Modeling the transport phenomena within arterial wall: porous media approach

The transport of macromolecules, such as low-density lipoprotein (LDL), and their accumulation in the layers of the arterial wall play a critical role in the creation and development of atherosclerosis. Atherosclerosis is a disease of large arteries e.g., the aorta, coronary, carotid, and other proximal arteries that involves a distinctive accumulation of LDL and other lipid-bearing materials in the arterial wall. Over time, plaque hardens and narrows the arteries. The flow of oxygen-rich blood to organs and other parts of the body is reduced. This can lead to serious problems, including heart attack, stroke, or even death. It has been proven that the accumulation of macromolecules in the arterial wall depends not only on the ease with which materials enter the wall, but also on the hindrance to the passage of materials out of the wall posed by underlying layers. Therefore, attention was drawn to the fact that the wall structure of large arteries is different than other vessels which are disease-resistant. Atherosclerosis tends to be localized in regions of curvature and branching in arteries where fluid shear stress (shear rate) and other fluid mechanical characteristics deviate from their normal spatial and temporal distribution patterns in straight vessels. On the other hand, the smooth muscle cells (SMCs) residing in the media layer of the arterial wall respond to mechanical stimuli, such as shear stress. Shear stress may affect SMC proliferation and migration from the media layer to intima. This occurs in atherosclerosis and intimal hyperplasia. The study of blood flow and other body fluids and of heat transport through the arterial wall is one of the advanced applications of porous media in recent years. The arterial wall may be modeled in both macroscopic (as a continuous porous medium) and microscopic scales (as a heterogeneous porous medium). In the present study, the governing equations of mass, heat and momentum transport have been solved for different species and interstitial fluid within the arterial wall by means of computational fluid dynamics (CFD). Simulation models are based on the finite element (FE) and finite volume (FV) methods. The wall structure has been modeled by assuming the wall layers as porous media with different properties. In order to study the heat transport through human tissues, the simulations have been carried out for a non-homogeneous model of porous media. The tissue is composed of blood vessels, cells, and an interstitium. The interstitium consists of interstitial fluid and extracellular fibers. Numerical simulations are performed in a two-dimensional (2D) model to realize the effect of the shape and configuration of the discrete phase on the convective and conductive features of heat transfer, e.g. the interstitium of biological tissues. On the other hand, the governing equations of momentum and mass transport have been solved in the heterogeneous porous media model of the media layer, which has a major role in the transport and accumulation of solutes across the arterial wall. The transport of Adenosine 5´-triphosphate (ATP) is simulated across the media layer as a benchmark to observe how SMCs affect on the species mass transport. In addition, the transport of interstitial fluid has been simulated while the deformation of the media layer (due to high blood pressure) and its constituents such as SMCs are also involved in the model. In this context, the effect of pressure variation on shear stress is investigated over SMCs induced by the interstitial flow both in 2D and three-dimensional (3D) geometries for the media layer. The influence of hypertension (high pressure) on the transport of lowdensity lipoprotein (LDL) through deformable arterial wall layers is also studied. This is due to the pressure-driven convective flow across the arterial wall. The intima and media layers are assumed as homogeneous porous media. The results of the present study reveal that ATP concentration over the surface of SMCs and within the bulk of the media layer is significantly dependent on the distribution of cells. Moreover, the shear stress magnitude and distribution over the SMC surface are affected by transmural pressure and the deformation of the media layer of the aorta wall. This work reflects the fact that the second or even subsequent layers of SMCs may bear shear stresses of the same order of magnitude as the first layer does if cells are arranged in an arbitrary manner. This study has brought new insights into the simulation of the arterial wall, as the previous simplifications have been ignored. The configurations of SMCs used here with elliptic cross sections of SMCs closely resemble the physiological conditions of cells. Moreover, the deformation of SMCs with high transmural pressure which follows the media layer compaction has been studied for the first time. On the other hand, results demonstrate that LDL concentration through the intima and media layers changes significantly as wall layers compress with transmural pressure. It was also noticed that the fraction of leaky junctions across the endothelial cells and the area fraction of fenestral pores over the internal elastic lamina affect the LDL distribution dramatically through the thoracic aorta wall. The simulation techniques introduced in this work can also trigger new ideas for simulating porous media involved in any biomedical, biomechanical, chemical, and environmental engineering applications.

