Original citation:
Bhalerao, Abhir and Summers, P. B. (2001) Angiotool : a tool for interactive visualization
of MRI vector and tensor fields. University of Warwick. Department of Computer
Science. (Department of Computer Science Research Report). (Unpublished)
CS-RR-382
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MRI vetor and tensor elds
Abhir Bhalerao Paul Summers
Department of Computer Siene Clinial Neurosienes University of Warwik Kings CollegeMedial Shool
Coventry London
UK UK
abhirds.warwik.a.uk p.summersiop.kl.a.uk
May 30, 2001
Abstrat
MR imaging is a uniquely powerful tool for non-invasively mapping blood ow and moleulardiusion. These propertieshavelinialsignianebut thelakofeÆientand intuitive,displayandexplorationtoolsforthelinialexpertisanobstaletobringingthese imagesinto diagnostiuse. Wehavedeveloped avisualizationappliation (Angiotool) for vetorandtensorelddataderivedfromMRphaseontrastangiographianddiusion ten-sorimage(DTI)sequeneswhihaugmentsroutinedisplayfuntionswithbothquantitative andqualitativeexplorationfeatures. Oneofitsuniqueapabilitiesistoperforminterative traking of streamlines in bothveloity and diusion tensor data. We desribe the GUI modelusedbyAngiotoolandillustrateitsinterativeapabilitywithexampleresultsfrom linial ases. Central to the design of Angiotool is the ability to interat and navigate throughthe data in both2D and 3D displays. Although implementations may dier, we seeourinterationmodelaswellsuitedtonewappliationsofthistype.
1 Introdution
Motion,whether dueto blood ow ormoleular diusionan have measurableeets on both thephase and umulative magnetisation arisingfrom hydrogen nulei(spins) inthe body[1℄. Developing ways and means for visualising and analysing these data that meet the needs of radiologists and surgeons has been a goal of researhers following various paths, inluding: visualisingand traking blood ow data [2 , 3 ℄; vasular segmentation [4 , 5 , 6℄; and analysing diusiondata[7, 8,9,10 ℄.
gradient, highly random motion of the spins, i.e. moleular diusion,an be imaged [7 ℄. As veloity is a vetor quantity, three omponent images (plusa referene unenoded image) are needed to produe a veloity eld. Similarly, diusion in a loally homogeneous material is desribed by a 2nd order tensor (a 3x3 symmetri matrix) and requires at least seven images forits desription.
The veloity or diusionomponent maps may be further proessed to produe summary images. A ommon endpoint of phase ontrast angiography (PCA) is an angiographi speed image produed by taking a square root of thesum of squared the veloity omponents. The ommonest wayof post-proessing diusionimages is to determine thenet oranisotropi dif-fusionoeÆient (ADC) by usingthe prinipal eigenvalue of the diusion tensor. In general, these imagesprovide aonise desriptionof some aspetof thevetor ortensoreld. Aswell asthealulated and derived images,it istypial foran anatomial (modulusimagefrom the unsensitizeddataaquisition)tobereonstrutedalso. Altogether,atypialPCAsequenewill produeof 5image sets ofsize256x256x120 voxels whilea diusiondatasetmightonsist of 7 imagesets ofsize128x128x60 voxels. The vastnessof thedatasetsposeuniqueomputational hallenges.
In this artile, we outline linial uses of MR motion imaging whih motivate our work toward an intuitive graphial tool that meets the requirements of linial experts. The GUI designmodelofourappliation,Angiotool,isthendesribed. Itsdisplayandinterativeanalysis funtions,whih anbeused equallyforvetor valuedveloityand tensordata, areillustrated from linialases whih highlightof Angiotool's apabilities.
2 Use of images and Existing tools
Clinially,theattration ofPCA hasbeenits abilityto depitowingblood without ontami-nationfrom stati tissues. As distintfrom other methodsof MR angiography, PCA also has theabilitytodelineateowpatternsandquantifyveloity. Diusionimagingontheotherhand ismostommonly assoiatedwith thedepitionof strokes, whererestrited diusionindiates reent ourrene (aute stroke and unertainfate of thetissue)and elevated diusionis seen when dead neurons are replaed by erebrospinal uid (hroni stroke). Considerable further interest in diusion imagingis assoiated with the potential to identifypatterns orpathways of onnetivitywithin thebrainon the basisof how diusionanisotropy reets theourse of myelinated(messageonduting)neurons. Therearesimilaritiesinthespeiquestionsasked byexperts forthetwo typesof MR images:
isa vessel patent /is a neuronaltrat intat?
