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Investigating Reading Processes Using Diffusion Tensor ImagingDai, Wenjun Unknown Date
No description available.
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Multi-parametric MRI Study of Brain Insults (Traumatic Brain Injury and Brain Tumor) in Animal ModelsJanuary 2014 (has links)
abstract: The objective of this small animal pre-clinical research project was to study quantitatively the long-term micro- and macro- structural brain changes employing multiparametric MRI (Magnetic Resonance Imaging) techniques. Two separate projects make up the basis of this thesis. The first part focuses on obtaining prognostic information at early stages in the case of Traumatic Brain Injury (TBI) in rat animal model using imaging data acquired at 24-hours and 7-days post injury. The obtained parametric T2 and diffusion values from DTI (Diffusion Tensor Imaging) showed significant deviations in the signal intensities from the control and were potentially useful as an early indicator of the severity of post-traumatic injury damage. DTI was especially critical in distinguishing between the cytotoxic and vasogenic edema and in identification of injury regions resolving to normal control values by day-7. These results indicate the potential of quantitative MRI as a clinical marker in predicting prognosis following TBI. The second part of this thesis focuses on studying the effect of novel therapeutic strategies employing dendritic cell (DC) based vaccinations in mice glioma model. The treatment cohorts included comparing a single dose of Azacytidine drug vs. mice getting three doses of drug per week. Another cohort was used as an untreated control group. The MRI results did not show any significant changes in between the two treated cohorts with no reduction in tumor volumes compared to the control group. The future studies would be focused on issues regarding the optimal dose for the application of DC vaccine. Together, the quantitative MRI plays an important role in the prognosis and diagnosis of the above mentioned pathologies, providing essential information about the anatomical location, micro-structural tissue environment, lesion volume and treatment response. / Dissertation/Thesis / Masters Thesis Bioengineering 2014
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Imagens de tensor de difusão em idosos deprimidos: um estudo baseado na análise estatística do voxel / Diffusion tensor images in elderly depressed: a voxelwise statistical analysis studyDiana Moitinho Bezerra 16 September 2011 (has links)
Introdução: Os transtornos depressivos constituem um problema de saúde pública na terceira idade, e estima-se que a depressão será uma das três principais causas de sobrecarga de doença no mundo nas próximas decadas. Métodos de neuroimagem têm sido amplamente utilizados em estudos de depressão em idosos, pois são técnicas não invasivas que permitem a detecção de alterações cerebrais estruturais e funcionais. Fração de Anisotropia (FA) e Difusividade Média (MD) são índices indiretos da integridade micro-estrutural da substância branca, mensurados através de imagens de tensor de difusão (DTI). A maioria dos estudos a respeito de depressão e neuroimagem tem focado apenas em possíveis diferenças em regiões de interesse (ROI) previamente determinadas. Pesquisas sobre depressão em idosos e as alterações estruturais por tensor de difusão em todo o cérebro são escassos. O objetivo deste estudo foi investigar a existência de alterações nos parâmetros de FA ou MD em todo o cérebro, sem uma região de interesse previamente definida, comparando idosos deprimidos a idosos sem depressão. Métodos: Exames de imagem cerebral por ressonância magnética foram obtidos de 47 idosos deprimidos (idade média=70,94 ± 6,98), segundo critérios diagnósticos do DSM-IV, e 36 idosos sem depressão (idade média=69,39 ± 7,21) (p=0,32). O exame de neuroimagem dos sujeitos foi realizado em aparelho de ressonância magnética (RM) de 1,5 T, (TE mínimo, TR=10000ms, FOV=26, matriz=128x128, espessura=5mm). Os parâmetros de difusão das imagens de RM foram obtidos a partir de 25 direções não colineares com um b-valor de 1000s/mm2 juntamente com imagem sem gradientes de difusão b=0. Antes da aquisição dos exames de imagem, um psiquiatra administrou os seguintes testes: Mini-Exame do Estado Mental (MEEM), Teste Cognitivo Cambridge (CAMCOG), Escala Montgomery-Aberg de Depressão (MADRS) e Escala de Depressão de Hamilton (HAM-D). Não foram encontradas diferenças significativas nos dados demográficos entre os grupos. A análise estatística baseada no voxel dos dados de FA foi realizada com uso da ferramenta TBSS, parte do programa FSL, que projeta a FA de cada indivíduo em um esqueleto de FA média antes de aplicar a análise estatística baseada no voxel entre os sujeitos da amostra. Diferenças entre os grupos foram controladas para idade. Resultados: Os escores médios da avaliação cognitiva para o grupo de idosos deprimidos foram: CAMCOG=82,94 ± 13,95 e MEEM=25,21 ± 3,74; e para o grupo controle: CAMCOG=90,83 ± 8,88 (p=0,017) e MEEM=27,86 ± 1,99 (p=0,004). Quanto às escalas de sintomatologia depressiva, tem-se no grupo de idosos deprimidos: MADRS=23,23 ± 8,60 HAM-D=18,64 ± 6,17; e no grupo de idosos sem depressão: MADRS=1,39 ± 1,20, HAM-D=2,67 ± 1,57. Após o ajuste por idade, o grupo de idosos deprimidos não apresentou diferenças significativas nos parâmetros de FA e de MD. Os escores da avaliação cognitiva (CAMCOG e MEEM) não se correlacionaram significativamente aos parâmetros de FA nem de MD. Resultados semelhantes foram obtidos após a correlação com escores das escalas de sintomatologia depressiva (MADRS e HAM-D). Conclusão: Não houve diferença significativa, na amostra estudada, dos parâmetros de FA ou MD entre os idosos deprimidos e idosos sem depressão quando o cérebro é analisado sem a utilização de ROI. Não houve correlação, na presente amostra, entre avaliação cognitiva e FA ou MD nem entre gravidade da depressão e estes parâmetros de avaliação de alteração de substância branca / Introduction: Depressive disorders constitute a public health problem in old age, and depression is projected to be one of the three leading causes of burden of disease worldwide in the next decades. Neuroimaging methods have been widely used in studies of depression in the elderly, because they are noninvasive techniques that allow the detection of structural and functional brain changes. Fractional Anisotropy (FA) and Mean Diffusivity (MD) are neuroimaging index of micro-structural white matter integrity, measured using diffusion tensor imaging. Most studies investigating depression and neuroimaging have focused only in possible differences in regions of interesting (ROI) previously selected. Studies investigating correlation between elderly depression and structural alterations measured by diffusion tensor in the whole brain are scarce. The aim of this study was to investigate the existence of FA or MD differences in the whole brain, without a region of interest previously determined, between elderly depressed and elderly without depression. Methods: Brain magnetic resonance imaging scans were obtained on 47 elderly depressed subjects (mean age=70.9 ± 6.9), according to DSM-IV criteria, and 36 healthy elderly controls (mean age=69.4 ± 7.2) (p=0.32). Scanning of subjects was performed on a 1,5T MRI scanner (TE minimum, TR=10000ms, FOV=26, matrix=128x128, section thickness=5mm). Diffusion MR images were obtained from 25 non-colinear directions with a b-value of 1000 s/mm2 along with a b=0 image with no diffusion gradients. Before MRI acquisition, a psychiatrist administered the following psychiatric tests: Cambridge Cognitve Test Examination (CAMCOG), Mini-Mental State Examination (MMSE), Montgomery-Aberg Depression Rating Scale (MADRS), and Hamilton Rating Scale of Depression (HAM-D). No significant differences were found on demographic data between groups. Voxelwise statistical analysis of FA data was carried out using Tract-Based Spatial Statistics (TBSS), part of FSL program. TBSS projects all subjects\' FA data onto a mean FA tract skeleton, before applying voxelwise cross-subject statistics. Differences between groups were assessed controlling for age. Results: The mean score from cognitive assessment for the whole depression group was: CAMCOG=82,94 ± 13,95 and MMSE=25,21 ± 3,74; and for controls: CAMCOG=90,83 ± 8,88 (p=0,017) and MMSE=27,86 ± 1,99 (p=0,004). Results of depressive symptom assessment for the patient group were MADRS=23.23 ± 8.60 HAM-D=18.64 ± 6.17 and MADRS=1.39 ± 1.20, HAM-D=2.67 ± 1.57 for control group. After controlling for age, geriatric depressed subjects had no significant differences on FA and on MD parameters. No significant correlations were found between scores from cognitive tests (CAMCOG and MMSE), and FA or MD parameters. Similar results were obtained after correlating scores from scales measuring depressive symptoms (MADRS and HAM-D) and FA or MD parameters. Conclusions: There was no significant difference in FA or MD values between elderly depressed and elderly without depression when the brain is analyzed without a ROI previously determined. There was no correlation, in the present sample, between cognitive assessment and FA or MD, neither between severity of depression and these brain white matter parameters
