574 research outputs found

    Joint Brain Parametric T1-Map Segmentation and RF Inhomogeneity Calibration

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    We propose a constrained version of Mumford and Shah's (1989) segmentation model with an information-theoretic point of view in order to devise a systematic procedure to segment brain magnetic resonance imaging (MRI) data for parametric T1-Map and T1-weighted images, in both 2-D and 3D settings. Incorporation of a tuning weight in particular adds a probabilistic flavor to our segmentation method, and makes the 3-tissue segmentation possible. Moreover, we proposed a novel method to jointly segment the T1-Map and calibrate RF Inhomogeneity (JSRIC). This method assumes the average T1 value of white matter is the same across transverse slices in the central brain region, and JSRIC is able to rectify the flip angles to generate calibrated T1-Maps. In order to generate an accurate T1-Map, the determination of optimal flip-angles and the registration of flip-angle images are examined. Our JSRIC method is validated on two human subjects in the 2D T1-Map modality and our segmentation method is validated by two public databases, BrainWeb and IBSR, of T1-weighted modality in the 3D setting

    Entwicklung von Fluor-19 und Protonen-Magnetresonanztomographie und ihre Anwendung bei Neuroentzündung

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    The experimental autoimmune encephalomyelitis (EAE) is used to study multiple sclerosis (MS) pathology and develop novel technologies to quantify inflammation over time. Magnetic resonance imaging (MRI) with gadolinium-based contrast agents (GBCAs) is the state-of-the-art method to assess inflammation in MS patients and its animal model. Fluorine (19F)-MRI is one novel technology to quantify inflammatory immune cells in vivo using 19F-nanoparticles. T1 mapping of contrast-enhancing images is another method that could be implemented to quantify inflammatory lesions. Transient macroscopic changes in the EAE brain confound quantification and necessitate registration methods to spatially align images in longitudinal studies. For 19F-MRI, an additional challenge is the low signal-to-noise ratio (SNR) due to low number of 19F-labeled immune cells in vivo. Transceive surface radiofrequency (RF) probes and SNR-efficient imaging techniques such as RARE (Rapid Acquisition with Relaxation Enhancement) are combined to increase sensitivity in 19F-MRI. However, the strong spatially-varying RF field (B1 inhomogeneity) of transceive surface RF probes further hampers quantification. Retrospective B1 correction methods typically use signal intensity equations, unavailable for complex acquisition methods like RARE. The main goal of this work is to investigate novel B1 correction and registration methods to enable the study of inflammatory diseases using 1H- and 19F-MRI following GBCA and 19F-nanoparticle administration, respectively. For correcting B1 inhomogeneities in 1H- and 19F-MR transceive surface RF probes, a model-based method was developed using empirical measurements and simulations, and then validated and compared with a sensitivity method and a hybrid of both. For 19F-MRI, a workflow to measure anatomical images in vivo and a method to compute 19F-concentration uncertainty after correction using Monte Carlo simulations were developed. To overcome the challenges of EAE brain macroscopic changes, a pipeline for registering images throughout longitudinal studies was developed. The proposed B1 correction methods demonstrated dramatic improvements in signal quantification and T1 contrast on images of test phantoms and mouse brains, allowing quantitative measurement with transceive surface RF probes. For low-SNR scenarios, the model-based method yielded reliable 19F-quantifications when compared to volume resonators. Uncertainty after correction depended linearly on the SNR (≤10% with SNR≥10.1, ≤25% when SNR≥4.25). The implemented registration approach provided successful image alignment despite substantial morphological changes in the EAE brain over time. Consequently, T1 mapping was shown to objectively quantify gadolinium lesion burden as a measure of inflammatory activity in EAE. The 1H- and 19F-MRI methods proposed here are highly relevant for quantitative MR of neuroinflammatory diseases, enabling future (pre)clinical investigations.Die experimentelle Autoimmun-Enzephalomyelitis (EAE) wird zur Untersuchung Multipler Sklerose (MS) und zur Entwicklung neuer Technologien zur Entzündungsquantifizierung eingesetzt. Magnetresonanztomographie (MRT) mit