Monte Carlo simulation of water diffusion through cardiac tissue models.

Monte Carlo diffusion simulations are commonly used to establish a reliable ground truth of tissue microstructure, including for the validation of diffusion-weighted MRI. However, selecting simulation parameters is challenging and affects validity and reproducibility. We conducted experiments to investigate critical conditions in Monte Carlo simulations, such as tissue representation complexity, simulated molecules, update duration, and compartment size. Results show significant changes in microstructure characteristics when parameters are altered, emphasizing the importance of careful control for a reliable ground truth.

Measurement of local orientation of cardiomyocyte aggregates in human left ventricle free wall samples using X-ray phase-contrast microtomography.

Most cardiomyocytes in the left ventricle wall are grouped in aggregates of four to five units that are quasi-parallel to each other. When one or more "cardiomyocyte aggregates" are delimited by two cleavage planes, this defines a "sheetlet" that can be considered as a "work unit" that contributes to the thickening of the wall during the cardiac cycle. In this paper, we introduce the skeleton method to measure the local three-dimensional (3D) orientation of cardiomyocyte aggregates in the sheetlets in three steps: data segmentation; extraction of the skeleton of the sheetlets; and calculation of the local orientation of the cardiomyocyte aggregates inside the sheetlets. These data include a series of virtual tissue volumes and five transmural human left ventricle free wall samples, imaged with 3D synchrotron radiation phase-contrast microtomography, and reconstructed with a 3.5×3.5×3.5µm3 voxel size. We computed the local orientation of the cardiomyocyte aggregates inside the sheetlets with a working window of 112×112×112µm3 in size. These data demonstrate that the skeleton method can provide accurate 3D measurements and reliable screening of the 3D evolution of the orientation of cardiomyocyte aggregates within the sheetlets. We showed that in regions that contain one population of quasi-parallel sheetlets, the orientation of the cardiomyocyte aggregates undergo "oscillations" along the perpendicular direction of the sheetlets. In regions that contain two populations of sheetlets with a different angular range, we demonstrate some discontinuity of the helix angle of the cardiomyocyte aggregates at the interface between the two populations.

Extraction of the 3D local orientation of myocytes in human cardiac tissue using X-ray phase-contrast micro-tomography and multi-scale analysis.

This paper presents a methodology to access the 3D local myocyte arrangements in fresh human post-mortem heart samples. We investigated the cardiac micro-structure at a high and isotropic resolution of 3.5 µm in three dimensions using X-ray phase micro-tomography at the European Synchrotron Radiation Facility. We then processed the reconstructed volumes to extract the 3D local orientation of the myocytes using a multi-scale approach with no segmentation. We created a simplified 3D model of tissue sample made of simulated myocytes with known size and orientations, to evaluate our orientation extraction method. Afterwards, we applied it to 2D histological cuts and to eight 3D left ventricular (LV) cardiac tissue samples. Then, the variation of the helix angles, from the endocardium to the epicardium, was computed at several spatial resolutions ranging from 3.63 mm3 to 1123 µm3. We measure an increased range of 20° to 30° from the coarsest resolution level to the finest level in the experimental samples. This result is in line with the higher values measured from histology. The displayed tractography demonstrates a rather smooth evolution of the transmural helix angle in six LV samples and a sudden discontinuity of the helix angle in two septum samples. These measurements bring a new vision of the human heart architecture from macro- to micro-scale.

Cardiac fiber tracking using adaptive particle filtering based on tensor rotation invariant in MRI.

Diffusion magnetic resonance imaging (dMRI) is a non-invasive method currently available for cardiac fiber tracking. However, accurate and efficient cardiac fiber tracking is still a challenge. This paper presents a probabilistic cardiac fiber tracking method based on particle filtering. In this framework, an adaptive sampling technique is presented to describe the posterior distribution of fiber orientations by adjusting the number and status of particles according to the fractional anisotropy of diffusion. An observation model is then proposed to update the weight of particles by rotating diffusion tensor from the primary eigenvector to a given fiber orientation while keeping the shape of the tensor invariant. The results on human cardiac dMRI show that the proposed method is robust to noise and outperforms conventional streamline and particle filtering techniques.