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Imagem por tensor de difusão da substância branca aparentemente normal no comprometimento cognitivo leve e na doença de Alzheimer / Diffusion tensor imaging of normal-appearing white matter in mild cognitive impairment and early Alzheimer diseaseMartins, Sergilaine Pereira, 1965- 25 August 2018 (has links)
Orientador: Elizabeth Maria Aparecida Barasnevicius Quagliato / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Ciências Médicas / Made available in DSpace on 2018-08-25T22:29:43Z (GMT). No. of bitstreams: 1
Martins_SergilainePereira_D.pdf: 2688714 bytes, checksum: 50e69a64ddbe919094b642d6fcc2f77a (MD5)
Previous issue date: 2014 / Resumo: A ressonância magnética por tensor de difusão (DTI) proporciona aumento da sensibilidade para estudar a alterações na microestrutura da substância branca aparentemente normal (SBAN) in vivo e é especialmente indicada para estudar doenças que apresentam lesão axonal e desmielinização. No presente estudo, sugerimos a hipótese de que a neurodegeneração produz alterações microestruturais na SBAN de indivíduos com DA e CCL, especialmente em regiões específicas do cérebro. Foram estudados 71 participantes (21 com DA leve, 25 com CCL e 25 controles normais-CN) que foram recrutados de serviço médico neurológico em Campinas. Os indivíduos foram avaliados por um protocolo de avaliação clínica padronizada que incluiu: escala de depressão geriátrica (GDS), questionário de atividades funcionais (FAQ - Pfeffer), mini exame do estado mental (MEEM), teste de aprendizado auditivo-verbal de REY (RAVLT), testes de memória prospectiva (MP) (consulta e pertence) (subtestes do Teste de Memória Comportamental Rivermead), teste de fluência verbal (FV) (animais e FAS), teste desenho do relógio (TDR) e teste de nomeação de Boston (TNB). As imagens de RNM foram adquiridas usando um scanner MRT 1.5. A anisotropia fracionada (FA) e as difusividades axial (DAx) e radial (DRa) foram analisadas em regiões de interesse (ROI) alocados nos lobos frontal, parietal, temporal e occipital. FA, DAx e DRa foram calculadas para cada ROI. Em seguida, calculamos as médias de todas as seções para FA, DAx, e DRa para cada região da SBAN bilateralmente. Resultados: Nossos resultados mostraram que: (1) Comparado com CN, o grupo CCL demonstrou diminuição da FA no lobo frontal (parte do fórceps menor e do fascículo uncinado e coroa radiada), região importante para a memória episódica. (2) Na avaliação por análise de regressão múltipla, FA e DAx frontal, DAx temporal e parietal e FA occipital formaram um padrão de parâmetros associados ao maior risco para CCL e DA. (3) O estudo da acurácia revelou que a DTI da região frontal é a que apresenta maior sensibilidade e especificidade para identificar CCL. Em relação à DA, as variáveis FA frontal e temporal e DAx parietal apresentaram maior especificidade para identificar DA. (4) Não encontramos correlação robusta entre variáveis neuropsicológicas e de neuroimagem / Abstract: MRI technique, diffusion tensor imaging (DTI), provides increased sensitivity to alterations in the microstructure of white matter in vivo and is especially indicative for diseases causing axonal damage and demyelination. In the present study, we hypothesized that neurodegeneration produces microstructural changes in the cerebral white matter of subjects with AD and MCI, especially in specific regions in the brain. We studied 71 participants (21 mild AD, 25 MCI, and 25 normal controls-NC) that were recruited from neurological medical service in Campinas. Subjects were evaluated by using a standardized clinical evaluation protocol, which included: Geriatric depression Scal (GDS), the functional activities questionnaire (FAQ-Pfeffer), mini-mental status examination (MMSE), Rey auditory verbal learning test (RAVLT), prospective memory (Rivermead Behavioral Memory Test), verbal fluency test (animal and FAS), clock drawing test and Boston naming test. MR images were acquired using a 1.5 T MR scanner. Fractional anisotropy (FA) and axial and radial diffusivities (DA and DR) were analyzed