The tutorial below is designed for use with OpenSim version 4.0 and later. A version of the tutorial compatible with OpenSim version 3.3 is available here .

I. Objectives


The purpose of this tutorial is to demonstrate how musculoskeletal models can be used to study orthopaedic surgical techniques and to illustrate how muscle moment arm, optimal muscle fiber length, and tendon slack length influence the variation of muscle force with respect to changes in joint angle. In this tutorial, you will:


Each section of the tutorial guides you through certain tools within OpenSim's GUI and asks you to answer a few questions. The menu titles and option names you must select and any commands you must type to run OpenSim will appear in bold face. The questions can be answered based on information from OpenSim and basic knowledge of the human musculoskeletal system. As you complete each section of the tutorial, feel free to explore OpenSim and the wrist model further on your own. Depending on the amount of exploration you do, this tutorial will take about 1-2 hours to complete.

II. Musculoskeletal Model of the Wrist

In this section, you will load a model of the human wrist [1] and examine its motions. You will then explore the wrist muscles and their functions.

Use the Coordinate sliders to investigate the wrist model. In particular, become familiar with wrist flexion and extension and radial and ulnar deviation. It is important to understand the angle conventions to interpret the plots you will make later in the tutorial.
Note: Radial deviation is defined as wrist motion toward the radius bone, or thumb side. Wrist flexion is defined as wrist motion that faces the palm towards the forearm, while wrist extension faces the palm away from the forearm. 

In this OpenSim model, muscles are grouped based on their function.


1. Which motion is expressed in positive angles: wrist flexion or wrist extension?

2. Which motion is expressed in positive angles: radial deviation or ulnar deviation?

3. What are the functions of the Extensor Carpi Ulnaris (ECU) muscle? Check or circle all that apply.
    Ο wrist extension  Ο wrist flexion  Ο radial deviation  Ο ulnar deviation  Ο hip extension

4. What are the functions of the Extensor Carpi Radialis Brevis (ECRB)? Check or circle all that apply.
    Ο wrist extension  Ο wrist flexion  Ο radial deviation  Ο ulnar deviation  Ο hip extension

III. Simulation of a Tendon Transfer

Spinal cord injury at the level of the cervical spine causes a loss of hand function. In some patients, the ability to grasp and release objects may be restored through electrical stimulation of paralyzed muscles, called functional electrical stimulation (FES). However, FES is only feasible in those muscles where the connection between the nervous system and the muscle remains intact within the muscle. In many cases, the muscles that perform the desired functions (e.g., finger flexion, thumb abduction) have been damaged too greatly to respond to FES. In addition, there is often a loss of balance at the wrist joint, causing the wrist to remain in a flexed and ulnarly deviated position [2]. In these situations, tendon transfers are performed to i) alter the paths of muscles that do respond to FES to locations where they can enhance hand function, and ii) restore a more functional configuration of the wrist joint so that grasp and release tasks can be accomplished.

In this section of the tutorial, you will transfer the ECU tendon to the ECRB tendon and evaluate the mechanism by which this tendon transfer restores balance to the wrist.

To simulate the surgery, you will edit the paths of the muscles in the visualizer window. Each end of a muscle-tendon complex connects to bone. In this model, the most proximal connection is the origin, and the most distal connection is the insertion point. You will first select the insertion point of the ECU_pre-surgery muscle and move its location. Then you will perform a similar operation for the two via points proximal to it. All muscle via points are graphically represented as small red spheres on the muscle path, and coincide with the "kinks" in the muscle path.

IV. Biomechanical Effects of Tendon Transfer

To analyze the effects of the surgery, you need a model of the ECU muscle both before and after surgery. Although you did a great job moving the muscle points, a muscle with a path similar to the transfer you just completed has already been built into the model.

Now you will investigate the effect of the transfer on wrist extensor strength by creating plots of the maximum isometric wrist moments before and after the simulated surgery. To see how the surgery will affect wrist extension strength, you will examine maximum isometric wrist extension moments (i.e., the moments generated when all the extensor muscles are maximally excited).
Note: Isometric moments assume zero muscle velocity.


A curve labeled "Before Transfer" should appear on the plot, which is the sum of the isometric moments generated by all of the wrist extensors before the surgery. Now you will add another curve to compare the strength of the extensors after the transfer.


Now let's examine the effects of the transfer on the deviation strength of the wrist muscles.


5. In these plots, given how the model defines the wrist flexion degree of freedom, is wrist extension moment denoted by positive or negative values?

