Multiscale Modelling Of Aortic Dissections Using Asymptotic Homogenisation And A Damage Phase-Field Model #

Andrew Brown

Poster session

Abstract #

An aortic dissection is a lethal cardiovascular disease in which a tear occurs in the inner layers of the aortic wall. This allow blood to rush through the tear and pressurise the aortic wall causing the inner layers of the aortic wall to delaminate. These tears are extremely dangerous and life threatening but we still struggle to understand all the underlying mechanics, especially how microscopic changes in the structure which may be caused by certain underlying soft tissue diseases. We approach this problem by approximating the microstructure of each layer of the aortic wall as a composite material, made up of many continua representative of the tissue’s constitutive parts. Assuming each continuum is hyperelastic we can use a multiplicative ansatz to incorporate a damage degradation function in the component’s constitutive properties. This allows us to employ a damage phase-field modelling method that can be expressed through power functionals for each continuum. One can then create a balance of external and internal power on the microstructure and use appropriate thermodynamic arguments to provide us with several irreversibility conditions of tearing and damage, an equation of motion and an equation of damage evolution. Non-dimensionalisation of the microscopic system shows an inherent length scale disparity in our model between the microstructure and the macroscale of the aortic wall. Assuming a locally periodic microstructure we can approach the problem with the multiscale technique, asymptotic homogenisation, allowing us to create a closed system of macroscopic partial differential equations. Our main result is the derivation of a macroscopic system of PDEs which describe both the motion and propagation of damage in the aorta. This system relates the macroscale and the microscale, through effective coefficients which can be calculated by solving closed linear cell problems on the microscale. Moreover, the role of the microstructure can be analysed and explored through the effective coefficients of the model. This means the model can be analysed numerically, at a great convenience. Our formulation may be relevant to understand the role that the microscopic properties and geometry play in the dissection process. To understand this relevance, we can create simulations with the model and compare these to existing theoretical models and experimental data. Understanding this model may help us understand how and when dissections propagate in the aorta, helping to clinically diagnose and treat the disease.