Minkowski Tensors of Anisotropic Spatial Structure

This article describes the theoretical foundation of and explicit algorithms for a novel approach to morphology and anisotropy analysis of complex spatial structure using tensor-valued Minkowski functionals, the so-called Minkowski tensors. Minkowski tensors are generalisations of the well-known scalar Minkowski functionals and are explicitly sensitive to anisotropic aspects of morphology, relevant for example for elastic moduli or permeability of microstructured materials. Here we derive explicit linear-time algorithms to compute these tensorial measures for three-dimensional shapes. These apply to representations of any object that can be represented by a triangulation of its bounding surface; their application is illustrated for the polyhedral Voronoi cellular complexes of jammed sphere configurations, and for triangulations of a biopolymer fibre network obtained by confocal microscopy. The article further bridges the substantial notational and conceptual gap between the different but equivalent approaches to scalar or tensorial Minkowski functionals in mathematics and in physics, hence making the mathematical measure theoretic method more readily accessible for future application in the physical sciences

In vivo morphometric and mechanical characterization of trabecular bone from high resolution magnetic resonance imaging

La osteoporosis es una enfermedad ósea que se manifiesta con una menor densidad ósea y el deterioro de la arquitectura del hueso esponjoso. Ambos factores aumentan la fragilidad ósea y el riesgo de sufrir fracturas óseas, especialmente en mujeres, donde existe una alta prevalencia. El diagnóstico actual de la osteoporosis se basa en la cuantificación de la densidad mineral ósea (DMO) mediante la técnica de absorciometría dual de rayos X (DXA). Sin embargo, la DMO no puede considerarse de manera aislada para la evaluación del riesgo de fractura o los efectos terapéuticos. Existen otros factores, tales como la disposición microestructural de las trabéculas y sus características que es necesario tener en cuenta para determinar la calidad del hueso y evaluar de manera más directa el riesgo de fractura. Los avances técnicos de las modalidades de imagen médica, como la tomografía computarizada multidetector (MDCT), la tomografía computarizada periférica cuantitativa (HR-pQCT) y la resonancia magnética (RM) han permitido la adquisición in vivo con resoluciones espaciales elevadas. La estructura del hueso trabecular puede observarse con un buen detalle empleando estas técnicas. En particular, el uso de los equipos de RM de 3 Teslas (T) ha permitido la adquisición con resoluciones espaciales muy altas. Además, el buen contraste entre hueso y médula que proporcionan las imágenes de RM, así como la utilización de radiaciones no ionizantes sitúan a la RM como una técnica muy adecuada para la caracterización in vivo de hueso trabecular en la enfermedad de la osteoporosis. En la presente tesis se proponen nuevos desarrollos metodológicos para la caracterización morfométrica y mecánica del hueso trabecular en tres dimensiones (3D) y se aplican a adquisiciones de RM de 3T con alta resolución espacial. El análisis morfométrico está compuesto por diferentes algoritmos diseñados para cuantificar la morfología, la complejidad, la topología y los parámetros de anisotropía del tejido trabecular. En cuanto a la caracterización mecánica, se desarrollaron nuevos métodos que permiten la simulación automatizada de la estructura del hueso trabecular en condiciones de compresión y el cálculo del módulo de elasticidad. La metodología desarrollada se ha aplicado a una población de sujetos sanos con el fin de obtener los valores de normalidad del hueso esponjoso. Los algoritmos se han aplicado también a una población de pacientes con osteoporosis con el fin de cuantificar las variaciones de los parámetros en la enfermedad y evaluar las diferencias con los resultados obtenidos en un grupo de sujetos sanos con edad similar.Los desarrollos metodológicos propuestos y las aplicaciones clínicas proporcionan resultados satisfactorios, presentando los parámetros una alta sensibilidad a variaciones de la estructura trabecular principalmente influenciadas por el sexo y el estado de enfermedad. Por otra parte, los métodos presentan elevada reproducibilidad y precisión en la cuantificación de los valores morfométricos y mecánicos. Estos resultados refuerzan el uso de los parámetros presentados como posibles biomarcadores de imagen en la enfermedad de la osteoporosis.Alberich Bayarri, Á. (2010). In vivo morphometric and mechanical characterization of trabecular bone from high resolution magnetic resonance imaging [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/8981Palanci

