J. Mazumdar

Unsteady stenosis flow prediction: a comparative study of non-Newtonian models with operator splitting scheme.

This paper presents a comparative study of non-Newtonian and Newtonian models of blood. A non-Newtonian incompressible 2-D Navier-Stokes (N-S) solver has been developed using Fasttalk language within the Fastflo environment. It is based on the method of operator splitting with artificial compressibility technique. The Power law and Casson models have been used as the constitutive equations for blood with a hematocrit of approximately 45%. These two non-Newtonian models and the Newtonian model are used to simulate unsteady flow through a hypothetical stenotic geometry over an aperiodic time interval of 1 s. Through comparison of the results of the three models, it was found that the wall shear stress (WSS) distribution over the time interval was comparable for both non-Newtonian models. The peak WSS for the Newtonian model had the lowest value. The peak wall shear stress gradient (WSSG) for the Power law was the highest, followed by the Casson and Newtonian models. Flow characteristics such as higher pressure drop across the stenosis, location and movement of vortex were similar in all three models. Non-Newtonian effects were most significant in the vicinity of the stenosis.

A mathematical study of peristaltic transport of a casson fluid

In this paper, the peristaltic flow of rheologically complex physiological fluids when modelled by a non-Newtonian Casson fluid in a two-dimensional channel is considered. A perturbation series method of solution of the stream function for zeroth and first order in amplitude ratio is sought. Of interest is the difference between peristaltic transport of Newtonian and non-Newtonian fluids. It is found that Newtonian fluid is an important subclass of non-Newtonian fluids that may adequately represent some physiological phenomena. Analytical and numerical solutions are found for the zeroth and first order in stream function and compared to well-documented research in the literature. It is shown that for a Casson fluid, when certain approximations are made in the most generalized form of constitutive equation, the fluid may be adequately represented as an improvement of a Newtonian fluid.

Cardiac Flow Analysis Applied to Phase Contrast Magnetic Resonance Imaging of the Heart

Phase contrast magnetic resonance imaging is performed to produce flow fields of blood in the heart. The aim of this study is to demonstrate the state of change in swirling blood flow within cardiac chambers and to quantify it for clinical analysis. Velocity fields based on the projection of the three dimensional blood flow onto multiple planes are scanned. The flow patterns can be illustrated using streamlines and vector plots to show the blood dynamical behavior at every cardiac phase. Large-scale vortices can be observed in the heart chambers, and we have developed a technique for characterizing their locations and strength. From our results, we are able to acquire an indication of the changes in blood swirls over one cardiac cycle by using temporal vorticity fields of the cardiac flow. This can improve our understanding of blood dynamics within the heart that may have implications in blood circulation efficiency. The results presented in this paper can establish a set of reference data to compare with unusual flow patterns due to cardiac abnormalities. The calibration of other flow-imaging modalities can also be achieved using this well-established velocity-encoding standard.

Transverse vibration of elastic plates by the method of constant deflection lines

Abstract This paper deals with the determination of the fundamental frequency of vibration of elastic plates of arbitrary shape by a recently developed method. As an illustration, the case of an elliptical plate, for both clamped and simply-supported edge conditions, is discussed. The values compare reasonably well with other existing results in the literature.

Cardiac flow component analysis

In a chamber of the heart, large-scale vortices are shown to exist as the result of the dynamic blood flow and unique morphological changes of the chamber wall. As the cardiovascular flow varies over a cardiac cycle, there is a need for a robust quantification method to analyze its vorticity and circulation. We attempt to measure vortex characteristics by means of two-dimensional vorticity maps and vortex circulation. First, we develop vortex component analysis by segmenting the vortices using an data clustering algorithm before histograms of their vorticity distribution are generated. The next stage is to generate the statistics of the vorticity maps for each phase of the cardiac cycle to allow analysis of the flow. This is followed by evaluating the circulation of each segmented vortex. The proposed approach is dedicated to examining vortices within the human heart chamber. The vorticity field can indicate the strength and number of large-scale vortices in the chamber. We provide the results of the flow analysis after vorticity map segmentation and the statistical properties that characterize the vorticity components. The success of the cardiac measurement and analysis is illustrated by a case study of the right atrium. Our investigation shows that it is possible to utilize a data clustering algorithm to segment vortices after vorticity mapping, and that the vorticity and circulation analysis of a chamber vorticity can provide new insights into the blood flow within the cardiovascular structure.

