intima - media thickness ( imt ) of the carotid artery and its increase is associated with several cardiovascular risk factors and manifest cardiovascular disease ( cvd ) ( 1 , 2 ) . the walls of the common carotid artery are straight and run parallel to the skin 's surface . the walls of the proximal internal carotid artery are usually divergent and curvilinear , and the vessel frequently descends deeper into the neck and is no longer parallel to the skin 's surface . even without such detractions as acoustic shadowing , which can occur when lesions are present , it is to be expected that measurements of the common carotid artery would be usually more precise than those of the internal carotid artery ( 3 ) . moreover , the pattern of wall thickening in brachial artery is quite diffuse than carotid artery , which may be a more sensitive index of long systemic exposure to risk factors ( 4 ) . therefore , evaluating mechanical parameters changes of common carotid and brachial arteries attracted researcher 's attention . using ultrasound for this aim is proper , because it is a noninvasive and non - radiation method . its cost is low and it has capability of forming real time imaging ( 5 ) . to attain the best possible diagnosis , it is essential that medical images be clear , sharp and without noise and artifacts . by nature , ultrasound image includes a lot of noise contents , especially speckle noise than other imaging modalities ( 6 ) . it reduces image resolution and contrast and blurs necessary details ; thereby , speckle noise reduces diagnostic value of this imaging modality . therefore , speckle noise reduction is essential whenever ultrasound imaging is used ( 6 , 7 ) . the traditional speckle removal filters , like the lee filter and frost filter have greater restrictions in edge preserving and characteristics preserving ( 8) . yu et al . presented the speckle reducing anisotropic diffusion ( srad ) filter ( 9 ) based on a partial different equation ( pde ) . the pde - based speckle removal approach allows the generation of set of filtered images that vary from fine to coarse . srad not only protects edges , but also enhances edges by eliminating diffusion across edges and allowing diffusion on either side of the edge ( 8) . besides , the topological derivative is a branch of computational mathematics with the aim of solving problems when the domain under consideration is perturbed by introduction of heterogeneity ( 10 ) . discrete topological derivative ( dtd ) algorithm is an indicator function that finds best pixels to introduce the holes or cracks that would most reduce noise conserving suitable image features in presence of diffusion ( 11 ) . continuum topological derivative ( ctd ) algorithm goes through a gradual transition from one state to a different state , without sudden changes ( 11 ) . ctd finds scaling parameter for the cost function and percentages of pixel that is re - classified in iteration and dtd calculates fined weighted for both terms in the cost function . thus , it is essential to have noise reduction filters to preserve the features , so that noise reduction causes no blurred or distorted edges . the aim of this study was to analyze performance of srad , dtd and ctd filters in ultrasound images of common carotid and brachial arteries for optimum removing noise with preservation of edges . in a cross - sectional design , an examination was performed on forty - two human subjects with a mean age of 44  6 years from april 2013 to june 2013 . cvd , the most frequent and lethal form of atherosclerosis disease , reaches a significant incidence at the age of 40 years in men ( 13 ) . our study group consisted of healthy volunteers who came to beheshti hospital affiliated to kashan university of medical sciences . patients medical history , physical examination , electrocardiography ( ecg ) and echocardiography were recorded . none of the subjects had history of cardiovascular and/or cerebrovascular disease , hypertension , diabetes mellitus and tobacco abuse ( 14 ) . this study was approved by the ethics committees of kashan university of medical sciences and beheshti hospital ( iran ; code ethical approval , 9139 ; approval date , 05/08/2012 ) . in our study , before ultrasonography , subjects rested for at least 10 minutes in supine position until their heart rate and blood pressure reached a steady state . blood pressure and heart rate were recorded with a calibrated oscilloscopic blood manometer ( alp k2 , adult cuff ,  1 mmhg , tokyo , japan ) and a wrist manometer ( microlife ,  3 mmhg , germany ) on the left brachial and radial arteries with the subject in a supine