Classifying Knee Pathologies using Instantaneous Screws of the Six Degrees-of-Freedom Knee Motion

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1 Proceeding of the 26 IEEE International Conference on Robotic and Automation Orlando, Florida - May 26 Claifying Knee Pathologie uing Intantaneou Screw of the Six Degree-of-Freedom Knee Motion Alon Wolf a Dept. of Mechanical Engineering Technion, Irael Intitute of Technology Technion City, Haifa 32, Irael alonw@tx.technion.ac.il Amir Degani a The Robotic Intitute Carnegie Mellon Univerity Pittburgh PA 15213, USA degani@cmu.edu Abtract We addre the problem of knee pathology aement by uing crew theory to decribe the knee motion and by uing the crew repreentation of the motion a an input to a machine learning claifier. The flexion of knee with different pathologie are tracked uing an optical tracking ytem. The crew parameter which decribe the tranformation of the tibia with repect to the femur in each two ucceive obervation are repreented a the intantaneou crew axi of the motion given in it Plücker line coordinate, along with it correponding pitch. The et of crew parameter aociated with a particular knee with a given pathology i then identified and clutered in R 6 to form a ignature of the motion for the given pathology. Bone model and two cadaver knee with different pathologie were tracked, and the reulting crew were ued to train a claifier ytem. The ytem wa then teted uccefully with new, never trained before data. The claifier demontrated a very high ucce rate in identifying the knee pathology. Index Term - Knee Kinematic, Screw Axi, Pathology Claification, Support Vector Machine. I. INTRODUCTION Aement of joint pathology i not alway trivial and require, in mot cae, a combination of viualization data (i.e. CT, X-ray, MR) combined with phyical ubjective tet performed by the phyician. Diagnoi i particularly complex for the knee joint due to it complex tructure and ix degree of freedom (DOF) motion. For example, in order to ae anterior cruciate ligament (ACL) deficient knee, there are currently three main tet that are performed by phyician: Lachman tet, pivot hift tet and the anterior drawer tet [1]. All of thee tet are performed manually by the phyician while manipulating the patient lower limb. In our tudy, we demontrate a method in which kinematic meaurement of the knee are ued to automatically identify the knee pathology. In order to decribe both tranlation and rotation motion of the knee, i.e. a 6-DOF motion between the tibia and the femur, tudie have ued the helical axi method [2-9]. Helical motion, alo known a crew motion wa mathematically formulated by Sir. Ball in 19 [1]. According to Ball, a crew i a traight line with which a definite linear magnitude termed the pitch i aociated. In hi book, Ball alo tate that any given diplacement of a rigid body can be effected by a rotation about an axi combined with a tranlation parallel to that axi. Intantaneou crew repreentation wa previouly ued to decribe knee motion. Soudan et.al [2] identified the intant axi, or crew axi a one of the widepread method for invetigating the mechanic of the human joint. Although not implemented, the reearcher point out that the intantaneou axi of the joint change in both place and direction during joint movement. Woltring [3] preented an analytical model to decribe the effect of meaurement error from landmark poition data on the definition of the finite centroid and the finite helical axi. Blankevoort et.al. [4] decribed the finite helical axe for a flexion motion and checked the repeatability of the reult by placing marker on four human knee and tracking them. In a tudy by Jonon [6] the author ued tereo-photogrammetric analyi to calculate the helical axi of the knee during flexion. In our tudy not only do we ue crew coordinate to repreent knee motion, but we alo ue thi repreentation to automatically claify knee pathologie uing a machine learning claifier. The idea of claifying knee motion in order to identify knee deficiencie ha been previouly purued. Andriacchi [11] tudied the anterior poterior (AP) linear motion of the femur with repect to the tibia during gait cycle. The experimental data were preented by a one dimenion curve correlating flexion angle to AP diplacement. Thi curve wa later ued to ae the dynamic AP motion of the knee in patient with ACL-deficient pathology [12] that did not develop the neuromucular adaptation. So far machine learning claifier in biomechanic have been ued to claify data that relate