방사선학적 골 소실량과 치주염 단계의 딥러닝 기반 컴퓨터 보조진단 방법: 다기기 연구

학위논문 (박사) -- 서울대학교 대학원 : 융합과학기술대학원 융합과학부(방사선융합의생명전공), 2021. 2. 이원진.Periodontal diseases, including gingivitis and periodontitis, are some of the most common diseases that humankind suffers from. The decay of alveolar bone in the oral and maxillofacial region is one of the main symptoms of periodontal disease. This leads to alveolar bone loss, tooth loss, edentulism, and masticatory dysfunction, which indirectly affects nutrition. In 2017, the American Academy of Periodontology and the European Federation of Periodontology proposed a new definition and classification criteria for periodontitis based on a staging system. Recently, computer-aided diagnosis (CAD) based on deep learning has been used extensively for solving complex problems in radiology. In my previous study, a deep learning hybrid framework was developed to automatically stage periodontitis on dental panoramic radiographs. This was a hybrid of deep learning architecture for detection and conventional CAD processing to achieve classification. The framework was proposed to automatically quantify the periodontal bone loss and classify periodontitis for each individual tooth into three stages according to the criteria that was proposed at the 2017 World Workshop. In this study, the previously developed framework was improved in order to classify periodontitis into four stages by detecting the number of missing teeth/implants using an additional convolutional neural network (CNN). A multi-device study was performed to verify the generality of the method. A total of 500 panoramic radiographs (400, 50, and 50 images for device 1, device 2, and device 3, respectively) from multiple devices were collected to train the CNN. For a baseline study, three CNNs, which were commonly used for segmentation tasks and the modified CNN from the Mask Region with CNN (R-CNN) were trained and tested to compare the detection accuracy using dental panoramic radiographs that were acquired from multiple devices. In addition, a pre-trained weight derived from the previous study was used as an initial weight to train the CNN to detect the periodontal bone level (PBL), cemento-enamel junction level (CEJL), and teeth/implants to achieve a high training efficiency. The CNN, trained with the multi-device images that had sufficient variability, can produce an accurate detection and segmentation for the input images with various aspects. When detecting the missing teeth on the panoramic radiographs, the values of the precision, recall, F1-score, and mean average precision (AP) were set to 0.88, 0.85, 0.87, and 0.86, respectively, by using CNNv4-tiny. As a result of the qualitative and quantitative evaluation for detecting the PBL, CEJL, and teeth/implants, the Mask R-CNN showed the highest dice similarity coefficients (DSC) of 0.96, 0.92, and 0.94, respectively. Next, the automatically determined stages from the framework were compared to those that were developed by three oral and maxillofacial radiologists with different levels of experience. The mean absolute difference (MAD) between the periodontitis staging that was performed by the automatic method and that by the radiologists was 0.31 overall for all the teeth in the whole jaw. The classification accuracies for the images from the multiple devices were 0.25, 0.34, and 0.35 for device 1, device 2, and device 3, respectively. The overall Pearson correlation coefficient (PCC) values between the developed method and the radiologists’ diagnoses were 0.73, 0.77, and 0.75 for the images from device 1, device 2, and device 3, respectively (p < 0.01). The final intraclass correlation coefficient (ICC) value between the developed method and the radiologists’ diagnoses for all the images was 0.76 (p < 0.01). The overall ICC values between the developed method and the radiologists’ diagnoses were 0.91, 0.94, and 0.93 for the images from device 1, device 2, and device 3, respectively (p < 0.01). The final ICC value between the developed method and the radiologists’ diagnoses for all the images was 0.93 (p < 0.01). In the Passing and Bablok analysis, the slopes were 1.176 (p > 0.05), 1.100 (p > 0.05), and 1.111 (p > 0.05) with the intersections of -0.304, -0.199, and -0.371 for the radiologists with ten, five, and three-years of experience, respectively. For the Bland and Altman analysis, the average of the difference between the mean stages that were classified by the automatic method and those diagnosed by the radiologists with ten-years, five-years, and three-years of experience were 0.007 (95 % confidence interval (CI), -0.060 ~ 0.074), -0.022 (95 % CI, -0.098 ~ 0.053), and -0.198 (95 % CI, -0.291 ~ -0.104), respectively. The developed method for classifying the periodontitis stages that combined the deep learning architecture and conventional CAD approach had a high accuracy, reliability, and generality when automatically diagnosing periodontal bone loss and the staging of periodontitis by the multi-device study. The results demonstrated that when the CNN used the training data sets with increasing variability, the performance also improved in an unseen data set.