Alfio Quarteroni. MATHICSE - EPFL - Lausanne and MOX - Politecnico di Milano GEOMETRIC PRE- PROCSSING MODEL VALIDATION OUTCOME

Transcription

1 Mathematical Models for Technology, Medicine and Sports SATW, Bern - 15 April 2010 GEOMETRIC PRE- PROCSSING MODEL VALIDATION OUTCOME Alfio Quarteroni MATHICSE - EPFL - Lausanne and MOX - Politecnico di Milano

2 Mathematics and Nature People who wish to analyze Nature without using Mathematics must settle for a reduced understanding Richard P. Feynman ( ) Alfio Quarteroni 2 EPFL and POLIMI

3 Galileo Galilei, GEOMETRIC PRE- PROCSSING MODEL VALIDATION OUTCOME

4 The Book of Nature (Il Saggiatore, 1623) In 1623 Galileo crafted a famous metaphor (which he used to defend the work of scientists from religious authorities): GEOMETRIC PRE- PROCSSING Nature, he wrote, is a book written in "the language of mathematics". If we cannot understand that language, we will be doomed to wander about as if "in a dark labyrinth". MODEL VALIDATION It captures our sense that nature's truths are somehow imposed on us that they are already imprinted in the world and underlines the key role played by mathematics in expressing those truths. OUTCOME

5 Towards Math Modeling: the Galilean Method Compositive/synthetic period INDUCTION Analytical step Theoretical hypothesis Hypothetical/deductive step DEDUCTION/SYLLOGISM Law/New hypothesis Sensate esperienze Observation of phenomena Mathematical measures of data Necessarie dimostrazioni Factual consequences The rational step of science, reasoning based on logical mathematical arguments Experiment (cimento) Verification/ Refutation

6 THE PARADIGM SCIENCE Reality (isomorphism /specularity) Representation REALISTIC METAPHYSICS

7 Mathematics and Nature People who wish to analyze Nature without using Mathematics must settle for a reduced understanding Richard P. Feynman ( ) Alfio Quarteroni 7 EPFL and POLIMI

8 Mathematical Modeling: a Mathematician s Perspective Data/Uncertainty Data / Uncertainty Experimental Model Validation Verification Mathematical Model In Vivo Geometry Labs Literature & Benchmark EDP and Analysis Scientific Computation Numerical Model Feedback Post-Processing 3D Visualization Alfio Quarteroni Politecnico di Milano & EPFL Lausanne

9 Falcon/AMD geometric model

10 Simulazione Finite element del analysis numero di Mach Euler equations of gas dynamics: compressible inviscid flows Conservation of momentum and mass M.Sala Mach number distribution

11 Deductivism - generality X29 Mach: 0.75 Alpha: M nodes 7.35M unknowns

12 Models for preservation of architectural heritage

13 A geometric model In colore diverso i vari materiali La griglia di calcolo ( elementi esaedrici)

14 Elastodynamics deformations (Maggio,Massidda,Fotia, CRS4)

15 THE CARDIOVASCULAR SYSTEM QuickTime and a Microsoft Video 1 decompressor are needed to see this picture.

16 Blood-flow Modeling: Main Motivations GEOMETRIC PRE- PROCSSING Medical research. A number of vascular diseases are linked to local haemodynamics. For instance atherosclerosis or cerebral aneurysms Surgical planning and optimization. Alterated flow conditions following a surgical procedure (i.e. a bypass) may have negative effects and cause post-surgical failure MODEL VALIDATION Design of prostheses. The design of endoprosthesis or other devices (such as stents) may be aided by the knowledge of haemodynamics OUTCOME Training surgeons and anesthesiologists. Simulator of the cardiovascular system may be used for training purposes

17 M.Prosi Pulsatile Blood Flow in the Carotid Artery GEOMETRIC PRE- PROCSSING MODEL VALIDATION QuickTime and a YUV420 codec decompressor are needed to see this picture. OUTCOME

