View Full Version : biarticular muscle length

Sylvain Grenier, University Of Ottawa
04-29-1996, 05:59 AM
This a summary of responses to a posting I did in March/96.
Actually the first seven or so are from the intial posting in
December/95. Nevertheless here are the responses I got to the latest
posting (they are at the end) which was basically a call for software.
Thanks to all who responded, I got many good references from you. If
there are any further comments please feel free in francais or english!

Dear Sylvain,

My colleague, P. Klein, has done a lot of work on lever arms of the lower=20
extremity, including biarticular muscles. You can contact him at:


But I suppose that he will read your message himself and answer personally.

Best regards,


V=E9ronique Feipel
Laboratory for Functional Anatomy
ULB - CP 619
808, route de Lennik
B-1070 Brussels
Phone: ++ 32 2 555 63 29
Fax: ++ 32 2 555 63 78
Email: vfeipel@ulb.ac.be

Unfortunately, you don't mention if you are looking at specific two-joint
muscles, or what research question you are attempting address (e.g.,
theoretical modelling of musculoskeletal system, or interpreting the
function of specific muscles during an action). Therefore, this info.
may or may not be useful.

Hawkins and Hull (J. Biomechanics, 23, 1990) presented a technique to
estimate muscle length. However, similar to some of the other references
you have noted, their model assumes that total muscle-tendon length
changes as a function of joint angle is what is required to interpret
muscle function. What would be more useful would be fiber length as a
function of joint angle.

Winter and Scott (J Electromy, Kines., 1, 1992) have presented a model
for estimating muscle shortening velocities based on the assumption that
all changes in length of total muscle-tendon unit are attributable to
changes in pennation angle and sarcomere length, with tendon length
remaining fixed. Unfortunately, their model does not provide estimates
of muscle fiber length. Note also, that if, more some tasks, tendon
stretch occurs, all models will have some degree of error in estimating
either muscle length or muscle velocity changes. However, for many
actions, Winter and Scott's model should be helpful for interpreting
function of the lower-limb muscles that they modeled.

If you do not post a summary, please send me one.

Raymond P. Young, Ph.D.

We measured last year on human cadavers length changes of biceps cruralis,
semi-tendinosous, membranosous and rectus femoris during simulation of
squatting down or up. The experimental data for four specimens each five
trials is so big we didn't found time to calculate all.
The experimental set up was briefly as follows:
Hemi pelvis fixed to a wooden support sliding on linear bear balls up and
down ( by means of a motor). The hip and knee joint were nearly completely
cleaned from all muscles. Capsule and ligaments were left intact.
On tendons of the before mentionned muscles were fine steel wires sewn.
Tibia and foot were left intact, no dissection, just cutting of Achilles
tendon to allow dorasal flexion of the foot.
By means of pulleys the steel wires run over potentiometers conneccted to a
PC (ADboard and so on).
We could determine length changes due to each of the joint angular changes
and to both during the same movement (concomiitent flexion or extension of
hip, knee and talocrural joints).
This study was performed as a PT diploma final work. It is not yet published
and it exists only in a french version.
Tell me if I could help you more.
* Klein Paul Ph.D. *
* Free University of Brussels *
* CP 168, Avenue P. Heger, 28 *
* 1050 Brussels, Belgium *
* *
* Phone 32-2-6502470 Fax: 32-2-6502473 *
* pklein@resulb.ulb.ac.be *


You may want to look at some older papers we published on biarticular muscles
in the frog hindlimb:

1. Lieber, R. L. Hypothesis: biarticular muscles transfer moments between
joints. Developmental Medicine and Child Neurology 32: 456-458, 1990.
2. Lieber, R. L., and J. L. Boakes. Sarcomere length and joint kinematics
during torque production in the frog hindlimb. Am. J. Physiol. 254: C759-C768,
3. Lieber, R. L., and C. G. Brown. Sarcomere length-joint angle relationships
of seven frog hindlimb muscles. Acta Anat. 145: 289-295, 1993.
4. Lieber, R. L., M. E. Leonard, C. G. Brown, and C. L. Trestik. Frog
semitendinosus tendon load-strain and stress-strain properties during passive
loading. Am. J. Physiol. 261: C86-C92, 1991.
5. Mai, M. T., and R. L. Lieber. A model of semitendinosus muscle sarcomere
length, knee and hip joint interaction in the frog hindlimb. J. Biomech. 23:
271-279, 1990.

