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Experimental estimation of blood flow velocity through simulation of intravital microscopic imaging in micro-vessels by different image processing methods

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Quantization of red blood cell (RBC) velocity in micro-vessel is one of the techniques for dynamic observation of microvascular mechanisms. The flow measurement of RBC in micro-vessels is still a challenge nowadays. Image processing for velocity
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  Regular Article Experimental estimation of blood  fl ow velocity through simulation of intravitalmicroscopic imaging in micro-vessels by different image processing methods Tzung-Chi Huang a, ⁎ , Wen-Chen Lin b , Chih-Chieh Wu b , Geoffrey Zhang c , Kang-Ping Lin b a Department of Biomedical Imaging and Radiological Science, China Medical University, Taiwan b Department of Electrical Engineering, Chung Yuan University, Taiwan c Radiation Oncology, H. Lee Mof   fi tt Cancer Center and Research Institute, Tampa, FL, USA a b s t r a c ta r t i c l e i n f o  Article history: Received 27 May 2010Revised 18 July 2010Accepted 19 July 2010Available online 24 July 2010 Keywords: Red blood cellBlood  fl owVelocity measurementOptical  fl owMicro-vessel Quantization of red blood cell (RBC) velocity in micro-vessel is one of the techniques for dynamicobservation of microvascular mechanisms. The  fl ow measurement of RBC in micro-vessels is still a challengenowadays. Image processing for velocity measurement using a frame by frame analysis is a commonapproach. The accuracy of the calculations, which is algorithm dependant, has rarely been examined. In thispaper, we evaluated the accuracy of the existing methods, which includes cross correlation method, Houghtransform method, and optical  fl ow method, by applying these methods to simulated micro-vessel imagesequences. Simulated experiments in various micro-vessels with random RBC motion were applied in theevaluation. The blood  fl ow variation in the same micro-vessels with different RBC densities and velocitieswas considered in the simulations. The calculation accuracy of different fl ow patterns and vessel shapes werealso examined, respectively. Based on the comparison, the use of an optical fl ow method, which is superior toa cross-correlation method or a Hough transform method, is proposed for measuring RBC velocity. The studyindicated that the optical  fl ow method is suitable for accurately measuring the velocity of the RBCs in smallor large micro-vessels.© 2010 Elsevier Inc. All rights reserved. Introduction The relationship between blood  fl ow in microcirculation and theclinical physiology in blood circulation has been a wide-reaching andin-depthunderstanding.Variousriskfactorsofdiseasescanberelatedtocorrespondingchangesin microcirculation.For instance,Raynaud'ssyndrome(Wollersheim et al., 1988; Bertuglia et al., 1999), hyperten-sion(Bonacci et al., 1996; Cesarone, 2000) or diabetes(Chang et al., 1997; Tibiriçá et al., 2007) are usually accompanied with impairedmicrocirculation. Therefore, information in blood  fl ow of microcircu-lation plays an important role in health assessment and angiopathyprevention. Dynamic observation of microvascular mechanisms thusprovides a deeper understanding of diseases and their relationship tothe physiological function of microcirculation.Quantization of the red blood cell (RBC) velocity in micro-vesselsis a means of such observation. However, the  fl ow measurement of RBC in micro vessels is still a challenge with current techniques. The fl ow in large vessels is able to be measured by using electro-magneticblood  fl owmeter or ultrasonic Doppler  fl owmeter. Plenty usefulinformation has been obtained on alterations in  fl ow duringphysiological events and in the viscous properties of blood. A majorlimitation of such measurements has been their inability to relatemicrovascular perfusion observed within individual micro-vessels tothe topographical succession of arterioles, capillaries, and venulespeculiar to a given tissue.Imageprocessingisanalternative,non-invasiveapproachtoachievethis goal. Several literatures have been published in RBC velocitymeasurement in micro-vessels using dynamic video microscopy(Bollinger et al., 1974). The measurement of the displacement of relevant patterns (RBCs or plasma gaps) between two frames and thetime separating them give an estimation of the RBC velocity. But itrequires the selection of a good tracking pattern which appears to bedif  fi cult in larger vessels such as venules and arterioles. Several studieshave focused on the use of crosscorrelations for the assessment of RBCvelocity(Tsukadaetal.,2000;BroxandWeickert,2002).Thesemethodscan be divided into