asymptomatic carotid plaques are very commonly encountered in daily clinical practice , with prevalence ranging from 0.1% to 7.5% in the general population . asymptomatic carotid stenosis refers to narrowing of the carotid artery caused by atherosclerosis in patients who have not experienced a stroke or transient ischemic attack in the territory of that artery . the pathogenesis of carotid plaque from asymptomatic to cerebrovascular events is a complex process which is still not completely understood . although many systemic risk factors predispose to development of atherosclerosis , plaque is not uniformly distributed in the carotid arteries and it preferentially affects certain regions of circulation ( e.g. , the inner curve , close to side branches , and in the bulbs of the carotid artery [ 46 ] ) , suggesting that local mechanical factors might determine plaque development and growth . plaque morphology and composition are evidently related to blood flow , which therefore influences the local predisposition to atherosclerosis progression , plaque rupture , and thrombosis . furthermore , there is ample evidence that low wall shear stress is involved in plaque initiation and progression through various molecular mechanisms that influence endothelial cell morphology and function . atherosclerosis is considered to be a disease caused by a variety of clinical environmental factors and genetic factors . in recent years , numerous polymorphisms of genes related to atherosclerosis have been found by genome - wide association study ( gwas ) and meta - analysis in large - scale studies [ 913 ] . on the other hands , other hemodynamic parameters related to atherosclerosis include wall pressure , shear strain rates , and flow velocity . cfd is mechanical engineering field which is widely used in mechanical engineering to solve complex problems by analyzing fluid flow , heat transfer , and associated phenomena by using computer simulations . examples are aerodynamics and hydrodynamics of vehicles , power plants and turbines , electronic engineering , chemical engineering , external and internal environmental architectural design , marine and environmental engineering , hydrology , meteorology , and biomedical engineering . in recent years , cfd biomedical research is more accessible because high - performance hardware and software are easily available with advances in computer science . few studies have investigated the relationship between carotid plaque hemodynamic characteristics and risk of stroke in asymptomatic patients . therefore , in this study , we aimed to investigate the relationship between hemodynamic parameters of asymptomatic carotid plaques by using cfd and magnetic resonance angiography ( mra ) , including flow velocity across the lesion , wall shear stress ( wss ) , wall pressure ( wp ) , and the risk of stroke . this prospective study was performed at the chinese pla general hospital , beijing , china from march 2011 to june 2013 . for the purpose of our study , asymptomatic participants with carotid plaque ( thickness 2 mm ) in one of the carotid arteries were enrolled . the exclusion criteria included : 1 ) images were not suitable for cfd analysis : the stenosis degree greater than 95% or less than 10% ; and 2 ) contraindications for mra : any electrically , magnetically , or mechanically activated implant , intracranial aneurysm clips ( unless made of titanium ) , ferromagnetic surgical clips or staples , metallic foreign body in the eye , or pregnancy . demographics , histories of common diseases ( previously diagnosed or taking corresponding medications at baseline ) , and results of laboratory tests at baseline were collected from computerized medical records and ultrasound reports . the primary endpoint was defined as a stroke based on typical clinical symptoms and confirmed by follow - up brain ct or mra . secondary endpoints included any ischemic stroke or tia , and all - cause death . a flow chart explaining the final data used for analysis is shown in figure 1 . the participants were divided into a stroke group and a non - stroke group according to follow - up data . written informed consent the study was approved by the ethics committee for medical research of the chinese pla general hospital . carotid plaques mras were obtained by a signal 1.5 t mr systems ( general - electric healthcare , milwaukee , wi ) using a bilateral phased - array surface coil with a slice thickness of 1.2 mm . mra scan range was from the aortic arch to the skull base , and we selected the 4 cm within the scope of the original image of the carotid bifurcation ( i.e. , within the 4-cm scope of the cca , ica , and eca ) . after the scan was completed , the digital imaging and communications in medicine ( dicom ) format images were derived . all images were imported to the post - processing workstation adw4.5 - 1 ( general - electric healthcare , milwaukee , wi ) for image evaluation and analysis . luminal area ( la ) was defined as the area encompassed by the inner boundary of the intimal surface in plaque slices . total vessel area ( tva ) was defined by the outer boundary of the vessel . wall area ( wa ) was calculated by the software , subtracting tva from la ( wa = tvala ) . geometric modeling