in regions of interest (ROIs) in frontal, parietal, temporal and occipital lobes. FA, DA, and DR were calculated for each ROI. Then the measures of FA, DA, and DR were averaged across all the sections of each white matter region bilaterally. Our results showed that: (1) Compared to NC, MCI group showed decreased FA in the frontal lobe (the minor forceps and the uncinate fasciculus, and corona radiata), important region to episodic memory. (2) The evaluation by multiple regression analysis, frontal FA and DA, temporal and parietal DA and occipital FA formed a pattern of parameters associated with increased risk for MCI and AD. (3) The accuracy revealed that the frontal area has the greatest sensitivity and specificity to identify MCI. Regarding the AD, the frontal FA and temporal and parietal DA have the greatest specificity for identifying AD. (4) We did not find correlation between neuropsychological and neuroimaging variables / Doutorado / Neurologia / Doutora em Ciências Médicas
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Diffusion Tensor Imaging of the Human Skeletal Muscle : Contributions and Applications / IRM du tenseur de diffusion du muscle squelettique humain : contributions et applicationsNeji, Radhouène 09 March 2010 (has links)
Cette thèse propose des techniques pour le traitement d'images IRM de diffusion. Les méthodes proposées concernent l'estimation et la régularisation, le groupement et la segmentation ainsi que le recalage. Le cadre variationnel proposé dans cette thèse pour l'estimation d'un champ de tenseurs de diffusion à partir d'observations bruitées exploite le fait que les données de diffusion représentent des populations de fibres et que chaque tenseur peut être reconstruit à partir d'une combinaison pondérée de tenseurs dans son voisinage. La méthode de segmentation traite aussi bien les voxels que les fibres. Elle est basée sur l'utilisation de noyaux défini-positifs sur des probabilités gaussiennes de diffusion afin de modéliser la similarité entre tenseurs et les interactions spatiales. Ceci permet de définir des métriques entre fibres qui combinent les informations de localisation spatiale et de tenseurs de diffusion. Plusieurs approches de groupement peuvent être appliquées par la suite pour segmenter des champs de tenseurs et des trajectoires de fibres. Un cadre de groupement supervisé est proposé pour étendre cette technique. L'algorithme de recalage utilise les noyaux sur probabilités pour recaler une image source et une image cible. La régularité de la déformation est évaluée en utilisant la distortion induite sur les distances entre probabilités spatialement voisines. La minimisation de la fonctionnelle de recalage est faite dans un cadre discret. La validation expérimentale est faite sur des images du muscle du mollet pour des sujets sains et pour des patients atteints de myopathies. Les résultats des techniques développées dans cette thèse sont encourageants. / In this thesis, we present several techniques for the processing of diffusion tensor images. They span a wide range of tasks such as estimation and regularization, clustering and segmentation, as well as registration. The variational framework proposed for recovering a tensor field from noisy diffusion weighted images exploits the fact that diffusion data represent populations of fibers and therefore each tensor can be reconstructed using a weighted combination of tensors lying in its neighborhood. The segmentation approach operates both at the voxel and the fiber tract levels. It is based on the use of Mercer kernels over Gaussian diffusion probabilities to model tensor similarity and spatial interactions, allowing the definition of fiber metrics that combine information from spatial localization and diffusion tensors. Several clustering techniques can be subsequently used to segment tensor fields and fiber tractographies. Moreover, we show how to develop supervised extensions of these algorithms. The registration algorithm uses probability kernels in order to match moving and target images. The deformation consistency is assessed using the distortion induced in the distances between neighboring probabilities. Discrete optimization is used to seek an optimum of the defined objective function. The experimental validation is done over a dataset of manually segmented diffusion images of the lower leg muscle for healthy and diseased subjects. The results of the techniques developed throughout this thesis are promising.