Computational modeling of stented coronary arteries

The application of computational fluid dynamics (CFD) and finite element analysis (FEA) has been growing rapidly in the various fields of science and technology. One of the areas of interest is in biomedical engineering. The altered hemodynamics inside the blood vessels plays a key role in the development of the arterial disease called atherosclerosis, which is the major cause of human death worldwide. Atherosclerosis is often treated with the stenting procedure to restore the normal blood flow. A stent is a tubular, flexible structure, usually made of metals, which is driven and expanded in the blocked arteries. Despite the success rate of the stenting procedure, it is often associated with the restenosis (re-narrowing of the artery) process. The presence of non-biological device in the artery causes inflammation or re-growth of atherosclerotic lesions in the treated vessels. Several factors including the design of stents, type of stent expansion, expansion pressure, morphology and composition of vessel wall influence the restenosis process. Therefore, the role of computational studies is crucial in the investigation and optimisation of the factors that influence post-stenting complications. This thesis focuses on the stent-vessel wall interactions followed by the blood flow in the post-stenting stage of stenosed human coronary artery. Hemodynamic and mechanical stresses were analysed in three separate stent-plaque-artery models. Plaque was modeled as a multi-layer (fibrous cap (FC), necrotic core (NC), and fibrosis (F)) and the arterial wall as a single layer domain. CFD/FEA simulations were performed using commercial software packages in several models mimicking the various stages and morphologies of atherosclerosis. The tissue prolapse (TP) of stented vessel wall, the distribution of von Mises stress (VMS) inside various layers of vessel wall, and the wall shear stress (WSS) along the luminal surface of the deformed vessel wall were measured and evaluated. The results revealed the role of the stenosis size, thickness of each layer of atherosclerotic wall, thickness of stent strut, pressure applied for stenosis expansion, and the flow condition in the distribution of stresses. The thicknesses of FC, and NC and the total thickness of plaque are critical in controlling the stresses inside the tissue. A small change in morphology of artery wall can significantly affect the distribution of stresses. In particular, FC is the most sensitive layer to TP and stresses, which could determine plaque’s vulnerability to rupture. The WSS is highly influenced by the deflection of artery, which in turn is dependent on the structural composition of arterial wall layers. Together with the stenosis size, their roles could play a decisive role in controlling the low values of WSS (<0.5 Pa) prone to restenosis. Moreover, the time dependent flow altered the percentage of luminal area with WSS values less than 0.5 Pa at different time instants. The non- Newtonian viscosity model of the blood properties significantly affects the prediction of WSS magnitude. The outcomes of this investigation will help to better understand the roles of the individual layers of atherosclerotic vessels and their risk to provoke restenosis at the post-stenting stage. As a consequence, the implementation of such an approach to assess the post-stented stresses will assist the engineers and clinicians in optimizing the stenting techniques to minimize the occurrence of restenosis.

Cell wall thickness and tangential and radial cell diameter of fertilized and irrigated Norway spruce

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Slits in container wall improve root structure and stem straightness of outplanted Scots pine seedlings

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Intra-specific variation in cell wall constituents of needle age classes of Pinus sylvestris in relation to soil fertility status in Southwest England

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Measurement systems in wall production applications

Tässä tutkimuksessa kehitettiin prototyyppi betonielementin dimension mittaus järjestelmästä. Tämä järjestelmä mahdollistaa kolmiulotteisen kappaleen mittauksen. Tutkimuksessa kehitettiin myös stereonäköön perustuva kappaleen mittaus. Prototyyppiä testailin ja tulokset osoittautuivat luotettaviksi. Tutkimuksessa selvitetään ja vertaillaan myös muita lähestymistapoja ja olemassa olevia järjestelmiä kappaleen kolmiuloitteiseen mittaukseen, joita Suomalaiset yhtiöt käyttävät tällä alalla.