to a ingle quantitative meaurement change (i.e. tep width) and not data that repreent the 6-DOF motion of the knee. For example in [13] the reearcher ued machine learning to claify change in gait characteritic of elderly non-faller. Thi reearch ha particularly hown that ome foot placement gait meaure (e.g., tep width and tride variability) diplayed greater aociation with fall prediction. In [14] the reearcher ued Support Vector Machine (SVM) claifier in order to form an automatic recognition of gait change, due to ageing, uing two type of gait meaure: walking velocitie and foot-ground reaction force in the vertical and anterior poterior direction. During the experiment, the gait of 12 young and 12 elderly participant were recorded during normal walking. Altogether, 24 gait feature decribing the two type of gait characteritic were extracted for developing gait recognition model and later /6/$2. 26 IEEE 2946

2 teting of generalization performance. Tet reult indicated an overall accuracy of 91.7% by the SVM claifier in it ability to ditinguih the two gait pattern. A can be oberved, mot of thee work try to claify data that relate to a ingle quantitative meaurement, e.g, anterior poterior linear motion [11], tep width and tride variability [13] etc. In our propoed method, the data incorporate all ix degree of freedom of the knee motion. We ue the intantaneou crew parameter (alo known a twit parameter) of the knee, which provide the 6-DOF tranformation of the knee while in motion. In our experiment we track bone model (Sawbone ) a well a two cadaver knee during flexion uing an optical tracking ytem. The information provided i compoed of multiple obervation of relative bone tate. We then calculate the intantaneou crew parameter that decribe the momentary tranformation between each two ucceive frame that are acquired during motion. The crew parameter incorporate into a extuple vector the pitch of the crew (i.e. the ratio between the rotation and tranlation component of the invetigated motion) and the Plücker coordinate decription of the crew axi (i.e. the axi in pace about which the momentary motion occur). The collection of all the intantaneou crew form a et of continuou twit that decribe the motion. Each crew within a et repreent a point in R 6 ince it i a extuple. We how that a et of intantaneou crew that decribe a motion of a given knee form a variety of point or a cluter in R 6. Moreover, we how that knee with imilar clae (e.g. healthy or ACL/PCL deficient) have imilar cluter. Finally, we hypotheize that once a large data et of different knee with different pathologie i created and claified (uing upervied learning technique), the kinematic of an untrained knee can be aociated with one or more of the cluter. Therefore, the knee pathology can be identified without uing ubjective tet. In thi report we decribe the tool and experimental etup that were ued to demontrate our method. We further preent the reult obtained from experiment with a Sawbone model and two cadaver right knee. II. METHOD A. Repreentation of crew motion (twit) Any given diplacement of a rigid body can be effected by a rotation about an axi combined with a tranlation parallel to that axi [1]. Thi way of defining rigid body diplacement i termed crew motion or twit. In the preent work, we ue the crew parameter to decribe the intantaneou, finite motion of two ucceive obervation of the tibia movement while in flexion. A finite crew diplacement decribe the relative location of two rigid bodie or two different location of the ame body in a global reference frame [15]. The motion of a free body undergoing a finite tranformation can be decribed a a combination of a tranlation, d, parallel to a fixed axi A in pace, and a rotation about the ame axi. The ratio of the tranlation component to the rotation component i known a the pitch of the crew, p, and i given a: d p (1) Thi type of motion i alo known a a helical motion, crew motion, or imply a twit with an axi A and a pitch p a i illutrated in Fig. 1. The ix intantaneou parameter of the unit crew ˆ$ i are given a: ˆ$ p * * * LM NP Q R Where,, i a unit vector along the direction of the crew axi, o i a poition vector of a point on the crew axi, and p i the pitch a defined in (1). Five independent quantitie, four for the axi and one for the pitch, can uniquely pecify a crew motion. Two extreme example are pure rotation and pure tranlation. For a pure rotation motion i.e. p the crew i reduced to: ˆ$ For a pure tranlation motion i.e. p, the crew i reduced to: ˆ$ The decription of the diplacement of a rigid body can not be completely determined without the pecification of the amplitude or intenity of the crew axi. Letting q be the intenity of a twit, the twit can be expreed a: T (2) (3) (4) $ q $ ˆ (5) We refer the reader to [15-17] for a deeper dicuion on crew motion and it ue for repreenting motion of two rigid bodie. x z p A Fig. 1: Screw motion (Helical motion) x 1 y x

