Segmentation of anatomical structures in medical imagery is a key step in a variety of clinical applications. Designing a generic, automated method that works for various structures and imaging modalities is a daunting task. Instead of proposing a new specific segmentation algorithm, in this paper, we present a general design principle on how to integrate user interactions from the perspective of control theory. In this formulation, Lyapunov stability analysis is employed to design an interactive segmentation system. The effectiveness and robustness of the proposed method are demonstrated.
It was recently shown that the brain-wide cerebrospinal fluid (CSF) and interstitial fluid exchange system designated the ‘glymphatic pathway’ plays a key role in removing waste products from the brain, similarly to the lymphatic system in other body organs . It is therefore important to study the flow patterns of glymphatic transport through the live brain in order to better understand its functionality in normal and pathological states. Unlike blood, the CSF does not flow rapidly through a network of dedicated vessels, but rather through para-vascular channels and brain parenchyma in a slower time-domain, and thus conventional fMRI or other blood-flow sensitive MRI sequences do not provide much useful information about the desired flow patterns. We have accordingly analyzed a series of MRI images, taken at different times, of the brain of a live rat, which was injected with a paramagnetic tracer into the CSF via the lumbar intrathecal space of the spine. Our goal is twofold: (a) find glymphatic (tracer) flow directions in the live rodent brain; and (b) provide a model of a (healthy) brain that will allow the prediction of tracer concentrations given initial conditions. We model the liquid flow through the brain by the diffusion equation. We then use the Optimal Mass Transfer (OMT) approach to derive the glymphatic flow vector field, and estimate the diffusion tensors by analyzing the (changes in the) flow. Simulations show that the resulting model successfully reproduces the dominant features of the experimental data. Keywords: inverse problem, optimal mass transport, diffusion equation, cerebrospinal fluid flow in brain, optical flow, liquid flow modeling, Monge Kantorovich problem, diffusion tensor estimation
Constrained registration is an active area of research and is the focus of this work. This note describes a non-rigid image registration framework for incorporating landmark constraints. Points that must remain stationary are selected, the user chooses the spatial extent of the inputs, and an automatic step computes the deformable registration, respecting the constraints. Parametrization of the deformation field is by an additive composition of a similarity transformation and a set of Gaussian radial basis functions. The bases’ centers, variances, and weights are determined with a global optimization approach that is introduced. This approach is based on the particle filter for performing constrained optimization; it explores a series of states defining a deformation field that is physically meaningful (i.e., invertible) and prevents chosen points from moving. Results on synthetic two dimensional images are presented.
This note describes a non-rigid image registration approach that parametrizes the deformation field by an additive composition
of a similarity transformation and a set of Gaussian radial basis functions. The bases’ centers, variances, and
weights are determined with a global optimization approach that is introduced in this work. This approach consists of
simulated annealing with a particle filter based generator function to perform the optimization. Additionally, a local refinement
is performed to capture the remaining misalignment. The deformation is constrained to be physically meaningful
(i.e., invertible). Results on 2D and 3D data sets demonstrate the algorithm’s robustness to large deformations.