# Musculoskeletal modeling – quantification of upper limb internal efforts during movement

## Authors

Maria Laitenberger^{a}, Aurelie Sarcher^{a}, Mickael Begon^{b} and Maxime Raison^{a}

^{a }Chaire de recherche en génie de la réadaptation pédiatrique

Institut de génie biomédical, École Polytechnique de Montréal, Montréal QC, Canada

Centre de réadaptation Marie-Enfant – CHU Sainte-Justine, Montréal QC, Canada

^{b }Laboratoire de simulation et modélisation du mouvement

Département de kinésiologie, Université de Montréal, Montréal QC, Canada

## Abstract

This project consists in the development of a robust multibody model of the upper limb, which can be used for rehabilitation applications such as joint torque and muscle force quantification in the evaluation of musculoskeletal pathology severities.

## Aim of the project:

Like clinical gait analysis, an integrated model of the upper limb for quantitative and functional assessment has the potential to become an important clinical tool in rehabilitation. However, forearm three-dimensional (3D) dynamics still presents some modeling challenges due to the complexity of its multiple degrees of freedom and overactuation. In order to obtain clinically exploitable results, the challenge is also to develop a patient-specific multibody model of the upper limb. Therefore, relevant biomechanical parameters, such as segmental inertial parameters and joint centers of rotation, need to be personalized. In this context, the present work attempts to refine and personalize the musculoskeletal model of the upper limb.

The incentive behind this work is to develop a clinical tool that may help clinicians for their evaluation, follow-up, therapy choices, and also to distinguish different musculoskeletal disorders and pathologies as well as their severity.

## Experimental protocol

The experimental protocol and set-up mainly includes:

### 1. Kinematic data acquisition:

Twenty-nine passive markers are placed on the upper limb in order to ensure a minimum of four markers per rigid body for redundancy, as depicted in Figure 1.

Figure 1 : Upper limb markers placement

Absolute 3D displacements of markers are collected and sampled at 100 Hz by a motion capture system (Figure 2) composed of 12 cameras (T40S, Vicon-Oxford, UK).

Figure 2 : Vicon motion capture system composed of twelve cameras (T40S, Vicon-Oxford, UK)

### 2. Electromyography (EMG) data acquisition:

Six EMG wireless surface electrodes (BTS FREEEMG 300, BTS Bioengineering, Italy) are placed on the upper limb in order to measure the activation of the *biceps brachii (BIC), triceps brachii (TRI), brachialis (BRA), brachioradialis (BRD), pronator teres (PT) and pronator quadratus (PQ) *muscles during the motion (Figure 3).

Figure 3 : EMG wireless surface electrodes (BTS FREEEMG 300, BTS Bioengineering, Italy)

The kinematic and EMG data are synchronized during movement acquisition (Video 1).

Video 1: Kinematic and EMG data synchronization during trial

## Model special features

The model is EMG-driven since EMG data are used as redundant information for the muscle overactuation solving process. This approach ensures a biofidelic representation of the muscle contraction dynamics. The general calculation process to assess the joint torques and muscle forces is schematically outlined in Figure 4.

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Figure 4 : Joint torque and muscle force quantification process [1]

The refined model includes the following features:

- Patient-specific inertial parameters: recognized as one of the main sources of error in the inverse dynamics process, the estimation of segment inertial parameters based on a geometric model [2] will help to represent different morphology types in rehabilitation using simple anthropometric measurements at the upper limb (Figure 5);

Figure 5 : Geometric model used for estimating the upper limb segmental inertial parameters

- Kinematic and dynamic model refinement: a 3D multibody inverse dynamic model of the human upper limb including seven rigid bodies:
- thorax (moving base);
- clavicle;
- scapula;
- humerus;
- ulna;
- radius;
- hand;

articulated by seven joints describing the shoulder, elbow and wrist motion :

- shoulder: sternoclavicular (SC), acriomioclavicular (AC) and glenohumeral (GH) joints;
- elbow: humero-ulnar (HU) and humero-radial (HR) joints;
- wrist: radio-ulnar (RU) and radio-carpal (RC) joints ;

and actuated by the major muscle acting in forearm flexion/extension (F/E) and pronation/supination (P/S):

*biceps brachii*(BIC);*triceps brachii*(TRI);*brachialis*(BRA);*brachioradialis*(BRD);*pronator teres*(PT);*pronator quadratus*(PQ).

- Functional definition of the joint centers and axes of rotation (CoR/AoR) by using coordinate frame transformation methods [3-4].

## Benefits of using Robotran

The multibody dynamical equations are symbolically generated by the Robotran software based on recursive Newton–Euler formalism. Thus, the inverse dynamics process provides the vector of internal interaction torques and forces at the joints for any configuration of the multibody system:

where:

- is the vector of joint relative generalized coordinates ;
- and
is the system generalized mass matrix ;**M(q)**- is the centrifugal and Coriolis loading ;
- is the gravitational loading ;
- is the external forces and torques vector applied to the system

This software allows to directly interface these equations with any numerical process in MATLAB (Mathworks) such as inverse kinematic optimization, numerical filtering, etc. By using the Robotran’s symbolic Jacobian matrix, the global optimization process to estimate the joint coordinates , velocities , and accelerations of the multibody model that best fit the experimental joint positions is successfully implemented at a low computational cost. Furthermore, the Robotran software allows adapting the geometrical model to each subject via MATLAB.

**Typical results**

The results showed that the proposed model is suitable for 3D dynamic motion analysis of the forearm and would be useful as a clinical tool in rehabilitation.

Video 2: Typical results after inverse kinematic optimization and inverse dynamics – F/E movements

Video 3: Typical results after inverse kinematic optimization and inverse dynamics – P/S movements

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## Collaborations

iMMC/CEREM Center for Research in Mechatronics, Université catholique de Louvain, Louvain-la-Neuve, Belgium

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## References

Laitenberger, M., Begon, M., Raison, M. (2012). On the reﬁnement of muscular dynamical modeling for muscle force quantiﬁcation. *Proceedings of* *t**he 2 ^{nd} Joint International Conference on Multibody System Dynamics, *Stuttgart, Germany, May 29 - June 1.

[1] Raison, M., Detrembleur, C., Fisette, P., Samin, J.C. (2011). Assessment of Antagonistic Muscle Forces During Forearm Flexion/Extension. Multibody Dynamics: Computational Methods and Applications 23: 215-38.

[2] Yeadon, M.R. (1990). The simulation of aerial movement-II. A mathematical inertia model of the human-body. Journal of Biomechanics 23 (1): 67-74.

[3] Ehrig, R.M., Taylor, W.R., Duda, G.N., Heller, M.O. (2006). A survey of formal methods for determining the centre of rotation of ball joints. Journal of Biomechanics 39 (15): 2798-809.

[4] O’Brien, J.F., Bodenheimer, R.E. (2000). Automatic joint parameter estimation from magnetic motion capture data. In Proceedings of Graphics Interface pp. 53–60.