치주염과 치은염을 포함한 치주질환은 인류가 겪고 있는 가장 흔한 질환 중 하나이다. 구강 및 악안면 부위 치조골의 침하는 치주질환의 주요 증상이며, 이는 골 손실, 치아 손실, 치주염을 유발할 수 있으며, 이를 방치할 경우 저작 기능 장애로 인한 영양실조의 원인이 될 수 있다. 2017년 미국치주학회(American Academy of Periodontology)와 유럽치주학회(European Federation of Periodontology)는 공동 워크샵을 통해 치주염에 대한 새로운 정의와 단계 분류 및 진단에 관련된 기준을 발표하였다. 최근, 딥러닝을 기반으로 한 컴퓨터 보조진단 기술 (Computer-aided Diagnoses, CAD)이 의료방사선영상 분야에서 복잡한 문제를 해결하는 데 광범위하게 사용되고 있다. 선행 연구에서 저자는 파노라마방사선영상에서 치주염을 자동으로 진단하기 위한 딥러닝 하이브리드 프레임워크를 개발하였다. 이는 해부학적 구조물 분할을 위한 딥러닝 신경망 기술과 치주염의 단계 분류를 위한 컴퓨터 보조진단 기술을 융합하여 단일 프레임워크에서 치주염을 자동으로 분류, 진단하는 방법이다. 이를 통해 각 치아에서 방사선적 치조골 소실량을 자동으로 정량화하고, 2017년 워크샵에서 제안된 기준에 따라 치주염을 3단계로 분류하였다. 본 연구에서는 선행 개발된 방법을 개선하여 상실 치아와 식립된 임플란트의 수를 검출, 정량화하여 치주염을 4단계로 분류하는 방법을 개발하였다. 또한 개발된 방법의 일반화 정도를 평가하기 위해 서로 다른 기기를 통해 촬영된 영상을 이용한 다기기 연구를 수행하였다. 3개의 기기를 이용하여 총 500매의 파노라마방사선영상을 수집하여 CNN 학습을 위한 데이터셋을 구축하였다. 수집된 영상 데이터셋을 이용하여, 기존 연구에서 의료영상 분할에 일반적으로 사용되는 3개의 CNN 모델과 Mask R-CNN을 학습시킨 후, 해부학적 구조물 분할 정확도 비교 평가를 실시하였다. 또한 CNN의 높은 학습 효율성 확보와 및 다기기 영상에 대한 추가 학습을 위해 선행 연구에서 도출된 사전 훈련 가중치(pre-trained weight)를 이용한 CNN의 전이학습을 실시하였다. CNNv4-tiny를 이용하여 상실 치아를 검출한 결과, 0.88, 0.85, 0.87, 0.86, 0.85의 precision, recall, F1-score, mAP 정확도를 보였다. 해부학적 구조물 분할 결과, Mask R-CNN을 기반으로 수정된 CNN은 치조골 수준에 대해0.96, 백악법랑경계 수준에 대해 0.92, 치아에 대해 0.94의 분할정확도(DSC)를 보였다. 이어 개발된 방법을 이용하여 학습에 사용되지 않은 30매(기기 별 10매)에서 자동으로 결정된 치주염의 단계와 서로 다른 임상경험을 가진 3명의 영상치의학 전문의가 진단한 단계 간 비교 평가를 수행하였다. 평가 결과, 모든 치아에 대해 자동으로 결정된 치주염 단계와 전문의들이 진단한 단계 간 0.31의 오차(MAD)를 보였다. 또한 기기1, 2, 3의 영상에 대해 각각 0.25, 0.34, 0.35의 오차를 보였다. 개발된 방법을 이용한 결과와 방사선 전문의의 진단 사이의 PCC 값은 기기1, 2, 3의 영상에 대해 각각 0.73, 0.77, 0.75로 계산되었다 (p<0.01). 전체 영상에 대한 최종 ICC 값은 0.76 (p<0.01)로 계산되었다. 또한 개발된 방법과 방사선 전문의의 진단 사이의 ICC 값은 기기1, 2, 3의 영상에 대해 각각 0.91, 0.94, 0.93으로 계산되었다 (p <0.01). 마지막으로 최종 ICC 값은 0.93으로 계산되었다 (p<0.01). Passing 및 Bablok 분석의 경우 회귀직선의 기울기와 x축 절편은 교수, 임상강사, 전공의에 대해 각각 1.176 (p>0.05), 1.100 (p>0.05), 1.111 (p>0.05)와 -0.304, -0.199, -0.371로 나타났다. Bland와 Altman 분석의 경우 자동으로 결정된 영상 별 평균 단계와 영상치의학 전공 치과의사의 진단 결과 간 교수, 임상강사, 전공의에 대해 0.007 (95 % 신뢰 구간 (CI), -0.060 ~ 0.074), 각각 -0.022 (95 % CI, -0.098 ~ 0.053), -0.198 (95 % CI, -0.291 ~ -0.104)로 계산되었다. 결론적으로, 본 논문에서 개발된 딥러닝 하이브리드 프레임워크는 딥러닝 신경망 기술과 컴퓨터 보조 진단 기술을 융합하여 환자의 파노라마 방사선 영상에서 치주염을 4단계로 분류하였다. 본 방법은 높은 해부학적 구조물 및 상실 치아 검출 정확도를 보였으며, 자동으로 결정된 치주염 단계는 임상의의 진단 결과와 높은 일치율과 상관성을 보여주었다. 또한 다기기 연구를 통해 개발된 방법의 높은 정확성과 일반화 정도를 검증하였다.CONTENTS Abstract •••••••••••••••••••••••••••••••••••••••••••••••••••••••••• i Contents •••••••••••••••••••••••••••••••••••••••••••••••••••••••• vi List of figures ••••••••••••••••••••••••••••••••••••••••••••••••• viii List of tables •••••••••••••••••••••••••••••••••••••••••••••••••••• x List of abbreviations ••••••••••••••••••••••••••••••••••••••••• xii Introduction •••••••••••••••••••••••••••••••••••••••••••••••••••• 1 Materials and Methods •••••••••••••••••••••••••••••••••••••••• 5 Overall process for deep learning-based computer-aided diagnosis method ‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 5 Data preparation of dental panoramic radiographs from multiple devices ‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 7 Detection of PBL and CEJL structures and teeth using CNNs ‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 10 Detection of the missing teeth using CNNs ‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧14 Staging periodontitis by the conventional CAD method ‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧17Evaluation of detection and classification performance ‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧20 Results ••••••••••••••••••••••••••••••••••••••••••••••••••••••••• 22 Detection performance for the anatomical structures ‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 22 Detection performance for the missing teeth ‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 26 Classification performance for the periodontitis stages ‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧‧ 30 Classification performance of correlations, regressions, and agreements between the periodontitis stages ‧‧‧‧‧‧‧ 36 Discussion ••••••••••••••••••••••••••••••••••••••••••••••••••••• 42 References ••••••••••••••••••••••••••••••••••••••••••••••••••••• 55 Abstract in Korean ••••••••••••••••••••••••••••••••••••••••••• 73Docto