two categories: the temporal correlation and thespatial correlation methods. Umetani et al. (1989) have used imagegradient method to measure microvascular red blood cell velocity andpointed out the time-varying relationship between the blood  fl owvelocities. Recently, Optical  fl ow has been proposed as a quantitativemethodofmeasuringthedetailedvelocitydistributioninmicro-vessels(Sugii et al 2002, Tsukada et al., 2000). The authors have developed aparticle image velocimetry (PIV) technique with improved dynamicrange, spatial resolution and measurementaccuracy, and also analyzedthe blood velocity pro fi le in microvessels of arterioles in rat mesentery(Sugiietal.,2002).ManjunathaandSingh(2002)alsousedoptical fl ow Microvascular Research 80 (2010) 477 – 483 ⁎  Corresponding author. 91, Hsueh-Shih Road, Taichung, 404 Taiwan. Fax: +886 42205 4179. E-mail address:  tzungchi.huang@mail.cmu.edu.tw (T.-C. Huang).0026-2862/$  –  see front matter © 2010 Elsevier Inc. All rights reserved.doi:10.1016/j.mvr.2010.07.007 Contents lists available at ScienceDirect Microvascular Research  journal homepage: www.elsevier.com/locate/ymvre  method to measure velocity pro fi les of a blood  fl ow in the multiplebranching of frog mesentery employing microscopic video imaging(Manjunatha and Singh, 2002). In the literature by Kempczynski and Grzegorzewski (2008), the Hough transform technique has beenadopted to estimate the velocity of RBC aggregates during sedimenta-tion. RBC velocity was also estimated by using the Hough transformmethod in a simulation experiment. The results show that velocityassessmentperformsexcellentlyupto750pixels/s.Athighervelocities( N 1250pixels/s),themethodfailsandselectsanalternativeorientationthat results in a large velocity error (Dobbe et al., 2008).Generally, the blood  fl ow velocity inside microvessels in vivo isestimated along the central line of vessels. The accuracy of calculatedresults, which is algorithm dependant, has rarely been examined. Inthis paper, the red blood cell velocities in microvessels werecalculated using the three mentioned measurement methods: crosscorrelation method, Hough transform method, and optical  fl owmethod, through simulation of intravital microscopic imaging. Theaccuracy of the methods was evaluated by applying these methods tosimulated microvessel image sequences, of which the RBC velocitiesare known. The calculation accuracy of different  fl ow patterns andvessel shapes were also examined respectively. Materials and methods Image generation In microcirculation, the capillaries lie between, or connect, thearteriolesandvenules.Capillariesformextensivebranchingnetworksin avivobody,whichdramaticallyincreasethesurfaceareasavailablefor rapid exchange of molecules. A capillary is a thin size form of vessel. Pre-capillary is a vessel lacking complete coats, located just tothe arterial side of a capillary, and is about 3 – 5 times in diameter. It isnot much different from capillary in other respects. Pre-capillary andcapillary branch off from metarteriole and terminal arteriole. Thesimulation images were generated based on the physical (orphysiological) and anatomical characteristics of microcirculation.The capillary bed is simulated in various forms, with one of them instraight line, and another clip shaped for one RBC to pass. Branchingbed of pre-capillary into capillary is also simulated. A Matlab basedcomputer program (MathWorks, version 7. 1) was used to generatethe micro-vessel image sequences.Blood is a complicate heterogeneous liquid with its viscosityvarying with shear rate. It possesses non-Newtonian characteristics.Twokindsofdynamicblood fl owimagesweresimulatedinthisstudy.One was to simulate the random motion of RBC in various shapes of blood vessels. Individual RBCs suspended in autologous plasma thathave random motion were studied too in this category. The other onefocused on the blood  fl ow variation with different RBC densities. Thisis included in our study because the density of RBC, or hematocrit, isthe most important factor in blood hydrodynamic variation. The RBCdensity also dominates the variation in viscosity. The higher RBCdensity, or the higher hemotocrit, results in higher friction betweenthe blood layers, which causes higher viscosity. Normal hematocrit isabout 50% of blood in volume. In the simulation, the RBC densitieswere grouped to high, medium and low levels. Vessel size and shapes Vesselsizevariesinawiderangeinhumananatomy.Microvesselswere generated with various sizes: (1) 1-RBC wide in diameter(Fig. 1a), (2) 2-RBCs wide in diameter (Fig. 1b) and 4-RBCs wide in diameter (Fig. 1c). Different vessel shapes were generated with theMatlab-based program in order to cover various real conditions asblood  fl ow in micro-vessels. The RBC movement in vessels followedthe