Good Luck,
Dr. Rick Lieber
Professor of Orthopaedics and Bioengineering
La Jolla, CA 92093-9151

Re: Concerning your recent query to BIOMCH-L

Dear Sylvain Grenier:

There are some articles have been published regarding changes in the muscle

1. Aruin, A.S., Prilutsky, B.I.(1987) Prediction of Changes in Length of
Different Heads of Triceps Surae by the Angles in the Ankle and Knee
Joints. XI International Congress of Biomechanics. Abstracts. p.16.

2. Aruin, A.S., Prilutsky, B.I.(1986) Dependence of Lengthening of the
Triceps Surae Muscle on Knee and Joint Angles. Physiologiya Cheloveka 12:
244-247. (The English translation has published in Human Physiology, USA)

3. Aruin, A.S., Zatsiorsky, V.M., & Prilutsky, B.I. (1988) Arms of the
Forces and Elongation of the Lower Extremity Muscles at Various Values of
Joint Angles. Arhiv Anatomi, Gistologii i Embriologii. (Archives of
Anatomy, Histology, and Embryology) 6:52-55 (in Russian).
In the article regressive equations have been calculated for predicting
arms of the forces and for elongations 9 muscles of the lower extremities
according to the known values of the angles in the joints.

If you are interested in such information, send me you address and I will
mail you photocopies of the articles and equations (translated into
English) by regular mail.


Alexander S. Aruin, Ph.D..

200 Biomechanics Laboratory
Pennsylvania State University
State Collage, PA 16802

Phone (814) 863-5374
FAX: (814) 865-2440

e-mail: aruin@psu.edu

Bonjour Sylvain,

Comme tu vois, je prend pour acquis que tu comprend le francais! J'ai lu
ton message resumant les reponses que tu avais recues concernant les
muscles biarticulaires. Je suis un peu en retard avec ma contribution
(j'ai manque ton message original), mais bon, ca peut toujours t'etre utile.

J'ai ecrit une note technique qui va bientot paraitre dans le Journal of
Biomechanics sur les variations de bras de levier et de longueur
musculaire de 13 muscles du membre superieur, dont 5 muscles
biarticulaires. J'ai utilise des donnees deja publiees dans la
litterature pour developper des equations donnant les bras de levier et
les longueurs en fonction de l'angle de flexion/extension de l'epaule
(dans le plan horizontal), de flexion/extension au coude et de flex/ext
et deviation radio/ulnerale au poignet. Je devrais recevoir les epreuves
d'ici un mois ou deux. Si ca t'interesse, fais-moi signe et je t'en
enverrai une copie.

Bonne chance dans ton project,


************************************************** ************************
* Pascale Pigeon * Ecole Polytechnique de Montreal *
* Institut de genie biomedical * C.P. 6079, Succ. Centre-Ville *
* E-mail: pigeon@grbb.polymtl.ca * Montreal, Quebec, Canada, H3C 3A7 *
* Tel:(514) 340-4179 * Fax:(514) 340-4611 *
************************************************** *************************

Hi Sylvain,

I do not know whether you intend to calculate muscle lengths or moment arms, but I assume that you
will in fact be interested in the latter. If you intend to calculate moment arms on the basis of the length
change versus angle change method (dL/dphi) you will find that estimation of moment arms will be
impossible when you assume that the particular joint you look at has more than 1 d.o.f. dL will in that
case give you insufficient information to solve the equation. You will at least need information on dXYZ,
i.e. tendon displacement in 3D, in combination with dphi.
I tried to do a tendon displacement study on the bi/tri-articular biceps brachii and triceps brachii, as
well as relevant mono-articular muscles in the arm relative to rotations in the glenohumeral joint, the
elbow and the forearm. These measurement worked out to be technically very difficult (elasticity of
material, hysteresis, friction in the experimental setup) and we decided to go for a combination of
origin-insertion distance measurements and muscle wrapping. The moment arm of f.i. brachialis is
estimated from its distance between origin and insertion AND the radius of a cylinder that can be fitted
to the elbow joint surface. The advantage of this method is that the common problem of the moment arm
aproximating zero when elbow flexion angle is zero, does not exist. The smallest moment arm is equal
to the radius of the fitted cilinder.
You can find descriptions of this method in:
Veeger et al, JB 1992 (shoulder)
Van der Helm et al, JB 1992 (shoulder)
We hope to get the results of the arm study published soon.