was performed by importing the dicom format mra data into reverse engineering 3d reconstruction software mimics ( materialise inc . , belgium ) , by threshold segmentation ( figure 2a ) , region growing , and use of mask film editing ( figure 2b ) tools to get a sense of vessels in the region of interest ( roi ) mask by mimics the 3-dimensional ( 3d ) transport calculation functions , connection of the extracted two - dimensional ( 2d ) section , and generating a 3d carotid arteries geometric model ( figure 2c ) . we then imported the 3d models into the forward engineering software 3-matic to remesh the surface of the arteries ( figure 2d ) and improve the quality of the grid . we imported stl format images into the icem - cfd software to identify the 3d space structure , and defined the 1-inlet , 2-outlets , the vessel wall , and other parts of arteries . then , we set the parameters required for the tetrahedral mesh according to the size of the arteries . to guarantee the accuracy of the boundary of the target artery , we set up a 3-layer boundary calculate condition , and the growth factor was increased by 1.2 times . we imported tetrahedral mesh files into a fluent model with ansys software and set the following boundary conditions : ( 1 ) vascular wall characteristics : vascular walls were set to smooth , no penetration of rigid ; ( 2 ) blood characteristics : the blood flow was assumed laminar , incompressible , and newtonian , with density of 1060 kg / m and viscosity of 0.0035pas ; ( 3 ) the inlet velocity was measured by mra and the blood flow of internal and external carotid arteries were 55% and 45% , respectively ; and ( 4 ) the calculation was based on continuity equation and navier - storks equation . the workflow of cfd analysis is shown in figure 4 
 ux+vy+wz=0  ( u)t+div(uu)=div(gradu)-px+su  ( v)t+div(vu)=div(gradv)-py+sv  ( w)t+div(wu)=div(gradw)-pz+sw all continuous variables are presented as means sd . the normal distribution test for continuous variables was conducted using the kolmogorov - smirnov test . statistical analysis of normal distribution data was performed using an unpaired t test between 2 groups . non - normal distribution data were analyzed using the mann - whitney u test for continuous variables and the x test for discrete variables . receiver operator characteristic curve ( roc ) and c - statistic testing were utilized to assess the performance of the constructed model in comparison with a previous published model . differences were considered statistically significant at a two - tailed p value of less than 0.05 . this prospective study was performed at the chinese pla general hospital , beijing , china from march 2011 to june 2013 . for the purpose of our study , asymptomatic participants with carotid plaque ( thickness 2 mm ) in one of the carotid arteries were enrolled . the exclusion criteria included : 1 ) images were not suitable for cfd analysis : the stenosis degree greater than 95% or less than 10% ; and 2 ) contraindications for mra : any electrically , magnetically , or mechanically activated implant , intracranial aneurysm clips ( unless made of titanium ) , ferromagnetic surgical clips or staples , metallic foreign body in the eye , or pregnancy . demographics , histories of common diseases ( previously diagnosed or taking corresponding medications at baseline ) , and results of laboratory tests at baseline were collected from computerized medical records and ultrasound reports . the primary endpoint was defined as a stroke based on typical clinical symptoms and confirmed by follow - up brain ct or mra . secondary endpoints included any ischemic stroke or tia , and all - cause death . a flow chart explaining the final data used for analysis is shown in figure 1 . the participants were divided into a stroke group and a non - stroke group according to follow - up data . written informed consent the study was approved by the ethics committee for medical research of the chinese pla general hospital . carotid plaques mras were obtained by a signal 1.5 t mr systems ( general - electric healthcare , milwaukee , wi ) using a bilateral phased - array surface coil with a slice thickness of 1.2 mm . mra scan range was from the aortic arch to the skull base , and we selected the 4 cm within the scope of the original image of the carotid bifurcation ( i.e. , within the 4-cm scope of the cca , ica , and eca ) . after the scan was completed , the digital imaging and communications in medicine ( dicom ) format images were derived . all images were imported to the post - processing workstation adw4.5 - 1 ( general - electric healthcare , milwaukee , wi ) for image evaluation and analysis . luminal area ( la ) was defined as the area encompassed by the inner boundary of the intimal surface in plaque slices . total vessel area ( tva ) was defined by the outer boundary of the vessel . wall area ( wa ) was calculated by the software , subtracting tva from la ( wa = tvala ) . geometric modeling was performed by importing the dicom format mra data into reverse engineering 3d reconstruction software mimics ( materialise inc . , belgium ) , by threshold segmentation ( figure 2a ) , region growing , and use of mask film editing ( figure 2b ) tools to get a sense of vessels