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Diffusion tensor magnetic resonance imaging of the brain : Tractography analysis with application in healthy individuals and patientsMårtensson, Johanna January 2017 (has links)
In study 1, thirty-eight healthy controls were used for optimization of the method. Fifteen patients with progressive supranuclear palsy and an equal number of age-matched healthy controls underwent diffusion tensor MRI and were then investigated and compared groupwise. It was shown that tractography analyses may preferably be performed regionally, such as along the tracts or in different segments of the tracts. Normalization of white matter tracts can be performed using anatomical landmarks. In study 2, 104 males and 153 females in the age interval 13 to 84 years of age participated as healthy individuals in order to investigate age-related changes with diffusion tensor MRI. It was shown that spatially differences in age-related changes exist between subdivided segments within white matter tracts. The aging processes within the CB and the IFO vary regionally. In study 3, 38 human brains were used for investigation of the white matter tract inferior longitudinal fasciculus (ILF) and its subcomponents. Of these, white matter anatomical dissection was performed in 14 post-mortem normal human brains. The remaining 24 brains were investigated in vivo with diffusion tensor MRI in healthy individuals. It was validated that fibers of the ILF in the occipito-temporal region have a clear, constant and detailed organisation. The anatomical connectivity pattern, and quantitative differences between the ILF subcomponents, confirmed a pivotal role of the ILF. In study 4, 12 patients with iNPH were included in the study and examined with diffusion tensor at three time points. For comparison, 12 healthy controls, matched by gender and age were also included. Controls were examined with MRI only once. It was shown that DTI measures differ significantly between patients with iNPH and healthy controls. DTI measures of the CC, the CST and the SLF, correlated to changes in clinical symptoms after shunt surgery. Deeper knowledge about functions of the brain increases possibilities to take advantages from DTI analyses with tractography.
