Coronary arterial dynamics computation with medica

Authors: Kenji Takizawa Ryo Torii Hirokazu Takagi Tayfun E Tezduyar Xiao Y Xu

Publish Date: 2014/07/03

Volume: 54, Issue: 4, Pages: 1047-1053

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Abstract

We propose a method for coronary arterial dynamics computation with medicalimagebased timedependent anatomical models The objective is to improve the computational analysis of coronary arteries for better understanding of the links between the atherosclerosis development and mechanical stimuli such as endothelial wall shear stress and structural stress in the arterial wall The method has two components The first one is elementbased zerostress ZS state estimation which is an alternative to prestress calculation The second one is a “mixed ZS state” approach where the ZS states for different elements in the structural mechanics mesh are estimated with reference configurations based on medical images coming from different instants within the cardiac cycle We demonstrate the robustness of the method in a patientspecific coronary arterial dynamics computation where the motion of a thin strip along the arterial surface and two cut surfaces at the arterial ends is specified to match the motion extracted from the medical imagesComputational analysis in cardiovascular fluid and solid mechanics now has powerful methods encouraging the development of even more powerful ones and can deal with a wide range of biomechanics problems encouraging efforts to further increase that range For examples of the methods developed and problems analyzed see 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 In this paper we focus on the human coronary arteries specifically the right coronary artery RCAThe coronary arteries feeding arteries to the myocardium are known as common sites of atherosclerotic narrowing which typically leads to myocardial infarction and sudden cardiac death 33 Links have been suggested between the atherosclerosis development and mechanical stimuli such as endothelial wall shear stress WSS and structural stress in the arterial wall 34 35 This has motivated studies on quantification of the biomechanical stresses with computational fluid and structural mechanics methods and medicalimagebased anatomical models Among such studies those on structural mechanics 36 and fluid–structure interaction FSI 37 38 are rather sparse compared to those on fluid mechanics and WSS 39 40 One reason for that is the difficulty in acquiring the wall thickness and the motion of a coronary artery which is substantial in the RCA Approaches used for acquiring such timedependent anatomical data 39 41 42 43 include the timedependent anatomicalmodel extraction method introduced in 43 which is based fully on magnetic resonance imaging MRI This MRIbased method was used in 43 for blood flow analysis with cardiacinduced arterial motionIn this paper we focus on coronary arterial dynamics analysis with the medicalimagebased timedependent anatomical model coming from 43 The longterm objective is to have a better understanding of the interaction between the blood flow and arterial dynamics which is difficult to observe experimentally This requires FSI analysis which in turn requires a robust method for the coronary arterial dynamics computation The method has to be able to deal with the computational challenges involved such as the large deformation of an incompressible material including stretch bending and torsionMedicalimagebased arterial geometries come from configurations that are not stressfree Therefore coronary arterial dynamics computations with such timedependent anatomical models require prestress calculations or zerostress ZS state estimations More explanation of this requirement and references to some of the methods introduced to meet this requirement can be found in 28 The methods mentioned in 28 include the original version of the technique for calculating an estimated zeropressure EZP arterial geometry 44 and newer EZP versions introduced in 10 17 45 which were also presented in 19 22 They also include the prestress technique introduced in 15 and further refined in 18 which was also presented in 19 22A method was introduced in 28 for elementbased ZS state estimation The method has three parts 1 An iterative method which starts with an initial guess for the ZS state is used for computing the elementbased ZS state such that when a given pressure load is applied the imagebased target shape is matched 2 A method for straighttube geometries with single and multiple layers is used for computing the elementbased ZS state so that we match the given diameter and longitudinal stretch in the target configuration and the “opening angle” 3 An elementbased mapping between the arterial and straighttube configurations is used for mapping from the arterial configuration to the straighttube configuration and for mapping the estimated ZS state of the straight tube back to the arterial configuration to be used as the initial guess for the iterative method that matches the imagebased target shapeIn coronary arterial dynamics computation with medicalimagebased timedependent anatomical model the method we use for the ZS state estimation has two components The first one is the method introduced in 28 for elementbased ZS state estimation The second one is a “mixed ZS state” approach where the ZS states for different elements in the structural mechanics mesh are estimated with reference configurations based on medical images coming from different instants within the cardiac cycle The overall method used in the coronary arterial dynamics computation carried out here including the mixed ZS state approach is described Sect 2 The results are presented in Sect 3 and the concluding remarks are given in Sect 4The medicalimagebased timedependent anatomical model comes from 43 The MRIbased method used in extracting that model can be found in 43 The arterial crosssectional images were acquired at 14 instants within the cardiac cycle 0 50 150 200 250 300 350 400 450 500 550 600 725 and 850 ms with 0 ms corresponding to the Rwave of the electrocardiogram The timedependent lumen geometry was constructed by associating to the points along the moving centerline cycleaveraged crosssections The crosssection for each point along the centerline was obtained by averaging over the cardiac cycle from the MRIobtained crosssections for that point From that for the computations carried out here we reconstruct the lumen geometry by mapping the crosssection for each point along the centerline to a circular crosssection We construct the wall volume by extruding the lumen outward with a constant wall thickness assumed to be 05 mm from 42 Then we generate a volume mesh that has 135450 nodes and 108000 hexahedral elements with 4 90 and 300 elements in the thickness circumferential and length directions The mesh is represented over the cardiac cycle by using cubic Bsplines in time and the STC technique see 46

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