position respectively . measurements were performed in a temperature - controlled room according to current guidelines ( 15 ) . the left common carotid of subjects , 2 - 3 cm proximal to the bifurcation and the left brachial artery ( 3 - 5 cm upper than elbow ) were examined in the longitudinal direction with a high resolution sonoline antrases ( siemens , henkestrabe , erlangen , mittelfranken , bayern , germany ) ultrasound system equipped with a 5 - 13 mhz linear transducer ( 16 ) . dynamic range , depth of focus , maximum display depth , acoustic aperture , number of elements , array length and spatial pulse length were 55 db , 3.5 cm , 6 cm , 45  9 mm , 192  3 , 39 mm and 55 , respectively ( 17 ) . the audio video interleaves ( avi ) format of the consecutive images of the common carotid and brachial arteries with a frame rate of 43 frames per second was captured from hard drive and transferred to a pc ( computer ) for post processing . the recording contained 90 frames ( almost three cardiac cycles ) , while the left common carotid and brachial arteries were scanned in the longitudinal direction . a program was designed using matlab software version 7.01 ( math software co. , math works , usa ) to extract consecutive images in the bitmap ( bmp ) format from the avi ( image size : 547  692 pixel 2 ) . images were normalized so that the average gray scale median of the pixels in blood ranged between 0 and 5 , whereas that of the adventitia as 180 - 190 according to widely accepted specifications ( 18 ) . region of interest ( roi ) with a size of approximately 53  42 pixel2 applied on the imt of the posterior wall of common carotid and brachial arteries ( 19 ) . then , different noise reduction filters ( srad , dtd and ctd ) with the canny edge detection were performed in roi separately . finally , the program measured mean squared error ( mse ) ( 20 ) , peak signal to noise ratio ( psnr ) ( 20 ) , normalized absolute error ( nae ) ( 19 , 20 ) , normalized cross - correlation ( ncc ) ( 21 ) , structure similarity image measures ( ssim ) ( 22 ) , speckle index ( si ) ( 20 ) , structural content ( sc ) ( 23 ) , image quality index ( iqi ) ( 20 , 21 ) , maximum difference ( md ) ( 23 ) , average difference ( ad ) ( 23 ) and equivalent number of looks ( enl ) ( 18 , 24 ) ( table 1 ) . all measurements of both arteries were performed by a single operator to eliminate inter - observer variability ( 25 ) . , this detector searches local maximum of the gradient of the image function ( f ( x , y ) ) . there are two different thresholds to detect strong and weak edges and weak edges are connected to the strong edges in this method . in this study , we assumed here that the speckle pattern in ultrasound images has a white , gaussian noise model ( 26 - 28 ) and for consecutive images , the canny edge detection with different common de - specking methods ( srad , dtd , and ctd filters ) were performed in roi on the imt of the posterior wall of common carotid and brachial arteries . speckle noise with a random granular pattern corrupts the acquired image and delays interpretation of image content ( 27 ) . a speckle image is commonly modeled as multiplicative noise in ultrasound images ( 26 , 28 ) . the srad method ( 29 , 30 ) is used directly for suppressing speckle noise in ultrasound images with instant coefficient . srad equation used in this study is given in equation 1 : where t is the diffusion time index , t is the time step responsible for the convergence rate of the diffusion process ( range : 0.05 to 0.25 ) and g(icov(u ' ) ) is the diffusion function and is given by equations 2 and 3 where q is the measure of speckle coefficient of variation in a homogenous region of the image . continuum is anything that goes through a gradual transition from one condition to a different condition without any abrupt changes . a single point is a continuum that contains more than one point ( 11 ) . it is the same as discrete but designed vector b = { 1 , 2 , , n}. 