Splitting method for elliptic equations with line sources

In this paper, we study the mathematical structure and numerical approximation of elliptic problems posed in a (3D) domain $\Omega$ when the right-hand side is a (1D) line source $\Lambda$. The analysis and approximation of such problems is known to be non-standard as the line source causes the solution to be singular. Our main result is a splitting theorem for the solution; we show that the solution admits a split into an explicit, low regularity term capturing the singularity, and a high-regularity correction term $w$ being the solution of a suitable elliptic equation. The splitting theorem states the mathematical structure of the solution; in particular, we find that the solution has anisotropic regularity. More precisely, the solution fails to belong to $H^1$ in the neighbourhood of $\Lambda$, but exhibits piecewise $H^2$-regularity parallel to $\Lambda$. The splitting theorem can further be used to formulate a numerical method in which the solution is approximated via its correction function $w$. This approach has several benefits. Firstly, it recasts the problem as a 3D elliptic problem with a 3D right-hand side belonging to $L^2$, a problem for which the discretizations and solvers are readily available. Secondly, it makes the numerical approximation independent of the discretization of $\Lambda$; thirdly, it improves the approximation properties of the numerical method. We consider here the Galerkin finite element method, and show that the singularity subtraction then recovers optimal convergence rates on uniform meshes, i.e., without needing to refine the mesh around each line segment. The numerical method presented in this paper is therefore well-suited for applications involving a large number of line segments. We illustrate this by treating a dataset (consisting of $\sim 3000$ line segments) describing the vascular system of the brain

Optical Cerebral Blood Flow Monitoring of Mice to Men

This thesis describes cerebral hemodynamic monitoring with the optical techniques of diffuse optical spectroscopy (DOS) and diffuse correlation spectroscopy (DCS). DOS and DCS both employ near-infrared light to investigate tissue physiology millimeters to centimeters below the tissue surface. DOS is a static technique that analyzes multispectral tissue-scattered light intensity signals with a photon diffusion approach (Chapter 2) or a Modified Beer-Lambert law approach (Chapter 3) to derive tissue oxy- and deoxy-hemoglobin concentrations, which are in turn used to compute tissue oxygen saturation and blood volume (Section 2.13). DCS is a qualitatively different dynamic technique that analyzes rapid temporal fluctuations in tissue-scattered light with a correlation diffusion approach to derive tissue blood flow (Chapter 4). Further, in combination these measurements of blood flow and blood oxygenation provide access to tissue oxygen metabolism (Section 7.6). The new contributions of my thesis to the diffuse optics field are a novel analysis technique for the DCS signal (Chapter 5), and a novel approach for separating cerebral hemodynamic signals from extra-cerebral artifacts (Chapter 6). The DCS analysis technique extends the Modified Beer-Lambert approach for DOS to the DCS measurement. This new technique has some useful advantages compared to the correlation diffusion approach. It facilitates real-time flow monitoring in complex tissue geometries, provides a novel route for increasing DCS measurement speed, and can be used to probe tissues wherein light transport is non-diffusive (Chapter 5). It also can be used to filter signals from superficial tissues. For separation of cerebral hemodynamic signals from extra-cerebral artifacts, the Modified Beer-Lambert approach is employed in a pressure modulation scheme, which determines subject-specific contributions of extra-cerebral and cerebral tissues to the DCS/DOS signals by utilizing probe pressure modulation to induce variations in extra-cerebral hemodynamics while cerebral hemodynamics remain constant (Chapter 6). In another novel contribution, I used optical techniques to characterize neurovascular coupling at several levels of cerebral ischemia in a rat model (Chapter 7). Neurovascular coupling refers to the relationship between increased blood flow and oxygen metabolism and increased neuronal activity in the brain. In the rat, localized neuronal activity was increased from functional forepaw stimulation. Under normal flow levels, I (and others) observed that the increase in cerebral blood flow (surrogate for oxygen delivery) from forepaw stimulation exceeded the increase in cerebral oxygen metabolism by about a factor of 2. My measurements indicate that this mismatch between oxygen delivery and consumption are more balanced during ischemia (Chapter 7). In Chapters 2 and 3, I review the underlying theory for the photon diffusion model and the Modified Beer-Lambert law for DOS analysis. I also review the correlation diffusion approach for analyzing DCS signals in Chapter 4. My hope is that readers new to the field will find these background chapters helpful

Aerospace medicine and biology: A continuing bibliography with indexes (supplement 327)

