Ivan Kolesov

Anatomic and Morphological Evaluation of the Quadriceps Tendon Using 3-Dimensional Magnetic Resonance Imaging Reconstruction Applications for Anterior Cruciate Ligament Autograft Choice and Procurement

Background: The autograft of choice for anterior cruciate ligament (ACL) reconstruction remains controversial. The quadriceps tendon is the least utilized and least studied of the potential autograft options. Purpose: To determine if the quadriceps tendon has the anatomic characteristics to produce a graft whose length and volume are adequate, reproducible, and predictable when compared with the other commonly used autografts. Study Design: Cross-sectional study; Level of evidence, 3. Methods: Axial proton density magnetic resonance imaging (MRI) scans of 60 skeletally mature patients (30 male and 30 female) were evaluated. Volumetric analysis of 3-dimensional models of the patellar and quadriceps tendons was performed before and after the removal of a 10 mm–wide graft from both tendons. Length, thickness, and width measurements of the quadriceps tendon were made at predetermined locations. Anthropometric data were collected, and subgroup analysis, sex analysis, and linear regression were performed. Results: The mean percentage of volume remaining after removal of a 10 mm–wide graft from the patellar tendon was 56.6%, compared with 61.3% when harvesting an 80 mm–long graft of the same width from the quadriceps tendon. The intra-articular volume of the proposed quadriceps tendon graft was 87.5% greater than that of the patellar tendon graft. The mean length of the quadriceps tendon was 73.5 ± 12.3 mm in female patients and 81.1 ± 10.6 mm in male patients. These measurements were most highly correlated with patient height. The width of the quadriceps tendon decreased as one proceeded proximally from its insertion, and the thickness of the quadriceps tendon remained relatively constant. Conclusion: The quadriceps tendon has the anatomic characteristics to produce a graft whose length and volume are both reproducible and predictable, while yielding a graft with a significantly greater intra-articular volume than a patellar tendon graft with a similar width.

Fire and smoke detection in video with optimal mass transport based optical flow and neural networks

Detection of fire and smoke in video is of practical and theoretical interest. In this paper, we propose the use of optimal mass transport (OMT) optical flow as a low-dimensional descriptor of these complex processes. The detection process is posed as a supervised Bayesian classification problem with spatio-temporal neighborhoods of pixels;feature vectors are composed of OMT velocities and R,G,B color channels. The classifier is implemented as a single-hidden-layer neural network. Sample results show probability of pixels belonging to fire or smoke. In particular, the classifier successfully distinguishes between smoke and similarly colored white wall, as well as fire from a similarly colored background.

Optical Flow Estimation for Flame Detection in Videos

Computational vision-based flame detection has drawn significant attention in the past decade with camera surveillance systems becoming ubiquitous. Whereas many discriminating features, such as color, shape, texture, etc., have been employed in the literature, this paper proposes a set of motion features based on motion estimators. The key idea consists of exploiting the difference between the turbulent, fast, fire motion, and the structured, rigid motion of other objects. Since classical optical flow methods do not model the characteristics of fire motion (e.g., non-smoothness of motion, non-constancy of intensity), two optical flow methods are specifically designed for the fire detection task: optimal mass transport models fire with dynamic texture, while a data-driven optical flow scheme models saturated flames. Then, characteristic features related to the flow magnitudes and directions are computed from the flow fields to discriminate between fire and non-fire motion. The proposed features are tested on a large video database to demonstrate their practical usefulness. Moreover, a novel evaluation method is proposed by fire simulations that allow for a controlled environment to analyze parameter influences, such as flame saturation, spatial resolution, frame rate, and random noise.