Gadolinium-haltigen Kontrastmitteln (GBCAs) ist die modernste Methode zur Beurteilung von Entzündungen bei MS-Patienten und im Tiermodell. Fluor (19F)-MRT unter Verwendung von 19F-Nanopartikeln ist eine neue Technologie zur Quantifizierung entzündlicher Immunzellen in vivo. T1-Kartierung ist eine MRT-Methode, die zur Quantifizierung entzündlicher Läsionen eingesetzt werden könnte. Temporäremorphologische Veränderungen im EAE-Gehirn erschweren die Quantifizierung und erfordern Registrierungsmethoden, um MRT-Bilder in Längsschnittstudien räumlichabzugleichen. Das niedrige Signal-Rausch-Verhältnis (SNR) ist aufgrund der geringen Anzahl 19F-markierter Immunzellen in vivo eine zusätzliche Herausforderung der 19F-MRT. Um deren Empfindlichkeit zu erhöhen, werden Sende-/Empfangsoberflächen-Hochfrequenzspulen (TX/RX-HF-Spule) und SNR-effiziente MRT-Techniken wie RARE (Rapid Acquisition with Relaxation Enhancement) kombiniert. Jedoch verhindert die starke räumliche Variation des HF-Feldes (B1-Inhomogenität) dieser Spulen die Signalquantifizierung. Retrospektive B1-Korrekturmethoden verwenden in der Regel Signalintensitätsgleichungen, die für komplexe MRT-Techniken wie RARE nicht existieren. Das Hauptziel dieser Arbeit ist die Untersuchung neuartiger B1-Korrektur- und Bildregistrierungsmethoden, um in vivo 1H- und 19F-MRT Studien von Entzündungsprozessen zu ermöglichen. Zur Korrektur von B1-Inhomogenitäten wurde eine modellbasierte Methode entwickelt. Diese verwendet empirische Messungen und Simulationen, wurde in Phantomexperimenten validiert und mit Referenzmethoden verglichen. Für 19F-MRT wurden ein Protokoll zur Messung anatomischer Bilder in vivo und eine Methode zur Berechnung der 19F-Konzentrationsunsicherheit nach Korrektur mittels Monte-Carlo-Simulationen entwickelt. Um morphologische Veränderungen im EAE-Gehirn in longitudinalen Studien zu kompensieren, wurde zur Bildregistrierung eine Software-Bibliothek entwickelt. Die B1-Korrekturmethoden zeigten in Testobjekten und Mäusehirnen drastische Verbesserungen der Signal- und T1 Quantifizierung und ermöglichten so quantitative Messungen mit TX/RX-HF-Spulen. Die modellbasierte Methode lieferte für geringe SNRs zuverlässige 19F-Quantifizierungen, deren Genauigkeit mit dem SNR korrelierte. Die implementierte Registrierungsmethode ermöglichte einen erfolgreichen Abgleich von Bildserientrotz erheblicher morphologischer Veränderungen im EAE-Hirn. Folglich wurde gezeigt, dass MRT basierte T1-Kartierung die Gadolinium-Läsionslast als Maß entzündlicher Aktivität bei EAE objektiv quantifizieren kann. Die hier unterscuhten Methoden sind für quantitative 1H- und 19F-MRT neuroinflammatorischer Erkrankungen sehr relevant und ermöglichen künftige (prä)klinische Untersuchungen

    Towards in vivo g-ratio mapping using MRI: unifying myelin and diffusion imaging

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    The g-ratio, quantifying the comparative thickness of the myelin sheath encasing an axon, is a geometrical invariant that has high functional relevance because of its importance in determining neuronal conduction velocity. Advances in MRI data acquisition and signal modelling have put in vivo mapping of the g-ratio, across the entire white matter, within our reach. This capacity would greatly increase our knowledge of the nervous system: how it functions, and how it is impacted by disease. This is the second review on the topic of g-ratio mapping using MRI. As such, it summarizes the most recent developments in the field, while also providing methodological background pertinent to aggregate g-ratio weighted mapping, and discussing pitfalls associated with these approaches. Using simulations based on recently published data, this review demonstrates the relevance of the calibration step for three myelin-markers (macromolecular tissue volume, myelin water fraction, and bound pool fraction). It highlights the need to estimate both the slope and offset of the relationship between these MRI-based markers and the true myelin volume fraction if we are really to achieve the goal of precise, high sensitivity g-ratio mapping in vivo. Other challenges discussed in this review further evidence the need for gold standard measurements of human brain tissue from ex vivo histology. We conclude that the quest to find the most appropriate MRI biomarkers to enable in vivo g-ratio mapping is ongoing, with the potential of many novel techniques yet to be investigated.Comment: Will be published as a review article in Journal of Neuroscience Methods as parf of the Special Issue with Hu Cheng and Vince Calhoun as Guest Editor