This bibliography lists 127 reports, articles and other documents introduced into the NASA Scientific and Technical Information System during August, 1989. Subject coverage includes: aerospace medicine and psychology, life support systems and controlled environments, safety equipment, exobiology and extraterrestrial life, and flight crew behavior and performance

Dynamic glucose enhanced chemical exchange saturation transfer MRI : Optimization of methodology and characterization of cerebral transport kinetics

Dynamic glucose enhanced (DGE) chemical exchange saturation transfer (CEST) MRI is an emerging imaging technique that provides a molecular-specific type of image contrast, based on magnetic labelling of exchangeable protons. The technique enables the use of biodegradable sugars as contrast agents, and such compounds are believed to have less side effects than conventional MRI contrast agents. However, as with most novel techniques, DGE MRI is associated with technical challenges, including small contrast enhancement compared to conventional techniques, sensitivity to motion and long scan durations. Therefore, DGE MRI is not yet ready for clinical implementation, and further evaluation and methodological development are required. The focus of the work presented in this thesis has been on the optimization and development of DGE MRI in humans. We first implemented the DGE MRI technique at 7 T for evaluation in healthy volunteers, and subsequently optimized and applied the DGE imaging protocol at 3 T. We demonstrated that it is possible to measure arterial input functions using DGE MRI data, and that the arterial DGE MRI signal is correlated to the venous blood glucose level. Our experiments also showed that the glucose infusion duration should preferably be prolonged to minimize the sensory side effects of the injection. We also evaluated and compared DGE MRI tissue response curves in healthy tissue and in brain tumours and confirmed that DGE MRI enables differentiation of tumour from normal tissue, but that motion-related artefacts may complicate the interpretation. We developed a post-processing method for DGE MRI based on visualization of tissue response curve types with different characteristic temporal enhancement patterns. Finally, we developed a model for kinetic analysis of DGE MRI, accounting for the different signal origin and uptake kinetics of normal D-glucose. In summary, DGE MRI has potential for tumour detection in humans and can provide information on glucose delivery, transport, and metabolism. However, further optimization of imaging and post-processing techniques is necessary, especially at lower field strengths

Diffuse Optical Biomarkers Of Breast Cancer

Diffuse optical spectroscopy/tomography (DOS/DOT) and diffuse correlation spectroscopy (DCS) employ near-infrared light to non-invasively monitor the physiology of deep tissues. These methods are well-suited to investigation of breast cancer due to their sensitivity to physiological parameters, such as hemoglobin concentration, oxygen saturation, and blood flow. This thesis utilizes these techniques to identify and develop diffuse optical biomarkers for the diagnosis and prognosis of breast cancer. Notably, a novel DOS prognostic marker for predicting pathologic complete response to neoadjuvant chemotherapy using z-score normalization and logistic regression was developed and demonstrated. This investigation found that tumors that were not hypoxic relative to the surrounding tissue were more likely to achieve complete response. Thus, the approach could enable dynamic feedback for the optimization of chemotherapy. Similar logistic regression models based on other optical parameters distinguished tumors from the surrounding normal tissue and diagnosed whether a lesion was malignant or benign. These diagnostic markers improve the ability of DOS/DOT to accurately localize tumors and could serve as a type of optical biopsy to classify suspicious lesions. Another study carried out the first longitudinal DCS blood flow monitoring over a full course of neoadjuvant chemotherapy in humans; this work explored initial correlations between blood flow and response to therapy and showed how DCS and DOS together can more accurately probe tumor physiology than either modality alone. Finally, still other thesis research included the final construction and initial imaging tests of a DOT instrument incorporated into a clinical MRI suite and the optimization of the DOT reconstruction algorithm. In total, these instrumental and algorithmic advances improved DOT image quality, helped to increase contrast between malignant and normal tissue, and eventually could lead to better understanding of tumor microvasculature. These contributions represent important steps towards the translation of diffuse optics into the clinic, demonstrating significant roles for optics to play in the diagnosis, prognosis, and physiological understanding of breast cancer

