Flow in the Iliac Artery

Transcription

1 Flow in the Iliac Artery

2 Flow in an iliac artery

3 Modeling the electromechanical activity of the heart (with R. Ruiz-Baier, D.Ambrosi, F.Nobile, L.Pavarino and S.Rossi)

4 Al Cuore del problema..! Left ventricle is the chamber responsible for pumping oxygenated blood into the major organs! Cardiac muscle consists of cardiomyocyte cells aligned along fiber directions and collagen sheets! Ca^{2+} is the positively charged bivalent calcium ion. The intracellular calcium concentration triggers the sliding of thin and thick filaments inside sarcomeres.! This is the most basic mechanical process, from which the whole contraction mechanism starts

5 IH - Necessity of multiscale!electrophysiology dictates the cardiac cycle!muscle contraction driven by cell-level Ca2+ processes!tissue mechanics and activation dictate the contraction!fluid mechanics dictates the pumping function!neglecting any one aspect would lead to an incomplete model

6 IH - Cardiac electromechanics Models:! Orthotropic hyperelastic passive material! Thermodynamically consistent anisotropic activation mechanism! Bidomain equations for electrophysiology Fiber directions and electric potential Ventricular pressure profile Coupling:! Segregated approach for the solution of the electromechanics (Newton and Picard iterations) Electric propagation and ventricular contraction

7 IH - Multiphysics - The global model picture!strongly coupled physical systems representing challenging frameworks on their own velocity deformation PDEs for electrophysiology PDEs for fluid dynamics PDEs for nonlinear elasticity stress & deformation ionic currents potential fiber stretch active strain ODEs for ionic activity Cardiac electro-fluidstructure coupling [Ca] 2+ Activation generation

8 IH - Mathematical setting : the components!wave of electrical excitation initiates a cascade of biochemical reactions in the cells PDEs for electrophysiology (bidomain eqns on deformed tissue) (ionic model) ionic currents ODEs for ionic activity potential (Ca, Na, K)

9 IH - Mathematical setting : the components!activation initiates contraction of the tissue in the direction of the muscle fibers PDEs for electrophysiology (local strain in the fiber direction) PDEs for nonlinear elasticity fiber stretch active strain ODEs for ionic activity Activation generation [Ca] 2+

10 IH - Mathematical setting : the components!contracting muscle raises pressure in the ventricle, causing ejection of blood into the aorta (incompressible activated hyperelasticity) PDEs for fluid dynamics (Navier-Stokes eqns) velocity stress & deformation PDEs for nonlinear elasticity

11 Modelling Physiology The electrical signal dictates the contraction, the strain of the soft tissue activates ionic currents (electromechanical feedback). Diseases Altered patterns of electrical signals may originate cardiac arrhythmias, yielding an ineffective mechanical contraction and poor fluid ejection volume. Dissincronia ventricolare: il ventricolo destro si contrae prima del ventricolo sinistro. Questo non garantisce una adeguata erogazione di sangue in aorta. A metà del filmino gli elettrodi posizionati alle terminazioni nei ventricoli si attivano, forzando una contrazione simultanea

12 IH - Physiopathological aspects!resynchronization!hypertrophies (concentric, eccentric)!myocardial scarring and heterogeneities (influence on the ventricular flow dynamics, tissue elastic properties and reduced conductivity) RV LV RA LA RV LV Scar Tissue!Altered patterns of electrical signals may originate arrhythmias, yielding an ineffective mechanical contraction and poor fluid ejection volume. Ventricular contraction Tachycardia re-entrant patterns

13 Increasing Complexity: Global Flow Analysis Morphological complexity: the diameter of blood vessels ranges from 10-2 m down to 10-6 m. Consequently, the flow regime varies considerably. Vessel Aorta Arteries Arterioles Capillaries Venules Veins Vena cava Radius(cm) x x x Number x x x Reynolds number Functional complexity: the cardiovascular system is able to react to changes in the external environment and presents several non-linear components (e.g. valves). We need to account for the local/systemic interactions.