Fluid structure interaction in fully collapsible tubes

Paper presented at the 8th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics, Mauritius, 11-13 July, 2011.The main goal of the developed theory is to formulate the biomechanical conditions (geometrical dimensions, viscoelastic properties of veins and blood fluid flow conditions) at which an unstable behavior or even the vein collapse can occur. The above problems are numerically modeled by the finite element method. The weak formulation of the tube deformation is based on the virtual work principle. The mixed formulation of the finite element method with the separately interpolated pressure is used for the structure. The strong coupling of both structure and fluid solvers allow us to simulate self-induced large deflection oscillations of the tube. Provided that the Neo-Hook’s material model was applied the analytical formula for the collapse conditions was found. It was proved that for the brain vein contraction about 5%, the vein collapse can occurs even under normal physiological condition – the angiosynizesis. The fluid structure interaction is studied experimentally on the special experimental line. The fluid structure phenomenon is investigated both for the continuous and pulsating flow and it is evaluated by a non-invasive optical. The method is based on optical measurements of radial displacement of the pulsating tube wall. The simultaneous clinics observation (histological findings), in vitro experiments and numerical modeling gives sufficient data to predict biomechanical conditions of the angiosynizesis.mp201

Title: Ex vivo coronary stent implantation evaluated with digital image correlation

Abstract: Intracoronary stenting (PCI) has become standard revascularization technique to reopen blocked arteries. Although significant progress in stenting technology and implantation techniques has been made a number of problems remain. Specifically, stent sizing and inflation pressures are still a matter of scientific debates. Despite a large number of biomechanical computational simulations experimental data are rare, likely due to technical difficulties to measure dilatation pressures and coronary dimensions in the same settings. Our study shows that valuable data can be obtained by employing digital image correlation for 3D strain measurement during stent inflation ex-vivo that can provide further insight into the stent-artery wall interactions. Keywords: Artery wall-stent interaction; coronary stent; digital image correlation; experimental implantation; strain. 3 Abstract/Introduction Intracoronary stenting (PCI) has become standard revascularization technique to reopen blocked arteries. Although significant progress in stenting technology and implantation techniques has been made a number of problems remain Despite a large number of biomechanical computational simulations [3, Methods Stent and PCI equipment The balloon-expandable CoCr coronary stent Kaname TM (Terumo Corporation, Tokyo, Japan) with nominal diameter 3.5 mm, and length 15 mm (at pressure 0.9 MPa; and diameter 3.73 mm at 1.6 MPa) was used in this study. The stent was premounted on PCI dilatation catheter RX-2 (Terumo Corporation). Sample The sample of the main branch of the left coronary artery was obtained from autopsy. The male donor was 40 years old and atherosclerotic lesions were presented inside the sample. The experiment was performed 70 hours post mortem. Experiment The sample was mounted into the experimental setup ( Displacement measurement was based on 3D digital image correlation (DIC) conducted with commercial system Dantec Q-450 (Dantec Dynamics, Ulm, Germany). 4 DIC is non-contact optical method based on the stereoscopic principle which is becoming more popular especially within the strain measurement of geometrically nonuniform objects. The algorithm identifies material points on the object surface and the correlation between consecutive images allows material point tracking. Detailed description can be found in the literature The artery was recorded with two digital cameras (NanoSens Mk III, Dantec Dynamics; 1MPx CCD chip; lens Sigma EX, 105 mm, 1:2.8 D Macro) during the balloon expansion (sampling rate 25 Hz). In fully expanded state, the object ROI approx. 18*3 mm*mm was projected onto 600*300 px*px (in each camera). RX2 manometer was recorded with another camera to obtain time course of change of the balloon distending pressure (pressure transducer connected with PC was not available at the time of experiment). The stent was deployed within manual pressurization up to 1.6 MPa which spanned approximately 42 seconds. Results DIC revealed significant overloading of the artery by the expanded stent. The results are depicted in Principal strains' distribution (Green-Lagrange strain is considered within this study) shows artery response within maximally expanded stent. Principal vectors are predominantly aligned with the circumferential and longitudinal direction which is supposed to be the consequence of the cylindrical stent expansion. Circumferential deformation attains 0.5 mm/mm at the peak value which is far beyond physiological situation. The circumferential strain concentration appears non-symmetrically with respect to the length of the sample which is supposed to be the result of irregular reference geometry (an asymmetrical partially occluded lumen of the artery). Six points (P1-6) were chosen to illustrate specific strain values resulting from different loading conditions and atherosclerotic specimen in our experiment. Discussion This is a preliminary report concerning a stent implantation in ex-vivo settings employing a human coronary artery harvested from autopsy. The results suggest that 3D DIC is promising tool suitable for the evaluation of ex-vivo stent implantation potentially useful for validation of computational models and clinical considerations. Presented results suggest that overexpansion of a stent during deployment may overstretch the target site potentially resulting in implantation injury associated with restenosis and/or intimal tears associated with dissections. To obtain exact intraluminal dimensions during stent deployment optical coherence tomography or intravascular ultrasound (IVUS) would be required, currently not available in our laboratory. Nevertheless we plan to combine IVUS with 3D DIC in future experiments