Feature-preserving smoothing of diffusion weighted images using nonstationarity adaptive filtering.

Although promising for studying the microstructure of in vivo tissues, the performance and the potentiality of diffusion tensor magnetic resonance imaging are hampered by the presence of high-level noise in diffusion weighted (DW) images. This paper proposes a novel smoothing approach, called the nonstationarity adaptive filtering, which estimates the intensity of a pixel by averaging intensities in its adaptive homogeneous neighborhood. The latter is determined according to five constraints and spatiodirectional nonstationarity measure maps. The proposed approach is compared with an anisotropic diffusion method used in DW image smoothing. Experimental results on both synthetic and real human DW images show that the proposed method achieves a better compromise between the smoothness of homogeneous regions and the preservation of desirable features such as boundaries, even for highly noisy data, thus leading to homogeneously consistent tensor fields and consequently more coherent fibers.

MRI reconstruction from 2D truncated k-space.

PURPOSE: To shorten acquisition time by means of both partial scanning and partial echo acquisition and to reconstruct images from such 2D partial k-space acquisitions. MATERIALS AND METHODS: We propose an approach to reconstructing magnetic resonance images from 2D truncated k-space in which the k-space is truncated in both phase- and frequency-encoding directions. Unlike conventional reconstruction techniques, the proposed approach is based on a newly developed 2D singularity function analysis (SFA) model and a sparse representation of an image whose parameters can be estimated from the 2D partial k-space data. Such a sparse representation leads to an accurate recovery of the missing k-space data and, hence, an accurate reconstruction of the image. RESULTS: The proposed approach can reconstruct an image from as little as 20%-30% of the k-space data and the quality of the reconstructed image is comparable to the reference image that is reconstructed from the complete k-space data. CONCLUSION: Despite the high asymmetry of a 2D truncated k-space, the proposed approach allows for accurate reconstruction without the need of phase correction and, thus, overcomes the assumption of slow phase variations that is usually required by the existing reconstruction methods. It provides a new way of fast imaging for applications that require a significant reduction of the acquisition time.

Multiscale modeling and simulation of the cardiac fiber architecture for DMRI.

Cardiac fiber architecture plays an important role in the study of mechanical and electrical properties of the wall of the human heart, but still remains to be elucidated. This paper proposes to investigate, in a multiscale manner, how the arrangement patterns and morphological heterogeneity of cardiac myocytes influence the fibers orientation. To this end, different virtual cardiac fiber structures are modeled, and diffusion tensor imaging at multiple scales are simulated using the Monte Carlo method. The results show that the proposed modeling and simulation allow us to quantitatively describe the variation of the measured tissue properties (fiber orientation and fractional anisotropy) as a function of the observation scale.

Feature-based interpolation of diffusion tensor fields and application to human cardiac DT-MRI.

Diffusion tensor interpolation is an important issue in the application of diffusion tensor magnetic resonance imaging (DT-MRI) to the human heart, all the more as the points representing the myocardium of the heart are often sparse. We propose a feature-based interpolation framework for the tensor fields from cardiac DT-MRI, by taking into account inherent relationships between tensor components. In this framework, the interpolation consists in representing a diffusion tensor in terms of two tensor features, eigenvalues and orientation, interpolating the Euler angles or the quaternion relative to tensor orientation and the logarithmically transformed eigenvalues, and reconstructing the tensor to be interpolated from the interpolated eigenvalues and tensor orientations. The results obtained with the aid of both synthetic and real cardiac DT-MRI data demonstrate that the feature-based schemes based on Euler angles or quaternions not only maintain the advantages of Log-Euclidean and Riemannian interpolation as for preserving the tensor's symmetric positive-definiteness and the monotonic determinant variation, but also preserve, at the same time, the monotonicity of fractional anisotropy (FA) and mean diffusivity (MD) values, which is not the case with Euclidean, Cholesky and Log-Euclidean methods. As a result, both interpolation schemes remove the phenomenon of FA collapse, and consequently avoid introducing artificial fiber crossing, with the difference that the quaternion is independent of coordinate system while Euler angles have the property of being more suitable for sophisticated interpolations.

