattering angle via g =< cos θ >. Here, θ is the angle between photon’s scattered direction and the normal vector of an infinitesimal area in which the amount of radiant power is transported across.
Scattering events are accounted for all heterogeneity in tissue due to different types of cells. Most of the scattering in tissue comes from static scatterers. The major dynamic scatterers (i.e., scatterers that are moving) in tissue are red blood cells [17, 18]. Such a medium can be considered as a turbid medium in NIR range, as the scattering coefficient is about two orders of magnitude higher than the absorption coefficient(µ0s≈ 100µa) [19, 20].
Figure 2.1: Absorption coefficients of main blood in the optical window: i ) water; ii ) oxyhemoglobin and iii ) deoxyhemoglobin. Adapted from [16].
The next section describes a simplified model of light propagation through tissue that can be applied in several cases in order to study blood flow characteristics. Each of these will be further exploited from the theory and the instrumentation used for experimentation will be discussed in separate sections.
2.2
NIR Light Propagation Modeling in Turbid Media
2.2.1
Radiative Transport Theory
Due to the higher scattering compared to absorption, the macroscopic behavior of NIR light propagation is diffusive (Figure 2.2). A complete classical description of the electromagnetic phenomena such as light absorption and scattering can be obtained by the means of Maxwell Equation and Lorentz force law. However, in order to solve Maxwell’s equations to calcu-late NIR light propagation on a turbid media one would require excessive computational performance, and it would only be solvable for few scattering events.
Figure 2.2: Light propagation under diffusive regime inside a turbid medium. Light propagates spherically and the intensity vanishes for longer distances from the source. Photons are also scattered back to illumination surface and can be collected by a detector.
Adapted from [16].
A simplification of the Maxwell theory for light propagation modeling is known as Ra-diative Transport theory, in which instead of describing the electric fields of the incident light, the quantity of interest becomes the light radiance, L(r, bΩ, t, λ) [W cm−2sr−1]. The radiance represents the power per unit area per unit solid angle traveling in bΩ direction at time t and position r. The amount of radiant power transported across an element of area dσ in directions confined to an element of solid angle dΩ is thus given by
W (bΩ) = L cos θdσdΩ. (2.1)
Here, the angle between bΩ and the element’s normal vector, bn, is written as θ. Figure 2.3 illustrates the variables described by Radiative Transport Theory.
As mentioned before, the two most important light-matter interaction parameters are absorption and scattering, which can be characterized by the absorption µa(bΩ, r, t, λ) [cm−1]
Figure 2.3: Variables described by the Radiative Transport Theory. The radiance rep-resents the power per unit area per unit solid angle traveling in bΩ direction at time t and position r. The amount of radiant power transported across an element of area dσ in di-rections confined to an element of solid angle dΩ is calculated from equation 2.1. Figure
obtained from [18].
and scattering coefficients, µs(bΩ, bΩ0, r, t, λ) [cm−1]. The former can be understood as a
sta-tistical measurement of the mean number of absorption events per unit length (cm−1) and the latter as the measurement of the mean number of scattering events per unit length. Scat-tering coefficient depends on incident light wavenength, relative size of scatScat-tering particles, medium refractive index and the scattering phase-function, p(bΩ, bΩ0, r, t, λ), defined as the probability of a photon to be scattered into the direction bΩ given the incident direction bΩ0 at (r,t).
Another quantity of interest is the total amount of incident radiance scattered in all di-rections. This is again described by what we defined as the scattering coefficient, µs(bΩ, r, t, λ),
which relates to the scattering phase-function according to the following integral over all 4π steradians of space
µs(bΩ, r, t, λ) =
Z
4π
Figure 2.4: The light radiance L(r + dr, bΩ, t + dt, λ) emerging from an infinitesimal volume differs from the incident radiance L(r, bΩ, t, λ) due to light-tissue interactions. The absorbed portion is µa(r, bΩ, t, λ)L(r, bΩ, t, λ)|dr| and the portion scattered by tissue in bΩ direction is p(r, bΩ0, bΩ, t, λ)L(r, bΩ, t, λ)|dr|. The term |dr| denotes the magnitude of vector dr (|dr| = vdt) where v = c/n is the speed of light in the considered volume element.
Adapted from [18].
From the definitions above the total amount of radiance scattered by an infinitesimal tissue volume is µs(bΩ, r, t, λ)L(bΩ, r, t, λ)|dr|, whereas µs is the probability density for tissue
scattering light in any direction.