1 , 2 ,  , n are structures that modeled as a continuum . topological derivative quantifies the sensitivity of a problem when the domain is perturbed by the introduction of heterogeneity ( 31 , 32 ) . let the domain  under consideration is perturbed by the introduction of small holes ( topology changes ) in  as shown in figure 1 . in this   is the domain under perturbation ,  is the crack of length centered at the pixel n , ( ) is the cost function assigned before perturbation and (/ ) is the cost function after perturbation . n = 2 , 3 ) and  as a crack of length centered at point x   ( 11 , 12 ) :   where ( ) is known positive function going to zero with , and dt ( x ) is the topological derivative at point given in equation 4 . it was given by the equation 5 : where k is the diffusion of pixel s with neighbors p and n = { w , e , n , s } indicating the neighbors of the pixel s and ui is the intensity of the image pixel . also , ui is defined by the equation 6 : and ui is clearly calculated using the equation 7 : where i  1 indicates the iteration number , k = { k , k , k , k } indicates the set of diffusion factor associated with the pixel s and t is the artificial time step size . normal distribution and homogeneity of variance of data were checked by kolmogorov - smirnov test ( k - s ) and levene s test , respectively . the statistical significance in mean values of mse , psnr , nae , ncc , ssim , si , sc , iqi , md , ad and enl variables of the canny edge detection with all filters were assessed by anova test . the maximum sample size for the analysis of variance ( anova ) was estimated from equation 8 : n and  were sample size and non - centrality parameter , respectively and estimated with a confidence level of 95% and power test of 80% . the value of  was calculated from equation 9 : k ,  , i , and m were number of groups , standard deviation , mean of each group and overall mean ( 33 ) . in a cross - sectional design , an examination was performed on forty - two human subjects with a mean age of 44  6 years from april 2013 to june 2013 . cvd , the most frequent and lethal form of atherosclerosis disease , reaches a significant incidence at the age of 40 years in men ( 13 ) . our study group consisted of healthy volunteers who came to beheshti hospital affiliated to kashan university of medical sciences . patients medical history , physical examination , electrocardiography ( ecg ) and echocardiography were recorded . none of the subjects had history of cardiovascular and/or cerebrovascular disease , hypertension , diabetes mellitus and tobacco abuse ( 14 ) . this study was approved by the ethics committees of kashan university of medical sciences and beheshti hospital ( iran ; code ethical approval , 9139 ; approval date , 05/08/2012 ) . in our study , before ultrasonography , subjects rested for at least 10 minutes in supine position until their heart rate and blood pressure reached a steady state . blood pressure and heart rate were recorded with a calibrated oscilloscopic blood manometer ( alp k2 , adult cuff ,  1 mmhg , tokyo , japan ) and a wrist manometer ( microlife ,  3 mmhg , germany ) on the left brachial and radial arteries with the subject in a supine position respectively . measurements were performed in a temperature - controlled room according to current guidelines ( 15 ) . the left common carotid of subjects , 2 - 3 cm proximal to the bifurcation and the left brachial artery ( 3 - 5 cm upper than elbow ) were examined in the longitudinal direction with a high resolution sonoline antrases ( siemens , henkestrabe , erlangen , mittelfranken , bayern , germany ) ultrasound system equipped with a 5 - 13 mhz linear transducer ( 16 ) . dynamic range , depth of focus , maximum display depth , acoustic aperture , number of elements , array length and spatial pulse length were 55 db , 3.5 cm , 6 cm , 45  9 mm , 192  3 , 39 mm and 55 , respectively ( 17 ) . the audio video interleaves ( avi ) format of the consecutive images of the common carotid and brachial arteries with a frame rate of 43 frames per second was captured from hard drive and transferred to a pc ( computer ) for post processing . the recording contained 90 frames ( almost three cardiac cycles ) , while the left common carotid and brachial arteries were scanned in the longitudinal direction . a program was designed using matlab software version 7.01 ( math software co. , math works , usa ) to extract consecutive images in the bitmap ( bmp ) format from the avi ( image size : 547  692 pixel 2 ) . images were normalized so that the average gray scale median of the pixels in blood ranged between 0 and 5 , whereas that of the adventitia as 180 - 190 according to widely accepted specifications ( 18 ) . region of interest ( roi ) with a size of approximately 53  42 pixel2 applied on the imt of the posterior wall of common carotid and brachial arteries ( 19 ) . then , different noise reduction filters ( srad , dtd and ctd ) with the canny edge detection were performed in roi separately . finally , the program measured mean squared error ( mse ) ( 20 ) , peak signal to noise ratio ( psnr ) ( 20 ) , normalized absolute error ( nae ) ( 19 , 20 ) , normalized cross - correlation ( ncc ) ( 21 ) , structure similarity image measures ( ssim ) ( 22 ) , speckle index ( si ) ( 20 ) , structural content ( sc ) ( 23 ) , image quality index ( iqi ) ( 20 , 21 ) , maximum difference ( md ) ( 23 ) , average difference ( ad ) ( 23 ) and equivalent number of looks ( enl ) ( 18 , 24 ) ( table 1 ) . all measurements of both arteries were performed by a single operator to eliminate inter - observer variability ( 25 ) . , this detector searches local maximum of the gradient of the image function ( f ( x , y ) ) . there are two different thresholds to detect strong and weak edges and weak edges are connected to the strong edges in this method . in this study , we assumed here that the speckle pattern in ultrasound images has a white , gaussian noise model ( 26 - 28 ) and for consecutive images , the canny edge detection with different common de - specking methods ( srad , dtd , and ctd filters ) were performed in roi on the imt of the posterior wall of common carotid and brachial arteries . speckle noise with a random granular pattern corrupts the acquired image and delays interpretation of image content ( 27 ) . a speckle image is commonly modeled as multiplicative noise in ultrasound images ( 26 , 28 ) . the srad method ( 29 , 30 ) is used directly for suppressing speckle noise in ultrasound images with instant coefficient . srad equation used in this study is given in equation 1 : where t is the diffusion time index , t is the time step responsible for the convergence rate of the diffusion process ( range : 0.05 to 0.25 ) and g(icov(u ' ) ) is the diffusion function and is given by equations 2 and 3 where q is the measure of speckle coefficient of variation in a homogenous region of the image . continuum is anything that goes through a gradual transition from one condition to a different condition without any abrupt changes . a single point is a continuum that contains more than one point ( 11 ) . it is the same as discrete but designed vector b = { 1 , 2 , , n}. 1 , 2 ,  , n are structures that modeled as a continuum . topological derivative quantifies the sensitivity of a problem when the domain is perturbed by the introduction of heterogeneity ( 31 , 32 ) . let the domain  under consideration is perturbed by the introduction of small holes ( topology changes ) in  as shown in figure 1 . in this   is the domain under perturbation ,  is the crack of length centered at the pixel n , ( ) is the cost function assigned before perturbation and (/ ) is the cost function after perturbation . we considered bounded open set in r ( n = 2 , 3 ) and  as a crack of length centered at point x   ( 11 , 12 ) :   where ( ) is known positive function going to zero with , and dt ( x ) is the topological derivative at point given in equation 4 . it was given by the equation 5 : where k is the diffusion of pixel s with neighbors p and n = { w , e , n , s } indicating the neighbors of the pixel s and ui is the intensity of the image pixel . also , ui is defined by the equation 6 : and ui is clearly calculated using the equation 7 : where i  1 indicates the iteration number , k = { k , k , k , k } indicates the set of diffusion factor associated with the pixel s and t is the artificial time step size . normal distribution and homogeneity of variance of data were checked by kolmogorov - smirnov test ( k - s ) and levene s test , respectively . the statistical significance in mean values of mse , psnr , nae , ncc , ssim , si , sc , iqi , md , ad and enl variables of the canny edge detection with all filters were assessed by anova test . the maximum sample size for the analysis of variance ( anova ) was estimated from equation 8 : n and  were sample size and non - centrality parameter , respectively and estimated with a confidence level of 95% and power test of 80% . the value of  was calculated from equation 9 : k ,  , i , and m were number of groups , standard deviation , mean of each group and overall mean ( 33 ) . ultrasonic examination was performed for the left common carotid and brachial arteries of forty - two men ( aged 44  6 years ) with no history of cardiovascular and/or cerebrovascular disease , hypertension , diabetes mellitus and tobacco abuse . body mass index ( bmi ) of participants was 23  3 ; systolic pressure as 122  14 mmhg ; diastolic pressure as 83  5 mmhg and heart rate ( hr ) of 71  6 bpm ( beat per minute ) . figure 2 shows original and filtered common carotid and brachial arteries in a study subject . the results of de - noising filters with the canny edge detection are summarized in table 2 for imt of the left common carotid and left brachial arteries in 90 frames ( almost three cardiac cycles ) . according to values of mse , psnr , nae , ncc , ssim , si , sc , iqi , md , ad and