Knee Segmentation and Registration Toolkit (KSRT)

Transcription

1 Knee Segmentaton and Regstraton Toolkt (KSRT) Automatc Cartlage Segmentaton and Cartlage Thckness Analyss Software Release: Junpyo Hong Lang Shan Marc Nethammer January 22, 2015 Contents 1 Lcense 2 2 Overvew 2 3 Analyss Approaches Cartlage Segmentaton Preprocessng Mult-Atlas-Based Bone Segmentaton Mult-Atlas-Based Cartlage Segmentaton Longtudnal Segmentaton Cartlage Thckness Computaton Statstcal Thckness Analyss KSRT Software Overvew of the Software Ppelne Overvew of Scrpts Prerequstes Tasks Image Data Format Buldng the Software Dependences Utlty Applcatons Buld Instructon Supported Platform Tutoral: Pfzer Longtudnal Study Dataset PLS Dataset Runnng the Software Ppelne Preprocessng Tranng Classfers Automatc Cartlage Segmentaton Longtudnal Segmentaton Cartlage Thckness Computaton Statstcal Analyss on the Thckness

2 1 Lcense The Knee Segmentaton and Regstraton Toolkt (KSRT) s dstrbuted under the Apache 2.0 lcense. For more nformaton, please see the lcense fle wthn the gt repostory gt@btbucket.org:marcnethammer/ ksrt.gt. Copyrght (c) 2014 Department of Computer Scence, Unversty of North Carolna at Chapel Hll Lcensed under the Apache Lcense, Verson 2.0 (the "Lcense"); you may not use ths fle except n complance wth the Lcense. You may obtan a copy of the Lcense at Unless requred by applcable law or agreed to n wrtng, software dstrbuted under the Lcense s dstrbuted on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, ether express or mpled. See the Lcense for the specfc language governng permssons and lmtatons under the Lcense. 2 Overvew Ths software s an open source dstrbuton of algorthms to automatcally quantfy cartlage thckness from magnetc resonance (MR) mages and to perform related statstcal analyses. The mplemented algorthms are n detal descrbed n [3]. Ths document serves as a hgh-level overvew, contans an nstallaton gude, as well as a tutoral to gude a user through a data analyss. In partcular, the software descrbed n ths user manual allows to automatcally performs the followng analyss tasks: 1) Segmentng cartlage from knee Magnetc Resonance Imagng (MRI) data. 2) Computng cartlage thckness from the automatc cartlage segmentatons. 3) Establshng spatal correspondence across MRI data approprate for statstcal analyss. 4) Performng statstcal analyss of localzed cartlage changes for cross-sectonal and longtudnal data. The purpose of ths document s to provde background nformaton necessary for understandng and usng the software so that t can be used on other datasets. The software has so far successfully been appled to analyze data from the Pfzer Longtudnal Study [2, 3] as well as from the MICCAI SKI10 challenge on cartlage segmentaton [2]. A summary of the obtaned results can be found n [2]. Secton 3 gves an overvew of the analyss approaches used. For a more detaled explanaton please refer to [3]. Secton 4 llustrates how to buld the software. Secton 5 presents a tutoral on how to use the software to analyze the Pfzer Longtudnal Dataset. 3 Analyss Approaches Ths secton descrbes brefly the analyss approaches used n KSRT. Specfcally, Secton 3.1 descrbes how cartlage segmentaton s performed, Secton 3.2 dscusses the cartlage thckness computatons, and Secton 3.3 descrbes the statstcal analyss approach. 2

3 Fgure 1: Flowchart of overall cartlage segmentaton ppelne 3.1 Cartlage Segmentaton KSRT uses a mult-atlas-based segmentaton approach [3] wth non-local patch-based label fuson. Fgure 1 shows a flow-chart of the overall analyss ppelne, whch conssts of the followng steps. Frst, both the femur bone and the tba bone are automatcally segmented usng a mult-atlas strategy. These bone segmentatons are used for an ntal rough mage algnment and to automatcally extract a smaller regon around the knee jont wthn whch a refned regstraton and the segmentaton of cartlage s performed. Focusng on ths smaller regon sgnfcantly reduces the computatonal cost of the approach. The cartlage segmentaton tself s based on a spatal pror obtaned from mult-atlas regstraton of labeled jont regons and a datalkelhood terms obtaned through local feature-based probablstc classfcaton. Both the spatal pror and the data-lkelhoods are used wthn a three-label convex segmentaton formulaton to obtan the segmentaton labels for femoral and tbal cartlage as well as background. The three-label segmentaton makes use of an ansotropc spatal regularzaton term to smultaneously suppress nose whle respectng the thn cartlage structures. In the context of atlas-based segmentaton, an atlas [1] s defned as the par of an orgnal structural mage and the correspondng segmentaton. The segmentaton n the atlas par s assumed to be obtaned for example by manual segmentaton by a doman expert. 3

4 Suppose we have N atlases, then n each atlas A ( = 1, 2,..., N), we have A Structural Image, I A Manual Segmentaton of the Femur bone, S F B A Manual Segmentaton of the Tba bone, S T B A Manual Segmentaton of the Femoral cartlage, S F C A Manual Segmentaton of the Tbal cartlage, S T C The remander of ths secton provdes bref descrptons for each stage of the segmentaton ppelne. Secton gves an overvew of the preprocessng requred for datasets pror to cartlage segmentaton and statstcal analyss. Secton explans the mult-atlas-based automatc segmentaton of the femur and the tba. Secton explans how femoral and tbal cartlage are segmented usng a mult-atlas segmentaton strategy guded by the segmentatons of femor and tba. Fnally, Secton shows how cartlage segmentatons can be refned for longtudnal data (as avalable for example from the Pfzer Longtudnal Study or the data of the Osteoarthrts Intatve) by enforcng temporal regularty Preprocessng Before we can use the data for analyss some preprocessng needs to be performed. We frst remove artfacts n mages caused by the nonhomogenety n magnetc felds. Then we rescale mage ntenstes so that values range from 0 to 100. We perform edge preservng smoothng to further remove nose n the mages. Fnally we downsample the mages by a factor of 4 for the frst 2 dmensons to make mage regstraton more effcent whle not losng too much nformaton. Note that ths only affects the regstraton, segmentaton s stll performed at the full mage resoluton Mult-Atlas-Based Bone Segmentaton After the data s pre-processed approprately for the analyss, we automatcally segment knee bones from the mages usng a mult-atlas strategy. The labelng cost c of each voxel locaton x n the query mage for each label l n F B, BG, T B ( F B, BG, and T B denotes the femur bone, the background, and the tba bone respectvely) are defned by log-lkelhoods : ( ) p(i(x) l) P (l) c(x, l) = log (P (l I(x))) = log log (p(i(x) l) P (l)) (1) p(i(x)) We frst segment femur bone and tba bone from the query mage by performng the followng steps: 1) Regstraton: We compute spatal transformaton to regster each of the atlases to the query mage. We frst compute affne transformaton based on structural mages of each atlases and the query such that T affne : I I q. (2) Then we apply T affne computed from (2) to I, S F B, and S T B ( = 1, 2,..., N). T affne T affne T affne I S F B S T B (3) Ths s followed by a B-Splne transformaton such that T bsplne : (T affne I ) I q (4) 4