Let us now understand what the typical length transport scales involved in this descrip-tion are. Consider a homogeneous medium in which a packet of N0 photons are propagating
through. We define N (r) as the number of photons that have not been scattered after trav-eling a distance r inside the geometry. Since N (r + dr) is less than N (r) in dr, µsdr, we can
write
N (r + dr) = N (r) − N (r)µsdr, (2.3)
dN (r)
dr = −µsN (r). (2.4)
The above equation has a known solution as it describes an exponential decay with rate µs:
N (r) = N0exp(−µsr) = N0exp(−r/`s). (2.5)
We have introduced the scattering length, defined from the equation above as `s = 1/µs.
In order to understand its physical meaning let us consider the probability density function for a photon to scatter after traveling a distance r inside the medium without encountering scattering events before (Ps(r)dr). This factor can be written as the probability of a
pho-ton traveling a distance r without scattering (N (r)/N0(r)) multiplied by the probability of
scattering in distance dr (µsdr)
Ps(r)dr =
N (r) N0
µsdr = µsexp(µsr)dr. (2.6)
The mean distance that a photon travels between scattering events can thus be calculated as < r >= Z ∞ 0 rPs(r)dr = Z ∞ 0 rµsexp(µsr)dr = 1 µs = `s. (2.7)
We conclude that the previously defined scattering length, `s, is the mean distance
traveled by a photon between scattering events. The same procedure can be directly applied to the absorption length, `a = 1/µa, and understood at the mean distance photons travel
The introduction of scattering and absorption lengths are in fact imposed as a first limi-tation of the Radiative Transport Theory. In order to properly apply the Radiative Transport Equation (RTE) as a model one has to make sure that a photon travels distances of several wavelengths between interactions with particles present in the medium. If we consider the NIR light spectra, this holds true, where typical values of scattering and absorption lengths in biological tissue are on the order of 0.1 and 10 cm, respectively. Under these conditions we may model light propagation under geometrical optics theory, or small wavelength limit of Maxwell’s equations.
As of now we will introduce another constrain in our experimentation setup in order to simplify the model of light transport inside a tissue of interest. We will only consider unpolarized light with its electric field represented by local quasi plane waves. The light radiance can be written in terms of the propagating fields as
L(r, bΩ, t) = |Ek(r, bΩ, t)|2+ |E⊥(r, bΩ, t)|2. (2.8)
Here, Ek and E⊥ are the two orthogonal polarization components of a complex electric field
E(r, bΩ, t) at distance r and time t that transported a quasi plane wave with wave vector KΩ = 2πn/λΩ, amplitude E0 and angular frequency ω
E(r, bΩ, t) = E0(r, t) exp(i(kΩ· r − ωt)). (2.9)
Let us know calculate the changes in light radiance from the conservation equation for the radiance in each volume element within the medium.
dL ≡ L(r + dr, bΩ, t + dt) − L(r, bΩ, t) = ∂L(r, bΩ, t)
∂t dt + r · ∇L(r, bΩ, t) = ∂L(r, bΩ, t)
∂t dt + vdtΩ · ∇L(r, bΩ, t).