Automatic detection of abnormal vascular cross-sections based on density level detection and support vector machines.

PURPOSE: The goal is to automatically detect anomalous vascular cross-sections to attract the radiologist's attention to possible lesions and thus reduce the time spent to analyze the image volume. MATERIALS AND METHODS: We assume that both lesions and calcifications can be considered as local outliers compared to a normal cross-section. Our approach uses an intensity metric within a machine learning scheme to differentiate normal and abnormal cross-sections. It is formulated as a Density Level Detection problem and solved using a Support Vector Machine (DLD-SVM). The method has been evaluated on 42 synthetic phantoms and on 9 coronary CT data sets annotated by 2 experts. RESULTS: The specificity of the method was 97.57% on synthetic data, and 86.01% on real data, while its sensitivity was 82.19 and 81.23%, respectively. The agreement with the observers, measured by the kappa coefficient, was substantial (κ = 0.72). After the learning stage, which is performed off-line, the average processing time was within 10 s per artery. CONCLUSIONS: To our knowledge, this is the first attempt to use the DLD-SVM approach to detect vascular abnormalities. Good specificity, sensitivity and agreement with experts, as well as a short processing time, show that our method can facilitate medical diagnosis and reduce evaluation time by attracting the reader's attention to suspect regions.

Denoising by averaging reconstructed images: application to magnetic resonance images.

A novel denoising approach is proposed that is based on averaging reconstructed images. The approach first divides the spectrum of the image to be denoised into different parts. From every such partial spectrum is then reconstructed an image using a 2-D singularity function analysis model. By expressing each of the reconstructed images as the sum of the same noise-free image and a different smaller noise, the denoising is achieved through averaging the reconstructed images. The theoretical formulation and experimental results on both simulated and real images consistently demonstrated that the proposed approach can efficiently denoise while maintaining high image quality, and presents significant advantages over conventional denoising methods.

SIMONE: a realistic neural network simulator to reproduce MEA-based recordings.

Contemporary multielectrode arrays (MEAs) used to record extracellular activity from neural tissues can deliver data at rates on the order of 100 Mbps. Such rates require efficient data compression and/or preprocessing algorithms implemented on an application specific integrated circuit (ASIC) close to the MEA. We present SIMONE (Statistical sIMulation Of Neuronal networks Engine), a versatile simulation tool whose parameters can be either fixed or defined by a probability distribution. We validated our tool by simulating data recorded from the first olfactory relay of an insect. Different key aspects make this tool suitable for testing the robustness and accuracy of neural signal processing algorithms (such as the detection, alignment, and classification of spikes). For instance, most of the parameters can be defined by a probabilistic distribution, then tens of simulations may be obtained from the same scenario. This is especially useful when validating the robustness of the processing algorithm. Moreover, the number of active cells and the exact firing activity of each one of them is perfectly known, which provides an easy way to test accuracy.

Fast-marching contours for the segmentation of vessel lumen in CTA cross-sections.

This work deals with the segmentation of the arterial lumen in cross-sections of CT angiography (CTA) images, by means of active contours. Within the context of the fast-marching method, a new speed-control function is proposed in order to cope with strongly variable contrasts along the perimeter of the contour. This function was devised to guarantee the existence of a time T at which the fast-marching front fits the actual boundary of the vessel lumen, despite calcifications and other neighboring structures. Instead of using the magnitude of the image intensity gradient alone, this function includes exponential factors that strongly decrease the propagation speed when the front moves beyond the local maxima of the gradient magnitude and beyond the range of luminal intensities in CTA images. The propagation is stopped when the the growth of the area A encompassed by the front becomes very slow, which is characterized by a large value of dT/dA . The segmentation was evaluated in 65 cross-sections of carotid arteries from 13 different patients, by comparison with contours traced by a radiologist. The mean sensitivity was 0.849 and the mean positive predictive value was 0.797.

