Gwm Gerrit Peters

A three-dimensional computational analysis of fluid–structure interaction in the aortic valve

Numerical analysis of the aortic valve has mainly been focused on the closing behaviour during the diastolic phase rather than the kinematic opening and closing behaviour during the systolic phase of the cardiac cycle. Moreover, the fluid-structure interaction in the aortic valve system is most frequently ignored in numerical modelling. The effect of this interaction on the valves behaviour during systolic functioning is investigated. The large differences in material properties of fluid and structure and the finite motion of the leaflets complicate blood-valve interaction modelling. This has impeded numerical analyses of valves operating under physiological conditions. A numerical method, known as the Lagrange multiplier based fictitious domain method, is used to describe the large leaflet motion within the computational fluid domain. This method is applied to a three-dimensional finite element model of a stented aortic valve. The model provides both the mechanical behaviour of the valve and the blood flow through it. Results show that during systole the leaflets of the stented valve appear to be moving with the fluid in an essentially kinematical process governed by the fluid motion.

A two-dimensional fluid–structure interaction model of the aortic value

Failure of synthetic heart valves is usually caused by tearing and calcification of the leaflets. Leaflet fiber-reinforcement increases the durability of these valves by unloading the delicate parts of the leaflets, maintaining their physiological functioning. The interaction of the valve with the surrounding fluid is essential when analyzing its functioning. However, the large differences in material properties of fluid and structure and the finite motion of the leaflets complicate blood-valve interaction modeling. This has, so far, obstructed numerical analyses of valves operating under physiological conditions. A two-dimensional fluid-structure interaction model is presented, which allows the Reynolds number to be within the physiological range, using a fictitious domain method based on Lagrange multipliers to couple the two phases. The extension to the three-dimensional case is straightforward. The model has been validated experimentally using laser Doppler anemometry for measuring the fluid flow and digitized high-speed video recordings to visualize the leaflet motion in corresponding geometries. Results show that both the fluid and leaflet behaviour are well predicted for different leaflet thicknesses.

Development and validation of a recoverable strain-based model for flow-induced crystallization of polymers

Full Paper: A model for the description of the combined process of quiescent and flow-induced crystallization of polymers is presented. The model allows to predict in detail the spatial distribution of the crystalline structure in semi-crystalline products. Based on this structure, the final mechanical properties, shape and dimension stability of those products can be modeled. For quiscent crystallization kinetics we use the Schneider rate equations. [1] For flow-induced crystallization we have modified the Eder rate equations. [2] Where Eder used the shear rate as the driving force for flow-induced nucleation and crystallization, the modification proposed here adds a viscoelastic equation to account for molecular orientation, in particular that of the high-end tail of the molecular weight distribution. This is expressed in terms of the elastic Finger tensor with the highest relaxation time. The second invariant of this tensor, equivalent to the order parameter for a nematic phase, is used as the driving force for flow-induced nucleation and crystallization and, consequently, a coupling between rheology and structure formation is obtained.

Mechanical properties of brain tissue by indentation: Interregional variation

Although many studies on the mechanical properties of brain tissue exist, some controversy concerning the possible differences in mechanical properties of white and gray matter tissues remains. Indentation experiments are conducted on white and gray matter tissues of various regions of the cerebrum and on tissue from the thalamus and the midbrain to study interregional differences. An advantage of indentation, when compared to standard rheological tests as often used for the characterization of brain tissue, is that it is a local test, requiring only a small volume of tissue to be homogeneous. Indentation tests are performed at different speeds and the force relaxation after a step indent is measured as well. White matter tissue is found to be stiffer than gray matter and to show more variation in response between different samples which is consistent with structural differences between white matter and gray matter. In addition to differences between white matter and gray matter, also different regions of brain tissue are compared.

The influence of test conditions on characterization of the mechanical properties of brain tissue.

To understand brain injuries better, the mechanical properties of brain tissue have been studied for 50 years; however, no universally accepted data set exists. The variation in material properties reported may be caused by differences in testing methods and protocols used. An overview of studies on the mechanical properties of brain tissue is given, focusing on testing methods. Moreover, the influence of important test conditions, such as temperature, anisotropy, and precompression was experimentally determined for shear deformation. The results measured at room temperature show a stiffer response than those measured at body temperature. By applying the time-temperature superposition, a horizontal shift factor a(T)=8.5-11 was found, which is in agreement with the values found in literature. Anisotropy of samples from the corona radiata was investigated by measuring the shear resistance for different directions in the sagittal, the coronal, and the transverse plane. The results measured in the coronal and the transverse plane were 1.3 and 1.25 times stiffer than the results obtained from the sagittal plane. The variation caused by anisotropy within the same plane of individual samples was found to range from 25% to 54%. The effect of precompression on shear results was investigated and was found to stiffen the sample response. Combinations of these and other factors (postmortem time, donor age, donor type, etc.) lead to large differences among different studies, depending on the different test conditions.