(2.10)
As light interference effects are negligible in geometrical optics we can write the change in radiance as dL = −µaL(r, bΩ, t)|dr| − L(r, bΩ, t) Z b Ω06=bΩ p(bΩ0, bΩ, r, t)dbΩ0|dr|+ Z b Ω06=bΩ p(bΩ0, bΩ, r, t)L(r, bΩ, t)dbΩ0|dr| + Q(r, bΩ, t)vdt. (2.11)
We have introduced a term Q(r, bΩ, t) [W cm−3sr−1] which accounts for the light power per volume emitted by sources at position r and time t in the bΩ direction. The first term on the right-hand side of the equation described the changed in light radiance due to absorption events and the second accounts for losses on light radiance due to scatter-ing in all directions bΩ0 other than bΩ. The third term is a gain on radiance scattered into bΩ from all different bΩ0 directions and lastly, the fourth term adds the gains from light sources inside the considered volume. If we now substitute vdt for |dr| and add −p(bΩ0, bΩ, r, t)L(r, bΩ, t)|dr| + p(bΩ0, bΩ, r, t)L(r, bΩ, t)|dr| to the right-hand side of equation 2.11 we obtain dL = −[µa(bΩ, r, t) + µs(bΩ, r, t)]L(bΩ, r, t)vdt+ Z 4π p(bΩ, bΩ0, r, t)L(bΩ, r, t)dbΩ0vdt + Q(bΩ, r, t)vdt. (2.12)
As a last step for arriving at the so called Radiative Transport Equation we have to combine the results from equations 2.10 and 2.12
1 v ∂L(bΩ, r, t) ∂t = −bΩ · ∇L(bΩ, r, t) − µt(bΩ, r, t)L(bΩ, r, t) + Q(bΩ, r, t)+ µs(bΩ, r, t) Z 4π L(bΩ0, r, t)f (bΩ, bΩ0, r, t)dbΩ0. (2.13)
The sum of absorption and scattering coefficients was introduced as a total transport coefficient, µt [cm−1], and a normalized scattering phase function, f , was defined as
f (bΩ, bΩ0, r, t) = p(bΩ, bΩ
0, r, t)
µs(bΩ, r, t)
. (2.14)
Note that the integral over all 4π steradians of space equals the unity:
Z
4π
f (bΩ, bΩ0, r, t)dbΩ0 = 1. (2.15)
The Radiative Transport Equation (2.13) can be comprehended as a conservation equa-tion in which the number of photons leaving a specific region and direcequa-tion inside the con-sidered medium is a sum of light gained from sources (first term on the right-hand side) and what is scattered into it from other directions (second term) minus what is lost through absoption or scattering to other directions. Let us summarize the assumptions behind the development of RTE [21]:
• light intensity is transferred element-wise;
• the back-scattering is insignificant when compared to the scattering to other directions; • scattering particles do not interact;
• incident light-source has a Dirac function distribution wave spectrum;
• the far-field approximation can be applied as scattering particles are distant from each other.
Although the Radiative Transport equation is a simplified model to describe light prop-agation it still involves a high computational requirement when solving multiple-scattering events and can be only solved for simple geometries. Thus, a further approximation for light transport in turbid media (Photon Diffusion Model) can be derived for the light radiance by means of PN approximation and will be discussed in the next Section.
2.2.2
Photon Diffusion Equation
A simplification for the Radiative Transport Equation can be derived by expanding the light radiance in terms of spherical harmonics with coefficients φl,m and truncating it at l = N .
This is the so-called PN approximation
L(r, bΩ, t) = N X l=0 l X m=−1 φl,mYl,m(bΩ). (2.16)
Under diffusive light transport regime the radiance is accurately described by the P1
approximation with the assumption that it is uniformly scattered in all directions, meaning the scattering and absorption coefficients do not depend on the direction of light travel. Another assumption is that the normalized scattering phase function, f , only depends on the angle (θ) between incident and scattered wave vectors
µa(bΩ, r, t) = µa(r, t); µs(bΩ, r, t) = µs(r, t),
f (bΩ0, bΩ, r, t) = f (bΩ, bΩ0, r, t) = f (bΩ · bΩ0, r, t).
Under the assumptions on the equation 2.17 one can write the radiance as a linear contribution of the photon fluence rate φ(r, t) and flux J(r, t) [18].
L(r, bΩ, t) = 1 4πφ(r, t) + 3 4πJ(r, t) · bΩ, (2.18) where φ(r, t) = Z L(r, bΩ, t)dΩ, J(r, t) = Z L(r, bΩ, t)bΩdΩ. (2.19)
We can now substitute the expression on equation 2.18 into the Radiative Transport Equation 2.13 to obtain [22]
3D(r) v
∂J(r, t)
∂t = D(r)∇φ(r, t) + J(r, t), (2.20)
where D ≡ v/3(µ0s + µa) ≈ v/3µ0s is the photon diffusion coefficient and µ 0
s the reduced
scattering coefficient, which accounts for the scattering anisotropy factor, g, defined as
g(r, t) = Z
4π
f (bΩ · bΩ0, r, t)bΩ · bΩ0dbΩ0 =< cos θ >, (2.21)
µs(r, t)0 ≡ µs(1 − g(r, t)). (2.22)
∂φ(r, t)
∂t = v∇ · (J(r, t) − vµa(rφ(r, t) + vS(r, t))). (2.23) Here, the source term S(r, t) [W cm−3] is total power per volume emitted radially outward from position r at time t
S(r, t) ≡ Z
4π
Q(r, bΩ, t)dbΩ. (2.24)
Taking the divergence of equation 2.20 and combining with equation 2.23 one arrives at the Photon Diffusion Equation [23]
1 v ∂φ(r, t) ∂t = D∇ 2φ(r, t) − µ aφ(r, t) + S(r, t). (2.25)
The Photon Diffusion Equation (PDE) represented in equation 2.25 can be understood as a consequence of a large number of photons each executing random walk as it propagates through tissue [24, 25]. These photons are considered to travel in straight lines until it is suddenly absorbed or has its propagation direction changed due to a scattering event. Figure 2.5 represents an illustration of a photon executing this movement, in which the quantity `tr represents the average length of straight-line segments known as the transport
mean-free path. In the case of NIR light propagating through a biological tissue the scattering anisotropy factor defined earlier is close to the unity, which means that `tr is much greater
than the scattering length defined as `s = 1/µs [18]. The high bias for forward scattering
makes it so that even though photons scatter many times over the length scale of `tr this
movement is not fully randomized before it has moved a distance comparable to that of `tr.