3 B. Calculating the crew parameter of a finite motion Calculating the crew parameter of a rigid body undergoing a motion i not intuitive. Few method have been preented in the literature regarding thi iue. However, the final goal i the ame: given two finite configuration of a rigid body, one need to find the crew parameter that would reult in thi motion, i.e. the intantaneou crew axi parameter ($), and it correponding pitch (p). Two work preent formulation for uch an algorithm [15, 18]. The main difference between the algorithm i the input which they require. In Davidon [15], the algorithm input i a homogeneou tranformation matrix from which the crew parameter are extracted. In Angele [18] the algorithm input i a et of three point on the rigid body, prior and pot tranformation (ame point), from which the crew parameter that decribe the motion are derived. Since the output of our experiment are homogeneou tranformation between tracking ytem we ue the algorithm preented in Davidon [18]. We refer the reader to [18] for a full decription of the algorithm. C. Cluter analyi of the crew parameter One of our reearch hypothee i that different abnormalitie would reult in different path that the knee follow when going through flexion, ince it i likely that the abnormality affect the geometry or the mechanical contraint of the knee. Thee different path reult in different et of crew that form different cluter in R 6 (Fig. 2). We exploit thee propertie to train a claification ytem (uing upervied learning technique) that learn the pattern of motion of different knee abnormalitie. Thi ytem i later given a new et of crew from a new knee and i aked to identify which of the predefined cluter it belong to (Fig. 3). In thi work we ue the upport vector machine (SVM) technique a decribed in [19, 2]. Generally peaking, the SVM algorithm create a hyperplane that eparate the data into two clae with the maximum margin. Given training example labeled either "ye" or "no", a maximum margin hyperplane plit the "ye" and "no" training example, uch that the ditance from the cloet example (the margin) to the hyperplane i maximized. For more precie explanation of SVM we refer the reader to [21]. Obervation Claification ytem Knee pathology Fig. 3: AI ytem to identify knee pathology III. EXPERIMENTAL SETTINGS A. Sawbone experiment For our firt experiment we ued Sawbone model of the femur and tibia. The two bone were connected by four rubber tube to imulate the lateral collateral ligament (LCL), medial collateral ligament (MCL), poterior cruciate ligament (PCL), and the anterior cruciate ligament (ACL). During the experiment, optical tracker were attached to both bone (Fig. 4), and were tracked uing the Polari optical tracking ytem. In our experiment etting, the femur wa rigidly fixed and ued a the reference ytem, while the tibia wa quaitatically manipulated from flexion to full extenion by pulling the bone through a long wire connected a cloe a poible to the mechanical axi of the bone. A oppoed to a phyician manipulating the tibia while graping it, the manipulation of the tibia by a long wire produce a minimally contrained motion, and may provide more information on the kinematic of the knee. During the experiment, an optical ytem recorded the location of the tibia, a it wa ubjected to a flexion motion (Fig. 5). The data obtained were then ued for claifying the different pathologie uing the SVM technique. In the training proce we trained the claifying ytem uing five clae; one healthy knee model and four different pathologie: ruptured ACL, ruptured LCL, ruptured MCL, and a combination of a ruptured MCL and ruptured ACL. Thirty training run, coniting of approximately 25 intantaneou crew for each of thee pathologie were taken. Thirty additional run were ued for teting our claification method. In order to tet our claification, for each teting run, each intantaneou crew wa compared with the reulting claifier. The claifier then decided to which cla thi intantaneou crew belonged. 6 Pathology 1 Pathology 2 Pathology 3 Pathology 4 Fig. 2: Different cluter correlating to different path/et of crew Fig. 4: Experimental etup with optical tracker attached (Sawbone) 2948