5 Just as for the affne transformaton, we apply the transformaton computed n (4) to T affne I, S F B, and T affne S T B T affne T bsplne T bsplne T bsplne T affne T affne T affne I S F B S T B 2) Label Fuson: We propagate the regstered segmentaton masks,.e., T bsplne T affne S T B p(t B), for the query mage I q : T bsplne T affne S F B and to form the spatal pror of the femur bone and the tba bone,.e., p(f B) and p(f B) = 1 N p(t B) = 1 N N =1 N =1 ( T bsplne T affne ( T bsplne T affne ) S F B ) S T B where F B and T B respectvely denote the femur bone and the tba bone. Recall from that we have downsampled the mage to make regstraton effcent whle not losng too much nformaton. After summaton and dvson n (6), we upsample p(f B) and p(t B) back to the orgnal dmenson. 3) Segmentaton: Fnally, we segment the femur bone and the tba bone from the query by mnmzng the labelng cost of each voxel locaton for the femur bone and the tba bone. Recall from (1) that ths cost s expressed n terms of posteror probablty: (5) (6) c(x, F B) = log (p (F B I (x))) log (p(i(x) F B) p(f B)) c(x, T B) = log (p (T B I (x))) log (p(i(x) T B) p(t B)) (7) where x denotes each voxel locaton n the mage, and I(x) denotes ntensty value at x. The lkelhood of the femur bone and the tba bone,.e., p(i(x) F B) and p(i(x) T B), are computed as the followng. p(i(x) F B) = p(i(x) T B) = exp( βi(x)) (8) where β s set to 0.02 and the ntensty values I(x) range from 0 to 100 as a result of the preprocessng descrbed n We use the three-label segmentaton descrbed n [3] to segment the femur bone and the tba bone by mnmzng labelng costs (7) Mult-Atlas-Based Cartlage Segmentaton After segmentng the knee bones from the query (denoted by S F B and S T B ), we can use these segmentaton masks to gude cartlage segmentaton. The labelng cost for the femoral cartlage and the tbal cartlage s expressed n terms of posteror probabltes: wth prors computed from mult-atlas-based regstraton followed by non-local patch-based label fuson and lkelhoods computed from probablstc classfcaton (we use a Support Vector Machne (SVM)). The labelng cost c of each voxel x for each label l n F C, BG, T C ( F C, BG, T C respectvely denote the femoral cartlage, the background, and the tbal cartlage) s, ( ) p (f (x) l) p (l) c(x, l) = log (P (l f (x))) = log log (p (f (x) l) p (l)) (9) p (f (x)) We perform the followng steps to automatcally segment both cartlages from the query. 5

6 1) Jont Regon Extracton: We automatcally extract a smaller regon around the jont. Ths regon s computed based on the bone segmentaton from the prevous stage of the ppelne. Ths process makes the further processng more effcent whle not affectng the cartlage segmentaton performance. 2) Probablstc Classfcaton: We compute lkelhood terms p(f(x) l) for the labelng cost c va probablstc classfcaton. For features, we used: ntenstes on three scales frst-order dervatves n three drectons on three scales second-order dervatves n the axal drectons on three scales where three scales are obtaned by convolvng wth Gaussan kernels of σ = 0.3 mm, 0.6 mm, and 1.0 mm. All features are normalzed to be centered at 0 and have unt standard devaton. We use an SVM for classfcaton. 3) Regstraton: We use mult-atlas-based regstraton to propagate segmentaton masks for the femoral cartlage and the tbal cartlage. We regster each atlas A to the query va computng affne transformatons: T affne,f C T affne,t C : S F B S F B : S T B S T B (10) We apply T affne,f C to the femoral cartlage segmentaton S F C and the structural mage I, and T affne,t C to the tbal cartlage segmentaton S T C and the structural mage I. S F C Ĩ F C S T C Ĩ T C = T affne,f C = T affne,f C = T affne,t C = T affne,t C S F C I S T C I (11) 4) Label Fuson: After the regstraton, we form prors for the femoral cartlage (.e., p(f C)) and the tbal cartlage (.e., p(t C)) usng the warped label mages,.e., S F C and S T C. Note that the non-local patch based strategy n label fuson s robust to local errors ntroduced by regstraton. Let p F C (x) denote p(f C) at the voxel locaton x and p T C (x) denote p(t C) at the voxel locaton x. p F C (x) s computed as: N y N p F C (x) wf C (x, y) S F C (y) =1 (x) =, (12) N y N (x) wf C (x, y) w F C (x, y) = exp =1 x P(x)y P(y) ( I(x ) ĨF C (y ) h F C (x) ) 2, (13) where x s a voxel n the patch P(x) centered at x (smlarly y a voxel n the patch P(y) centered at y) and h F C (x) s defned by h F C (x) = mn 1 N y N (x) x P(x) y P(y) ( I(x ) ĨF C (y )) 2 + ɛ (14) 6

