Comments on the “Effect of Tibial Tuberosity Advancement on Femorotibial Shear in Cranial Cruciate-Deficient Stifles. An In Vitro Study”

Effect of tibial tuberosity advancement on femorotibial shear in cranial cruciate-deficient stifles

This paper[1] has been one of the bases for the mechanical establishment of the tibial tuberosity advancement (TTA) procedure. The third paragraph opens with the statement, “In the human knee, the femorotibial forces that act during the weight-bearing phase of the gait are almost parallel to the patellar ligament.”

The author cannot find where this statement is made or deduced from in the manuscript.[2] Fig. 6b of Nisell² shows that the direction of the patellar tendon force relative to the tibial plateau changed, during knee flexion, from anterior to posterior at a mean joint angle of 100°. However, the direction of the shear force, and hence of the joint reaction force, changed direction relative to the tibial plateau between angles 50° and 90° depending on the subject's sex and the weight attached to the distal tibia (refer the Fig. 8c of Nisell²). Let's assume that at some point during the gait, the forces are parallel (same or opposite direction). Their direction changes almost linearly as a function of the joint angle (refer the Figs. 6b and 8c of Nisell²). For the forces to remain parallel, the rate of change in their direction needs to remain the same throughout flexion. This means that their direction would change signs at the same joint angle. But this happens at significantly different angles. So, their direction is also different during the various joint angles. Moreover, the results above were from isometric knee extension against a resistance attached to the anterior side of the distal tibia and not during weight-bearing as the authors state.[1] During weight-bearing the ground reaction force is one of the main determinants of the direction of the joint reaction force ([Fig. 1]).

Fig. 1 Idealized mechanical model of the stifle joint with intact (left image) and ruptured (right image) cruciate ligaments. The directions of the forces are for illustration purposes only. F _P: patellar ligament force from the quadriceps muscle, F _C: compression stifle joint force, F _S: shear stifle joint force, F _H: hamstrings force, F_G: gastrocnemius force, GRF: ground reaction force, F _T: tarsal joint reaction force, F _Tx: the component of F _T in the x-axis, F _Ty: the component of F _T in the y-axis. A: center of the tibiotarsal joint, B: center of stifle joint, C: contact point between the paw and the ground. If GRF is known and the relative distances and angles are given, all joint reaction forces can be calculated. Forces from major muscle groups other than the quadriceps are illustrated but are omitted from calculations for simplification purposes. Left image: the stifle acts as a hinge joint. The red vector force on the hinge diagram represents the tibiofemoral force and the blue vector force represents the reaction of the joint to this force. The joint will react to both components of the action force. Right image: the cruciate ligaments are ruptured. As the cruciate ligaments are absent, the shear component of the tibiofemoral force will not be transferred to the femur. The tibia will slip on the femur. The femur will only react to the transverse component of the tibiofemoral force which is on the common normal. The circles represent the curve of the femoral and tibial joint surfaces. The red line is the common normal. The green line is the common tangent. The GRF tends to translate the tibia caudally. The F _P is parallel to the common normal (perpendicular to the common tangent). And the stifle joint reaction force F is, by definition, on the common normal. So, the GRF will tend to translate the tibia caudally which would have been prevented by an intact caudal cruciate ligament.

An intact stifle joint is a hinge in idealized models ([Fig. 1]). When the femur pushes the tibia in one direction (action force), the tibia pushes the femur back in the same direction (reaction force). The joint reaction force is described by its two component vectors. One parallel (shearing component) and one perpendicular (compressive component) to the contact surface. When both cruciate ligaments are absent, the vector parallel to the surface does not exist, as the joint allows for translation in that direction. So, after the transection of the cruciate ligaments, the joint reaction force F _J is, by definition, perpendicular to the common tangent. The tibia's surface now acts as a smooth-surface-type support, not as a hinge.[3] If the caudal cruciate ligament remains intact and without the cranial cruciate ligament, there will be a caudally directed joint reaction force parallel to the joint surface only when the femur tends to translate cranially. If both surfaces are curved, then it is more accurate to say that the joint reaction force will be perpendicular to the common tangent[4] ([Fig. 1]).