Computer-aided modeling for efficient and innovative product-process engineering

Model baserede computer understøttet produkt process engineering har opnået øget betydning i forskelligste industrielle brancher som for eksampel farmaceutisk produktion, petrokemi, finkemikalier, polymerer, bioteknologi, fødevarer, energi og vand. Denne trend er forventet at fortsætte på grund af substantielle fordele, hvilke computer understøttede metoder medfører. Den primære forudsætning af computer understøttet produkt process engineering erselvfølgelig den tilgængelighed af modeller af forskellige typer, former og anvendelser. Udviklingen af den påkrævet modellen for de undersøgte systemer er normalt en tidskrævende udfordring og derfor mest også dyrt. Den involverer forskelligste trin, fagekspert viden og dygtighed og forskellige modellerings værktøjer. Formålet af dette projekt er at systematisere den model udviklings proces og anvendelse og dermed øge effektiviteten af modeller såvel somkvaliteten. Den væsentlige bidrag af denne PhD afhandling er en generisk metodologi for proces model udviklingen og anvendelse i kombination med grundige algoritmiske arbejdes diagrammer for de forskellige involverede modeller opgaver og udviklingen af computer understøttede modeller rammer hvilke er strukturbaseret på den generiske metodologi, delvis automatiseret i de forskellige arbejdstrin og kombinerer alle påkrævet værktøjer, understøttelseog vejledning for de forskellige arbejdstrin. Understøttede modelleringsopgaver er etableringen af modeller mål, indsamling af de nødvendige informationer, model formulering inklusive numeriske analyser, etablering af løsningsstrategier og forbinding med den passende løsningsmodul, model identificering og sondering såvel som model anvendelse for simulation og optimering. Den computer understøttede modeller ramme blev implementeret i en brugervenlig software. En række forskellige demonstrationseksempler fra forskellige områder i kemisk ogbiokemiske engineering blev løst for udvikling og validering af den generiske modellerings metodologi og den computer understøttet modeller ramme anvendt på den udviklet software værktøj.Model-based computer aided product-process engineering has attained increased importance in a number of industries, including pharmaceuticals, petrochemicals, fine chemicals, polymers, biotechnology, food, energy and water. This trend is set to continue due to the substantial benefits computer-aided methods provide. The key prerequisite of computer-aided productprocess engineering is however the availability of models of different types, forms andapplication modes. The development of the models required for the systems under investigation tends to be a challenging, time-consuming and therefore cost-intensive task involving numerous steps, expert skills and different modelling tools. The objective of this project is to systematize the process of model development and application thereby increasing the efficiency of the modeller as well as model quality.The main contributions of this thesis are a generic methodology for the process of model development and application, combining in-depth algorithmic work-flows for the different modelling tasks involved and the development of a computer-aided modelling framework. This framework is structured, is based on the generic modelling methodology, partially automates the involved work-flows by integrating the required tools and, supports and guides the userthrough the different work-flow steps. Supported modelling tasks are the establishment of the modelling objective, the collection of the required system information, model construction including numerical analysis, derivation of solution strategy and connection to appropriate solvers, model identification/ discrimination as well as model application for simulation and optimization. The computer-aided modelling framework has been implemented into an userfriendlysoftware.A variety of case studies from different areas in chemical and biochemical engineering have been solved to illustrate the application of the generic modelling methodology, the computeraided modelling framework and the developed software tool

Translação de um sistema de óptica de difusão para monitoramento de pacientes neurocríticos