7 We compute p T C (x) exactly the same way by substtutng F C wth T C n equatons: (12), (13), and (14). 5) Segmentaton: Fnally wth spatal prors computed from (12) and the lkelhood computed va classfcaton, we use the three-label segmentaton wth ansotropc regularzaton to segment cartlage. In order to make use of ansotropc regularzaton, we compute the normal drectons Longtudnal Segmentaton The segmentaton result computed so far s assumed to be temporally ndependent. I.e., each tmepont s segmented ndependently. However, f we know the dataset s longtudnal, then we can further enforce temporal consstences across mage data at dfferent tme ponts. Our longtudnal segmentaton also follows a smlar framework: regstraton followed by three-label segmentaton. 1. Regstraton: To algn longtudnal mages of a gven subject, we regster all of the tme ponts to the frst tme-pont (baselne mage). We frst compute a rgd transformaton between the t th tme pont and the frst tme pont based on the femur bone segmentaton. R F B t : S F B t S F B 0 (15) where subscrpt t denotes t th tme pont. Then we apply the transformatons (15) to: the segmentaton mask of the femoral cartlage, the local lkelhood map of the femoral cartlage, spatal pror map of the femoral cartlage, and the structural mage around the jont from Jont Regon Extracton stage. R F B t S F C t R F B t p t (f(x) F C) R F B t p t (F C) R F B t I jont t Then we compute another rgd transformaton based on the transformed femoral cartlage segmentaton mask. Rt F C : ( Rt F B St F C ) S F C 0 (17) We apply Rt F C to all of the transformed: the segmentaton mask of the femoral cartlage, the local lkelhood map of the femoral cartlage, the spatal pror map of the femoral cartlage, and the structural mage around the jont. S F C t = R F C t R F B t p t (f(x) F C) = R F C t p t (F C) = R F C t Ĩ jont t = R F C t S F C t R F B t p t (f(x) F C) R F B t p t (F C) R F B t I jont t We repeat the above procedure to algn the tbal segmentaton mask, the tbal cartlage lkelhood map, the spatal pror for the tbal cartlage, and the structural mage around the jont based on the tba bone segmentaton and the tbal cartlage segmentaton. 2. Segmentaton: Once the dfferent tme pont are algned to the baselne, we compute the labelng cost c for t th tme pont, ( ) pt (f (x) l) p t (l) c(x, l, t) = log (p t (l f(x))) = log log ( p t (f (x) l) p t (l)) (19) p t (f (x)) Then we compute the normal drectons because we make use of ansotropc regularzaton for the longtudnal segmentaton. We longtudnally segment cartlages by mnmzng the labelng cost (19) wth each terms computed from (18). (16) (18) 7

8 Fgure 2: Thckness Computaton ppelne. Extract the jont regon and automatcally segment cartlages. Compute cartlage thckness. Regster all of the 3D thckness maps to a common atlas space. Project 3D thckness maps onto a 2D plane along axal drecton. 3.2 Cartlage Thckness Computaton Once both femoral and tbal cartlages are segmented we use the method descrbed n [4] to compute thckness of those cartlages. Please refer [4] for more detals on computng tssue thckness. 3.3 Statstcal Thckness Analyss Once cartlage thcknesses are computed we establsh spatal correspondence of the thcknesses by mappng them to a common atlas space. We use an affne followed by B-Splne transform whch are computed based on bone segmentatons for each cartlage thckness volume. Then these transformed thcknesses are projected down to an axal slce by takng the medan thckness value along the axal drecton (where thcknesses are approxmately constant). Then these thckness maps are comparable across tme-ponts and subjects. Note that all segmentatons and thcknesses are computed n natve mage space. Fgure 3.3 llustrates how the thckness maps are computed. Once the 2D thckness maps are created we frst ft a lnear mxture model to model dfferences between normal control subjects and OA subjects. Then we cluster OA subjects such that subjects n the same cluster have smlar patterns n thnnng of the cartlages. Then we ft another lnear mxture models to each OA cluster for a refned statstcal analyss. See [3] for more detals. 4 KSRT Software Ths secton descrbes the software avalable mplementng the algorthms descrbed n Secton 3. Specfcally, Secton 4.1 gves an overvew of the software ppelne. Secton 4.2 dscusses the mage format used. Secton 4.3 dscusses how to buld the software. Secton 4.4 dscusses the supported platforms. 8

9 4.1 Overvew of the Software Ppelne Ths software package contans several components for automatc segmentaton of cartlage. In what follows, we wll gve an overvew of all the stages of the analyss ppelne. The source code dstrbuton contans the followng drectores: src: Ths drectory contans C++ mplementaton of the algorthm. lb: Ths drectory contans varous applcatons used. scrpts: Ths drectory contans scrpts to run the segmentaton on a compute cluster. matlab: Ths drectory contans scrpts wrtten n MATLAB to perform statstcal analyss on cartlage thckness Overvew of Scrpts In the source code dstrbuton we provde scrpts to submt jobs on clusters usng the qsub command to automatcally segment cartlage from query mages. Under the scrpts drectory, you wll fnd the followng job submsson scrpts: submt_preprocess: Ths scrpt performs preprocessng on the dataset as descrbed n submt_transvm: Ths scrpt trans SVM classfers usng the lbsvm mplementaton. Three SVM classfers for the femoral cartlage, the background, and the tbal cartlage are traned. The traned classfers are saved to be used durng the cartlage segmentaton. submt_cartseg_ndp: Ths scrpt s the man scrpt that automatcally segments femoral and tbal cartlage from query mages as descrbed n 3.1. In order to run ths scrpt successfully, some prerequste tasks need to be performed pror to executng the scrpt. Please refer to Secton for the detals on these tasks. submt_temporal_algn: Ths scrpt enforces temporal consstences across segmentaton results of dfferent tme ponts of a sngle subject. In order to run ths scrpt successfully the dataset needs to be longtudnal and also needs to be organzed n a specfc way as descrbed later n ths document. submt_cartseg_long: Ths scrpt refnes segmentaton results va establshng spatal correspondence across dfferent tme ponts Prerequstes Tasks To run the ppelne usng the provded scrpts the followng path varables need to be defned. If you are usng bash, then follow the nstructons below to defne path varables n your.bashrc so that scrpts runnng the ppelne can access the approprate paths. In addton, you need to create two text fles to denote query mages and atlas mages n the dataset so that the aforementoned scrpts can access and process data approprately. Path Varables ksrt Applcaton Drectory: You have to defne ksrt Applcaton drectory as ksrtappdir n your system settng fle. If you are usng bash, then put the followng n your.bashrc. AppDIR=/home/username/ksrt/buld/Applcaton export AppDIR ksrt Lbrary Drectory: If you choose to use the provded scrpts to run the ppelne, then put the followng n your.bashrc. 9