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In-vivo Darstellung hypothalamischer Substrukturen mit Hilfe von Diffusions-Tensor-BildgebungPetzold, Friederike 23 July 2014 (has links)
In der vorliegenden Arbeit wird der Hypothalamus, eine kleine, aber bedeutsame Struktur des Zwischenhirns untersucht. Er spielt unter anderem eine Rolle bei der Regulation des Schlaf-Wach-Rhythmus, des Sexualverhaltens, der Stimmungslage, autonomer und Stoffwechsel-Funktionen. Veränderungen einzelner oder mehrerer spezifischer Kerngruppen sind bei neuropsychiatrischen bzw. -endokrinologischen Erkrankungen, wie Narkolepsie, Schizophrenie, affektiver Störung, Demenz, Borderline-Persönlichkeitsstörung, Pädophilie oder Adipositas zu beobachten. Die Substrukturierung und Darstellung der einzelnen Kerngruppen gelang bisher nur in Postmortem-Studien. Im Rahmen dieser Studie konnte mit Hilfe der Diffusions-Tensor-Bildgebung erstmals eine in-vivo Substrukturierung des Hypothalamus konsistent bei zehn gesunden Probanden vorgenommen werden. Dabei wurden nach einem Algorithmus zunächst die Segmentierung und anschließend die Parzellierung durchgeführt, woraus sich drei konsistente Cluster ergaben. Der topografische Vergleich der erhaltenen Cluster mit Postmortem-Studien der Literatur ergab vergleichbare und anatomisch plausible Korrelate. Mit der von uns entwickelten Methode könnten anhand einer größeren Patientengruppe pathophysiologische Zusammenhänge neuropsychiatrischer und –endokrinologischer Störungen genauer eruiert werden und zu einem besseren Verständnis des Krankheitsverlaufs und der Therapie beitragen.:1 Einleitung
1.1 Topographie und Funktion des Hypothalamus
1.2 MRT- Kartierung des Hypothalamus
1.3 Diffusions-Tensor- Bildgebung
1.3.1 Diffusionsellipsoid
1.3.2 Fraktionelle Anisotropie
1.3.3 Clusteranalyse
1.3.4 k-means- Clusteralgorithmus
1.4 Pathomorphologische Veränderungen des Hypothalamus bei neuropsychiatrischen Erkrankungen
1.4.1 Narkolepsie
1.4.2 Schizophrenie
1.4.3 Affektive Störung
1.4.4 Demenz
1.4.5 Borderline- Persönlichkeitsstörung
1.4.6 Pädophilie
1.4.7 Adipositas
1.4.8 Zusammenfassung
2 Fragestellung: Ist eine Subpartialisierung des Hypothalamus in-vivo mit struktureller Bildgebung möglich?
3 Material und Methoden
3.1 Probanden
3.2 Bilderfassung und -bearbeitung
3.3 Segementierung des Hypothalamus - Definition der ROI`s („region of interest“)
3.3.1 Präoptischer Hypothalamus
3.3.2 Anteriorer Hypothalamus
3.3.3 Tuberaler Hypothalamus
3.3.4 Posteriorer Hypothalamus, Mamillarkörperchen
3.4 Parzellierung und Clusteranalyse
4 Ergebnisse: Mit qualitativen Analysen konnte gezeigt werden, dass eine Subpartialisierung des Hypothalamus möglich ist.
4.1 Segmentierung des Hypothalamus
4.2 Substrukturen/Cluster
5 Diskussion der Ergebnisse
5.1 Neuroanatomie des Hypothalamus
5.1.1 Kerngruppen des Hypothalamus
5.1.2 Faserverbindungen des Hypothalamus
5.1.3 Zusammenfassung der Faserverbindungen der Kerngruppen
5.2 Interpretation der einzelnen Cluster
5.2.1 Anteriore Substruktur
5.2.2 Posteromediale Substruktur
5.2.3 Laterale Substruktur
5.3 Topografische Beziehung der drei Cluster untereinander
5.3.1 Ähnlichkeiten der Cluster der zehn Probanden
5.3.2 Unterschiede der Cluster der zehn Probanden
5.4 Verbesserung der Hypothalamusmaske
6 Zusammenfassung
7 Literaturverzeichnis
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Optimization of Magnetic Resonance Diffusion Tensor Imaging for Visualization and Quantification of Periprostatic Nerve FibersNordbrøden, Mats January 2015 (has links)
Prostatectomy, surgical resection of the whole prostate is a common treatment for high- risk prostate cancer. Common side effects include long-time urinary and or erectile dysfunction due to damage inflicted to periprostatic nerves. The aim of this study was to identify an optimal magnetic resonance diffusion tensor imaging protocol for visualization and quantification of these nerves, as pre-surgery visualization may help nerve-sparing surgery. Both scanner filter, parameters for accelerated scan techniques, diffusion-related acquisition parameters and post- processing tractography parameters were investigated. Seven healthy volunteers were scanned with a state-of-art 3 T MRI scanner with varying protocol parameters. Diffusion data were processed and analysed using Matlab and Explore DTI. The resulting protocol recommendation included a normalized scanner filter, a parallel imaging acceleration factor of 2, partial Fourier sampling of 6/8, a right-left phase encoding direction, a b-value of 600 s/mm2, monopolar gradient polarity with applied eddy current correction, four acquisitions of 12 diffusion- sensitizing gradient directions, and a reverse phase encoding approach for correction of geometrical image distortions induced by static field inhomogeneity. For post-processing tractography, the recommended parameters were a lower limit for fractional anisotropy of 0.05, a minimum tract length of 3 centimetres and a maximum turning angle between voxels of 60 degrees. The limited parameter range that was tested and the low number of volunteers can be regarded as limitations to this study. Future work should address these issues. Furthermore, feasibility of periprostatic nerve tracking with the optimized protocol should be tested in a patient study.
