Degrees of Freedom of the Knee

For Medical Students

The Principle

A rigid body in space has six degrees of freedom: it can rotate about three axes and translate along three. Any joint's motion can be described as some combination of the six.

A hinge uses one. A ball and socket uses three rotations. The knee uses all six, which is the formal reason it is not a hinge.

Having a degree of freedom is not the same as having much of it. Several of the knee's six have a range measured in millimetres, and those are the ones ligaments control most tightly.

At the Knee

The three rotations are flexion and extension, internal and external rotation of the tibia, and varus and valgus angulation.

The three translations are anterior and posterior, medial and lateral, and compression and distraction.

Their ranges differ by orders of magnitude. Conventional teaching gives flexion and extension about 140 degrees, axial rotation up to about 30 degrees at 90 degrees of flexion, varus and valgus a few degrees, anteroposterior translation about 5 to 10 mm, and medial to lateral translation and compression to distraction one or two millimetres each.

The large ranges are what the joint is for. The small ones are what it has to be prevented from doing, and ligament injury is usually detected as an increase in one of them.

What Changes It

Flexion angle changes the available range in every other degree of freedom. Rotation is almost absent in full extension and largest around 90 degrees.

Load changes it. A compressed joint rotates and translates less than an unloaded one, which is why examination findings differ between a relaxed and a guarding patient.

Muscle activity restrains several degrees of freedom at once, so a tense limb measures tighter than the same limb asleep.

Clinical Relevance

Every stability test is an attempt to isolate one degree of freedom and measure it. Knowing which one a test loads is how its result is interpreted. Section 4 covers the tests.

Isolation is never complete, because the knee couples its motions. 3.2.9 covers that.

A reconstruction restores restraint in some degrees of freedom and not others, so describing what an operation restores means naming which.

MRCS Level

The Principle

Name a reference frame before quoting any figure. Motion is described relative to axes, and two studies using different axes produce different numbers for the same movement.

The joint coordinate system usually credited to Grood and Suntay is the convention: a femoral flexion axis, a tibial long axis, and a floating axis perpendicular to both.

Rotations about those three axes are flexion and extension, internal and external rotation, and varus and valgus. Translations along them are proximal and distal, anterior and posterior, and medial and lateral.

At the Knee

Give the ranges with their flexion angle attached. Axial rotation is close to zero in full extension and conventional teaching puts it at about 25 to 30 degrees total at 90 degrees of flexion.

Varus and valgus angulation is a few degrees in the intact knee and conventional teaching puts the increase in a complete collateral injury at several millimetres of joint line opening rather than many degrees.

Anteroposterior translation is the degree of freedom clinical measurement is built around, and side to side difference is the quantity that matters rather than the absolute figure.

Compression and distraction is the degree of freedom least discussed and most relevant to cartilage, because it is where load is transmitted rather than where motion occurs.

What Changes It

Flexion angle, load, muscle activity and the integrity of each restraint. Every one of those changes a measured range, which is why a measurement without its conditions is uninterpretable.

Previous surgery changes several at once. A reconstruction that restores anteroposterior restraint may leave rotation unchanged, which 3.11 covers.

Generalised laxity shifts the whole set, so an individual's uninjured side is a better comparator than a published range.

How It Is Measured

Instrumented arthrometry measures anteroposterior translation and is the only degree of freedom with a widely used clinical instrument.

Optical motion capture and fluoroscopy measure the rotations in vivo, with soft tissue artefact and field of view as their respective limits.

Robotic testing in cadavers measures all six with a known applied load, which is where most restraint apportionment comes from and why those figures carry the cadaver's limits with them.

Clinical grading of varus and valgus opening is in millimetres by convention rather than degrees, which is a measurement of translation used to describe a rotation.

Clinical Relevance

State the flexion angle whenever a laxity figure is recorded, because the same knee gives different answers at different angles.

Compare with the other side rather than with a published range, since individual variation exceeds most injury effects in the smaller degrees of freedom.

Expect a test to load more than one degree of freedom, and read a combination of findings rather than one.

Describe what a reconstruction restores by degree of freedom, since that is the language in which two constructs can be compared.

FRCS Level

At the Knee

Treat the six as a set whose members trade against each other. Constraining one reduces the available range in others, which is why over-constraint in one plane shows up as stiffness in another.

The small range degrees of freedom are where injury is detected and where surgery is judged, which gives them an importance out of proportion to their magnitude.

Coupling means the six are not independent in the intact knee, so a construct that restores one in isolation has changed the relationship between several. 3.2.9 covers it.

What Changes It

Every reconstruction alters the set. A graft adds restraint in a direction and, being stiffer than the tissue it replaces, alters compliance in others.

Alignment changes the load distribution rather than the kinematics directly, and then changes the kinematics through the load.

Arthroplasty replaces the surfaces that constrain several degrees of freedom at once, which is why implant constraint is described in those terms.

How It Is Measured

Robotic cadaveric testing with a universal force moment sensor is the reference method for restraint apportionment, and its order effect is the limit to state alongside any figure it produces.

In vivo kinematics from fluoroscopy and from motion capture disagree, with soft tissue artefact the usual explanation, and the disagreement is larger in rotation than in flexion.

No clinical instrument measures rotation reliably, which is why rotational instability is still graded by a hand test rather than a number. 3.11.4 covers the pivot shift.

Clinical Relevance

Assess rotation as well as translation before accepting that a knee is stable, since the instrument exists for one and not the other.

Consider what a construct constrains beyond its target, because the trade is real and is reported by patients as stiffness rather than as over-constraint.

Record laxity with its flexion angle and its comparison side, so a later assessment can be read against it.

Avoid describing a knee as stable on the basis of the degree of freedom that happens to have an instrument.