10 LbDIR=/home/username/ksrt/lb export LbDIR Dataset Drectory: You have to defne DataDIR to be the path to your dataset. Please put the followng n your.bashrc. DataDIR=/home/username/your_path_to_data export DataDIR Slcer Drectory: If you choose to use the provded scrpts to run the ppelne on a compute cluster, some of applcatons that are part of Slcer3 are needed. Please put the followng lnes n your.bashrc. SlcerDIR=/home/username/your_path_to_Slcer export SlcerDIR Text fles: Below are the text fles needed. Place these two text fles where the dataset s. That s the drectory ponted by $DataDIR defned n.bashrc. lst.txt: Ths text fle contans a lst of all query mages to be segmented. Ths text fle needs to lst relatve paths to the query mages from $DataDIR. For example, lst.txt used later n 5 looks lke the followng. ste ste ste ste ste ste Wth each row correspondng to a sngle query mage. There are three columns per row. The frst column denotes whch ste drectory the query mage resdes n. The second column denotes the subject d of the query mage. Lastly, the thrd column denotes the tme pont of the query mage (n month). lst_atlas.txt: Ths text fle contans a lst of all atlas mages. The format s exactly the same as lst.txt. 4.2 Image Data Format We use the Nearly Raw Raster Data (NRRD) format throughout the analyss. See teem.sourceforge.net/ nrrd for a detaled descrpton of ths format. Ths data format s supported by ITK ( AS our analyss software uses ITK to read and wrte mages other ITK supported fle-formats could n prncple also easly be supported n future releases of the software. For now please convert all your data to NRRD format before runnng ths software. Ths converson could for example be done usng Slcer or usng a smple ITK scrpt. 4.3 Buldng the Software KSRT depends on a number of dfferent open-source packages whch are freely avalable onlne. CMake s used to confgure the buld and s avalable from Earler versons of CMake may not be supported so we recommend downloadng CMake at least hgher than verson

11 4.3.1 Dependences To buld the software, you wll need the followng packages. If you have already bult Slcer-3, then you only need to buld the Approxmate Nearest Neghbor lbrary and the ImageMath package. InsghtToolkt 3.20 (ITK3) s requred for all of applcatons n KSRT package. Both ITK3 and ITK4 are avalable to download at Slcer-3 s also requred to buld KSRT successfully. It s avalable to download from slcer.org/slcerwk/ndex.php/slcer3:downloads. ann s requred to buld KSRT. Ths s an open-source lbrary for approxmate nearest neghbor search and s avalable to download at Ths s provded as a part of the software dstrbuton Utlty Applcatons In addton, the software uses several applcatons. These applcatons are not requred to buld KSRT, but these are requred to run the ppelne usng the provded scrpts successfully. These applcatons are ncluded as part of the source code dstrbuton. Below are the lst of the applcatons used along wth short descrptons. ImageMath s an open-source C++ lbrary for mathematcal operatons on mages. It s avalable to download at ExtractLargestConnectedComponentFromBnaryImage s used to segment the largest connected component from a bnary mage. Ths s used to segment out bones and cartlages after the labelng cost of each object s computed. Ths applcaton can be found under /path_to_ksrt_source/lb/extractlargestc A detaled descrpton of the applcaton s avalable at ImageSegmentaton/ExtractLargestConnectedComponentFromBnaryImage. lbsvm-3.17 s a C++ mplementaton of Support Vector Machne lbrares. Ths s needed f you wsh to use SVM to compute lkelhoods whch n turn are used to compute labelng costs. It s avalable to download at Buld Instructon CMake s used to confgure the buld and generate Makefles or Vsual Studo Soluton fles. After successfully confgurng, the software can be bult usng the natve compler. For nformaton on usng CMake, please refer to The followng secton provdes step-by-step nstructon on how to buld dependent packages. Slcer3 Please refer for buld nstructons on buldng Slcer3 ndex.php/slcer3:buld_instructons. When fnshed buldng Slcer3, ITK3 wll also be downloaded and nstalled. Once all of dependent applcatons are bult, then please follow the steps below to buld KSRT. 1. Clone the gt source code dstrbuton at gt@btbucket.org:marcnethammer/ksrt.gt by executng g t c l o n e gt@btbucket. org : marcnethammer/ k s r t. g t 2. Create a separate drectory for your buld fles and executables. For example, f you cloned the source code dstrbuton n /home/username/ksrt, then you may create a separate drectory named /home/username/ksrt-buld. 11

12 3. Change nto the buld drectory created n the prevous step. Then runccmake../ksrt n the termnal to confgure KSRT. 4. Below are the lst of path varables needed to confgure KSRT successfully. ANN LIB s a path to actual lbrary fle whch s located at ksrt/lb/ann_1.1.2/lb/lbann.a drectory of the source code dstrbuton. ANN PATH s path to nclude drectory of ann package. Ths drectory s at ksrt/lb/ann_1.1.2/nclude Slcer3 DIR s a path buld drectory of Slcer3. GenerateCLP DIR s a path to a package that comes wth Slcer3. Ths package should be located at under the buld drectory of Slcer3 that looks lke the followng. your_path_to_slcer3/slcer3-buld/lbs/slcerexecutonmodel/generateclp ITK3 DIR s also nstalled along wth Slcer3. Ths should be set to somethng lke the followng. your_path_to_slcer3/slcer3-lb/insght-buld Once these path varables are set, then let CMake confgure agan and agan untl CMake can confgure the buld wthout any errors. 5. Once Confgured, you can generate the buld,.e., Makefle for KSRT. 6. Use make command to buld KSRT. 4.4 Supported Platform We have bult and tested the software package under Unx-based system (e.g. Lnux and MacOSx). We recommend runnng the system on a cpmpute cluster as some parts of the ppelne are computatonally demandng, but can be computed n parallel on a cluster. 5 Tutoral: Pfzer Longtudnal Study Dataset We wll llustrate how to segment cartlage usng the Longtudnal Mult-Atlas Approach based on the Pfzer Longtudnal Dataset. The software can be run n a smlar way on the SKI10 and the OASIS datasets. Ths tutoral provdes step-by-step nstructons to run the software for analyzng longtudnal changes n cartlage thckness on subjects. In ths example, we wll use the Mult-Atlas based cartlage segmentaton wth longtudnal constrants. 5.1 PLS Dataset The Pfzer Longtudnal Study (PLS) dataset contans 706 T1-weghted (3D SPGR) mages for 155 subjects, maged at baselne, 3, 6, 12, and 24 months at a resoluton of mm 3. Some subjects have mssng scans. The kellgren-lawrence grades (KLG) were determned for all subjects from the baselne scans, classfyng 82 as normal control subjects (KLG0), 40 as KLG2, and 33 as KLG3. For the dstrbuton of ths dataset that was avalable to us the top level drectory of the dataset conssted of seven drectores, each representng dfferent stes where subjects receved longtudnal MRI assessments of ther knees. ste1001 ste1002 ste1003 ste