what isthedegree of stenosis(narrowing) / isan ishaemi (stroke)lesionold ornew?
doesapartiular vessel feedordraina given region/ what aretheterminal onnetions ofa neuronaltrat?
what istheowpatternina given region/ what istheonnetivityof aortialregion?
how has a ow pattern beenaeted post-operatively/ is the neuronaltrat inuened byadjaent pathology?
rea(Voxelview) (Vital ImagesIn. MinneapolisMinn.) whihtakesfulladvantageof hardware and software aeleration to failitate rapid view rendering. Perhaps the most widely-used, multi-platformsoftware-onlyapproahisAnalyze(Analyze, Mayo Clini,USA). Whereas Vox-elview isdesigned partiularlyfor volumerendering and visualization, Analyze inorporates a wide range of additionaltools forsuh tasks as segmentation, imageregistration, format on-version,surfaerendering,overlaysoftwoimagesets,andthemeasurementofdistanes,angles andareas. Both pakages supporttheloadingof imagesfromanumberofsannertypes,allow the generation of orthogonal and obliquely reformatted images, and providemaximum inten-sity projetion (MIP) and other rendering tools. A notable dierene in approah is seen in thegenerationofdynami\y-throughs" of rendereddisplays. Whereas Analyze hasrelied on sriptingtools to ontrol objetand viewerpoise, Voxelview uses apointand likinterative approah whih reords theviewer'smovements through and aroundthe dataset. We feel the latter approah better represents the type of intuitive interation we hope to ahieve within Angiotool. Neither Analyze nor Voxelview support the viewing or manipulation of vetor or tensordatasets.
Asyet,thereisnouniversallyaeptedparadigmforuserinterationwithandvisualisation of vetor and tensordata forlinial use. In fat, to ourknowledge,noneof the ommerially available platforms for medial image viewing deal with vetor or tensor data as suh. In general, do they allow interationwith more thana single 3D image volume at a time exept foruse inimage registration ormultispetral segmentation routines. In fat, of the 5 ormore datasets assoiated with a PCA study, only the derived \speed" images reeive attention -typiallythrough use of a MIP display. For tensordata, ADC and frational anisotropy may be rendered in similar fashion(e.g. [11 , 9℄). In neither ase does the MIP of these derived salar metris onvey the diretional information ontained in the aquired data. Moreover, MIP viewing is performed independentlyof displayof the orresponding tissue images,whih ompliatesthetaskofdeterminingrelationshipsbetweenvasularandnon-vasularstrutures. A nalrestrition of mostlinial imageviewing pakages, is thatquantitative analysisof the vetorortensordataisoftenpreludedbydisardingtheunderlyingdataforthebrevityofthe derivedsalar images.
3 Angiotool: Data Visualization and Navigation
We have attempted to develop a GUI based approah to interative visualization of vetor and tensor data whih meets linial needs by inorporating both traditional ut plane and MIPdisplaysofderivedimages,withtheaddedabilitiesto aesstheunderlyingdatathrough quantitative and dynami qualitative visualization. The GUI presented by Angiotool an be deomposed into three main displays areas: a square 3D rendering window, an adjaent 3D analysis windowof equal size, and a triplet of smaller windows displayingslie-by-slie views of the data (Figure 1). Quantitative information is displayed in a srolling text window and, whereappropriate, auxiliarygraphialwindows.
3.1 Orthogonal Slie Views: Tissue and MIP images
Anatomialdataisbeingviewedintheleft-mostandright-mostdisplays;funtionaldatainthe entredisplay. Thepoint-and-lik3DursornavigationontinuestooperatewhenMIPviewis shownallowinguserstomanuallytrakalong avesselorbretrat todisplayorthogonalross setionsatthesepointsinassoiatedtissuevolume. Next/Previousbuttonsenableexplorations ofslies eithersideofurrent ursorposition.