Graph Curvature for Differentiating Cancer Networks

Cellular interactions can be modeled as complex dynamical systems represented by weighted graphs. The functionality of such networks, including measures of robustness, reliability, performance, and efficiency, are intrinsically tied to the topology and geometry of the underlying graph. Utilizing recently proposed geometric notions of curvature on weighted graphs, we investigate the features of gene co-expression networks derived from large-scale genomic studies of cancer. We find that the curvature of these networks reliably distinguishes between cancer and normal samples, with cancer networks exhibiting higher curvature than their normal counterparts. We establish a quantitative relationship between our findings and prior investigations of network entropy. Furthermore, we demonstrate how our approach yields additional, non-trivial pair-wise (i.e. gene-gene) interactions which may be disrupted in cancer samples. The mathematical formulation of our approach yields an exact solution to calculating pair-wise changes in curvature which was computationally infeasible using prior methods. As such, our findings lay the foundation for an analytical approach to studying complex biological networks.

Interactive Medical Image Segmentation Using PDE Control of Active Contours

Segmentation of injured or unusual anatomic structures in medical imagery is a problem that has continued to elude fully automated solutions. In this paper, the goal of easy-to-use and consistent interactive segmentation is transformed into a control synthesis problem. A nominal level set partial differential equation (PDE) is assumed to be given; this open-loop system achieves correct segmentation under ideal conditions, but does not agree with a human experts ideal boundary for real image data. Perturbing the state and dynamics of a level set PDE via the accumulated user input and an observer-like system leads to desirable closed-loop behavior. The input structure is designed such that a user can stabilize the boundary in some desired state without needing to understand any mathematical parameters. Effectiveness of the technique is illustrated with applications to the challenging segmentations of a patellar tendon in magnetic resonance and a shattered femur in computed tomography.

Optimal-mass-transfer-based estimation of glymphatic transport in living brain

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

Interactive MRI segmentation with controlled active vision

Partitioning Magnetic-Resonance-Imaging (MRI) data into salient anatomic structures is a problem in medical imaging that has continued to elude fully automated solutions. Implicit functions are a common way to model the boundaries between structures and are amenable to control-theoretic methods. In this paper, the goal of enabling a human to obtain accurate segmentations in a short amount of time and with little effort is transformed into a control synthesis problem. Perturbing the state and dynamics of an implicit functions driving partial differential equation via the accumulated user inputs and an observer-like system leads to desirable closed-loop behavior. Using a Lyapunov control design, a balance is established between the influence of a data-driven gradient flow and the humans input over time. Automatic segmentation is thus smoothly coupled with interactivity. An application of the mathematical methods to orthopedic segmentation is shown, demonstrating the expected transient and steady state behavior of the implicit segmentation function and auxiliary observer.

A stochastic approach for non-rigid image registration

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.

A video analytics framework for amorphous and unstructured anomaly detection

Video surveillance systems are often used to detect anomalies: rare events which demand a human response, such as a fire breaking out. Automated detection algorithms enable vastly more video data to be processed than would be possible otherwise. This note presents a video analytics framework for the detection of amorphous and unstructured anomalies such as fire, targets in deep turbulence, or objects behind a smoke-screen. Our approach uses an off-line supervised training phase together with an on-line Bayesian procedure: we form a prior, compute a likelihood function, and then update the posterior estimate. The prior consists of candidate image-regions generated by a weak classifier. Likelihood of a candidate region containing an object of interest at each time step is computed from the photometric observations coupled with an optimal-mass-transport optical-flow field. The posterior is sequentially updated by tracking image regions over time and space using active contours thus extracting samples from a properly aligned batch of images. The general theory is applied to the video-fire-detection problem with excellent detection performance across substantially varying scenarios which are not used for training.

A Stochastic Approach to Diffeomorphic Point Set Registration with Landmark Constraints

This work presents a deformable point set registration algorithm that seeks an optimal set of radial basis functions to describe the registration. A novel, global optimization approach is introduced composed of simulated annealing with a particle filter based generator function to perform the registration. It is shown how constraints can be incorporated into this framework. A constraint on the deformation is enforced whose role is to ensure physically meaningful fields (i.e., invertible). Further, examples in which landmark constraints serve to guide the registration are shown. Results on 2D and 3D data demonstrate the algorithms robustness to noise and missing information.