A three-force member (a body where forces are applied at three points) can only be in equilibrium if the forces are parallel or concurrent (their lines of action meet at a point within or distant from the body).[3] The experiment of this study represents the mechanics of a three-force member ([Fig. 2D–F]). An action force is applied to the system (F _FT), generating two reaction forces (F _J, F _P)

Fig. 2 Free-body diagrams of the femur, patella, and tibia. Orange vectors are action forces, red vectors are reaction forces acting on the femur, and green vectors are reaction forces acting on the patella. (A) Force F _FT is applied on the femur in a direction parallel to the patella tendon. A reaction force F _J is applied from the tibia to the femur, and a reaction force F _P is applied from the tibia to the patella. Force F _P is a tension force, and the patella acts as a pulley redirecting it to the proximal femur (red vector F _P). The patella applies force (F _Px1+ F _Px2) on the distal femur. All vectors are analyzed into an x-component (parallel to the tibial surface) and a perpendicular y-component. The y-components of the F _P forces acting on the patella are omitted from calculations as they do not act on the femur. Forces directed caudally and proximally take a positive sign. The sum of forces on the x-axis is ΣF _x = F _Px1 + F _Px2 − F _Px3 + F _FTx. But F _Px1 = F _Px3 = F _P (cosθ). Hence, ΣF _x = F _Px2 + F _FTx . From this, it is concluded that the sum of the forces on the x-axis has a positive direction. The femur will tend to translate caudally on the tibial surface. In the absence of a cranial cruciate ligament, force F _J will be perpendicular to the articular surface. (B) After a TTA, F _P applied on the patella from the tibia to the patella will be perpendicular to the tibial surface. Now F _Px2 = 0, and ΣF _x = F _FTx. Hence, the femur will still tend to translate caudally due to F _FTx. (C) If F _FT is re-directed to be perpendicular to the tibial surface (parallel to the patella), then F _FTx will not exist, and the femur will not translate on the x-axis as ΣF _x = 0. But this is not due to the TTA but to the deliberate re-direction of F _FT. (D) A simplified way of looking at the mechanics of this experiment is to use the femur as our frame of reference and envision the tibial surface moving relative to it. If force F _FT is applied on the tibia or the ground on which the tibia sits, the femur will react by force F _J and F _P. If F _FT and F _P are mutually parallel, the tibia will tend to translate cranially relative to the femur. Hence, in the absence of a cranial cruciate ligament, F _J will be perpendicular to the articular surface. (E) After a TTA, F _P will be perpendicular to the articular surface, but the tibia will still tend to translate cranially due to F _FT. (F) If F _FT is re-directed to be parallel to all other forces, then no translation will occur in the direction of the tibia surface. TTA, tibial tuberosity advancement.

In the study,[1] before the TTA was performed, the forces F _P and the force F _FT were set to be mutually parallel and not perpendicular to the common tangent ([Fig. 2A] and [D]). So, two of the applied forces were parallel to each other (F _P and F _FT), and one (F _J) was not ([Fig. 2D]). Hence, it was mathematically certain that the system would not be in equilibrium and the femur would translate caudally relative to the tibia.[3]

The TTA redirected F _P perpendicular to the common tangent ([Fig. 2C] and [F]). But F _J was already perpendicular to the common tangent as the cranial cruciate ligament was transected. At the same time, force F _FT was redirected to remain parallel to F _P. Hence, all forces were set to be parallel to each other ([Fig. 2F]). Again, it was mathematically certain that the system would be in equilibrium and that there would be no translation of the femur relative to the tibia.[3]

The only reason the stifles of the study are stable after the TTA was the re-direction of force F _FT ([Fig. 2B] and [E]). This set the experiment to be successful. Also, by setting this force parallel to the patellar tendon before the TTA, the authors made sure that the forces of the three-force member were far from being concurrent, maximizing the cranial thrust after the cranial cruciate ligament was transected, which contributed to the statistically significant difference found.

The conclusion of the study[1] that the TTA counteracts cranial subluxation of the tibia is based on an experiment set to succeed which does not represent a real-life situation. Also, the references made are misleading.[2] No justification is provided as to why re-directing the patellar tendon causes a natural automatic re-direction of the F _FT force. A correct conclusion statement would be, “The TTA can be used to counteract cranial subluxation of the tibia in a cranial cruciate ligament deficient joint if and only if (1) the sum of all forces except the patellar tendon force (F _FT) remains parallel to the patellar tendon during the stance phase of the gait, and (2) re-directing the patellar tendon causes an automatic re-direction or a change in the magnitude of all other forces, so their sum remains parallel to the patellar tendon.

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Artikel online veröffentlicht:
24. Februar 2025

• References

• 1 Kipfer NM, Tepic S, Damur DM, Guerrero T, Hässig M, Montavon PM. Effect of tibial tuberosity advancement on femorotibial shear in cranial cruciate-deficient stifles. An in vitro study. Vet Comp Orthop Traumatol 2008; 21 (05) 385-390
• 2 Nisell R. Mechanics of the knee. A study of joint and muscle load with clinical applications. Acta Orthop Scand Suppl 1985; 216 (Suppl): 1-42
• 3 Hibbeler RC. In: Engineering Mechanics, Statics. R.C. Hibbeler ed. Equilibrium of a rigid body. United Kingdom: Pearson; 2023: 220-240
• 4 Book F. Mathematical methods, models and modelling. . Systems of particles. London: The Open University; 2015: 99