    Improvements in the registration of multimodal medical imaging : application to intensity inhomogeneity and partial volume corrections

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    Alignment or registration of medical images has a relevant role on clinical diagnostic and treatment decisions as well as in research settings. With the advent of new technologies for multimodal imaging, robust registration of functional and anatomical information is still a challenge, particular in small-animal imaging given the lesser structural content of certain anatomical parts, such as the brain, than in humans. Besides, patient-dependent and acquisition artefacts affecting the images information content further complicate registration, as is the case of intensity inhomogeneities (IIH) showing in MRI and the partial volume effect (PVE) attached to PET imaging. Reference methods exist for accurate image registration but their performance is severely deteriorated in situations involving little images Overlap. While several approaches to IIH and PVE correction exist these methods still do not guarantee or rely on robust registration. This Thesis focuses on overcoming current limitations af registration to enable novel IIH and PVE correction methods.El registre d'imatges mèdiques té un paper rellevant en les decisions de diagnòstic i tractament clíniques així com en la recerca. Amb el desenvolupament de noves tecnologies d'imatge multimodal, el registre robust d'informació funcional i anatòmica és encara avui un repte, en particular, en imatge de petit animal amb un menor contingut estructural que en humans de certes parts anatòmiques com el cervell. A més, els artefactes induïts pel propi pacient i per la tècnica d'adquisició que afecten el contingut d'informació de les imatges complica encara més el procés de registre. És el cas de les inhomogeneïtats d'intensitat (IIH) que apareixen a les RM i de l'efecte de volum parcial (PVE) característic en PET. Tot i que existeixen mètodes de referència pel registre acurat d'imatges la seva eficàcia es veu greument minvada en casos de poc solapament entre les imatges. De la mateixa manera, també existeixen mètodes per la correcció d'IIH i de PVE però que no garanteixen o que requereixen un registre robust. Aquesta tesi es centra en superar aquestes limitacions sobre el registre per habilitar nous mètodes per la correcció d'IIH i de PVE

    Accelerated Quantitative Mapping and Angiography for Cerebral and Cardiovascular Magnetic Resonance Imaging

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    Magnetic resonance imaging (MRI) produces images with anatomical and functional information. These images can be obtained without the use of contrast agents, which generally require long scan times. This dissertation investigates existing techniques for accelerating such functional MRI methods, contributes novel fast acquisition and reconstruction techniques, and proposes new ways of analyzing real-time MRI data. First, we aim to determine an advantageous approach for accelerating high spatial resolution 3D cardiac T2 relaxometry data by comparing the performance of different data undersampling patterns and reconstruction methods over a range of acceleration rates. Quantitative results on healthy and edematous hearts reveal that the relaxometry maps are more sensitive to undersampling than anatomical images. The 3-fold variable density random undersampling with model-based or joint-sparsity sensitivity encoding (SENSE) is recommended. Second, we develop a rapid T2 mapping protocol using spiral acquisition and novel model-based approach joined with compressed sensing (CS) and model-based reconstruction. We also develop a sequence that suppresses cerebrospinal fluid (CSF). Quantitative evaluation on digital phantoms and healthy volunteers demonstrates the feasibility of T2 quantification with 3D high-resolution and whole-brain coverage in 2-3 min. Third, we propose a Golden Angle (GA) rotated Spiral Sparse Parallel imaging (GASSP) method for high spatial (0.8mm) and high temporal (<21ms) resolution for measuring coronary blood flow in a single breath-hold. We reduce k-space gaps using novel binning and triggered GA schemes. Velocity and flow metrics are validated against two existing methods and show high reproducibility. Fourth, we construct an abdominal non-contrast-enhanced magnetic resonance angiography (MRA) protocol with a large spatial coverage at 3.0T. The protocol uses advanced velocity-selective (VS) pulse trains. MRA with a large spatial coverage is slow and accelerated using CS. The VS-MRA sequences generate high-quality angiograms and arteriograms with high blood contrast. Finally, physiological changes in real-time (RT) MRI (30-100 frames/sec) are explored using Fourier transform (FT), principal component analyses (PCA), and perfusion modeling. We detect spectral patterns in pharyngeal images acquired during speaking and obtain T1-weighted, pulsation-weighted, and respiration-weighted images in healthy volunteers and heart patients with wall motion abnormalities with FT and PCA. RT perfusion maps are estimated from a proposed perfusion model in ongoing work in progress

