Hemodynamics In Circle Of Willis With Internal Carotid Artery Stenosis Under Cervical Rotatory Manipulation:a Finite Element Analysis

Target:1. The Circle of Willis (CoW) plays an important role in cerebral collateral circulation, but not any model which include both vessel and blood have been created and rarely literature had been found focusing in the he hemodynamics of the cirle. A 3-D finite element model of normal Cow will be created to find out the hemodynamics situation and the openness of communicationg arteries in the circle.2. Internal carotid artery was found to be a popular site of angiostenosis and associated with cerebral ischemic diseases. Hemodynamics changes in the circle have usually been associated with the ICA stenosis, but rarely research focused on it. A serial of CoW models with different degree of stenosis will be created to find out the hemodynamics and stress-strain situation in those circles under pathological condition, to find out the relationship between stenosis and cerebral ischemic disease on mechanics.3. Cervical rotatory manipulation is a frequently applied therapy in clinical practice. According with its pupular application, serious complications has been reported occasionly. Whether the rotatory manipulation will affect the hemodynamics or not and lead to serious complication still remains unknown. A condition of rotatory manipulation will be applied to both healthy model and pathological models by mean of FEA, to find out the affection of the manipulation to the circles and demonstrate the safety.Material/Methods1. Based on a serial of magnetic resonance angiography (MRA) images of a volunteer and the average anatomy date of Chinese human, a rough geometric model of blood inside the CoW was built by the software Mimics. The centerline was extracted from the model. Based on this rough model, faces and bodies of blood were made, and then a 3-D geometric model of blood inside CoW was built by preprocessing module of Ansys, the SCDM (Space Claim Direct Modeler). Blood was assumed to be incompressible Newtonian fluid, after the meshing and the given of the materials properties, a 3-D finite element model of blood which inside the CoW was constructed. A serial of shell units were attached to the surface of the rough geometric model of blood, based on this rough model and the average anatomy date of Chinese human, a 3-D geometric model of vessel was built by preprocessing module of Ansys, the DM (Design module). The vessel was assumed to be incompressible linearly elastic material, after the meshing and the given of the materials properties, a 3-D finite element model of the vessels of the CoW was constructed. The complete model which contains both vessel and blood was then constructed by the coupling of both parts.2. A finite element analysis was carried out after the setting of boundary conditions in both the structural module and the fluent module and the setting of coupling parameter in coupleing module. There were 3 presure inlets,6 mss flow rate outlets and 3 monitor surfaces in the 3 communicating arteies in Fluent. Fix supportr and intracranial pressure were applied in Transient moduler. Result of hemodynamic change of the blood, stress distribution and the strain of the vessels will be obtained at the healthy model.3. A serials of 3-D geometric models of CoW with different degree of stenosis(15%、30%,45%,60%,70%,80%,90%) at right ICA were set up via SCDM, by endowing shell unit on the face of blood,thickness of shell unit was the thickness of vessel. After the meshing and the given of the materials properties, a serial of stenosis models were built. The way to build the model of normal segment of ICA was the same as it was mentioned above in stepl. Vessel of stenosis was also built by endow a shell unit on the surface of the segment of stenosis, thickness of shell unit differ by the degree of stenosis.4. A finite element analysis was carried out after the setting of boundary conditions in both the structural module and the fluent module and the setting of coupling parameter in coupleing module as it was at step 2, result of hemodynamic change of the blood, stress distribution and the strain of the vessels will be obtained at the stenosis models.5. A finite element analysis was carried out after a remote displacement was applied in the healthy model to simulate the cervical rotatory manipulation and other boundary conditions being equal, result of hemodynamic change of the blood, stress distribution and the strain of the vessels will be obtained at the healthy model.6. A finite element analysis was carried out after a remote displacement was applied in the stenosis models to simulate the cervical rotatory manipulation and other boundary conditions being equal, result of hemodynamic change of the blood, stress distribution and the strain of the vessels will be obtained at the stenosis models.Results1. A healthy 3-D finite element model of CoW was built here, the model contains both the vessel and the blood, and is the first coupled model and most preciseone so far. Then a serial of CoW models with different degree of stenosis at right ICA were built based on it. Comparing to the average anatomy date, mass flow rate inside was the same as average human data, pressure was the same as blood pressure, and the velocity of flow (1.2m/s) also equal to reality, meanwhile, there isn’t any obvious deformation in vessels or blood. The models were validated and can be used in further research.2. The mass flow rate which pass throught ACOA and both side of PCOA can be obtained in both healthy model and stenosis models. Before the application of cervical rotatory manipulation, mass flow rate which pass the ACOA、Right PCOA and Left PCOA was0.14 g/s,0.11 g/s and 0.10g/s in healthy model. Flux in ACOA and right PCOA increased gradually according to the increase of stenosis rate, up to 2.8g/s and 2.3g/s when the stenosis rate as high as 90%. The flux in left PCOA increased no