A stochastic continuation approach to piecewise constant reconstruction.

We address the problem of reconstructing a piecewise constant 3-D object from a few noisy 2-D line-integral projections. More generally, the theory developed here readily applies to the recovery of an ideal n-D signal (n > or =1) from indirect measurements corrupted by noise. Stabilization of this ill-conditioned inverse problem is achieved with the Potts prior model, which leads to a challenging optimization task. To overcome this difficulty, we introduce a new class of hybrid algorithms that combines simulated annealing with deterministic continuation. We call this class of algorithms stochastic continuation (SC). We first prove that, under mild assumptions, SC inherits the finite-time convergence properties of generalized simulated annealing. Then, we show that SC can be successfully applied to our reconstruction problem. In addition, we look into the concave distortion acceleration method introduced for standard simulated annealing and we derive an explicit formula for choosing the free parameter of the cost function. Numerical experiments using both synthetic data and real radiographic testing data show that SC outperforms standard simulated annealing.

MRI intensity nonuniformity correction using simultaneously spatial and gray-level histogram information.

A novel approach for correcting intensity nonuniformity in magnetic resonance imaging (MRI) is presented. This approach is based on the simultaneous use of spatial and gray-level histogram information. Spatial information about intensity nonuniformity is obtained using cubic B-spline smoothing. Gray-level histogram information of the image corrupted by intensity nonuniformity is exploited from a frequential point of view. The proposed correction method is illustrated using both physical phantom and human brain images. The results are consistent with theoretical prediction, and demonstrate a new way of dealing with intensity nonuniformity problems. They are all the more significant as the ground truth on intensity nonuniformity is unknown in clinical images.

A level set framework with a shape and motion prior for segmentation and region tracking in echocardiography.

We describe a level set formulation using both shape and motion prior, for both segmentation and region tracking in high frame rate echocardiographic image sequences. The proposed approach uses the following steps: registration of the prior shape, level set segmentation constrained through the registered shape and region tracking. Registration of the prior shape is expressed as a rigid or an affine transform problem, where the transform minimizing a global region-based criterion is sought. This criterion is based on image statistics and on the available estimated axial motion data. The segmentation step is then formulated through front propagation, constrained with the registered shape prior. The same region-based criterion is used both for the registration and the segmentation step. Region tracking is based on the motion field estimated from the interframe level set evolution. The proposed approach is applied to high frame rate echocardiographic sequences acquired in vivo. In this particular application, the prior shape is provided by a medical expert and the rigid transform is used for registration. It is shown that this approach provides consistent results in terms of segmentation and stability through the cardiac cycle. In particular, a comparison indicates that the results provided by our approach are very close to the results obtained with manual tracking performed by an expert cardiologist on a Doppler Tissue Imaging (DTI) study. These preliminary results show the ability of the method to perform region tracking and its potential for dynamic parametric imaging of the heart.

Quantification of multicontrast vascular MR images with NLSnake, an active contour model: in vitro validation and in vivo evaluation.