Orientador: Rickson Coelho MesquitaTese (doutorado) - Universidade Estadual de Campinas, Instituto de Física Gleb WataghinResumo: As doenças cerebrovasculares são uma das principais causas de morte e incapacidade em todo o mundo. Em 2015, mais de 590.000 pacientes foram hospitalizados por estas doenças no Brasil, com aproximadamente 100.000 óbitos. A prevenção de danos secundários é um dos principais objetivos no tratamento de doenças cerebrovasculares graves, como o acidente vascular cerebral (AVC). No entanto, atualmente há uma falta de métodos não invasivos para monitoramento contínuo da fisiologia cerebral. Neste contexto, a espectroscopia óptica de difusão (DOS) e a espectroscopia de correlação de difusão (DCS) foram recentemente propostas como potenciais monitores não invasivos e contínuos capazes de fornecer informações neurofisiológicas em pacientes neurocríticos. Ao incidir luz infravermelha no escalpo, DCS pode medir o fluxo sanguíneo cerebral (CBF) e DOS pode medir as concentrações de oxi e desoxi-hemoglobina. A combinação de DOS e DCS foi explorada anteriormente para monitorar pacientes em vários cenários clínicos, como monitoramento neonatal, durante intervenções cerebrovasculares e para monitoramento de pacientes neurocríticos. No entanto, a confiabilidade da técnica para fornecer informações precisas em tempo real durante medições longitudinais, bem como durante alguns tipos de intervenções clínicas, permanece em grande parte não estudada. O principal objetivo desta tese foi mostrar que as técnicas de óptica de difusão podem auxiliar de maneira confiável e no monitoramento em tempo real de doenças cerebrovasculares. Para isso, desenvolvemos sistemas baseados em óptica de difusão e testamos a viabilidade destes sistemas em diferentes ambientes clínicos, envolvendo o monitoramento de pacientes dentro de uma unidade de terapia intensiva (UTI), bem como durante o tratamento endovascular de AVC. Primeiro, relatamos a construção e a translação de um sistema híbrido de óptica de difusão, combinando DOS e DCS, para o monitoramento em tempo real da fisiologia cerebral de pacientes internados em uma UTI. Mais especificamente, apresentamos dois estudos de caso, onde mostramos que os parâmetros neurofisiológicos medidos pelas técnicas de óptica de difusão são consistentes com a evolução clínica destes pacientes. Em seguida, relatamos a translação das técnicas de óptica de difusão para monitorar a hemodinâmicas cerebral durante o tratamento endovascular de dois pacientes com oclusões na artéria carótida interna. Nossos resultados identificaram um aumento induzido pela recanalização no CBF ipsilateral, com pouca ou nenhuma alteração no CBF contralateral e no fluxo sanguíneo extracerebral. Nossos resultados mostraram que a óptica de difusão tem grande potencial para monitorar os danos secundários em pacientes neurocríticos, sem interferir com práticas clínicas. Além disso, nossos resultados sugerem que o monitoramento hemodinâmico cerebral com as técnicas ópticas tem potencial para guiar terapias baseadas na fisiologia individual de pacientes. Por fim, para melhorar a confiabilidade das técnicas de ópticas de difusão, também propusemos a implementação de algoritmos aprimorados para a análise de dados. Mostramos que, usando um modelo de duas camadas para DOS/DCS, podemos melhorar a precisão na recuperação das alterações hemodinâmicas cerebraisAbstract: Cerebrovascular diseases are one of the main causes of death and disability worldwide. In 2015, there were more than 590.000 patients hospitalized due to cerebrovascular diseases in Brazil, with approximately 100.000 deaths. Prevention of secondary damage is an important goal in the treatment of severe neurological conditions, such as head trauma and stroke. However, there is currently a lack of non-invasive methods for continuous monitoring of cerebral physiology in real-time. More recently, diffuse optical spectroscopy (DOS) and diffuse correlation spectroscopy (DCS) have been proposed as noninvasive and continuous bedside monitors capable of providing neurophysiology information in neurocritical patients. By shining near-infrared light from the scalp, DCS can measure microvascular cerebral blood flow (CBF), and DOS can measure oxy- and deoxy-hemoglobin concentrations. The combination of DOS and DCS has been previously explored to monitor patients in several clinical scenarios, such as neonatal monitoring, during cerebrovascular interventions, and for monitoring of neurocritical patients. However, the reliability of the technique to provide accurate real-time information during longitudinal (i.e., across multiple days) measurement as well as during a few different clinical interventions remains largely unaddressed. The main goal of this thesis was to show that diffuse optics can reliably aid in monitoring cerebrovascular diseases, in real-time. To that end, we have translated a diffuse optical system to different clinic environments: during long-term monitoring of patients inside an intensive care unit, as well as during an endovascular treatment of stroke. First, we reported the construction and translation of a hybrid diffuse optical system combining DOS and DCS for real-time monitoring of cerebral physiology in a neuro intensive care unit. By presenting two representative case-studies, we show that the neurophysiological parameters measured by diffuse optics at the bedside are consistent with the clinical evolution of the patients. Then, we reported the translation of diffuse optics to monitor frontal-lobe cerebral hemodynamic changes during endovascular treatment of two patients with ischemic stroke due to internal carotid artery occlusions. The monitoring instrument identified a recanalization-induced increase in ipsilateral CBF with little or no concurrent change in contralateral CBF and extracerebral blood flow. Taken together, our results showed that diffuse optics holds promise for monitoring secondary damage in neurocritical patients, with minimal interference with current clinical practices. Additionally, our results suggest that cerebral hemodynamic monitoring with diffuse optics has the potential to guide therapy based on the individual physiology of neurocritical patients. Last, to improve the reliability of the diffuse optical techniques, we have also proposed the implementation of improved algorithms for data analysis. We showed that by using a two-layer model for DOS/DCS, we can improve the accuracy of diffuse optics in recovering the cerebral hemodynamic changesDoutoradoFísicaDoutor em Ciências2014/25486-61504865/2015FAPESPCAPE