Modeling and material characterization of cerebral aneurysms

The vascular system of the human body transports blood to the different parts of the body. Aneurysms are abnormal dilatations of the vascular wall and tend to appear most prevalently in the abdominal aorta and close to the brain. Aneurysms close to the brain are denoted cerebral aneurysms or intracranial aneurysms. These lesions often form a sac-like expansion on the vessel wall. Cerebral aneurysms appear in about 5% of the adult population in the Western World, and they are more prevalent in females than in males. The causes for aneurysms are not fully understood, but genetic factors and drug consumption are factors likely to be influential. The aneurysm wall is usually very thin compared to the healthy arterial wall, and there is therefore an impending risk of rupture. If a cerebral aneurysm ruptures, it causes a sub-arachnoid hemorrhage. This is a very severe event, with a high risk of mortality. The present project consists roughly of three parts: (a) development of a constitutive model for aneurysmal tissue, (b) modeling of growth of cerebral aneurysms, and (c) estimation of the material properties of aneurysmal tissue by use of inverse analysis. The three parts are described in some more detail below: The mechanical behavior of a material is characterized by a constitutive model. The development of a new constitutive model for aneurysmal tissue is based on the structural features of this kind of tissue. Healthy arterial tissue is dominated by its fibrous components and the same holds for aneurysmal tissue. In addition, aneurysmal tissue is often very thin and can, for practical purposes, be considered as a membrane. In the proposed constitutive model, the tissue is modeled as a hyperelastic, multi-layered membrane. Each ply of the membrane laminate consists of nonlinearly elastic fibers. Since fibers can have different stiffnesses, the model is able to describe anisotropic material behavior. The constitutive model has been applied to experiments on a healthy adventitia, and the model was able to reproduce the experimental results. The proposed material model for aneurysmal tissue supplies the basis for the growth model that has also been proposed. Healthy arterial tissue and aneurysmal tissue continuously renew itself by the turnover of its fibrous content. In aneurysmal tissue, the main fibrous constituent is collagen. Thus, new collagen is continuously deposited and old collagen is degraded. This collagen turnover is believed to be the driving mechanism in the development of aneurysms. When modeling the growth of aneurysms, the production rate of collagen is an important factor to consider. The proposed growth model is based on the principle that the material production of new collagen fibers in the aneurysm wall is governed by the stretching of the wall. In numerical simulations, the growth model is able to reproduce realistic aneurysm shapes found in the literature, and the resulting stresses in the aneurysm wall also agree well with experimental findings. When modeling aneurysmal tissue, a suitable constitutive model needs to be developed and the material parameters of this model have to be determined. For many materials, such as steels and polymers, this can readily be done by use of ordinary mechanical testing in the form of uniaxial tensile tests or biaxial tensile tests on manufactured rectangular or cylindrical test specimens. However, in some cases, it is not possible to simply manufacture a test specimen that fits the purposes of ordinary testing. This applies for example to testing of some soft biological tissues, including cerebral aneurysmal tissue. In these cases, the geometry of the test specimen is governed by nature. This also means that the test method has to be adjusted to the geometry of the test specimen, and it means that the experimental results cannot be directly interpreted in terms of material parameters, but an inverse analysis is needed. In an inverse analysis, some physical entity resulting from the experimental testing is predicted by a theoretical analysis, which depends on the material parameters that are to be determined. The discrepancy between the experimental outcome and the theoretical prediction is quantified by an error function. This error function is minimized with respect to the sought material parameters, which in this way are estimated. In our case, we propose an inverse method of this type to determine the material parameters of cerebral aneurysmal tissue. We propose a method where experiments are performed on a piece of tissue, clamped along its boundary and exposed to a surface pressure. The displacements of nodal points at different pressure levels are registered during the experiment. A finite element model of the test specimen is also defined, in which the constitutive behavior is governed by the material parameters that are to be determined. An error function, quantifying the discrepancy between the outcome of the experiments and the finite element analysis, is defined and minimized with respect to the material parameters. The proposed inverse method has been assessed in numerical simulations, and has been proved to work very well.