Being symmetric positive-definite (SPD), covariance matrix has traditionally been used to represent a set of local descriptors in visual recognition. Recent study shows that kernel matrix can give considerably better representation by modelling the nonlinearity in the local descriptor set. Nevertheless, neither the descriptors nor the kernel matrix is deeply learned. Worse, they are considered separately, hindering the pursuit of an optimal SPD representation. This work proposes a deep network that jointly learns local descriptors, kernel-matrix-based SPD representation, and the classifier via an end-to-end training process. We derive the derivatives for the mapping from a local descriptor set to the SPD representation to carry out backpropagation. Also, we exploit the Daleckiǐ-Kreǐn formula in operator theory to give a concise and unified result on differentiating SPD matrix functions, including the matrix logarithm to handle the Riemannian geometry of kernel matrix. Experiments not only show the superiority of kernel-matrixbased SPD representation with deep local descriptors, but also verify the advantage of the proposed deep network in pursuing better SPD representations for fine-grained image recognition tasks.
Purpose: B-Mode ultrasound imaging is commonly used for detection and measurement of atherosclerotic carotid plaques, which are an important cause of ischemic stroke. However, accurate interpretation of ultrasound can be difficult and subjective. Artificial Intelligence (AI) models can assist in image interpretation, reducing subjectivity, and speeding up the process of detection and measurement of carotid plaques. We evaluated the accuracy of a deep learning model for automatic detection of carotid plaques in b-mode ultrasound compared against expert interpretation of the images. Methods: We propose an automated method using convolutional neural networks to detect atherosclerotic plaques and measure intima-media thickness (IMT) in B-Mode carotid images. In contrast to most of the existing methods, our goal was to not only measure IMT in healthy subjects (max IMT below 1.2 mm) but also to provide accurate detection of plaques and other vessel wall pathology. Given the B-mode longitudinal image as the input, the neural network first finds a region of interest (ROI) surrounding the artery and then segments both near wall and far wall of the artery. The network was trained and tested on two separate datasets obtained retrospectively from 3 stroke centers and 4 different ultrasound machine manufacturers. The training dataset was comprised of 1021 images. Results: The performance of the method was assessed on an independent dataset not used for model development to prevent bias, consisting of 205 images, where 54% (111 out of 205) of the images had pathology. The ground truth was determined by an expert reader interpreting images, and Pearson coefficient (IMT correlation) and Bland-Altman analysis were used to assess the performance of the method. The obtained correlation coefficient was 0.93 and r-squared was 0.87, showing a strong correlation. There was no significant over or under estimation of IMT (bias = -0.002 mm, lower limit of agreement (LOA) = -0.246 mm, upper LOA = 0.242 mm). Conclusion: The results show that the proposed deep learning method can be used for accurate analysis and interpretation of carotid ultrasound scans in a clinical setting and potentially reduce the reporting time while increasing objectivity of the reports.
Purpose: Ultrasound imaging is commonly used for patients with atheroscelerotic plaques in the carotid artery. While B-mode ultrasound can be used for detection and measurement of these plaques, interpreting these images can be a subjective and time-consuming task. Deep learning algorithms have been proven to be an effective tool for interpreting medical images, especially for classification and segmentation tasks. Here, we propose a deep learning model to automatically detect and measure plaques in transverse B-mode images of the carotid artery. Methods: The proposed automated method takes a transverse B-mode image of the carotid artery as an input and segments the vessel wall in the transverse cross section image using convolutional neural networks. To ensure that the method can perform well in clinical settings, the method has been evaluated on not only healthy subjects (max IMT below 1.2 mm) but also on patients with atheroscelerotic plaques and other vessel wall pathology. Given the B-mode transverse image as an input, the neural network first finds a region of interest (ROI) surrounding the artery and then segments both the inner and outer wall of the carotid artery. We determined the accuracy of the system by F1 Score, a common metric to evaluate the performance of machine learning algorithms. Results: The network was trained and tested on a transverse ultrasound carotid artery dataset that has 506 images, gathered from 4 hospitals. Annotations of an expert reader were used as the ground truth and the performance of the method was evaluated using 5-fold cross validation. The proposed method reaches an F1 score of 0.91 for correctly detecting the ROI and an F1 score of 0.78 for detecting and segmenting the vessel walls in transverse B-mode images. Conclusions: The results show that the proposed deep learning method can be used for accurate analysis and interpretation of carotid ultrasound scans in a clinical setting and potentially reduce the reporting time while increasing objectivity of the analysis.
Purpose: Modelling blood flow in cerebral arteries presents an opportunity to go beyond current luminal stenosis. These models could improve stroke prognostication by adding hemodynamic biomarkers such as translesional shear stress and pressure gradient. Such models, however, are rarely validated against real clinical data. We evaluated the accuracy of a computational fluid dynamics (CFD) model which uses allometric scaling laws against population-based Phase Contrast MRI (PC-MRI) measurements of blood flow in the brain. Methods: 3D models of the anterior circulation of 23 healthy subjects were reconstructed based on their MRA Time of Flight (TOF) images and CFD was used for modelling the blood flow. Lumped parameter Windkessel models were used as boundary conditions and allometric scaling laws were used to divide the flow and tune these boundary conditions, i.e. the resistance at each boundary was automatically adjusted based on the dimensions and branching of upstream vasculature. The results were compared against 4 PC-MRI studies from literature, covering a combined number of 417 healthy subjects. Results: The flow rate across 3 major intracranial arteries (ICA, MCA, and ACA) was obtained from the CFD simulations and was in good agreement with population-based PC-MRI studies. The agreement was 82.6% for the ICA, 85.9% for the MCA, and 80.4% for the ACA when comparing the average flow rate. The inter-patient variability of the flow rate (i.e. standard deviation) obtained from CFD simulations matched closely with the variation range measured in the literature. Allometric scaling enabled the model to accurately divide the flow at bifurcations (MCA/ICA flow ratio was 58.6% for the model vs 56.3% in the literature). We observed an average of 8 mmHg in pressure drop along the anterior circulation of healthy subjects (from ICA to MCA-M1 and ACA-A1), which agrees with the physiological range reported in the literature. Conclusion: This study shows the potential of accurately modelling blood flow based only on static images and demonstrates the validity of using allometric scaling in intracranial CFD simulations. The current modelling approach can potentially assist in stroke prognostication by obtaining hemodynamic risk factors from standard MRA TOF or CTA.
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