Data Assimilation for Cardiovascular Modeling with Applications to - - PowerPoint PPT Presentation

Data Assimilation for Cardiovascular Modeling with Applications to Optimal Flow Control

• Z. Zainib1, Z. Chen2, F. Ballarin1,
• P. Triverio2, L. Jimenez-Juan3,
• A. Crean4 and G. Rozza1

1 mathLab, Mathematics Area, SISSA-International

School for Advanced Studies, Trieste, Italy

2University of Toronto, Canada 3Sunnybrook Health Sciences Centre, Toronto,

Canada

4University Health Network, Toronto, Canada

Poster Blitz, QUIET 2017

19 July, 2017

MOTIVATION & INTRODUCTION

Figure: Normal and blocked artery Figure: Bypass grafts

1/ 2 Zakia Zainib Data assimilation for cardiovascular modeling with applications to optimal flow control

RESEARCH WORK

• Geometry reconstruction and mesh generation from CT scan or

MRI.

• Solving the mathematical model,

a (v (µ) , w) + b (w, p (µ)) = f , w ∀ w ∈ H subject to the constraint, b (v (µ) , q) = g, q ∀ q ∈ Q and appropriate boundary conditions, using finite-element and reduced-order methods for velocity (v (µ) ∈ H) and pressure (p (µ) ∈ Q), of the blood.

• Solving an optimal flow control problem:

For µ ∈ D ⊂ R, find y (µ) = (v (µ) , p (µ)) ∈ Yad = Had × Qad, u (µ) ∈ Uad such that, J (y (µ) , u (µ)) is minimized, subject to F (y (µ) , u (µ)) = 0 using one-shot approach, to address the clinical queries. THANK YOU!

2/ 2 Zakia Zainib Data assimilation for cardiovascular modeling with applications to optimal flow control