enl , there was a significant difference between ctd , dtd and srad filters - canny edge detection status in the common carotid artery ( all p values < 0.001 ) . according to values of mse , psnr , nae , ncc , ssim , si , sc , iqi , md , ad and enl , there was a significant difference between ctd , dtd and srad filters - canny edge detection status in brachial artery ( all p values < 0.001 ) . dtd and ctd filters with the canny edge detection were better than srad filter with the canny detection for speckle suppression and details preservation in the common carotid and brachial arteries ultrasound images ( lower mse , si , md , ad , nae higher psnr , enl and near to 1 for ncc , sc , iq , ssim ; all proved that their performance are high in de - noising ultrasound images ) . abbreviations : mse , mean squared error ; psnr , peak signal to noise ratio ; nae , normalized absolute error ; ncc , normalized cross - correlation ; ssim , structure similarity image measures ; si , speckle index ; sc , structural content ; iqi , image quality index ; md , maximum difference ; ad , average difference ; enl , equivalent number of looks . data are presented as mean  sd . all p values for anova and post hoc multiple comparisons lsd test were < 0.001 . nowadays , one of the main methods for prediction of cardiovascular diseases is measuring imt of the common carotid artery . therefore , precise measurement of imt is useful for assessing the risk of cardiovascular diseases or its progress ( 34 ) . moreover , weidinger et al . ( 4 ) showed that assessment of brachial artery may have some potential advantages . second , the pattern of wall thickening in the brachial artery is rather defused than carotid artery , which may be a more sensitive indicator of long - term systemic exposure to risk factors . besides , study of the blood flow in arteries is a rich field surrounding unsteady flows , changing geometries and secondary structures . diseased arteries can create high levels of turbulence , head loss and a choked - flow condition in which arteries can collapse . the pulsatile nature of the flow creates a dynamic environment that raises many interesting and fundamental unsteady fluid and arterial wall mechanics questions . answers to these questions can be used to predict and change blood flow to alter the course of disease . each fluid and wall mechanics aspect plays a role in the generation , detection and treatment of arterial disease . besides , quantities of stress and mass transfer at the blood saccular intracranial aneurysms usually occur at arterial curves and bifurcations in the circle of willis , with strong implication of a critical role for hemodynamics in such vascular geometry ( 36 ) . wall shear stress and strain distributions and extreme values are broadly accepted to be responsible for aneurysm initiation , growth and rupture ( 37 ) . moreover , artery stenosis may induce disturbance and flow separation , and consequently create significant flow resistance , large pressure drop and complex flow pattern ( 38 ) . castro et al . showed that for higher stenosis grades , the recirculation pattern results in more velocity and wall shear stress values over a big area . for distal aneurysms ipsilateral to the high degree stenosis , the vortex may reach the aneurysm basing on the stenosis grade and the distance between the aneurysm and the stenosis . under this situation , the part of the neck closer to the aneurysm witnesses high velocities upstream , resulting in the higher wall shear stress values . for the use of computational fluid dynamics in the study involving aneurysm and stenosis has gained significance , focusing on different shape and size of aneurysms and stenosis severity with idealized geometries ( 35 , 39 ) . due to the above - mentioned matters , fluid and arterial wall structure and mechanics would continue to play a major role in the future diagnosis , understanding and treatment of cardiovascular diseases . ultrasound is a broadly used and safe medical imaging technique due to its noninvasive nature , low cost and capability of forming real time imaging ( 40 ) . however , the efficacy of ultrasound imaging is reduced by presence of signal dependent noise known as speckle . speckles pend to mask the presence of low - contrast lesion and reduce the ability of observers to resolve the real information . moreover , presence of speckles in common carotid artery ultrasound images hinders enhancement in them . therefore , it is very important to suppress speckle noise and the image with losing worth image features is enhanced before making any image analysis ( 5 ) . it is a form of multiplicative