velocity variation shown in Fig. 1d through e. Fig. 1f and g gives 2 examples of shapes: branching and clip (or clip-shape). These shapescan often be found in various parts of a human body. For example, theclip-shape vessel is very common in  fi nger nail-fold. Spatial distribution of RBC velocity in micro-vessel The RBC velocity varies depending on the RBC location in a vessel.Mathematical expression of the RBC motion model is showing inFig.2.TheRBCvelocity V  wassimulatedasafunctionofradius r  insideavessel, V  ( r  )= Vc  (1 − r  2 / R 2 ),inwhich Vc  isthecentervelocity( r  =0), R  is the vessel radius. Due to viscosity, the velocity is less in value as  r  increases (closer to the vessel wall). Motion in vessels of various RBCdensities was also modeled. Low, medium and high density of RBC isde fi ned based on the number of cells per unit volume. Fig. 3 showsexamples of vessels with different RBC densities. With differentdensities, the image sequences were generated with various maxi-mumRBCvelocitiesof1,3,5,and10pixelsperframerespectively.TheRBC velocities have a parabolic curve function in relation to thelocation inside a micro-vessel. RBC velocity estimationCross correlation method (CCM) Severalstudieshavefocusedontheuseofcrosscorrelationsfortheassessment of RBC velocity (Tsukada et al., 2000). The use of thesemethods corresponds to the tracking of characteristic patterns inspace or in time. In this study, temporal correlation was used tomeasuretheblood fl owvelocityinthemicro-vessels.Forthetemporalcrosscorrelationmethods,thetransittimebetweentworegionsofthemicro-vessel is estimated by measuring the intensity of twoindependent windows positioned on the skeleton of micro-vessel.This transit time, estimated using an image correlation functionbetween the windows, is used to estimate the velocity. Fig. 1.  Various micro-vessels. Different sizes in diameter: (a)-(c) the diameter of themicro-vessel is one, two and four times of the RBC size, respectively. (d)-(e) micro-vessel changes from narrow to wide and vice versa. (f)-(g) Two vessel shapes: (f)branching (g) clip.478  T.-C. Huang et al. / Microvascular Research 80 (2010) 477  – 483  In particular correlation computation, the question resolves itself into the following three points. First, skeleton extraction is applied onthe image to sketch the center line (i.e., skeleton) of the vessel whichisalsoregardedastheblood fl owpathinthecapillary.Theintensityof each skeleton pixel as in each section is determined from the images.Pixel intensitywas averagedoverthe neighborpixelswithina 7-pixelwide square which is similar to the physical size of a RBC. Second, themaximum value of the one demotion cross-correlation between thetwo sequential images was calculated to obtain the frame-to-frameRBC displacement and the velocity correspondingly. Considering twoseries  x  and  y  where window length  i =0, 1, 2... n , the correlationcoef  fi cient  r   is de fi ned as r   =  S   xy  ffiffiffiffiffiffiffiffiffiffiffiffiffi S   xx S   yy q   = ∑ ni =1  x i −  P  x    ×  y i −  P  y  h i ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ∑ ni =1  x i −  P  x   2 ∑ ni =1  y i −  P  y   2 s   ;  − 1 ≤ r  ≤ 1  ð 1 Þ where  P  x  and  P  y  are the means of the corresponding series. Third, twowindowswiththesamesizewereusedin eachsite ofvesselforcross-correlation computation. For two window cross-correlation, thewindow length was equal to a half of segment length of each site.For example, one windowwas locatedin the fi rst half of the arteriolarlimb and the other window was in the second half. Furthermore, twomaximum values were obtained from these windows in each site andwere averaged to present the RBC displacement in two sequentialframes. Hough transform method (HTM) The conventional Hough transform is a method for detectingstraight lines (or curves) in images. It is basically a point-to-curvetransformation that detects straight lines in images. In this study,pixel intensity of a pro fi le image was extracted from pixels on thecentral line of a vessel. The intensity was averaged over the neighborpixels within a 7-pixel wide square that is similar to the physical sizeof a RBC. Space-time diagram method is based on the pro fi le imagethat is composed of pixel intensity on the central line of continuousframes.Whentheplasmagapand/orRBCinblood fl owarevisible,thepro fi les of the space-time diagram will present clear slopes forvelocitydetermination. The horizontalaxis of the space-time diagramis vessel length (distance) and the vertical axis is frame number(time). The space-time diagram was divided into small squarediagrams with a size of 16×16 pixels. Slopes were automaticallyestimated by using Hough transform. The RBC velocity was deter-mined by the slope of most apparently oblique line in all of the smallspace-time diagrams. In other words, Hough transform techniqueconsiders the polar representation of a line (Kempczynski andGrzegorzewski, 2008): R  =  x cos θ  +  y sin θ  ð 2 Þ where (  x ,  y ) is the coordinate of each line pixel in the space – timediagram, θ theorientationofthevectornormaltothelineandstarting Fig. 2.  