their simultaneous display is a powerful yet omfortable extension of the traditional linial approahwhihis failitatedbyomputer display. InAngiotool,aswithotherorthogonal slie viewers, the views are linked by a 3D ursor (Figure 2). This allows for a simple point and liknavigation throughthe data: a likin anyof the three views willupdatethe other two with the `ross-setion' assoiated with X and Y o-ordinates entred on the lik position. Suh a displaymodel is widely used inCAD and arhiteture whereentre lines link thetwo elevation and plan views. Within Angiotool, we typially use the T1 weighted tissue images from PCA dataor eitherthe T2weighted tissue orderived ADCimagefrom diusion studies to provideomprehensive overviewsof generalanatomyintheorthogonal slieviewer. In fat, anyo-registereddataset, suhasCT,an benominatedasthe`anatomial'imageand viewed simultaneously with the phase ontrast (funtional) image. For eah of the orthogonal view diretions,a orrespondingMIP of thespeed (PCA)orADC(diusion)data ispreomputed. With a single mouse lik the user an toggle between the MIP and anatomial slie data. To aid relatingtheanatomial view to theangiographi ordiusionstrutures of interest, the point-and-likursornavigationontinuesto operate on the MIPimage. Withthis, when an imagefeaturesuh asa vessel,ismanuallytraked withtheursorin theMIPview,theother two views are automatially re-entred on the ursor position. Within the orthogonal slie viewer, view-independent next-slie and previous-slie buttonsallow the user to make limited explorationson eithersideof aninitial loation.
3.2 3D display
() (d)
whihthe(x;y;z) ursorpositionan bemapped. When eahMIP value (orsurfaeolour)is projeted onto the view plane, its voxel positionis reorded in a 2D buerZ(i;j) = (x;y;z). When the user selets a point [i;j℄ in the MIP using the ursor, Angiotool `looks-up' the appropriate voxel address (x;y;z). This may be used to redene the slie positions in the orthogonal viewer or to provide initial points for analysis as desribed below. Beause the projetedvalue (x;y;z) ina MIP maybe frombrightervalueseitherin front of orbehindthe vessel of interest. To prevent suh depth ambiguity errors when traking a vessel, a limited-MIPwhere onlyvoxels whih liebetweentwo planesz
min and z
max
parallelto the view plane are projeted an be used. By reduing this depth value to be about the size of the voxel dimensionality (e.g. 1mm), the projeted image redues to a ut slie through the urrent ursorpositionprovidinga meansof generatingobliqueslies.
The right hand window (3D analysis window) is used to display results of analyses on the vetor or tensor data volume. Whereas the render window displays voxel information by ray asting, the analysis window displays graphis geometry (points, lines, planes and text). The3Dursor, theboundingnavigationube,axes anddataorientationlabelobjets areever present in analysis window. The natural assoiation of vetors with line segments or arrows provides a simple means of onveying the underlying data for PCA. The ow eld may be displayed by renderingthe 3Dvetor eld asa grid of smalllines throughthe entres of eah voxel. The vetor diretionand magnitudeareolourodedasfollows:
Veloityorientationisodedsuhthateah omponent (v x
;v y
;v z
) ismappedto a orre-spondingolourhannel(r;g;b)e.g. r=(v
x
+max(jv x
j))=2,normalisedtotheappropriate olourhannelrange. Thismappinghastheeet thatall vetorswiththesame orienta-tionhave thesame olour.
Veloity magnitude (i.e. speed of ow) proportionally ontrols the length of the line representingthevetor.
A user dened threshold is used to avoid lutter from stationary tissues and air permitting vetordisplayasillustratedinFigure3(a). Severalauthorshave usedellipsoidsasavoxel-wise displayanalogyfordiusiontensordata(e.g.[8℄). Asmuh oftheattention inourinstitutions has foussed on questions of onnetivity, we have simplied the ellipsoid model to one of displayingthepriniple eigenvetor ofthe diusiontensor foreah voxel3(d).
Diretrenderingofvetordataatthevoxellevelisarststeptomakinguseoftheavailable information. This approah is however, not without its limitations. For instane, the identi-ationof likelypaths throughthe data - blood ow streamlines orneural onnetivity, must be inferred. Also, strutural boundariesare often diÆultto distinguishin thevetor display thanintheanatomial orMIPimages. Theanatomialrenderingfromtherenderwindowan be superposed onto ontents of the3D analysis window. This allows the user to visually fuse thevasularstruture withthevetor information(e.g. Figure6()). A ompliationof PCA, phase wrappingartefats [14 ℄, an be learly seen inthis way (Figure3(b)). The viewer may also visually `interpolate' noisy ordisjoint ow insmallvessels. The results of analysis of the rawvoxeldata oftensuitgraphialrepresentation(e.g. surfae ofow lines). The 3Danalysis windowmaybeusedfordisplayof suh results,examples ofwhihare disussedbelow.