13 ste1005 ste1006 ste1007 Insde each of the aforementoned ste drectores, MRI data s grouped by drectores named after unque subject ds that contan longtudnal knee MRI measurements of the subject wth that d. These folders contan varyng number of subjects. For example, under the drectory ste1001, there are 29 folders, each storng longtudnal knee MRI data of a subject maged at ths ste , , , Lastly nsde of each of the subject folder s a longtudnal collecton of knee MRI data that are stored separately for dfferent tme ponts of the measurement. The name of folders s the number of the months after the ntal scan; therefore, the frst MRI measurement (baselne MRI data) s under 0. For example, under , there are fve folders named 0, 3, 6, 12, 24. The aforementoned folders contan the followng fles: Structural MR mage: cor_t1.nhdr and cor_t1.raw.gz Manual segmentaton of the femoral cartlage: fem.nhdr and fem.raw.gz Manual segmentaton of the tbal cartlage: tb.nhdr and tb.raw.gz Both manual segmentaton of the femoral cartlage and of the tbal cartlage (drawn by a doman expert, Dr. Felx Ecksten) are avalable for all mages. However these manual segmentatons are only used for evaluatng the qualty of automatc cartlage segmentaton; therefore these segmentatons are not strctly needed to run the software. Recall from 3.1, we make use of the knee bone segmentatons to gude cartlage segmentatons. Expert segmentaton on the femur bone and on the tba bone are only avalable for us for the baselne mages of 18 subjects. These 18 baselne mages serve as atlases A whch are necessary to run our software ppelne. When the aforementoned folder s one of these 18 baselne mage (atlas mage) folders, then the folder contans the followng fles: Structural MR mage: cor_t1.nhdr and cor_t1.raw.gz Manual segmentaton of the femur bone: femur.nhdr and femur.raw.gz Manual segmentaton of the femoral cartlage: fem.nhdr and fem.raw.gz Manual segmentaton of the tba bone: tba.nhdr and tba.raw.gz Manual segmentaton of the tbal cartlage: tb.nhdr and tb.raw.gz There are a total of 706 mages n the PLS dataset. 13

14 5.2 Runnng the Software Ppelne In ths secton we descrbe the expected output after runnng the provded scrpts. Recall that prerequste tasks descrbed n need to be done pror to runnng the scrpts Preprocessng As prevously dscussed, the frst step s to process the data approprately for analyss. By executng preprocess.sh we perform the preprocessng on the entre dataset as descrbed n Type the followng command to run preprocessng scrpts on the dataset. qsub submt Preprocess We store all of the ntermedate results of the preprocessng. Below are the lst of fles that are saved as the ntermedate results of the preprocessng. cor_t1_correct: Bas feld caused by magnetc non-homogenety s corrected from the orgnal mage cor_t1. cor_t1_correct_scale: Intensty values of cor_t1_correct are rescaled so that values are between 0 and 100 cor_t1_correct_scale_smooth: The result of the prevous step,.e., cor_t1_correct_scale, are smoothed whle preservng edges n the mage. cor_t1_correct_scale_smooth_small: The smoothed mage,.e., cor_t1_correct_scale_smooth, s downsampled to be used durng regstraton. Fgure 3 shows the result of the preprocessng on an mage taken at baselne for subject

15 (a) (b) (c) (d) Fgure 3: Result of preprocessng of a subject baselne mage: (a) bas-feld corrected mage, (b) ntenstyscaled mage, (c) smoothed mage, (d) downsampled mage Tranng Classfers The next step s to tran SVM classfers to be used durng cartlage segmentaton to provde lkelhood terms for the labelng cost n (9). We tran SVM classfers to perform probablstc classfcaton of the femoral cartlage, the background, and the tbal cartlage. The classfer outputs probabltes of each voxels n the mage belongng to the femoral cartlage, the background, and the tbal cartlage. The classfer s traned usng features descrbed n extracted from the atlas mages. Type the followng command n the termnal to tran the SVM classfer. qsub submt TranSVM The scrpt frst creates a folder named SVM at the dataset drectory to save traned classfers and extracted features. The path to ths folder looks somethng lke the followng. $DataDIR/SVM Once the drectory s created (or already exsts) the followng fles are saved n the folder after the executon of the scrpt. cor_t1_correct_scale_30000: Intensty values of the atlas mages are rescaled to range from 0 to pror to feature extracton. Recall that after the preprocessng ntensty values of the mage 15

16 range from 0 to 100. tranlabel.nhdr: Label mage extracted to be used n the tranng tran_1: Features extracted for the femoral cartlage. tran_2: Features extracted for the background. tran_3: Features extracted for the tbal cartlage. tran_1_small: subset of tran_1 to be used durng tranng tran_2_small: subset of tran_2 to be used durng tranng tran_3_small: subset of tran_3 to be used durng tranng tran_small: Concatenaton of tran_1_small, tran_2_small, and tran_3_small tran_balance.model: traned SVM classfer Automatc Cartlage Segmentaton Once the classfers are traned we are now ready to process the query mages. Please type the followng command n the termnal. qsub submt CartSeg ndp In ths secton we provde what to expect as an output for each stage n the scrpt along wth vsualzaton of ntermedate results. Bone Regstraton We regster all of atlases to a gven query mage va computng a seres of spatal transformatons. Durng executon, fles are saved to an output drectory of the form $DataDIR/$SITEID Q/$ID Q/$VISIT Q/ moved atlas where $SITEID_Q s one of the ste drectores descrbed n 5.1, $ID_Q s one of the subject d drectores under the SITEID_Q, and $VISIT_Q s one of the measurement tme ponts of that subject denoted by $ID_Q. If the output drectory does not exst, the scrpt creates the output drectory frst. Once the output drectory s created (or already exsts), you should fnd the followng fles n the output drectory. affne transform fle: affne_$id_a.tfm B-Splne transform fle: bsplne_$id_a.tfm transformed structural mage: moved_$id_a.nhdr and moved_$id_a.raw.gz transformed femur bone segmentaton: moved_femur_$id_a and moved_femur_$id_a.raw.gz transformed tba bone segmentaton: moved_tba_$id_a and moved_tba_$id_a.raw.gz $ID_A denotes dfferent IDs of atlas subjects. 16