    Doctor of Philosophy

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    dissertationMagnetic Resonance (MR) is a relatively risk-free and flexible imaging modality that is widely used for studying the brain. Biophysical and chemical properties of brain tissue are captured by intensity measurements in T1W (T1-Weighted) and T2W (T2-Weighted) MR scans. Rapid maturational processes taking place in the infant brain manifest as changes in co{\tiny }ntrast between white matter and gray matter tissue classes in these scans. However, studies based on MR image appearance face severe limitations due to the uncalibrated nature of MR intensity and its variability with respect to changing conditions of scan. In this work, we develop a method for studying the intensity variations between brain white matter and gray matter that are observed during infant brain development. This method is referred to by the acronym WIVID (White-gray Intensity Variation in Infant Development). WIVID is computed by measuring the Hellinger Distance of separation between intensity distributions of WM (White Matter) and GM (Gray Matter) tissue classes. The WIVID measure is shown to be relatively stable to interscan variations compared with raw signal intensity and does not require intensity normalization. In addition to quantification of tissue appearance changes using the WIVID measure, we test and implement a statistical framework for modeling temporal changes in this measure. WIVID contrast values are extracted from MR scans belonging to large-scale, longitudinal, infant brain imaging studies and modeled using the NLME (Nonlinear Mixed Effects) method. This framework generates a normative model of WIVID contrast changes with time, which captures brain appearance changes during neurodevelopment. Parameters from the estimated trajectories of WIVID contrast change are analyzed across brain lobes and image modalities. Parameters associated with the normative model of WIVID contrast change reflect established patterns of region-specific and modality-specific maturational sequences. We also detect differences in WIVID contrast change trajectories between distinct population groups. These groups are categorized based on sex and risk/diagnosis for ASD (Autism Spectrum Disorder). As a result of this work, the usage of the proposed WIVID contrast measure as a novel neuroimaging biomarker for characterizing tissue appearance is validated, and the clinical potential of the developed framework is demonstrated

    MR-based pseudo-CT generation using water-fat decomposition and Gaussian mixture regression

