Coupling fluid and solid domains in modeling drug transport within tumor

Development of a feasible model for transport within complex vasculature network and tissue remains a challenge. Such a model is particularly important when considering drug transport within tumor environment. A drug used to cure the cancer is first transported through blood vessels, then it attaches to the vessel endothelium and faces biological barriers in the vessel wall to reach cancerous cells. We have developed a model for convective-diffusive drug transport which is simple and computationally efficient. One of the challenges was to couple fluid domain within blood vessels and solid domain of the tumor microenvironment. We have introduced fictitious 1D finite elements which appropriately take into account transport characteristics of the vessel walls. These characteristics include leakage and permeability of the walls. In evaluating wall permeability of a drug, we implemented our hierarchical multiscale methodology which couples molecular dynamics (MD) and continuum FE model. A numerical homogenization procedure was employed to obtain equivalent continuum transport parameters which account for interaction on molecular level between drug and solid components of the wall microstructure. Also, a possibility of using equivalent continuum transport models for capillary beds is investigated in order to further simplify and increase efficiency for the overall model of tumor. As a numerical example, we calculate transport through a capillary bed to illustrate applicability of our methodology

CFD - Mature Technology?

Over the past 30 years, numerical methods and simulation tools for fluid dynamic problems have advanced as a new discipline, namely, computational fluid dynamics (CFD). Although a wide spectrum of flow regimes are encountered in many areas of science and engineering, simulation of compressible flow has been the major driver for developing computational algorithms and tools. This is probably due to a large demand for predicting the aerodynamic performance characteristics of flight vehicles, such as commercial, military, and space vehicles. As flow analysis is required to be more accurate and computationally efficient for both commercial and mission-oriented applications (such as those encountered in meteorology, aerospace vehicle development, general fluid engineering and biofluid analysis) CFD tools for engineering become increasingly important for predicting safety, performance and cost. This paper presents the author's perspective on the maturity of CFD, especially from an aerospace engineering point of view

A model of blood flow in the mesenteric arterial system

<p>Abstract</p> <p>Background</p> <p>There are some early clinical indicators of cardiac ischemia, most notably a change in a person's electrocardiogram. Less well understood, but potentially just as dangerous, is ischemia that develops in the gastrointestinal system. Such ischemia is difficult to diagnose without angiography (an invasive and time-consuming procedure) mainly due to the highly unspecific nature of the disease.</p> <p>Understanding how perfusion is affected during ischemic conditions can be a useful clinical tool which can help clinicians during the diagnosis process. As a first step towards this final goal, a computational model of the gastrointestinal system has been developed and used to simulate realistic blood flow during normal conditions.</p> <p>Methods</p> <p>An anatomically and biophysically based model of the major mesenteric arteries has been developed to be used to simulate normal blood flows. The computational mesh used for the simulations has been generated using data from the Visible Human project. The 3D Navier-Stokes equations that govern flow within this mesh have been simplified to an efficient 1D scheme. This scheme, together with a constitutive pressure-radius relationship, has been solved numerically for pressure, vessel radius and velocity for the entire mesenteric arterial network.</p> <p>Results</p> <p>The computational model developed shows close agreement with physiologically realistic geometries other researchers have recorded <it>in vivo</it>. Using this model as a framework, results were analyzed for the four distinct phases of the cardiac cycle – diastole, isovolumic contraction, ejection and isovolumic relaxation. Profiles showing the temporally varying pressure and velocity for a periodic input varying between 10.2 kPa (77 mmHg) and 14.6 kPa (110 mmHg) at the abdominal aorta are presented. An analytical solution has been developed to model blood flow in tapering vessels and when compared with the numerical solution, showed excellent agreement.</p> <p>Conclusion</p> <p>An anatomically and physiologically realistic computational model of the major mesenteric arteries has been developed for the gastrointestinal system. Using this model, blood flow has been simulated which show physiologically realistic flow profiles.</p

Simulation of flow in an artery under pathological hemodynamic conditions: The use of a diagnostic disease descriptor

A numerical model for simulating and predicting blood flow dynamics in diseased arterial vessels has been developed. The time-dependent one-dimensional hyperbolic system of quasilinear partial differential equations which incorporates a diagnostic disease descriptor (kD) was used to simulate transient flow distribution for idealized healthy and diseased states. Blood flow simulations in the iliac arteries over about 125% of a cardiac cycle were generated and calibrated using the kD values from 0 to 3 representing hypothetical diseased states. Early results indicate that disease conditions induce abnormal flow in the artery, generating disorder and increased amplitude of blood pressure, flow and distensibility with increasing numerical values of the disease factor kD. More so, the prospective use of the kD-approach with documentation of in vivo adverse flow visualizations for diagnostic purposes was decisively discussed

Parameter estimation to study the immediate impact of aortic cross-clamping using reduced order models

Aortic cross-clamping is a common strategy during vascular surgery, however, its instantaneous impact on hemodynamics is unknown. We, therefore, developed two numerical models to estimate the immediate impact of aortic clamping on the vascular properties. To assess the validity of the models, we recorded continuous invasive pressure signals during abdominal aneurysm repair surgery, immediately before and after clamping. The first model is a zero-dimensional (0D) three-element Windkessel model, which we coupled to a gradient-based parameter estimation algorithm to identify patient-specific parameters such as vascular resistance and compliance. We found a 10% increase in the total resistance and a 20% decrease in the total compliance after clamping. The second model is a nine-artery network corresponding to an average human body in which we solved the one-dimensional (1D) blood flow equations. With a similar parameter estimation method and using the results from the 0D model, we identified the resistance boundary conditions of the 1D network. Determining the patient-specific total resistance and the distribution of peripheral resistances through the parameter estimation process was sufficient for the 1D model to accurately reproduce the impact of clamping on the pressure waveform. Both models gave an accurate description of the pressure wave and had a high correlation (R2 >.95) with experimental blood pressure data.Fil: Ventre, Jeanne. Centre National de la Recherche Scientifique; FranciaFil: Politi, Teresa. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Fisiología y Biofísica Bernardo Houssay. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Fisiología y Biofísica Bernardo Houssay; ArgentinaFil: Fernández, Juan M.. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Fisiología y Biofísica Bernardo Houssay. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Fisiología y Biofísica Bernardo Houssay; ArgentinaFil: Ghigo, Arthur R.. Université de Toulouse; FranciaFil: Gaudric, Julien. Centre National de la Recherche Scientifique; Francia. Université de Toulouse; FranciaFil: Wray, Sandra. Universidad Favaloro; ArgentinaFil: Lagaert, Jean Baptiste. Université Paris Sud; FranciaFil: Armentano, Ricardo Luis. Universidad de la República; UruguayFil: Capurro, Claudia Graciela. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Fisiología y Biofísica Bernardo Houssay. Universidad de Buenos Aires. Facultad de Medicina. Instituto de Fisiología y Biofísica Bernardo Houssay; ArgentinaFil: Fullana, José Maria. Centre National de la Recherche Scientifique; FranciaFil: Lagrée, Pierre Yves. Centre National de la Recherche Scientifique; Franci

Analytical solutions for the free surface hydrostatic Euler equations

International audienceIn this paper we propose a large set of analytical solutions (FRESH-ASSESS) for the hydrostatic incompressible Euler system in 2d and 3d. These solutions mainly concern free surface flows but partially free surface flows are also considered. These analytical solutions can be especially useful for the validation of numerical schemes