Multi-scale imaging and modelling of bone

The multi-level organization of bone facilitates the exploitation of in-vivo micro-scale information which is currently lacking for clinical applications. The three sub-projects presented in this thesis investigate the human skeletal system at multiple scales using magnetic resonance imaging (MRI) with the aim of providing new techniques for extracting finer scale information in-vivo. At the whole organ level, human knee joint kinematics was studied using a combined MRI strategy. This new strategy enables the in-vivo investigation of tibiofemoral locomotion under body weight-bearing conditions by modelling the knee flexion angle as a function of the femur and tibia cartilage surfaces in contact. The resultant "contact" trajectory may potentially be used to understand the mechanical cause of cartilage degeneration and as a biomarker to detect abnormalities in the lower limb. At the molecular level, in-vivo MR diffusion tensor imaging (DTI) has been performed for the first time in the human tibia epiphysis. By tracking the water molecules inside the red marrow, the organization of trabecular bone network may be understood as the streamlines formed by anisotropic diffusion trajectories. This sub-project aims to understand the organization of trabecular bone networks non-invasively, which is usually performed ex-vivo through biopsies. The feasibility and reproducibility of DTI is studied. Finally, a new MR imaging protocol named multi-directional sub-pixel enhancement (mSPENT) is proposed and developed to quantify the trabecular bone structural arrangement at the meso-scale. By modulating a dephasing gradient to manipulate the underlying spin system inside each voxel, the resulting mSPENT image contrast varies with gradient at different directions based on the magnetization at the corresponding voxel. A tensor-based method is further developed to model this contrast change, leading to a localized quantification of tissue structural orientation beyond the conventional MR imaging resolution

Comparison of trabecular bone anisotropies based on fractal dimensions and mean intercept length determined by principal axes of inertia

The mechanical quality of trabecular bone depends on both its stiffness and its strength characteristics, which can be predicted indirectly by the combination of bone volume fraction and architectural anisotropy. To analyze the directional anisotropy of the trabecular bone, we applied the fractal geometry technique to plain radiographs. The anisotropy of the bone was quantified from an ellipse, based on the directional fractal dimensions (FD), by the principal axes of inertia. The anisotropies based on the FD were compared with those determined using the common method of mean intercept length (MIL). The directional FD gave the fractal information obtained from a projection along the MIL orientation. For this reason, the spatial variations associated with the bone length in any direction were manifested in a related frequency band of the power spectrum determined along the direction. The directional FD and MIL plots were highly correlated, although they originated from quite different geometries. Of the angle, premolar, and incisor regions of the human mandible, the anisotropies calculated using both FD and MIL showed the highest correlation in the trabecular bone of the angle region. The method using directional FDs as determined by the principal axis of inertia measures the anisotropy directly, using two-dimensional plain radiographs. This kind of method will be a useful to provide better estimates of bone quality in vivo compared with the density measurements alone, especially for the indirect diagnosis of jawbone quality in dental clinics.This work was supported by grant No.R01- 2006-000-10011-0 from the Basic Research Program of the Korea Science and Engineering Foundation