in the region of interest ( roi ) mask by mimics the 3-dimensional ( 3d ) transport calculation functions , connection of the extracted two - dimensional ( 2d ) section , and generating a 3d carotid arteries geometric model ( figure 2c ) . we then imported the 3d models into the forward engineering software 3-matic to remesh the surface of the arteries ( figure 2d ) and improve the quality of the grid . we imported stl format images into the icem - cfd software to identify the 3d space structure , and defined the 1-inlet , 2-outlets , the vessel wall , and other parts of arteries . then , we set the parameters required for the tetrahedral mesh according to the size of the arteries . to guarantee the accuracy of the boundary of the target artery , we set up a 3-layer boundary calculate condition , and the growth factor was increased by 1.2 times . we imported tetrahedral mesh files into a fluent model with ansys software and set the following boundary conditions : ( 1 ) vascular wall characteristics : vascular walls were set to smooth , no penetration of rigid ; ( 2 ) blood characteristics : the blood flow was assumed laminar , incompressible , and newtonian , with density of 1060 kg / m and viscosity of 0.0035pas ; ( 3 ) the inlet velocity was measured by mra and the blood flow of internal and external carotid arteries were 55% and 45% , respectively ; and ( 4 ) the calculation was based on continuity equation and navier - storks equation . the workflow of cfd analysis is shown in figure 4 
 ux+vy+wz=0  ( u)t+div(uu)=div(gradu)-px+su  ( v)t+div(vu)=div(gradv)-py+sv  ( w)t+div(wu)=div(gradw)-pz+sw the normal distribution test for continuous variables was conducted using the kolmogorov - smirnov test . statistical analysis of normal distribution data was performed using an unpaired t test between 2 groups . non - normal distribution data were analyzed using the mann - whitney u test for continuous variables and the x test for discrete variables . receiver operator characteristic curve ( roc ) and c - statistic testing were utilized to assess the performance of the constructed model in comparison with a previous published model . all tests were carried out using spss version 17.0 ( spss inc . , chicago , il , usa ) statistical software . differences were considered statistically significant at a two - tailed p value of less than 0.05 . the study population included 120 men ( 52.63% ) and 108 women ( 47.37% ) , the mean age was 59.218.48 years , and the mean follow - up duration was 1147.56224.84 days . the follow - up results showed 16 of 228 patients with asymptomatic carotid plaques had experienced a stroke . the participants were divided into a stroke group and a non - stroke group according to whether stroke had occurred . detail information on demographics , medical history , physical examination , and results of laboratory tests of the 2 groups are shown in table 1 . there were no significant differences between the 2 groups in terms of age , sex , history of smoking , medical history , physical examination , or laboratory test results . figure 5a is a streamlined picture of the flow , showing turbulent regions with obvious velocity slowing above and below the plaques . local amplification of the velocity vector ( figure 5b ) shows the blood flow velocity was accelerated in the stenosis region . contours of wp ( figure 5c ) show the wall pressure was gradually decreased from the inlet to the outlets of the carotid artery . however , the wp of the bifurcation site of the common carotid artery was abnormally high , and atherosclerotic lesions showed decreased wp . on the other hand , contours of wss the stroke group and non - stroke group were similar with respect to la , wa , and tva . the nwi of the stroke group was higher than in the non - stroke group ( 0.540.15 vs. 0.520.19 , p=0.043 ) . qualitative assessment of hemodynamic parameters showed no significant difference between the stroke group and non - stroke group in wp ; however , wss of the stroke group was higher than in the non - stroke group ( 7.871.34 vs. 5.862.14 , p=0.013 ) . logistics regression analysis indicated that nwi and wss were associated with the development of carotid plaques ( table 3 ) . carotid artery with higher other hemodynamic and mra characteristics of carotid artery did not show significant associations with the risk of stroke . to assess the predictive utility of wss , nwi , and wss+nwi , we compared the roc curves of these 3 parameters . the area under the roc curve values for wss , nwi , and wss+nwi were 0.772 , 0.798 , and 0.903 , respectively ( table 4 ) . wss+nwi predicted the onset of stroke better than wss and nwi ( p<0.05 ) , with no statistically significant differences between wss and nwi ( figure 6 ) . the study population included 120 men ( 52.63% ) and 108 women ( 47.37% ) , the mean age was 59.218.48 years , and the mean follow - up duration was 1147.56224.84 days . the follow - up results showed 16 of 228 patients with asymptomatic carotid plaques had experienced a stroke . the participants were divided into a stroke group and a non - stroke group according to whether stroke had occurred . detail information on demographics , medical history , physical examination , and results of laboratory tests