noise ( 8) . the traditional speckle removal filters , like the lee filter and frost filter have greater restrictions in edge preserving and characteristics preserving ( 9 ) . noise reduction filter such as conventional anisotropic diffusion is not proper to speckle suppression ( 8) . it is proper for additive noise . according to these problems , srad , dtd and ctd these filters not only preserve edges , but also reduce noise ( 6 , 24 , 41 ) . edge detection has been used as a tool for evaluating the performance of noise reduction filters . maini and aggraval et al . proposed that the canny edge detection algorithm is a proper method , which reduces false and misses real edges . this study showed that dtd and ctd filters with the canny edge detection are better than srad filter with the canny detections for speckle noise reduction and details in the common carotid and brachial arteries ultrasound images . the present study is in agreement with others ( 11 , 20 ) . using the automatic method for measuring the imt in b - mode ultrasound images , a few researches showed that changes in imt happen during cardiac cycle ( 44 - 46 ) . selzer et al . ( 47 ) showed that common carotid imt was lower at peak - systolic than end - diastolic by an average of 5.3% in 24 samples . another study showed that averaged change of imt in the common carotid was 0.041 mm ( 48 ) . therefore , in this study we tried to provide a condition that noise reduction followed at approximately three cardiac cycles . moreover , noise reduction was used on ultrasound images of imt in both arteries ( carotid and brachial arteries ) . probably , our study contained more comprehensive information than other studies that noise reduction was performed only on one frame or one artery . one limitation of this study was that despite we used four orders pde in srad algorithm , consumed time in de - noising of this filter was a little more than the ultrasound images . another limitation was that the translation movement of the common carotid and brachial arteries which came from the probe movement during scanning and suppression of artery of artery pulsating movement were more complicated . we concluded that dtd and ctd filters with the canny edge detection were better than srad filter with the canny detection for speckle suppression and details preservation in the common carotid and brachial arteries ultrasound images . our finding may help physicians to measure carotid and brachial imt better than non - denoising ultrasound images .
background : ultrasonic evaluation of intima - media thickness ( imt ) is an early marker of assessing the development of atherosclerosis and determining cardiovascular risk . to attain the best possible diagnosis , 
 it is essential that medical images be clear , sharp and without noise and artifacts.objectives:comparison of speckle reducing anisotropic diffusion ( srad ) , discrete ( dtd ) and continuum topological derivative ( ctd ) on b - mode ultrasound images of common carotid and brachial arteries throughout the cardiac cycle.patients and methods : in a cross - sectional design , an examination was performed on forty - two human subjects with a mean age of 44  6 years from april 2013 to june 2013 . 
 this study was approved by the ethics committees of kashan university of medical sciences and beheshti hospital . 
 an ultrasonic examination of common carotid and brachial arteries of forty - two human subjects was performed . 
 the program was designed in matlab software to extract consecutive b - mode images and apply region of interest ( roi ) on the imt of the common carotid and brachial arteries . 
 then , three different noise reduction filters with the canny edge detection were used in roi separately . 
 finally , the program measured the image quality metrics.results:according to values of eleven different image quality metrics ( mentioned in the main text ) , there was a significant difference between ctd , dtd and srad filters with the canny edge detection status in the common carotid and brachial arteries throughout the cardiac cycle ( all p values < 0.001 ) . 
 for example , peak signal to noise ratios ( psnr ) using ctd , dtd and srad filters were 95.43  0.64 , 88.86  0.82 and 73.02  0.20 in common carotid and 
 96.39  1.25 , 92.58  0.11 and 88.27  0.63 in brachial arteries , respectively ( both p values < 0.001).conclusions : by measuring image quality metrics , this study showed that dtd and ctd filters with the canny edge detection respectively , are better than srad filter with the canny detection for speckle suppression and details preservation in both arteries in the ultrasound images .