17 Bone Label Fuson After the regstraton, we fuse all of the moved segmentatons of the atlases to form the pror probablty of a voxel belongng to the femur bone. We smply take an arthmetc mean of all of the transformed segmentaton masks to form the pror probablty map for the femur bone p(f emur) and the tba bone p(t ba) respectvely. Two mages named pfemur and ptba are saved after the label fuson. Fgure 4 llustrates what these pror probablty maps look lke. (a) (b) Fgure 4: Spatal pror probablty map for the femur bone (left, a) and the tba bone (rght, b). Bone Segmentaton We compute bone lkelhoods for each voxel, whch are saved as pbone. Gven bone lkelhoods and prors we compute the labelng cost map for the femur bone, the background, and the tba bone; these are saved as cost_femur, cost_bkgrd, and cost_tba respectvely. These labelng cost maps are used wthn a threelabel segmentaton method to segment the femur bone and the tba bone. Fgure 5 shows vsualzatons of these costs. 17

18 Fgure 5: Labelng costs for the femur bone (top), the background (mddle), and the tba (bottom). 18

19 There s a regularzaton parameter to choose n segmentaton method (see [3] for detals); ths optmzaton; we set ths parameter to 0.5. Fgure 6 shows the fnal bone segmentatons. Fgure 6: Fnal bone segmentatons. Extract Jont Regon We automatcally extract a smaller regon (from ths pont on, we refer ths regon as jont regon) from the orgnal mages to make the further processng more effcent. These regons are automatcally extracted usng the bone segmentaton masks from the structural mage, the femur bone segmentaton mask, and the tba bone segmentaton mask. In addton, we create another structural mage whch s a rescaled verson of the structural mage of the jont regon. The ntensty values are rescaled so that they range from 0 to (Recall that after the preprocessng, ntensty values range from 0 to 100.) Ths rescaled mage s used for extractng features to be used n classfcaton. Durng executon of the scrpt, we store all of the smaller mages extracted around the jont regon to an output drectory. The output drectory has the form $DataDIR/$SITEID Q/$ID Q/$VISIT Q/ j o n t / where $SITEID_Q s one of the ste drectores descrbed n 5.1, $ID_Q s one of the subject d drectores under the SITEID_Q, and $VISIT_Q s one of the measurement tme ponts of that subject denoted by $ID_Q. 19

20 If the output drectory does not exst, the scrpt frst creates the drectory. The followng fles are saved under the output drectory after the scrpt has fnshed extractng the jont regon: Structural mage of ths regon: cor_t1_correct_scale The rescaled structural mage: cor_t1_correct_scale_30000 The femur bone segmentaton mask of the regon: seg_femur The tba bone segmentaton mask of the regon: seg_tba Fgure 7 shows the results for a sample query mage. 20

21 Fgure 7: Structural mage extracted around the jont regon (top), segmentaton mask for the femur bone extracted around the jont regon (mddle), and segmentaton mask for the tba bone extracted around the jont regon (bottom). 21

22 Cartlage Regstraton Just as for the bone segmentaton, we frst regster all of the atlas subjects to the query subject as a frst step of cartlage segmentaton. The scrpt frst creates a folder to save the results generated durng the cartlage regstraton of the form $DataDIR/$SITEID Q/$ID Q/$VISIT Q/ m o v e d c a r t a t l a s where $SITEID_Q s one of the ste drectores descrbed n 5.1, $ID_Q s one of the subject d drectores under the SITEID_Q, and $VISIT_Q s one of the measurement tme ponts of that subject denoted by $ID_Q. If the output drectory does not exst, the scrpt creates the output drectory frst. Once the output drectory s created (or already exsts), the followng fles are saved n the output drectory: T affne,f C : affne_femur_$id_a.tfm ĨF C : moved_mr_femur_$id_a S F C : moved_fem_$id_a T affne,t C : affne_tba_$id_a.tfm ĨT C : moved_mr_tba_$id_a S T C : moved_tb_$id_a $ID_A denotes dfferent IDs of atlas subjects. Cartlage Tssue Classfcaton We perform probablstc classfcaton to output probabltes of a voxel belongng to three classes: the femoral cartlage, the background, and the tbal cartlage. Recall that these probabltes wll be used to compute the lkelhood terms for the labelng cost n (9). The scrpt frst creates a folder of the followng form to save results of the SVM classfcaton: $DataDIR/$SITEID Q/$ID Q/$VISIT Q/ j o n t s e g e m e n t a t o n where $SITEID_Q s one of the ste drectores descrbed n 5.1, $ID_Q s one of the subject d drectores under the SITEID_Q, and $VISIT_Q s one of the measurement tme ponts of that subject denoted by $ID_Q. Then features are extracted from cor_t1_correct_scale_30000 and are saved n a fle named f_$id_$visit n the SVM folder ($ID and $VISIT denote subject d and the tme pont of the current query mage respectvely). We use the traned classfer to perform probablstc classfcaton; the output of the classfcaton s saved n a fle named p_$id_$visit under the SVM folder. The classfcaton output s then transformed to lkelhood probablty maps for the femoral cartlage and the tbal cartlage respectvely; these lkelhood maps are saved under jont_segmentaton. The followng fles are generated as a result of classfcaton: The lkelhood map for the femoral cartlage: pfem_svm The lkelhood map for the tbal cartlage: ptb_svm Fgure 8 shows the lkelhood probablty maps of the femoral cartlage and the tbal cartlage for one of queres. 22

23 Fgure 8: The classfcaton map of the femoral cartlage (top) and of the tbal cartlage (bottom). Cartlage Label Fuson Once all of the atlases are regstered to the query, we now fuse the regstered labels of the atlases to form spatal prors for the femoral cartlage and the tbal cartlage. We use non-local patch-based label fuson technques to fuse all of deformed label mages. We frst upscale both deformed structural mage and deformed segmentaton masks by a factor of 3 to make them approxmately sotropc. Then we compute 12 for each voxel locatons wth patch sze beng set to 2, neghborhood sze set to 2, and nearest neghbor set to 5. The resultng fused labels for the femoral cartlage and the tbal cartlages are downsampled to the orgnal sze. After the label fuson s fnshed, the results are saved as mages under jont_segmentaton created n the prevous step. Ths results n: Non-local patch based label fuson of the femoral cartlage: fem_fuson_patch Non-local patch based label fuson of the tbal cartlage: tb_fuson_patch Fgure 9 shows the label fuson results for the femoral and the tbal cartlage for an example query mage. 23