3.3 Cut-view
Figure 4: The user an performa virtual`ut' of avessel. The utplane is always orthogonal totheview-plane. Itsorientationisseleted byorientingarubber-bandedlineasshownin(a). (b)Shows theresulting utplane highlightedinpinkand thespeeddataaross theut (inset view (b)). Angiotool an plot the proleof thealibrated speed arossthe vessel asshown in ().
inludedisplayingthespeedprolearossavesselatahosenpoint(Figure4()),andpreisely positioningthe 3D ursore.g. forseeding partiles inow simulationsas desribed below. In relation to diusiondata, projetions of the eigenvetor diretions onto or through the plane maybedisplayed. Theut-plane isalways perpendiularto theviewof therenderdisplayand entredat themostreentlyseleted 3Dursorposition. Avirtualknife(a rubberbandedline thatfollowstheursor)isusedto denetheorientationoftheut-planesimplybydeningthe ends of the ut with mouse liks (Figure 4(a)). Alternatively, Angiotool an auto-selet the ut-plane orientationto beperpendiularto theaverage loalveloity.
4 Analysis tools
Angiotool'sanalysistools anbeategorised asstati,whereasingle,oftenquantitative result isoutput,ordynami,wherestepbystepinterationproduesqualitativeresults. Ifthestati tehniquesanswerthequestion`whatis',thedynamitehniques,bysimulation,tryto answer thequestion`whatif'.
4.1 Stati analyses
Figure 5: Summary displays of veloity informationprodued by a multiresolution averaging proess [15 ℄. (a)Centre lineand diretioninformationofmainloalfeatures. (b)Estimates of vesseldiameters aredisplayed asbarrelmotifs.
Manyimageproessingtehniqueswhoseendpointsaredataredutionandextrationhave outputs suitablefor graphial representation. Segmentation for exampleis a ommon step in establishingautomating the detetion of vessel narrowing and indening theow boundaries for omputation uid dynamis studies. Elsewhere we have reported on the use of the raw veloity informationina multiresolutionaveraging proess bothfor segmentation and to pro-due summary entreline and bounding shell estimates for vessel segments [15 ℄. These lend themselvesto rendering with lineand barrel motifs respetivelyas illustrated in Figure 5 (a) and (b)respetively.
4.2 Dynami analyses
The potential for dynami interation with vetor and tensor eld data in Angiotool is ex-emplied by its faility for streamline traking. The estimation of streamlines is a means of approximating the pathof bloodowingalong a vessel [3 ℄ orputative onnetivityof neurons byfollowingtheanisotropi omponent ofdiusionalong anerve bundle[7 , 8 ,10 ℄. Streamline trakingisinitiatedbysettinganumberofpartiles(orseeds)intotheveloityvetor(diusion tensor)eld. Foreah seedAngiotooldeterminessubsequent positionsonthebasisoftheloal veloity (diusion anisotropy). The resulting trak is displayed asa 3D urve in the analysis window.
The traking proess is loal and relies solely on the veloity data at eah point using a physialspae, pointtrakingalgorithm. Anytimedependent owstreaman beexpressed by theordinarydierentialequation forthehangeinposition~r giventhe loalveloity~v:
d~r dt
=~v(~r(t);t) (1)
giving,
~r(t+Æt)=~r+ Z
t+Æt
t
~v(~r(t);t)dt: (2)
SineourPCAdataisatimeaveragedveloityeld~v(~r),asimple1storderEulerintegration an solve for the integral on the rhs without having to resort to an elaborate multi-stage numerialintegration (e.g.[16 ℄) i.e.
~
dimensionality e.g. 0.5 or 1mm. Linear interpolation is used to estimate the veloity at the real o-ordinates ~r given the disretely sampled data ~v
i
. For displaypurposes a spline urve is interpolatedthroughthe set of points~r(t). The traking proess is terminated ifthe speed falls below a threshold value set by the user, or the trak exits the data volume. Blood-ow traking is illustrated inFigure 1 for a normal subjet, and Figure 6(a)-() for a patient with a giant erebralaneurysm.
With diusiontensor data, the traking is performed on a derived vetor eldsuh asthe prinipaleigenvetorwhihrepresentstheloalanisotropymodulatedbyasalar. Thediusion tensor an be expressed as a linear sum of the outer produt of its priniple omponents or using tensors of rank 1 i 3, T
i
whih have a geometri interpretation dependingon the relative 3D`shape'of theloal diusionoeÆient:
T=( 1 2 )T 1 +( 2 3 )T 2 + 3 T 3 (4) where i
aretheeigenvalues,andT i = P i j ~e j ~ e T j
arethesumoftheouterprodutofeigenvetors respetively [8 ℄. For thetensor traking, we simply use the rank 1 (line) ase where diusion hastakenplae anisotropiallyinthediretion~e
1 :
~
v(~r)=f(~r)~e 1
(~r) (5)
and f an be any appropriate salar measure e.g. 1 = P 3 i i
. Our traking proess does not deal optimally with points where bre trats meet or ross (where rank 2 and rank 3 tensors are required). A more sophistiated approah (see for example [8℄) will be needed to better handlethissituations.
