A 3D Virtual Model of the Knee Driven by EMG Signals

A 3D Virtual Model of the Knee Driven by EMG Signals
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  A 3D Virtual Model of the Knee Driven byEMG Signals Massimo Sartori 1 , Gaetano Chemello 2 , and Enrico Pagello 3 1 Department of Information Engineering, University of Padua, Via Gradenigo 6/B,35131, Padova, Italy, 2 ISIB-CNR, Corso Stati Uniti, 4, 35127 Padova, Italy, 3 Department of Information Engineering, University of Padua and ISIB-CNR, Abstract. A 3D virtual model of the human lower extremity has beendeveloped for the purpose of examining how the neuromuscular systemcontrols the muscles and generates the desired movement. Our virtualknee currently incorporates the major muscles spanning the knee jointand it is used to estimate the knee joint moment. Beside that we devel-oped a graphical interface that allows the user to visualize the skeletalgeometry and the movements imparted to it. The purpose of this paperis to describe the design objectives and the implementation of our EMG-driven virtual knee. We finally compared the virtual knee behavior withthe torque performed by the test subject in order to obtain a qualitativevalidation of our model. Within the next future our aim is to develop areal-time EMG-driven exoskeleton for knee rehabilitation. Index Terms - EMG signals, human knee, exoskeleton, simulation  1 Introduction Muscles and tendons actuate movements by developing and transmitting forcesto the skeleton [20]. We investigate how individual muscles are activated to gen-erate joint moments and movements, and to produce coordinated knee torques.This knowledge is instrumental to design a robotic exoskeleton suitable to sup-port a neurologically injured human knee and to provide the proper rehabilita-tive treatment to the patient. Since exoskeletons necessitate of great amount of resources to be developed, the availability of realistic simulators to be used intesting different situations of rehabilitation is a must. Furthermore, from a me-chanical point of view, exoskeletons are becoming more and more cost effectiveand reliable. On the other hand, the increasing availability of small computingdevices with considerable embedded computational power makes now possibleto endow exoskeletons with more and more intelligence and autonomy. Followingour former research experiences with service robotics and humanoids, we are nowinvestigating how more intelligence can be brought on-board exoskeletons. We  particularly wish to develop control systems capable of learning a specific motorgait and independently move the robotic orthosis when the injured patient can’t.The virtual knee presented in this manuscript is actually a three-dimensionalgraphical representation of a human knee which moves in response to electromyo-graphic activity pre-recorded from the legs of different test subjects as they per-form time varying knee flexion and extension tasks. Our virtual knee is suitablefor the study of the neural control mechanisms involved in the transition betweentwo knee postures. 2 Initial Observations We mainly focused on the study of the knee torsion. In order to keep simplethe structure of the model (see Sect. 5), we decided to limit to a number of twothe EMG signals to acquire for the control of the virtual knee. Adding moremuscles, already in this first experimentation, would have indeed leaded to acomplex model very hard to handle. We chose to record the contractile activityof the biceps femoris because, among all the flexor muscles, it has the highest Physiological Cross-sectional Area  (PCA) [22], therefore its contribution to thetotal force generated at the knee articulation will be the highest one [13–16].Among the extensor muscles we chose the rectus femoris because of its proximityto the skin surface. For this reason it’s possible to record its activity withoutexperiencing too much cross-talk  interferences [10,12]. 3 Graphical Interface The Fig. 1 depicts the virtual leg which is driven by the biomechanical model ac-cording to the pre-recorded electromyograms. The 3D Human Lower Extremityhas been developed at the Department of Anatomy of the University of Brussels(ULB) and it is anatomically correct. The srcinal 3D image was a *.msf file.By using the Data Manager  program, also developed at the University of Brus-sels, we exported every single part of the lower extremity in the *.wrl format.Successively we wrote a VRML program in order to put all the exported partstogether again and to form the image shown in the Fig. 1. We chose to adoptVRML for rendering the 3D knee, mainly because it makes the communicationwith the MATLAB Simulink biomechanical model easier to set up [5].The 3D model of the human skeleton developed at the University of Brussels(ULB) is available online [2]. 4 A Forward Dynamics Approach We have used a forward dynamic approach in the study of the human movement(Fig. 1). This choice has been encouraged by the results obtained by Buchanan et al. [8,19]. A detailed description of the phases involved in the control of thevirtual knee will be offered in the following subsections.  