4 Fig. 6: Experimental etting; Male, 81 (left), Male, 68 (right) Fig. 5: Obervation while flexing the knee (Sawbone) B. Cadaver experiment Following the Sawbone experiment, we ran a et of tet on two cadaver right knee (Fig. 6). The firt knee wa of an 81 year old male, who had Parkinon dieae, and the econd knee wa of a 68 year old male who had protate cancer. Similar to the Sawbone experiment, the tibia tracker poition were recorded in the femur tracker reference frame. Focuing on the cruciate ligament, three clae were recorded, i.e. healthy knee, ACL deficient knee, and a combined ACL, PCL deficient knee. For each of the clae 2 run (flexion to full extenion) were recorded while quaitatically pulling the leg with a tring attached to it. Next, we obtained the crew parameter that decribe the finite motion between two ucceive obervation. Half of the obervation were ued for training, wherea the other half were ued for teting. Moreover, in order to confirm that our method i not enitive to ampling frequency (i.e. number of point per unit of time) we created everal teting et of crew by ampling the crew parameter at different ampling frequencie. Thi apect of the procedure i important ince it i very hard to control and ynchronize the ampling frequency of the data and velocity of the knee flexion per patient. The ame SVM claifying technique wa ued a in the Sawbone experiment. C. Regitration of anatomical reference frame Although the crew repreentation of a motion i invariant in the ame reference frame, it i till dependent on the global reference ytem in which it i decribed. Therefore, it i crucial to etablih a common (global) coordinate ytem between patient ince the optical tracker, camera, and anatomy, can be placed differently reulting in different reference ytem. Without a proper definition of a global reference ytem between patient, the reulting crew will differ, though till decribing the ame motion. For thi purpoe we ue the anatomical reference frame (ARF) of both tibia and femur a our global ytem among patient. We will further dicu thi iue in ection V. IV. RESULTS A. Sawbone experiment reult A dicued earlier, each obervation of the flexion of the knee can be repreented a a et of crew parameter (a extuple vector) which are decompoed into crew axi coordinate given in their Plücker repreentation aociated with their correponding pitch value. When the intantaneou crew axe are plotted equentially, they form a 1-parameter rolled urface of line [22]. The et of axe for the Sawbone model are hown in Fig. 7. In order to make ure that the ue of all ix DOF i not redundant we conducted Principle Component Analyi (PCA) of the data and concluded that the ix DOF have equal energy, thu are all valuable and hould be ued. Thirty et of crew parameter were ued for training the SVM claifier and different thirty et were ued for teting it. The reult of thi proce are given in table I. The column correpond to the different clae (e.g. healthy, ruptured ACL, etc.) and the row preent the average and tandard deviation of the ucce rate in identifying the clae. Note that the average given in the table correpond to the mean percentage of the crew per et that were aociated with the correct cla (averaged over all run). Referring to table I, if we et the threhold for determining a pathology to 82% of the crew being claified to that pathology, we would get 1% ucce in identification. While teting thee clae, we oberved that the main ditinction between the different cae occurred in the lat third portion of the flexion-extenion motion. Thi obervation uggeted that it i ufficient to ue the lat third portion for the training phae. A a reult of thi modification, ucce percentage in ome of the clae increaed (table II). The poibility of gaining increaed accuracy by performing the identification and clutering on a ubet of the experimental data hould be further invetigated. Fig. 7: Screw axi of all obervation: coronal (left), 3D view (right) 2949