Thebasitrakingproessan bemodiedbyreversingthetimestepstotrak`bakwards' throughtheow i.e. Æt! Æt. This is partiularlyusefulto identifypotentialfeedingvessels to arterio-venous malformationsand aneurysms (see Figure 6(b)). For traking white matter trats, both forward and bakward steps are taken from the seed point. This overomes the arbitrary hoie between eigenvetors and theirnegatives when deomposingthe tensor eld. An exampleoftrakingwithindiusiontensordatais shownin Figure6(d).
Multiple seed points an also be traked simultaneously (Figure 6() and (d)): either by seeding a 26-neighbourhood of voxels around theseed point, orall points inthe data volume ata speiedstepintervalanbeseeded. Thelattermodiationisquiteslow, buttheresults an give a better impression of ow onnetivity than the stati vetor display alone. For displaypurposes,arrow heads an be added to start/ends of the individual stream lines. For ner disriminationof ow streams, start points an be seeded with greater preision on the ut-view displaywindow. Thisoveromes thepossibleambiguities indepthinsetting theseed positionfrom theMIP alone.
() (d)
(e)
Therehasbeengrowinginterest inthedevelopment ofimageproessingand analysismethods for angiographi and diusion data. Examples of methods range from simply enhaning the displayof urvilinear strutures [4 , 5 , 6 ℄ to analysing ow and onnetivity e.g. [2 , 4 , 3, 16 , 10 ℄. Inevitably, most suh methods are spei to the nature of the data: time of ight or phaseontrast PCA,and,on thewhole,have beenimplementedforthepurposesof algorithm development making them awkward or unsuitable for linial use. Consideration of the end useris a reognisedfator inmaking post-proessingmethodsaepted androutinely used.
Angiotool provides funtionalitythat fouseson a setof aountable and responsive oper-ations for data exploration. The urrent implementation is built upon open standards teh-nologies: GUItoolkitsusingXand Motifand3DgraphisusingOpenGL.AlthoughAngiotool is not as generalised and extensible a framework asother pakages (e.g. AVS, Analyze, IDL, VTK)oer,webelievethatits speialisednature makesiteasierto useinthelinial environ-ment and better suited to partiular diagnosti tasks at hand. Its strength lies in the design being tailored to the requirements of its expert users: radiologists and surgeons. Where the experts demand up-and-oming proessing, analysis and display algorithms an be appended to the existing features of Angiotool without substantive hanges to the look-and-feel of the GUI.
SeveralaspetsoftheGUIandrenderingapabilitiesouldbeundoubtedlyimprovedupon. Theorganisationoftheommandsyntax(layoutoflemenusandontrolpanels)hasnotbeen partiularly well optimised and there is no built-in way to undo, log, and reord operations, apabilities whih are important in a linial setting. The ray-ast renderingengine ould be augmented with volume rendering. A funtion whih would be of use when studying groups of patients is a way to atalogue quantitative and qualitative results against the geometry of the patient's anatomy (e.g the vasulature). We are urrentlyin the proess of inorporating strutureddata reordingmethods. Also, whilethelinial interest drivingAngiotool's devel-opment haslargely foussedPCA and diusiontensor imaging, other vetor and tensorelds suh as temperature gradients, and deformation are already being mapped withMRI. Never-theless,we believe thatthepresentedGUImodelouldusefullyformthebasisofother linial appliationsof thistype, where the need for eÆienyin data visualisation and interrogation proesses remains.
Aknowledgements
The authors would like to gratefully aknowledge the ontributions of both linial and om-putersiene olleaguesat the SurgialPlanning Laboratory, HarvardMedial Shool, Boston and fromthe Divisionof RadiologialSienes,Kings CollegeMedialShool, Guy'sHospital, London. Notably: Drs Westin, Nakajima (MD), Cox (MD) and Profs Kikinis (MD), Jolesz (MD) and Hawkes. Thanks also to Dr Neil Roberts and Tom Barrik (MRI Analysis Centre, UniversityofLiverpool) forprovidingexampleDTI data.
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