Solutions for PDE are shown in Appendix A for selected geometries of interest. These characteristics have been previously tested by several researchers and experimental data has
Figure 2.5: Representation of a photon (red dot) taking two random walks with length `tr. Each random walk consists of many scattering events that occur after a photon travels
`s length. Adapted from [18].
shown that the diffusion model is a good approximation for NIR light transport in biological tissues [26–29].
Before moving to a more general approach on a Photon Diffusion Equation that describes light propagation on a media with moving scatterers, let us summarize the assumptions that were made for deriving the PDE [30, 31]: i ) light radiance is nearly isotropic; ii ) tissue optical properties are independent of light propagation direction; iii ) the Radiative Transport Equation (2.13) is valid; iv ) photon flux varies on a time scale much longer than the time it takes for photons to move one transport length; v ) photons travel with the same velocity within the medium (homogeneous refractive index); vi ) light sources are isotropic.
2.3
Diffuse Correlation Spectroscopy (DCS)
The theoretical aspects of light-matter interaction presented so far were discussed for static particles. But one might be interested in describing the movement of scattering particles that compose the medium. When NIR light is shined into biological tissue the main dynamic
light scatterers are red blood cells and so characterizing their movement allows an indirect measurement of blood flow. Diffuse Correlation Spectroscopy (DCS) is an optical technique capable of assessing deep-tissue changes of blood flow on a macroscopic scale by quantifying light intensity fluctuations on a detector [1, 2, 7]. DCS provides a measurement of the light intensity auto-correlation function which is properly described by a Photon Diffusion Equation similar to that explored in the above section by taking into account a term that is proportional to the mean-square displacement of scattering particles. A summary of the theoretical approach on DCS is presented on the next sections together with application examples and discussion of technique limitations. A more detailed derivation may be found in Appendix B and is of fundamental importance for this work. The connections between Speckle Contrast Optical Tomography and DCS will be discussed later in chapter 4.
2.3.1
Experimental Methods of DCS
Diffuse Correlation Spectroscopy uses a similar idea to that shown in section 2.2.1 in order to describe light propagation on a media where particles that scatter the light are moving. It also works on the multiple scattering limit (Appendix B), which means light scatters many times before it is absorbed or leaves the tissue. DCS relies on a diffusion equation for the electric field auto-correlation function, g1(r, τ ), defined as
g1(τ ) =
< ET(t) · ET∗(t + τ ) >
| < ET(t) · ET∗(t) > |
. (2.26)
Here, τ is the correlation time, ET is the total electric field at position r and time t, and <>
denotes ensemble average. The mathematical description of this variable takes into account the mean-square displacement < ∆r2(τ ) > of moving scatterers according to the following
vµa+
1 3`0
s
k20 < ∆r2(τ ) >G1(r, τ ) − ∇ · [D(r)∇G1(r, τ )] = vS0exp(iωτ )δ(r − Rs). (2.27)
We recall that equation 2.27 can be written as a Helmholtz equation for the unnormalized field auto-correlation function
(∇2− K2(τ ))G 1(r, τ ) = − vS Dδ 3(r − r s), (2.28)
where K2(τ ) = v(µa+ 13µ0sk02 < ∆r2(τ ) >)/D. The CW source is considered point-like and
is located at position r. The two loss terms, µa and 13µ0sk02 < ∆r2(τ ) >, account for light
absorption and loss of auto-correlation due to scattering, respectively.