18 THE MATHEMATICAL MODEL GEOMETRIC PRE- PROCSSING The coupled fluid-structure problem Equations for the geometry: Equations for the fluid: MODEL VALIDATION Equations for the structure: OUTCOME Istituto Lombardo, 5 febbraio 2009

19 RHEOLOGY GEOMETRIC PRE- PROCSSING Rouleax aggregation ( rate of deformation, or shear rate) Fahraeus-Lindquist effect MODEL VALIDATION OUTCOME Red blood cells aggregate as in stack of coins In small vessels (below 1mm radii) red blood cells move toward the central part of the vessel, whence blood viscosity shifts toward plasma viscosity (much lower) Istituto Lombardo, 5 febbraio 2009

20 FSI for carotid bifurcation : wall deformation QuickTime and a Microsoft Video 1 decompressor are needed to see this picture. (G.Fourestey)

21 Flow motion and wall deformation QuickTime and a decompressor are needed to see this picture.

22 From Medical Images to Grid Generation DICOM image segmentation unstructured mesh (e.g. CT scan) (e.g. vmtk, 3DSlicer) (e.g. gmsh, netgen) FSI, Navier-Stokes Finite Elements Solvers (e.g. P2,P1,...) (e.g. LifeV, Trilinos) Alfio Quarteroni 22 Politecnico di Milano & EPFL Lausanne

23 Aorta modeling: flowfield and wall pressure QuickTime and a mpeg4 decompressor are needed to see this picture.

24 Aorta deformation QuickTime and a mpeg4 decompressor are needed to see this picture.

25 Cerebral Aneurysms Cerebral aneurysms: deformations of cerebral arteries, mostly placed on vessels belonging to or connected to the Circle of Willis. GEOMETRIC PRE- PROCSSING EPIDEMIOLOGICAL STATISTICS Incidence rate of cerebral aneurysms: 1/20 people Incidence rate of ruptured cerebral aneurysms per year: 1/10000 people per year MODEL VALIDATION Mortality due to a ruptured aneurysm: > 50%: Out of 9 patients with a ruptured aneurysm: Circle of Willis 3 are expected to die before arriving at the hospital OUTCOME 2 to die after having arrived at the hospital 2 to survive with permanent cerebral damages 2 to survive without permanent cerebral damages Aneurysm on ICA Istituto Lombardo, 5 febbraio 2009

26 Flow in a cerebral aneurysm during a full cardiac pulse GEOMETRIC PRE- PROCSSING QuickTime and a decompressor are needed to see this picture. QuickTime and a Motion JPEG OpenDML decompressor are needed to see this picture. MODEL VALIDATION OUTCOME Simulation by T. Passerini

27 WSS - Wall Shear Stress QuickTime and a xvid decompressor are needed to see this picture.

28 The Whole Picture Pulmonary circulation The Heart Pulmonary Arteries Pulmonary Veins The Heart Right Ventricle Left Atrium Right atrium The Veins Vena Cava The lungs Arteries Arterioles Capillaries Venules Veins Left Ventricle The Arteries Aorta Veins Venules The Capillaries Systemic Circulation Arteries Arterioles Alfio Quarteroni 28 Politecnico di Milano & EPFL Lausanne

29 Geometric multiscaling in the circulatory system QuickTime and a Motion JPEG OpenDML decompressor are needed to see this picture. Local (level1): 3D flow model (FSI between NS equations and elastodynamic eqs) Global (level 2): 1D network of major arteries and veins (Euler hyperbolic system) Global (level 3): 0D capillary network (DAE system) Alfio Quarteroni 29 Politecnico di Milano & EPFL Lausanne

