View Full Version : BioNet Controversial Topic #4: knee joint DoUF

02-25-2002, 02:55 AM
Dear Colleagues,

After a good start with the discussions of the controversial issues in
biomechanics (TOPICS 1, 2 and 3), here we are with the launch of a
TOPIC 4 for this series. This Topic seems particularly indicated for one of
the discussion workgroups within Session "Get it Off Your Chest" at the
Event in Bruxelles (http://www.mk.dmu.ac.uk/bionet/index.htm). As usual, we
invite all contributors to formulate their own opinions and comments. Sorry
in advance for any possible missing work of other important contributions
from the literature in this respect: this is a good opportunity to collect
all relevant views and eventually to make a summary.

on behalf of the BIONET Consortium
Alberto Leardini

The BioNet event is approaching quickly. I'd like to remind to all
prospective attendees that "Early Bird" Registration ends on 28th March!!
Go and see the faschinating programme.

T O P I C # 4

How many independent degrees of unresisted freedom has the human knee joint?

What's the matter
Under load, the knee, as every human joint, shows important motion, i.e.
both rotations and translations can occur, no matter on the extent of this
motion. It is however also well documented that the resistance offered by
the joint to externally imposed displacements and rotations is different
from an anatomical plane to another, and from one direction to another
(flexion is less resisted than ab/adduction, antero-posterior displacement
less than separation/penetration, separation less than penetration, etc.).
It is clear that this resistance is offered even before any muscle
activity, for example even on cadavers, therefore it must be provided
primarily by the joint passive structures. It has also been shown that this
resistance changes also from joint position to joint position. The
questions are: how many independent degrees of freedom has the human knee
joint? Are there series of joint positions at stable equilibrium, that is
positions in which resistance is not offered by the joint until an external
displacement is performed? Are these positions in large combinations or a
narrow path of unresisted motion is prescribed? Because we want to
characterise the joint in itself, these questions should be addressed by
looking at passive motion, i.e. in virtually unloaded conditions, therefore
the number of 'degrees of unresisted freedom (DoUF)' is here under
discussion. This parameter represents therefore the number of input
quantities required to specify fully the relative position of the two
segments involved when motion of the joint is observed in the condition of
virtually absence of external forces. Note all these considerations are
unaffected by the type and complexity of the motion performed, whether this
is a ball-and-socket or hinge-like or a complex mechanism or whatever.

Does it matter?
Characterising the knee (as any of the human diarthrodial joints) according
to the number of DoUF may seem merely an academic exercise, but in fact it
is a fundamental question for any new investigation on the joint mobility
and stability by geometrical and mechanical models. This knowledge is very
useful in modelling studies because it determines the most appropriate
approach for the analysis. Knowing the joint is a flexible structure (0
DoUF), structural mechanics can immediately be applied to combine external
load and relevant displacements/rotations in the single resisted joint
position (as the vertebrae?). With a single DoUF, the joint can still be
cylindrical (hinge-like, elbow?). If, conversely, the articular surfaces
become incongruent during motion, and if some rolling occurs and a moving
instantaneous axis of rotation is observed, this may suggest that the joint
is constrained in a single DoUF 'mechanism'. In two or three (hip?) DoUF
joints, a large spectrum of unresisted positions are allowed, and joint
resistance is felt only when close to the extremes of the range of motion.
If the number of DoUF at the knee is more than 0, a profound knowledge of
these series of joint positions would be a necessary preliminary part of
any study addressing knee mechanics. It is also evident that any change to
the original geometry of the intact joint, such as erosion of the articular
surfaces, ligament injury and reconstruction, or total joint arthroplasty,
will alter the original number of DoUF and lead to abnormal kinematics of
the joint.

>From the literature
Since the first observations of the screw-home mechanism of the knee,
scientists and clinicians have given up the idea that this joint is a
simple mechanical pair, such as an hinge or a ball-and-socket joint
[1,2,3,4,5,6]. Therefore in modern biomechanics the knee translations and
rotations are usually described along and about the 3 anatomical axes, both
during passive and weight-bearing motion [13,14,15,16]. In clinical
practice and standard gait analysis, either for diagnostic purposes or to
evaluate surgical treatments, clinicians consider separately the 3
rotations and the 3 translations at the knee, alluding implicitly to 6
independently degrees of freedom, no matter on whether these are coupled or
In 1907 Fisher stated that "the knee has 2 dof" referring to the
flexion-extension and the internal-external rotation [7]. Also Hollister
[8], Freeman and Pinskerova et al. [9] have recently proposed that the knee
motion is the result of a combination of 2 rotations around an appropriate
axis of flexion-extension (located with respect to femoral anatomy, roughly
joining the centres of the two condyles) and an axis of longitudinal
rotation (described with respect to the tibial anatomy and roughly parallel
to the tibial shaft), without mentioning eventual translations occurring
during the motion. In [10,11] Wilson et al. concluded that the "passive
knee flexion can be described by a coupled path", and predicts that the
knee motion is prescribed by ligaments and articular surfaces alone along a
path [11], thus alluding at a single DoUF. Both statements however, [9] and
[10-11], allude to a single DoUF, although with different views on the type
of motion. On the other hand, ``envelopes'' of motion for was reported for
the knee joint [14] by the limits of internal and external tibial rotation
at a series of flexion angles when the tibia was subjected to 3~Nm of
internal and external torque. The motion was presented as an ``envelope''
because no consistent path was found in the completely unloaded state.