Fig.1. The Forward Dynamics Approach and the Graphical Interface. The flowchartdepicts the neural commands and forces for two muscles and moments and the jointangle used to control the virtual human lower extremity. 4.1 Signal Acquisition and Muscle Activation The acquisition stage comprises the sampling and the processing of the EMGsignals while the subject executes flexions and extensions of his leg. The signalshave been sampled at 1 kHz while the BIOPAC MP35 data acquisition unit [1]was connected to a personal computer with an Intel Centrino processor and a512 MB RAM memory. The disposable differential surface electrodes have beenplaced as shown by the Fig. 2. We retrieved information on how to correctlyplace the electrodes and on how to adequately prepare the skin tissue from theSENIAM Project web site [3]. During the acquisition stage the signals have beenamplified (gain of 1000 V V  ) on both channels and successively bandpass filteredfrom 20 to 450 Hz [4,11]. In software, the resulting signals have been full waverectified and normalized to approximate the activation  of the muscles, a i ( t ). 4.2 Muscle Force We now want to obtain some kind of measure of the force, starting from themuscle activation, a i ( t ), previously computed. We can theoretically express themuscular force, F  i ( t ), as a function of  a i ( t ): F  i ( t ) = f  ( a i ( t )) (1)We approximated it with the following formula: f  ( t ) =1 T    tt − T  | a ( t ) | dt (2)  Fig.2. Electrodes placed in the correspondence of: the rectus femoris neuromuscular junction (a), the biceps femoris neuromuscular junction (b) and the ankle intended asa neutral area (c). where T is a temporal window specifying the dimension of the interval duringwhich the calculation of every sample is executed. The equation (2) is actuallya very rough approximation of the muscular force. However, we should keep inmind that our aim is not performing a careful clinical analysis of the musclesbehavior. For our purposes it’s enough understanding the time interval duringwhich the muscles are active along with the intensity of contraction. Refer toSect. 6 to see how our approximations did not negatively affect our simulations. 4.3 Driving the Virtual Knee Once all the muscle forces are calculated, it is important to compute the cor-responding contribution to the joint moment. This requires knowledge of themuscle’s moment arms. We evaluated them as follow: r i ( θ ) = b 0 + b 1 · θ + b 2 · θ 2 + b 3 · θ 3 + b 4 · θ 4 (3)where θ is the knee joint angle expressed in degrees, while b 0 ,b 1 ,b 2 ,b 3 ,b 4 are co-efficients related to the i-th muscle (see [18] for more details). The corresponding joint moment M  can now be estimated: M  ( θ,t ) = m  i =1 ( r i ( θ ) · F  i ( t )) . (4)The muscle’s force F  i ( t ) is obtained from (2). In this case the index i has beenintroduced, and it corresponds to a particular muscle. The joint moment, inturn, will cause the movements. The knee angular acceleration and the relatedcommand signal are calculated directly from the computed joint moment asshown in the following section. 5 The Biomechanical Model 5.1 Modeling the Human Lower Extremity The human lower extremity has been modeled as a rigid body swinging between0 ◦ and 130 ◦ (Fig. 3). Our software mainly simulates the action of the gravity  Fig.3. The human lower extremity has been modeled as a rigid body capable of swing-ing in the interval of 0 ◦ < α < 130 ◦ . force affecting the rigid body during its movement, the action of the extensormuscle force and the action of the flexor muscle force. It also simulates the forcethat takes place when the leg is extended until reaching the angular position α = 0 ◦ . At this point an impulsive force is generated in order to stop the motion of the leg preventing it from extending beyond the threshold α = 0 ◦ . As soon as theleg is blocked, the effect of the force fades away and the leg is free again to flexitself under the action of the successive contraction. The anthropometric datafor modeling the rigid body has been taken from [9]. We particularly considereda centre of mass of the rigid body placed at 21.67 cm from the knee joint andwith a weigh of 3.805 Kg. 5.2 The Structure of the Model The Fig. 4 shows the structure of the biomechanical model which evaluates aprediction of the torque executed by the subject. In the first stage the muscularforces, along with the gravity, are coupled with their respective moment arms(according to the formula 4). The net knee joint moment, M  , is then combinedwith the inertial coefficient and the resulting acceleration¨ ϑ is composed withthe action of the Virtual Walls placed at α = 0 ◦ and at α = 130 ◦ . The resultingsignal is integrated twice to obtain the angular position ϑ used as a commandsignal for the virtual knee depicted in the Fig. 1.
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