The schema is to show that the RBC velocity  V   with the same fl ow direction was simulated as a function of radius  r   inside a micro-vessel,  V  ( r  )= Vc  (1- r  2 / R 2 ), in which  Vc   is thecenter velocity ( r  =0),  R  is the micro-vessel radius. Due to viscosity, the velocity is less in value as  r   increases (closer to the vessel wall). Fig. 3.  An example of different RBC densities and simulated RBC velocities as functionsof location in micro-vessel. In the left diagrams, low density (a), medium density (b),and high density (c) of RBCs are shown from top to bottom. The right diagram (d)indicates that RBCs in blood  fl ow have motion with a parabolic curve function inrelation to the location inside a micro-vessel.479 T.-C. Huang et al. / Microvascular Research 80 (2010) 477  – 483  at the srcin, and  R  the length of this vector, which is equal to thedistance of the line to the srcin. The discrete image of parameterspace consists of accumulated cells,  H  ( θ ,  R ), that are incremented foreach sinusoidal curve that passes the cell.On a pro fi le image, border detection is performed using the Cannyedge method. Characteristic curves, straight lines in this study, arethen detected using HTM. The angle  θ  is calculated using the straightlines. The blood  fl ow velocity  V   is calculated by equation V   = 1 = tan  θ ð Þ :  ð 3 Þ The horizontal axis of a pro fi le image is the grey level distributionalong the central line of a blood vessel. The spatial resolution of theimage determined by hardware is 1.42  μ  m, and if the temporalresolutionis1/30 s,determinedbythemaximumsamplingrateofthesystem. From the velocity equationV =  △ D = △ T ;  ð 4 Þ we know that the horizontal axis of a pro fi le image corresponds todistance while the vertical corresponds to time. As the gaps betweenRBCs, or the variation among the RBCs, are re fl ected as the grey levelvariationalongthecentralaxis,thecharacteristiclinesorstripscanbeobtained from the pro fi le image. Using the angle between the linesand the horizontal axis  θ , the velocity equation becomesV =  △ D = △ T = 1 = tan  θ ð Þ ð 5 Þ An example of using Hough Transform to get the angle  θ  from ablood  fl ow pro fi le image is given here. The Canny characteristicimages are generated by applying Hough transform to the pro fi leimage which is shown as schema in Fig. 4a. The resulted images areshown as (b) in Fig. 4. The coordinates of the brightest spots are thenlocated, which are the maximum values of the transform. Since thepoint of the longest line appears many times at the same angle, byanalyzing c to f in Fig. 4, the maximum number of appearance and thecorresponding angle are obtained for each image. Such brightestcoordinates ( R ,  θ ) calculated for c, d, e and f are (23, − 18°), (43, − 19°),(40, − 20°)and(26, − 19°)respectively.Theaverageblood fl owvelocityis thus 284.22  μ  m/s . Optical  fl ow method (OFM) Optical  fl ow computation results in motion direction and motionvelocity at image points. The immediate aim of OFM-based imageanalysis is to determine a motion  fi eld. It re fl ects the image changesdue to motion during a time interval d t  , and the optical  fl ow  fi eld isthe velocity  fi eld that represents the three-dimensional motion of object points across a two-dimensional image. In the present study,this gradient-base OFM (Horn and Schunck, 1981; Wu et al., 2009;Huang et al., 2006; Zhang et al., 2008a; Guerrero et al., 2004; Zhanget al., 2008b) was applied to calculate the RBC velocity on twosuccessive images. The velocity matrix of displacement, includinghorizontalandverticalmovementrespectivelyonthevesselimageforeach single pixel, was acquired using OFM. The velocity calculationequation in OFM is shown below. v  n  + 1 ð Þ =  v  n ð Þ + ∇  f   ∇  f  ⋅ v  n ð Þ +  ∂  f  ∂ t  α 2 + ‖ ∇  f   ‖ 2  !  ð 6 Þ where n isiterationtimesand v  n ð Þ istheaveragevelocityderivedfromthe surrounding pixel.Optical fl ow equation calculates the difference of images and fi ndsthe deformed image to match the next frame. Originally, optical  fl owmethod (OFM) requires a very small time interval betweenconsecutive images and no signi fi cant change occurs between two Fig. 4.  (a) An image of temporal pro fi le which was composed of intensity of pixels on the central line of micro-vessel. In this example, the length of central line is 256 pixels. (b) Theedgeoftemporal pro fi le(256×100pixels)wasobtainedbyusingCannyedgedetection,which wasdivided intofourofsmallsquarediagramswithasizeof64×100pixelsfromtopto bottom. (c)-(f) are the Hough transformations which correspond to Canny edge detection as in (b). The angle of the maximal aggregate value of appearance for each image is (c)-18°, (d) -19°,(e) -20°and (f) -19° respectively.480  T.-C. Huang et al. / Microvascular Research 80 (2010) 477  – 483  consecutive images. The srcinal OFM developed by Horn andSchunck was not reliable in velocity calculations when object motionis signi fi cant between two consecutive frames, in which no featuresare overlapping.To overcome this problem, optical  fl ow calculations are repro-cessed for a number of times with continuously updated deformedimages, which converges the velocity  fi eld to accurately match the fi naldeformationtothetargetimage.WiththisimplementationintheOFM, large motions can be accurately calculated and the quality of registration is signi fi cantly improved, regardless of the motion size. Results and discussion The velocities calculated using CCM, HTM and OFM, respectively,were compared to each other and with the known values from thesimulations by the Matlab based program. This comparison wasapplied to various RBC densities, velocities, shapes, vessel sizes andsize variations. In order to evaluate the performances of the proposedalgorithms,asimulatedexperimentwithrandomRBCsmotionisusedat  fi rst. The mean and standard deviation of differences among thecalculated values in number of pixels by using the three imageprocessing methods were listed in Table 1, which shows overallaverageerrorsofthevelocityestimationinvariousmicro-vesselcases.Forthevelocityestimationinvariousmicro-vesselbeds,OFMgavetheminimum value in average error while CCM yielded the maximum.According to calculations using the window diameter of 30~40pixels for CCM, the  fl ow velocity of the centre micro-vessel werewithin 2.741±5.925 pixels/frame. The window size is equal to thesizeofsensorsforCCM.TheimageintensityofanRBCinmicro-vesselswas similar to each other. This could cause uniform signal in thewindow, which in turn decreases accuracy signi fi cantly. For HTM, themage of temporal pro fi le was previously intensi fi ed by the Cannyedge detection to avoid this problem. Consequently, the calculationsusing OFM and HTM show better agreement with known values forhigher densities. The standard deviations for HTM and OFM are about1 pixels/frame. Judging from the above, the results indicate that theOFM is a suitable image processing option.The attention was thus focused on the evaluation of OFM in ourfurther studies with various vessel shapes. The data analysis pointswere selected as shown in Fig. 5. Fig. 6a through d shows the OFM estimations of the random RBC velocities of various vessel shapes andcompares them with the known values from the simulated images.The typical difference between the OFM estimations and knownvelocities were lessthan 2 pixels/frame for variousmicro-vessel beds.Anotherexperiment,whichsimulatesthe fl owofRBCsinastraightline in micro-vessel with a single arteriole (diameter: 33 pixels), wasgenerated with 50 frames. Both CCM and HTM failed and resultedwith an alternative orientation and large velocity errors. Therefore,the two methods were not able to measure velocities in a largermicro-vessel, which left OFM the only choice for such cases.The calculated velocities using OFMarecomparedwiththe knownvalues in Table 2 and Table 3 for different RBC densities. With higherdensity of RBCs, more detailed structures help improving pixel-to-pixel correspondence between the images in sequence, thus betteraccuracy can be achieved in OFM calculations. For the low densitycases, the relatively larger areas of non-cell regions in the imagesweaken the correspondence, which introduces larger errors in optical fl owcalculations. Asshownindiagramaof Fig.7,theaveragevelocityerror is less than 0.3 pixels/frame for all densities studied with  Table 1 The velocity estimation in various micro-vessel cases by using three measurementmethods. The vessel shape labeling is the same as it in Fig. 1.The average error for different image processing methods, Mean±S.D.(pixel/frame)MeasurementMicrovessel method shapepatternCross-correlationHoughtransformOptical  fl ow(a) 2.693±5.628 1.872±0.798 0.718±1.158(b) 2.705±5.619 1.958±1.029 1.053±1.166(c) 2.721±5.653 1.877±0.986 1.115±1.188(d) 2.716±5.822 2.011±0.975 1.275±1.166(e) 2.704±5.7107 2.043±1.0931 1.070±1.162(f) 2.362±4.323 2.040±1.026 1.220±1.171(g) 3.288±8.116 2.350±0.925 1.155±1.180The overall average error of RBCdisplacement2.741±5.925 2.022±1.001 1.087±1.173 Fig. 5.  The measurement position in various cases of micro-vessel bed.481 T.-C. Huang et al. / Microvascular Research 80 (2010) 477  – 483
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