Confirming or contrasting evidence or opinions on this issue are welcome.
The issue is still open to any possible solution. Devising
methods/experiments to draw robust conclusions is also valuable for the

[1] Weber W, Weber E: Mechanics of the human walking apparatus.
Springer-Verlag, New York 1991 (translated from German by P. Maquet and
R. Furlong - from original work in 1836).
[2] Langer K., Das Kniegelenk des Menschen. In Sitzungsberichte der
Akademie der Wissenschaften. Mathematisch - Naturwissenschaftliche
Classe, Bde 2, 3. Wien, Karl Gerolds Sohn, p. 99, 1858
[3] Bugnon E., Le mécanisme du Genou., Lausanne, CH Viret-Genton, 1892
[4] Fick R., Mechanik des Gelenkes, in Handbuch del Anatomie und
Mechanik der Gelenke. Jena, Gustav Fischer , 1911
[5] Pinskerova V, Maquet P, Freeman MA :"Writings on the knee
between 1836 and 1917", J Bone Joint Surg Br. 2000 Nov;82(8):1100-2 .
[6] Pio A., Carminati L., Stennardo, Pedrotti L :"Evolution of the
concepts of functional anatomy of the knee joint", Chir. Organi Mov.
1998, LXXXIII, 401-411 .
[7] Fischer O., Kinematik Organischer Gelenke. Braunschweig, F. Vieweg
und Sohn, 1907.
[8] Hollister, A.M., S. Jatana, A.K. Singh, W.W. Sullivan, A.G.
Lupichuck: "The axes of rotation of the knee", Clinical Orthopaedics and
Related Research, 290:259-268, 1993
[9] Pinskerova V., Freeman MA et al :"Tibiofemoral movement 1/2/3/4",
Bone Joint Surg Br. 2000 Nov;82(8):1189-95 / 1196-8 / 1199-200 / 1201-3.
[10] Wilson DR, Feikes JD, Zavatsky AB, O'Connor JJ.: "The components
of passive knee movement are coupled to flexion angle", J Biomech ,
33(4):465-73, 2000.
[11] Wilson DR, Feikes JD, O'Connor JJ. "The Ligaments and articular
surfaces guide passive knee flexion", J Biomech, 31:1127-1136, 1998.
[12] Piazza SJ, Cavanagh PR: Measurement of the screw-home motion of the
knee is sensitive to errors in axis alignment. J Biomech 33:1029-1034, 2000.
[13] Grood, E.S., W.J. Suntay,. A joint coordinate system for the
clinical description of three-dimensional motions: application to the
knee. Journal of Biomechanical Engineering., 105:136-144, 1983.
[14] Blankevoort, L.R Huiskes, A. De Lange. Helical axes of passive
knee joint motions. Journal of Biomechanics, 23:1219-1229, 1990.
[15] Pennock, G.R., K.J. Clark. An anatomy-based coordinate system
for the description of the kinematic displacements in the human knee.
Journal of Biomechanics, 23:1209-1218, 1990.
[16] Martelli S., S. Zaffagnini, B. Falcioni, M. Marcacci.
Intraoperative kinematic protocol for knee joint evaluation. Computer
Methods and Programs in Biomedicine, 62:77-86, 2000.

************************************************** ************************
Alberto Leardini, DPhil
Movement Analysis Laboratory
Centro di Ricerca Codivilla-Putti
Istituti Ortopedici Rizzoli
Via di Barbiano 1/10, 40136 Bologna ITALY
tel: +39 051 6366522
fax: +39 051 6366561
email: leardini@ior.it

"Where is the Life we have lost in living,
Where is the wisdom we have lost in knowledge,
Where is the knowledge we have lost in information."
Thomas Stearns Eliot, Choruses from ''The Rock'' (1934)
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