In order to properly apply equation 2.28 to human tissues one last modification must be made in our model. Under the development leading to equation 2.28 we have considered that all scatterers are moving, although human tissue has both static and dynamic particles capable of scattering light. As static scatterers do not contribute to the loss of correlation we introduce a new parameter, α, such that K2(τ ) = v(µa+ α13µ0sk02 < ∆r2(τ ) >)/D. This
new parameter accounts for the probability of photon to be scattered by a moving particle and is defined as α = µ 0 s(moving) µ0 s(moving) + µ0s(static) , (2.29)
where again µ0s denotes the reduced scattering coefficient of (moving) and (static) tissue portions.
The mathematical methods behind solving equation 2.28 are shown in appendix A for selected geometries. For a semi-infinite medium we arrive at the following expression for the field auto-correlation function:
G1(r, τ ) = v 4πD exp(−K(τ )r1) r1 − exp(−K(τ )rb) rb , (2.30)
where r1 = p(z − `t)2+ ρ2 and rb = p(z + 2zb+ `t)2+ ρ2 are both defined in Figure A.1
in Appendix A. According to this notation, G1(r, τ ) has a dependence on µa, µ0s and α <
∆r2(τ ) >.
A common DCS detector has access to the light intensity and a parallel system is capable of calculating its auto-correlation function, G2 =< I(t)I(t + τ ) >, which is related to the
previously defined g1(τ ) through the Siegert Relation derived in Appendix B in Reference
[16]:
g2(τ ) = 1 + β|g1(τ )|2. (2.31)
Here, g2(τ ) = G2(τ )/ < I(0) >2 and g1(τ ) = G1(τ )/ < I(0) > are the normalized intensity
and electric field auto-correlation functions, respectively, and β is an experimental parameter of fundamental importance for both DCS and SCOT theories and will be discussed in more details in Chapter 3.
Figure 2.6 shows a scheme of the usual procedure for collecting DCS data. A coherent NIR laser is shined into a sample and the back-scattered light is collected at some distance ρ from the incident light. The typical detection consists of a single-mode fiber and a single photon counter used to feed a physical correlator for computing the measured intensity autocorrelation function, g2. Using a non-linear fit of the data with the solution of the
Figure 2.6: Illustration of a common Diffuse Correlation Spectroscopy experiment scheme. A NIR coherent laser beam is shined on a sample on a point-like manner and a photon counter receives the rapid (µs scale) light intensity fluctuations obtained at a distance away from the source. A correlator is fed with the measurement and calculates the light intensity auto-correlation function. A non-linear fit relating the measured intensity auto-correlation and the electric field auto-correlation function obtained from the Photon Diffusion Theory
allows spectroscopic measurements of blood flow dynamics. Figure obtained from [16].
correlation diffusion equation with appropriate boundary conditions (shown in Appendix A) one can estimate the values for β and α < ∆r2(τ ) >.
As previously mentioned in section 2 there are two main possibilities of movements we must consider in order to model the scatterers dynamics: (i) the brownian motion and; (ii) random flow. We can write the mean square displacement of those types of movement as [32–34]:
Brownian Motion: < ∆r2(τ ) >= 6DBτ
Random Flow: < ∆r2(τ ) >=< V > τ2.
(2.32)
Although Red Blood Cell movement withing capilaries and arteries remind of a Random Flow it has been shown that the Brownian Motion better fits the measured auto-correlation
curves and so has been the accepted model for measuring Blood Flow [16]. In DCS experi-ments we are not capable of obtaining the parameter α from measureexperi-ments, so the quantity representing the flow is usually called Blood Flow Index (BFI), and is defined as
BF I = αDB. (2.33)
Diffuse Correlation Spectroscopy has been validated against several standard techniques [4, 9, 35]. It enables real-time non-invasive monitoring at the bedside, and it has been ex-tensively used in clinical environments [3, 7, 17]. Nevertheless, DCS has shown to be an efficient technique for measuring macroscopic tissue lacking on spatial resolution for solv-ing micro-circulation. The next section describes an imagsolv-ing technique capable of resolvsolv-ing micro-circulation with high spatial resolution with the employment of low-cost instrumenta-tion.