6. What happens to the maximum moment of the wrist extensors if the ECU muscle is transferred to the ECRB?
Hint: Remember, one of the goals of the surgery is to increase wrist extension strength. 

7. In these plots, is the sign of an ulnar deviation moment positive or negative?

8. What happens to the maximum moment of the ulnar deviators if the ECU muscle is transferred to the ECRB location?

9. One goal of this tendon transfer surgery is to decrease excessive ulnar deviation. Has your simulated surgery achieved this goal? Why or why not?

After answering these questions, close the plotter window.

You are now going to take a more in-depth look at the effects of the tendon transfer on the function of the ECU muscle.


10. What is the peak value of the ECU extension moment before transfer? At what flexion angle does it occur?
 Note: Remember, extension moments are negative on the plots.

11. What is the peak value of the ECU extension moment after transfer? At what flexion angle does it occur?

12. Does the moment-generating capacity of the ECU vary more with flexion angle before or after the simulated surgery?

Investigate the differences in wrist strength further by creating plots of 1) flexion moment vs. flexion, 2) tendon force vs. flexion, and 3) flexion moment arm vs. flexion for the ECU_pre-surgery and ECU_post-surgery muscles. Note: You can open multiple plotter windows simultaneously. When finished, you should have created three plots (flexion moment, tendon force, moment arm) in three separate plotter windows with two curves each.


13. Write down the peak values of each curve (flexion moment, tendon force, moment arm), the joint angle at which the peak occurs, and describe the general shapes of the curves.

OpenSim's Property Editor allows you to examine and edit the muscle parameters used to estimate the force-length curve of this muscle.


14. What is the optimal fiber length of the ECU_pre-surgery muscle?  

15. What is the optimal fiber length of ECU_post-surgery?

16. Calculate the ratio of optimal fiber length to peak moment arm for ECU_pre-surgery and ECU_post-surgery.   

17. Explain the differences in the isometric moment vs. wrist flexion angle plots for the ECU_pre-surgery and ECU_post-surgery muscles, based on the plots of force and moment arm and the ratio of optimal fiber length to peak moment arm.   

18. Specifically, what does the difference between the ratios of optimal fiber length to moment arm for the ECU before and after the tendon transfer tell you?

After answering these questions, close all of the plotter windows. 

V. The Effect of Tendon Slack Length on the Isometric Force-Angle Curve

The previous simulation illustrated how the moment arm and optimal fiber length of a muscle influence its isometric strength and the portion of the force-angle curve over which the muscle operates. Another factor in determining the isometric force vs. joint angle relationship is tendon slack length. Tendon slack length is the length at which the tendon begins to generate force.


19. What is the tendon slack length of the ECRB muscle?

20. What is the optimal fiber length of the ECRB muscle?

Now you will examine the effect of changing muscle parameters.


21. How did changing the tendon slack length of the ECRB alter the tendon force vs. flexion angle curve? 

22. How did changing the tendon slack length of the ECRB alter muscle-tendon length vs. flexion angle curve?

23. How did changing the tendon slack length of the ECRB alter the fiber length vs. flexion curve?

24. At what flexion angles do the fiber lengths of the ECRB and the edited ECRB reach the optimal fiber length? Compare these angles with the peaks of the force vs. flexion plots.

25. Explain the effect of tendon slack length on the force-angle relationship of a muscle based on what you have learned about its effect on fiber length and muscle-tendon length.

Feel free to change the tendon slack length and make more curves to further demonstrate the effects you have seen. For additional information, refer to the references below.


1. Gonzalez, R.V., Buchanan, T.S., Delp, S.L. How muscle architecture and moment arms affect wrist flexion-extension moments. Journal of Biomechanics, vol. 30, pp. 705-712, 1997.

2, Herrmann, A., Delp, S.L. Moment arms and force-generating capacity of the extensor carpi ulnaris after transfer to the extensor carpi radialis brevis. Journal of Hand Surgery, vol. 24A, pp. 1083-1090, 1999.

3. Zajac, F.E. Muscle and tendon: properties, models, scaling, and application to biomechanics and motor control. Critical Reviews Biomedical Engineering, vol. 17, pp. 359-411, 1989.

4. Delp, S.L. and Zajac, F.E. Force- and moment-generating capacity of lower-limb muscles before and after tendon lengthening. Clinical Orthopaedics and Related Research, vol. 284, pp. 247-259, 1992.