Counting number of cells and cell segmentation using advection-diffusion equations

summary:We develop a method for counting number of cells and extraction of approximate cell centers in 2D and 3D images of early stages of the zebra-fish embryogenesis. The approximate cell centers give us the starting points for the subjective surface based cell segmentation. We move in the inner normal direction all level sets of nuclei and membranes images by a constant speed with slight regularization of this flow by the (mean) curvature. Such multi- scale evolutionary process is represented by a geometrical advection-diffusion equation which gives us at a certain scale the desired information on the number of cells. For solving the problems computationally we use flux-based finite volume level set method developed by Frolkovič and Mikula in [FM1] and semi-implicit co-volume subjective surface method given in [CMSSg, MSSgCVS, MSSgchapter]. Computational experiments on testing and real 2D and 3D embryogenesis images are presented and the results are discussed

Data-driven Flood Emulation: Speeding up Urban Flood Predictions by Deep Convolutional Neural Networks

Computational complexity has been the bottleneck of applying physically-based simulations on large urban areas with high spatial resolution for efficient and systematic flooding analyses and risk assessments. To address this issue of long computational time, this paper proposes that the prediction of maximum water depth rasters can be considered as an image-to-image translation problem where the results are generated from input elevation rasters using the information learned from data rather than by conducting simulations, which can significantly accelerate the prediction process. The proposed approach was implemented by a deep convolutional neural network trained on flood simulation data of 18 designed hyetographs on three selected catchments. Multiple tests with both designed and real rainfall events were performed and the results show that the flood predictions by neural network uses only 0.5 % of time comparing with physically-based approaches, with promising accuracy and ability of generalizations. The proposed neural network can also potentially be applied to different but relevant problems including flood predictions for urban layout planning

Computer Simulation of a Nitric Oxide-Releasing Catheter with a Novel Stable Convection-Diffusion Equation Solver and Automatic Quantification of Lung Ultrasound Comets by Machine Learning

Biological transport processes often involve a boundary acting as separation of flow, most commonly in transport involving blood-contacting medical devices. The separation of flow creates two different scenarios of mass transport across the interface. No flow exists within the medical device and diffusion governs mass transport; both convection and diffusion exist when flow is present. The added convection creates a large concentration gradient around the interface. Computer simulation of such cases prove to be difficult and require proper shock capturing methods for the solutions to be stable, which is typically lacking in commercial solvers. In this thesis, we propose a second-order accurate numerical method for solving the convection-diffusion equation by using a gradient-limited Godunov-type convective flux and the multi-point flux approximation (MPFA) L-Method for the diffusion flux. We applied our solver towards simulation of a nitric oxide-releasing intravascular catheter. Intravascular catheters are essential for long-term vascular access in both diagnosis and treatment. Use of catheters are associated with risks for infection and thrombosis. Because infection and thrombosis lead to impaired flow and potentiality life threatening systemic infections, this leads to increased morbidity and mortality, requiring catheters to be replaced among other treatments for these complications. Nitric oxide (NO) is a potent antimicrobial and antithrombotic agent produced by vascular endothelial cells. The production level in vivo is so low that the physiological effects can only be seen around the endothelial cells. The catheter can incorporate a NO source in two major ways: by impregnating the catheter with NO-releasing compounds such as S-nitroso-N-acetyl penicillamine (SNAP) or using electrochemical reactions to generate NO from nitrites. We applied our solver to both situations to guide the design of the catheter. Simulations revealed that dissolved NO inside the catheter is depleted after 12 minutes without resupplying, and electrochemical release of NO requires 10.5 minutes to reach steady state. Lung edema is often present in patients with end-stage renal disease due to reduced filtration functions of the kidney. These patients require regular dialysis sessions to manage their fluid status. The clinical gold standard to quantify lung edema is to use CT, which exposes patients to high amounts of radiation and is not cost efficient. Fluid management in such patients becomes very challenging without a clear guideline of fluid to be removed during dialysis sessions. Hypotension during dialysis can limit fluid removal, even in the setting of ongoing fluid overload or congestive heart failure. Accurate assessment of the pulmonary fluid status is needed, so that fluid overload and congestive heart failure can be detected, especially in the setting of hypotension, allowing dialysis to be altered to improve fluid removal. Recently, reverberations in ultrasound signals, referred to as ``lung comets'' have emerged as a potential quantitative way to measure lung edema. Increased presence of lung comets is associated with higher amounts of pulmonary edema, higher mortality, and more adverse cardiac events. However, the lung comets are often counted by hand by physicians with single frames in lung ultrasound and high subjectivity has been found to exist among the counting by physicians. We applied image processing and neural network techniques as an attempt to provide an objective and accurate measurement of the amount of lung comets present. Our quantitative results are significantly correlated with diastolic blood pressure and ejection fraction.PHDBiomedical EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/163182/1/micw_1.pd

