Simulation of Treatment to Counteract Conditions of ...



TO: Professor Andreas Linninger/ Chih-Yang HsuFrom:Shidrukh Ali Date: December 2nd, 2013Subject:Project PaperSimulation of Treatment to Counteract Conditions of Spontaneous Occlusion of the Circle of Willis Shidrukh Ali*, Andreas Linninger, PhD* and Chih-Yang Hsu**University of Illinois at Chicago-Department of Bioengineering11/26/2013Abstract:The spontaneous occlusion of the Circle of Willis, also known as Moyamoya disease, is a cerebrovascular disorder caused by the constriction of certain arteries in the brain. [1], [2] The Circle of Willis or the cerebral arterial circle, is the circulatory anastomosis through which blood is supplied to the brain. [1] Blood vessel constriction leads to blockage of blood supply, followed by hemorrhage in severe cases. Employing the knowledge of conservation balance and Hagen-Poiseuille, the prime goal was to analyze the input and output blood pressure and the blood flow rate within the network required in order to avoid any kind of cerebrovascular diseases. The arterial blood flow in the Circle of Willis was determined. The diameter of one of the inlet arteries was reduced by 50% to analyze blood flow in a diseased brain. A stent was introduced which caused dilation of LICA such that the diameter of the artery will be 25% of the diameter of that in a patient without MMD. Predicted results show that using a stents, which will dilate the constricted vessel, will reduce the probability of hemorrhage. Key words: Moyamoya disease, BA, LICA, LMCA, LPCA, LACA, RICA, RACA, RMCA, and RPCA.Introduction: Spontaneous occlusion of the Circle of Willis is a progressive arterial disease in which the branches of the internal carotid artery are affected. [7] Spontaneous occlusion of the Circle of Willis, also known as the Moyamoya disease (MMD), is a cerebrovascular disorder where it can affect both sides of the brain; in some cases it is one-sided or has been found to be linked with systemic diseases and is referred to as Moyamoya syndrome. [7] Since this syndrome has been more frequent among the Japanese populations, it is commonly addressed by the Japanese term ‘Moyamoya’. [2] In Japanese, ‘moyamoya’ means hazy or vague which perfectly describes the appearance of the anomalous vascular network. [2] Adults with Moyamoya disease commonly have the following symptoms: hemorrhage, ischemic stroke and transient ischemic attacks. [2]The clinical diagnosis of the Moyamoya disease depends on a few measures derived by using cerebral angiography: 1. atypical vascular networks noted in the arterial phase in the vicinity of the arterial occlusion; 2. occlusion of the terminal rations of internal cranial arteries and proximal portions of anterior and/or middle cerebral arteries; and 3. bilateral involvement. [1] Figure 1 contains angiography results showing the progress from isolated middle cerebral artery stenosis into Moyamoya disease. The angiography results have been obtained twice, with an interval of four year and eight months apart.7937519875500Fig. 1 (A) Isolated stenosis of the right middle cerebral artery; (B) Typical features of Moyamoya disease, including severe stenosis of the bilateral ICA and basal collateral network.[6]The Circle of Willis, also known as the cerebral arterial circle, is the circulatory anastomosis through which blood is supplied to the brain. [1] Cerebral blood flow (CBF) is the rate of blood flow through the brain, which is usually?750 mL/min, approximately 15% of the cardiac output. [3] The nine main arteries of focus in Circle of Willis are: the basilar artery (BA), left anterior inferior carotid artery (LICA), right anterior inferior carotid artery (RICA), left anterior cerebral artery (LACA), left middle cerebral artery (LMCA), left posterior cerebral artery (LPCA), right anterior cerebral artery (RACA), right middle cerebral artery (RMCA), and right posterior cerebral artery (RPCA). An illustration of the network of the Circle of Willis is provided below in figure 2.6007109080500 Fig 2 The Circle of Willis [9] (adapted from the book Human Anatomy and Physiology 9th ed.) The main goal of this project is to investigate the effects of a stent that will help to treat the Moyamoya disease by counteracting the vasoconstriction present in the Circle of Willis of the patient. In the process of investigation, the relationship between the pressure, resistance and flow of the blood flow through the Circle of Willis has been stated. A change in diameter of the vessel affects the resistance and eventually increases the pressure of blood which leads to hemorrhage. Method:As mentioned, the main arteries in focus are: BA, LICA, LMCA, LPCA, LACA, RICA, RACA, RMCA, and RPCA. Blood enters the Circle of Willis through BA, LICA and RICA and exits via LMCA, LPCA, LACA, RACA, RMCA and RPCA. Figure 3 provides a schematic of the main arteries: Fig. 3 The inlets BA, LICA and RICA; and outlets LMCA, LACA, LPCA, RMCA, RACA, and RPCA in the Circle of Willis Computation of Blood flow and Pressure:Utilizing the properties provided by the network, the unknown variables were determined. In order to calculate the flow rates, pressure changes and the resistances, the inlet and outlet pressures (boundary conditions) and the viscosity had to be determined. Furthermore, the following assumptions were made: 1. the blood is a newtonic fluid (thus, it cannot be compressed); 2. there is no accumulation in arteries; and 3. to reduce complexity the main focus was on nine arteries only. In order to determine the blood flow through the network, two prime concepts were utilized: (a) conservation of balance and (b) constitutive equations. According to the conservation of volumetric blood flow, at a node the total volumetric flow in must be equal to the total volumetric blood flow out: Fin= Fout (1) Eventually, the change in pressure was computed using constitutive equations: ?P= αF(2)where, α is the resistance of flow, F is the flow of blood through the faces and ?P is the change of pressure at the node which connects two or more faces. Accordingly, the change in pressure at any junction is equal to the product of the resistance and the flow of blood through the vessels connected by the junction. Hence, the