Survival and Quality of Life among Patients with Severe Lower Extremity Peripheral Arterial Disease

Lower extremity peripheral arterial disease (PAD) is associated with decreased functional status, diminished quality of life (QoL), amputation, myocardial infarction, stroke, and death. Nevertheless, public awareness of PAD as a morbid and mortal disease is low. The aim of this study was to assess the incidence of major lower extremity amputation due to PAD, the extent of reamputations, and survival after major lower extremity amputation (LEA) in a population based PAD patient cohort. Furthermore, the aim was to assess the functional capacity in patients with LEA, and the QoL after lower extremity revascularization and major amputation. All 210 amputees due to PAD in 1998–2002 and all 519 revascularized patients in 1998–2003 were explored. 59 amputees alive in 2004 were interviewed using a structured questionnaire of QoL. Two of each amputee age-, gender- and domicile-matched controls filled in and returned postal self-administered QoL questionnaire as well as 231 revascularized PAD patients (the amount of these patients who engaged themselves to the study), and one control person for each patient completed postal self-administered QoL questionnaire. The incidence rate of major LEA was 24.1/100 000 person-years and it was considerably high during the years studied. The one-month mortality rate was 21%, 52% at one-year, and the overall mortality rate was 80%. When comparing the one-year mortality risk of amputees, LEAs were associated with a 7.4-fold annual mortality risk compared with the reference population in Turku. Twenty-two patients (10%) had ipsilateral transversions from BK to AK amputation. Fifty patients (24%) ended up with a contralateral major LEA within two to four amputation operations. Three bilateral amputations were performed at the first major LEA operation. Of the 51 survivors returning home after their first major LEA, 36 (71%) received a prosthesis; (16/36, 44%) and were able to walk both in- and outdoors. Of the 68 patients who were discharged to institutional care, three (4%) had a prosthesis one year after LEA. Both amputees and revascularized patients had poor physical functioning and significantly more depressive symptoms than their controls. Depressive symptoms were more common in the institutionalized amputees than the home-dwelling amputees. The surviving amputees and their controls had similar life satisfaction. The amputees felt themselves satisfied and contented, whether or not they lived in long-term care or at home. PAD patients who had undergone revascularizations had poorer QoL than their controls. The revascularized patients’ responses on their perceived physical functioning gave an impression that these patients are in a declining life cycle and that revascularizations, even when successful, may not be sufficient to improve the overall function. It is possible that addressing rehabilitation issues earlier in the care may produce a more positive functional outcome. Depressive symptoms should be recognized and thoroughly considered at the same time the patients are recovering from their revascularization operation. Also primary care should develop proper follow-up, and community organizations should have exercise groups for those who are able to return home, since they very often live alone. In rehabilitation programs we should consider not only physical disability assessment but also QoL.

Pulsatile Blood Flow Simulations in Computed Tomography(CT) Scan-Based and Idealized Geometries of Human Aorta

Blood flow in human aorta is an unsteady and complex phenomenon. The complex patterns are related to the geometrical features like curvature, bends, and branching and pulsatile nature of flow from left ventricle of heart. The aim of this work was to understand the effect of aorta geometry on the flow dynamics. To achieve this, 3D realistic and idealized models of descending aorta were reconstructed from Computed Tomography (CT) images of a female patient. The geometries were reconstructed using medical image processing code. The blood flow in aorta was assumed to be laminar and incompressible and the blood was assumed to be Newtonian fluid. A time dependent pulsatile and parabolic boundary condition was deployed at inlet. Steady and unsteady blood flow simulations were performed in real and idealized geometries of descending aorta using a Finite Volume Method (FVM) code. Analysis of Wall Shear Stress (WSS) distribution, pressure distribution, and axial velocity profiles were carried out in both geometries at steady and unsteady state conditions. The results obtained in thesis work reveal that the idealization of geometry underestimates the values of WSS especially near the region with sudden change of diameter. However, the resultant pressure and velocity in idealized geometry are close to those in real geometry

Application of Computational Fluid Dynamics in Modeling Blood Flow in Human Thoracic Aorta