of the 2 groups are shown in table 1 . there were no significant differences between the 2 groups in terms of age , sex , history of smoking , medical history , physical examination , or laboratory test results . figure 5a is a streamlined picture of the flow , showing turbulent regions with obvious velocity slowing above and below the plaques . local amplification of the velocity vector ( figure 5b ) shows the blood flow velocity was accelerated in the stenosis region . contours of wp ( figure 5c ) show the wall pressure was gradually decreased from the inlet to the outlets of the carotid artery . however , the wp of the bifurcation site of the common carotid artery was abnormally high , and atherosclerotic lesions showed decreased wp . on the other hand , contours of wss ( figure 5d ) showed the uneven distribution of wss of the carotid artery . the stroke group and non - stroke group were similar with respect to la , wa , and tva . the nwi of the stroke group was higher than in the non - stroke group ( 0.540.15 vs. 0.520.19 , p=0.043 ) . qualitative assessment of hemodynamic parameters showed no significant difference between the stroke group and non - stroke group in wp ; however , wss of the stroke group was higher than in the non - stroke group ( 7.871.34 vs. 5.862.14 , p=0.013 ) . logistics regression analysis indicated that nwi and wss were associated with the development of carotid plaques ( table 3 ) . carotid artery with higher high wss increased the chance of the stroke by 6.974 times . other hemodynamic and mra characteristics of carotid artery did not show significant associations with the risk of stroke . to assess the predictive utility of wss , nwi , and wss+nwi , we compared the roc curves of these 3 parameters . the area under the roc curve values for wss , nwi , and wss+nwi were 0.772 , 0.798 , and 0.903 , respectively ( table 4 ) . wss+nwi predicted the onset of stroke better than wss and nwi ( p<0.05 ) , with no statistically significant differences between wss and nwi ( figure 6 ) . the present study used morphologic data derived from mra and geometric parameter data obtained by cfd to examine the relationship between carotid plaques and the risk of stroke in patients with asymptomatic carotid plaques . of the 228 participants with asymptomatic carotid plaques , 16 ( 7.02% ) had stroke in the territory of the carotid artery , which was comparable to kakkos s and chung s studies . additionally , the probability of stroke was much lower than in sadat s study . the difference may be that sadat s cohort had suffered a stroke before and were not asymptomatic as such . for the cfd analysis , most of the previous studies used standard flow velocity . instead of this , we used person - specific inlet flow velocity measured by mra , which allowed us to get more accurate parameters of fluid dynamics . several studies have investigated the association between carotid plaques progression and risk of cerebrovascular events in patients with asymptomatic carotid stenosis [ 1,22,2428 ] . these risk factors including age , sex , severity of stenosis , increased plaque area , carotid artery end - diastolic velocity , systolic blood pressure , and increased serum creatinine . our analysis suggests that plaque morphology characteristics nwi and hemodynamics parameter wss are independent risk factors for the progression from asymptomatic to stroke . logistics regression analysis and roc curve suggest that the combination of nwi and wss is better at predicting the risk of stroke . during the early stages of atherosclerotic plaque growth , the vessel may remodel and accommodate plaque growth without compromising luminal size . there are few plaque morphology characteristics , such as wa , used to assess plaques . clinical trials have shown that in human carotid arteries , luminal stenosis has limited value as an indicator of atherosclerotic plaque vulnerability , enabling prediction of only 1 of 10 strokes in asymptomatic patients . plaque burden , which is represented by plaque volume and maximum wall area ( mwa ) , as a direct measure of the lesion itself , may have substantial usefulness in the assessment of atherosclerosis . studies have shown nwi is a sensitive factor for early detection of carotid atherosclerosis plaques , and it can reflect the progression of plaque more accurately than other morphology characteristics such as la and wa . calculated as wa / tva , nwi contains information about lumen stenosis and thickening of the wall , which make nwi is the most effective indicator for evaluating the severity of atherosclerosis . furthermore , it can avoid the difference in the wall area caused by different vascular thicknesses . therefore , nwi may also be used as a dynamic index to measure the dynamic changes of plaques . even though morphology characteristics of plaques were thought to relate to the progression of local lesion , as mentioned above , plaque rupture is not solely dependent on plaque morphology , and other local factors are probably involved . as a consequence of improvements in imaging of atherosclerosis and in computational power , there is increasing evidence that hemodynamic factors are important in the atherogenic process and in the development of unstable plaque and