Challenges in imaging and predictive modeling of rhizosphere processes

Background Plant-soil interaction is central to human food production and ecosystem function. Thus, it is essential to not only understand, but also to develop predictive mathematical models which can be used to assess how climate and soil management practices will affect these interactions. Scope In this paper we review the current developments in structural and chemical imaging of rhizosphere processes within the context of multiscale mathematical image based modeling. We outline areas that need more research and areas which would benefit from more detailed understanding. Conclusions We conclude that the combination of structural and chemical imaging with modeling is an incredibly powerful tool which is fundamental for understanding how plant roots interact with soil. We emphasize the need for more researchers to be attracted to this area that is so fertile for future discoveries. Finally, model building must go hand in hand with experiments. In particular, there is a real need to integrate rhizosphere structural and chemical imaging with modeling for better understanding of the rhizosphere processes leading to models which explicitly account for pore scale processes

Form, shape and function: segmented blood flow in the choriocapillaris

The development of fluid transport systems was a key event in the evolution of animals and plants. While within vertebrates branched geometries predominate, the choriocapillaris, which is the microvascular bed that is responsible for the maintenance of the outer retina, has evolved a planar topology. Here we examine the flow and mass transfer properties associated with this unusual geometry. We show that as a result of the form of the choriocapillaris, the blood flow is decomposed into a tessellation of functional vascular segments of various shapes delineated by separation surfaces across which there is no flow, and in the vicinity of which the transport of passive substances is diffusion-limited. The shape of each functional segment is determined by the distribution of arterioles and venules and their respective relative flow rates. We also show that, remarkably, the mass exchange with the outer retina is a function of the shape of each functional segment. In addition to introducing a novel framework in which the structure and function of the metabolite delivery system to the outer retina may be investigated in health and disease, the present work provides a general characterisation of the flow and transfers in multipole Hele-Shaw configurations

A mathematical system for human implantable wound model studies

In this work, we present a mathematical model, which accounts for two fundamental processes involved in the repair of an acute dermal wound. These processes include the inflammatory response and fibroplasia. Our system describes each of these events through the time evolution of four primary species or variables. These include the density of initial damage, inflammatory cells, fibroblasts and deposition of new collagen matrix. Since it is difficult to populate the equations of our model with coefficients that have been empirically derived, we fit these constants by carrying out a large number of simulations until there is reasonable agreement between the time response of the variables of our system and those reported by the literature for normal healing. Once a suitable choice of parameters has been made, we then compare simulation results with data obtained from clinical investigations. While more data is desired, we have a promising first step towards describing the primary events of wound repair within the confines of an implantable system

Cell Detection by Functional Inverse Diffusion and Non-negative Group Sparsity−-Part I: Modeling and Inverse Problems

In this two-part paper, we present a novel framework and methodology to analyze data from certain image-based biochemical assays, e.g., ELISPOT and Fluorospot assays. In this first part, we start by presenting a physical partial differential equations (PDE) model up to image acquisition for these biochemical assays. Then, we use the PDEs' Green function to derive a novel parametrization of the acquired images. This parametrization allows us to propose a functional optimization problem to address inverse diffusion. In particular, we propose a non-negative group-sparsity regularized optimization problem with the goal of localizing and characterizing the biological cells involved in the said assays. We continue by proposing a suitable discretization scheme that enables both the generation of synthetic data and implementable algorithms to address inverse diffusion. We end Part I by providing a preliminary comparison between the results of our methodology and an expert human labeler on real data. Part II is devoted to providing an accelerated proximal gradient algorithm to solve the proposed problem and to the empirical validation of our methodology.Comment: published, 15 page

3D + t Morphological Processing: Applications to Embryogenesis Image Analysis

We propose to directly process 3D + t image sequences with mathematical morphology operators, using a new classi?cation of the 3D+t structuring elements. Several methods (?ltering, tracking, segmentation) dedicated to the analysis of 3D + t datasets of zebra?sh embryogenesis are introduced and validated through a synthetic dataset. Then, we illustrate the application of these methods to the analysis of datasets of zebra?sh early development acquired with various microscopy techniques. This processing paradigm produces spatio-temporal coherent results as it bene?ts from the intrinsic redundancy of the temporal dimension, and minimizes the needs for human intervention in semi-automatic algorithms

Memory effects and L\'evy walk dynamics in intracellular transport of cargoes

We demonstrate the phenomenon of cumulative inertia in intracellular transport involving multiple motor proteins in human epithelial cells by measuring the empirical survival probability of cargoes on the microtubule and their detachment rates. We found the longer a cargo moves along a microtubule, the less likely it detaches from it. As a result, the movement of cargoes is non-Markovian and involves a memory. We observe memory effects on the scale of up to 2 seconds. We provide a theoretical link between the measured detachment rate and the super-diffusive Levy walk-like cargo movement.Comment: 9 pages, 6 figure