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Articles 31 - 42 of 42

Full-Text Articles in Partial Differential Equations

Computational Fluid Dynamics In A Terminal Alveolated Bronchiole Duct With Expanding Walls: Proof-Of-Concept In Openfoam, Jeremy Myers Jan 2017

Computational Fluid Dynamics In A Terminal Alveolated Bronchiole Duct With Expanding Walls: Proof-Of-Concept In Openfoam, Jeremy Myers

Theses and Dissertations

Mathematical Biology has found recent success applying Computational Fluid Dynamics (CFD) to model airflow in the human lung. Detailed modeling of flow patterns in the alveoli, where the oxygen-carbon dioxide gas exchange occurs, has provided data that is useful in treating illnesses and designing drug-delivery systems. Unfortunately, many CFD software packages have high licensing fees that are out of reach for independent researchers. This thesis uses three open-source software packages, Gmsh, OpenFOAM, and ParaView, to design a mesh, create a simulation, and visualize the results of an idealized terminal alveolar sac model. This model successfully demonstrates that OpenFOAM can be …

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Multi-Scale Cardiovascular Flow Analysis By An Integrated Meshless-Lumped Parameter Model, Leonardo A. Bueno, Eduardo A. Divo, Alain J. Kassab Jan 2017

Multi-Scale Cardiovascular Flow Analysis By An Integrated Meshless-Lumped Parameter Model, Leonardo A. Bueno, Eduardo A. Divo, Alain J. Kassab

Publications

A computational tool that integrates a Radial basis function (RBF)-based Meshless solver with a Lumped Parameter model (LPM) is developed to analyze the multi-scale and multi-physics interaction between the cardiovascular flow hemodynamics, the cardiac function, and the peripheral circulation. The Meshless solver is based on localized RBF collocations at scattered data points which allows for automation of the model generation via CAD integration. The time-accurate incompressible flow hemodynamics are addressed via a pressure-velocity correction scheme where the ensuing Poisson equations are accurately and efficiently solved at each time step by a Dual-Reciprocity Boundary Element method (DRBEM) formulation that takes advantage …

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Low Energy Defibrillation By Synchronization; 90 % Less Energy Compared To One Shock., Flavio H. Fenton, Yanyan Ji, Ilija Uzelac, Niels Otani, Elizabeth M. Cherry May 2016

Low Energy Defibrillation By Synchronization; 90 % Less Energy Compared To One Shock., Flavio H. Fenton, Yanyan Ji, Ilija Uzelac, Niels Otani, Elizabeth M. Cherry

Biology and Medicine Through Mathematics Conference

No abstract provided.

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Hydrodynamic Modeling Of Ns-Laser Ablation, David Autrique, Vasilios Alexiades, Harihar Khanal Jan 2013

Hydrodynamic Modeling Of Ns-Laser Ablation, David Autrique, Vasilios Alexiades, Harihar Khanal

Publications

Laser ablation is a versatile and widespread technique, applied in an increasing number of medical, industrial and analytical applications. A hydrodynamic multiphase model describing nanosecond-laser ablation (ns- LA) is outlined. The model accounts for target heating and mass removal mechanisms as well as plume expansion and plasma formation. A copper target is placed in an ambient environment consisting of helium and irradiated by a nanosecond-laser pulse. The effect of variable laser settings on the ablation process is explored in 1-D numerical simulations.

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Time-Stepping For Laser Ablation, Harihar Khanal, David Autrique, Vasilios Alexiades Jan 2013

Time-Stepping For Laser Ablation, Harihar Khanal, David Autrique, Vasilios Alexiades

Publications

Nanosecond laser ablation is a popular technique, applied in many areas of science and technology such as medicine, archaeology, chemistry, environmental and materials sciences. We outline a computational model for radiative and collisional processes occurring during ns-laser ablation, and compare the performance of various low and high order time-stepping algorithms.

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Models Of Phototransduction In Rod Photoreceptors, Harihar Khanal, Vasilios Alexiades Jan 2008

Models Of Phototransduction In Rod Photoreceptors, Harihar Khanal, Vasilios Alexiades

Publications

Phototransduction is the process by which photons of light generate an electrical response in retinal rod and cone photoreceptors, thereby initiating vision. We compare the electrical response in salamander rods from increasingly more (spacialy) detailed models of phototransduction: 0-dimensional (bulk), 1-dimensional (longitudinal), 2-dimensional (axisymmetric), and 3-dimensional (with incisures). We discuss issues of finding physical parameters for simulation and validation of models, and also present some computational experiments for rods with geometry of mouse and human photoreceptors.