Chapter 3
Speckle-based Imaging of Blood Flow
The scientific community has started studying speckle-based techniques back in the 1960s with the development of theoretical analysis of speckle intensity fluctuations due to dynamic light scattering. Over the next decade an effort was made to relate speckle temporal fluctu-ations to particle dynamics in single-scattering suspensions and it was just in the 1980s that highly scattering systems were introduced. Although capable of obtaining system dynamic information these techniques were slow for acquiring and processing data. Laser Speckle Imaging (LSI) was introduced as a technique that allows quick snapshots of a time-integrated speckle pattern and was first used to estimate blood flow in the retina [36]. Since its first appearance LSI has gained attention from both scientific and clinical community and so nu-merous efforts have been made to improve flow images resolution and computing time as well as to develop models relating speckle fluctuations to blood flow.
The next sections will be dedicated to explain what a speckle pattern is and how Laser Speckle Imaging uses this measurement to give information on hemodynamics of a complex turbid medium such as biological tissue.
Figure 3.1: Simulation of Speckle Patterns with an exposure time of 1, 5 and 25 ms conducted by [37].
3.1
Speckle Pattern
Once a very large number of light waves interfere the observable result might be what is known as speckles. There are two conditions required for obtaining observable speckles: i ) the incident waves remain their phase constant under the observable time scale (coherence); ii ) the multiple waves have an angular spread. The waves arriving at a detector placed some distance away from the illuminated object can be recalled as planar waves, with its phases varying according to the screen position. As a result, the total electric field at each location can be written as a sum of individual contribution from each of the planar waves.
A speckle pattern might be considered static if both light source and object remain constant over time. If we now consider a medium with moving particles the observed inter-ference pattern changes over time due to Doppler shifts of the light and the speckle pattern is thus considered dynamic. The next section is focused on the mathematical properties behind speckle phenomena.
3.2
Speckle Statistics
For highly scattering media such as biological tissue in the NIR spectral regime the polarized light electric field at position rd and time t is described by a random phasor1 sum
E(rd, t) = N
X
n=1
anexp(iφn)· (3.1)
Here, N 1 is the number of phasor components and the pair (an, φn) are the amplitude
and phase of the nth phasor. A speckle field is considered “fully developed” if it meets the three following assumptions: i ) The amplitudes and phases of the nthspeckle are statistically
independent of those from the mth providing n 6= m; ii ) the phase and amplitude of the nth speckle are statistically independent of each other; iii ) all phase values are uniformly
distributed on the interval (−π, +π). According to [38] equation 3.1 represents a random walk in the complex plane and the electric field is a Gaussian-distributed variable with zero mean whose probability density function can be represented as
PE(|E|) = |E| 2πσ2 exp −|E| 2 2σ2 , (3.2)
where σ2 is the distribution’s variance.
Instead of the electric field, speckle-based techniques measure the light intensity, I(rd, t) ∝
|E(rd, t)|2. The probability density function for the intensity of a fully developed speckle field
is then represented by a negative exponential distribution [38].
PI(I) = d|E| dI PE( √ I) = 1 < I >exp − I < I > . (3.3)
1Complex representation of a sinusoidal function with time-invariant amplitude, angular frequency and
Figure 3.2: Light intensity negative exponential probability function profile on a fully developed Speckle Pattern. Note that the origin on x axis correspond to null values of light intensity. It is more likely to measure a dark spot (intensity values below the mean) than
bright spots. Figure obtained from [39].
A histogram of measured light intensity over many time points all at the same location rd is thus characterized by an exponential distribution with many more dark spots (i.e.,
intensity values below the mean) than bright spots. In practice, the detected light intensity is a sum over many independent fully developed speckles.
Speckle flow techniques use a camera to record the dynamic speckle pattern generated by a medium with moving particles. Speckles have a decorrelation time on the order of microseconds. Previous experimental data demonstrated that the interval between 1-5ms is the optimal for the application of Speckle Techniques for visualizing biological tissue perfusion [40]. As the camera exposure is typically longer than the speckle decorrelation time (in the milisecond range), the speckle pattern will be blurred in the regions where scattering particles are moving.
