Elastic properties of anisotropic vascular membranes examined by inverse analysis

• An inverse method for estimating the distributions of the nonlinear elastic properties of inhomogeneous and anisotropic vascular membranes such as cerebral aneurysms is proposed. The material description of the membrane is based on a versatile structural model able to represent multiple collagen layers and the passive response of the vascular wall. Each individual layer is assumed to behave transversely isotropic following exponential stiffening with increasing loading. The model includes four parameters to be explainable physically: two initial stiffnesses of the collagen fabric, a parameter related to the nonlinearity of the collagen fabric, angle between the principal directions of the collagen fabric and a reference coordinate system. For this finite deformation problem a finite element framework for membranous structures considering pressure boundary loading is outlined. i.e. the principle of virtual work, its linearisation and the related spatial discretisation. The estimation procedure consists of the following three steps: (i) in vivo or in vitro approaches record the mechanical responses of membranous structures whose properties are to be determined; (ii) define a corresponding finite element model; (iii) minimise an error function (regarding the unknown parameters) that quantifies the deviation of the numerical prediction from the recorded data. To achieve a robust parameter estimation, an element partition method is employed. The outcome of the procedure is affected by the number of nodes defined on the membrane surface and the number of load steps. In a numerical example, the proposed procedure is assessed by reestablishing given reference distributions in a reference membrane. The deviations of the estimated material parameter distributions from the related reference fields are within just a few percent. In most of the investigated cases the standard deviation for the resulting maximum principal stress was even below 1%, which is accurate enough for rupture risk assessment of vascular membranes.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Maskinteknik -- Teknisk mekanik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering -- Applied Mechanics (hsv//eng)

TEKNIK OCH TEKNOLOGIER  -- Medicinteknik -- Medicinsk laboratorie- och mätteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Medical Engineering -- Medical Laboratory and Measurements Technologies (hsv//eng)

MEDICIN OCH HÄLSOVETENSKAP  -- Medicinsk bioteknologi -- Biomedicinsk laboratorievetenskap/teknologi (hsv//swe)

MEDICAL AND HEALTH SCIENCES  -- Medical Biotechnology -- Biomedical Laboratory Science/Technology (hsv//eng)

MEDICIN OCH HÄLSOVETENSKAP  -- Klinisk medicin -- Kardiologi (hsv//swe)

MEDICAL AND HEALTH SCIENCES  -- Clinical Medicine -- Cardiac and Cardiovascular Systems (hsv//eng)

Nyckelord

Anisotropic

Artery

Constitutive modelling

Hyperelastic

Inhomogeneous

Inverse analysis

Membrane

Solid mechanics

Fastkroppsmekanik

Medical engineering

Medicinsk teknik

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