30 Geometric multiscaling in the circulatory system A preview Acnowledgments: L.Formaggia, F.Nobile, A.Veneziani 3D 1D 0D 3D Navier-Stokes (F) + 3D ElastoDynamics (V- W) 1D Euler (F) + Algebraic pressure law 0D lumped parameters (system of linear ODEs) Alfio Quarteroni 30 Politecnico di Milano & EPFL Lausanne

31 3D-1D for the carotid: pressure pulse GEOMETRIC PRE- PROCSSING MODEL VALIDATION QuickTime and a Motion JPEG OpenDML decompressor are needed to see this picture. OUTCOME (A.Moura) Istituto Lombardo, 5 febbraio 2009

32 Blood Flow and Oxygen Transport in the Brain QuickTime and a mpeg4 decompressor are needed to see this picture. Application to oxygen transport in the brain: isosurface of oxygen concentration. Impairment due to left carotid artery occlusion. Alfio Quarteroni 32 (Simulations by C.D Angelo) Politecnico di Milano & EPFL Lausanne

33 Blood Flow and Oxygen Transport in the Brain QuickTime and a mpeg4 decompressor are needed to see this picture. 1D (vessels) and 3D (brain tissue) blood pressures with pulsatile input blood flow rate and left carotid artery occlusion Alfio Quarteroni 33 Politecnico di Milano & EPFL Lausanne

34 Drug release from Stents Angiography after stent placement Alfio Quarteroni 34 Politecnico di Milano & EPFL Lausanne

35 Stent deployement QuickTime and a Microsoft Video 1 decompressor are needed to see this picture. Alfio Quarteroni 35 Politecnico di Milano & EPFL Lausanne

36 Some Commercial Drug-eluting stents A B Different stent design may affect the local drug distribution across the arterial wall C D Alfio Quarteroni 36 Politecnico di Milano & EPFL Lausanne

37 Some Commercial Drug-eluting stents A B Different stent design may affect the local drug distribution across the arterial wall C D The final configuration reached after the stent deployment has to be taken into account: an incorrect expansion may cause sites of toxic dose Alfio Quarteroni 37 Politecnico di Milano & EPFL Lausanne

38 Mathematical Modeling of Stents: Problem Overview Mechanical analysis: inflation of the baloon and stent expansion 1. Mass Transfer: Drug release from a polymer Fluid Dynamics: Blood flow Drug release to the arterial walls Filtration through arteries Zunino P, D'Angelo C, Petrini L, Vergara C, Capelli C, Migliavacca F. Numerical simulation of drug eluting coronary stents: mechanics, fluid dynamics and drug release (second revision under way for publication in Computational Methods in Applied Mechanics and Engineering, 2008). Alfio Quarteroni 38 Politecnico di Milano & EPFL Lausanne

39 Reduced Models for Drug Delivery Stent struts modeled as 1D objects Real geometries are easily handled since refining the meshes near the struts is no more required Mass fluxes are regarded as sources for the 3D problems Alfio Quarteroni 39 Politecnico di Milano & EPFL Lausanne

40 Isosurfaces of drug concentration (lumen) QuickTime and a mpeg4 decompressor are needed to see this picture. Alfio Quarteroni 40 Politecnico di Milano & EPFL Lausanne

41 QuickTime and a mpeg4 decompressor are needed to see this picture. Alfio Quarteroni 41 Politecnico di Milano & EPFL Lausanne

42 Mathematics and Sports Real and Virtual Swimmers

43 QuickTime and a YUV420 codec decompressor are needed to see this picture. Alfio Quarteroni 43 Politecnico di Milano & EPFL Lausanne

44 Math Modelling and AMERICA S CUP Coppa America (N.Parolini, D.Detomi)

45 America s Cup in a nutshell GEOMETRIC PRE- PROCSSING Premier international yacht race First race in 1851 around Isle of Wight America was the name of the winner yacht of the first edition MODEL VALIDATION OUTCOME Held by U.S.A. for 132 years, the cup was won in 1983 by the winged-keel Australia II New Zealand s Black Magic has dominated the two editions of 1995 and 2000 Alinghi has won the two editions (ended March 2003 and July 2007)