Vessel-wall measurements from multicontrast MRI provide information on plaque structure and evolution. This requires the extraction of numerous contours. In this work a contour-extraction method is proposed that uses an active contour model (NLSnake) adapted for a wide range of MR vascular images. This new method employs length normalization for the purpose of deformation computation and offers the advantages of simplified parameter tuning, fast convergence, and minimal user interaction. The model can be initialized far from the boundaries of the region to be segmented, even by only one pixel. The accuracy and reproducibility of NLSnake endoluminal contours were assessed on vascular phantom MR angiography (MRA) and high-resolution in vitro MR images of rabbit aorta. An in vivo evaluation was performed on rabbit and clinical data for both internal and external vessel-wall contours. In phantoms with 95% stenoses, NLSnake measured 94.3% +/- 3.8%, and the accuracy was even better for milder stenoses. In the images of rabbit aorta, variability between NLSnake and experts was less than interobserver variability, while the maximum intravariability of NLSnake was equal to 1.25%. In conclusion, the NLSnake technique successfully quantified the vessel lumen in multicontrast MR images using constant parameters.

Towards ultrasound cardiac image segmentation based on the radiofrequency signal.

In echocardiography, the radio-frequency (RF) image is a rich source of information about the investigated tissues. Nevertheless, very few works are dedicated to boundary detection based on the RF image, as opposed to envelope image. In this paper, we investigate the feasibility and limitations of boundary detection in echocardiographic images based on the RF signal. We introduce two types of RF-derived parameters: spectral autoregressive parameters and velocity-based parameters, and we propose a discontinuity adaptive framework to perform the detection task. In classical echographic cardiac acquisitions, we show that it is possible to use the spectral contents for boundary detection, and that improvement can be expected with respect to traditional methods. Using the system approach, we study on simulations how the spectral contents can be used for boundary detection. We subsequently perform boundary detection in high frame rate simulated and in vivo cardiac sequences using the variance of velocity, obtaining very promising results. Our work opens the perspective of a RF-based framework for ultrasound cardiac image segmentation and tracking.

A 3-D model-based registration approach for the PET, MR and MCG cardiac data fusion.

In this paper, a new approach is presented for the assessment of a 3-D anatomical and functional model of the heart including structural information from magnetic resonance imaging (MRI) and functional information from positron emission tomography (PET) and magnetocardiography (MCG). The method uses model-based co-registration of MR and PET images and marker-based registration for MRI and MCG. Model-based segmentation of MR anatomical images results in an individualized 3-D biventricular model of the heart including functional parameters from PET and MCG in an easily interpretable 3-D form.

Stochastic nonlinear image restoration using the wavelet transform.

The dominant methodology for image restoration is to stabilize the problem by including a roughness penalty in addition to faithfulness to the data. Among various choices, concave stabilizers stand out for their boundary detection capabilities, but the resulting cost function to be minimized is generally multimodal. Although simulated annealing is theoretically optimal to take up this challenge, standard stochastic algorithms suffer from two drawbacks: i) practical convergence difficulties are encountered with second-order prior models and ii) it remains computationally demanding to favor the formation of smooth contour lines by taking the discontinuity field explicitly into account. This work shows that both weaknesses can be overcome in a multiresolution framework by means of the 2-D discrete wavelet transform (DWT). We first propose to improve convergence toward global minima by single-site updating on the wavelet domain. For this purpose, a new restricted DWT space is introduced and a theoretically sound updating mechanism is constructed on this subspace. Next, we suggest to incorporate the smoothness of the discontinuity field via an additional penalty term defined on the high frequency subbands. The resulting increase in complexity is small and the approach requires the specification of a unique extra parameter for which an explicit selection formula is derived.

Exploratory analysis of the spatio-temporal deformation of the myocardium during systole from tagged MRI.

Myocardial contractile function is, with perfusion, one of the main affected factors in ischemic heart diseases. In this paper, we propose an original framework based on functional data analysis for the quantitative study of spatio-temporal parameters related to the myocardial contraction mechanics. The mechanical strains in the left-ventricular (LV) myocardium are computed from tagged magnetic resonance imaging cardiac sequences. A statistical functional model of the normal contractile function of the LV is build from the study of eight examinations on healthy subjects. We show that it is possible to detect abnormal strain patterns comparatively to this model, by generating distance maps at rest and under pharmacological stress. We demonstrate the consistency of the results for the circumferential deformation parameter on healthy and pathological data sets.