24 Fgure 9: The label fuson result for the femoral cartlage (top) and the tbal cartlage (bottom). Compute Normal Drectons The scrpt also computes the normal drectons for each dmenson. These normal drectons are needed because we use ansotropc regularzaton durng segmentaton. Normal drectons are saved as nx, ny, and nz under the folder where the current query mage s. Cartlage Segmentaton Once we have computed pror probabltes from label fuson and lkelhood probabltes provded by SVM, we can now compute the labelng cost for each of the classes n terms of posteror probabltes. There are two parameters g and a that control two regularzaton terms used n the optmzaton process. In our example, we set g to be 1.4 and a to be 0.2. We use the normal drectons computed prevously because we are segmentng the mages usng ansotropc regularzaton. For more detals on these parameters, please refer [3]. The scrpt saves the followng fles under the jont_segmentaton folder: Labelng cost of background: bkg_cost 24

25 Labelng cost of the femoral cartlage: fem_cost Labelng cost of the tbal cartlage: tb_cost Segmentaton mask of the femoral cartlage: seg_fem Segmentaton mask of the tbal cartlage: seg_tb Fgure 10 shows the labelng costs for background, and the femoral and tbal cartlage respectvely. Fgure 11 shows the resultng segmentatons for femur and tba. 25

26 Fgure 10: Labelng cost for the femur (top), background (mddle), and tba (bottom). 26

27 Fgure 11: Fnal segmentaton mask of the femoral cartlage (top) and the tbal cartlage (bottom). Temporal Algnment If we know the dataset s longtudnal, then we can encourage temporal consstences among resultng cartlage segmentaton masks of dfferent tme ponts. We need the followng two text fles for the longtudnal segmentaton: n_anso.txt: A text fle lstng nput fles needed for longtudnal segmentaton. Each lne corresponds to the femoral cartlage labelng cost, background labelng cost, the tbal cartlage labelng cost and normal drectons of dfferent tme ponts of a subject. out_anso.txt: A text fle lstng output fles of longtudnal segmentaton. Each lne corresponds to the longtudnal segmentaton of the femoral cartlage and the tbal cartlage of dfferent tme ponts of a subject. These text fles are automatcally generated by runnng the followng bash scrpt; please type the followng command n the termnal. sh k s r t / s c r p t / CartSeg Long Preprocess. sh 27

28 Notce that ths scrpt s run as a standard bash scrpt. Please run ths scrpt only once. After runnng CartSeg_Long_Preprocess.sh, please type the followng command n termnal to rgdly algn segmentaton masks of dfferent tme ponts. qsub s u b m t t e m p o r a l a l g n The scrpt frst creates ntermedate output folders for each subjects to store ntermedate results of the temporal algnment. It frst creates the followng folder: $DataDIR/$SITE/$ID/ jont4d (Recall that $ID and $SITE denote subject d and the ste d of the current query patent). Then the scrpt creates another folder under the jont4d folder just created to save ntermedate results of regstratons. $DataDIR/$SITE/$ID/ jont4d / transform As noted n the prevous secton (.e. secton 3.1.4) we use a seres of rgd regstratons to temporally algn segmentaton results of dfferent tme ponts to the baselne. The followng fles are the results of the frst regstraton whch s based on bone segmentaton masks. These fles are saved n the transform folder. Dfferent tme ponts of a subject are denoted by $VISIT. $VISIT_femur.tfm: Rgd transformaton computed based on femur bone segmentaton masks $VISIT_femurBased.nhdr: Rgdly transformed orgnal structural mage accordng to the above transformaton (.e., $VISIT_femur.tfm) $VISIT_femur_femurBased.nhdr: Rgdly transformed femur bone segmentaton mask accordng to the above transformaton (.e., $VISIT_femur.tfm) $VISIT_seg_fem_femurBased.nhdr: Rgdly transformed femoral cartlage segmentaton mask accordng to the above transformaton (.e., $VISIT_femur.tfm) $VISIT_fem_fuson_patch_femurBased.nhdr: Rgdly transformed femoral cartlage spatal pror map accordng to the above transformaton (.e., $VISIT_femur.tfm) $VISIT_pFem_femurBased.nhdr: Rgdly transformed femoral cartlage lkelhood map accordng to the above transformaton (.e., $VISIT_femur.tfm) $VISIT_tba.tfm: Rgd transformaton computed based on tba bone segmentaton masks $VISIT_tbaBased.nhdr: Rgdly transformed orgnal structural mage accordng to the above transformaton (.e., $VISIT_tba.tfm) $VISIT_tba_tbaBased.nhdr: Rgdly transformed tba bone segmentaton mask accordng to the above transformaton (.e., $VISIT_tba.tfm) $VISIT_seg_tb_tbaBased.nhdr: Rgdly transformed tbal cartlage segmentaton mask accordng to the above transformaton (.e., $VISIT_tba.tfm) $VISIT_tb_fuson_patch_tbaBased.nhdr: Rgdly transformed tbal cartlage spatal pror map accordng to the above transformaton (.e., $VISIT_tba.tfm) $VISIT_pTb_tbaBased.nhdr: Rgdly transformed tbal cartlage lkelhood map accordng to the above transformaton (.e., $VISIT_tba.tfm) 28