A good description of the moment arm calculations following the tendon displacement method can be found
Murray et al (JB, 1995) have calculated tendon displacement for elbow flexion and prosupination in the
human arm.


DirkJan Veeger
Department of Human Movement Sciences,
VU Amsterdam

To: IN%"s497546@aix1.uottawa.ca" 20-MAR-1996 21:07:13.46
Subj: Biarticular muscle length

Sylvain: I applied the method from Frigo & Pedotti(1976) to calculate
muscle lengths of 5 lower limb muscles during verticle jumping, 3 of
which were biarticular muscles (rectus femoris gastrocnemius and biceps
femoris) as part of my masters thesis from the University of Waterloo, 1981.
In addition to the assumptions made by Frigo and Pedotti of a point origin
and insertion, and a straight line representation of the muscle, I had to
make some other assumptions and calculations since the original paper
was extremely sketchy. The code is in an appendix at the back of the
thesis, and it is based on their model and my measurements and
other assumptions.
I have two conference papers that utilized this model and if you are
interested I can send them to you. The model is a very simple one and while
I have not continued to work in that area I know that there have been more
sophisticated ones developed in the meantime. The relationships are based
on relative joint angular displacements. If you are interested I can
send you the complete reference to my thesis as simply sending the Fortran code
may not explain the interpretation or the original model used in the code.
Let me know if
you are interested.

Cheryl Hubley-Kozey

Dear Sylvian,

YOUR Q: Does anyone have software applying either [Grieves et al.(1976);
Frigo & Pedotti(1976); Hawkins & Hull (1990) or any other relevent
method] to this end?

A couple of years ago we did an extensive comparison between the different
methods available at that time (Grieve, Visser et al, Hawkins, Frigo and
Pedotti). There is quite a difference!! For instance, increasing versus
decreasing moment arm length when joint angle increases for the same muscle.
If you are interested I can fax you some graphs we made for the moment arms
of different leg muscles. Let me know.

The methods we had chosen are published in for instance:
Jacobs and Ingen Schenau in Journal of Physiology 1992 457:611-626.
Jacobs and Ingen Schenau in Journal of Biomechanics 25:953-965, 1992
What we calculate in these articles is not absolute Loi but relative changes
of Loi.
A0 or B0 are basically meaningless.

Hope this is of any help to you,
Best regards,
Ron Jacobs

Ron Jacobs
University of Twente, WB/BW
Institute for Biomedical Technology
P.O. Box 217
7500 AE Enschede


I am writing in response to your posting on biomech/l requesting
information on multijoint muscle lengths during walking. We recently
published an article that is relevant to your query. The reference is
listed below.

Delp, S. L., Arnold, A. A., Speers, R. A., Moore, C.: The lengths of the
hamstrings and psoas muscles during normal and crouch gait: implications
for muscle-tendon surgery, Journal of Orthopaedic Research, vol. 14, pp.
144-151, 1996

I hope this information is helpful.

Scott Delp>
Hello or salut!

France responds to Canada

I never eared about softwares for Grieves et al. or Hawkins & Hull fitting
equations. For myself, I have programmed these equations in Excel.
Nevertheless, be carefull with these equations for bi-articular actuators
like the gastrocnemii as they turn arround the femoral condyles at their
insertions on the femur. Therefore, the best method I found for calculating
in in vivo conditions the length variations of the three chiefs of the
triceps surae was to use the scaled 3D-data proposed by White et al. (1989)
and applied in 2D in the sagital plane (plantarflexion usual plane). For
review, you could see Yamagushi et al. (1990) too.

So, have a good work!

White, S.C., Yack, H.J. et Winter, D.A. (1989) A three-dimensional
musculoskeletal model for gait analysis. Anatomical variability estimates.
J. Biomechanics 22(8,9), 885-893.
Yamagushi, G.T., Sawa, A.G.U., Moran, D.W., Fessler, M.J. et Winters, J.M.
(1990) A survey of human musculotendon actuator parameters. In Multiple
Muscle Systems. Biomechanical and Movement Organization (edited by Winters,
J.M. and Woo, S.L.-Y.) pp. 717-772. Springer, New York.

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