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    Tese de mestrado integrado em Engenharia Biomédica e Biofísica, apresentada à Universidade de Lisboa, através da Faculdade de Ciências, 2017O uso de tomografia computorizada (CT) é considerado como a prática clínica adequada para aplicações clínicas onde a simulação da atenuação de radiação pelos tecidos corporais é necessária, tais como a correcção de atenuação dos fotões em Tomografia de Emissão de Positrões (PET) e no cálculo da dosagem a ser administrada durante o planeamento de radioterapia (RTP). Imagens de ressonância magnética (MRI) têm vindo a substituir o uso de TC em algumas aplicações, sobretudo devido ao seu superior contraste entre tecidos moles e ao facto de não usar radiação ionizante. Desta forma, técnicas como PET-MRI e o planeamento de radioterapia apenas com recurso a imagens de ressonância magnética são alvo de uma crescente atenção. No entanto, estas técnicas estão limitadas pelo facto de imagens de ressonância magnética não fornecerem informação acerca da atenuação e absorção de radiação pelos tecidos. Normalmente, de forma a solucionar este problema, uma imagem de tomografia computorizada é adquirida de forma a realizar a correcção da atenuação dos fotões, assim como a dose a ser entregue em radioterapia. No entanto, esta prática introduz erros aquando do alinhamento entre as imagens de MRI e CT, que serão propagados durante todo o procedimento. Por outro lado, o uso de radiação ionizante e os custos adicionais e tempo de aquisição associado à obtenção de múltiplas modalidades de imagem limitam a aplicação clínica destas práticas. Assim, o seguimento natural prende-se com a completa substituição do uso de CT por MRI. Desta forma, o desenvolvimento de um método para a obtenção de uma imagem equivalente a CT usando MRI é necessário, sendo a imagem resultante designada de pseudo-CT. Vários métodos foram desenvolvidos de forma a construir pseudo-CT, usando métodos baseados na anatomia do paciente ou em métodos de regressão entre CT e MRI. No entanto, no primeiro caso, erros significativos são frequentes devido ao difícil alinhamento entre as imagens em casos em que a geometria do paciente é muito diferente da presente no atlas. No segundo caso, a ausência de sinal no osso cortical em MRI, torna-o indistinguível do ar. Sequências que usam um tempo de eco muito curto são normalmente utilizadas para distinguir osso cortical de ar. No entanto, para áreas com maior dimensão, como a área pélvica, dificuldades relacionadas com o equipamento e com o ruído limitam a sua aplicação nestas áreas. Por outro lado, estes métodos utilizam frequentemente diferentes imagens de MRI de forma a obter diferentes contrastes, aumentando assim o tempo de aquisição das imagens. Nesta dissertação, é proposto um método para a obtenção de um pseudo-CT baseado na combinação de um algoritmo de decomposição de água e gordura e um modelo de regressão de mistura gaussiana para a região pélvica através da aquisição de sequências de MRI convencionais. Desta forma, a aquisição de diferentes contrastes é obtida por pós-processamento das imagens originais. Desta forma, uma imagem ponderada em T1 foi adquirida com 3 tempos de eco. Um algoritmo de decomposição do sinal de ressonância magnética em sinal proveniente de água e gordura foi utilizado, permitindo a obtenção de duas imagens, cada uma representando apenas o sinal da água e gordura, respectivamente. Usando estas duas imagens, uma imagem da fracção de gordura em cada voxel foi também calculada. Por outro lado, usando o primeiro e o terceiro eco foi possível calcular o decaimento de sinal devido a efeitos relacionados com o decaimento T2*. O método para gerar o pseudo-CT baseia- se num modelo de regressão duplo entre as variáveis relacionadas com MRI e CT. Assim, o primeiro modelo aplica-se aos tecidos moles, enquanto que o segundo modelo se aplica aos tecidos ósseos. A segmentação entre estes tecidos foi realizada através da delineação manual dos tecidos ósseos. No caso do modelo de regressão para os tecidos moles, o modelo consiste numa regressão polinomial entre as imagens da fracção de gordura e os valores de CT. A ordem do polinómio usada foi obtida pela minimização do erro absoluto médio. No caso do modelo de regressão para os tecidos ósseos, um modelo de regressão de mistura gaussiana foi aplicado usando as imagens de gordura, água, de fracção de gordura e de R2*. Estas variáveis foram selecionadas, uma vez que estudos prévios correlacionam esta com a densidade mineral óssea, que por sua vez está relacionada com as intensidades em CT. A influência de incluir no modelo de regressão informação acerca da vizinhança foi estudada através da inclusão de imagens do desvio padrão nos 27 voxéis na vizinhança das variáveis previamente incluídas no modelo. O número de componentes a usar no modelo de regressão de mistura gaussiana foi obtido através da minimização do critério de Akaike. O pseudo-CT final foi obtido pela sobreposição das imagens obtidas através do duplo modelo de regressão, seguido da aplicação de um filtro gaussiano com desvio padrão de 0.5 de forma a mitigar os erros na segmentação dos tecidos ósseos. Este método foi validado usando imagens da zona pélvica de 6 pacientes usando um procedimento leave-one-out-cross-validation (LOOCV). Durante este procedimento, o modelo foi estimado através das variáveis de 5 pacientes (imagens de treino) e aplicado às variáveis relacionadas com MRI do paciente restante (imagem de validação), de forma a gerar o pseudo-CT. Este procedimento foi repetido para todas as seis combinações de imagens de treino e de validação e os pseudo-CT obtidos foram comparados com a