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Polymorphism within a neuronal activity-dependent enhancer of NgR1 is associated with corpus callosum morphology in humans / NgR1遺伝子の神経活動依存性エンハンサー領域の遺伝子多型はヒトの脳梁の形態に関連するIsobe, Masanori 24 September 2015 (has links)
京都大学 / 0048 / 新制・課程博士 / 博士(医学) / 甲第19270号 / 医博第4034号 / 新制||医||1011(附属図書館) / 32272 / 京都大学大学院医学研究科医学専攻 / (主査)教授 髙橋 良輔, 教授 渡邉 大, 教授 富樫 かおり / 学位規則第4条第1項該当 / Doctor of Medical Science / Kyoto University / DFAM
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Computation of Effective Local Diffusion Tensor / Beräkning av effektiv lokal diffusionstensorPontéus, Viktor January 2022 (has links)
Numerical simulations of large complex systems such as biomolecules often suffer from the full description of the system having too many dimensions for direct numerical calculations and Monte Carlo methods having trouble overcoming energy barriers. It is therefore desirable to formulate a description in lower dimension which captures the system’s macroscopic behaviour. Recently, Lindahl et al [1] proposed a metric, g(λ), on the extended space Λ based on the dynamics of the system to optimize Monte Carlo sampling within extended ensemble formalism. In this thesis, we formulate a low-dimensional effective coarse-grained dynamic on Λ as a diffusion process and ask if it is possible to use this metric to calculate thelocal effective diffusion matrix as D(λ) = g−1(λ). By testing various scenarios we conclude that computing D(λ) in this manner indeed gives a correct effective dynamic in most cases, where the scale of coarse-graining can be tuned. However, an incorrect dynamic is received for example when the scale of coarse-graining is comparable to the size of oscillations in the energy landscape. / Numeriska simuleringar av stora komplexa system såsom biomolekyler lider ofta av att den fulla beskrivningen av systemet har för många dimensioner för direkta numeriska beräkningar samt att Monte Carlo-metoder har svårt att komma över energibarriärer. Det är därför önskvärt att formulera en beskrivning i lägre dimension som fångar systemets makroskopiska beteende. Nyligen föreslog Lindahl et al [1] en metrik g(λ) på det utvidgade rummet Λ baserad på dynamiken av systemet för att optimera Monte Carlo-sampling inom formalismen av utvidgade ensembler. I den här uppsatsen formulerar vi en lågdimensionell effektiv grov dynamik på Λ som en diffusionsprocess och frågar om det är möjligt att använda den här metriken för att beräkna den lokala effektiva diffusionsmatrisen som D(λ) = g(λ)−1. Genom testning av flera scenarier drar vi slutsatsen att beräkna D(λ) på det här sättet ger en korrekt effektiv dynamik i de flesta fall, där skalan på förgrovningen kan ställas in. Däremot fås en inkorrekt dynamik till exempel när skalan på förgrovningen ärjämförbar med storleken på oscillationer i energilandskapet.
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