Effects of Age and Loading Velocity on the Delamination Strength of the Human Aorta

Delamination strength is the mechanical property which plays a key role in the pathological process referred to as Arterial Dissection. This dissection, known especially for its occurrence in the thoracic aorta, is manifested by a separation of the layers of an artery wall, and may end with total rupture and internal haemorrhaging. Although its incidence is relatively rare, from 3 to 6 cases per 100 000 per year, it is a life-threating disease with a significant lethality [1-3]. The exact conditions under which the dissection is initiated, and as a crack propagates through the arterial wall, remain an open topic in computational as well as experimental mechanics. The aim of our study is to contribute to the deepening of our knowledge of Arterial Dissection, by collecting experimental data which is suitable for the purpose of showing how the delamination strength measured in the peeling experiments depends on age and anatomical location. In addition to the effects of age and location, our study also focuses on the effect of loading rate. The experimental branch of our research is complemented by a computational modelling of the delamination interface, in which we are looking for a numerical characterization of the material parameters describing discontinuity propagation. An XFEM model of the peeling experiment is built in Abaqus, which in our approach plays the role of the regression analysis, incorporating the cohesive zone (CZ) in order to model the delaminating arterial layers. The main objective is to obtain a detailed description of a set of constitutive parameters, which would be age- and location-specific. Our present data suggest that delamination strength strongly depends on age, and furthermore, the anatomical site also seems to be a significant factor. On the other hand, the loading velocity does not cause significant changes in results

Biological and hydrodynamic stress influences on brewing yeast strains' physiological status during beer production

Biological hydrodynamic stress influences on yeast and the resulting consequences on beer stability have been investigated. Yeast cells subjected to stress during beer production have a negative effect on its physiological status. Cell wall and membrane constituents determine the cells capacity to adapt to stress. A relationship has been established that yeast cell wall mannan, an unfilterable haze constituent, as a function of hydrodynamic stress exposure, is released from the cell wall while concurrently, particle size in the supernatant, and beer haze increased. In high gravity wort (20 °Plato), compared to lower gravity wort (12 °Plato), there is an increase in the number of damaged cells and lower intracellular glycogen and trehalose levels, indicating stressed cells. Cell viability and intracellular pH decreased due to processing conditions encountered during yeast cropping with a centrifuge. Furthermore, yeast intracellular glycogen and trehalose levels were depleted as a result of centrifugation. A comprehensive evaluation of yeast fermentation predictors such as viability, damaged cells, intracellular pH (PHi), intracellular glycogen and trehalose is of vital importance. The flow cytometer is able to rapidly reform numerous accurate yeast physiology analyses, providing information that will optimize yeast management circuits, improve fermentation efficiency resulting in enhanced beer quality.IBD Grants Committe

Approximation solution of 0D pulsatile flow within a capillary

This action is realized by the project NEXLIZ - CZ.1.07/2.3.00/30.0038, which is co-financed by the European social fund and the state budget of the Czech republic

A comparison between the exponential and limiting fiber extensibility pseudo-elastic model for the Mullins effect in arterial tissue

This study compares the capability of two different mathematical forms of the so-called softening variable to describe strain-induced stress softening observed within cyclic uniaxial tension of the human thoracic aorta. Specifically, the softening variable, which serves as the stress reduction factor, was considered to be tangent hyperbolic-based and error function-based. The mechanical response of the aorta was assumed to be pseudo-hyperelastic, incompressible and anisotropic. The strain energy density function was employed in a classical exponential form and in a not well-known limiting fiber extensibility model. This study revealed that both the limiting fiber extensibility and exponential models of the strain energy describe mechanical the response of the material with similar results. It was found that it is not a matter which kind of the softening variable is employed. It was concluded that such an approach can fit the Mullins effect in the human aorta, however the question of the best fitting model still remains.Praca zawiera analizę porównawczą poprawności dwóch różnych matematycznych sformułowań tzw. zmiennej osłabienia przy opisie zjawiska osłabienia naprężeń indukowanych odkształceniem obserwowanym podczas cyklicznego jednoosiowego rozciągania aorty piersiowej. W szczególności, zmienną osłabienia jako czynnika redukującego poziom naprężeń opisano funkcją typu tangens hiperboliczny oraz funkcją błędu. Założono, że mechaniczne właściwości aorty odpowiadają modelowi pseudohipersprężystemu, nieściśliwemu i anizotropowemu. Funkcję gęstości energii odkształcenia przyjęto w klasycznej formie wykładniczej i mało rozpoznanej postaci, która ogranicza zakres rozszerzalności włókien. Badania wykazały, że obydwa podejścia opisują właściwości mechaniczne tkanki z podobnym skutkiem. Pokazano, że rodzaj przyjętej zmiennej osłabienia nie ma wpływu na rezultaty badań. W konkluzji podkreślono, że obydwa modele nadają się do analizy efektu Mullinsa w aorcie, jakkolwiek nadal otwartą kwestią pozostaje problem znalezienia najlepiej dopasowanego modelu do opisu tego zjawiska