Quantification of this blurring is made by calculating a quantity known as the speckle contrast, K, defined as the ratio of the standard deviation of light intensity measured over a collection of camera pixels to the mean intensity over the speckle pattern:
K ≡ σ < I > =
p
< I2 > −< I >2
< I > . (3.4)
The movement of particles that compose the medium influence the observed speckle contrast in such a way that the slower the movement within the medium the less speckles will be blurred. Some characteristics of this quantity were studied by Goodman and Parry [39] and will be discussed here. A speckle is considered fully developed if the standard deviation in equation 3.4 is equal to the mean intensity, so that K = 1. This situation occurs under ideal conditions such as perfectly monochromatic polarized light and total absence of noise. A movement of medium particles create a blurring effect on the observed speckle pattern and as a result the standard deviation on equation 3.4 becomes small compared to the unchanged mean leading to reduced speckle contrast values.
The next section will be focused on a blood flow imaging technique that uses a camera to record variations in speckle pattern created by an object illuminated with coherent NIR light. Laser Speckle Imaging (LSI) instrumentation and methodology is described with sev-eral examples elucidating its importance on clinical and research environments. Technique limitations have been evaluated from bench experiments and the results are shown in Section 3.5.
3.3
Laser Speckle Imaging (LSI)
Laser Speckle Imaging (LSI) uses the analysis of spatial fluctuations on the speckle pattern generated by shining coherent light onto a moving sample and recording the intensity profile on a camera. A typical LSI setup is shown in Figure 3.3. As mentioned in section 3.2 moving scatterers will produce a blurring on the observed speckle pattern and so this can be
Figure 3.3: Illustration of a Laser Speckle Imaging setup. A coherent NIR source ilu-minates the object in a full-field manner. The speckle pattern is recorded by a CCD for
calculation of contrast images.
quantified by the use of equation 3.4 to produce a contrast image that carries information on blood flow.
Speckle contrast is a measurement of light intensity fluctuations and so is sensitive to the scattering of moving particles. Absorption phenomena directly affects the mean light intensity at the detector, but does not contribute directly to the speckle fluctuations. Since its first application on the retina [36] LSI has gained the attention of the scientific commu-nity and is now applied in clinical environment [37, 41]. Neuroscience has adopted LSI as a complementary measurement to access information on blood flow in the brain [42, 43]. Im-portant technological development have been made involving each individual component as the detector [40], light source [44] and speckle contrast calculation algorithms [45, 46]. Laser Speckle Imaging is being implemented in multi-modal imaging schemes to obtain additional information about the tissue. A cheap instrumentation for the technique was also proposed [40] and showed great potential of monitoring blood flow alterations in tissue.
Laser Speckle Imaging has a low processing time. Therefore images can be obtained in real-time, which makes the technique useful in many situations. Two major drawbacks
Figure 3.4: Raw speckle pattern (left) with its computed speckle contrast (right) showing clear distinction between regions with increased flow (dark areas in the right image). The
images show a cortical surface of 5 × 4 mm2 area. Adapted from [41].
of LSI are specular reflections from the imaging scheme and low signal-to-noise ratio due to static scatterers [47] which contribute to limit LSI measurements to superficial tissue. Deeper measurements have been studied on surgically exposed tissue as shown in Figure 3.4.
The speckle contrast image shown in Figure 3.4 was able to accurately differ between regions with and without blood flow, but clearly shows no depth information. The spatial resolution of a speckle imaging system can be as low as 10 to 25µm (depending on the optical system) with a field of view of 1 to 20mm. Monte Carlo simulations were performed and showed the penetration depth in LSI is between 500µm and 1mm in skin tissue [48], and up to 5mm penetration may be achieved on a controlled phantom experiment as shown in Section 3.5. With the implementation of real-time algorithms for speckle contrast calculations [45, 46], the temporal resolution of LSI is defined by the camera exposure time, which is on the order of milliseconds range [40]. Averaging successive frames have shown to improve the signal-to-noise ratio and so improving the spatial resolution with a slight the cost on computing time [42].
Although LSI resolves blood flow circulation its results provide a contrast map which is relative, only. Attempts have been made to connect the absolute measure of speckle contrast
and blood velocity but a model has not yet been accepted by the scientific community [37].
3.4
Design of a Laser Speckle Imaging System
Laser Speckle Imaging uses a coherent NIR light on a wide-field illumination and records images of the intensity pattern generated on a CCD detector. We aimed to build a low cost LSI system which can be easily reproduced and assembled on other laboratories and clinical environments. In order to build and validate a LSI instrument capable of obtaining high spatial resolution images of blood flow in small animals, phantom experiments were conducted in our laboratory. The next sections present the main components of our home-made LSI system and a validation of our instrumentation by application on bench experiments.