5 TABLE I SAWBONES EXPERIMENT:% OF SCREWS WITH CORRECT CLASSIFICATION Healthy Knee ACL LAT MED Combination MED+ACL AVG STD TABLE II SAWBONES EXPERIMENT: TESTING THE LAST 3% OF SCREWS PER RUN (% OF SCREWS WITH CORRECT CLASSIFICATION) Healthy Knee ACL LAT MED Combination MED+ACL AVG STD B. Cadaver experiment reult It i very difficult to ditinguih the difference between the motion of the three knee clae (healthy knee motion, and ACL, ACL+PCL deficient knee) a preented in Fig. 8. However, looking at the intantaneou crew axe it i eaier to ditinguih the clae. A ample plot of the crew axe of the intantaneou crew for an ACL deficient knee i given in Fig. 9. The reulting plot i a 1-parameter rolled urface. Fig. 1 i imilar to Fig. 9 except that all crew axe of the three clae of one knee are plotted in the ame graph. Alo plotted in Fig. 9 and Fig. 1 (marked with an arrow) i the triction curve of the rolled urface [22]. Thi curve can alo erve a a mean of claifying kinematic pathologie, however, we do not ue thi extra data in thi report. The reult of the SVM claifier are given in table III. A can be oberved for all clae, the ytem wa able to identify the cla with high accuracy. The reult of the claifier for a different ampling frequency, i.e. the knee wa manipulated in a different peed reulting in a coarer ampling, are preented in table IV. Since the ucce rate for the claification proce for both cadaver knee acro all three pathologie did not decreae ubtantially with the change in ampling frequency, it appear that ampling frequency doe not have to be maintained among experiment (patient) Y Fig. 8: Cadaver Experiment reult: motion of tibia in three clae (Healthy, ACL and ACL+PCL deficient) X Fig. 9: Screw axe for ACL deficient knee (knee #2) Fig. 1: Screw axe for all three pathologie (knee #2) -5-1 V. DISCUSSION AND FUTURE WORK In thi paper we introduced a new method for identifying knee pathologie olely baed on kinematic obervation. During the experiment we computed the intantaneou crew that decribe the knee flexion. Thee crew were later ued for training a claifier to identify different pathologie. The reult from both the Sawbone experiment and the two cadaver experiment indicate that it i poible to cluter a et of intantaneou crew which correlate to different knee pathologie. Moreover, when given a et of intantaneou crew of a knee which wa never ued during the training phae, the claifier wa able to aociate thee crew to one of the cluter created in the learning phae, hence identify the pathology for which the new et of intantaneou crew TABLE III CADAVER EXPERIMENT: TESTING ALL SCREWS (2 KNEES) (% OF SCREWS WITH CORRECT CLASSIFICATION) Healthy Combination Knee ACL ACL+PCL AVG STD TABLE IV CADAVER EXPERIMENT: SAMPLING HALF OF THE SCREWS (2 KNEES) (% OF SCREWS WITH CORRECT CLASSIFICATION) Healthy Combination Knee ACL ACL+PCL AVG STD Striction curve Striction curve 295

6 belonged to. The SVM claifier wa able to claify the different pathologie with a high ucce percentage of 8 to 9 percent. We further demontrate that the capability of the claifier to identify pathologie doe not depend on the ampling frequency, i.e. ampling frequency and motion velocity do not have to be ynchronized between patient. In thi report we ued the SVM algorithm a our claifier. Although thi tool ha been reported a uitable for biomechanic and gait analyi tudie [14], thi method ha at leat one noticeable drawback which i the teting method of the claifier. In our SVM claification method, each crew i independently teted againt the whole training et while diregarding it relative location in the flexion-extenion motion. One poible improvement to explore i to ue a different claifier uch a the Hidden Markov Model method which will alo take into account the equence and relative location of each intantaneou crew within the et of crew which define the motion, i.e. the ytem internal dynamic. It i worth noting that for thi report we ued a regitration procedure in order to define the anatomical reference ytem of both the tibia and the femur a our global reference ytem among patient. More pecifically, we calculated the poition of the tibial anatomical reference ytem in the femoral global reference ytem. The intantaneou crew were then calculated in the femoral anatomical reference ytem. We are currently exploring two other option which may implify the regitration proce which currently require a CT can and i performed in the CT reference ytem. One option to implify thi proce i to ue tracked ultraound to identify anatomical landmark which define the anatomical reference ytem [23]. The econd approach that we are currently exploring i to ue a parameterize triction curve (Fig. 9, Fig. 1). The triction curve of a rolled urface of line can be approximated by the interection point of the common normal between each two ucceive line and the line themelve [22]. Future work will alo require further invetigation of the ue of noninvaive mounting of the optical tracker ince thi