Inflation tests and modelling of Human Saphenous Veins

This action is realized by the project NEXLIZ - CZ.1.07/2.3.00/30.0038, which is co-financed by the European social fund and the state budget of the Czech republic

Limiting fiber extensibility model for arterial wall

Arterial walls exhibit anisotropic, nonlinear and inelastic response to external loads. Moreover arterial wall is non–homogenous material with complicated internal structure. These facts make the question about the best material model for arterial wall still unanswered. Nowadays approach to building constitutive models is characterized by incorporating structural information when considering e.g. layers, fibers, fiber orientation or waviness. The most frequent method how to incorporate structural information is to regard arterial wall as a fiber reinforced composite. Considerations about preferred directions are subsequently implemented into the framework of continuum mechanics. Constitutive models are usually based on the theory of hyperelastic materials. Thus mechanical response of an arterial wall is supposed to be governed by a strain energy (or free energy) density function like in (1). The theory of hyperelastic materials is widely applied and studied in details in polymer science. Due to some phenomenological and structural similarities between rubber–like materials and biological tissues, methods of polymer physics are frequently applied in biomechanics, see Holzapfel [1]. Gent [2] suggested the new isotropic model for strain energy density function which was based on an assumption of limiting chain extensibility in polymer materials. The Gent model expresses strain energy y as a function of first invariant I1 of the right Cauchy-Green strain tensor as follows [formula]. In equation (1) μ denotes stress–like parameter, so–called infinitesimal shear modulus. Jm denotes limiting value of I 1 -3. The domain of logarithm requires [formula]. Thus, Jm can be interpreted as limiting value for macromolecular chains stretch. Horgan and Saccomandi in [3] suggested its anisotropic extension. They recently published modification based on usual concept of anisotropy related to fiber reinforcement, see paper [4]. Horgan and Saccomandi use rational approximations to relate the strain energy expression to Cauchy stress representation formula. We adopted this term with small modification as follows [formula] In (2) μ denote shear modulus. J m is the material parameter related to limiting extensibility of fibers. The similar definitional inequality like in (1) must be hold for logarithm in (2). Thus I 4 must satisfy [formula] denotes so called fourth pseudo–invariant of the right Cauchy-Green strain tensor which arises from the existence of preferred direction in continuum. It is worth to note that total number of invariants of the strain tensor is five in the case of transversely isotropic material and nine in the case of orthotropy. Details can be found in e.g. Holzapfel [5]. Model (2) presumes two preferred directions in continuum which are mechanically equivalent. Due to cylindrical shape of an artery we can imagine it as helices with same helix angel but with antisymmetric rientation. This is illustrated in the FIG. 1 I 4 can be expressed in the form given in (3) [formula] Stretched configuration of the tube is characterized by λ t , what denotes circumferential stretch and λ z what denotes axial stretch, respectively. Model (2) contains three material parameters. Above described μ, J m and β. The third material parameter β has the meaning of angle between fiber direction and circumferential axis. There are two families of fibers with angle ±β, however, I 4 is symmetric with respect to ±β. In order to verify capability of (2) to govern multi–axial mechanical response of an artery regression analysis based on previously published experimental data was performed. Details of experimental method and specimen can be found in Horny et al. [6]. Briefly we resume basic facts. Male 54–year–old sample of thoracic aorta underwent inflation test under constant axial stretch. The tubular sample was 6 times pressurized in the range 0kPa–18kPa–0kPa under axial pre–stretch λ z =1.3 and 3 times in the pressure range 0kPa–20kPa–0kPa under λ z =1.42, respectively. The opening angle was measured in order to account residual strains. Radial displacements were photographed and evaluated by image analysis. Regression analysis based on least square method gave the estimations for material parameters μ, Jm and β. The vessel was modeled as thick–walled tube with residual strains. The material was supposed to be hyperelastic and incompressible. No shear strains were considered. Fitting of material model was based on comparison of model predicted and measured values of internal pressure. Results are illustrated in FIG. 2. We can conclude that proposed material model fits experimental data successfully. Thus strain energy given in (2) is suitable to govern arterial response during its inflation and extension. Estimated values of parameters for material model (2) are as follows: μ =26kPa; J m =1.044; β=37.2