3.4.1
Light Source
In Diffuse Correlation Spectroscopy experiments we shine a continuous, long coherent NIR light source on a sample region in a point-like manner. In practice, the laser source will have a finite spot size and coherence, but the latter can be considered infinite if the coherence length is much greater than the mean photon pathlength. For biological samples this means that the coherence has to be much larger than 1m [16, 18].
Laser Speckle Imaging uses the same light source as in DCS with a wide-field illumination scheme to homogeneously shine coherent NIR light on a sample. Our current laser model (CrystaLaser LC 852nm wavelength with a coherence length of ≈ 50m) provides a point-like (≈ 1mm diameter) illumination and delivers 125mW/cm2 output power. The light source is
focused on a microscope objective (Nikon PM5 0.1 with 5× magnification) that collimates and broadens the laser spot. In order to meet the power delivered to tissue required by [49] and guarantee that the detector does not saturate, a neutral density filter was placed between
Figure 3.5: Scheme of the optical tray built in our laboratory. A coherent NIR light source has its intensity lowered by a Neutral Density Filter and is amplified and collimated
by a microscope objective to provide wide-field illumination of a biological sample.
the source and the objective. Figure 3.5 shows a scheme of our current illumination system. All of the components were mounted on an optical tray designed and printed with low-cost Polylactic Acid (PLA). Current system allows uniform circular illumination of 5mm radius.
3.4.2
Detector
The detector employed on Laser Speckle Imaging has to be able to record a speckle pattern image with an exposure on the millisecond range. Most available cameras have this as their minimal range and so we have removed NIR absorption lenses from a low-cost webcam (Logitech Webcam C920 Full HD) so that we could measure the Speckle Pattern produced by our light source. This webcam is currently available on the market for around US$50,00. The webcam parameters are controlled by software provided by the manufacturer which allows the user to control the following parameters: Exposure, Gain, Brightness, Contrast, Color Intensity and White Balance. Our current model does not provide information on the absolute exposure value (in milliseconds) and so optimal parameters were adjusted experimentally focusing on obtaining more clear laser speckle images of blood flow as described in Section 3.5. Gain and Brightness were set to minimum value in order to reduce inherent noise of the detection system, while Color Intensity and White Balance were adjusted automatically.
Figure 3.6: Logitech webcam sofware user interface that allows the control of some pa-rameters related to the employed detector. Although the exposure time is available for
manual set it does not provide the user exact value in a milli-second scale.
Contrast values were set to zero so that the detector does not prioritize bright or dark spots. Figure 3.6 shows the user control panel on Logitech Webcam Software. Although useful for adjusting the optimal parameters for experimentation this interface does not support sequential image shoots which can be useful for improving the signal-to-noise ratio of the observed Speckle Patterns.
Therefore a home-made LABVIEW [50] script was coded on Vision Acquisition module to control sequential picture capturing using our detector. It enables the user to control the same parameters described earlier with the advantage of allowing sequential capturing. Image processing can also be performed on LABVIEW for real time visualization of results but as of now our instrument works with post-processing on MATLAB environment. Figure 3.7 shows the user control panel on Vision Acquisition module.
In this work Speckle Pattern images are obtained with a 20 × 20mm field-of-view dis-tributed on a 1080×1080 pixel grid, with each pixel corresponding to approximately 0.02mm. A typical light intensity image obtained from our detector when static scattering media is shined with coherent NIR source is shown in Figure 3.8. The detector is placed 6.5cm above
Figure 3.7: Labview Vision Acquisition user interface allowing the same parameters to be adjusted on a scale to that corresponding to Logitech Webcam Software.
the sample as this distance seems reasonable for performing small animal imaging. As it can be seen from Figure 3.8 there is a dark region surrounding the region where the light is scattered by the sample. Our current camera does not allow the user to change on its Magnification as it has an inbuilt wide field-of-view lens which cannot be easily handled on a non-clean environment.
In order to achieve optimal results on Speckle Contrast images, Ramirez-San-Juan [51] suggested that the pixel size matches that of speckle size. A pictorial representation of four pixels covering a single speckle area is shown in Figure 3.9.
As discussed before our current pixel size is 0.02mm. Speckle size, on the other hand, is related to the diffraction-limit equation used in optical imaging [51] with the minimum-resolvable speckle size, dmin, given by
dmin = 1.22
f f − d0
!