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Global Stability Results Of An Sis Age-Structured Epidemic Model With Vertical Transmission, M. El-Doma Jun 2007

Global Stability Results Of An Sis Age-Structured Epidemic Model With Vertical Transmission, M. El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

An SIS age-structured epidemic model for a vertically as well as horizontally transmitted disease is investigated when the fertility, mortality and cure rates depend on age and the force of infection of proportionate mixing assumption type. We determine the steady states and prove the global stability for the endemic equilibriums.

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Multiphoton Response Of Retinal Rod Photoreceptors, Vasilios Alexiades, Harihar Khanal Jan 2007

Multiphoton Response Of Retinal Rod Photoreceptors, Vasilios Alexiades, Harihar Khanal

Publications

Phototransduction is the process by which light is converted into an electrical response in retinal photoreceptors. Rod photoreceptors contain a stack of (about 1000) disc membranes packed with photopigment rhodopsin molecules, which absorb the photons. We present computational experiments which show the profound effect on the response of the distances (how many discs apart) photons happen to be absorbed at. This photon-distribution effect alone can account for much of the observed variability in response.

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Global Stability Results And Well Posedness Of An Si Age-Structured Epidemic Model With Vertical Transmission, M. El-Doma Dec 2006

Global Stability Results And Well Posedness Of An Si Age-Structured Epidemic Model With Vertical Transmission, M. El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

An SI age-structured epidemic model for a vertically as well as horizontally transmitted disease is investigated when the fertility and mortality rates depend on age and the force of infection of proportionate mixing assumption type. We prove the well posedness of the model as well as the global stability for endemic equilibriums.

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Analysis Of An Sirs Age-Structured Epidemic Model With Vaccination And Vertical Transmission Of Disease, Mohammed El-Doma Jun 2006

Analysis Of An Sirs Age-Structured Epidemic Model With Vaccination And Vertical Transmission Of Disease, Mohammed El-Doma

Applications and Applied Mathematics: An International Journal (AAM)

An SIRS age-structured epidemic model for a vertically as well as horizontally transmitted disease under vaccination is investigated when the fertility, mortality and removal rates depend on age and the force of infection of proportionate mixing assumption type, and vaccination wanes over time. We prove the existence and uniqueness of solution to the model equations, and show that solutions of the model equations depend continuously on the initial age-distributions. Furthermore, we determine the steady states and obtain an explicitly computable threshold condition, in terms of the demographic and epidemiological parameters of the model; we then study the stability of the …

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Response Of Dark-Adapted Retinal Rod Photoreceptors, H. Khanal, V. Alexiades, E. Dibenedetto Jan 2004

Response Of Dark-Adapted Retinal Rod Photoreceptors, H. Khanal, V. Alexiades, E. Dibenedetto

Publications

The process of phototransduction, whereby light is converted into an electrical response, in rod and cone photoreceptors in the retina, involves as a key setp, the diffusion of the cytoplasmic, signaling molecules cGMP (cyclic guanosime monophosphate) and Ca2+ diffuse in the cytoplasm (the fluid surrounding the discs). the complex geometry of the rod creates computational difficulties. We present spatio-temporal compuational models for interacctions and diffusion of cGMP and Ca2+ in the cytoplasm of vertebrate rod photoreceptors, as well as numerical simulations fo the response to light of dark-adapted Salamander rods.

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Computational Models For Diffusion Of Second Messengers In Visual Transduction, Harihar Khanal Aug 2003

Computational Models For Diffusion Of Second Messengers In Visual Transduction, Harihar Khanal

Publications

The process of phototransduction, whereby light is converted into an electrical response in retinal rod and cone photoreceptors, involves, as a crucial step, the diffusion of cytoplasmic signaling molecules, termed second messengers. A barrier to mathematical and computational modeling is the complex geometry of the rod outer segment which contains about 1000 thin discs. Most current investigations on the subject assume a well-stirred bulk aqueous environment thereby avoiding such geometrical complexity. We present theoretical and computational spatio-temporal models for phototransduction in vertebrate rod photoreceptors, which are pointwise in nature and thus take into account the complex geometry of the …

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