The aim of this study was to simulate blood flow in thoracic human aorta and understand the role of flow dynamics in the initialization and localization of atherosclerotic plaque in human thoracic aorta. The blood flow dynamics in idealized and realistic models of human thoracic aorta were numerically simulated in three idealized and two realistic thoracic aorta models. The idealized models of thoracic aorta were reconstructed with measurements available from literature, and the realistic models of thoracic aorta were constructed by image processing Computed Tomographic (CT) images. The CT images were made available by South Karelia Central Hospital in Lappeenranta. The reconstruction of thoracic aorta consisted of operations, such as contrast adjustment, image segmentations, and 3D surface rendering. Additional design operations were performed to make the aorta model compatible for the numerical method based computer code. The image processing and design operations were performed with specialized medical image processing software. Pulsatile pressure and velocity boundary conditions were deployed as inlet boundary conditions. The blood flow was assumed homogeneous and incompressible. The blood was assumed to be a Newtonian fluid. The simulations with idealized models of thoracic aorta were carried out with Finite Element Method based computer code, while the simulations with realistic models of thoracic aorta were carried out with Finite Volume Method based computer code. Simulations were carried out for four cardiac cycles. The distribution of flow, pressure and Wall Shear Stress (WSS) observed during the fourth cardiac cycle were extensively analyzed. The aim of carrying out the simulations with idealized model was to get an estimate of flow dynamics in a realistic aorta model. The motive behind the choice of three aorta models with distinct features was to understand the dependence of flow dynamics on aorta anatomy. Highly disturbed and nonuniform distribution of velocity and WSS was observed in aortic arch, near brachiocephalic, left common artery, and left subclavian artery. On the other hand, the WSS profiles at the roots of branches show significant differences with geometry variation of aorta and branches. The comparison of instantaneous WSS profiles revealed that the model with straight branching arteries had relatively lower WSS compared to that in the aorta model with curved branches. In addition to this, significant differences were observed in the spatial and temporal profiles of WSS, flow, and pressure. The study with idealized model was extended to study blood flow in thoracic aorta under the effects of hypertension and hypotension. One of the idealized aorta models was modified along with the boundary conditions to mimic the thoracic aorta under the effects of hypertension and hypotension. The results of simulations with realistic models extracted from CT scans demonstrated more realistic flow dynamics than that in the idealized models. During systole, the velocity in ascending aorta was skewed towards the outer wall of aortic arch. The flow develops secondary flow patterns as it moves downstream towards aortic arch. Unlike idealized models, the distribution of flow was nonplanar and heavily guided by the artery anatomy. Flow cavitation was observed in the aorta model which was imaged giving longer branches. This could not be properly observed in the model with imaging containing a shorter length for aortic branches. The flow circulation was also observed in the inner wall of the aortic arch. However, during the diastole, the flow profiles were almost flat and regular due the acceleration of flow at the inlet. The flow profiles were weakly turbulent during the flow reversal. The complex flow patterns caused a non-uniform distribution of WSS. High WSS was distributed at the junction of branches and aortic arch. Low WSS was distributed at the proximal part of the junction, while intermedium WSS was distributed in the distal part of the junction. The pulsatile nature of the inflow caused oscillating WSS at the branch entry region and inner curvature of aortic arch. Based on the WSS distribution in the realistic model, one of the aorta models was altered to induce artificial atherosclerotic plaque at the branch entry region and inner curvature of aortic arch. Atherosclerotic plaque causing 50% blockage of lumen was introduced in brachiocephalic artery, common carotid artery, left subclavian artery, and aortic arch. The aim of this part of the study was first to study the effect of stenosis on flow and WSS distribution, understand the effect of shape of atherosclerotic plaque on flow and WSS distribution, and finally to investigate the effect of lumen blockage severity on flow and WSS distributions. The results revealed that the distribution of WSS is significantly affected by plaque with mere 50% stenosis. The asymmetric shape of stenosis causes higher WSS in branching arteries than in the cases with symmetric plaque. The flow dynamics within thoracic aorta models has been extensively studied and reported here. The effects of pressure and arterial anatomy on the flow dynamic were investigated. The distribution of complex flow and WSS is correlated with the localization of atherosclerosis. With the available results we can conclude that the thoracic aorta, with complex anatomy is the most vulnerable artery for the localization and development of atherosclerosis. The flow dynamics and arterial anatomy play a role in the localization of atherosclerosis. The patient specific image based models can be used to diagnose the locations in the aorta vulnerable to the development of arterial diseases such as atherosclerosis.