A Method of Analysing Fluid Flow in a Conduit
The invention relates to a method of analysing fluid flow in a conduit and especially, but not solely, analysing spiral fluid flow.
There is a well developed scientific knowledge linking blood flow pattern or haemodynamics with altered arterial wall stress and arterial disease development. Increased haemodynamic stress and turbulent flow induces a complex process that promotes atherogenesis by enhancing its three phases of development1. In the first phase, the vascular endothelium is damaged/denuded exposing the subendothelial surface to circulating blood2. Platelet aggregation and adhesion occur with subsequent microthrombi formation over the micro-fissures induced by the abnormal shear stresses and turbulent flow. The second phase is inflammatory, caused in part by the release of growth factors that induce smooth muscle cell proliferation and stenoses. Lipid accumulation is mediated through abnormal macrophage behavior and changes in local lipid metabolism, e.g. in sterol regulatory element-binding proteins3, which increase the mRNA encoding of the low-density lipoprotein (LDL) receptor and therefore the binding of LDL. Thus both vascular stenoses and lipid-laden plaque formation are promoted. The third phase, that of abnormal adaptive vascular remodeling is also enhanced, as the shear stresses and turbulent flow increase. Whereas exercise promotes improved remodeling vascular risk factors such as LDL cholesterol impair it4. Shear stress also attenuates appropriate remodeling, inducing growth factor release and cytokine production which stimulates extracellular matrix formation by both autocrine and paracrine pathways. All of these processes, occurring as a result of
the abnormal vascular shear stresses, increase atherogenesis. In addition, high wall shear stress has been reported in association with atheromatous disease in the great vessels.
The flow patterns in the arterial system are complex and difficult to analyse. A greater understanding of the blood flow patterns is being achieved with the use of non-invasive imaging. While trans-oesophageal ultrasound has been used to assess blood flow patterns in the ascending and descending arch5 velocity mapping using MRI is well tolerated and allows a number of methods to be employed. Two dimensional velocity maps can be displayed as vector maps in the vessels or heart6"11. Vector mapping has been used in the normal aorta12, in aortic coarctation6 and in aneurysms and grafts13. More complex time resolved particle paths have been visualised in the whole volume of the vessel11'14,15.
However, these known methods have the disadvantage that they do not produce a flow and three dimensional geometry of the vessel architecture and relate these to the arterial wall disease process. The combination of vessel geometry, flow data and wall haemodynamics, including stress would be a significant improvement.
In accordance with an aspect of the present invention, there is provided a method of analysing fluid flow in a conduit, the method comprising:
(a) scanning the internal volume of the conduit to generate data representing three dimensional geometry of the conduit architecture and fluid flow within the conduit;
(b) constructing a three dimensional geometry of the conduit architecture from the generated data;
(c) selecting a computational mesh to apply to the geometry;
(d) applying the computational mesh to the geometry to process data from the geometry for analysis;
(e) selecting a first fluid analysis model;
(f) selecting a first set of boundary conditions; and
(g) performing a first analysis of the processed data using the first fluid analysis model and the first set of boundary conditions.
Preferably, the method further comprises:
(h) selecting a second set of boundary conditions; (j) performing a second analysis of the processed data using the first fluid analysis model and the second set of boundary conditions; and (k) comparing the results of the first and the second analyses.
Preferably, the method further comprises verifying the appropriateness of the mesh, typically by comparing the mesh with the constructed geometry.
Typically, the first set of boundary conditions are selected based on actual fluid flow within the conduit and the second set of boundary conditions are selected based on desired fluid flow within the conduit.
Preferably, the method is for analysing flow in a conduit where the desired fluid flow is spiral flow. Typically, the second set of boundary conditions comprises a
boundary condition for a desired spiral flow within the conduit. Typically, in the
second set of boundary conditions the inlet condition is for the desired spiral flow.
The term "spiral" as used herein covers the mathematical definitions of spiral and
helical, and any combination of spiral and helical.
Typically, the results of the first and second analyses are compared by comparing
the ratio of the first analysis to the second analysis.
Typically, the scanning is performed using a magnetic resonance imaging
technique, but is not limited this technique.
Preferably, the fluid is a liquid. Typically, the method can be used to analyse flow of fluid in blood vessels in the human or animal body. However, the method can
also be used to analyse fluid flow in other types of conduit.
An example of a method of analysing fluid flow in a conduit in accordance with the
invention will now be described with reference to the accompanying drawings, in
which: Figure 1 shows a mesh of a bifurcated arterial segment;
Figure 2 is an enlarged view of a portion of the mesh; and
Figure 3 is a graph of turbulent kinetic energy versus distance for each of
the two vessels in the bifurcated arterial segment showing a comparison of spiral and non-spiral flow.
Fluid flow in a bifurcated arterial segment was analysed. First, a magnetic resonance imaging (MRI) scan was performed, the data from the scan was then used to construct a three dimensional geometry of the architecture of the vessel from which the arterial segment to be analysed was selected.
A computational fluid dynamic cellular matrix (or "mesh") of the segment was then selected. Computational meshes are a conventional analytical tool used in computational fluid dynamics. Typically, such a mesh is a closed cell mesh that comprises a number of cells. First the mesh size is selected to ensure sufficient resolution but not so small that it takes too long to process. The geometry of the cells within the mesh is then selected. Typical cell geometries include "tet" cells which are useful for highly deformed, complex images and "hex" cells which are useful at wall boundaries. The size and type of cells within the mesh can be mixed within the mesh. Normally, the mesh will be constructed using conventional computational fluid dynamics best practice guidelines.
Figure 1 shows a constructed mesh 1 for the arterial segment showing a small vessel 2 and a large vessel 3. Figure 2 shows an enlarged view of a portion of the mesh 1.
The mesh is then applied to the three dimensional geometry to process data for analysis. The appropriateness of the mesh 1 for the arterial segment is then verified by comparing the mesh 1 with the constructed three dimensional geometry of the arterial segment. If the mesh is determined not to be appropriate, the mesh 1 is modified accordingly or a new mesh is constructed.
Provided that it is verified that the mesh is appropriate, an analysis model is selected to analyse the processed data. The analysis model is a conventional fluid dynamics model and may be, for example, an inviscid flow model, a laminar flow model, a high Reynolds number turbulent flow model or a low Reynolds number turbulent flow model. The particular model chosen depends on the characteristics of the flow that it is desired to analyse.
The physical properties of the blood for the particular flow analysis model selected are then determined and then the boundary conditions are chosen for the analysis model. Two sets of boundary conditions are chosen. The first set of boundary conditions are derived from the actual flow pattern within the arterial segment and the second set of boundary conditions are based on a desired flow pattern within the arterial segment. Normally, the desired flow pattern would be an "ideal" spiral flow pattern.
After the analysis model, the fluid properties and the boundary conditions are determined, analyses are performed for both sets of boundary conditions. The results of both sets of analyses are then compared. Analyses for a non-spiral flow and a spiral flow are shown in Figure 3 for both the large vessel 3 and the small vessel 2 in the bifurcated arterial segment for turbulent kinetic energy versus distance along the arterial segment.
The invention has the advantage of providing an analysis of fluid flow in a conduit. It is particularly useful for analysing fluid flow in blood vessels in the human or
animal body as it provides the physician with additional information that the physician can then use to assess the condition of blood vessels for subsequent diagnosis and/or treatment. In particular, the physician can use the invention to compare actual fluid flow pattern in a blood vessel with a desired or ideal flow pattern.
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