as distinct as it was in the other communicating arteries, mass flow rate was 0.29g/s when the stenosis rate was up to 90%. There is ischemia in A1 segment of ACA when the rate of stenosis reached 70%, flux in the 3 communicating arteries increased gradually to maintain the outlet of ACA. It seems that increasing blood was imported mostly form ACOA. Blood went from the back half of the circle to the front half of the circle, from left side to the right side, which means from the normal area to the ischemia area. Even so output mass flow rate can be maintained, but it need more time to complete the procedure, which means that there was less flow in right ACA in unit time. Meanwhile, pressure was almost the same in all the models. In mechanical modual, it was found that stress concentrated on the area of right ICA, especial on the area of stenosis, then decreased along the passway of blood flow. Strain in vessels was light, in the class of 1e-4 meters. The most obvious part of the deformation located in the proximal part of stenosis at right ICA, proximal of ICA was expanded under the situation of high-grade stenosis. The right ICA was wiggled before the totally perfusion of blood. Nearly any displacement can be seen in dynamic vedio after the coupling.3. Direct of blood did not have any change after the application of cervical rotatory manipulation. Mass flow rate according the 3 communicating arteries kept steady at first. Situation of ischemia in ACA when the stenosis was rate up to 70% also did not vary after the manipulation. Mass flow rate in ACOA, right PCOA and left PCOA was 0.15g/s,0.10g/s and 0.11g/s in the healthy model. Mass flow rate increased barely even when the rate of stenosis was up to 80% and can be seem as negligible, mass flow rate decreased sharply as long as the stenosis rate was up to 90%, from 2.8 g/s to 1.4 g/s, from 2.3 g/s to 1.2 g/s and from 0.29 g/s to 0.21g/s in those three communicating arteries. Blood which imported from right ICA went almost to the right side of ACA and MCA, few of it went to the left side of ACA via ACOA in the healthy model, and it was too little to take into account. Flux can be seen from the left circle to the right circle via ACOA, and from back half to the front half of the circle as well via right PCOA. When it comes to stenosis models, flux can be seen went from left side of the circle to the right side of the circle via ACOA, and from the back half of the circle to the front half. After the application of the rotatory manipulation, change of mass flow rate can be obtained, but direct of the blood keep on the same way, which was from the normal area to the ischemia area. In mechanical modual, pressure kept almost the same as before, velocity of blood did not differ from before, it was found that stress concentrated on the area of right ICA, especial on the area of stenosis, the concentration of stress did not show more apparent than it was in those models without cervical rototary manipulation, and then decreased along the passway of blood flow. Strain in vessels was light, in the class of 1e-4 meters. The ICA spin on its own axis after the apply of manipulation, nearly any displacement in the sagittal and coronal plane can be seen in dynamic vedio, deform occurred in the area of stenosis, shape of vessel keep almost the same in other place of CoW.Conclusions:1. The ACOA and both side of PCOA keep almost close in the healthy CoW model, flux flow though those 3 communicating arteries can rarely be seen, blood go from right ICA to both right ACA and MCA. Stress-strain value is too small to be took into account, no any displacement and deformation can be seen after the coupling of blood and vessels.2. Blood flow through the 3 communicating arteries increased gradually according to the increase of rate of stenosis in the right ICA. Direct of the flow went from left side to right side and from the back half of the circle to the front half of the circle, which menas from the normal area to the ischemia area. Even so there is ischemia in Al segment of ACA when the rate of stenosis reached 70%, the increase in ACOA was sufficient to make up the ischemia, but need more time to finish, which meas that there was less flow from right ACA in unit times. The compensation role of CoW as collateral circulation in ICA stenosis patients can be verified. Stress-strain concentrated on the area of stenosis, not any obvious displacement or deformation can be found. A mild expandsion was found at the proximal part of stenosis of right ICA, the extent of expandsion increased according to the increase of stenosis. Besides, there was no any obvious stress-strain concentration and deformation in the 3 communicating arteries. The blood slows only in the aera of stenosis.3. There was no significant change in mass flow rate and direction of blood in the circle after the application of cervical rotatory manipulation in healthy model. There was also no significant change in mass flow rate and direction of blood in the early period of stenosis. Ischemia can be seen in right ACA when the degree of stenosis was up to 70%, this situation kept almost the same after the apply of manipulation. Obviously decrease of mass flow rate can be seen when the rate of stenosis was up to 90%, but the direction kept on the same way. Pressure and velocity of blood remain stable after the application of manipulation. There was no any obvious changed of stress-strain distribution in the 3 communicating arteries, stress-strain situation kept almost the same kind as it was before the application of cervical rotatory manipulation. Thus, despite some limitations, we suggest that rotatory manipulation is safe for most patients, but can be dangerous to those who have severe stenosis in ICA by intervene its collateral circulation ability. Clinicians should be cautious in recommending cervical rotary manipulation to individuals who potentially have severe (>90%) stenosis of the internal carotid artery.