Theoretical modeling of micro-scale biological phenomena in human coronary arteries

This paper presents a mathematical model of biological structures in relation to coronary arteries with atherosclerosis. A set of equations has been derived to compute blood flow through these transport vessels with variable axial and radial geometries. Three-dimensional reconstructions of diseased arteries from cadavers have shown that atherosclerotic lesions spiral through the artery. The theoretical framework is able to explain the phenomenon of lesion distribution in a helical pattern by examining the structural parameters that affect the flow resistance and wall shear stress. The study is useful for connecting the relationship between the arterial wall geometries and hemodynamics of blood. It provides a simple, elegant and non-invasive method to predict flow properties for geometrically complex pathology at micro-scale levels and with low computational cost.

Transverse vibration of membranes of arbitrary shape by the method of constant-deflection contours

Abstract A method for approximate computation of the fundamental frequency of membranes of arbitrary shape vibrating harmonically is developed. The method is based upon the concept of contour lines of equal deflection on the surface of the membrane. A similar method for elastic plates has recently been developed by the author in a series of papers. As illustrations of the procedure, the method is applied to the calculation of the gravest mode of an annular, an elliptic, and a parabolic membrane.

Medical image diagnostics based on computer-aided flow analysis using magnetic resonance images.

Most of the cardiac abnormalities have an implication on hemodynamics and affect cardiovascular health. Diagnostic imaging modalities such as computed tomography and magnetic resonance imaging provide excellent anatomical information on myocardial structures, but fail to show the cardiac flow and detect heart defects in vivo condition. The computerized technique for fluid motion estimation by pixel intensity tracking based on magnetic resonance signals represents a promising technique for functional assessment of cardiovascular disease, as it can provide functional information of the heart in addition to analysis of its anatomy. Cardiovascular flow characteristics can be measured in both normal controls and patients with cardiac abnormalities such as atrial septal defect, thus, enabling identification of the underlying causes of these flow phenomena. This review paper focuses on an overview of a flow analysis scheme based on computer-aided evaluation of magnetic resonance intensity images, in comparison with other commonly used medical imaging modalities. Details of the proposed technique are provided with validations being conducted at selected abnormal cardiovascular patients. It is expected that this new technique can potentially extend applications for characterizing cardiovascular defects and their hemodynamic behavior.

Vibration and buckling of plates at elevated temperatures

Abstract The linear and non-linear dynamic behavior of plates at elevated temperatures are examined. Analytical solutions for the buckling and post-buckling behavior are obtained. A general formula is then presented which links the fundamental frequency of vibration to the critical buckling temperature and the corresponding frequency of the unheated plate. The behavior of certain visco-elastic plates is also considered and a criterion for thermal buckling is presented. The analysis may be interpreted as an extension of Williams analysis of long narrow plates, for plates of finite aspect ratio.

Vibration analysis of plates of arbitrary shape—A new approach

Abstract The so-called finite strip method combined with the deflection contour method has proved highly successful in the analysis of bending of thin elastic plates of arbitrary shape. Here the same technique is used to obtain the fundamental frequency of plates of arbitrary shape. The method of approach is much simpler than the conventional finite element method since it requires less programming effort and a reduction in both memory space and time on the computer. Several representative plate problems of irregular boundaries are treated by the proposed method. For all cases, comparison of the results are made with other known solutions and the agreement appears to be excellent.