imagem TC correspondente. No caso do modelo para os tecidos moles, verificou-se que a utilização de um polinómio de segundo grau permitia a obtenção de melhores resultados. Da mesma forma, verificou-se que a inclusão de informação acerca da vizinhança permitia uma melhor estimativa dos valores de pseudo-CT no caso dos tecidos ósseos. A segmentação dos tecidos ósseos foi considerada adequada uma vez que o valor médio do coeficiente de Dice entre estes tecidos e o osso em CT foi de 0.91 ±0.02. O valor médio do erro absoluto entre o pseudo-CT e a correspondente CT para todos os pacientes foi de 37.76±3.11 HU, enquanto que no caso dos tecidos ósseos o valor foi de 96.61±10.49 HU. Um erro médio de -2.68 ± 6.32 HU foi obtido, denotando a presença de bias no processo. Por outro lado, valores médios de peak-to-signal-noise-ratio (PSNR) e strucutre similarity índex (SSIM) de 23.92±1.62 dB e 0.91±0.01 foram obtidos, respectivamente. Os maiores erros foram encontrados no recto, uma vez que o ar não foi considerado neste método, nas interfaces entre diferentes tecidos, devido a erros no alinhamento das imagens, e nos tecidos ósseos. Desta forma, o método de obtenção de um pseudo-CT proposto nesta dissertação demonstrou ter potencial para permitir uma correcta estimativa da intensidade em CT. Os resultados obtidos demonstram uma melhoria significativa quando comparados com outros métodos encontrados na literatura que se baseiam num método relacionado com a intensidade, enquanto que se encontram na mesma ordem de magnitude de métodos baseados na anatomia do paciente. Para além disso, quando comparados com os primeiros, este método tem a vantagem de apenas uma sequência MRI ser utilizada, levando a uma redução no tempo de aquisição e nos custos associados. Por outro lado, a principal limitação deste método prende-se com a segmentação manual dos tecidos ósseos, o que dificulta a sua implementação clínica. Desta forma, o desenvolvimento de técnicas de segmentação automáticas dos tecidos ósseos torna-se necessária, sendo exemplos destas técnicas a criação de um shape model ou através da segmentação baseada num atlas. A combinação destes métodos com o método descrito nesta dissertação pode permitir a obtenção de uma alternativa às imagens de CT para o cálculo das doses em radioterapia e correcção de atenuação em PET-MRI.Purpose: Methods for deriving computed tomography (CT) equivalent information from MRI are needed for attenuation correction in PET-MRI applications, as well as for dose planning in MRI based radiation therapy workflows, due to the lack of correlation between the MR signal and the electron density of different tissues. This dissertation presents a method to generate a pseudo-CT from MR images acquired with a conventional MR pulse sequence. Methods: A T1-weighted Fast Field Echo sequence with 3 echo times was used. A 3-point water-fat decomposition algorithm was applied to the original MR images to obtain water and fat-only images as well as a quantitative fat fraction image. A R2* image was calculated using a mono-exponential fit between the first and third echo of the original MR images. The method for generating the pseudo-CT includes a dual-model regression between the MR features and a matched CT image. The first model was applied to soft tissues, while the second-model was applied to the bone anatomy that were previously segmented. The soft-tissue regression model consists of a second-order polynomial regression between the fat fraction values in soft tissue and the HU values in the CT image, while the bone regression model consists of a Gaussian mixture regression including the water, fat, fat fraction and R2* values in bone tissues. Neighbourhood information was also included in the bone regression model by calculating an image of the standard deviation of 27-neighbourhood of each voxel in each MR related feature. The final pseudo-CT was generated by combining the pseudo-CTs from both models followed by the application of a Gaussian filter for additional smoothing. This method was validated using datasets covering the pelvic area of six patients and applying a leave-one-out-cross-validation (LOOCV) procedure. During LOOCV, the model was estimated from the MR related features and the CT data of 5 patients (training set) and applied to the MR features of the remaining patient (validation set) to generate a pseudo-CT image. This procedure was repeated for the all six training and validation data combinations and the pseudo-CTs were compared to the corresponding CT image. Results: The average mean absolute error for the HU values in the body for all patients was 37.76±3.11 HU, while the average mean absolute error in the bone anatomy was 96.61±10.49 HU. No large differences in method accuracy were noted for the different patients, except for the air in the rectum which was classified as soft tissue. The largest errors were found in the rectum and in the interfaces between different tissue types. Conclusions: The pseudo-CT generation method here proposed has the potential to provide an accurate estimation of HU values. The results here reported are substantially better than other voxel-based methods proposed. However, they are in the same range as the results presented in anatomy-based methods. Further investigation in automatic MRI bone segmentation methods is necessary to allow the automatic application of this method into clinical practice. The combination of these automatic bone segmentation methods with the model here reported is expected to provide an alternative to CT images for dose planning in radiotherapy and attenuation correction in PET-MRI
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