29 The followng fles are the results of the second regstraton whch s based on cartlage segmentaton masks. The rgd transformaton s computed among deformed cartlage segmentaton masks (.e., $VISIT_seg_fem_femurBased.nhdr and $VISIT_seg_tb_tbaBased.nhdr). Then ths transformaton s appled to deformed mages, deformed segmentaton masks, deformed fuson results, and deformed lkelhood maps. These fles are also saved n transform folder. $VISIT_fem.tfm: Rgd transformaton computed based on the femoral cartlage segmentaton masks $VISIT_femBased.nhdr: Rgdly transformed orgnal structural mage accordng to the above transformaton (.e., $VISIT_fem.tfm) $VISIT_femur_femBased.nhdr: Rgdly transformed femur bone segmentaton mask accordng to the above transformaton (.e., $VISIT_fem.tfm) $VISIT_seg_fem_femBased.nhdr: Rgdly transformed femoral cartlage segmentaton mask accordng to the above transformaton (.e., $VISIT_fem.tfm) $VISIT_fem_fuson_patch_femBased.nhdr: Rgdly transformed femoral cartlage spatal pror map accordng to the above transformaton (.e., $VISIT_fem.tfm) $VISIT_pFem_femBased.nhdr: Rgdly transformed femoral cartlage lkelhood map accordng to the above transformaton (.e., $VISIT_fem.tfm) $VISIT_tb.tfm: Rgd transformaton computed based on the tbal cartlage segmentaton masks $VISIT_tbBased.nhdr: Rgdly transformed orgnal structural mage accordng to the above transformaton (.e., $VISIT_tb.tfm) $VISIT_tba_tbBased.nhdr: Rgdly transformed tba bone segmentaton mask accordng to the above transformaton (.e., $VISIT_tb.tfm) $VISIT_seg_tb_tbBased.nhdr: Rgdly transformed tbal cartlage segmentaton mask accordng to the above transformaton (.e., $VISIT_tb.tfm) $VISIT_tb_fuson_patch_tbBased.nhdr: Rgdly transformed tbal cartlage spatal pror map accordng to the above transformaton (.e., $VISIT_tb.tfm) $VISIT_pTb_tbBased.nhdr: Rgdly transformed tbal cartlage lkelhood map accordng to the above transformaton (.e., $VISIT_tb.tfm) In addton to the transform folder, the scrpt creates another folder under the jont4d folder to save results of the longtudnal segmentaton. The folder name s of the followng form: $DataDIR/$SITE/$ID/ jont4d / segmentaton The scrpt computes labelng cost for the femoral cartlage, background, and the tbal cartlage based on rgdly deformed cartlage segmentaton masks, fuson results, and the lkelhood maps. Normal drectons are also computed because we are usng ansotropc regularzaton for the longtudnal segmentaton. The followng fles are saved under the segmentaton folder. $VISIT_fem_cost.nhdr: Labelng cost of the femoral cartlage $VISIT_bg_cost.nhdr: Labelng cost of the background $VISIT_tb_cost.nhdr: Labelng cost of the tbal cartlage $VISIT_nx.nhdr: Normal drecton along the frst dmenson $VISIT_ny.nhdr: Normal drecton along the second dmenson $VISIT_nz.nhdr: Normal drecton along the thrd dmenson 29

30 5.3 Longtudnal Segmentaton Please type the followng command for longtudnal three label based segmentaton wth ansotropc regularzaton. qsub submt CartSeg long The followng fles are saved under segmentaton folder. $VISIT_seg_fem_long.nhdr: Longtudnal segmentaton masks for the femoral cartlage $VISIT_seg_tb_long.nhdr: Longtudnal segmentaton masks for the tbal cartlage 5.4 Cartlage Thckness Computaton Please type the followng command to compute tssue thckness based on the longtudnal segmentaton masks. qsub submt Thckness long The scrpt wll create a folder to save ntermedate results of the followng form: $DataDIR/ t h c k Then 3D tssue thckness s computed on the results of the longtudnal segmentaton. The followng fles are saved under the thck folder. fem_$id_$visit.nhdr: 3D thckness computed on longtudnal segmentaton masks for the femoral cartlage tb_$id_$visit.nhdr: cartlage 3D thckness computed on longtudnal segmentaton masks for the tbal Then we deform each of these 3D thckness maps to the baselne of a subject pror to creatng 2D thckness maps. Ths s acheved va affne transformaton followed by B-Splne transformaton. The scrpt creates another folder to save the results of these spatal transformatons of the followng form: $DataDIR/ t h c k / transform After the transform folder s created, the followng fles are saved. affne_$id_$visit_femur.tfm bsplne_$id_$visit_femur.tfm affne_$id_$visit_tba.tfm bsplne_$id_$visit_tba.tfm After applyng the affne followed by the B-Ssplne transform, the resultng deformed 3D thckness s saved under the folder of the followng form: $DataDIR/ t h c k /moved fem_$id_$visit.nhdr: Deformed 3D thckness computed on longtudnal segmentaton masks for the femoral cartlage tb_$id_$visit.nhdr: Deformed 3D thckness computed on longtudnal segmentaton masks for the tbal cartlage 30

31 Fnally 2D thckness maps are generated va projecton of these deformed 3D thckness. The scrpt creates a folder to save these 2D projected thckness maps of the followng form: $DataDIR/ t h c k /moved 2d The followng fles are saved under moved_2d folder as a result of the computaton: fem_$id_$visit.nhdr: Projected 2D thckness computed on longtudnal segmentaton masks for the femoral cartlage tb_$id_$visit.nhdr: Projected 2D thckness computed on longtudnal segmentaton masks for the tbal cartlage 5.5 Statstcal Analyss on the Thckness Once the 2D thckness maps are generated, we use MATLAB scrpts to perform localzed analyss of changes on cartlage thckness. The Statstcal Toolbox s requred to run the analyss. To assocate the mages wth KLG grades we need to provde a textfle named lst_klg.txt. Ths fle s formatted n the followng way:... TODO... We can then run the analyss based on the followng scrpts: 1. Frst run the followng scrpt n MATLAB >> create_mask Ths scrpt wll compute a bnary mask for a regon where the majorty of pxels n the projected 2D thckness map le. The bnary mask s computed for the femoral cartlage and the tbal cartlage separately. These bnary masks are saved as fem_mask.mat (bnary mask for the femoral cartlage) and tb_mask.mat (bnary mask for the tbal cartlage). Ths scrpt also reads n prevously computed 2D thckness maps and saves as fem.mat and tb.mat. These.mat fles are saved under the mat folder whch s created f the folder does not exst. 2. Then run the followng scrpts to ft ntal lnear mxed-effects model to model dfference between OA subjects and Normal Control subjects. >> ftlme_fem >> ftlme_tb These two scrpts wll ft the models respectvely based on KLG score specfed n lst_klg.txt and 2D thckness values. Just as the prevous scrpt, these scrpts save the results n.mat fles. These scrpts save the computed models as lme_cell_fem.mat and lme_cell_tb.mat respectvely. 3. Run the followng scrpts to cluster OA subjects. >>cluster_fem >>cluster_tb We cache fxed effects, random effects, standard devatons, and p-values n.mat fles. We use a standard K-means cluster method to cluster OA subjects. The result of cluster ndces for OA subjects are saved as ndex_fem.mat and ndex_tb.mat. 4. Then fnally run the followng scrpts to ft models to each clusters. There are total of 8 scrpts to run. 31