could introduce meaurement error due to oft tiue motion [24]. To conclude, in thi paper we report the very firt tep in the development proce of an expert ytem which i capable of identifying knee pathologie baed on kinematic obervation of the knee while in flexion. The major advantage of the preented method i the ue of intantaneou crew to repreent the 6-DOF knee kinematic, combined with the ue of the SVM claifier. Further invetigation hould be conducted in order to olidify the method; however, the initial reult are very promiing. It i worth noting that although we report our reult for knee kinematic, the ame concept can be applied to any other joint or mechanical ytem of moving rigid bodie. ACKNOWLEDGEMENT Thi work i partially upported by NSF grant IIS-32592, ITR: Data-driven Human Knee Modelling for Expert Surgical Planning Sytem. REFERENCES [1] R. J. Scholten, W. Optelten, C. G. van der Pla, D. Bijl, and W. L. Deville, "Accuracy of phyical diagnotic tet for aeing rupture of the anterior cruciate ligament: a meta-analyi," J. Fam. Pract., vol. 52, no. 9, pp , 23. [2] K. Soudan, R. Van Audekercke, and M. Marten, "Method, difficultie and inaccuracie in the tudy of human joint kinematic and pathokinematic by the intant axi concept. Example: the knee joint," J. Biomech., vol. 12, no. 1, pp , [3] H. J. Woltring, R. Huike, A. de Lange, and F. E. Veldpau, "Finite centroid and helical axi etimation from noiy landmark meaurement in the tudy of human joint kinematic," J. Biomech., vol. 185, pp , [4] L. Blankevoort, R. Huike, and A. De Lange, "Helical axe of paive knee joint motion," J. Biomech., vol. 23, no. 12, pp , 199. [5] R. Hart, C. J. Mote, and H. Skinner, "A finite helical axi a a landmark for kinematic reference of the knee," J. Biomech. Eng., vol. 113, no. 2, pp , May [6] H. Jonon and J. Karrholm, "Three-dimenional knee joint movement during a tep-up: evaluation after anterior cruciate ligament rupture," J. Orthp. Re., vol. 12, no. 6, pp , November [7] M. Bottlang, J. L. Marh, and T. D. Brown, "Factor influencing accuracy of crew diplacement axi detection with a D.C.-baed electromagnetic tracking ytem," J. Biomech. Eng.-T ASME, vol. 12, no. 3, pp , [8] T. R. Duck, L. M. Ferreira, G. J. W. King, and J. A. Johnon, "Aement of crew diplacement axi accuracy and repeatability for joint kinematic decription uing an electromagnetic tracking device," J. Biomech., vol. 37, no. 1, pp. 163, 24. [9] R. Shiavi, et al., "Helical motion analyi of the knee--i. Methodology for tudying kinematic during locomotion," J. Biomech., vol. 2, no. 5, pp , [1] R. S. Ball, A Treatie on the Theory of Screw, Cambridge, U.K.: Cambridge Univ. Pre, 19. [11] T. P. Andriacchi, E. J. Alexander, M. K. Toney, C. O. Dyrby, and J. A. Sum, "A point cluter method for in vivo motion analyi: applied to a tudy of knee kinematic," J. Biomech. Eng., vol. 12, no. 6, pp , Dec [12] S. S. Haan, D. E. Hurwitz, C. A. Buh-Joeph, B. B. J. Bach, and T. P. Andriacchi, "Dynamic evaluation of knee intability during gait in anterior cruciate ligament deficient patient," Tran. Orthop. Re. Soc., vol. 44, pp. 85, [13] B. E. Maki, "Gait Change in Older Adult: Predictor of Fall or Indicator of Fear?" J. Am. Geriatr. Soc., vol. 45, no. 3, [14] R. Begg and J. Kamruzzaman, "A machine learning approach for automated recognition of movement pattern uing baic, kinetic and kinematic gait data," J. Biomech., vol. 38, pp , 25. [15] J. K. Davidon and K. H. Hunt, Robot and Screw Theory: Application of Kinematic and Static to Robotic: Oxford Univerity Pre, 24. [16] B. Roth, "Screw, Motor, and Wrenche That Cannot Be Bought in a Hardware Store," 1984, pp [17] K. H. Hunt, Kinematic Geometry of Mechanim, Oxford: Clarendon Pre, [18] J. Angele, "Automatic computation of the crew parameter of rigidbody motion. Part I: Finitely-eparated poition," J. Dyn. Syt.-T ASME, vol. 18, no. 1, pp , [19] V. N. Vapnik, The nature of tatitical learning theory, New York, NY: Springer-Verlag New York, Inc., [2] V. N. Vapnik, Statitical learning theory, New York: Wiley, [21] C. J. Burge, "A Tutorial on Support Vector Machine for Pattern Recognition," Data Min. Knowl. Dic., vol. 2, no. 2, pp , [22] H. Pottmann and J. Wallner, Computational line geometry, Berlin: Springer, 21. [23] P. Keppler, "Ultraound for meauring the mechanical leg axi in total knee arthroplaty," in CAOS international, 24, pp. 48. [24] W. R. Taylor, et al., "On the influence of oft tiue coverage in the determination of bone kinematic uing kin marker," J. Orthp. Re., vol. 23, pp ,