Linear viscoelastic behavior of subcutaneous adipose tissue

Subcutaneous adipose tissue contributes to the overall mechanical behavior of the skin. Until today, however, no thorough constitutive model is available for this layer of tissue. As a start to the development of such a model, the objective of this study was to measure and describe the linear viscoelastic behavior of subcutaneous adipose tissue. Although large strains occur in vivo, this work only focuses on the linear behavior to show the applicability of the described methods to adipose tissue. Shear experiments are performed on porcine samples on a rotational rheometer using parallel plate geometry. In the linear viscoelastic regime, up to 0.1% strain, the storage and loss modulus showed a frequency- and temperature-dependent behavior. The ratio between the two moduli, the phase angle, did not show any dependency on temperature and frequency. The shear modulus was found to be 7.5 kPa at 10 rad/s and 37 degrees C. Time-temperature superposition was applicable through shifting the shear modulus horizontally. A power-law function model was introduced to describe both the frequency dependent behavior at constant temperature and the stress relaxation behavior. In addition, the effect of snap freezing as a preservation method was analyzed. Histological examination demonstrated possible tissue damage after freezing, but the mechanical properties did not change. Since results were reproducible, it is concluded that the methods we used are most probably suited to explore the non-linear behavior of subcutaneous adipose tissue.

Remodelling of continuously distributed collagen fibres in soft connective tissues

Extracellular matrix remodelling plays an essential role in tissue engineering of load-bearing structures. The goal of this study is to model changes in collagen fibre content and orientation in soft connective tissues due to mechanical stimuli. A theory is presented describing the mechanical condition within the tissue and accounting for the effects of collagen fibre alignment and changes in fibre content. A fibre orientation tensor is defined to represent the continuous distribution of collagen fibre directions. A constitutive model is introduced to relate the fibre configuration to the macroscopic stress within the material. The constitutive model is extended with a structural parameter, the fibre volume fraction, to account for the amount of fibres present within the material. It is hypothesised that collagen fibre reorientation is induced by macroscopic deformations and the amount of collagen fibres is assumed to increase with the mean fibre stretch. The capabilities of the model are demonstrated by considering remodelling within a biaxially stretched cube. The model is then applied to analyse remodelling within a closed stented aortic heart valve. The computed preferred fibre orientation runs from commissure to commissure and resembles the fibre directions in the native aortic valve.

Design and numerical implementation of a 3-D non-linear viscoelastic constitutive model for brain tissue during impact

Finite Element (FE) head models are often used to understand mechanical response of the head and its contents during impact loading in the head. Current FE models do not account for non-linear viscoelastic material behavior of brain tissue. We developed a new non-linear viscoelastic material model for brain tissue and implemented it in an explicit FE code. To obtain sufficient numerical accuracy for modeling the nearly incompressible brain tissue, deviatoric and volumetric stress contributions are separated. Deviatoric stress is modeled in a non-linear viscoelastic differential form. Volumetric behavior is assumed linearly elastic. Linear viscoelastic material parameters were derived from published data on oscillatory experiments, and from ultrasonic experiments. Additionally, non-linear parameters were derived from stress relaxation (SR) experiments at shear strains up to 20%. The model was tested by simulating the transient phase in the SR experiments not used in parameter determination (strains up to 20%, strain rates up to 8s(-1)). Both time- and strain-dependent behavior were predicted accurately (R2>0.96) for strain and strain rates applied. However, the stress was overestimated systematically by approximately 31% independent of strain(rate) applied. This is probably caused by limitations of the experimental data at hand.

Electrospinning versus knitting: two scaffolds for tissue engineering of the aortic valve

Two types of scaffolds were developed for tissue engineering of the aortic valve; an electrospun valvular scaffold and a knitted valvular scaffold. These scaffolds were compared in a physiologic flow system and in a tissue-engineering process. In fibrin gel enclosed human myofibroblasts were seeded onto both types of scaffolds and cultured for 23 days under continuous medium perfusion. Tissue formation was evaluated by confocal laser scanning microscopy, histology and DNA quantification. Collagen formation was quantified by a hydroxyproline assay. When subjected to physiologic flow, the spun scaffold tore within 6 h, whereas the knitted scaffold remained intact. Cells proliferated well on both types of scaffolds, although the cellular penetration into the spun scaffold was poor. Collagen production, normalized to DNA content, was not significantly different for the two types of scaffolds, but seeding efficiency was higher for the spun scaffold, because it acted as a cell impermeable filter. The knitted tissue constructs showed complete cellular in-growth into the pores. An optimal scaffold seems to be a combination of the strength of the knitted structure and the cell-filtering ability of the spun structure.

Collagen fibers reduce stresses and stabilize motion of aortic valve leaflets during systole

The effect of collagen fibers on the mechanics and hemodynamics of a trileaflet aortic valve contained in a rigid aortic root is investigated in a numerical analysis of the systolic phase. Collagen fibers are known to reduce stresses in the leaflets during diastole, but their role during systole has not been investigated in detail yet. It is demonstrated that also during systole these fibers substantially reduce stresses in the leaflets and provide smoother opening and closing. Compared to isotropic leaflets, collagen reinforcement reduces the fluttering motion of the leaflets. Due to the exponential stress-strain behavior of collagen, the fibers have little influence on the initial phase of the valve opening, which occurs at low strains, and therefore have little impact on the transvalvular pressure drop.