Preface.- Preface to the 2nd edition.- Notational conventions.- 1 Preliminary general material.- I Steady-state problems.- 2 Pseudomonotone or weakly continuous mappings.- 3 Accretive mappings.- 4 Potential problems: smooth case.- 5 Nonsmooth problems variational inequalities.- 6. Systems of equations: particular examples.- II Evolution problems.- 7 Special auxiliary tools.- 8 Evolution by pseudomonotone or weakly continuous mappings.- 9 Evolution governed by accretive mappings.- 10 Evolution governed by certain set-valued mappings.- 11 Doubly-nonlinear problems.- 12 Systems of equations: particular examples.- References.- Index.

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Nonlinear partial differential equations with applications

https://www.zora.uzh.ch/id/eprint/146170/1/1-s2.0-S1078588416301782-main.pdf

Editor's Choice - Management of Descending Thoracic Aorta Diseases: Clinical Practice Guidelines of the European Society for Vascular Surgery (ESVS)

ESC Guidelines for the diagnosis and treatment of acute and chronic heart failure 2008 (ending).

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Esc guidelines for the diagnosis and treatment of acute and chronic heart failure 2008 (ending)

We present a weakly compressible form of the Smoothed Particle Hydrodynamics method (SPH) for fluid flow based on the Tait equation. In contrast to commonly employed projection approaches that strictly enforce incompressibility, time-consuming solvers for the Poisson equation are avoided by allowing for small, user-defined density fluctuations. We also discuss an improved surface tension model that is particularly appropriate for single-phase free-surface flows. The proposed model is compared to existing models and experiments illustrate the accuracy of the approach for free surface flows. Combining the proposed methods, volume-preserving low-viscosity liquids can be efficiently simulated using SPH. The approach is appropriate for medium-scale and small-scale phenomena. Effects such as splashing and breaking waves are naturally handled.

Weakly compressible SPH for free surface flows

Embodiments include a system for determining cardiovascular information for a patient. The system may include at least one computer system configured to receive patient-specific data regarding a geometry of the patient's heart, and create a three-dimensional model representing at least a portion of the patient's heart based on the patient-specific data. The at least one computer system may be further configured to create a physics-based model relating to a blood flow characteristic of the patient's heart and determine a fractional flow reserve within the patient's heart based on the three-dimensional model and the physics-based model.

Method and system for patient-specific modeling of blood flow

There is a growing need for patient-specific and holistic modelling of the heart to support comprehensive disease assessment and intervention planning as well as prediction of therapeutic outcomes. We propose a patient-specific model of the whole human heart, which integrates morphology, dynamics and haemodynamic parameters at the organ level. The modelled cardiac structures are robustly estimated from four-dimensional cardiac computed tomography (CT), including all four chambers and valves as well as the ascending aorta and pulmonary artery. The patient-specific geometry serves as an input to a three-dimensional Navier-Stokes solver that derives realistic haemodynamics, constrained by the local anatomy, along the entire heart cycle. We evaluated our framework with various heart pathologies and the results correlate with relevant literature reports.

/pdf/patient-specific-modelling-of-whole-heart-anatomy-dynamics-52wjl4jt5g.pdf

Patient-specific modelling of whole heart anatomy, dynamics and haemodynamics from four-dimensional cardiac CT images.

In order to assess coronary artery disease from medical image data, an anatomical model of a coronary artery is generated from the medical image data. A velocity of blood in the coronary artery is estimated based on a spatio-temporal representation of contrast agent propagation in the medical image data. Blood flow is simulated in the anatomical model of the coronary artery using a computational fluid dynamics (CFD) simulation using the estimated velocity of the blood in the coronary artery as a boundary condition.

Method and system for non-invasive assessment of coronary artery disease

A method and system for patient-specific modeling of the whole heart anatomy, dynamics, hemodynamics, and fluid structure interaction from 4D medical image data is disclosed. The anatomy and dynamics of the heart are determined by estimating patient-specific parameters of a physiological model of the heart from the 4D medical image data for a patient. The patient-specific anatomy and dynamics are used as input to a 3D Navier-Stokes solver that derives realistic hemodynamics, constrained by the local anatomy, along the entire heart cycle. Fluid structure interactions are determined iteratively over the heart cycle by simulating the blood flow at a given time step and calculating the deformation of the heart structure based on the simulated blood flow, such that the deformation of the heart structure is used in the simulation of the blood flow at the next time step. The comprehensive patient-specific model of the heart representing anatomy, dynamics, hemodynamics, and fluid structure interaction can be used for non-invasive assessment and diagnosis of the heart, as well as virtual therapy planning and cardiovascular disease management. Parameters of the comprehensive patient-specific model are changed or perturbed to simulate various conditions or treatment options, and then the patient specific model is recalculated to predict the effect of the conditions or treatment options.

Method and System for Comprehensive Patient-Specific Modeling of the Heart

Controlling fluids is still an open and challenging problem in fluid animation. In this paper we develop a novel fluid animation control approach and we present its application to controlling breaking waves. In our Slice Method framework an animator defines the shape of a breaking wave at a desired moment in its evolution based on a library of breaking waves. Our system computes then the subsequent dynamics with the aid of a 3D Navier-Stokes solver. The wave dynamics previous to the moment the animator exerts control can also be generated based on the wave library. The animator is thus enabled to obtain a full animation of a breaking wave while controlling the shape and the timing of the breaking. An additional advantage of the method is that it provides a significantly faster method for obtaining the full 3D breaking wave evolution compared to starting the simulation at an early stage and using solely the 3D Navier-Stokes equations. We present a series of 2D and 3D breaking wave animations to demonstrate the power of the method.

/pdf/animation-and-control-of-breaking-waves-1x4m9wvrrx.pdf

Animation and control of breaking waves

A method and system for multi-scale anatomical and functional modeling of coronary circulation is disclosed. A patient-specific anatomical model of coronary arteries and the heart is generated from medical image data of a patient. A multi-scale functional model of coronary circulation is generated based on the patient-specific anatomical model. Blood flow is simulated in at least one stenosis region of at least one coronary artery using the multi-scale function model of coronary circulation. Hemodynamic quantities, such as fractional flow reserve (FFR), are computed to determine a functional assessment of the stenosis, and virtual intervention simulations are performed using the multi-scale function model of coronary circulation for decision support and intervention planning.

Viorel Mihalef

Papers

Patient-specific modelling of whole heart anatomy, dynamics and haemodynamics from four-dimensional cardiac CT images.

Method and system for non-invasive assessment of coronary artery disease

Method and System for Comprehensive Patient-Specific Modeling of the Heart

Animation and control of breaking waves

Method and system for multi-scale anatomical and functional modeling of coronary circulation