46 From Concept to Design New concept (shape, size, positioning) GEOMETRIC PRE- PROCSSING CAD representation MODEL VALIDATION Numerical solution Grid generation OUTCOME New design

47 GEOMETRIC PRE- PROCSSING MODEL VALIDATION QuickTime and a YUV420 codec decompressor are needed to see this picture. OUTCOME

48 Two-phase flow equations GEOMETRIC PRE- PROCSSING Air Phase MODEL VALIDATION Interface Conditions OUTCOME Water Phase

49 Turbulence The flow features a turbulent regime over the vast majority of the yacht surface GEOMETRIC PRE- PROCSSING MODEL VALIDATION Unsteady, three-dimensional flow Contains vortices and coherent structures which stretch and increase the intensity of turbulence Fluctuates over a broad range of scales (both in space and time), high Reynolds number DNS (Direct Numerical Simulation) unaffordable OUTCOME Roma, Festival della Matematica, March 16, 2008

50 SST (Shear Stress Transport) Turbulence Model GEOMETRIC PRE- PROCSSING SST (k- based) Turbulence Model (Menter, 1994) Turbulent kinetic energy (k) equation t (ρk) + x j (ρu j k) = P k D k + x j ( μ + σ k μ t ) k x j Specific turbulence dissipation rate ( ) equation MODEL VALIDATION t (ρω ) + x j (ρu j ω) = α P k υ t D ω + Cd ω + x j ( ) ω μ + σ k μ t x j OUTCOME Production terms Destruction term Roma, Festival della Matematica, March 16, 2008

51 GEOMETRIC PREPROCSSING MODEL VALIDATION OUTCOME Turbulent flow behind appendages

52 Free surface analysis GEOMETRIC PRE- PROCSSING Incoming wave: /L=0.05 =6.68 QuickTime and a YUV420 codec decompressor are needed to see this picture. QuickTime and a YUV420 codec decompressor are needed to see this picture. MODEL VALIDATION OUTCOME Wave pattern ICFD 2007

53 GEOMETRIC PRE- PROCSSING QuickTime and a YUV420 codec decompressor are needed to see this picture. MODEL VALIDATION OUTCOME

54 GEOMETRIC PRE- PROCSSING MODEL VALIDATION OUTCOME

55 A Large scale computational problem GEOMETRIC PRE- PROCSSING unknowns Which cost to achieve the desired accuracy? CPU Time (120 MD ops) 24 hrs =10 16 op MODEL VALIDATION RAM Memory 30 gigabytes of RAM OUTCOME Number of Processors 32 processors Mizar epfl (450 AMD Opteron processors, 900 Gb distributed RAM, Myrinet Network)

56 Mathematical Models for Urban Planning Alfio Quarteroni 56 Politecnico di Milano & EPFL Losanna

57 Le Grand Pari(s) In , President N.Sarkozy invited 10 international teams to propose new visions for the French capital. The Italian team was led by architects B.Secchi, P.Viganò and included the MOX labs. MOX: to extract synthetic data describing the influence of the geometry on transport fluxes

58 Embedded models of traffic flows in large urban area Transportation in modern mega-cities occurs at different scales: Big roads (highways) (macroscale, fast and directional flow) Small roads (microscale, slow dispersed flow) Venice They interact and determine flow patterns Padua Alfio Quarteroni 58 Politecnico di Milano & EPFL Lausanne

59 The Sponge Analogy (metropolis=porous media) Alfio Quarteroni 59 CMCS - SMA - EPFL

60 A Three-Layer (micro-meso-macro) Model: QuickTime and a mpeg4 decompressor are needed to see this picture. Alfio Quarteroni 60 CMCS - SMA - EPFL

61 The End GEOMETRIC PRE- PROCSSING MODEL VALIDATION OUTCOME