thromboembolic stroke . disturbances of hemodynamics are thought to have a role in several aspects of this process , particularly in the causation of plaque rupture and in the formation of surface thrombus . the follow - up radiographic results confirmed that the culprit sites were consistent with the regions of high wss . wss is the parallel frictional force exerted by blood flow on the endoluminal surface of the arterial wall . the magnitude of wss is influenced by changes in luminal geometry , blood flow velocity , and plasma viscosity . although studies suggested that a certain degree of high wss has anti - atherosclerosis effect , the increase of wss is not necessarily a protective factor for atherosclerosis . lovett   showed that plaque ruptures more frequently in the upper side of the lumen , which is affected by the high wss and leads to the production of vulnerable plaque with a thin fibrous cap . studies of clinical pathological autopsies also showed that plaque rupture mainly occurred in the upper side of the lesion , consistent with the area of high wss . although the absolute value of the wss is not enough to directly damage the structure of the fiber cap , the increased wss in the upper side of the lesion is the primary factor causing rupture of the plaque . studies have confirmed that wss is associated with regulation of many vascular functions , such as maintenance of acute vessel tone , vascular permeability , adhesion of leukocytes , development of blood vessels , and secretion of pro - thrombotic and antithrombotic signaling molecules . activated ecs produce chemokines , cytokines , and adhesion molecules that interact with leukocytes and platelets , and target inflammation to specific tissues as a host defense mechanism . balaguru s team developed a versatile model based on cfd simulation to explore the shear stress - associated changes of biological function in endothelial cells ( ecs ) . cell morphology , cytoskeletal arrangement , cell death , reactive oxygen species profile , nitric oxide production , and disturbed flow markers under certain wss condition were assessed . they observed a 2~4-fold increase in vegfr2 expression in high - wss regions , but the increase in expression was not observed in low - wss areas . mcp-1 involved in the recruitment of leukocytes plays a significant role in the development of atherosclerotic plaque formation . there was a 2-fold increase in expression of hif1- in high - wss regions , and a less than 2-fold increase in low - wss areas . plaques that contain a large lipid - rich necrotic core , intraplaque hemorrhage , inflammation , and/or are covered by a thin fibrous cap are considered the most vulnerable to rupture . in animal studies and small case studies , an association between wss and plaque composition was observed . although low wss may induce plaque initiation , it has been hypothesized that plaque destabilization can be caused by high shear stress on the plaque . tuenter s study evaluated the association between shear stress and plaque components in asymptomatic persons . we found that the combination of plaque morphology characteristics nwi and hemodynamics parameter wss can improve the ability to identify patients at highest risk of rapid disease progression and may predict the risk of stroke in patients with asymptomatic carotid plaques . more prospective studies with larger sample sizes are necessary to validate the findings of this study and to discover new risk factors for imaging and fluid mechanics .
backgroundatherosclerosis plaques in the carotid arteries frequently have been found in patients with stroke . however , the pathogenesis of carotid plaque from asymptomatic to cerebrovascular events is a complex process which is still not completely understood . 
 we aimed to investigate the prognosis of asymptomatic carotid atherosclerotic plaques by use of magnetic resonance angiography ( mra ) combined with computational fluid dynamics ( cfd).material / methodswe prospectively studied a cohort of 228 participants ( mean age 59.218.48 ) with asymptomatic carotid atherosclerotic plaques ; mean follow - up duration was 1147.56224.84 days . 
 plaque morphology parameters were obtained by mra analysis . 
 lumen area ( la ) and total vessel area ( tva ) were measured , and wall area ( wa = tvala ) and normalized wall area index ( nwi = wa / tva ) were calculated . 
 cfd analysis was performed to evaluate hemodynamic characteristics , including wall pressure ( wp ) and wall shear stress ( wss ) . 
 independent risk factors for stroke were obtained by cox regression analysis . 
 the area under the curve ( auc ) of receiver operator characteristic ( roc ) and z - statistic test were used to evaluate risk factors.resultslogistics regression analysis showed nwi ( or : 3.472 , 95% ci : 2.9434.096 , p=0.11 ) and wss ( or : 6.974 , 95% ci : 1.07045.453 , p=0.42 ) were independent risk factors of stroke for patients with asymptomatic carotid plaques . 
 the area under the roc curve values for wss , nwi , and wss+nwi were 0.772 , 0.798 , and 0.903 , respectively.conclusionsthe combination of plaque morphology characteristics nwi and hemodynamic parameter wss may predict the risk of stroke in patients with asymptomatic carotid plaques .