Constitutive equations for human saphenous vein coronary artery

Constitutive equations for human saphenous vein coronary artery bypass graft Hynek Chlup, Lukas Horny, Rudolf Zitny, Svatava Konvickova and Tomas Adamek Faculty of Mechanical Engineering Czech Technical University in Prague Czech Republic

Introduction n This report deals with a constitutive modeling of human saphenous vein implanted as coronary artery bypass graft (CABG) n CABG is standard revascularization method Image sources: http: //privatecardiology. com/41. html http: //www. texheartsurgeons. com/CABG. htm

Goals n Identification of suitable constitutive model for CABG n Estimation of material parameters n Comparison of different models

Constitutive behavior n Significant features of blood vessels behavior • Arteries undergo large strains Nonlinear description of deformation • Large strain stiffening Nonlinear material behavior • Significant internal structure Anisotropic behavior • Inelastic behavior Creep, relaxation, viscoelasticity, preconditioning, pseudoelasticity

Constitutive behavior n Anisotropy n Inelastic behavior

Constitutive model n z Anisotropy Composite material – fibers + matrix b t n Nonlinear elastic behavior Stored energy function y - hyperelastic material

Constitutive model n Exponential model n Logarithmic model z c , k 1 , k 2 , b c , m, J m , b material parameters b t

Constitutive model n Material parameters must be determined experimentally n Inflation – extension test

Experiment • Experimental setup • Sample

Measurement n Digital image correlation – DANTEC Q 450 • Stereoscopic sensor – two cameras • Calibration – knowing of dimensions • Correlation – one object in two images – dimensions of object • Correlation with previous and following images – deformation process Temporal record of displacements

Measurement n Pressurization • Manually by a syringe • Pressure record in PC DIC PC unit Pressure probe PC unit

Measured data

Estimation of material parameters n Computational model for inflation – extension test • Thick–walled tube • Fiber reinforced composite • Hyperelastic material • Incompressibility • No shear strains • No residual strains • Model predictions

Results of nonlinear regression Type I models Type II models

Conclusion n Both, exponential and logarithmic model fits experimental data successfully n Exponential model fits data better than logarithmic, especially in low pressures n Neo–Hook member in stored energy functions had not significant contribution to fitting data

Constitutive equations for human saphenous vein coronary artery bypass graft The End