Hagen-Poiseuille equation was used to compute the resistances (α): α = 128?LπD4 (3) where ? is the viscosity, set as 0.0035Pa*s, L is the length and D is the diameter of the blood vessels in the network. All the conservation balances, constitutive equations and the boundary conditions were then placed into a matrix form and listed symbolically: Ax= b(4)where A is a matrix and x and b are vectors. Matrix A is filled by the coefficients of the conservation balances, constitutive equations and the boundary conditions and vector b consists of the resulting values of this equations. Thus, using equation 5 vector x is calculated.The computational results were obtained by using MATLAB programming. In the MATLAB code, the vessels are represented by the face and the point represents the connectivity between the faces; also the diameter of the vessels was provided. Results:Studies in the past have shown systolic and diastolic pressures in afferent and efferent conditions, which provide the mean inlet and outlet pressures respectively. The total blood flow to the brain has been noted to be 12,500mm3/s (by unit conversion of 750 mL/min). [3] The lengths and the diameters were used to calculate the resistance in each inlet. Then, pressure of blood flowing in through LICA and RICA were subtracted from the total pressure of blood flowing in, to compute the pressure of blood in BA. Table 1 shows the baseline average diameters and the mean pressures at the inlets and outlets in the Circle of Willis. Table 1. Baseline average diameters and mean pressures at the inlets and outlets in the Circle of Willis [5] It has been noted that changes in the mean blood flow in one of the vessels, affects the mean blood flow and pressure in the entire circulation. The mean flow rates and pressures in the three inlet arteries, BA, LICA and RICA, for a patient without disease, have been obtained from previous studies and recorded as zero percent vasoconstriction. Simulations were used such that diameter of LICA would reduce by 50 percent of its original diameter; then mimicking the effects of the use of stents, the diameter of LICA was now increased such that it is 25 percent of the original diameter. The data for the three cases, 0, 50 and 25 percent vasoconstriction, and change in blood pressure and flow rates in BA, LICA and RICA have been provided in table 2 and in graphical form in figure 4:Table 2. Change in blood pressure and flow rates in BA, LICA and RICA, with respect to change in diameter of LICA Fig 4 The change in blood flow rate with change in diameter of LICA (Graphical representation of all the data obtained) Discussion: In Spontaneous occlusion of the Circle of Willis, abnormal narrowing and/or a blockage of a vessel occurs, leading to conditions like ischemic attacks, cerebral hemorrhage, etc. Hence, the mean blood flow rate in the vessels were noted for a subject who does not have MMD, and then the flow rate was altered in one the vessels in order to note the effect on the flow in the circulation. At first, the average diameters and pressures of the inlet and outlet arteries were recorded. The mean blood flow rate in the major arteries of the Circle of Willis circulation was obtained. The diameter of LICA was reduced by 50% and the effect on the flow rate of the three inlet arteries was predicted using MATLAB simulation and was tabulated. A stent was introduced which will cause dilation of LICA such that the diameter of the artery will be 25% less than the diameter of LICA in a patient without MMD. In order to mimic the effects of a stent, MATLAB simulation was used to predict the flow rate of the three inlet arteries when the diameter of the increased such that the dilated LICA would be 25% less than the diameter of LICA in a brain condition in absence of disease. Figure 4 is a graphical representation of the changes in blood flow in the three main inlet arteries with respect to change of diameter of LICA. Conclusion:Moyamoya disease, or Spontaneous occlusion of the Circle of Willis, has been documented as a cause of strokes and hemorrhage in adults as well as in children. Accordingly, reduction in the diameter of blood vessels increases the resistance to flow in the blood vessels, which eventually increasing the pressure. Since, in patients with Moyamoya syndrome, blood vessels supplying blood to the brain are constricted, the pressure of blood flowing throughout their brains is comparatively higher; thus, they are more prone to strokes and hemorrhage. One possible way to reduce the probability of hemorrhage could be by using a stent which could dilate the constricted vessel. However, the investigation is still in progress. At present, the only potential treatment for Moyamoya disease is direct or indirect bypass surgery; for children indirect bypass surgery is more preferred. References:Fukui, M. "Guidelines for the diagnosis and treatment of spontaneous occlusion of the circle of Willis (Moyamoya'disease)."?Clinical neurology and neurosurgery 99 (1997): S233-S235.Scott, R. Michael, and Edward R. Smith. "Moyamoya disease and moyamoya syndrome."?New England Journal of Medicine?360.12 (2009): 1226-1237. Shepherd S. 2004.?“Head Trauma” . Accessed January 4, 2007. Alnea, M, and et al. “Computation of Hemodynamics in the Circle of Willis.”stroke(2007):2500-2504.Fahy, Paul, et al. "An Experimental Investigation of the Hemodynamic Variations Due to Aplastic Vessels Within Three-Dimensional Phantom Models of the H.-Y Choi, J. E. Lee, Y. H. Jung, et al. Circle of Willis."?Annals of Biomedical Engineering?(2013): 1-16. "Progression of isolated middle cerebral artery stenosis into moyamoya disease."?Neurology. 68. (2007): 954. Web. 21 Oct. 2013.Smith, Edward R., and R. Michael Scott. "Spontaneous occlusion of the circle of Willis in children: pediatric moyamoya summary with proposed evidence-based practice guidelines: A review."?Journal of Neurosurgery: Pediatrics?9.4 (2012): 353-360.Zhao, M., et al. "Regional cerebral blood flow using quantitative MR angiography."?American Journal of Neuroradiology?28.8 (2007): 1470-1473.Marieb, Elaine N., and Katja Hoehn.?Human Anatomy & Physiology. 9th. 2013.eBook. ................
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